Application

of

the

method

to

modeling

the

solid

state

The

applicability

of

the

recently

developed

method

for

modeling

various

properties

of

a

wide

range

of

organic

and

inorganic

crystalline

solids

has

been

investigated

Although

the

geometries

of

most

systems

examined

were

reproduced

with

good

accuracy

severe

errors

were

found

in

the

predicted

structures

of

a

small

number

of

solids

The

origin

of

these

errors

was

investigated

and

a

strategy

for

improving

the

method

proposed

Introduction

The

semiempirical

method

-LSB-

-RSB-

was

designed

primarily

for

the

investigation

of

molecular

species

of

biochemical

interest

That

is

the

objective

of

parameter

optimization

was

to

reproduce

the

properties

of

molecules

When

other

semiempirical

methods

e.g.

MNDO

-LSB-

-RSB-

-LSB-

-RSB-

and

-LSB-

-RSB-

were

developed

initial

reports

indicated

that

they

were

significantly

more

accurate

than

earlier

methods

But

later

when

each

new

method

was

used

for

modeling

species

that

were

significantly

different

from

those

used

in

the

training

set

average

errors

typically

increased

quite

significantly

This

unfortunate

result

was

a

natural

consequence

of

the

way

in

which

semiempirical

method

development

was

done

if

during

a

survey

a

systematic

fault

was

identified

then

the

training

set

would

be

modified

in

such

a

way

as

to

correct

the

fault

The

close

relationship

between

the

survey

set

and

the

training

set

meant

that

by

its

nature

properties

of

species

in

the

survey

set

were

reproduced

with

a

higher

accuracy

than

those

of

species

not

in

the

survey

set

During

the

development

of

efforts

were

made

to

minimize

the

potential

for

this

increase

in

error

Among

these

were

the

construction

and

use

of

very

large

survey

and

training

sets

In

contrast

to

previous

methods

in

which

the

training

set

was

a

subset

of

the

survey

set

during

the

development

of

the

training

set

was

a

superset

of

the

survey

set

No

solids

were

used

in

either

the

training

set

or

the

survey

set

while

was

being

developed

because

inclusion

of

even

one

solid

in

the

parameter

optimization

would

have

made

the

whole

process

extremely

slow

which

in

turn

would

have

precluded

optimization

of

the

parameters

in

any

reasonable

time

Because

of

this

solids

were

excluded

from

the

parameterization

and

therefore

they

form

an

ideal

clearly

defined

set

of

systems

for

testing

the

applicability

of

to

species

that

were

not

used

in

the

development

of

the

method

Theory

There

are

several

problems

associated

with

solid-state

calculations

that

do

not

exist

when

discrete

molecules

are

modeled

all

of

which

are

related

to

the

fact

that

there

are

an

infinite

number

of

interacting

atoms

The

most

obvious

consequence

of

this

is

that

the

electric

potential

experienced

by

each

of

these

atoms

is

the

result

of

the

contributions

of

an

infinitely

large

number

of

electrostatic

terms

arising

from

the

partial

charges

of

all

the

other

atoms

Another

implication

is

that

the

number

of

one-electron

wavefunctions

contributing

to

the

density

matrix

during

the

solution

of

the

self-consistent

field

-LRB-

SCF

-RRB-

equations

is

also

infinite

Various

techniques

have

been

developed

for

solving

these

problems

Thus

in

all

solid-state

methods

the

assumption

is

made

that

the

wavefunctions

exhibit

a

perfect

periodicity

this

assumption

is

formalized

in

the

Born

von

Kármán

-LSB-

-RSB-

periodic

boundary

conditions

The

electrostatic

contribution

or

Madelung

integral

can

be

solved

analytically

using

the

Ewald

sum

-LSB-

-RSB-

In

this

procedure

an

elegant

mixture

of

real

and

reciprocal

space

contributions

is

used

in

the

evaluation

of

the

potential

To

assist

in

the

solution

of

the

SCF

equations

the

near

infinite

number

of

occupied

wavefunctions

contributing

to

the

density

matrix

is

replaced

by

an

integration

over

the

Brillouin

zone

In

turn

this

integration

is

approximated

by

a

Simpson

's

rule

technique

involving

a

weighted

sampling

of

points

within

the

zone

Several

complete

procedures

have

been

developed

for

modeling

solids

using

semiempirical

methods

One

of

these

the

MOSOL

program

-LSB-

-RSB-

used

sampling

of

the

Brillouin

Zone

but

because

it

used

complex

mathematics

it

was

impractical

for

application

to

anything

more

complicated

than

simple

binary

solids

If

the

unit

cell

used

is

sufficiently

large

then

instead

of

sampling

the

Brillouin

Zone

using

a

regular

mesh

of

points

only

one

point

need

be

used

and

if

the

point

chosen

is

at

the

origin

of

k-space

i.e.

the

Γ

point

then

complex

mathematics

can

be

avoided

entirely

This

is

the

basis

for

the

large

unit

cell

-LSB-

-RSB-

or

cluster

-LSB-

-RSB-

approximation

More

recently

Gale

-LSB-

-RSB-

has

addressed

the

problem

of

solving

the

Ewald

sum

when

neglect

of

diatomic

differential

overlap

-LRB-

NDDO

-RRB-

methods

are

used

and

developed

a

technique

that

would

allow

the

Madelung

integral

to

be

solved

more

rapidly

In

turn

this

has

allowed

the

structures

and

energies

of

some

crystalline

oxides

such

as

corundum

and

some

of

the

polymorphs

of

silica

and

of

ice

to

be

modeled

During

the

development

of

a

procedure

to

allow

to

be

applied

to

solids

various

deficiencies

and

limitations

were

found

in

earlier

procedures

Some

of

these

and

the

resulting

modifications

that

had

to

be

made

in

order

to

allow

to

be

used

for

modeling

solids

will

now

be

described

NDDO

error

The

NDDO

methods

pioneered

by

Dewar

and

Thiel

use

the

Dewar-Sabelli

-LSB-

-RSB-

Klopman

-LSB-

-RSB-

-LRB-

DSK

-RRB-

approximation

Eq

which

is

equivalent

to

the

Ohno

approximation

-LSB-

-RSB-

for

the

two-electron

two

center

integral

γAB

involving

atoms

A

and

B

separated

by

a

distance

RAB

The

DSK

approximation

has

the

correct

behavior

at

the

extremes

That

is

it

converges

to

the

exact

point-charge

expression

as

the

interatomic

distance

becomes

very

large

and

also

converges

to

the

exact

two-electron

one-center

term

GA

when

the

interatomic

separation

becomes

zero

Additionally

it

has

good

behavior

at

chemical

bonding

distances

Over

the

past

years

the

DSK

approximation

has

proven

very

successful

in

NDDO

models

when

applied

to

both

discrete

species

and

to

polymers

Surprisingly

in

its

unmodified

form

the

DSK

approximation

gives

rise

to

an

infinite

error

when

applied

correctly

to

any

non-elemental

crystalline

solid

This

error

arises

from

the

fact

that

the

one-center

two-electron

integrals

differ

from

element

to

element

The

origin

of

the

error

can

be

understood

by

considering

the

potential

at

an

atom

A

in

a

simple

binary

solid

AB

arising

from

all

atoms

on

the

surface

of

a

spherical

shell

of

radius

R

in

such

a

solid

if

the

charge

on

atom

A

is

Q

then

the

charge

on

atoms

of

type

B

would

be

Q

When

R

becomes

large

enough

the

fraction

of

atoms

of

type

A

and

B

at

that

distance

will

be

the

same

and

the

resulting

electric

potential

V

at

atom

A

could

then

be

represented

by

Eq

A

Taylor

series

expansion

of

this

function

shows

that

V

is

proportional

to

the

reciprocal

of

the

distance

For

all

values

of

R

greater

than

about

Å

this

potential

is

clearly

very

small

In

solids

however

the

potential

at

an

atom

is

the

result

of

the

summed

electric

fields

of

all

such

shells

out

to

infinity

For

convenience

this

sum

can

be

replaced

by

an

integral

Eq

The

value

of

this

integral

is

infinity

which

means

that

if

the

DSK

approximation

is

used

and

the

integration

is

done

correctly

the

potential

experienced

by

an

atom

of

type

A

arising

from

the

electrostatic

contributions

of

all

other

atoms

would

then

be

either

plus

infinity

or

minus

infinity

depending

on

the

sign

of

its

partial

charge

This

is

an

obviously

unphysical

result

This

catastrophe

can

readily

be

avoided

by

modifying

the

DSK

approximation

to

ensure

that

it

converges

to

the

point

charge

expression

for

large

values

of

R

The

simplest

modification

would

be

to

ensure

that

as

the

interatomic

separation

increased

a

smooth

transition

is

made

from

the

DSK

equation

to

the

exact

point

charge

equation

Several

trial

functions

were

examined

and

from

these

a

Gaussian

function

was

selected

as

having

the

best

characteristics

this

function

is

shown

in

Eq

Below

Å

the

unmodified

DSK

equation

would

be

used

at

larger

distances

Eq

would

be

used

This

function

is

well-behaved

in

that

it

is

single-valued

and

has

finite

first

and

second

derivatives

Electrostatic

interaction

Evaluating

the

electrostatic

potential

at

an

atom

in

a

crystal

involves

summing

interactions

from

all

surrounding

atoms

and

since

there

are

for

all

practical

purposes

an

infinite

number

of

these

the

direct

sum

must

be

replaced

by

a

tractable

alternative

The

simplest

and

most

efficient

method

of

evaluating

the

electrostatic

potential

arising

from

an

infinite

lattice

of

point

charges

is

the

Ewald

sum

-LSB-

-RSB-

In

this

summation

the

contribution

to

the

potential

is

divided

into

two

terms

a

real-space

and

a

reciprocal

or

Fourier-space

term

When

an

appropriate

error

function

is

used

the

Ewald

sum

is

both

accurate

and

readily

evaluated

and

is

the

method

of

choice

when

the

model

used

represents

the

electrostatic

potential

as

the

sum

of

contributions

from

classical

point

charges

Gale

successfully

applied

a

modified

version

of

the

Ewald

sum

-LSB-

-RSB-

in

evaluating

the

electrostatic

potential

used

in

MNDO

and

solid

state

calculations

In

all

NDDO

-LSB-

-RSB-

methods

including

the

electrostatic

contribution

to

the

potential

at

an

atom

arising

from

the

charges

on

distant

atoms

can

be

represented

by

the

classical

point

charge

equation

at

small

distances

by

the

DSK

and

at

intermediate

distances

by

the

modified

DSK

approximation

Gale

-LSB-

-RSB-

noted

that

a

modification

must

be

made

to

the

potential

in

order

for

the

Ewald

summation

to

be

used

in

an

NDDO

method

This

change

requires

the

point-charge

contribution

to

the

potential

of

each

atom

that

arises

from

all

nearby

atoms

to

be

replaced

by

the

exact

NDDO

contribution

Derivatives

of

the

energy

with

respect

to

geometry

require

all

potential

functions

to

be

continuous

but

if

corrections

of

the

type

just

described

were

made

the

resulting

function

would

obviously

be

discontinuous

and

further

corrections

would

be

needed

So

although

the

Ewald

sum

is

aesthetically

attractive

its

practical

implementation

would

necessarily

involve

aesthetically

unattractive

corrections

An

alternative

to

the

Ewald

sum

would

be

to

modify

the

way

in

which

the

electrostatic

sum

is

evaluated

In

this

approach

use

is

made

of

the

fact

that

an

integer

number

of

interacting

unit

cells

are

used

in

a

solid

state

calculation

If

the

DSK

equation

either

unmodified

or

modified

as

in

Eq

is

used

then

the

potential

at

any

given

atom

arising

from

the

direct

summation

of

the

NDDO

electrostatic

terms

from

all

the

other

atoms

would

contain

artifacts

reflecting

the

asymmetric

environment

In

other

words

the

presence

of

boundary

effects

introduces

spurious

terms

into

the

potential

If

these

terms

were

not

eliminated

they

would

have

a

perturbative

effect

on

the

optimized

geometry

that

would

severely

compromise

the

validity

of

the

results

A

method

for

removing

these

spurious

effects

was

developed

that

involves

modifying

the

distance

term

in

the

DSK

approximation

The

potential

experienced

by

each

atom

in

a

solid

that

arises

from

the

partial

charges

on

other

atoms

falls

off

rapidly

with

increasing

distance

This

is

a

natural

result

of

the

fact

that

the

net

charge

arising

from

all

atoms

in

a

spherical

shell

must

rapidly

converge

to

zero

as

the

radius

increases

An

implication

of

this

is

that

for

large

radii

the

precise

value

of

the

radius

used

in

evaluating

the

potential

is

unimportant

Conversely

when

the

radius

is

small

and

there

are

relatively

few

atoms

the

potential

arising

from

the

associated

partial

charges

is

large

In

that

case

the

value

of

the

interatomic

separation

used

is

of

great

importance

This

behavior

can

be

used

as

the

basis

for

modifying

the

electrostatic

sum

At

large

distances

because

the

electrostatic

effect

of

the

distant

atoms

is

small

the

value

of

the

interatomic

distance

used

in

calculating

the

potential

can

be

different

from

the

actual

value

and

in

fact

can

be

set

to

any

arbitrary

large

fixed

value

That

is

all

potentials

arising

from

distant

atoms

can

be

treated

as

if

their

partial

charges

were

moved

in

to

the

surface

of

a

sphere

of

fixed

radius

A

result

of

this

is

that

the

gradient

or

force

arising

from

a

charge

that

was

initially

outside

the

sphere

would

be

exactly

zero

any

potential

motion

of

the

central

atom

in

response

to

the

presence

of

a

charge

on

the

surface

of

the

sphere

would

be

accompanied

by

a

simultaneous

motion

of

that

charge

A

consequence

of

this

is

that

the

gradient

of

the

potential

arising

from

a

charge

on

the

surface

of

the

sphere

is

precisely

zero

This

modification

of

the

effective

interatomic

distance

-LRB-

EID

-RRB-

used

in

evaluating

the

electrostatic

potential

completely

eliminates

all

directional

effects

in

particular

all

artifacts

arising

from

the

use

of

a

finite

number

of

interacting

unit

cells

If

no

further

modifications

to

the

EID

were

made

then

there

would

be

a

discontinuity

in

the

gradient

arising

from

the

presence

of

the

sphere

The

gradient

arising

from

a

partial

charge

just

inside

the

sphere

would

be

finite

but

if

that

charge

were

to

move

just

outside

the

sphere

its

gradient

would

now

become

zero

and

there

would

be

a

discontinuity

The

presence

of

such

discontinuities

would

then

preclude

the

gradients

being

used

in

subsequent

operations

such

as

geometry

optimization

and

calculation

of

vibrational

frequencies

To

avoid

them

the

EID

must

be

further

modified

to

ensure

that

the

gradient

arising

from

an

atom

near

the

surface

of

the

sphere

drops

smoothly

to

zero

as

the

atom

approaches

the

surface

of

the

sphere

This

is

most

simply

accomplished

by

reducing

the

EID

of

an

atom

as

it

approaches

the

surface

of

the

sphere

To

summarize

the

value

of

the

EID

is

set

to

a

constant

for

all

atoms

separated

by

a

large

distance

is

set

less

than

the

actual

distance

for

intermediate

distances

and

is

equal

to

the

actual

distance

when

the

interatomic

separation

is

small

A

simple

function

that

satisfies

these

criteria

can

be

defined

using

three

domains

as

shown

in

Fig.

Fig.

approximation

for

Madelung

integral

C

Å

For

atoms

that

are

at

a

distance

less

than

some

predefined

value

the

exact

DSK

approximation

is

used

Between

and

the

EID

to

be

used

in

Eq

would

be

reduced

as

shown

in

Eq

and

at

distances

greater

than

the

value

of

the

EID

would

be

a

constant

C

The

effect

of

these

changes

when

applied

to

an

example

set

of

charges

is

illustrated

in

Fig.

with

the

original

charges

shown

in

black

and

the

locations

of

the

charges

that

would

be

used

in

evaluating

the

electrostatic

potential

shown

in

green

Fig.

of

truncation

on

apparent

position

of

charges

For

a

set

of

charges

-LRB-

black

-RRB-

the

position

used

in

evaluating

the

electrostatic

interactions

is

shown

in

green

Provided

enough

unit

cells

are

used

to

ensure

that

all

atoms

within

the

sphere

of

radius

are

present

the

effect

of

this

modification

is

to

remove

any

directional

influence

specifically

surface

effects

arising

from

the

presence

or

absence

of

distant

atoms

As

with

the

unmodified

DSK

equation

the

potential

arising

from

an

atom

at

any

distance

is

single-valued

and

its

first

derivative

is

finite

An

integer

number

of

unit

cells

is

always

used

in

the

evaluation

of

the

electrostatic

potential

therefore

the

net

charge

on

the

surface

of

the

sphere

of

radius

precisely

counterbalances

the

sum

of

all

the

charges

within

the

sphere

regardless

of

how

many

unit

cells

are

outside

the

sphere

This

is

a

natural

and

necessary

consequence

of

the

requirement

that

unit

cells

in

a

solid

must

have

a

zero

charge

The

electrostatic

potential

is

of

course

dependent

on

the

value

of

C.

With

increasing

values

of

C

the

potential

converges

rapidly

to

a

constant

but

also

as

C

increases

the

number

of

unit

cells

that

need

to

be

used

increases

rapidly

The

value

of

C

was

set

to

Å

this

being

the

best

compromise

between

computational

effort

and

numerical

stability

Unlike

the

Ewald

summation

this

modified

DSK

approximation

can

be

used

directly

in

evaluating

the

electrostatic

potential

The

new

approximation

is

relatively

simple

in

that

the

use

of

error

functions

and

reciprocal

space

terms

are

avoided

Solids

with

unpaired

electrons

Many

solids

particularly

those

containing

transition

metals

have

unpaired

electrons

Of

the

two

standard

methods

available

for

modeling

such

systems

when

only

molecules

are

involved

unrestricted

Hartree

Fock

-LRB-

UHF

-RRB-

and

restricted

Hartree

Fock

followed

by

configuration

interaction

-LRB-

RHF-CI

-RRB-

only

UHF

is

suitable

for

modeling

solids

The

use

of

RHF-CI

methods

is

precluded

because

of

the

very

large

active

space

involved

For

example

consider

the

garnet

uvarovite

calcium

chromium

silicate

Each

chromium

ion

in

this

mineral

has

three

unpaired

d

electrons

The

unit

cell

contains

eight

formula

units

so

if

the

RHF-CI

procedure

was

used

at

a

minimum

the

active

space

would

need

to

include

all

molecular

orbitals

of

predominantly

d

character

Even

if

the

reasonable

assumption

was

made

that

all

the

unpaired

electrons

had

the

same

spin

the

number

of

microstates

involved

would

still

be

very

large

and

evaluation

of

the

gradients

for

the

resulting

non-degenerate

state

would

be

prohibitively

slow

For

solids

in

which

the

ions

with

unpaired

electrons

are

well

separated

that

is

where

the

ions

are

electronically

isolated

from

each

other

the

assumption

can

be

made

that

the

spin-state

of

one

ion

will

not

interact

significantly

with

the

spin-state

of

any

adjacent

ion

In

addition

if

the

atom

in

question

is

a

transition

metal

ion

then

the

spin

state

can

usually

be

inferred

from

its

environment

In

the

case

of

uvarovite

each

chromium

ion

is

in

an

almost

octahedral

environment

-LRB-

the

exact

symmetry

is

-RRB-

being

surrounded

by

six

oxygen

atoms

so

the

three

d

electrons

would

be

in

a

manifold

and

would

therefore

be

unpaired

If

the

Hund

's

rule

assumption

is

made

that

the

spin

state

is

a

maximum

then

each

chromium

atom

would

be

in

a

local

state

and

any

Jahn-Teller

tendency

to

geometric

distortion

to

a

lower

symmetry

would

be

avoided

This

assumption

can

be

formalized

in

the

calculation

when

a

UHF

method

is

used

by

defining

the

difference

between

the

number

of

electrons

of

α

and

β

spin

to

correspond

to

the

maximum

possible

spin

state

of

the

entire

system

For

uvarovite

the

unit

cell

would

then

be

defined

as

having

a

spin

of

Ms

and

therefore

would

have

more

α

than

β

electrons

Applications

Organic

compounds

Data

sets

were

constructed

for

each

organic

compound

with

in

each

case

the

starting

geometry

being

the

X-ray

structure

i.e.

the

observed

geometry

In

contrast

to

molecular

calculations

where

internal

coordinates

are

normally

used

in

the

work

reported

here

Cartesian

coordinates

were

used

exclusively

An

attempt

was

made

initially

to

use

internal

coordinates

but

the

numerical

instabilities

associated

with

the

geometric

gradients

at

the

interfaces

of

the

unit

cells

rendered

their

use

impractical

no

such

difficulties

were

encountered

when

Cartesian

coordinates

were

used

Each

cluster

consisted

of

between

and

atoms

and

geometries

were

converged

until

the

gradient

norm

had

dropped

below

kcal

mol

Å

this

corresponding

to

an

uncertainty

in

the

optimized

geometry

of

about

Å

All

unit

cell

parameters

were

optimized

as

were

the

coordinates

of

all

atoms

within

the

unit

cell

Unless

indicated

otherwise

symmetry

was

not

used

to

accelerate

the

optimization

All

calculations

were

done

using

-LSB-

-RSB-

on

a

GHz

Pentium

computer

and

each

geometry

optimization

took

between

min

and

day

with

most

taking

about

h.

No

problems

were

encountered

in

any

of

the

optimizations

With

the

possible

exception

of

polymers

crystalline

organic

compounds

consist

of

discrete

molecules

held

together

by

relatively

weak

forces

As

has

been

shown

-LSB-

-RSB-

to

reproduce

bond

lengths

and

angles

of

simple

organic

compounds

with

useful

accuracy

in

this

work

attention

was

focused

on

the

prediction

of

the

structures

of

entire

molecules

and

on

the

forces

and

energies

arising

from

intermolecular

interactions

A

useful

measure

of

accuracy

of

prediction

of

molecular

structure

is

the

root-mean-square

-LRB-

RMS

-RRB-

difference

between

the

calculated

and

reference

geometries

of

a

single

molecule

or

ion

in

a

crystal

This

quantity

differs

from

the

geometric

quantities

reported

earlier

-LSB-

-RSB-

in

that

it

measures

the

accuracy

of

prediction

of

the

overall

structure

of

a

molecule

not

just

the

accuracy

of

prediction

of

individual

bond

lengths

and

angles

It

is

possible

for

only

relatively

small

distortions

to

exist

in

individual

angles

and

at

the

same

time

for

the

overall

structure

to

be

severely

in

error

The

RMS

error

is

therefore

complementary

to

the

errors

in

individual

bond

lengths

and

angles

In

order

to

probe

the

suitability

of

for

modeling

organic

solids

compounds

were

selected

that

illustrate

a

wide

range

of

common

intermolecular

interactions

the

most

important

of

these

being

in

order

of

the

energies

involved

ionic

hydrogen

bonding

and

π-stacking

Densities

Another

useful

measure

of

the

accuracy

of

prediction

of

organic

and

inorganic

solids

is

the

density

In

most

cases

when

the

density

is

accurately

reproduced

the

internal

structure

of

the

unit

cell

is

also

accurately

predicted

This

is

not

an

infallible

rule

in

that

it

is

possible

for

the

density

to

be

predicted

with

good

accuracy

and

at

the

same

time

the

unit

cell

structure

to

be

significantly

distorted

This

rare

occurrence

can

usually

be

detected

by

distortions

of

the

unit

cell

parameters

No

cases

were

found

where

the

unit

cell

parameters

were

predicted

with

good

accuracy

and

at

the

same

time

significant

errors

existed

in

the

internal

structure

of

the

unit

cell

A

comparison

of

and

X-ray

unit

cell

parameters

for

organic

solids

is

presented

in

Table

In

this

table

the

unit

cell

used

was

often

different

from

that

reported

in

the

literature

particularly

so

in

hexagonal

crystals

that

is

crystals

in

which

the

interface

angles

are

and

Unit

cells

were

chosen

that

would

maximize

the

size

of

sphere

that

could

be

contained

in

a

given

cluster

to

this

end

most

hexagonal

unit

cells

were

replaced

by

equivalent

orthorhombic

unit

cells

Predicted

densities

were

reproduced

with

good

accuracy

the

average

unsigned

error

in

density

being

with

the

bulk

of

this

error

arising

from

errors

in

the

calculated

intermolecular

distances

Although

most

systems

optimized

with

only

small

changes

in

the

geometry

in

three

instances

quantitative

changes

occurred

Table

and

X-ray

structural

parameters

for

organic

compounds

RMS

-LRB-

-RRB-

dabcαβγabcαβγ

-LRB-

Z

Z

-RRB-

N

N

Dimethylurea

-LRB-

NIJHUJ

-RRB-

0.119.694.3611.3890.992.396.410.354.5711.4090.090.0102.71.23

-LRB-

-RRB-

Dioxocine

acid

chloride

-LRB-

CUWWIA

-RRB-

0.2914.6712.303.9089.691.789.215.1512.493.8190.087.790.01.63

-LRB-

-RRB-

-LRB-

NIBZAM

-RRB-

0.0514.696.8413.8277.590.389.915.086.9814.0676.590.090.01.65

-LRB-

-RRB-

-LRB-

-LRB-

-RRB-

carbonyl

-RRB-

adamantane

α-ketoglutaric

acid

-LRB-

RIZWUS

-RRB-

0.149.9713.6610.7292.0113.167.210.5313.7310.7391.8114.767.81.42

-LRB-

-RRB-

-LSB-

-RSB-

octane

azelaic

acid

-LRB-

UNEGEZ

-RRB-

0.5030.368.335.9391.189.191.328.158.606.9890.093.090.01.33

-LRB-

-RRB-

-LSB-

-RSB-

octane

glutarate

-LRB-

UNEFIC

-RRB-

0.2910.5611.6710.3989.483.191.410.2812.4610.6890.066.190.01.42

-LRB-

-RRB-

-LRB-

-LRB-

-RRB-

-RRB-

-LRB-

-RRB-

0.1016.0710.747.20188.786.585.516.3110.787.1785.690.090.01.40

-LRB-

-RRB-

-LRB-

piperidyl

-RRB-

cyclotriphosphazene

-LRB-

POTKEO

-RRB-

0.238.1222.5017.2089.590.190.18.3222.0117.2690.090.090.01.68

-LRB-

-RRB-

-LRB-

BRANIL

-RRB-

0.094.2013.5912.9990.090.090.04.2614.6213.4490.090.090.02.96

-LRB-

-RRB-

-LRB-

Tetryl

-RRB-

-LRB-

MTNANL

-RRB-

0.3011.377.2715.9690.472.390.410.617.3714.1390.084.990.01.52

-LRB-

-RRB-

-LRB-

-RRB-

0.035.775.9312.7590.290.490.15.605.7913.5690.090.090.01.45

-LRB-

-RRB-

-LRB-

Dimethylamino

-RRB-

-LRB-

RISBIE

-RRB-

0.0610.3313.758.91107.790.390.110.6513.779.32107.090.090.01.36

-LRB-

-RRB-

acid

-LRB-

RILJEB

-RRB-

0.0530.908.664.8695.089.591.231.258.644.8793.790.090.01.41

-LRB-

-RRB-

-LRB-

phosphonomethyl

-RRB-

benzenesulfonic

acid

monohydrate

-LRB-

KIXQIR

-RRB-

0.178.499.717.60105.8108.699.48.499.257.92104.8110.097.41.74

-LRB-

-RRB-

acid

isonicotinamide

-LRB-

VAKTOR

-RRB-

5.4822.299.3790.390.091.96.0720.679.4090.090.095.31.51

-LRB-

-RRB-

-LRB-

b

f

-RRB-

saccharin

solvate

-LRB-

UNEZAO

-RRB-

0.1712.2311.467.1669.684.682.712.6810.457.5175.485.783.61.50

-LRB-

-RRB-

-LRB-

-LRB-

-RRB-

amino

-RRB-

-LRB-

QAXMEH

-RRB-

0.2318.5015.964.2488.789.688.918.6916.403.9586.290.090.01.38

-LRB-

-RRB-

-LRB-

-LRB-

-RRB-

amino

-RRB-

-LRB-

-RRB-

0.1116.428.328.5790.089.689.716.418.548.5088.290.090.01.47

-LRB-

-RRB-

-LRB-

-LRB-

-RRB-

amino

-RRB-

-LRB-

-RRB-

0.117.4811.907.91104.2117.078.67.4911.917.79104.5116.477.801.42

-LRB-

-RRB-

-LRB-

-LRB-

-RRB-

amino

-RRB-

-LRB-

-RRB-

0.178.0211.3613.6690.690.4106.57.9811.6813.3290.090.0104.81.44

-LRB-

-RRB-

-LRB-

-LRB-

-RRB-

amino

-RRB-

-LRB-

-RRB-

0.2010.9612.054.3789.690.573.011.2512.324.5990.291.871.21.56

-LRB-

-RRB-

-LRB-

-LRB-

-RRB-

amino

-RRB-

-LRB-

-RRB-

0.1213.2922.577.9190.690.190.513.1822.808.0290.090.090.01.45

-LRB-

-RRB-

-LRB-

-LRB-

-RRB-

amino

-RRB-

-LRB-

-RRB-

0.177.9312.1612.2590.890.9102.88.2312.3111.8290.090.0102.51.50

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

CUWWEW

-RRB-

0.197.6910.9110.9690.774.490.67.9110.8011.5890.070.490.01.53

-LRB-

-RRB-

-LRB-

-RRB-

adenine

-LRB-

FABFUJ

-RRB-

0.117.188.3413.9690.290.089.47.348.2713.5790.090.090.01.42

-LRB-

-RRB-

Acetophenone

-LRB-

ACETPH

-RRB-

0.048.718.459.7590.958.590.68.568.6810.2690.059.090.01.31

-LRB-

-RRB-

Acetylacetone

-LRB-

-RRB-

0.047.854.1115.4892.590.189.88.464.1516.0390.090.090.01.33

-LRB-

-RRB-

Acetylcholine

chloride

-LRB-

-RRB-

-LRB-

-RRB-

phosphate

dihydrate

-LRB-

ADPOSD

-RRB-

0.355.9111.6210.5588.690.090.26.3411.909.9487.890.090.01.76

-LRB-

-RRB-

diphosphate

dihydrate

-LRB-

HMADPH

-RRB-

0.2918.506.768.8991.789.393.018.446.899.2090.087.590.01.75

-LRB-

-RRB-

α

.105.095.5010.7790.190.069.65.105.4611.9790.090.068.31.77

-LRB-

-RRB-

α

.055.609.5910.3889.789.990.15.609.5310.5390.090.090.01.31

-LRB-

-RRB-

Anthracene

-LRB-

-RRB-

0.0210.367.326.8489.9109.489.811.176.028.5590.0124.690.01.21

-LRB-

-RRB-

Aqua-tris

-LRB-

-LRB-

-LRB-

dimethylamino

-RRB-

methyl

-RRB-

phenyl

-RRB-

borane

-LRB-

QEVYEV

-RRB-

0.1619.818.4114.9989.975.189.620.358.5715.2390.072.390.01.19

-LRB-

-RRB-

Aspartic

acid

-LRB-

LASPRT

-RRB-

0.205.136.387.7090.0106.290.05.146.987.6290.099.890.01.83

-LRB-

-RRB-

Barium

oxalate

oxalic

acid

dihydrate

-LRB-

-RRB-

4.7510.6813.0968.990.190.15.4112.4614.4563.890.090.03.77

-LRB-

-RRB-

Benzene

-LRB-

BENZEN

-RRB-

0.019.276.797.1590.190.289.89.556.927.4490.090.090.01.15

-LRB-

-RRB-

Berberine

sulfate

-LRB-

CISREB

-RRB-

0.1519.917.4327.5197.6117.390.720.377.4427.4397.7116.285.51.61

-LRB-

-RRB-

β

.085.346.095.1490.065.789.85.386.275.0890.066.890.01.64

-LRB-

-RRB-

β

.048.814.9912.3489.988.990.07.815.4312.6290.090.090.01.35

-LRB-

-RRB-

bis

-LRB-

-LRB-

-RRB-

octane

-RRB-

bis

-LRB-

-LRB-

-RRB-

octane

-RRB-

tetrakis

-LRB-

tribromide

-RRB-

dibromide

-LSB-

-RSB-

-LRB-

DAHGUO

-RRB-

15.3920.6012.81103.789.990.016.1721.3713.23101.090.090.02.65

-LRB-

-RRB-

bis

-LRB-

acid

-RRB-

-LRB-

-RRB-

ethane

-LRB-

LAPTUS

-RRB-

0.1812.0116.117.2775.489.794.112.7715.777.2773.191.193.41.56

-LRB-

-RRB-

bis

-LRB-

Pyridinium

-RRB-

oxalate

oxalic

acid

-LRB-

DEFCUM

-RRB-

4.1211.397.77102.199.891.04.0011.328.44102.097.388.61.60

-LRB-

-RRB-

bis

-LRB-

Urea

-RRB-

oxalic

acid

-LRB-

-RRB-

12.347.005.1384.289.890.012.376.885.0583.690.090.01.58

-LRB-

-RRB-

Bromo-tris

-LRB-

-RRB-

amine-manganese

-LRB-

ii

-RRB-

-LRB-

DAEAMN

-RRB-

0.2711.8511.8511.8390.290.389.712.2212.2212.2290.090.090.01.78

-LRB-

-RRB-

Calcium

acetate

chloride

pentahydrate

-LRB-

CALCLA

-RRB-

0.0413.2611.206.66119.189.788.613.7211.516.82116.790.090.01.73

-LRB-

-RRB-

Camphor

-LRB-

UGAHUF

-RRB-

0.068.4526.777.3290.891.189.98.9327.047.3890.090.090.01.22

-LRB-

-RRB-

Cholesteryl

acetate

-LRB-

-RRB-

0.1216.989.2116.2887.971.788.417.629.2216.5290.072.890.01.18

-LRB-

-RRB-

cis

Copper

Diglycinate

-LRB-

-RRB-

0.195.3312.6010.5489.990.189.95.1913.5510.6990.090.090.02.16

-LRB-

-RRB-

Citric

acid

-LRB-

-RRB-

0.3111.925.3812.1889.5115.289.611.475.6212.8190.2111.590.01.81

-LRB-

-RRB-

Coronene

-LRB-

CORONE

-RRB-

0.0316.024.799.8890.168.890.016.124.7010.1090.069.190.01.41

-LRB-

-RRB-

Cyclohexane

-LRB-

CYCHEX

-RRB-

0.028.126.4111.2390.0107.190.08.206.4411.2390.0108.890.01.00

-LRB-

-RRB-

Cyclotrimethylene-trinitramine

-LRB-

RDX

-RRB-

0.2211.2411.4814.3289.888.489.910.7111.5713.1890.090.090.01.60

-LRB-

-RRB-

Cystine

-LRB-

-RRB-

0.425.3454.255.3788.459.989.25.4256.285.4290.060.090.01.78

-LRB-

-RRB-

Cytosine

-LRB-

-RRB-

0.0410.217.097.7987.290.488.49.827.527.7379.590.090.01.52

-LRB-

-RRB-

Dinicotinic

acid

-LRB-

-RRB-

0.186.7111.099.6889.7111.990.16.5911.159.7090.0107.890.01.66

-LRB-

-RRB-

Dipyridinium

bis

-LRB-

hydrogen-oxalate

-RRB-

oxalic

acid

-LRB-

DUVLUB

-RRB-

27.718.307.3590.083.890.026.848.917.4590.087.190.01.69

-LRB-

-RRB-

Disodium

adenosine-triphosphate

trihydrate

-LRB-

ADENTP

-RRB-

0.766.2420.5831.3790.091.488.37.0720.8830.4590.090.090.02.00

-LRB-

-RRB-

acid

monohydrate

-LRB-

-RRB-

0.118.114.8319.8987.6102.390.68.404.9520.6090.0100.490.01.76

-LRB-

-RRB-

γ

.075.526.938.94114.450.990.75.487.048.92113.252.190.01.65

-LRB-

-RRB-

Glucose

-LRB-

GLUCSA

-RRB-

0.1910.274.2015.1290.090.090.010.364.9714.8490.090.090.01.84

-LRB-

-RRB-

.063.6216.849.8888.285.996.23.5516.349.6990.090.090.01.68

-LRB-

-RRB-

-LRB-

-RRB-

0.063.6711.8116.3889.6102.789.73.5611.4416.4790.095.190.01.46

-LRB-

-RRB-

Hydroquinone

bis

-LRB-

aniline

-RRB-

-LRB-

HIBFUT

-RRB-

5.038.2118.4276.890.090.05.398.2218.7477.590.090.01.33

-LRB-

-RRB-

Isonicotinamide

-LRB-

EHOWIH

-RRB-

0.089.985.8010.1190.079.389.910.035.7310.1790.081.890.01.41

-LRB-

-RRB-

Isonicotinamide

acid

-LRB-

LUNMEM

-RRB-

20.705.1622.1989.996.290.020.875.1422.4290.097.790.01.47

-LRB-

-RRB-

Keggin

pentakis

-LRB-

Tetraethylammonium

-RRB-

bis

-LRB-

meso-tetraphenyl-porphyrinato-zinc

-RRB-

tetraconta-oxo-silicon-dodeca-molybdenum

bromide

-LRB-

PIJFUJ

-RRB-

15.1432.0114.9890.190.390.115.2232.2815.2290.090.090.01.88

-LRB-

-RRB-

.9311.675.8690.089.989.95.7912.265.9390.090.090.01.46

-LRB-

-RRB-

Leucine

-LRB-

-RRB-

0.1313.855.249.4489.282.490.214.525.309.5690.085.890.01.28

-LRB-

-RRB-

Lithium

acetate

-LRB-

Li

-LRB-

-RRB-

-LRB-

-RRB-

-RRB-

0.0211.236.387.1598.394.488.210.886.626.8290.090.090.01.34

-LRB-

-RRB-

l-Lysine

monohydrochloride

dihydrate

-LRB-

LYSCLH

-RRB-

0.1112.355.7614.3881.690.489.813.325.8814.9881.290.090.01.44

-LRB-

-RRB-

Malonic

acid

bis

-LRB-

isonicotinamide

-RRB-

-LRB-

ULAWEJ

-RRB-

14.6514.6812.2565.881.868.815.6814.8611.9467.385.665.71.55

-LRB-

-RRB-

m-Aminophenol

-LRB-

-RRB-

0.028.246.1211.3390.089.589.98.286.1011.2390.090.090.01.27

-LRB-

-RRB-

m-Aminopyridine

-LRB-

AMIPYR

-RRB-

0.036.305.6815.2390.189.5111.46.195.7115.3090.090.0110.51.23

-LRB-

-RRB-

m-Cresol

N

N

N

N

tetraisopropyloxamide

-LRB-

DUGRIG

-RRB-

6.6226.7211.8893.489.889.86.8627.1912.0896.190.289.81.15

-LRB-

-RRB-

m-Diaminobenzene

-LRB-

REDDEJ

-RRB-

13.0710.399.8584.089.590.413.2610.459.8886.790.090.01.51

-LRB-

-RRB-

Methionine

-LRB-

-RRB-

0.115.1816.409.3185.393.883.35.2014.839.4981.090.090.01.27

-LRB-

-RRB-

Methyl

-LRB-

-RRB-

-LRB-

1α

β

α

α

β

-RRB-

-LRB-

-RRB-

oxalic

acid

monohydrate

-LRB-

HUZKOC

-RRB-

0.156.1918.358.1196.5101.681.76.6117.898.07102.399.883.21.47

-LRB-

-RRB-

m-Hydroxybenzoic

acid

-LRB-

BIDLOP

-RRB-

0.0323.804.975.0490.074.390.023.894.945.4990.074.390.01.60

-LRB-

-RRB-

tetrakis

-LRB-

-RRB-

octacyano-molybdenum

-LRB-

iv

-RRB-

-LRB-

PYCMOA

-RRB-

-LRB-

-LSB-

-RSB-

-LSB-

MoIV

-LRB-

CN

-RRB-

-RSB-

-RRB-

0.0917.9610.469.7093.391.489.218.5110.159.1789.890.090.01.46

-LRB-

-RRB-

m-Toluidine

-LRB-

FANDOO

-RRB-

0.089.135.7923.1291.780.989.48.765.8124.8790.079.990.01.18

-LRB-

-RRB-

Natroxalate

-LRB-

-LRB-

-RRB-

-RRB-

0.584.239.295.3890.190.286.53.4510.385.2490.090.090.02.11

-LRB-

-RRB-

N

N

-LRB-

diyl

-RRB-

bis

-LRB-

methylamine

-RRB-

-LRB-

ENIWIH

-RRB-

0.0710.6711.7710.1590.190.190.011.0912.0210.5790.090.090.01.25

-LRB-

-RRB-

N

-LRB-

FOCVOI

-RRB-

0.127.8516.177.6790.795.688.97.6418.087.6490.090.090.01.33

-LRB-

-RRB-

N

N-Dimethylaniline

-LRB-

-RRB-

0.087.0913.208.7182.4101.295.46.7812.338.2680.574.092.01.29

-LRB-

-RRB-

Nicotinamide

adenine

dinucleotide

tetrahydrate

-LRB-

-RRB-

0.258.898.2011.3383.269.7103.28.848.5911.1989.470.4103.91.66

-LRB-

-RRB-

N-Methylurea

-LRB-

MEUREA

-RRB-

0.096.856.648.0890.191.290.36.926.988.4890.090.090.01.34

-LRB-

-RRB-

N

N-Dimethylbenzamide

-LRB-

ODOTOQ

-RRB-

0.086.5116.197.4990.090.690.86.6316.307.6590.090.090.01.26

-LRB-

-RRB-

N

N-Dimethylurea

-LRB-

WIFKEB

-RRB-

0.099.278.496.0690.489.6109.39.278.606.0490.090.0108.81.30

-LRB-

-RRB-

o-Aminophenol

-LRB-

-RRB-

0.057.508.1019.7090.090.590.07.857.2519.7590.090.090.01.21

-LRB-

-RRB-

o-Aminopyridine

-LRB-

AMPYRD

-RRB-

0.047.415.6511.6290.085.989.97.595.6711.7190.084.590.01.29

-LRB-

-RRB-

o-Diaminobenzene

-LRB-

BAGFIY

-RRB-

0.047.727.579.9689.982.590.07.727.5410.3290.080.090.01.25

-LRB-

-RRB-

o-Dimethoxybenzene

-LRB-

TUKGEL

-RRB-

0.0612.949.355.5890.189.889.913.359.925.5390.090.090.01.36

-LRB-

-RRB-

Oxalic

acid

-LRB-

-RRB-

0.036.916.088.1689.989.990.06.566.097.8590.090.090.01.74

-LRB-

-RRB-

Oxalic

acid

dihydrate

-LRB-

-RRB-

0.044.9211.453.4489.790.0106.96.0911.933.4789.790.0106.92.26

-LRB-

-RRB-

Oxytocin

-LSB-

-RSB-

0.4422.068.8926.7390.699.188.423.049.0427.2790.0102.290.01.43

-LRB-

-RRB-

p-Aminophenol

-LRB-

-RRB-

0.037.9512.904.7890.190.190.18.1812.955.2690.090.090.01.48

-LRB-

-RRB-

p-Aminopyridine

-LRB-

AMPYRE

-RRB-

0.045.4811.927.1989.690.391.05.5712.127.3290.090.090.01.33

-LRB-

-RRB-

p-Chloroaniline

-LRB-

-RRB-

0.038.377.308.9890.089.790.28.597.249.1990.090.090.01.54

-LRB-

-RRB-

p-Diaminobenzene

-LRB-

PENDAM

-RRB-

0.038.2923.085.9489.990.093.58.3722.955.9790.090.093.61.27

-LRB-

-RRB-

Phenanthrene

-LRB-

-RRB-

0.049.165.738.5690.280.989.99.446.148.4490.082.090.01.34

-LRB-

-RRB-

Phenolphthalein

-LRB-

NIMDAO

-RRB-

0.0911.2414.5819.0190.089.889.511.3914.8219.2790.090.090.01.34

-LRB-

-RRB-

Phloroglucinol

-LRB-

PHGLOL

-RRB-

0.0312.719.354.8789.889.689.912.569.374.8390.090.090.01.45

-LRB-

-RRB-

p-Hydroxybenzoic

acid

-LRB-

JOZZIH

-RRB-

0.046.2110.0518.4689.885.790.16.3410.4618.5190.086.890.01.60

-LRB-

-RRB-

Picric

acid

-LRB-

PICRAC

-RRB-

19.499.3888.990.489.89.7019.139.2590.090.090.01.73

-LRB-

-RRB-

Potassium

hydrogen

.013.916.7725.0090.389.882.14.017.1923.8890.090.081.71.60

-LRB-

-RRB-

1-Dimethylamino-8-dimethylammonionaphthalene

saccharin

dihydrate

-LRB-

AJOHUC

-RRB-

0.098.819.5424.5090.299.690.19.259.1724.9390.095.890.01.42

-LRB-

-RRB-

Salicylaldoxime

-LRB-

SALOXM

-RRB-

0.0712.915.4510.0890.365.489.813.605.0810.4190.067.190.01.41

-LRB-

-RRB-

Sodium

acetate

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

11.6511.3915.4088.978.891.710.4010.4712.3590.068.390.00.90

-LRB-

-RRB-

Sodium

hydrogen

.3316.3316.3389.989.990.015.9215.9215.9290.090.090.01.30

-LRB-

-RRB-

Sucrose

-LRB-

-RRB-

0.2410.368.597.5090.0103.090.010.828.687.7290.0103.090.01.75

-LRB-

-RRB-

Tetramethylammonium

dihydrogen

phosphate

monohydrate

-LRB-

FIJHEL

-RRB-

90.190.098.18.528.4412.9090.090.099.11.59

-LRB-

-RRB-

Tetramethylurea

-LRB-

TIDBIR

-RRB-

0.168.696.0011.7392.193.191.69.976.2610.6390.093.090.01.27

-LRB-

-RRB-

Thymine

-LRB-

-RRB-

0.056.796.9611.7178.189.889.66.856.7812.8975.190.090.01.55

-LRB-

-RRB-

trans

Copper

digycinate

-LRB-

IWUBEH

-RRB-

0.329.5327.275.3289.092.388.59.4427.935.0690.090.090.01.85

-LRB-

-RRB-

Trinitrotoluene

-LRB-

-RRB-

0.115.4322.6314.7290.191.490.16.0820.0214.9990.090.090.01.67

-LRB-

-RRB-

tris

-LRB-

Acetylacetonato

-RRB-

titanium

-LRB-

iv

-RRB-

perchlorate

-LRB-

TIACPC

-RRB-

0.258.9711.739.7891.083.592.38.6811.749.8988.584.392.01.45

-LRB-

-RRB-

Tryptophan

-LRB-

TRYPTC

-RRB-

0.1315.265.176.9089.378.388.914.675.307.4590.081.290.01.50

-LRB-

-RRB-

Tyrosine

-LRB-

-RRB-

-LRB-

-RRB-

Urea

-LRB-

-RRB-

0.034.675.585.5890.090.090.04.695.575.5790.090.090.01.37

-LRB-

-RRB-

Urea

nitrate

-LRB-

-RRB-

7.818.209.7089.952.890.17.508.209.5490.055.890.01.65

-LRB-

-RRB-

Weddellite

-LRB-

Ca

-LRB-

-RRB-

-LRB-

-RRB-

7.2311.7211.7289.789.989.97.3612.3712.3790.090.090.02.20

-LRB-

-RRB-

Whewellite

-LRB-

Ca

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

6.049.7714.5789.990.5107.76.2910.1214.5890.090.0109.52.37

-LRB-

-RRB-

tris

-LRB-

-RRB-

yttrium

-LRB-

iii

-RRB-

-LRB-

-RRB-

0.289.578.8918.9589.686.490.210.639.9817.8790.090.090.01.32

-LRB-

-RRB-

dX-ray

densities

in

parenthesisValues

of

a

b

c

in

Ångstroms

α

β

γ

in

degrees

Reference

crystal

structures

from

the

Cambridge

Structural

Database

-LSB-

-RSB-

RMS

Root-mean-square

In

the

solid

state

individual

molecules

of

oxalic

acid

in

oxalic

acid

dihydrate

-LSB-

Cambridge

Structural

Database

-LSB-

-RSB-

-LRB-

CSD

-RRB-

entry

-RSB-

exist

as

the

neutral

species

incorrectly

predicts

them

to

be

fully

ionized

as

oxalate

-LSB-

-RSB-

plus

two

hydronium

ions

-LSB-

-RSB-

This

change

was

accompanied

by

a

very

large

increase

in

density

from

to

g/cc

a

direct

consequence

of

going

from

a

neutral

to

an

ionic

species

A

related

system

is

barium

oxalate

oxalic

acid

dihydrate

-LRB-

CSD

entry

-RRB-

in

which

there

exist

polymeric

chains

of

oxalate

groups

connected

by

bridging

protons

As

with

oxalic

acid

in

the

optimized

geometry

the

proton

is

abstracted

by

the

water

molecule

to

give

oxalate

groups

and

hydronium

resulting

in

an

increase

in

density

of

almost

Sodium

acetate

trihydrate

is

an

ionic

solid

consisting

of

sodium

ions

surrounded

by

an

acetate

group

and

five

water

molecules

four

of

which

form

bridges

between

pairs

of

sodium

ions

completely

fails

to

predict

the

observed

structure

the

distance

between

the

sodium

ions

increases

considerably

effectively

destroying

any

tendency

of

the

water

molecules

to

form

bridges

When

these

three

solids

were

removed

from

consideration

the

average

unsigned

error

-LRB-

AUE

-RRB-

in

density

decreased

to

The

most

common

intermolecular

interaction

is

hydrogen

bonding

which

predicts

to

be

too

short

by

about

Å

with

the

result

that

the

average

signed

error

in

calculated

densities

of

organic

compounds

is

too

high

by

When

a

systematic

correction

to

the

density

was

made

the

AUE

in

density

decreased

still

further

to

Heats

of

formation

Table

presents

a

comparison

of

experimental

and

calculated

heats

of

formation

of

organic

solids

The

largest

difference

occurs

with

which

is

predicted

to

be

too

stable

by

kcal/mol

The

optimized

structure

revealed

an

unrealistically

short

intermolecular

Br

N

distance

of

Å

indicating

that

the

Br

N

core-core

repulsion

was

severely

underestimated

Examination

of

the

values

of

the

parameters

for

the

Br

N

core-core

interaction

revealed

that

the

Voityuk

interaction

would

be

negligible

at

chemical

bonding

distances

This

error

in

can

be

attributed

to

the

absence

of

appropriate

reference

data

in

the

training

set

a

fault

that

could

be

readily

corrected

in

future

work

Table

of

calculated

and

experimental

heats

of

formation

of

organic

compounds

-LRB-

kcal/mol

-RRB-

-LRB-

Z

Z

-RRB-

N

N

Dimethylurea

-LRB-

NIJHUJ

-RRB-

-LRB-

BRANIL

-RRB-

α

Glycine

α

Resorcinol

β

Glycine

Camphor

Citric

acid

-LRB-

RDX

-RRB-

Cystine

γ

Glycine

Leucine

-LRB-

-RRB-

-LRB-

AMIPYR

-RRB-

acid

-LRB-

-RRB-

-LRB-

AMPYRD

-RRB-

-LRB-

BAGFIY

-RRB-

Oxalic

acid

-LRB-

-RRB-

-LRB-

AMPYRE

-RRB-

-LRB-

-RRB-

-LRB-

PENDAM

-RRB-

acid

Picric

acid

Salicylaldoxime

Sucrose

Trinitrotoluene

Tyrosine

Urea

aReference

values

taken

from

the

CRC

Handbook

-LSB-

-RSB-

Heats

of

sublimation

The

heat

of

sublimation

is

a

measure

of

the

intermolecular

interaction

energy

In

some

cases

sublimation

is

accompanied

by

large

geometric

and

electronic

changes

For

example

the

simple

amino

acids

exist

as

the

Zwitterion

in

the

crystal

phase

but

in

the

gas

phase

they

are

unionized

Representative

values

for

calculated

and

observed

heats

of

sublimation

are

presented

in

Table

Determining

the

accuracy

of

for

the

prediction

of

heats

of

sublimation

is

made

difficult

by

the

acknowledged

unreliability

of

many

experimental

measurements

Thus

in

the

reference

compendium

of

sublimation

enthalpies

-LSB-

-RSB-

the

authors

indicate

that

the

reported

value

for

aspartic

acid

kcal/mol

was

likely

unreliable

Table

of

calculated

and

experimental

heats

of

sublimation

Reference

-LSB-

-RSB-

-LRB-

Z

Z

-RRB-

N

N

Dimethylurea

-LRB-

NIJHUJ

-RRB-

α

Aspartic

-LRB-

-RRB-

-LRB-

AMIPYR

-RRB-

N

-LRB-

-RRB-

-LRB-

AMPYRD

-RRB-

-LRB-

BAGFIY

-RRB-

Oxalic

-LRB-

-RRB-

-LRB-

AMPYRE

-RRB-

-LRB-

-RRB-

-LRB-

PENDAM

-RRB-

6.1Phenanthrene22.030.28.2p-Hydroxybenzoic

Picric

Biomolecules

The

primary

objective

in

developing

was

to

more

accurately

model

systems

of

biochemical

interest

The

applicability

of

to

the

study

of

crystals

of

biochemical

importance

was

therefore

of

interest

Oligopeptides

The

X-ray

structures

of

many

small

polypeptides

have

been

determined

and

are

readily

available

in

the

Protein

Data

Bank

-LSB-

-RSB-

One

representative

entry

in

this

collection

is

the

nonapeptide

deamino-oxytocin

Cys-Tyr-Ile-Glu-Asp-Cys-Pro-Leu-Gly

The

structure

of

this

hormone

had

been

refined

to

a

resolution

of

slightly

better

than

Å

-LSB-

-RSB-

Each

deamino-oxytocin

molecule

contains

a

disulfide

bridge

between

atoms

and

and

two

strong

hydrogen

bonds

between

and

and

and

The

unit

cell

contains

four

deamino-oxytocin

molecules

related

by

a

pseudo

operation

that

is

there

are

two

inequivalent

polypeptide

molecules

and

water

molecules

The

coordinates

of

the

hydrogen

atoms

in

the

peptide

were

given

but

not

those

of

the

hydrogen

atoms

on

the

water

molecules

That

water

of

crystallization

exists

implies

that

peptide

water

hydrogen

bonds

also

exist

Because

the

positions

of

the

hydrogen

atoms

on

the

water

molecules

were

not

given

in

the

X-ray

structure

an

estimate

of

the

locations

of

the

hydrogen

atoms

had

to

be

made

before

the

geometry

could

be

optimized

For

this

operation

the

ice

rules

were

used

each

oxygen

atom

in

a

water

molecule

was

involved

in

forming

two

hydrogen

bonds

and

each

hydrogen

atom

formed

one

hydrogen

bond

Of

necessity

some

of

these

bonds

involved

atoms

on

the

peptide

Several

candidate

structures

each

of

which

satisfied

these

conditions

were

constructed

and

the

positions

of

all

hydrogen

atoms

optimized

while

those

of

the

other

atoms

were

held

constant

An

incidental

benefit

of

this

operation

was

that

any

potential

errors

in

the

X-ray

positions

of

some

hydrogen

atoms

in

particular

the

apparently

faulty

location

reported

for

were

automatically

corrected

After

the

positions

of

the

hydrogen

atoms

were

optimized

an

unconstrained

optimization

on

the

unit

cell

was

carried

out

This

involved

the

optimization

of

the

Cartesian

positions

of

all

the

atoms

in

the

unit

cell

of

formula

-LRB-

-RRB-

-LRB-

-RRB-

and

the

unit

cell

dimensions

i.e.

the

simultaneous

optimization

of

coordinates

Each

initial

geometry

optimized

to

give

a

different

final

structure

That

is

the

optimized

geometry

was

very

sensitive

to

the

choice

of

initial

locations

of

the

hydrogen

atoms

assigned

to

the

water

molecules

As

a

result

it

was

not

possible

to

unambiguously

define

an

optimized

structure

however

all

the

fully

optimized

structures

were

within

a

few

kcal/mol

of

each

other

so

one

structure

was

chosen

arbitrarily

and

used

in

the

following

analysis

The

optimized

unit

cell

dimensions

are

shown

in

Table

The

optimized

structure

of

the

entire

unit

cell

had

an

RMS

error

of

Å

and

an

RMS

error

of

Å

for

a

single

molecule

of

deamino-oxytocin

Deviations

from

the

symmetry

were

small

and

were

very

sensitive

to

the

initial

choice

of

hydrogen

bonds

it

is

likely

that

the

time-average

would

be

exactly

All

the

weak

intra-chain

bonds

were

preserved

predicted

the

disulfide

bridges

to

be

Å

and

Å

compared

with

the

X-ray

values

of

Å

and

Å

and

the

hydrogen

bonds

between

and

to

be

Å

versus

the

X-ray

value

of

Å

and

and

Å

compared

to

the

X-ray

Å

Acetylcholine

One

of

the

simplest

of

the

important

biochemicals

is

the

neurotransmitter

acetylcholine

-LSB-

-LRB-

-RRB-

-RSB-

-LRB-

ACh

-RRB-

In

one

form

this

ion

exists

in

the

solid

state

as

the

chloride

-LRB-

CSD

entry

-RRB-

reproduced

the

structure

of

ACh

in

this

salt

with

good

accuracy

the

RMS

error

for

a

single

ACh

being

only

Å

Part

of

this

error

can

be

attributed

to

the

C

H

and

N

H

bond-lengths

from

the

X-ray

structure

being

about

Å

too

small

when

only

the

heavy

atoms

are

used

in

the

comparison

the

RMS

error

decreased

to

Å

An

estimate

of

the

effect

of

the

crystal-packing

forces

can

be

obtained

by

comparing

the

predicted

structure

of

the

gas-phase

ion

with

that

found

in

the

crystal

when

this

was

done

the

RMS

difference

increased

to

Å

This

is

unequivocal

evidence

that

inclusion

of

crystal-packing

forces

is

essential

in

order

to

reproduce

the

observed

structure

Adenosine

diphosphate

Adenosine

diphosphate

-LRB-

ADP

-RRB-

is

an

important

intermediate

in

energy

transfer

in

biochemistry

ADP

contains

an

pyrophosphate

group

which

in

the

tris

-LRB-

hydroxymethyl

-RRB-

methylammonium

dihydrate

salt

-LRB-

CSD

entry

HMADPH

-RRB-

is

described

as

being

doubly

ionized

with

the

counterions

being

the

adenine

and

the

quaternary

ammonium

ion

Hydrogen

atoms

were

added

to

the

structure

given

in

the

CSD

and

in

a

preliminary

calculation

their

positions

were

optimized

using

the

rest

of

the

geometry

being

fixed

at

the

X-ray

structure

One

of

the

hydrogen

atoms

in

the

resulting

geometry

was

located

between

an

oxygen

of

the

terminal

group

on

one

ADP

ion

and

a

nitrogen

atom

on

an

adenine

in

an

adjacent

ADP

ion

Because

these

oxygen

and

nitrogen

atoms

were

only

Å

apart

it

is

likely

that

a

bridging

hydrogen

bond

exists

between

them

in

the

crystal

The

geometry

of

the

entire

system

was

then

optimized

This

resulted

in

an

insignificant

increase

in

the

N

O

distance

to

Å

and

gave

an

RMS

error

for

a

single

ADP

ion

of

Å

This

suggests

that

a

better

description

of

the

pyrophosphate

moiety

would

be

that

it

is

singly

ionized

and

that

it

is

part

of

a

two

molecule

ADP

adenine

system

connected

by

a

bridging

hydrogen

As

with

acetylcholine

the

structure

of

ADP

depends

strongly

on

its

crystal

environment

when

the

geometry

of

a

single

ATP

ion

was

optimized

using

the

structure

distorted

dramatically

and

the

resulting

RMS

error

relative

to

the

X-ray

structure

increased

to

Å

Adenosine

triphosphate

The

nucleotide

adenosine-triphosphate

-LRB-

ATP

-RRB-

is

a

source

of

energy

for

many

biochemical

reactions

and

as

such

its

structure

and

properties

are

of

considerable

interest

Only

one

simple

compound

of

ATP

was

found

in

the

CSD

disodium

adenosine-triphosphate

trihydrate

ADENTP

Its

structure

was

very

badly

reproduced

when

was

used

with

the

RMS

error

of

the

ATP

molecule

being

Å

Examination

of

the

unit

cell

revealed

that

the

sodium

ions

had

formed

spurious

weak

bonds

to

nearby

hydrogen

atoms

and

that

this

was

partially

responsible

for

the

distortion

of

the

ATP

ion

This

was

confirmed

when

potassium

was

used

in

place

of

sodium

and

the

RMS

error

dropped

to

Å

Because

of

this

and

other

results

there

is

convincing

evidence

that

sodium

has

severe

problems

when

solid

state

systems

are

being

modeled

and

it

is

highly

probable

that

part

of

the

error

in

prediction

of

the

structure

of

ADENTP

can

be

attributed

to

faults

in

sodium

parameters

Nicotinamide

adenine

dinucleotide

In

contrast

to

ATP

the

structure

of

nicotinamide

adenine

dinucleotide

-LRB-

NAD

-RRB-

tetrahydrate

-LRB-

CSD

entry

-RRB-

was

reproduced

with

good

accuracy

the

RMS

error

being

only

Å

Like

ATP

NAD

contains

a

polyphosphate

group

Hydrogen

bonding

Because

of

the

importance

of

hydrogen

bonding

in

biochemistry

a

range

of

types

of

hydrogen

bond

were

examined

Most

of

the

important

hydrogen

bonds

in

biochemistry

involve

a

proton

positioned

between

either

two

oxygen

atoms

two

nitrogen

atoms

or

an

oxygen

and

a

nitrogen

atom

the

more

exotic

bonds

such

as

those

involving

halogen

ions

while

interesting

being

of

secondary

importance

Individual

types

of

hydrogen

bonds

O

H

O

A

common

example

of

hydrogen

bonds

is

provided

by

simple

organic

compounds

that

contain

hydroxyl

groups

Examples

of

such

systems

are

sucrose

aspartic

acid

citric

acid

glucose

oxalic

acid

and

the

hydroxybenzoic

acids

In

all

such

simple

hydrogen

bonded

systems

the

geometry

predicted

by

was

similar

to

that

observed

Of

more

interest

are

those

hydrogen

bonds

that

occur

in

systems

in

which

relatively

large

charges

are

involved.The

tendency

for

a

proton

to

form

a

bridging

structure

between

two

oxygen

atoms

in

organic

acids

was

investigated

Such

a

situation

occurs

in

the

polymeric

solid

potassium

hydrogen

acetate

where

a

single

proton

is

shared

between

two

acetate

groups

the

whole

assembly

two

acetates

plus

the

proton

having

a

formal

charge

of

In

catena

-LRB-

-LRB-

-RRB-

-LRB-

acid

-RRB-

potassium

-RRB-

-LRB-

CSD

entry

-RRB-

this

structure

has

the

geometry

O

O

Å

O

H

Å

and

O

H

Å

the

three

atoms

forming

a

straight

line

For

this

solid

predicts

the

following

O

O

Å

O

H

Å

and

O

H

Å

with

the

O

H

O

angle

being

Solid

-LRB-

phosphonomethyl

-RRB-

benzenesulfonic

acid

monohydrate

-LRB-

CSD

entry

KIXQIR

-RRB-

exists

as

the

Zwitterion

In

this

system

the

sulfonic

acid

group

donates

a

proton

to

the

phosphono

group

giving

-LSB-

-RSB-

and

its

counterion

-LSB-

P

-LRB-

OH

-RRB-

-RSB-

One

of

the

hydrogen

atoms

of

the

phosphono

group

then

forms

a

strong

hydrogen

bond

with

the

nearby

water

molecule

incorrectly

predicts

this

bridging

hydrogen

to

be

nearer

to

the

water

than

to

the

phosphono

group

Where

the

X-ray

structure

has

the

PO

H

distance

of

Å

predicts

Å

the

corresponding

distances

for

the

H

are

Å

observed

and

Å

calculated.Another

interesting

hydrogen

bond

exists

in

crystalline

acetylacetone

-LRB-

CSD

entry

-RRB-

In

this

system

the

X-ray

structure

shows

that

the

hydrogen

atom

involved

in

hydrogen

bonding

is

disordered

over

two

equivalent

positions

within

a

single

molecule

with

the

result

that

the

observed

bond

lengths

and

angles

are

symmetric

about

the

central

C

H

unit

As

expected

when

the

geometry

is

optimized

using

the

extra

symmetry

is

destroyed

This

is

a

consequence

of

the

requirement

that

in

a

quantum

chemical

calculation

each

atom

must

be

in

a

defined

position

However

although

the

calculated

structure

was

of

lower

symmetry

when

the

optimized

geometries

of

the

two

halves

of

the

molecule

were

averaged

the

result

was

in

good

agreement

with

the

X-ray

structure

where

predicted

the

C

O

bond

to

be

Å

and

Å

the

X-ray

structure

gave

Å

and

where

gave

the

distance

as

Å

and

Å

the

observed

value

is

Å

The

structure

of

the

hydrogen

bond

was

also

well

reproduced

with

the

calculated

O

O

distance

being

Å

compared

with

the

observed

Å

albeit

the

calculated

O

H

bond

length

Å

was

much

greater

than

the

reported

value

of

Å

N

H

N

In

1-dimethylamino-8-dimethylammonionaphthalene

saccharin

dihydrate

-LRB-

CSD

entry

AJOHUC

-RRB-

saccharine

donates

a

proton

to

the

proton

sponge

-LRB-

dimethylamino

-RRB-

naphthalene

to

form

an

ionic

crystal

The

reported

structure

has

that

proton

asymmetrically

positioned

between

the

two

nitrogen

atoms

N

N

N

H

N

H

Å

The

optimized

structure

gives

N

N

N

H

N

H

thus

both

underestimates

the

bridging

power

of

the

proton

and

exaggerates

the

asymmetry

of

the

bond.A

closely

related

species

-LRB-

dimethylamino

-RRB-

exists

as

the

Zwitterion

in

the

solid

-LRB-

CSD

entry

RISBIE

-RRB-

In

this

system

the

geometry

of

the

N

H

N

structure

is

symmetric

N

H

Å

N

N

Å

and

the

O

H

O

structure

is

unsymmetric

O

H

Å

O

O

Å

predicts

both

the

N

H

N

-LRB-

N

H

Å

N

N

Å

-RRB-

and

the

O

H

O

structures

-LRB-

O

H

Å

O

O

Å

-RRB-

to

be

unsymmetric

In

the

gas

phase

-LRB-

dimethylamino

-RRB-

would

most

likely

exist

as

the

neutral

species

a

-LRB-

d

-RRB-

calculation

predicts

the

energy

of

the

Zwitterionic

form

to

be

kcal/mol

above

that

of

the

neutral

form

however

incorrectly

predicts

that

the

Zwitterion

should

be

kcal/mol

more

stable

than

the

neutral

form.In

an

even

stronger

proton

sponge

-LRB-

hexamethyltriaminophosphazenyl

-RRB-

naphthalene

HMPN

was

reported

-LSB-

-RSB-

The

effect

of

steric

crowding

in

HMPN

arising

from

the

N

P

-LRB-

N

-LRB-

-RRB-

-RRB-

groups

distorts

the

naphthalene

skeleton

so

that

the

reported

torsion

angle

Fig.

is

The

fully

optimized

crystal

structure

predicted

this

angle

to

be

For

the

gas-phase

structure

predicted

the

torsion

angle

to

be

-LSB-

-RSB-

while

gave

an

angle

of

indicating

that

the

model

was

producing

either

a

less

rigid

naphthalene

structure

or

a

greater

steric

repulsion

energy

Fig.

-LRB-

hexamethyltriaminophosphazenyl

-RRB-

naphthaleneAn

additional

example

of

the

importance

of

crystal

packing

forces

is

provided

by

the

accuracy

of

prediction

of

the

structure

of

HMPN

in

the

gas

and

solid

state

phases

Excluding

hydrogen

atoms

the

RMS

difference

between

the

gas-phase

structure

and

the

X-ray

structure

was

Å

while

for

the

crystal

structure

the

equivalent

difference

was

Å

and

for

the

gas-phase

structure

the

RMS

difference

was

Å

That

is

the

gas-phase

structure

was

a

significantly

better

fit

to

the

observed

crystal

structure

than

that

given

by

but

when

crystal

forces

were

included

in

the

calculation

the

gave

a

slightly

better

fit

than

the

result.The

energetics

involved

in

the

sublimation

process

for

HMPN

can

be

modeled

in

three

stages

In

the

solid

phase

gives

a

ΔHf

of

kcal/mol

for

HMPN

Using

the

optimized

geometry

for

the

crystal

form

gives

a

ΔHf

of

kcal/mol

for

HMPN

in

the

gas

phase

When

the

geometry

is

allowed

to

relax

the

ΔHf

of

the

optimized

gas-phase

geometry

decreased

to

kcal/mol

From

this

it

follows

that

crystal

packing

forces

distort

the

geometry

of

HMPN

so

that

its

energy

increases

by

kcal/mol

This

increase

is

however

more

than

offset

by

the

intermolecular

stabilization

energy

of

kcal/mol

resulting

in

a

net

sublimation

energy

of

kcal/mol

Because

HMPN

has

a

very

high

proton

affinity

it

is

interesting

to

speculate

about

the

minimum

energy

structure

of

gas-phase

-LRB-

hexamethyltriaminophosphazenyl

-RRB-

As

with

-LRB-

dimethylamino

-RRB-

predicts

this

system

to

exist

as

the

Zwitterion

in

the

gas

phase

yet

like

-LRB-

dimethylamino

-RRB-

a

calculation

suggests

that

the

neutral

form

is

the

more

stable

form

but

only

by

kcal/mol

That

is

the

possibility

exists

that

-LRB-

hexamethyltriaminophosphazenyl

-RRB-

might

form

a

stable

gas-phase

Zwitterion

but

the

probability

of

this

being

the

case

is

low.An

unusual

complex

resulting

from

the

reaction

of

elemental

bromine

and

-LSB-

-RSB-

octane

-LRB-

DABCO

-RRB-

-LRB-

DABCO

-RRB-

has

been

reported

-LSB-

-RSB-

to

contain

an

almost

linear

structure

of

three

DABCO

groups

and

seven

bromine

atoms

-LRB-

Fig.

-RRB-

with

the

bromine

atoms

split

into

three

fragments

of

and

Br

resulting

in

a

formal

charge

of

From

the

X-ray

structure

-LRB-

CSD

entry

DAHGUO

-RRB-

the

authors

concluded

that

partial

protonation

had

occurred

that

the

complex

of

three

DABCO

units

included

four

protons

and

that

the

remaining

isolated

DABCO

moiety

was

doubly

protonated

Fig.

of

bis

-LRB-

-LRB-

-RRB-

octane

-RRB-

bis

-LRB-

-LRB-

-RRB-

octane

-RRB-

tetrakis

-LRB-

tribromide

-RRB-

dibromideWhen

the

structure

suggested

by

the

authors

was

optimized

using

only

very

small

changes

occurred

in

the

geometry

as

shown

in

Table

all

the

essential

features

proposed

by

the

original

authors

were

reproduced

and

are

therefore

confirmed

These

included

the

conjectures

that

in

the

set

of

three

DABCO

units

the

central

DABCO

was

doubly

ionized

that

the

terminal

DABCOs

were

singly

ionized

and

that

the

isolated

DABCO

was

doubly

charged

The

two

tribromide

ions

had

charges

of

and

with

the

central

atom

in

each

group

carrying

only

an

insignificant

charge

in

accordance

with

the

postulated

existence

of

a

tribromide

anion

and

the

isolated

bromide

ion

had

a

partial

charge

of

again

in

accordance

with

the

proposed

structure

Table

distances

and

charges

in

bis

-LRB-

-LRB-

-RRB-

octane

-RRB-

bis

-LRB-

-LRB-

-RRB-

octane

-RRB-

tetrakis

-LRB-

tribromide

-RRB-

dibromideInteratomic

N

H

O

The

simple

amino

acids

exist

as

Zwitterions

in

the

solid

state

In

this

form

an

group

on

one

ion

electrostatically

interacts

strongly

with

a

COO

ion

on

a

neighboring

ion

In

all

cases

examined

the

structure

of

the

resulting

salt

was

reproduced

with

good

accuracy

This

included

the

structures

of

three

polymorphs

of

glycine

α

β

and

γ

a

set

of

systems

in

which

any

differences

in

heats

of

formation

could

arise

only

from

the

different

intermolecular

interactions

predicted

all

three

polymorphs

to

have

heats

of

formation

within

kcal/mol

of

each

other

albeit

not

in

the

order

observed

experimentally

Of

more

interest

are

those

cases

where

the

energy

of

interaction

is

smaller

and

consequently

the

geometry

of

the

N

H

O

system

would

be

more

sensitive

to

the

environment

A

good

example

of

such

a

system

is

methyl

-LRB-

-RRB-

-LRB-

1α

β

α

α

β

-RRB-

-LRB-

-RRB-

oxalic

acid

monohydrate

-LRB-

CSD

entry

HUZKOC

-RRB-

in

which

a

molecule

of

oxalic

acid

hydrogen

bonds

to

a

neutral

nitrogen

on

the

large

organic

fragment

In

this

system

predicts

the

N

O

distance

to

be

slightly

too

large

Å

compared

to

the

reported

Å.The

existence

of

a

uniquely

short

heteroatom

separation

in

a

hydrogen-bonded

compound

-LRB-

-LRB-

-RRB-

-RRB-

Fig.

was

reported

in

-LSB-

-RSB-

In

this

system

-LRB-

CSD

entry

-RRB-

the

pyridine

and

imidazole

rings

are

almost

coplanar

a

condition

essential

to

the

formation

of

the

strong

hydrogen

bond

The

optimized

gas-phase

geometry

predicted

by

and

and

now

all

have

large

twist

angles

and

respectively

In

the

solid

state

however

predicts

the

rings

to

be

coplanar

and

the

N

O

distance

to

be

Å

which

is

very

close

to

the

reported

Å

In

the

observed

crystal

structure

the

hydrogen

atom

is

asymmetrically

positioned

with

the

O-H

and

N-H

distances

being

Å

and

Å

and

the

O

H

N

angle

being

also

predicts

the

hydrogen

to

be

asymmetrically

positioned

but

in

the

opposite

sense

the

O

H

and

N

H

distances

being

and

Å

and

the

O

H

N

angle

to

be

Fig.

-LRB-

-LRB-

-RRB-

-RRB-

-4-isopropyl-4-methyl-5-oxo-imidazoleThe

tendency

of

to

incorrectly

favor

the

Zwitterionic

form

of

a

hydroxy

amine

over

the

neutral

was

investigated

by

modeling

the

three

isomers

of

hydroxyaniline

All

three

isomers

exist

in

the

solid

state

as

the

neutral

form

however

on

optimizing

the

geometry

using

the

ortho

and

para

forms

spontaneously

transitioned

to

the

Zwitterion

Meta-hydroxyaniline

optimized

to

the

neutral

form

but

when

the

calculation

was

repeated

starting

with

the

Zwitterionic

form

the

structure

optimized

to

the

Zwitterionic

form

and

in

that

form

was

kcal/mol

lower

in

energy

than

the

neutral

form

As

expected

the

density

increased

from

to

on

going

from

the

neutral

to

the

Zwitterion

thus

has

a

definite

and

demonstrable

error

in

its

exaggerated

tendency

to

form

Zwitterions.DABCO

forms

several

very

unusual

hydrogen-bonded

systems

among

which

are

-LSB-

-RSB-

octane

azelaic

acid

-LRB-

CSD

entry

UNEGEZ

-RRB-

where

each

DABCO

forms

two

different

types

of

bridging

N

H

O

bonds

to

adjacent

azelaic

acid

molecules

predicts

one

of

these

to

have

the

structure

N

O

-LRB-

-RRB-

N

H

-LRB-

-RRB-

and

O

H

-LRB-

-RRB-

-LRB-

X-ray

structures

in

parentheses

-RRB-

and

the

other

to

be

N

O

-LRB-

-RRB-

N

H

-LRB-

-RRB-

and

O

H

-LRB-

-RRB-

The

X-ray

structure

shows

the

existence

of

a

polymeric

chain

of

alternating

azelaic

acid

and

DABCO

units

from

which

it

follows

that

the

different

geometries

of

the

two

N

H

O

structures

can

only

be

attributed

to

crystal

packing

forces

A

closely

related

compound

is

-LSB-

-RSB-

octane

glutarate

-LRB-

CSD

entry

UNEFIC

-RRB-

in

which

a

similar

structure

exists

but

now

with

the

bridging

hydrogen

being

nearer

to

the

nitrogen

than

to

the

oxygen

In

UNECIF

the

N

H

distance

predicted

by

was

-LRB-

-RRB-

Å

and

the

O

H

-LRB-

-RRB-

Å

π

π

stacking

π

π

stacking

occurs

in

the

polycyclic

aromatic

hydrocarbons

where

it

is

the

result

of

Van

der

Waals

-LRB-

VDW

-RRB-

interactions

between

the

rings

In

general

VDW

interactions

are

weaker

than

hydrogen

bonding

interactions

and

historically

have

been

the

hardest

to

model

using

semiempirical

methods

Thus

when

the

default

single

determinant

wavefunction

is

used

VDW

terms

are

completely

absent

and

in

order

to

mimic

the

effects

of

VDW

attraction

the

normal

procedure

is

for

modifications

to

be

made

to

the

core

core

interaction

An

estimate

of

how

accurately

can

reproduce

the

VDW

interaction

is

provided

by

anthracene

-LRB-

CSD

entry

-RRB-

benzene

-LRB-

CSD

entry

BENZEN

-RRB-

and

coronene

-LRB-

CSD

entry

CORONE

-RRB-

In

anthracene

the

molecules

are

stacked

in

a

staggered

arrangement

While

reproduces

the

density

with

good

accuracy

the

optimized

structure

predicts

the

parallel

sheets

of

anthracene

molecules

to

be

separated

by

Å

rather

than

the

observed

Å

and

pairs

of

anthracene

molecules

forming

T

structures

rather

than

the

observed

V

configuration

Conversely

both

benzene

and

coronene

crystallize

with

a

perfect

herringbone

packing

and

this

structure

is

reproduced

with

very

good

accuracy

by

the

calculated

and

observed

inter-plane

distance

being

essentially

identical

Very

weak

interactions

In

small

saturated

hydrocarbons

the

strongest

intermolecular

interaction

energy

arises

from

instantaneous

correlation

or

VDW

forces

A

consequence

of

this

is

that

such

compounds

are

in

general

highly

volatile

and

most

have

very

low

melting

points

Another

characteristic

of

compounds

of

this

type

is

that

intermolecular

separations

are

typically

very

large

in

cyclohexane

the

smallest

intermolecular

separation

is

about

Å

When

the

structure

of

cyclohexane

was

optimized

from

the

experimental

structure

using

the

final

and

X-ray

structures

agreed

almost

exactly

However

the

heat

of

formation

of

each

cyclohexane

decreased

from

an

initial

kcal/mol

for

the

starting

X-ray

structure

to

the

final

kcal/mol

for

the

optimized

structure

reflecting

the

relaxation

of

the

X-ray

C

H

bond

lengths

which

are

normally

too

short

However

the

ΔHf

for

isolated

cyclohexane

is

predicted

to

be

kcal/mol

from

which

it

follows

that

the

energy

of

interaction

amounted

to

only

kcal/mol

much

less

than

the

reported

kcal/mol

The

implication

is

that

although

was

able

to

reproduce

the

observed

crystal

structure

the

magnitude

of

the

VDW

interaction

was

grossly

underestimated

In

solid

methionine

-LRB-

CSD

entry

-RRB-

the

molecules

form

double

layers

with

the

hydrophobic

end

S

on

the

outside

The

X-ray

structure

shows

that

these

layers

are

separated

by

about

Å

predicts

the

inter-layer

separation

to

be

much

larger

Å

Further

investigation

of

the

properties

of

sulfur

predicted

by

see

below

indicated

the

lack

of

any

sulfur

sulfur

VDW

attraction

This

deficiency

is

likely

responsible

for

the

unrealistically

large

inter-layer

separation

Most

acetylacetonato

transition

metal

complexes

such

as

tris

-LRB-

acetylacetonato

-RRB-

titanium

-LRB-

iv

-RRB-

perchlorate

-LRB-

CSD

entry

TIACPC

-RRB-

adopt

an

almost

octahedral

coordination

of

the

oxygen

atoms

around

the

central

metal

ion

An

exception

is

the

hexamethyl

acetylacetone

complex

of

yttrium

-LRB-

iii

-RRB-

tris

-LRB-

-RRB-

yttrium

-LRB-

iii

-RRB-

-LRB-

CSD

entry

-RRB-

where

the

oxygen

atoms

form

a

trigonal

prism

This

structure

was

reproduced

by

The

deviation

from

the

conventional

octahedral

structure

can

not

be

attributed

to

crystal

packing

forces

when

the

geometry

of

the

isolated

complex

ion

was

optimized

using

the

trigonal

prism

structure

was

retained

However

when

the

geometry

of

the

unsubstituted

complex

tris

-LRB-

acetylacetonato

-RRB-

yttrium

-LRB-

iii

-RRB-

was

optimized

the

expected

structure

resulted

suggesting

that

the

likely

driving

force

was

steric

crowding

arising

from

the

tertiary

butyl

groups

Polymorphs

-LRB-

-LRB-

-RRB-

amino

-RRB-

is

unique

in

the

CSD

in

that

there

are

seven

distinct

polymorphs

-LSB-

-RSB-

because

three

of

these

are

red

orange

and

yellow

this

chemical

is

commonly

referred

to

as

ROY

To

test

the

suitability

of

for

modeling

polymorphs

the

structure

of

each

of

the

polymorphs

of

ROY

was

optimized

using

starting

with

the

X-ray

geometry

In

every

case

the

optimized

structure

was

qualitatively

the

same

as

the

X-ray

structure

that

is

the

crystal

packing

arrangement

was

preserved

Within

each

unit

cell

the

structures

of

the

individual

molecules

were

reproduced

with

good

accuracy

-LRB-

Table

-RRB-

Although

the

calculated

heats

of

formation

of

the

X-ray

structures

spanned

a

range

of

kcal/mol

the

optimized

structures

all

had

similar

heats

of

formation

spanning

a

range

of

kcal/mol

as

would

be

expected

for

polymorphs

Co-crystals

Designing

crystal

structures

for

active

pharmaceutical

ingredients

presents

an

important

challenge

to

crystal

engineers

One

promising

avenue

of

research

involves

designing

co-crystals

so

determining

the

suitability

of

as

a

tool

for

this

work

is

of

obvious

interest

The

structures

of

several

co-crystals

were

optimized

using

all

the

resulting

geometries

were

in

good

agreement

with

the

structures

found

in

the

CSD

In

all

of

the

systems

investigated

the

two

components

were

held

together

by

hydrogen

bonds

Thus

in

the

bis-urea

oxalic

acid

co-crystal

-LRB-

Fig.

CSD

entry

-RRB-

each

oxalic

acid

forms

two

strong

O

H

O

hydrogen

bonds

to

the

keto

groups

of

the

neighboring

urea

molecules

this

resulting

in

a

tri-molecular

unit

In

turn

these

units

pack

together

in

the

crystal

using

weaker

N

H

O

hydrogen

bonds

predicts

that

the

co-crystal

would

be

significantly

more

stable

than

its

two

separate

precursors

the

predicted

ΔHf

of

the

co-crystal

is

kcal/mol

while

the

sum

of

the

ΔHf

of

the

precursors

Table

is

kcal/mol

Fig.

structure

of

the

co-crystal

of

urea

and

oxalic

acid

Another

example

of

such

a

co-crystal

is

provided

by

isonicotinamide

acid

Fig.

-LRB-

CSD

entry

LUNMEM

-RRB-

in

which

each

hydroxybenzoic

acid

forms

hydrogen

bonds

to

three

adjacent

isonicotinamide

molecules

in

a

complicated

three-dimensional

structure

As

with

the

previous

co-crystal

predicts

LUNMEM

to

be

more

stable

than

its

precursors

but

in

this

case

only

by

kcal/mol

Fig.

of

isonicotinamide

and

acid

showing

hydrogen-bond

lengths

-LRB-

X-ray

in

parenthesis

-RRB-

Metal-containing

species

Many

organic

compounds

that

contain

elements

of

Groups

I

or

II

are

ionic

salts

A

good

example

is

calcium

oxalate

which

forms

three

well

characterized

solids

whewellite

-LRB-

Ca

-LRB-

-RRB-

-LRB-

-RRB-

-RRB-

weddellite

-LRB-

Ca

-LRB-

-RRB-

-LRB-

-RRB-

-RRB-

and

caoxite

-LRB-

Ca

-LRB-

-RRB-

-LRB-

-RRB-

-RRB-

at

least

one

of

which

the

author

involuntarily

prepared

in

vivo

the

separation

of

which

from

the

surrounding

organic

material

was

accompanied

by

severe

algia

The

structures

of

all

three

minerals

are

reproduced

with

good

accuracy

Anhydrous

disodium

oxalate

exists

as

the

mineral

natroxalate

In

contrast

to

the

calcium

oxalates

the

structure

predicted

by

was

completely

different

to

that

observed

within

each

oxalate

dianion

one

carboxylate

group

was

rotated

by

to

give

an

approximately

structure

More

seriously

some

sodium

sodium

distances

became

unrealistically

short

Å

instead

of

the

observed

Å

This

specific

error

is

attributable

to

the

faulty

values

of

the

core

core

parameters

Solids

containing

metal

complex

ions

can

be

regarded

as

salts

that

is

as

molecular

metal

complexes

cations

or

anions

plus

counterions

An

example

is

bromo-tris

-LRB-

-RRB-

amine-manganese

-LRB-

ii

-RRB-

-LRB-

CSD

entry

DAEAMN

-RRB-

where

the

metal

complex

consists

of

the

neutral

tris

-LRB-

-RRB-

amine

that

chelates

a

manganese

dication

the

whole

complex

behaving

like

a

large

dication

Two

bromide

counterions

are

present

for

each

such

complex

ion

in

order

to

maintain

electroneutrality

predicts

the

single

N

Mn

distance

to

be

Å

versus

Å

in

the

X-ray

structure

and

the

three

N

Mn

to

be

Å

versus

Å

in

the

X-ray

Inorganic

compounds

In

general

most

inorganic

solids

differ

from

crystalline

organic

compounds

in

that

they

do

not

involve

discrete

molecules

Instead

they

exist

as

extended

covalently

or

ionically

bound

infinite

systems

A

consequence

of

this

is

that

identification

of

simple

structural

units

in

inorganic

solids

is

often

either

difficult

or

impossible

A

more

subtle

consequence

is

that

the

band-structure

of

inorganic

solids

is

usually

more

complicated

than

those

of

organic

solids

for

the

same

reciprocal

distance

bands

arising

from

inorganic

solids

generally

have

a

much

greater

curvature

than

those

for

organic

solids

this

being

a

consequence

of

the

strong

bonds

that

extend

throughout

such

solids

Conversely

in

most

organic

solids

there

is

an

intermolecular

gap

that

effectively

confines

molecular

orbitals

to

individual

molecules

This

means

that

the

band-structure

of

most

organic

compounds

consists

of

relatively

flat

bands

In

the

cluster

method

the

Γ

point

represents

the

entire

Brillouin

zone

so

that

a

much

larger

cluster

must

be

used

when

inorganic

solids

that

are

not

composed

of

discrete

molecules

are

modeled

In

practice

this

means

that

the

cluster

used

has

to

be

large

enough

to

contain

a

sphere

of

radius

Å

in

contrast

to

the

Å

used

in

modeling

organic

solids

A

survey

of

the

applicability

of

to

a

wide

range

of

inorganic

solids

was

carried

out

using

structural

reference

data

obtained

from

the

American

Mineralogist

Crystal

Structure

Database

-LSB-

-RSB-

As

with

organic

crystals

the

starting

geometry

was

the

X-ray

structure

But

in

contrast

to

most

organic

solids

many

inorganic

solids

had

to

be

modified

before

a

calculation

could

be

started

Semiempirical

calculations

require

that

a

definite

structure

be

used

However

some

minerals

such

as

forsterite

-LRB-

FeII

Mg

-RRB-

are

of

variable

composition

with

one

or

more

sites

occupied

by

the

two

types

of

metal

atoms

at

random

Before

a

calculation

on

such

a

system

can

be

performed

all

variable

atoms

have

to

be

replaced

by

definite

atoms

In

the

case

of

forsterite

all

iron

atoms

were

replaced

by

magnesium

atoms

In

a

few

solids

there

was

still

disorder

in

the

lattice

although

the

formula

was

stoichiometric

In

spinel

for

example

the

formula

is

but

in

the

observed

crystal

structure

a

small

fraction

of

the

aluminum

sites

are

replaced

by

magnesium

atoms

and

vice

versa

Of

necessity

the

model

used

in

the

calculation

was

idealized

so

that

sites

that

were

magnesium

were

made

magnesium

and

sites

that

were

aluminum

were

made

aluminum

Although

this

idealized

structure

does

not

occur

naturally

it

could

be

considered

a

good

approximation

to

the

observed

structure

Some

minerals

that

contain

hydrogen

atoms

did

not

have

the

positions

of

these

atoms

reported

In

those

cases

a

preliminary

calculation

was

carried

out

in

which

the

hydrogen

atoms

were

positioned

in

likely

sites

and

then

the

positions

of

those

atoms

optimized

During

this

operation

the

positions

all

the

other

atoms

were

fixed

at

the

experimental

values

The

results

can

conveniently

be

partitioned

according

to

the

types

of

solids

involved

and

sequenced

in

order

of

complexity

In

most

cases

the

calculated

structure

was

similar

to

the

X-ray

structure

in

that

no

bonds

were

made

or

broken

as

a

result

of

geometry

optimization

Unit

cell

parameters

for

those

solids

where

the

calculated

structure

inside

the

unit

cell

was

substantially

similar

to

the

reference

are

presented

in

Table

and

Table

and

heats

of

formation

are

given

in

Table

Table

and

X-ray

structural

parameters

for

inorganic

compounds

Values

of

a

b

c

are

in

Ångstroms

α

β

γ

in

-LRB-

-RRB-

dabcαβγabcαβγElementsDiamond

-LRB-

C

-RRB-

3.593.593.5990.090.090.03.573.573.5790.090.090.03.44

-LRB-

-RRB-

Glitter

-LRB-

C

-RRB-

.602.605.9690.190.190.02.602.605.9090.090.090.02.98

-LRB-

-RRB-

Graphite

-LRB-

C

-RRB-

2.472.4787.1789.690.060.02.462.466.7090.090.060.02.12

-LRB-

-RRB-

Silicon

-LRB-

Si

-RRB-

5.115.115.1190.090.090.05.435.435.4390.090.090.02.78

-LRB-

-RRB-

Sulfur

-LRB-

S

-RRB-

11.7714.0126.8190.490.289.810.4312.8324.3690.090.090.01.54

-LRB-

-RRB-

Group

I

HalidesCesium

bromide

-LRB-

CsBr

-RRB-

4.354.354.3590.090.090.04.304.304.3090.090.090.04.29

-LRB-

-RRB-

Cesium

chloride

-LRB-

CsCl

-RRB-

4.174.184.1890.389.889.74.124.124.1290.090.090.03.84

-LRB-

-RRB-

Cesium

fluoride

-LRB-

CsF

-RRB-

6.026.026.0290.090.090.06.016.016.0190.090.090.04.62

-LRB-

-RRB-

Cesium

iodide

-LRB-

CsI

-RRB-

4.734.734.7390.090.090.04.574.574.5790.090.090.04.07

-LRB-

-RRB-

Potassium

bromide

-LRB-

KBr

-RRB-

6.796.756.7587.690.090.06.616.616.6190.090.090.02.55

-LRB-

-RRB-

Potassium

chloride

-LRB-

KCl

-RRB-

6.126.126.1290.090.090.06.296.296.2990.090.090.02.16

-LRB-

-RRB-

Potassium

fluoride

-LRB-

KF

-RRB-

5.035.035.0390.090.090.05.385.385.3890.090.090.03.02

-LRB-

-RRB-

Potassium

iodide

-LRB-

KI

-RRB-

7.177.177.1790.190.090.07.077.077.0790.090.090.02.99

-LRB-

-RRB-

Lithium

bromide

-LRB-

LiBr

-RRB-

5.495.485.4890.090.090.05.505.505.5090.090.090.03.50

-LRB-

-RRB-

Lithium

chloride

-LRB-

LiCl

-RRB-

5.135.135.1390.090.090.05.145.145.1490.090.090.02.09

-LRB-

-RRB-

Lithium

fluoride

-LRB-

LiF

-RRB-

4.034.044.0590.089.990.04.034.034.0390.090.090.02.62

-LRB-

-RRB-

Lithium

iodide

-LRB-

LiI

-RRB-

6.046.036.0490.090.090.06.036.036.0390.090.090.04.04

-LRB-

-RRB-

Sodium

bromide

-LRB-

NaBr

-RRB-

6.276.206.2085.990.090.06.046.046.0490.090.090.02.84

-LRB-

-RRB-

Sodium

chloride

-LRB-

NaCl

-RRB-

6.246.246.2490.090.090.05.605.605.6090.090.090.01.60

-LRB-

-RRB-

Sodium

fluoride

-LRB-

NaF

-RRB-

4.794.794.7990.290.189.84.614.614.6190.090.090.02.54

-LRB-

-RRB-

Sodium

iodide

-LRB-

NaI

-RRB-

7.027.027.0290.090.090.06.476.476.4790.090.090.02.87

-LRB-

-RRB-

Rubidium

bromide

-LRB-

RbBr

-RRB-

6.876.886.8890.390.090.06.906.906.9090.090.090.03.38

-LRB-

-RRB-

Rubidium

chloride

-LRB-

RbCl

-RRB-

6.706.686.6889.190.090.06.636.636.6390.090.090.02.69

-LRB-

-RRB-

Rubidium

fluoride

-LRB-

RbF

-RRB-

5.865.865.8690.090.090.06.016.016.0190.090.090.03.45

-LRB-

-RRB-

Rubidium

iodide

-LRB-

RbI

-RRB-

7.847.767.7683.390.090.07.357.357.3590.090.090.03.01

-LRB-

-RRB-

HalidesCalcium

iodide

-LRB-

-RRB-

6.214.484.48119.990.090.16.964.484.48120.090.090.04.51

-LRB-

-RRB-

Carnallite

-LRB-

KMg

-LRB-

-RRB-

-RRB-

15.8622.3110.2473.192.895.916.1222.479.5590.090.090.01.61

-LRB-

-RRB-

Chloromagnesite

-LRB-

-RRB-

19.403.753.75119.989.190.917.593.603.60107.990.090.02.00

-LRB-

-RRB-

Cryolite

-LRB-

-RRB-

5.678.035.6990.190.089.95.467.805.6190.090.090.22.69

-LRB-

-RRB-

Fluorite

-LRB-

-RRB-

5.495.455.4890.090.090.05.465.435.4690.090.090.03.17

-LRB-

-RRB-

Frankdicksonite

-LRB-

-RRB-

6.226.226.2390.090.090.06.206.206.2090.090.090.04.83

-LRB-

-RRB-

Hydrophilite

-LRB-

-RRB-

4.286.426.3889.990.090.04.206.436.2490.090.090.02.10

-LRB-

-RRB-

Magnesium

dibromide

-LRB-

-RRB-

5.834.024.02119.191.688.36.263.813.81120.090.090.03.71

-LRB-

-RRB-

Magnesium

diiodide

-LRB-

-RRB-

6.284.274.24118.290.689.66.884.144.14120.090.090.04.61

-LRB-

-RRB-

-LRB-

-RRB-

10.237.357.0090.087.189.89.817.096.6890.089.790.02.08

-LRB-

-RRB-

Neighborite

-LRB-

-RRB-

8.148.138.1390.090.090.17.677.677.6791.490.090.02.57

-LRB-

-RRB-

Sal

ammoniac

-LRB-

-RRB-

4.074.073.6890.089.973.53.863.863.8690.090.090.01.52

-LRB-

-RRB-

Sellaite

-LRB-

-RRB-

3.074.624.6290.090.090.03.054.634.6390.090.090.03.16

-LRB-

-RRB-

Oxidesα

Crystobalite

-LRB-

-RRB-

5.365.367.4789.990.189.64.984.986.9590.090.090.01.86

-LRB-

-RRB-

α

Quartz

-LRB-

-RRB-

5.195.185.7490.090.0120.04.914.915.4190.090.0120.02.24

-LRB-

-RRB-

Anatase

-LRB-

-RRB-

10.293.923.9290.190.289.69.523.783.7890.090.090.03.36

-LRB-

-RRB-

Arkelite

-LRB-

-RRB-

6.094.915.5090.089.990.15.135.135.1390.090.090.04.97

-LRB-

-RRB-

Barium

oxide

-LRB-

BaO

-RRB-

5.645.645.6489.890.090.05.635.635.6390.090.090.05.69

-LRB-

-RRB-

β

Quartz

-LRB-

-RRB-

5.195.185.7490.090.060.05.005.005.4690.090.060.02.24

-LRB-

-RRB-

β

Tridymite

-LRB-

-RRB-

5.345.348.7290.090.0119.95.055.058.2790.090.0120.01.86

-LRB-

-RRB-

Brookite

-LRB-

-RRB-

5.425.679.6190.090.490.05.145.459.1790.090.090.03.59

-LRB-

-RRB-

Cassiterite

-LRB-

-RRB-

4.944.963.4990.090.089.94.744.743.1990.090.090.05.86

-LRB-

-RRB-

Chabazite

-LRB-

-RRB-

9.559.569.5693.993.993.89.409.409.4094.394.394.31.38

-LRB-

-RRB-

Coesite

-LRB-

-RRB-

7.4312.857.4990.060.890.07.1712.377.1490.059.790.02.56

-LRB-

-RRB-

Claudetite

-LRB-

-RRB-

14.005.435.0689.885.881.812.874.545.2586.290.090.03.46

-LRB-

-RRB-

Corundum

-LRB-

-RRB-

-LRB-

a

b

c

α

β

γ

-RRB-

5.135.125.1256.256.256.25.135.135.1355.355.355.33.91

-LRB-

-RRB-

Corundum

-LRB-

-RRB-

-LRB-

a

b

c

α

β

γ

-RRB-

4.834.8312.9190.090.0120.04.764.7612.9990.090.0120.03.91

-LRB-

-RRB-

Ice-I

-LRB-

Ice-Ih

-RRB-

7.454.367.0990.590.389.37.834.527.3890.090.090.01.04

-LRB-

-RRB-

.265.9189.9106.591.07.7812.986.2490.0105.590.01.43

-LRB-

-RRB-

.506.4689.989.590.76.736.736.7390.090.090.01.28

-LRB-

-RRB-

.448.8070.190.692.67.5310.359.2070.790.089.11.53

-LRB-

-RRB-

.945.9090.989.589.05.706.186.1890.090.090.01.59

-LRB-

-RRB-

.364.3690.090.590.16.414.454.4590.090.090.01.96

-LRB-

-RRB-

Ice-X

-LRB-

-RRB-

2.902.902.9090.090.090.02.732.732.7390.090.090.02.46

-LRB-

-RRB-

Ice-X

-LRB-

-RRB-

2.722.722.7290.090.090.02.732.732.7390.090.090.02.98

-LRB-

-RRB-

.267.1590.190.289.97.834.527.3890.090.090.01.03

-LRB-

-RRB-

.058.4690.569.590.610.297.479.2490.070.390.01.54

-LRB-

-RRB-

.077.8490.390.090.34.088.358.1490.090.090.01.48

-LRB-

-RRB-

Keggin

Dodecatungstophosphoric

acid

hexahydrate

-LRB-

-RRB-

-LRB-

-RRB-

13.0113.4313.0090.492.289.712.5112.5112.5190.090.090.04.37

-LRB-

-RRB-

Lime

-LRB-

CaO

-RRB-

4.954.954.9590.090.190.04.824.824.8190.090.090.03.07

-LRB-

-RRB-

Mordenite

-LRB-

-RRB-

18.6821.007.7590.290.090.018.1320.497.5290.090.090.01.58

-LRB-

-RRB-

Lead

oxide

-LRB-

PbO

-RRB-

3.834.743.8389.990.089.93.985.023.9890.090.090.010.68

-LRB-

-RRB-

Periclase

-LRB-

MgO

-RRB-

4.294.294.2990.090.090.04.224.224.2290.090.090.03.40

-LRB-

-RRB-

Perovskite

-LRB-

-RRB-

5.385.547.8489.789.990.15.385.447.6490.090.090.03.87

-LRB-

-RRB-

Plattnerite

-LRB-

-RRB-

-LRB-

Rutile

structure

-RRB-

3.504.664.7389.890.090.03.394.964.9690.090.090.010.31

-LRB-

-RRB-

Rutile

-LRB-

-RRB-

4.844.843.1290.090.090.04.594.592.9690.090.090.03.71

-LRB-

-RRB-

Stishovite

-LRB-

-RRB-

2.824.384.3890.090.090.02.674.184.1890.090.090.03.70

-LRB-

-RRB-

Zincite

-LRB-

ZnO

-RRB-

3.333.335.2690.090.060.33.253.255.2090.090.060.05.33

-LRB-

-RRB-

SpinelsChrysoberyl

-LRB-

-LRB-

BeO

-RRB-

-LRB-

-RRB-

-RRB-

4.589.585.7290.390.090.04.409.335.4490.090.090.03.36

-LRB-

-RRB-

Spinel

-LRB-

-RRB-

8.3116.6316.6390.290.090.08.2116.4116.4190.090.090.03.29

-LRB-

-RRB-

BoratesBoracite

-LRB-

MgO

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

78.548.5912.1190.090.090.08.558.5512.0990.090.090.02.93

-LRB-

-RRB-

Borax

-LRB-

-LRB-

-RRB-

-RRB-

12.3311.2716.20105.193.783.012.1910.7411.8990.073.490.01.18

-LRB-

-RRB-

Parahilgardite

-LRB-

-LRB-

-RRB-

Cl

-LRB-

-RRB-

-RRB-

17.196.396.18119.699.884.617.506.496.31119.2100.484.02.84

-LRB-

-RRB-

Ulexite

-LRB-

-LRB-

-RRB-

-RRB-

6.7713.628.8897.4108.2103.36.6812.878.82110.0109.190.41.82

-LRB-

-RRB-

CarbonatesAragonite

-LRB-

-RRB-

4.557.806.0890.090.090.14.967.975.7490.090.090.03.08

-LRB-

-RRB-

Azurite

-LRB-

-LRB-

CuO

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-RRB-

5.735.129.5091.090.190.05.855.0110.3492.490.090.04.10

-LRB-

-RRB-

Calcite

-LRB-

-RRB-

6.326.326.3245.245.245.26.366.366.3646.146.146.12.87

-LRB-

-RRB-

Cerussite

-LRB-

-RRB-

7.0989.391.489.35.186.148.4990.090.090.06.66

-LRB-

-RRB-

Dawsonite

-LRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-RRB-

6.735.985.7590.090.290.06.715.215.5890.090.090.02.07

-LRB-

-RRB-

Dolomite

-LRB-

CaMg

-LRB-

-RRB-

-RRB-

4.744.7415.3290.089.9120.04.814.8116.0290.090.0120.03.08

-LRB-

-RRB-

Huntite

-LRB-

-LRB-

-RRB-

-RRB-

9.409.357.6790.590.259.89.509.507.8290.090.060.03.02

-LRB-

-RRB-

Ikaite

-LRB-

-LRB-

CaO

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-RRB-

8.727.8510.8191.371.390.38.878.2311.0290.069.890.01.97

-LRB-

-RRB-

Kalicinite

-LRB-

-RRB-

19.634.164.1690.977.890.215.195.633.7190.075.590.02.00

-LRB-

-RRB-

Magnesite

-LRB-

-RRB-

14.914.577.9590.090.290.015.024.638.0390.090.090.03.11

-LRB-

-RRB-

Natrite

-LRB-

-RRB-

9.936.815.6690.290.0102.08.916.045.2490.090.0101.31.88

-LRB-

-RRB-

Thermonatrite

-LRB-

-LRB-

-RRB-

-RRB-

5.8511.817.8190.089.391.65.2610.726.4790.090.090.01.53

-LRB-

-RRB-

Otavite

-LRB-

-RRB-

5.564.7115.5990.088.990.94.934.2716.2790.090.090.04.21

-LRB-

-RRB-

Smithsonite

-LRB-

-RRB-

4.834.8314.4689.590.0120.04.654.6515.0390.090.0120.04.28

-LRB-

-RRB-

Strontianite

-LRB-

-RRB-

6.598.655.0290.190.090.06.008.365.0990.090.090.03.42

-LRB-

-RRB-

Witherite

-LRB-

-RRB-

4.997.268.4989.989.989.95.316.438.9090.090.090.04.26

-LRB-

-RRB-

Zabuyelite

-LRB-

-RRB-

5.268.806.2367.590.090.04.978.366.2065.290.090.01.84

-LRB-

-RRB-

Group

IVMoissanite

-LRB-

SiC

-RRB-

5.005.363.0990.090.090.05.055.333.0890.090.090.03.22

-LRB-

-RRB-

Silicon

carbide

-LRB-

SiC

-RRB-

4.394.394.3990.090.090.04.354.354.3590.090.090.03.16

-LRB-

-RRB-

Groups

III-VAluminum

antimonide

-LRB-

AlSb

-RRB-

5.945.945.9490.090.090.06.146.146.1490.090.090.04.71

-LRB-

-RRB-

Aluminum

arsenide

-LRB-

AlAs

-RRB-

5.915.915.9190.090.090.05.665.665.6690.090.090.03.27

-LRB-

-RRB-

Aluminum

nitride

-LRB-

AlN

-RRB-

4.404.404.4090.090.090.04.374.374.3790.090.090.03.20

-LRB-

-RRB-

Aluminum

phosphide

-LRB-

AlP

-RRB-

5.495.495.4990.090.090.05.425.425.4290.190.190.12.33

-LRB-

-RRB-

Boron

Nitride

-LRB-

BN

-RRB-

3.643.643.6490.090.090.03.613.613.6190.090.090.03.42

-LRB-

-RRB-

Gallium

arsenide

-LRB-

GaAs

-RRB-

5.665.665.6690.090.090.05.655.655.6590.090.090.05.31

-LRB-

-RRB-

Indium

arsenide

-LRB-

InAs

-RRB-

5.975.975.9790.090.090.06.066.066.0690.090.090.05.93

-LRB-

-RRB-

Group

VICadmium

telluride

-LRB-

CdTe

-RRB-

5.585.585.5890.090.090.06.366.366.3690.090.090.09.17

-LRB-

-RRB-

Coloradoite

-LRB-

HgTe

-RRB-

6.616.616.6190.090.090.06.326.326.3290.090.090.07.56

-LRB-

-RRB-

Lead

selenide

-LRB-

PbSe

-RRB-

4.344.344.3590.090.090.06.176.176.1790.090.090.023.18

-LRB-

-RRB-

Lead

telluride

-LRB-

PbTe

-RRB-

7.877.877.8790.090.090.07.107.107.1090.090.090.04.56

-LRB-

-RRB-

Stibnite

-LRB-

-RRB-

10.674.0511.4090.087.990.011.293.8311.2190.090.090.04.58

-LRB-

-RRB-

Stilleite

-LRB-

ZnSe

-RRB-

5.955.955.9590.090.090.05.545.545.5490.090.090.04.56

-LRB-

-RRB-

.824.245.2594.490.190.14.994.895.3990.090.090.00.96

-LRB-

-RRB-

HydroxidesBrucite

-LRB-

Mg

-LRB-

OH

-RRB-

-RRB-

3.203.214.3089.890.0120.13.143.144.7790.090.0120.02.53

-LRB-

-RRB-

Diaspore

-LRB-

AlO

-LRB-

OH

-RRB-

-RRB-

4.179.753.0090.089.989.84.409.432.8590.090.090.03.26

-LRB-

-RRB-

Gibbsite

-LRB-

Al

-LRB-

OH

-RRB-

-RRB-

9.0410.384.4590.190.090.09.7410.164.3490.085.590.02.48

-LRB-

-RRB-

MnO

-LRB-

OH

-RRB-

7.006.2313.4590.288.489.85.295.8013.3189.789.690.02.99

-LRB-

-RRB-

Orthoboric

acid

-LRB-

B

-LRB-

OH

-RRB-

-RRB-

10.977.267.26120.183.4100.46.357.047.02119.878.587.50.84

-LRB-

-RRB-

NitratesAmmonium

nitrate

-LRB-

-RRB-

8.8213.8510.7695.889.472.19.4912.2310.7690.089.991.31.71

-LRB-

-RRB-

Niter

-LRB-

-RRB-

8.965.386.5990.689.189.59.165.416.4390.090.090.02.11

-LRB-

-RRB-

Nitratine

-LRB-

-RRB-

18.665.434.0890.196.290.516.835.074.3990.090.090.02.06

-LRB-

-RRB-

PhosphatesBobierrite

-LRB-

-LRB-

-RRB-

-LRB-

-RRB-

-RRB-

10.4626.994.5889.4104.393.010.0727.934.6790.0105.090.02.16

-LRB-

-RRB-

Calcium

phosphate

-LRB-

-LRB-

-RRB-

-RRB-

5.5319.975.3488.756.990.35.2518.675.2590.060.090.03.13

-LRB-

-RRB-

Fluorapatite

-LRB-

-LRB-

-RRB-

-RRB-

9.289.296.8789.890.059.69.379.376.8890.090.060.03.28

-LRB-

-RRB-

Dorfmanite

-LRB-

-LRB-

-RRB-

-RRB-

8.4911.7715.9089.990.290.16.6010.3616.8790.090.090.01.48

-LRB-

-RRB-

Lithiophosphate

-LRB-

-RRB-

5.496.7511.6290.090.190.14.936.1210.5390.090.090.01.79

-LRB-

-RRB-

Newberyite

-LRB-

-LRB-

-RRB-

-RRB-

9.8710.0610.3290.090.090.410.0210.6810.2090.090.090.02.26

-LRB-

-RRB-

Phosphammite

-LRB-

-LRB-

-RRB-

-RRB-

7.756.7410.9189.966.490.18.036.7011.0490.066.690.01.68

-LRB-

-RRB-

Potassium

dihydrogen

phosphate

-LRB-

-RRB-

7.697.577.5988.091.088.76.977.457.4590.090.090.02.05

-LRB-

-RRB-

Potassium

oxovanadium

-LRB-

IV

-RRB-

phosphate

-LRB-

V

-RRB-

-LRB-

-RRB-

7.667.718.8190.289.890.07.617.318.4190.090.090.02.56

-LRB-

-RRB-

Sodalite

-LRB-

-RRB-

8.328.338.6089.490.590.49.049.049.0490.090.090.02.04

-LRB-

-RRB-

Wagnerite

-LRB-

-RRB-

12.1112.429.6590.074.690.011.9612.689.6490.071.790.03.09

-LRB-

-RRB-

SulfatesAlum

-LRB-

KAl

-LRB-

-RRB-

-LRB-

-RRB-

-RRB-

12.3112.3512.2789.389.890.512.1812.1812.1990.090.090.01.69

-LRB-

-RRB-

Aluminite

-LRB-

-LRB-

-RRB-

-RRB-

6.9015.3311.2990.2108.090.07.4415.5811.7090.0110.290.02.01

-LRB-

-RRB-

Alunite

-LRB-

-LRB-

-RRB-

-LRB-

OH

-RRB-

-RRB-

7.017.0017.3889.989.760.26.966.9617.3590.090.060.02.79

-LRB-

-RRB-

Ammonium

sulfate

-LRB-

-LRB-

-RRB-

-RRB-

10.995.757.2991.090.190.210.645.997.7890.090.090.01.90

-LRB-

-RRB-

Anglesite

-LRB-

-RRB-

7.406.337.0092.491.495.16.968.485.4090.090.090.06.18

-LRB-

-RRB-

Anhydrite

-LRB-

-RRB-

6.798.397.0987.190.090.26.996.257.0090.090.090.02.24

-LRB-

-RRB-

Arcanite

-LRB-

-RRB-

7.559.626.3889.990.190.27.4810.075.7690.090.090.02.50

-LRB-

-RRB-

Barite

-LRB-

-RRB-

7.445.379.3490.189.990.07.155.468.8890.090.090.04.15

-LRB-

-RRB-

Celestine

-LRB-

-RRB-

8.435.676.9390.189.891.18.395.366.8990.090.090.03.68

-LRB-

-RRB-

Epsomite

-LRB-

-LRB-

-RRB-

-RRB-

11.8211.816.1989.990.090.111.8912.016.8690.090.090.01.89

-LRB-

-RRB-

Glauberite

-LRB-

-RRB-

8.4110.5910.1850.590.190.18.318.5310.1376.790.090.02.64

-LRB-

-RRB-

Gypsum

-LRB-

-RRB-

5.5814.426.7190.2106.190.25.6715.106.4990.0118.590.02.21

-LRB-

-RRB-

Hanksite

-LRB-

KCl

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

411.6511.7621.8788.090.5119.210.4710.4621.1990.090.0120.01.99

-LRB-

-RRB-

Hexahydrite

-LRB-

-LRB-

-RRB-

-RRB-

24.306.929.6589.878.290.024.417.2110.1190.081.790.01.91

-LRB-

-RRB-

Langbeinite

-LRB-

-LRB-

-RRB-

-RRB-

10.7010.3810.5889.389.090.210.4310.4310.4390.090.090.02.52

-LRB-

-RRB-

Leonite

-LRB-

-LRB-

-RRB-

-LRB-

-RRB-

-RRB-

10.738.9913.0489.995.690.09.859.4711.7890.084.790.01.95

-LRB-

-RRB-

Mercallite

-LRB-

-RRB-

9.8517.858.71590.290.090.69.8018.968.4190.090.090.02.36

-LRB-

-RRB-

Thenardite

-LRB-

-RRB-

6.3413.2811.3190.291.190.25.8712.309.8390.090.090.01.98

-LRB-

-RRB-

Zinkosite

-LRB-

-RRB-

4.936.368.8590.186.690.14.776.758.6090.090.090.03.87

-LRB-

-RRB-

SulfidesCinnabar

-LRB-

HgS

-RRB-

4.314.319.8790.090.060.04.154.159.5190.090.060.07.30

-LRB-

-RRB-

Galena

-LRB-

PbS

-RRB-

5.875.875.8790.090.090.05.945.945.9490.090.090.07.86

-LRB-

-RRB-

Greenockite

-LRB-

CdS

-RRB-

6.707.154.1390.089.989.96.757.164.1390.090.090.04.85

-LRB-

-RRB-

Hawleyite

-LRB-

CdS

-RRB-

3.843.843.8490.090.090.05.835.835.8390.090.090.05.02

-LRB-

-RRB-

Metacinnabar

-LRB-

HgS

-RRB-

6.296.296.2990.090.090.05.855.855.8590.090.090.06.21

-LRB-

-RRB-

Niningerite

-LRB-

MgS

-RRB-

5.205.205.2090.090.090.05.205.205.2090.090.090.02.66

-LRB-

-RRB-

Sphalerite

-LRB-

ZnS

-RRB-

5.415.415.4190.090.090.05.435.435.4390.090.090.04.08

-LRB-

-RRB-

Wurtzite

-LRB-

ZnS

-RRB-

3.843.846.3090.090.090.03.813.816.2390.090.060.04.03

-LRB-

-RRB-

Vanadates

tungstates

chromates

molybdatesDescloizite

-LRB-

PbZn

-LRB-

-RRB-

-LRB-

OH

-RRB-

-RRB-

8.366.309.3594.788.990.87.606.079.4490.090.090.05.48

-LRB-

-RRB-

Ferberite

-LRB-

-RRB-

5.005.354.6489.995.489.94.955.704.7390.090.090.08.17

-LRB-

-RRB-

Phoenicochroite

-LRB-

-RRB-

5.677.7415.6742.191.888.25.677.1414.0064.890.090.07.90

-LRB-

-RRB-

Scheelite

-LRB-

-RRB-

5.455.7314.4391.087.892.45.245.2411.3890.090.090.04.25

-LRB-

-RRB-

Tarapacaite

-LRB-

-RRB-

10.576.057.7089.989.890.310.395.927.6690.090.090.02.62

-LRB-

-RRB-

Vanadinite

-LRB-

-LRB-

-RRB-

-RRB-

7.7811.9716.7487.492.391.67.3410.3317.8990.090.090.06.04

-LRB-

-RRB-

Wulfenite

-LRB-

-RRB-

5.6212.495.5990.390.089.25.4712.185.4790.090.090.06.22

-LRB-

-RRB-

Zincochromite

-LRB-

-RRB-

8.408.408.4090.090.090.08.338.338.3390.090.090.05.24

-LRB-

-RRB-

Zirconium

tungstate

-LRB-

-RRB-

9.439.499.5090.289.789.89.189.189.1890.090.090.04.59

-LRB-

-RRB-

dX-ray

densities

in

parenthesiseSee

-LSB-

-RSB-

Table

and

X-ray

structural

parameters

for

silicates

Values

of

a

b

c

are

in

Ångstroms

α

β

γ

in

degreesPM6X-rayDensitydabcαβγabcαβγCyclosilicateBenitoite

-LRB-

-RRB-

6.7611.609.8290.090.390.06.6011.439.7190.090.090.03.57

-LRB-

-RRB-

Beryl

-LRB-

-RRB-

19.0919.069.0290.090.0120.018.4318.439.2490.090.090.02.51

-LRB-

-RRB-

Dravite

-LRB-

-LRB-

-RRB-

-LRB-

-RRB-

-RRB-

16.1416.137.3989.989.960.215.9515.957.2190.090.060.02.99

-LRB-

-RRB-

InosilicateCummingtonite

-LRB-

-LRB-

-RRB-

-RRB-

9.0618.385.6790.0100.090.09.5118.195.3390.0101.990.02.79

-LRB-

-RRB-

Diopside

-LRB-

-RRB-

5.369.119.2290.076.390.05.258.909.7590.074.490.03.29

-LRB-

-RRB-

Enstatite

-LRB-

-RRB-

5.388.9617.6990.189.990.05.188.8218.2390.090.090.03.13

-LRB-

-RRB-

Jadeite

-LRB-

-RRB-

8.689.085.7290.1106.290.19.478.615.2490.0107.690.03.10

-LRB-

-RRB-

Johannsenite

-LRB-

-RRB-

9.795.269.7975.690.290.19.165.299.9874.590.090.03.36

-LRB-

-RRB-

Kosmochlor

-LRB-

-RRB-

5.699.3910.0790.076.290.25.278.729.5890.072.690.02.89

-LRB-

-RRB-

Spodumene

-LRB-

-RRB-

9.526.118.0464.086.287.48.395.229.4669.990.090.02.95

-LRB-

-RRB-

Tremolite

-LRB-

-LRB-

OH

-RRB-

-RRB-

9.3018.835.5890.177.490.09.8418.055.2790.075.390.02.83

-LRB-

-RRB-

Wollastonite

-LRB-

-RRB-

9.1611.127.63100.0102.182.710.1211.077.3199.5100.583.43.10

-LRB-

-RRB-

NesosilicateÅkermanite

-LRB-

-RRB-

7.917.734.7790.087.290.17.847.845.0190.090.090.03.11

-LRB-

-RRB-

Andalusite

-LRB-

-RRB-

6.137.965.9097.185.987.95.567.907.8090.090.090.03.78

-LRB-

-RRB-

Chromium

silicate

-LRB-

-RRB-

12.5211.385.7789.890.289.09.5911.175.7090.090.090.03.17

-LRB-

-RRB-

Euclase

-LRB-

-LRB-

BeO

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-RRB-

4.8315.124.4190.099.990.04.7814.324.6390.0100.390.03.03

-LRB-

-RRB-

Forsterite

-LRB-

-RRB-

4.776.1010.2390.189.990.14.766.0010.2290.090.090.03.14

-LRB-

-RRB-

Garnet

-LRB-

-LRB-

CaO

-RRB-

-LRB-

-RRB-

-RRB-

11.7511.7511.7590.090.090.011.8611.8511.8590.090.090.03.69

-LRB-

-RRB-

Kyanite

-LRB-

-RRB-

7.965.775.6582.184.978.37.857.135.5778.990.074.04.29

-LRB-

-RRB-

Pyrope

-LRB-

-LRB-

-RRB-

-LRB-

MgO

-RRB-

-LRB-

-RRB-

-RRB-

11.3611.3711.3689.889.789.811.5511.5511.5590.090.090.03.65

-LRB-

-RRB-

Sillimanite

-LRB-

-RRB-

12.497.365.7389.890.090.011.557.687.4990.090.090.04.09

-LRB-

-RRB-

Titanite

-LRB-

-RRB-

7.447.008.4389.989.6113.97.076.578.7290.090.0113.93.24

-LRB-

-RRB-

Topaz

-LRB-

-RRB-

7.114.188.9589.789.189.69.334.428.3990.090.090.04.60

-LRB-

-RRB-

Uvarovite

-LRB-

-RRB-

12.0712.0612.0689.990.190.012.0012.0012.0090.090.090.03.79

-LRB-

-RRB-

Willemite

-LRB-

-RRB-

8.948.938.95108.8108.7108.78.628.628.63107.9107.9107.93.93

-LRB-

-RRB-

Zircon

-LRB-

-RRB-

6.096.088.5390.690.190.36.616.615.9890.090.090.03.85

-LRB-

-RRB-

PhyllosilicateApophyllite

-LRB-

-LRB-

-RRB-

-LRB-

CaO

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-RRB-

9.559.8114.9192.185.989.08.978.9715.7790.090.090.02.08

-LRB-

-RRB-

Chlorite

-LRB-

-LRB-

MgO

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

-RRB-

5.459.3914.1689.397.289.25.249.0714.2990.097.090.02.57

-LRB-

-RRB-

Kanemite

-LRB-

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

75.1420.707.6090.490.091.14.9520.507.2890.090.090.01.76

-LRB-

-RRB-

Kaolinite

-LRB-

-LRB-

OH

-RRB-

-RRB-

6.599.655.3487.577.888.67.408.945.1689.975.188.32.59

-LRB-

-RRB-

Lithium

disilicate

-LRB-

-RRB-

5.3714.786.4690.090.090.04.7814.655.6890.090.090.01.95

-LRB-

-RRB-

Prehnite

-LRB-

-LRB-

OH

-RRB-

-RRB-

4.365.8818.4390.488.889.84.655.4818.4990.090.090.02.90

-LRB-

-RRB-

Pyrophyllite

-LRB-

-LRB-

OH

-RRB-

-RRB-

9.435.6320.7099.690.190.08.905.1618.64100.890.090.02.21

-LRB-

-RRB-

Talc

-LRB-

-LRB-

OH

-RRB-

-RRB-

5.579.619.7991.181.290.25.299.179.4690.481.389.92.43

-LRB-

-RRB-

SorosilicateBertrandite

-LRB-

-LRB-

BeO

-RRB-

-LRB-

-RRB-

-LRB-

-RRB-

16.264.928.7590.190.090.015.274.578.7190.090.090.02.26

-LRB-

-RRB-

Danburite

-LRB-

-RRB-

8.708.198.2490.090.090.08.048.757.7390.090.090.02.78

-LRB-

-RRB-

Hardystonite

-LRB-

-RRB-

8.048.044.8286.486.989.87.837.835.0190.090.090.03.36

-LRB-

-RRB-

Hemimorphite

-LRB-

-RRB-

-LRB-

OH

-RRB-

-LRB-

-RRB-

-RRB-

5.4010.618.3290.189.990.05.1210.738.3790.090.090.03.36

-LRB-

-RRB-

Lawsonite

-LRB-

-LRB-

OH

-RRB-

-LRB-

-RRB-

-RRB-

7.566.3313.3490.190.090.08.805.8513.1490.090.090.03.27

-LRB-

-RRB-

Rosenhahnite

-LRB-

-RRB-

9.376.706.8288.479.2105.09.486.816.9682.984.1108.63.01

-LRB-

-RRB-

Tanzanite

-LRB-

-LRB-

-RRB-

-LRB-

-RRB-

O

-LRB-

OH

-RRB-

-RRB-

15.615.529.9590.090.090.116.225.5410.0390.090.090.03.52

-LRB-

-RRB-

Thortveitite

-LRB-

-RRB-

7.444.468.9889.989.773.46.654.698.6290.090.077.83.00

-LRB-

-RRB-

TectosilicateAlbite

-LRB-

-RRB-

8.7612.697.0489.665.090.28.1512.877.1193.163.589.72.46

-LRB-

-RRB-

Mordenite

-LRB-

-RRB-

18.6721.007.7590.290.090.018.1320.497.5290.090.090.01.58

-LRB-

-RRB-

Nepheline

-LRB-

-RRB-

10.1510.298.2690.090.061.110.0510.058.3890.090.060.02.57

-LRB-

-RRB-

Paracelsian

-LRB-

-RRB-

7.059.379.3890.190.290.18.409.489.0090.089.390.04.40

-LRB-

-RRB-

Sodalite

-LRB-

-RRB-

8.918.908.9090.190.190.08.888.888.8890.090.090.02.28

-LRB-

-RRB-

Thomsonite

-LRB-

-RRB-

13.6913.5712.7480.775.884.213.2513.0613.1090.090.090.02.37

-LRB-

-RRB-

dX-ray

densities

in

parenthesisTable

of

calculated

and

experimental

heats

of

formation

of

inorganic

compounds

-LRB-

kcal/mol

-RRB-

Quartz

-LRB-

-RRB-

α

Crystobalite

-LRB-

-RRB-

β

Tridymite

-LRB-

-RRB-

β

Quartz

-LRB-

-RRB-

Chabazite

-LRB-

-RRB-

Coesite

-LRB-

-RRB-

Mordenite

-LRB-

-RRB-

Stishovite

-LRB-

-RRB-

Aluminum

nitride

-LRB-

AlN

-RRB-

Aluminum

phosphide

-LRB-

AlP

-RRB-

Ammonium

chloride

-LRB-

-RRB-

Ammonium

nitrate

-LRB-

-RRB-

Ammonium

sulfate

-LRB-

-LRB-

-RRB-

-RRB-

Anatase

-LRB-

-RRB-

Andalusite

-LRB-

-RRB-

Anglesite

-LRB-

-RRB-

Anhydrite

-LRB-

-RRB-

Aragonite

-LRB-

-RRB-

Arcanite

-LRB-

-RRB-

Arkelite

-LRB-

-RRB-

Barium

oxide

-LRB-

BaO

-RRB-

Barite

-LRB-

-RRB-

Boron

-LRB-

B

-RRB-

Boron

Nitride

-LRB-

BN

-RRB-

Brookite

-LRB-

-RRB-

Brucite

-LRB-

Mg

-LRB-

OH

-RRB-

-RRB-

Calcite

-LRB-

-RRB-

Calcium

Iodide

-LRB-

-RRB-

Cassiterite

-LRB-

-RRB-

Celestine

-LRB-

-RRB-

Chloromagnesite

-LRB-

-RRB-

Chrysoberyl

-LRB-

-LRB-

BeO

-RRB-

-LRB-

-RRB-

-RRB-

Cinnabar

-LRB-

HgS

-RRB-

Coloradoite

-LRB-

HgTe

-RRB-

Corundum

-LRB-

-RRB-

Cryolite

-LRB-

-RRB-

Enstatite

-LRB-

-RRB-

Fluorite

-LRB-

-RRB-

Forsterite

-LRB-

-RRB-

Frankdicksonite

-LRB-

-RRB-

Galena

-LRB-

PbS

-RRB-

Gallium

arsenide

-LRB-

GaAs

-RRB-

Graphite

-LRB-

C

-RRB-

Greenockite

-LRB-

CdS

-RRB-

Hawleyite

-LRB-

CdS

-RRB-

Hydrophilite

-LRB-

-RRB-

Indium

arsenide

-LRB-

InAs

-RRB-

Lead

selenide

-LRB-

PbSe

-RRB-

Lead

telluride

-LRB-

PbTe

-RRB-

Lime

-LRB-

CaO

-RRB-

Magnesite

-LRB-

-RRB-

Magnesium

dibromide

-LRB-

-RRB-

Magnesium

diiodide

-LRB-

-RRB-

Sodium

sulfate

-LRB-

-RRB-

Orthoboric

acid

-LRB-

B

-LRB-

OH

-RRB-

-RRB-

Lead

oxide

-LRB-

PbO

-RRB-

Lead

dioxide

-LRB-

-RRB-

-LRB-

Rutile

structure

-RRB-

Periclase

-LRB-

MgO

-RRB-

Rutile

-LRB-

-RRB-

Sellaite

-LRB-

-RRB-

Silicon

-LRB-

Si

-RRB-

Silicon

carbide

-LRB-

SiC

-RRB-

Smithsonite

-LRB-

-RRB-

Soda

Niter

-LRB-

-RRB-

Sphalerite

-LRB-

ZnS

-RRB-

Spinel

-LRB-

-RRB-

Sulfur

-LRB-

S

-RRB-

Willemite

-LRB-

-RRB-

Wurtzite

-LRB-

ZnS

-RRB-

Zincite

-LRB-

ZnO

-RRB-

Zinkosite

-LRB-

-RRB-

Zircon

-LRB-

-RRB-

aReference

values

taken

from

the

CRC

Handbook

-LSB-

-RSB-

Elements

Three

allotropes

of

carbon

were

modeled

diamond

consisting

of

pure

covalent

bonds

graphite

with

bonds

in-plane

and

π-stacking

or

VDW

forces

between

planes

and

glitter

a

hypothetical

structure

composed

of

cyclohexadiene

fragments

-LSB-

-RSB-

The

simple

C

C

bond

in

diamond

is

reproduced

with

good

accuracy

Å

versus

Å

observed

as

is

the

in-plane

bond

in

graphite

Å

versus

Å

This

last

result

was

unexpected

in

light

of

the

zero

band

gap

of

graphite

in

that

severe

difficulties

in

achieving

a

SCF

are

often

encountered

when

systems

with

very

small

band-gaps

are

modeled

graphite

appears

to

be

a

unique

exception

to

this

Graphite

layers

are

held

together

by

weak

VDW

forces

which

are

poorly

represented

in

all

NDDO

methods

One

consequence

of

this

is

that

the

predicted

interlayer

distance

Å

is

significantly

larger

than

the

observed

Å

Intermediate

between

graphite

and

diamond

is

the

hypothetical

glitter

a

tetragonal

allotrope

of

carbon

composed

of

single

and

double

bonds

A

calculation

predicted

that

the

structure

would

be

essentially

the

same

as

that

given

by

DFT

methods

-LSB-

-RSB-

The

standard

state

of

carbon

is

graphite

and

therefore

by

definition

the

value

of

its

ΔHf

is

kcal/mole-atom

predicts

the

ΔHf

of

graphite

to

be

kcal/mole-atom

in

good

agreement

with

the

reference

value

The

higher

energy

allotrope

diamond

has

a

reported

heat

of

formation

of

kcal/mole-atom

-LSB-

-RSB-

for

diamond

predicts

the

ΔHf

to

be

kcal/mole-atom

i.e.

kcal/mole-atom

above

graphite

Glitter

is

a

hypothetical

allotrope

but

is

predicted

by

to

be

unlikely

to

be

formed

under

equilibrium

conditions

both

and

DFT

predict

the

ΔHf

to

be

large

and

positive

kcal/mole-atom

and

kcal/mole-atom

-LSB-

-RSB-

respectively

Silicon

also

crystallizes

in

the

diamond

lattice

but

the

calculated

silicon

silicon

distance

Å

is

significantly

less

than

the

observed

value

of

Å

and

while

the

experimental

ΔHf

is

by

definition

zero

the

calculated

heat

of

formation

is

kcal/mole-atom

Sulfur

forms

eight-membered

rings

with

rings

per

unit

cell

Because

the

unit

cell

is

so

large

and

because

there

is

a

distinct

insulating

gap

between

each

ring

the

approximation

that

Γ

represents

the

entire

Brillouin

zone

is

valid

even

when

only

a

single

unit

cell

is

used

Within

each

ring

the

sulfur

sulfur

distance

is

Å

in

perfect

agreement

with

the

Å

observed

but

the

inter-ring

distance

is

badly

predicted

resulting

in

a

calculated

density

of

g/cc

considerably

less

than

the

observed

g/cc

This

lack

of

inter-ring

interaction

is

the

likely

cause

of

the

calculated

heat

of

formation

being

kcal/mole-atom

rather

than

being

nearer

to

the

reference

kcal/mole-atom

Halides

One

of

the

simplest

sets

of

inorganic

solids

are

the

alkali

metal

halides

Most

of

these

crystallize

with

the

rock-salt

lattice

the

exceptions

being

cesium

chloride

bromide

and

iodide

which

crystallize

in

the

body-centered

cubic

or

cesium

chloride

structure

Because

of

their

high

symmetry

there

is

only

one

geometric

variable

so

for

this

group

of

solids

symmetry

was

used

to

accelerate

the

geometry

optimization

Geometries

were

optimized

for

both

the

rock-salt

and

cesium

chloride

structures

for

each

salt

With

the

exception

of

rubidium

fluoride

the

calculated

heats

of

formation

-LRB-

Table

-RRB-

of

the

isolated

molecule

and

of

the

crystal

are

reproduced

with

good

accuracy

although

did

a

very

poor

job

of

predicting

which

of

the

two

crystal

forms

was

the

more

stable

Table

of

calculated

and

experimental

heats

of

formation

of

alkali

metal

halides

-LRB-

kcal/mol

-RRB-

-LSB-

-RSB-

-LRB-

NaCl

-RRB-

-LRB-

CsCl

-RRB-

Experimental

-LSB-

-RSB-

Lithium

fluoride

Lithium

chloride

Lithium

bromide

Lithium

iodide

Sodium

fluoride

Sodium

chloride

Sodium

bromide

Sodium

iodide

Potassium

fluoride

Potassium

chloride

Potassium

bromide

Potassium

iodide

Rubidium

fluoride

Rubidium

chloride

Rubidium

bromide

Rubidium

iodide

Cesium

fluoride

Cesium

chloride

Cesium

bromide

Cesium

iodide

Elements

of

Group

II

form

two

main

groups

of

halides

those

with

coordinate

metal

atoms

such

as

fluorite

and

frankdicksonite

and

the

six-coordinate

layer

structures

of

the

chlormagnesite

type

Other

structures

include

the

rutile

lattice

as

in

sellaite

and

the

distorted

rutile

lattice

hydrophilite

For

all

alkaline

earth

halides

investigated

the

calculated

structure

had

the

same

lattice

type

as

that

in

the

starting

geometry

A

more

complex

halide

is

carnallite

-LRB-

-RRB-

composed

of

isolated

potassium

and

chloride

ions

and

magnesium

ions

that

are

octahedrally

coordinated

by

water

molecules

For

the

X-ray

structure

predicted

the

charge

on

the

coordination

complex

ion

-LSB-

Mg

-LRB-

-RRB-

-RSB-

to

be

on

the

potassium

ion

and

on

the

chloride

Within

the

complex

ion

the

charge

on

magnesium

was

and

on

average

each

water

molecule

had

a

charge

of

The

complex

ion

thus

behaves

like

an

extremely

ionic

Group

II

element

the

net

charge

being

much

greater

than

that

on

any

Group

II

metal

ion

in

any

halide

Trisodium

hexachlorotitanate

crystallizes

in

a

cryolite-like

structure

-LSB-

-RSB-

Each

titanium

ion

has

one

unpaired

electron

and

although

the

Ti

Cl

bond

is

highly

covalent

the

smallest

distance

between

the

-LSB-

-RSB-

complex

ions

is

more

than

Å

therefore

from

an

electronic

perspective

the

unpaired

electrons

could

be

regarded

as

isolated

To

verify

the

validity

of

this

assumption

the

geometry

of

solid

was

optimized

using

the

UHF

Hamiltonian

A

cluster

of

formula

units

was

used

this

representing

unit

cells

In

one

calculation

the

magnetic

component

of

spin

Ms

was

set

to

zero

and

in

the

other

it

was

set

to

the

maximum

value

for

unpaired

electrons

i.e.

Ms

Both

optimized

geometries

were

essentially

the

same

geometric

differences

were

negligible

and

the

two

heats

of

formation

were

kcal/mol

and

kcal/mol

respectively

Therefore

the

assumption

that

the

unpaired

electrons

are

electronically

isolated

at

least

when

the

focus

of

interest

is

energetics

and

structure

is

justified

Oxides

predicts

the

Si

O

distance

in

silicon

dioxide

to

be

too

large

by

with

the

result

that

the

predicted

densities

of

the

polymorphs

of

silica

were

all

underestimated

This

is

best

seen

in

the

very

dense

stishovite

where

the

predicted

density

is

about

less

than

the

observed

Stishovite

has

a

rutile

structure

so

the

positions

of

the

atoms

in

the

unit

cell

can

be

defined

using

two

bond

lengths

and

one

angle

predicts

the

Si

O

Si

angle

correctly

compared

to

the

observed

but

overestimates

the

Si

O

bond-lengths

Å

and

Å

compared

to

the

Å

and

Å

observed

In

α-quartz

the

predicted

Si

O

distance

Å

is

also

larger

than

that

observed

Å

but

in

addition

the

Si

O

Si

angle

opens

from

the

observed

to

This

additional

decrease

in

density

results

in

the

predicted

density

of

α-quartz

being

too

low

by

The

error

in

the

Si

O

Si

angle

reaches

its

maximum

in

α-crystobalite

where

predicts

it

to

be

instead

of

the

observed

This

results

in

a

large

error

in

density

of

Linear

Si

O

Si

systems

are

not

unknown

in

nature

in

the

high

temperature

form

of

tridymite

hexagonal

β-tridymite

-LSB-

-RSB-

and

in

thortveitite

-LRB-

Sc

Y

-RRB-

-LSB-

-RSB-

these

atoms

form

a

straight

line

and

as

expected

this

angle

is

also

precisely

reproduced

by

addition

to

the

dense

phases

of

silica

there

are

open

lattice

structures

which

of

their

nature

necessarily

have

very

low

densities

Two

examples

are

mordenite

and

chabazite

Calculated

and

X-ray

structures

in

these

systems

are

shown

in

Figs.

and

Chabazite

has

the

lowest

density

of

any

silica

polymorph

reproduces

these

systems

but

as

with

the

higher

density

polymorphs

it

underestimates

the

density

but

in

this

case

by

about

Fig.

of

the

unit

cell

of

Mordenite

Left

X-ray

structure

right

optimized

mirror

image

structureFig

X-ray

structure

right

optimized

structure

Water

forms

several

polymorphs

In

Ice-I

or

Ice-Ih

the

common

polymorph

of

ice

oxygen

atoms

form

a

hexagonal

lattice

and

each

atom

has

two

hydrogen

atoms

strongly

covalently

bound

to

it

and

two

hydrogen

atoms

at

a

larger

distance

The

locations

of

the

hydrogen

atoms

can

be

specified

by

application

of

the

ice

rules

However

even

when

that

is

done

correctly

the

positions

of

the

hydrogen

atoms

are

not

unambiguously

defined

That

is

although

the

X-ray

structure

shows

that

the

oxygen

atoms

are

located

precisely

on

the

vertices

of

the

hexagonal

lattice

there

is

statistical

disorder

in

the

positions

of

the

hydrogen

atoms

between

each

pair

of

adjacent

oxygen

atoms

there

are

two

potential

positions

that

a

hydrogen

atom

can

occupy

and

in

the

observed

structure

each

position

has

a

occupancy

This

type

of

disorder

must

be

resolved

before

a

solid

state

calculation

can

be

carried

out

so

in

Ice-Ih

an

arbitrary

distribution

of

hydrogen

atoms

consistent

with

the

ice

rules

was

used.Geometry

optimization

of

the

Ice-Ih

structure

gave

a

recognizable

hexagonal

lattice

as

expected

but

as

a

result

of

the

asymmetric

distribution

of

hydrogen

atoms

each

oxygen

atom

was

slightly

displaced

relative

to

the

ideal

lattice.All

the

ices

except

Ice-IV

and

Ice-VII

were

modeled

successfully

The

simple

unit

cell

of

Ice-IV

contains

water

molecules

but

in

order

to

satisfy

the

ice

rules

and

have

the

hydrogen

atoms

disordered

a

large

cluster

would

be

needed

Assigning

hydrogen

atoms

in

such

a

cluster

in

order

to

achieve

both

randomness

and

compliance

with

the

ice

rules

would

be

a

non-trivial

task

However

Ice-VII

is

the

high-temperature

-LRB-

above

°C

-RRB-

modification

of

Ice-VIII

and

differs

from

Ice-VIII

only

in

that

the

positions

of

the

hydrogen

atoms

are

disordered

As

such

Ice-VII

is

trivially

different

from

Ice-VIII

With

the

exception

of

Ice-X

each

polymorph

optimized

to

the

correct

structure

That

is

the

structure

of

each

calculated

polymorph

was

qualitatively

similar

to

that

of

the

observed

polymorph

Ice-X

is

unique

in

that

the

oxygen

atoms

form

a

body-centered

cubic

lattice

with

hydrogen

atoms

equidistant

between

half

of

the

adjacent

pairs

of

oxygen

atoms

all

oxygen

atoms

are

symmetrically

tetrahedrally

coordinated

by

hydrogen

atoms

Unconstrained

optimization

of

this

structure

resulted

in

a

disordered

essentially

amorphous

solid

When

symmetry

constraints

were

imposed

the

geometry

of

Ice-X

optimized

to

give

an

O-H

distance

of

Å

Ice-X

is

stable

at

pressures

above

GPa

and

at

that

pressure

predicts

the

O

H

distance

to

be

Å

in

good

agreement

with

the

X-ray

value

-LSB-

-RSB-

of

Å

At

a

much

higher

pressure

about

GPa

predicts

that

the

antifluorite

structure

would

become

the

preferred

polymorph

in

this

structure

each

hydrogen

bonds

to

four

oxygen

atoms

and

each

oxygen

bonds

to

eight

hydrogen

atoms

An

attempt

-LSB-

-RSB-

by

Gale

to

use

the

MNDO

and

methods

to

predict

the

structure

of

corundum

met

with

only

limited

success

The

failure

to

reproduce

the

observed

structure

was

attributed

to

deficiencies

mainly

the

lack

of

d-orbitals

in

the

basic

semiempirical

methods

To

a

large

degree

these

deficiencies

have

been

corrected

in

as

can

be

seen

by

comparing

the

structures

predicted

by

the

various

methods

with

the

known

X-ray

structure

-LRB-

Table

-RRB-

Table

and

observed

structure

and

ΔHf

of

-LRB-

Å

-RRB-

c

-LRB-

Å

-RRB-

ΔHf

-LRB-

kcal/mol

-RRB-

aResults

for

MNDO

and

taken

from

Gale

-LSB-

-RSB-

Within

each

of

the

polymorphs

of

titanium

dioxide

all

the

titanium

atoms

are

in

the

same

approximately

octahedral

environment

surrounded

by

six

oxygen

atoms

This

is

illustrated

in

Fig.

for

rutile

the

commonest

polymorph

The

structures

of

all

three

polymorphs

were

qualitatively

reproduced

by

but

the

Ti

O

bond-length

was

over-estimated

by

as

shown

in

Table

for

rutile

resulting

in

the

predicted

density

being

too

low

by

about

Fig.

cell

of

rutile

-LRB-

-RRB-

Crossed-eyes

stereo

viewTable

distances

in

B

-LRB-

OH

-RRB-

Orthoboric

acid

B

-LRB-

OH

-RRB-

forms

a

layer

structure

in

which

individual

molecules

within

each

layer

are

held

together

by

hydrogen

bonds

and

the

layers

are

held

together

by

VDW

forces

and

very

weak

electrostatic

forces

Although

the

layer

structure

is

reproduced

with

good

accuracy

the

predicted

inter-layer

distance

Å

is

much

greater

than

the

observed

Å

The

lack

of

any

significant

inter-layer

interaction

can

be

attributed

to

the

absence

of

a

VDW

core

core

term

in

boron

It

is

likely

that

if

such

a

term

were

added

the

correct

interlayer

interaction

would

be

reproduced.During

the

survey

of

organic

solids

the

structure

of

the

very

complicated

organometallic

pentakis

-LRB-

tetraethylammonium

-RRB-

bis

-LRB-

meso-tetraphenyl-porphyrinato-zinc

-RRB-

tetraconta-oxo-silicon-dodeca-molybdenum

bromide

-LRB-

CSD

entry

PIJFUJ

-RRB-

was

accurately

reproduced

In

contrast

problems

had

been

encountered

with

various

other

complicated

solids

particularly

those

involving

protonated

species

To

determine

the

ability

of

to

model

complex

ionic

systems

a

solid

containing

an

archetypal

proton

ion

Zundel

's

cation

-LSB-

-RSB-

-LSB-

-RSB-

was

used

This

ion

had

been

identified

-LSB-

-RSB-

in

Keggin

's

-LSB-

-RSB-

pentahydrate

dodecatungstophosphoric

acid

hexahydrate

X-ray

analysis

indicated

that

the

-LSB-

-RSB-

ion

has

symmetry

and

that

the

O

O

separation

is

Å

However

a

calculation

on

the

isolated

ion

predicted

its

structure

to

be

with

an

O

O

separation

of

Å

This

was

not

unexpected

ab-initio

calculations

-LSB-

-RSB-

indicate

that

the

ion

should

have

symmetry

with

the

Cs

structure

being

only

about

kcal/mol

higher

in

energy

and

that

the

structure

should

be

significantly

higher

in

energy

When

symmetry

was

used

predicted

that

the

separation

would

decrease

to

Å

and

the

energy

would

increase

by

kcal/mol

Disorder

had

been

reported

in

Keggin

's

pentahydrate

with

Zundel

's

ion

assuming

two

different

orientations

each

having

a

occupancy

After

resolving

the

disorder

an

unconstrained

geometry

optimization

was

performed

Examination

of

the

optimized

structure

revealed

that

the

Zundel

ion

had

been

destroyed

and

that

the

proton

had

migrated

to

the

polyoxometalate

This

phenomenon

the

neutralization

of

a

polyanion

had

also

been

observed

in

tetrakis

-LRB-

-RRB-

octacyano-molybdenum

-LRB-

iv

-RRB-

-LSB-

-RSB-

-LSB-

MoIV

-LRB-

CN

-RRB-

-RSB-

CSD

entry

PYCMOA

where

predicted

that

protons

on

the

pyridinium

ions

would

migrate

to

the

metal

complex

Other

AB-type

solids

A

number

of

solids

of

the

type

AB

are

formed

from

elements

of

Group

III

and

V

while

others

involve

elements

of

Group

IV

and

still

more

involve

elements

of

Group

VI

and

heavy

elements

Some

of

these

occur

naturally

such

as

wurtzite

and

sphalerite

-LRB-

zinc

sulfide

-RRB-

and

coloradoite

-LRB-

mercury

telluride

-RRB-

while

others

are

formed

synthetically

often

by

chemical

vapor

deposition

methods

In

most

of

these

materials

each

atom

of

type

A

is

tetrahedrally

coordinated

to

four

atoms

of

type

B

This

results

in

two

types

of

packing

best

exemplified

by

the

two

polymorphs

of

zinc

sulfide

For

convenience

all

compounds

of

this

type

will

be

grouped

together

Many

of

these

compounds

are

semiconductors

and

have

small

band-gaps

between

the

occupied

and

virtual

orbitals

A

consequence

of

this

is

that

the

cluster

used

must

be

very

large

in

order

to

minimize

errors

arising

from

the

cluster

approximation

In

addition

it

was

anticipated

that

the

narrow

band-gap

would

give

rise

to

difficulties

in

solving

the

self-consistent

field

equations

such

difficulties

had

frequently

occurred

when

molecules

that

had

small

HOMO

LUMO

gaps

were

being

studied

Surprisingly

the

SCF

equations

were

solved

using

default

options

albeit

more

iterations

than

normal

were

needed

Symmetry

was

used

to

accelerate

the

geometry

optimization

of

those

solids

that

had

the

sphalerite

structure

such

solids

have

only

one

adjustable

parameter

In

most

cases

the

calculated

density

for

the

optimized

structure

was

close

to

that

expected

the

exceptions

being

cadmium

telluride

which

predicts

to

be

too

dense

and

coloradoite

where

the

density

was

predicted

to

be

too

low

Carbonates

nitrates

and

borates

Of

the

simple

carbonate

minerals

that

crystallize

in

the

calcite

lattice

-LRB-

Fig.

-RRB-

correctly

reproduces

the

structures

of

magnesite

smithsonite

otavite

and

calcite

itself

-LRB-

Table

-RRB-

was

unable

to

reproduce

the

structures

of

two

other

carbonates

rhodochrosite

and

siderite

The

UHF

method

was

used

in

modeling

both

of

these

minerals

because

they

contain

transition

metal

ions

that

have

unpaired

electrons

In

the

case

of

rhodochrosite

each

metal

ion

has

five

d-electrons

in

an

approximately

octahedral

environment

Because

the

crystal

field

of

the

carbonate

ions

is

too

weak

to

cause

a

large

separation

of

the

and

eg

levels

MnII

would

be

in

the

high-spin

configuration

This

implies

that

the

local

electronic

structure

would

be

approximately

and

that

there

would

be

no

angular

terms

arising

from

the

d-electrons

That

is

a

MnII

ion

would

be

expected

to

behave

like

a

Group

II

ion

The

failure

of

to

reproduce

the

calcite

structure

for

rhodochrosite

indicates

a

fault

in

the

parameterization

of

manganese

most

likely

attributable

to

errors

in

the

core-core

terms

Fig.

cell

of

calcite

Crossed-eyes

stereo

viewTable

distances

in

The

other

common

polymorph

of

calcite

is

aragonite

Other

minerals

that

have

the

aragonite

structure

are

cerussite

strontianite

and

witherite

Of

these

predicts

correctly

the

structures

of

aragonite

strontianite

and

witherite

albeit

some

carbonate

groups

were

rotated

slightly

about

their

axis

In

cerussite

the

carbonate

groups

were

tilted

out

of

plane

giving

rise

to

a

herringbone-like

structure

The

densities

of

all

Group

I

carbonates

are

predicted

by

to

be

too

low

This

includes

the

simple

carbonates

natrite

and

zabuyelite

potassium

hydrogen

carbonate

kalicinite

and

sodium

carbonate

monohydrate

thermonatrite

Nitrates

correctly

reproduces

the

structures

of

ammonium

nitrate

and

potassium

nitrate

-LRB-

niter

-RRB-

but

the

predicted

structure

of

sodium

nitrate

nitratine

is

completely

incorrect

as

with

other

sodium

compounds

the

predicted

distances

are

unrealistically

small

Borates

Several

borates

were

examined

including

the

simple

sodium

salt

borax

Like

other

solids

that

contain

a

large

amount

of

sodium

its

optimized

structure

was

severely

in

error

With

that

single

exception

the

structures

of

the

borates

were

reproduced

with

good

accuracy

Almost

all

minerals

have

some

symmetry

in

their

unit

cell

the

most

well

known

exception

being

the

naturally-occurring

calcium

chloroborate

parahilgardite

-LRB-

-RRB-

Cl

-LRB-

-RRB-

was

able

to

reproduce

the

unit

cell

of

this

almost

unique

mineral

with

good

accuracy

despite

the

fact

that

the

unit

cell

was

completely

devoid

of

any

symmetry

-LRB-

Fig.

-RRB-

This

system

was

unique

among

the

solids

studied

in

that

unlike

all

the

organic

compounds

there

were

no

readily

identifiable

discrete

molecular

fragments

and

unlike

the

other

inorganic

solids

it

is

devoid

of

any

elements

of

symmetry

Fig.

cell

of

parahilgardite

Crossed-eyes

stereo

view

Molybdates

tungstates

chromates

vanadates

sulfates

and

phosphates

This

group

of

solids

is

characterized

by

the

presence

of

tetrahedral

oxyanions

e.g.

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

-LSB-

-RSB-

and

-LSB-

-RSB-

with

counterions

ranging

from

the

highly

ionic

Group

I

and

Group

I-like

ions

e.g.

-LSB-

-RSB-

to

softer

cations

such

as

and

With

the

exception

of

descloizite

PbZn

-LRB-

-RRB-

-LRB-

OH

-RRB-

the

internal

structures

of

all

systems

modeled

were

quantitatively

reproduced

In

descloizite

the

distance

between

lead

and

zinc

ions

was

predicted

to

be

unrealistically

small

which

in

turn

resulted

in

severe

distortions

to

the

positions

of

the

other

entities

in

the

unit

cell

There

are

diatomic

core

core

repulsion

parameters

in

for

Pb

and

Zn

but

clearly

the

magnitude

of

the

term

was

too

small

As

with

other

errors

of

this

type

this

fault

could

readily

be

corrected

by

re-parameterizing

the

core

core

terms

only

Charges

on

the

ions

are

significantly

reduced

from

the

formal

values

Thus

in

fluorapatite

-LRB-

Fig.

Table

-RRB-

calcium

ions

have

charges

of

and

depending

on

environment

fluoride

is

and

each

phosphate

group

has

a

net

charge

of

all

indicating

a

high

degree

of

covalence

in

the

bonds

Fig.

cell

of

fluorapatite

Crossed-eyes

stereo

viewTable

distances

in

fluorapatite

Ca

on

a

vertex

Ca

on

an

edge

Ca

attached

to

Strong

hydrogen

bonding

can

occur

in

some

sulfates

and

phosphates

which

can

be

illustrated

by

salts

in

which

the

acid

is

partially

neutralized

such

as

compounds

of

the

type

and

where

M

is

a

Group

I

element

A

common

structure

in

systems

of

this

type

consists

of

a

hydrogen

atom

positioned

between

two

oxygen

atoms

on

two

different

acid

groups

The

positions

of

the

protons

as

determined

by

X-ray

analysis

are

of

limited

reliability

so

for

the

purposes

of

comparison

the

oxygen

oxygen

distances

were

used

In

mercallite

potassium

hydrogen

sulfate

-LRB-

Fig.

-RRB-

predicts

the

oxygen

oxygen

distance

-LRB-

Table

-RRB-

in

perfect

agreement

with

the

X-ray

structure

also

predicts

the

hydrogen

atoms

to

be

asymmetrically

positioned

between

the

two

oxygen

atoms

this

also

being

in

accord

with

the

published

X-ray

structure

Potassium

dihydrogen

phosphate

is

more

complicated

in

that

each

phosphate

forms

four

hydrogen

bonds

to

four

different

phosphate

groups

-LRB-

Fig.

-RRB-

Again

predicts

-LRB-

Table

-RRB-

the

oxygen

oxygen

distance

with

good

accuracy

and

predicts

the

hydrogen

atoms

to

be

asymmetrically

positioned

however

in

both

the

hydrogen

sulfate

and

hydrogen

phosphate

underestimates

the

degree

of

asymmetry

Fig.

of

hydrogen

sulfate

in

Top

X-ray

structure

bottom

structureFig

of

structure

of

dihydrogen

phosphate

in

-LRB-

upper

pair

-RRB-

and

in

-LRB-

-RRB-

Left

X-ray

structures

on

left

right

structureTable

distances

in

mercallite

-LRB-

-RRB-

-LRB-

H

-RRB-

O

S

Table

distances

in

hydrogen

phosphate

in

-LRB-

H

-RRB-

O

O

P

The

potassium

ion

is

relatively

small

in

comparison

to

a

phosphate

ion

so

in

the

phosphate

ions

can

form

a

three-dimensional

lattice

If

a

larger

cation

e.g.

tetramethylammonium

is

used

the

three-dimensional

phosphate

lattice

becomes

energetically

unfavorable

relative

to

a

one-dimensional

chain

of

phosphates

This

structure

was

also

reproduced

accurately

reproduces

the

structures

of

most

of

the

phosphates

but

as

expected

in

the

case

of

sodium

phosphate

the

predicted

structure

was

qualitatively

incorrect

Silicates

Silicates

form

the

largest

and

most

complicated

group

of

minerals

and

exhibit

a

very

wide

range

of

properties

From

a

chemical

perspective

however

they

are

relatively

simple

most

silicates

involve

tetrahedra

in

various

degrees

of

polymerization

and

in

turn

these

tetrahedra

interact

with

fully

oxidized

metal

ions

In

addition

for

any

given

empirical

formula

naturally

occurring

minerals

represent

the

most

stable

or

almost

the

most

stable

structure

Some

structures

might

be

quite

complicated

nevertheless

because

they

formed

under

equilibrium

conditions

they

are

near

or

at

the

energy

minimum

and

for

any

given

empirical

formula

an

accurate

computational

model

should

not

be

able

to

generate

a

polymorph

that

is

significantly

more

stable

than

any

that

occurs

naturally

This

is

in

contrast

to

organic

chemistry

where

high

energy

forms

of

the

same

empirical

formula

occur

frequently

for

example

dimethyl

ether

is

the

high

energy

isomer

of

with

ethanol

being

the

low

energy

form

For

the

purposes

of

this

study

the

silicates

can

be

divided

into

families

based

on

the

degree

of

aggregation

of

the

silicate

units

Isolated

tetrahedra

nesosilicates

The

simplest

of

the

silicates

are

the

nesosilicates

which

contain

isolated

groups

With

the

exception

of

the

three

polymorphs

of

kyanite

andalusite

and

sillimanite

the

structures

of

the

nesosilicates

are

reproduced

with

good

accuracy

In

the

aluminum

silicates

there

are

two

distinct

anions

an

-LSB-

-RSB-

ion

and

an

isolated

oxygen

ion

-LSB-

O

-RSB-

incorrectly

predicts

these

ions

to

coalesce

to

form

a

moiety

Double

and

triple

tetrahedra

sorosilicates

All

the

sorosilicates

examined

were

reproduced

with

good

accuracy

In

most

of

the

minerals

that

contained

the

-LSB-

-RSB-

moiety

the

Si-O-Si

system

is

bent

As

expected

reproduced

the

bent

structure

The

only

exception

was

thortveitite

an

important

source

of

scandium

which

exists

in

nature

as

-LRB-

Sc

Y

-RRB-

but

which

for

the

purposes

of

this

work

was

simplified

to

In

the

crystal

structure

of

this

mineral

-LSB-

-RSB-

the

-LSB-

-RSB-

moiety

has

symmetry

consequently

the

Si

O

Si

angle

is

precisely

When

the

structure

of

thortveitite

was

optimized

using

the

symmetry

did

not

change

the

predicted

Si

O

Si

angle

was

also

Chains

inosilicates

With

the

exception

of

spodumene

where

predicted

the

aluminum-silicon

distances

to

be

too

short

the

structures

of

all

the

chain

silicates

were

reproduced

with

good

accuracy

As

with

the

aluminum

silicates

the

fault

in

spodumene

can

be

attributed

to

errors

in

the

Al

Si

core

core

parameters

In

the

case

of

cummingtonite

-LRB-

-RRB-

hydrogen

atoms

were

added

before

the

structure

was

optimized

Cyclosilicates

Three

cyclosilicates

were

examined

benitoite

beryl

and

dravite

-LRB-

-RRB-

-LRB-

-RRB-

All

were

reproduced

with

good

accuracy

as

illustrated

by

the

bond

lengths

and

angles

-LRB-

Table

-RRB-

in

the

simplest

of

these

beryl

-LRB-

Fig.

-RRB-

Dravite

has

a

particularly

complicated

structure

involving

seven

different

elements

in

which

the

positions

of

the

cations

and

and

the

anions

-LSB-

O

-RSB-

-LSB-

-RSB-

and

-LSB-

-RSB-

are

determined

by

roughly

equal

contributions

of

covalent

and

ionic

terms

Fig.

cell

of

beryl

Crossed-eyes

stereo

viewTable

distances

and

angles

in

berylGeometric

Si-O

-LRB-

Al

-RRB-

-LRB-

Si

-RRB-

Sheets

phyllosilicates

The

structures

of

the

phyllosilicates

are

reproduced

with

modest

accuracy

In

talc

-LRB-

Fig.

-RRB-

for

example

in-plane

distances

are

reproduced

well

but

the

inter-plane

separation

-LRB-

Table

-RRB-

is

only

poorly

modeled

This

fault

can

be

attributed

to

the

absence

of

strong

inter-plane

interactions

any

errors

in

the

weak

long-range

interatomic

terms

would

give

rise

to

disproportionately

large

errors

in

inter-plane

separations

Fig.

cell

of

talc

Crossed-eyes

stereo

viewTable

distances

in

-LRB-

H

-RRB-

-LRB-

Si

-RRB-

-LRB-

Mg

-RRB-

-LRB-

Si

-RRB-

O

aDistance

between

layersThe

mineral

chlorite

has

a

variable

stoichiometry

-LRB-

Fe

Mg

Al

-RRB-

-LRB-

Si

Al

-RRB-

-LRB-

OH

-RRB-

which

does

not

allow

a

simple

resolution

into

a

fixed

stoichiometry

In

it

the

presence

of

main-group

metals

of

different

oxidation

states

-LRB-

MgII

and

AlIII

-RRB-

in

the

cationic

part

of

the

formula

requires

that

in

order

to

maintain

electrical

neutrality

for

any

given

ratio

of

magnesium

to

aluminum

there

should

be

a

corresponding

composition

in

the

anionic

part

In

nature

this

condition

would

be

satisfied

by

the

random

distribution

of

magnesium

aluminum

and

silicon

atoms

in

the

lattice

Computationally

however

such

a

distribution

is

currently

not

possible

and

fixed

stoichiometries

are

required

In

the

extremes

these

would

be

-LRB-

OH

-RRB-

and

-LRB-

OH

-RRB-

However

the

lattice

structures

of

these

two

extremes

would

likely

be

so

different

to

that

of

chlorite

that

comparison

between

any

computed

result

for

one

of

these

extremes

and

that

of

chlorite

would

be

meaningless

In

order

to

obtain

a

meaningful

result

an

unusually

large

cluster

was

used

in

which

the

ratios

of

the

elements

was

as

near

to

that

of

chlorite

as

possible

Frameworks

tectosilicates

With

the

exception

of

thomsonite

predicted

the

internal

structures

of

the

tectosilicates

accurately

As

with

the

other

aluminosilicates

in

thomsonite

the

predicted

aluminum-silicon

distance

was

unrealistically

short

Discussion

With

a

few

exceptions

the

geometries

of

individual

organic

molecules

and

ions

and

their

packing

arrangement

in

the

crystal

lattice

were

reproduced

with

good

accuracy

In

the

original

article

it

was

shown

that

the

average

error

in

predicted

bond-lengths

in

organic

compounds

was

about

The

effect

of

intermolecular

forces

on

the

geometries

of

the

component

molecules

is

likely

to

be

small

so

by

implication

the

accuracy

of

prediction

of

the

geometries

of

those

molecules

would

be

similar

to

that

reported

in

the

earlier

article

By

far

the

largest

structural

error

in

organic

solids

involves

intermolecular

separations

The

values

of

these

are

determined

by

several

forces

from

the

weak

VDW

and

π-stacking

attractions

in

cyclohexane

and

coronene

through

simple

hydrogen

bonding

of

the

type

found

in

sucrose

to

very

strong

intermolecular

interactions

usually

ionic

best

typified

by

the

Zwitterions

such

as

the

simple

amino

acids

Errors

in

intermolecular

separations

could

be

determined

by

a

direct

comparison

of

calculated

and

reference

structures

However

because

errors

in

intermolecular

separation

have

a

direct

impact

on

the

unit

cell

dimensions

and

consequently

on

the

density

a

convenient

and

reliable

estimate

of

the

accuracy

of

prediction

of

intermolecular

separations

of

molecules

in

the

unit

cell

can

be

obtained

from

a

comparison

of

predicted

and

X-ray

densities

The

internal

structures

of

three

organic

solids

were

incorrectly

predicted

using

for

all

other

solids

the

internal

packing

was

qualitatively

correct

Two

of

the

faulty

solids

involved

the

oxalate

and

water

moieties

From

analysis

of

other

systems

known

to

contain

neutral

species

but

which

predicts

to

be

ionic

it

appears

that

unrealistically

favors

the

formation

of

the

hydronium

ion

The

fault

in

sodium

acetate

trihydrate

appears

to

arise

from

faults

in

sodium

core

core

parameters

in

that

similar

faults

were

found

in

several

other

inorganic

sodium-containing

compounds

Interestingly

the

fault

was

not

present

in

the

closely

related

species

sodium

hydrogen

acetate

a

system

chosen

because

of

the

presence

of

the

hydrogen-bonded

structure

-LSB-

-RSB-

When

the

three

solids

that

were

badly

predicted

were

removed

from

consideration

the

average

error

in

density

decreased

to

with

most

of

this

attributable

to

the

average

error

in

intermolecular

separations

This

error

was

not

evenly

distributed

within

the

organic

solids

in

that

when

interaction

energies

were

large

as

in

the

ionic

solids

in

particular

Zwitterions

reproduced

the

intermolecular

separations

with

good

accuracy

but

when

the

interaction

energies

were

small

as

in

species

where

only

VDW

forces

are

involved

such

as

methionine

errors

in

intermolecular

separations

were

often

quite

large

The

structures

of

most

of

the

inorganic

solids

were

predicted

with

useful

accuracy

with

the

highest

accuracy

being

exhibited

by

minerals

in

which

metal

atoms

interact

with

oxygen

and

the

oxygen

then

interacts

with

a

main-group

element

Most

of

the

silicates

phosphates

and

sulfates

fall

into

this

group

One

reason

for

this

can

be

attributed

to

the

procedure

used

in

developing

in

that

a

large

quantity

of

reference

data

for

systems

that

had

metal-oxygen

or

main-group

oxygen

bonds

was

used

during

the

parameterization

This

naturally

resulted

in

increased

emphasis

being

placed

on

the

structure

and

thermochemistry

of

oxygen-containing

systems

On

the

other

hand

inorganic

systems

exhibit

a

much

wider

range

of

types

of

interaction

than

those

found

in

organic

chemistry

and

this

makes

the

general

application

of

to

inorganic

solids

more

difficult

An

implication

of

the

fact

that

uses

the

Voityuk

diatomic

core-core

term

is

that

parameters

must

be

present

for

each

pair

of

elements

in

a

system

unless

the

pair

of

elements

is

separated

by

a

distance

sufficiently

large

that

there

would

be

no

significant

core-core

interaction

Only

a

limited

number

of

types

of

interactions

were

surveyed

in

this

work

even

within

that

number

several

instances

were

found

in

which

the

values

of

the

Voityuk

parameters

were

severely

in

error

and

gave

rise

to

results

that

were

nonsense

Because

of

this

great

care

should

be

exercised

in

determining

the

suitability

of

for

modeling

solids

that

include

diatomic

interactions

of

types

not

found

in

any

of

the

species

reported

here

In

general

reproduced

the

X-ray

densities

of

both

organic

and

inorganic

crystals

with

useful

accuracy

Fig.

the

value

being

and

the

least

squares

fit

was

The

average

unsigned

error

in

the

predicted

densities

of

inorganic

solids

is

higher

than

that

of

organic

solids

although

the

average

signed

error

was

compared

to

the

equivalent

for

organic

solids

Fig.

of

calculated

and

X-ray

densities

Systems

that

are

badly

predicted

Of

the

systems

whose

properties

were

badly

predicted

three

types

could

be

identified

In

the

first

group

illustrated

by

lead

selenide

and

-LRB-

TBA

-RRB-

the

origin

of

the

error

could

be

traced

to

the

values

of

individual

diatomic

parameters

used

in

These

were

either

incorrect

as

in

lead

selenide

where

the

value

for

Voityuk

's

lead

selenium

core

core

repulsion

was

much

too

small

and

in

TBA

where

the

bromine

nitrogen

parameters

were

either

physically

unrealistic

or

absent

Errors

of

this

type

could

be

easily

corrected

by

carrying

out

a

small

parameterization

operation

involving

only

the

faulty

parameters

and

using

a

training

set

consisting

of

examples

of

the

two

atoms

in

close

proximity

The

second

type

of

error

was

found

in

some

solids

for

which

no

equivalent

error

was

found

in

the

isolated

molecule

This

is

best

illustrated

by

the

Group

I

halides

where

predicted

the

lowest

energy

structure

to

be

either

rock

salt

or

cesium

chloride

almost

at

random

During

the

development

of

only

small

representatives

of

I-VII

species

were

used

Apparently

these

systems

were

too

small

to

allow

the

lattice

properties

to

be

accurately

characterized

Errors

of

this

type

were

therefore

not

immediately

obvious

and

only

became

apparent

when

full

solid-state

calculations

were

done

The

implication

is

that

future

parameterizations

should

include

solids

in

the

training

set

The

best

solids

for

use

in

parameterization

would

be

those

that

were

badly

predicted

by

Addition

of

solids

to

the

parameterization

would

be

unlikely

to

cause

a

significant

increase

in

error

in

the

prediction

of

molecular

properties

Although

the

use

of

solids

in

parameterization

is

impractical

at

present

it

is

likely

that

increases

in

computer

power

will

make

such

calculations

possible

in

the

not-too-distant

future

The

third

type

of

error

is

specific

to

organic

compounds

where

predicts

some

ions

to

be

too

stable

Thus

the

aminophenols

are

predicted

to

exist

in

the

solid

state

as

the

Zwitterions

rather

than

as

the

neutral

species

The

hydrate

of

oxalic

acid

was

predicted

to

exist

as

oxalate

and

hydronium

ions

a

prediction

completely

in

variance

with

the

X-ray

structure

No

instances

were

found

where

underestimated

the

stability

of

ions

relative

to

their

neutral

counterparts

That

is

the

error

was

completely

systematic

and

unequivocally

indicated

a

fault

in

the

parameterization

The

origin

of

this

error

most

likely

lies

in

the

set

of

atomic

electronic

parameters

rather

than

in

the

diatomic

core

core

parameters

and

as

such

could

only

be

corrected

by

a

re-parameterization

There

was

no

evidence

that

any

faults

were

due

to

an

underlying

defect

in

the

set

of

approximations

Accuracy

of

geometry

vs

hardness

In

general

the

structures

of

solids

that

are

mechanically

extremely

hard

seven

or

more

on

Moh

's

scale

are

predicted

with

good

accuracy

whereas

the

geometries

of

many

softer

solids

such

as

most

organic

species

the

transition

metal

carbonates

and

various

layer

silicates

particularly

the

micas

are

predicted

with

significantly

less

accuracy

This

inverse

relationship

of

mechanical

hardness

and

computational

accuracy

can

be

rationalized

by

consideration

of

the

interatomic

forces

involved

In

hard

solids

all

atoms

are

connected

to

adjacent

atoms

by

strong

covalent

bonds

and

of

their

nature

those

bonds

have

large

force

constants

In

general

semiempirical

methods

predict

such

geometries

with

good

accuracy

Any

tendency

to

deviation

from

the

expected

geometry

would

result

in

a

large

energy

penalty

therefore

distortions

in

predicted

geometries

are

likely

to

be

small

Conversely

in

mechanically

weak

solids

some

atoms

interact

only

weakly

with

adjacent

atoms

Thus

the

layers

in

the

micas

and

in

boric

acid

are

held

together

by

low

energy

electrostatic

and

VDW

forces

Much

effort

was

expended

during

the

development

of

in

attempting

to

accurately

model

hydrogen

bonds

and

other

weak

interactions

because

of

their

importance

in

biochemical

systems

This

work

has

apparently

been

of

limited

success

and

as

a

result

in

solids

that

are

mechanically

weak

very

small

changes

in

energy

are

often

associated

with

large

geometric

distortions

The

nature

of

this

inverse

relationship

can

be

used

in

future

method

development

where

currently

the

use

of

solids

in

parameterization

is

precluded

because

of

the

heavy

computational

effort

required

At

the

present

time

however

solids

can

be

used

in

surveys

There

the

hardness-accuracy

relationship

can

be

used

in

the

choice

of

solids

to

be

used

in

that

potential

errors

in

any

new

method

are

more

likely

to

be

detected

in

a

survey

of

mechanically

weak

rather

than

very

hard

solids

Crystal

packing

automatically

considered

In

order

to

accurately

reproduce

molecular

structures

determined

from

X-ray

analysis

theoretical

methods

must

not

only

be

able

to

accurately

reproduce

gas-phase

geometries

but

must

also

be

able

to

include

crystal

packing

forces

When

these

forces

are

small

the

gas-phase

structure

is

a

good

approximation

to

that

of

the

solid

but

the

converse

is

also

true

in

that

in

systems

where

there

are

large

intermolecular

interactions

particularly

strong

ionic

forces

a

solid

state

calculation

is

essential

in

order

to

accurately

reproduce

such

structures

This

was

most

evident

in

the

case

of

HMPN-H

-LRB-

-RRB-

where

the

gas-phase

geometry

is

a

significantly

worse

match

to

the

observed

crystal

structure

than

that

generated

by

the

solid

state

calculation

despite

the

intrinsically

higher

accuracy

of

In

this

system

it

is

obvious

that

the

packing

forces

arising

from

the

electrostatic

interaction

of

the

-LSB-

-RSB-

ion

with

the

HMPN-H

-LRB-

-RRB-

have

significant

geometric

consequences

Conclusions

The

newly

developed

method

has

been

demonstrated

to

reproduce

the

geometries

and

heats

of

formation

of

many

solids

both

organic

and

inorganic

with

useful

accuracy

although

in

a

few

cases

the

geometries

predicted

by

were

severely

in

error

Most

of

these

errors

can

be

attributed

to

incorrect

values

of

the

Voityuk

core

core

parameters

Three

examples

of

this

type

of

error

were

identified

the

Pb

Sb

Br

N

and

Pb

Zn

interactions

all

had

serious

errors

Where

diatomic

parameters

were

either

missing

or

improperly

optimized

as

a

result

of

a

fault

in

the

training

set

used

a

simple

correction

to

the

method

can

be

made

This

would

involve

only

a

re-optimization

of

the

faulty

diatomic

parameters

and

would

not

alter

the

performance

of

when

applied

to

other

systems

One

general

error

was

found

in

the

treatment

of

organic

compounds

many

compounds

that

exist

in

the

solid

state

as

neutral

species

were

incorrectly

predicted

by

to

be

ionized

Examples

include

the

aminophenols

and

compounds

involving

oxalic

acid

and

water

such

as

oxalic

acid

dihydrate

and

barium

oxalate

oxalic

acid

dihydrate

In

contrast

to

the

errors

in

the

values

of

the

Voityuk

parameters

errors

of

this

type

involve

electronic

properties

and

can

only

be

corrected

by

a

complete

re-parameterization

The

error

was

not

detected

during

the

development

of

because

solids

were

not

used

Many

solids

particularly

those

that

are

mechanically

weak

can

be

used

as

sensitive

detectors

of

potential

faults

in

new

methods

and

as

such

they

should

be

used

for

quality

control

in

future

method

development

work

Electronic

supplementary

material

Below

is

the

link

to

the

electronic

supplementary

material

ESM

Archive

files

of

all

systems

both

organic

and

inorganic

described

in

this

article

are

provided

as

separate

files

in

a

ZIP

collection

Each

file

contains

a

complete

Z-matrix

of

the

geometry

optimized

using

together

with

all

keywords

used

in

the

calculation

The

archive

files

are

suitable

for

running

using

-LRB-

PDF

MB

-RRB-

pm6
solid state
periodic boundary conditions
minerals
unit cell
hydrogen bonding