empirical programs became available and ab

initio calculations of molecular and intermolecular properties could be carried out with quantitative accuracy.

Three advances catalyzed this progress:

the development of computational

methods by John Pople and many others

in the 1950’s,

the development of density functional

theory by Walter Kohn and others, and

the increasing availability and speed of

computers.

These methods were employed here to elucidate the molecular structures of the methane

derived halocarbons in fine detail. Schrödinger’s

equation was solved for each of the 15 molecules by approximating the atomic orbitals with

the 6-31G* basis set of Gaussian functions. The

results are shown in terms of two surfaces of

constant electron density (c). The electron density gives the number of electrons per unit volume

at each point in space. Summed over all space

this gives the total number of electrons in a molecule.

The outer mesh of each molecule represents

the isosurface of 0.002 e

-/ bohr3 electron density which comprises about 98% of a molecule.

John Pople Walter Kohn

Nobel Prize in Chemistry 1998

©

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©

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orbis. U

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with

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Electrostatic Potential

+ —

isosurface of electron density

0.08 e

-

/bohr

3

representing the

hard core of the molecule

isosurface of

electron density

0.002 e

-

/bohr

3

representing

98% of the

molecule

Electron density

distribution

Halocarbons I: Methane Derivatives

CH4

CH3Cl

CH2Cl2

CHCl3

CCl4

CF4

CH3F

CH2ClF

CH2F2

CHCl2F CHClF2

CHF3

CCl3F CCl2F2

CClF3

R32

R20

R14

R11 R12 R13

R10

R41

R50

R21 R22 R23

R30 R31

R40

(c)

Our Evolving View of Molecular Structure

CCl2F2

(a) (b)

Long Atmospheric Lifetime

Flammable and Toxic

Flammable

Toxic

Dipole moment:

μ = 1.68 debye (ab initio 6-31G* basis set)

μ = 0.55 debye (experimental value)

NIST Special Publication 954

Issued November 2000

For Sale by the Superintendant of Documents

U.S. Government Printing Office

Washington, DC 20402-9325

The molecular structure (size and shape) of a

compound determines its macroscopic physical

and chemical properties. Simple representations

of molecules as balls and sticks (a) reflect only

their shape in terms of bond lengths and angles

but not their size.

Space-filling representations (b) show the

individual atoms as spheres with their respective diameters. This structural picture is more

realistic than ball and stick models (a) because it

reflects also the size and shape of a molecule.

However, the atomic spheres are assumed to be

rigid (”hard”) instead of soft.

Bond lengths, angles, and atomic radii used to

be measured experimentally. In theory, they can

be determined with great accuracy by solving

Schrödinger’s equation. This quantum mechanical equation accounts for the motions of nuclei

and electrons in atoms or molecules. However,

for anything more complicated than the hydrogen atom, there are no exact solutions to this

equation.

Quantum mechanical chemistry dates back to

the late 1920’s when the hydrogen bond was

interpreted by Heitler and London using valence

bond theory. Hückel’s molecular orbi tal

approach followed a few years later. But the real

breakthrough came in the 1960’s when semiElectron density increases toward the nuclei of a

molecule. To illustrate this, a second isosurface

of electron density 0.08 e

-/bohr3 is rendered

solid for each molecule. As seen in Figure (c), the

distance between the inner and the outer electron density isosurface differs for different

atoms. It is larger for the chlorine atoms and

smaller for the fluorine atoms. Fluorine binds its

electrons more tightly so that it has a “harder”

electron cloud than chlorine. Therefore, collisions with fluorine atoms are more repulsive

than with the softer chlorine atoms. These differences on the atomistic level cause profound

variations in the bulk properties of matter.

Another important result of ab initio calculations is the charge distribution in a molecule.

The electrostatic potential describes the interaction energy of a positive probe at each point

around a molecule. This is color-mapped on the

electron densi ty isosurfaces. Blue marks

electron-poor regions while red indicates

electron-rich regions. Fluorine atoms are centers

of negative charge. Non-uniform charge distribution creates dipolar, quadrupolar, or higherorder polar species whose interactions are orientation dependent. It induces long range attractions which result in molecular associations via

hydrogen bonds. Such electrostatic effects contribute significantly to the macroscopic properties of matter.

Arno.Laesecke@Boulder.NIST.Gov

National Institute of Standards and Technology

Physical and Chemical Properties Division

Experimental Properties of Fluids Group

325 Broadway, MC 838.07

Boulder, CO 80305, U.S.A.