Menton
2018.6.19
9:45-10:15

Global Reaction Route Mapping andExploration of Novel Chemistryon Potential Energy Surfaces

Koichi Ohno1,2
Tohoku University1
Institute for Quantum Chemical Exploration2

Global Mapping of the WorldWe are here!

←Ptolemaios’s map

Discovery ofNew Routes
1492 Christpher
Columbus
1498 Vasco daGama
1497 Sebastien
Gabbot1499 Amerigo
Vespucci
1519 Ferdinand
MagellanEx plorationof New W orlds!

How to Ex plore
the Chem ical W orld?
Global M ap?
Tool for Ex ploration?

Basic Problems in Chemistry
for a given Chemical Formula, such as CNHMOL.
(1) What kinds of chemical species (isomers) exist?
(2) How are they converted each other?
(3) How do they dissociate into smaller species?
or How are they produced from smaller species?
To solve These Problems Theoretically, Global Mappingof Potential Energy Surfaces （PES） is needed.
•Minima：Equilibrium Structures （EQ）
•Saddles:Transition Structures （TS）
•Minimum Energy Paths:
Intrinsic Reaction Coordinates（IRC）

Reaction path search methods
1. Geometry optimization methods• Eigen Vector Following: Cerjan and Miller(1981)• Berny optimization: Shregel (1982)• Geometry DIIS: Császár and Pulay (1983)• Rational Function Optimization: Banerjee etal. (1985)
2. Double-ended methods• Synchronous Transit: Halgren andLipscomb (1977)• Saddle Optimization: Dewar, Healy, andStewart (1984)• Self-penalty Walk: Elber and Karplus (1987)• Ridge: Ionova and Carter (1993)• Nudged Elastic Band (NEB): Henkelman etal. (2000)• String: Ren and Vanden-Eijnden (2202)• Growing String: Peters et al. (2004)

TargetedMethods

3. Coordinate driving methods• Single Coordinate driving• Metadynamics: Laio and Parrinello (2002)• First Marching: Burger and Ayers (2010)

Unbiased
UntargetedMethods

4. Fully-automated methods.
• Gradient Extremal Following: Pancíl (1974)• Newton Trajectory: Quapp et al. (1998)• Isopotential Contour Following: Irikura andJohnson (2000)• Chemical Flooding: Müller et al. (2002)• Global Reaction Route Mapping(Anharmonic Downward Distortion
Following): Ohno and Maeda (2004)• Artificial Force Induced Reaction: Maedaand Morokuma (2010)

Traces along reaction pathways
Uphill-Walk

Downhill-WalkTSTSEQTSIRC

EQIRC

IRC
EQ
Steepest Descent Method can be usedfrom anywhere to find an EQ.
If a TS is known, IRC can be followed.

Anharmonic Downward
Distortion (ADD) Following:
K.Ohno & S.Maeda,
Chem. Phys. Lett.384,277(2004).

Uphill walks on PES enable us to perform
Global Reaction Route Mapping (GRRM) !
Repeated One-After-Another-Search
EQ-TS-EQ

Automated Search

GRRM

Start from an EQ

TS
EQ

EQ

TS

EQ

ADD Following

TSTS

Find all reaction routes

RepeatUphill-walking

Dissociation Transition
EQ

EQ

TS

EQTS(DC)

State （TS）

IRC Following : Downhill-walking
TSOhno, Maeda, J.Phys.Chem. A 110, 277 (2006)

Dissociation Equilibrium
Structure(EQ)(DC)

Anharmonic Downward Distortion Following (ADDF)
methodOhno, Maeda, Chem. Phys. Lett. 384, 277 (2004)
ADD• Anharmonic Downward Distortion (ADD) indicatesthe direction of reaction! The problem becomes to find minima on
the hypersphere, using frequency-scaled normal coordinates.

V=(1/2)ΣλiQi2=(1/2)Σqi2 : qi = λi1/2Qi• Can find all the EQ and TS automatically• Full-ADDF of GRRM is in general expensive, like a full-CI.
Limited-ADDF reduces computational costs drastically.
Options for GRRM/ADDF: Large ADDF method (LADD)
Double-ended Method (2P-SHS, d-ADDF)
Micro-iteration Method (μ-ADDF)

An example of Global Reaction Route Map

by full-ADDF

for 5-atom system H2CO2

13 EQ 30 TS

Formic Acid HCOOH is the global minimum

Acid < 350 kJ/mol

Peroxide > 450 kJ/mol

If you use an option ofLADD (large ADD following),
you may obtainthe lower energy partmuch more quickly!

Ohno, Maeda, J.Phys.Chem. A, 110, 8933 (2006)

Parallel GRRM saves computation time considerably
in Single GRRM

in Parallel GRRM

ADDF is applied to
one EQ at one time
EQ ListTS ListDC ListWith using
many cpu/multicores
ADDF
can be applied toMany EQs
at the same time

EQ ListTS ListDC List

EQ ListTS ListDC List

EQ ListTS ListDC ListDone List
TOTAL EQ List
TOTAL TS List
TOTAL DC List

EQ ListTS ListDC ListList of Global Search by GRRM/full-ADDF
for the ground singlet-state at the B3LYP/6-31G* level with a 16-core computer
Atom
334444444444555555555555555566Formula
H2O
HCN
H3N
H2O2
H2CO
H2N2
H2C2
H2OS
P4HCNO
CN2O
BCNO
H4C
H2CO2
H3CN
H3NO
HCCl3
H2CCl2
HC3N
H3CCl
CCl4
HCO2Cl
C2O3
HCN3
H2N2O
HC2NO
CN2O2
BCNOS
H4C2
H4N2

EQ
1212432349131511435531186261119204934122
23TS
1112127274223532144171517738232310337817719114843989cpu time/hour
0.3
0.7
2.8
3.1
5.1
5.5
5.9
7.7
13.8
2230
51.8
6.7
16.4
171718.1
19.6
25.1
32
32.9
40.1
5656.7
63.9
88.4
154.8
205
13.5
15.2

6H4CO
6H4NCl6 H3C2Cl
6C2O4
6H3N3
6 H2C2Cl2
6 H3C2N
6 HC2Cl3
6 H2C3O
6 H3CNO
6H4CO
6
H2C4
6C2Cl4
6 H2CO3
6 H2C2F2
6 H2C2O2
6 H2C2N2
6 H3CClCu
6 HC2NO2
6 H2CN2O
6Si3O3
6 H3C2NO
7H5CN
7
H4C3
7 H4CN2
7 H4CO27H5B2
7 H4C2O
7 H3CNO2258189181911363021372916506327217
8763201
271911714157

1424367949697354161
159
104421149
61
223
343
721054233
255
1218
1031143
50
39100
1027

16.9
18.6
26.2
26.6
42.7
44.8
57
63.2
81.3
92
98
117.3
122.5
148.2
150
233
375.1
559
588.3
647
727.2
1044.51656.1
89.9
100.6
134.6
137.5
461.5

7 H2C2O3
7 H3C3N
7 H3N3O
7 H2C3O2
8H6BN
8H6C28H6B2
8 H5CNO
8H6Si28 H5C2Cl
8 H4C2Cl2
8 H4C2O28H4N48H4C4
8 H4C3O
8S88 H5C2NO
8 H2C2O48 H3CNO3
9H6C3
9 H6C2O
10 H6C2O2
10 H6C3O
10 H5C2NO2
11H8C3
11 H7C2NO
11 H6C3O2
14
H10C417
H12C5179
7093207
2221672220118
58328460219
581
676
87951133210
11511243
381077452
384
1158
885126
25133
133
782
439
171
586415
957
3932
5181
4559697843
23278
12141310100
3570647792
937.9
1499.829.347.669.2
122.4
129.4
173.2
216.8
468.9
655.2
688
971.5
1157.2
1935.45873.2
8664
104.2
139.5
732.9
2290.51603.2514526.812455.7
176
972.1

・ Explored number of EQs ranges from only 1 to over 3000!
・ Explored number of TS increases with the increase of EQ.
・ cpu time expands from less than 1 hour to longer than 1 year!

Number of EQs
Number of EQ ranges from only one to over three thousands!

Only one EQ: H2O, NH3, CH4, C3H8（propane）
Many EQs (Many isomers / Many conformers)
3210 EQ: H5C2NO2 (glycine)1369 EQ: H6C3O2 (methyl acetate)
676 EQ: H3CNO3 (aminoxy formate)
Number of EQ does not simply depend on the number of atoms!
Even if N-atoms are the same, N-EQs can be very much different!

N-Atoms
C3H8 （propane）
11
H6C3O2（methyl acetate)
11N-EQs
11369

Number of TSs
Number of TS increases simply with the increase of EQ.

CPU time for GRRM/full-ADDF with a 16-core computer
cpu time expands from less than cpu time is not a simple functionof the EQ number (N-EQ) !
1 hour to longer than 1 year!
N-EQ
157
151

cpu time/hour

Formula cpu time/h
H3CNO2
H2O
0.3
H7C2NO2HCN
0.7
5000
4500
H2CO5.1
4000
3500
H2CO216.4
3000
2500
・・・・・・・・・・・・
2000
1500
H2C2O4 5873.2 (0.7 year) 1000
500
H3CNO3 8664.0 (1.0 year)00
H6C3O2 12455.7(1.4 year)

cpu time/h461.5
4526.8Ten times different!

100200

Number of EQ

300

To overcome explosion of cpu-time, we have developed

Multi-Node GRRM/ADDF : NeoGRRM
saving computation time drasticallyOne-Node
GRRM（Parallel）

EQList
TS ListDCList

EQList
TS ListDCList

EQList
TS ListDCList

EQList
TS ListDCListNeoGRRM (Multi-Node)

GRRM

GRRM

GRRM

GRRM

(FIRST ONLY)(FIRST ONLY)(FIRST ONLY)(FIRST ONLY)

EQ ListTS ListDC List

EQ ListTS ListDC List

EQ ListTS ListDC List

EQ ListTS ListDC ListDone List
TOTAL EQ List
TOTAL TS List
TOTAL DC List

NeoGRRM: K. Ohno (2012), and K. Ohno, Chem. Rec. 16, 2198 (2016)

Extensive GRRM
for the system of 8-atom

H3CNO3676 EQ
5181 TS
3161 DC (Dissociation Channel)
at B3LYP/6-31G(d) levelvia huge numbers ofForce Calculations 18719781
Hessian Calculations 534726

CPU time for this Job took
8661 h (just 1 year)
by One-node GRRM
with 16 cores

Ohno, Kishimoto, Iwamoto, Satoh,
J. Compt. Chem. 38, 669 (2017).

but it was shortened to240 h (only 10 days)by Multi-node GRRM
with 256 cores

GRRM ofH3CNO3676 EQsEQs areclassified into
465 isomers
・・・

211 clusters
・・・

Further, isomers
are classified into
many chemicalcompoundsStructural Formula of 47 H3CNO3

Conformers for some compounds of H3CNO3
1: Aminoxy formic acid (The most stable compound)
1-1

1-2

1-5

1-4

1-3

1-6

2: Hydroxy carbamic acid
2-1

2-2

4: Aminoperformic acid
4-1

4-2

2-3

2-4

2-5

2-6

2-7

10-4

10-5

10: Nitroso oxymethanol
10-1

10-2

10-3

12: Nitromethanol 21: Methyl nitrate 31: Nitrous acid methoxy ester 45: Methoxy dioxaziridine
1221

31-1

31-2

45-1

45-2

Reaction pathways via 5181 TS were explored by GRRM/full-ADDF.

Local Reaction Route Maps for H3CNO3
18 TS

8 TS

9 TSConnected! or Not connected!
Energy Barrier Heights Δ
Between the same compounds
Δ ＜ 70 kJ/mol
Between the different compounds
Δ ＞ 120 kJ/mol

Energy Diagram around compound 1 of H3CNO3Coformation changes ofAminoxy formic acid (1-n)

333.8
go to other compound

1-6

66.7 kJ/mol
63.6
EQ12 55.3

53.2

50.0
49.6

41.4
1-4

1-5

39.2
21.7
EQ8 19.1

EQ7 16.2

1-1

EQ2 6.6
EQ0 0.0

2-1

1-2

1-3

EQ3 9.1
EQ1 3.4

ZPVE corrected
Energy in kJ/mol
B3LYP/6-31G*

Energy Diagram around compound 2 of H3CNO3
131.9

Conformation changes forHydroxy carbamic acid (2-n)

EQ25 127.3
go to other compound

68.5 kJ/mol
61.2

2-7

48.3

43.3

46.1
2-4

42.1

EQ11 38.3

2-5

2-6

37.5
EQ10 32.4

EQ9 25.1

2-1
2-3

2-2

EQ6 11.3
EQ5 9.6

EQ3 9.1

67.2

9.5
EQ4 8.8

ZPVE corrected
Energy in kJ/mol
B3LYP/6-31G*

Energy Diagram between 10, 12, 21, 31, ＆ 45 of H3CNO3Different compounds are764.7
well separated from others
201
via high barriers388 kJ/mol
ZPVE corrected
Energy in kJ/mol
B3LYP/6-31G*

EQ43 166.6

EQ488 563.4
45-1536.2

173
427.6

51391.0220

10: Nitroso
oxymethanol
10-3121549.2

379

224

684.4

434
168
60

31-2EQ189 376.5
EQ179 368.0
31-1

45: Methoxy
dioxaziridine

286
211231: Nitrous acid
methoxy ester
EQ44 170.7
12: Nitromethanol

EQ89 250.2
21: Methyl nitrateEnergy Distribution of EQs
H3CNO3 (B3LYP/6-31G*)
800

676

EQ Number

700
600
500
400

Sigmoid300
2001000 ↑ global minimum
0500

ENERGY kJ/mol1000

GRRM elucidated
stereo reaction mechanisms,
which have been eluded
experimental observation!

Stereo Reaction Mechnisms (1)Stereo Reaction Mechnisms (2)Water-Gas-Shift Reaction
is a well-known process producing H2 from H2O.
This reaction has long been
understood as three-stepprocesses via HCOOH,
but GRRM/ADDF has shownthat it can be a single process.
Harabuchi, Maeda, Taketsugu, Ohno, Chem. Lett. 43, 193 (2014)

Reppe Reaction producing Benzene from acetylene
Fe3 HC≡CH →C6H6
GRRM/ADDF has shown that it can proceed
as one-step reaction without catalyst !
The mechanism is similar to the Diels-Alder reaction
pseudobutadiene

pseudo-ethylene

Tokoyama, Yamakado, Ohno, Bull. Chem. Soc, Jpn. 88, 1284 (2015)

1) Guided by ADDF,
GRRM openeda new world of chemistry.

2) Aided by GRRM/ADDF,
exploration of new chemistry
may be made further on PES.
Next, we made explorationof new carbon allotropes

Typical Carbons
are composed of C6 or C5 rings• Graphite & Graphene• Diamond• Fullerene• Carbon Nano TubeSome Hydrocarbons haveC4 rings
Prismane

Cyclobutadiene

CubaneButalene

We
We challenged
challenged toto produce
produce straightstraight planar
planar ladderladder forms
forms !!
Geometry
Optimization

GRRM/ADDFsearchPrism-C20
Regular Decagon Prism

D10hR(CC)=0.144-0.148 nm < 0.154 nm (typical single bond)Ohno, Satoh, Iwamoto, Chem. Lett. 44, 712 (2015)

Prism-C20
QTAIM electron density analysisa) Critical points● Bond Critical Point● Ring Critical Point● Cage Critical Pointb) Van der Waals Surfacec) Density on the decagon faced) Density on the square facee) Density on the vertical cut

Stability of Prism-C20
GRRM / FirstOnly Search
Lowest Barrier = 158.0 kJ/mol (ZPVE-corrected)
at B3LYP/6-31G(d)Stabilization Energy = 309.2 kJ/mol

Hamster Wheel Carbons

C8v
D8h

D3h

D10h
D20h
C2h

D4h

D14h

Ohno, Satoh, Iwamoto, Chem. Lett. 44, 712 (2015)

Noting unsaturated CC-bond characters, we obtained

Prism-C2n Dimer (n=8)
Exploration：
B3LYP/6-31G(d)Confirmation:
B3LYP/6-311++G(2d,2p)
B3LYP/cc-pVDZ
B3LYP/cc-pVTZ
QTAIM
Electron Density Analysis● Bond Critical Point● Ring Critical Point● Cage Critical Point

D2hStability Analysis
GRRM/ADDF FirstOnly Search

Lowest Barrier = 34.3 kJ/mol (B3LYP/6-31G(d))
33.4 kJ/mol (B3LYP/cc-pVDZ)
ZPVE-corrected
Stabilization Energy= 632.5 kJ/mol (B3LYP/6-31G(d))
625.8 kJ/mol (B3LYP/cc-pVDZ)

Prism-C2n Trimer (n=12)
Exploration:
B3LYP/6-31G(d)Confirmation:
B3LYP/cc-pVDZ
RHF/STO-3G
RHF/3-21G

D3hPrism Carbon Sheet
Periodic Boundary Condition Calculation (g09)
RHF/STO-3G
RHF/3-21Gba2
11’

All Prisms are purely hexagonal.
All C-atoms are equivalentand connected with 4-atoms

D6h

1-2: 0.1566 nm
1-1’: 0.1562 nm

Prism-C2n Sheets
n=8

n=12

D4h

D6h

n=6n=12D2h

D4h

Ohno, Satoh, Iwamoto, Chem. Phys. Lett. 633, 120 (2015)

Vertical polymerization of the prism-unit axially

Prism-Cn Tubes(n=3-8, 10, 12, 14, 16, 18, 20)

Stability Check by
GRRM/ADDF
Lowest Barrier
81.6 kJ/mol

C12H8
Lowest Barrier
83.6 kJ/mol

Polygon CC: 0.153 - 0.160 nm
Vertical CC: 0.160 - 0.161 nm
Ohno, Tokoyama, Yamakado, Chem. Phys. Lett. 635, 180 (2015)

C18H12

Exploration of Wavy Carbons

Wavy Carbon Sheet & Tube

Ohno, Satoh, Iwamoto, Tokoyama, Yamakado, Chem. Phys. Lett. 639, 178-182 (2015)

New Carbon Allotropes
explored on Quantum Chemical PES
Prism-C2n (n=8, 9, 10, 12, 14, 16, 18, 20)

Chem. Lett. 44, 712 (2015).
Prism-Carbon Tube

Prism-Carbon Sheet

Chem. Phys. Lett. 633, 120 (2015).

Wavy Carbons

Chem. Phys. Lett. 635, 180 (2015).
Chem. Phys. Lett. 639, 178 (2015).

Important : High Energy Carbons

Containing Excess Chemical Energyof 130-350 kJ/mol per one C-Atom.
It is expected that these carbons may
become ideal Energy Reservoirs.
Energy-Charge/Discharge will be madewith no consumption of materials andwith no production of wastes.

High energy Carbon
CHA
RGE

DISCA
RGE

Low energy Carbon
Zero Consumption
Zero Emission
Usable anywhereat anytime

Summary• Although only limited results were shown in this talk,

exploration of quantum chemicalpotential energy surfaces will open
various new chemistries.
• For such explorations,
GRRM program will help you;
GRRM programs (GRRM14, GRRM17)
are distributed, available at
http://iqce.jp/GRRM/index_e.shtml

Acknowledgement
Development of GRRM:
Satoshi Maeda(GRRM1.2-11-14-17)
Y. Osada (GRRM11-14)
Keiji Morokuma(GRRM11-14-17)
T. Taketsugu (GRRM14-17)
Y. Harabuchi (GRRM14-17)
Y. Sumiya (GRRM17)
M. Takagi (GRRM17)
K. Suzuki (GRRM17)
K. Sugiyama (GRRM17)
M. Hatanaka (GRRM17)

Application of GRRM:
X. Yang
B. Hajgato
Y. LuoY. Watanabe
M. Moteki
T. Iwamoto
H. Satoh
H. Isobe
S. OhnoK. Shudo
Y. Matsuda
N. Kishimoto
H. Yamakado
H. Tokoyama
Y. Kodaya

A View from a Saddle PointA View of a Saddle Point around
Mt ZAO near Sendai in JAPAN