Artificial Force Induced Reaction
2019/8/2
M1 Yuki Nishioka

Table of Contents• Introduction• Theory of AFIR
• Application of AFIR
• Summary2

Table of Contents• Introduction• Theory of AFIR
• Application of AFIR
• Summary3What is Artificial Force InducedReaction(AFIR)?
・One of the method of computational chemistry

・Prof. Maeda of Hokkaido University developed in2010.
・In AFIR, artificial force is applied between thereactants to efficiently search the reaction path.

ForceABForce

4

Satoshi Maeda
2002: B.S. from Tohoku University
2004: M.S. from Tohoku University
2007: Ph.D. from Tohoku University
2007-2010: Postdoc (JSPS PD), Tohoku University - Emory
University - Kyoto University
2010-2012: Assistant Professor (Hakubi Project), Kyoto
University
2012-2013: Assistant Professor, Hokkaido University
2014-2017: Associate Professor, Hokkaido University
2017-20xx: Professor, Hokkaido University
2017-20xx: Visiting Principle Investigator, National Institutefor Materials Science (NIMS)
2018-2028: Director, Institute for Chemical Reaction Designand Discovery (WPI-ICReDD)

Source: https://sites.google.com/site/grrmgroup/satoshi-maeda
5Table of Contents• Introduction• Theory of AFIR
• Application of AFIR
• Summary6Overview of AFIRPotential energy E as a function of rAB(distancebetween A and B)

Artificial energy function F as a function ofrAB(distance between A and B)

𝐹(𝑟𝐴𝐵 ) = 𝐸(𝑟𝐴𝐵 ) + 𝛼𝑟𝐴𝐵
Satoshi Maeda and Keiji Morokuma J. Chem. Phys. 2010, 132, 241102
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Function F
𝐹(𝑟𝐴𝐵 ) = 𝐸(𝑟𝐴𝐵 ) + 𝛼𝑟𝐴𝐵𝑝
𝑟𝑖𝑗𝑖∈𝐴 𝑗∈𝐵 𝑅𝑖 + 𝑅𝑗 /𝑟𝑖𝑗
𝐹 =𝐸+𝛼𝑝𝑖∈𝐴 𝑗∈𝐵 𝑅𝑖 + 𝑅𝑗 /𝑟𝑖𝑗
E is potential energy.
𝛼 ≥ 0 is a parameter of magnitude of artificial attractive force.
𝑅𝑖 𝑎𝑛𝑑 𝑅𝑗 are covalent radii of the ith and jth atoms, respectively.
𝑟𝑖𝑗 is a distance between the ith and jth atoms.
p is arbitrary integer.
↑問題に対する調整項(p=6のときフィッティング良かった(P=6でなくてもよい。）)

Satoshi Maeda and Keiji Morokuma J. Chem. Phys. 2010, 132, 241102
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Parameter 𝜶
When both A and B are composed of single atom…

𝐹 = 𝐸 + 𝛼𝑟𝐴𝐵
The last term in this equation represents a constant artificial
attractive force 𝛼 between the atoms A and B.

Satoshi Maeda and Keiji Morokuma J. Chem. Phys. 2010, 132, 241102
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Parameter 𝜶

Rewrite 𝜶 based on generic
Lennard-Jones 6-12 potential

Typical diatomic potential curves
E and F with small 𝛼 and large 𝛼
Satoshi Maeda and Keiji Morokuma J. Chem. Phys. 2010, 132, 241102

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Lennard-Jones Potential
２つの原子間のポテンシャルエネルギーの経験的なもの

Lennard-Jones potential is one of theempirical models representing theinteraction potential energy between twoatoms.
Potential energy U is
𝑈 𝑟 = 4𝜀Potential energy between two argonatoms

𝜎 𝑝𝜎 𝑞−.
𝑟𝑟

Especially, when 𝑞 = 6, 𝑝 = 12, it iscalled Lennard-Jones 6-12 potential.

Ronald A. Aziz J. Chem. Phys. 2010, 99, 4518
Source: https://ja.wikipedia.org/wiki/レナード-ジョーンズ・ポテンシャル

11Parameter 𝜶𝛾

𝛼=2−1/6 −1 + 1 + 𝛾/𝜀−1/6𝑅0𝛾 is a parameter related to collision energy on the LennardJones potential.
Prof. Maeda used 𝑅0 and 𝜀 to be the values for argonclusters(𝑅0 = 3.8164 Å, ε = 1.0061 kJ/mol).
However, this conversion itself is not essential.
Satoshi Maeda and Keiji Morokuma J. Chem. Phys. 2010, 132, 241102
12Four well-known Reaction
力をかける向きは自身で指定？
ラジカル的な反応は検証できる？
励起などもStarting from 𝛾 = 0 kJ/mol, authors
increased 𝛾 by 50 kJ/mol until aminimization converges to a productside for each reaction.
R1: 𝛾 = 100 kJ/mol
R2: 𝛾 = 200 kJ/mol
R3: 𝛾 = 150 kJ/mol
R4: 𝛾 = 50 kJ/mol

𝛾0

Satoshi Maeda and Keiji Morokuma J. Chem. Phys. 2010, 132, 241102
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Four well-known Reaction（R=2）TSにいたるまでに安定配座がなかったため、ガンマ(人工力)をかけても距離が短くならなかった。

Satoshi Maeda and Keiji Morokuma J. Chem. Phys. 2010, 132, 241102
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Intrinsic Reaction
Coordinate(IRC) Calculation
IRC…”the reaction coordinate as a curve passing throughthe initial and the transition points and orthogonal toenergy equipotential contour surface”(Kenichi Fukui, 1970)

Kenichi Fukui, J. Phys. Chem. 1970, 74, 23, 4161
Kazuhiro Ishida et al. J. Chem. Phys. 1977, 66, 2153
Source: https://computational-chemistry.com/top/blog/2016/01/11/transition-state/ 15

Intrinsic Reaction
Coordinate(IRC) Calculation
ヘッス行列を用いて定義

Kenichi Fukui, J. Phys. Chem. 1970, 74, 23, 4161
Kazuhiro Ishida et al. J. Chem. Phys. 1977, 66, 2153
Source: https://computational-chemistry.com/top/blog/2016/01/11/transition-state/ 16R1 and R2(a)…IRC profile(b)
Blue dashed curve…a profile of F
with 𝛾 = 100 kJ/mol starting from R1-1
Red solid curve…a profile of E(c)Blue dashed curve…a profile of F
with 𝛾 = 200 kJ/mol starting from R2-1
Red solid curve…a profile of E
R1 → 133 gradients and 2 Hessians
R2 → 90 gradients and 2 Hessians

Satoshi Maeda and Keiji Morokuma J. Chem. Phys. 2010, 132, 241102 17

Optimizations Starting fromRandom Orientation
New procedure…optimizations starting from random orientations for R1and R2 at 𝛾 = 100 kJ/mol, where generation ofrandom orientation was terminated when last ten
optimizations converged to the structures which werealready found in earlier optimizations.

R1 → 1943 gradients and 49 Hessians
R2 → 1355 gradients and 39 Hessians
GRRM

Conventional method

R1 → 25758 gradients and 747 Hessians
R2 → 24230 gradients and 653 Hessians

Satoshi Maeda and Keiji Morokuma J. Chem. Phys. 2010, 132, 241102 18

R3 and R4(a)…IRC profile of R3(b)Blue dashed curve…a profile of Fwith 𝛾 = 150 kJ/mol starting from R3-1
Red solid curve…a profile of E(c)…IRC profile of R4(d)Blue dashed curve…a profile of F
with 𝛾 = 50 kJ/mol starting from R4-1
Red solid curve…a profile of E

R3 → 103 gradients and 2 Hessians
R4 → 148 gradients and 2 Hessians

Satoshi Maeda and Keiji Morokuma J. Chem. Phys. 2010, 132, 241102 19

Short Summary
・AFIR is an efficient algorithm to obtain a TS ofA+B→X type reaction
・Conventional methods don’t have an ability tosystematically predict geometries of TS onquantum chemical potential energy surfaces. AFIR
can be used in automated prediction of unknown
reaction pathways.

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Table of Contents• Introduction• Theory of AFIR
• Application of AFIR
• Summary21

The Anomalous Formal Nucleophilic
Borylation of Organic Halides with Silylborane

The mechanism of thisreaction has not yet been
elucidated.

Rhohei Uematsu et al. J. Am. Chem. Soc. 2015, 137, 4090

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The Anomalous Formal Nucleophilic
Borylation of Organic Halides with Silylborane

AB

Rhohei Uematsu et al. J. Am. Chem. Soc. 2015, 137, 4090

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Reaction Mechanism of Case A

Rhohei Uematsu et al. J. Am. Chem. Soc. 2015, 137, 4090

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Reaction Mechanism of Case A

Rhohei Uematsu et al. J. Am. Chem. Soc. 2015, 137, 4090

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Reaction Mechanism of Case B
ラジカル的に反応しない（電子的に閉殻構造をとっている）

Rhohei Uematsu et al. J. Am. Chem. Soc. 2015, 137, 4090

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Iridium-Catalyzed Asymmetric Borylation of
Unactivated Methylene C(sp3)–H Bonds

Ronald L. Reyes, et al. J. Am. Chem. Soc. 2019, 141, 6817

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Substrate Scope

Ronald L. Reyes, et al. J. Am. Chem. Soc. 2019, 141, 6817

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Kinetic Analysis

Ronald L. Reyes, et al. J. Am. Chem. Soc. 2019, 141, 6817

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Chemical Diagrams
はじめ93個の構造が出てくる
そのうちえねるぎーの低い１０個をその後の計算に使う。

配位の位置
水素原子の鏡像異性体
イリジウム錯体120度づつ捻って計算
３✕4=12通り、手動で検討

Ronald L. Reyes, et al. J. Am. Chem. Soc. 2019, 141, 6817 30

3-D Representations with
Geometrical Features of the TS

Ronald L. Reyes, et al. J. Am. Chem. Soc. 2019, 141, 6817

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Table of Contents• Introduction• Theory of AFIR
• Application of AFIR
• Summary32

Summary・AFIR is an efficient algorithm to obtain a Ts andreaction pathway reaction.
・Conventional methods cannot calculate unknown
complex reaction, but AFIR can be used inautomated prediction of unknown reaction
pathways.

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Appendix

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Appendix

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Appendix

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Appendix

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Appendix

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Appendix

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Appendix

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Appendix

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