Applied Theoretical
Organic Chemistry

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Published by
World Scientific Publishing Europe Ltd.

57 Shelton Street, Covent Garden, London WC2H 9HE
Head office: 5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601

Library of Congress Cataloging-in-Publication Data
Names: Tantillo, Dean J., editor.
Title: Applied theoretical organic chemistry / edited by Dean J. Tantillo
(University of California, Davis, USA).
Description: New Jersey : World Scientific, [2018] | Includes bibliographical references.
Identifiers: LCCN 2017024260 | ISBN 9781786344083 (hc : alk. paper)
Subjects: LCSH: Chemistry, Organic.
Classification: LCC QD251.3 .A67 2018 | DDC 547/.12--dc23
LC record available at />
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.

Copyright © 2018 by World Scientific Publishing Europe Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance
Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy
is not required from the publisher.

Desk Editors: Anthony Alexander/Koe Shi Ying
Typeset by Stallion Press
Email:
Printed in Singapore


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Preface

When I think of Applied Theoretical Organic Chemistry,
I immediately think of Ken Houk, Roald Hoffmann and Paul
Schleyer. I am lucky enough to have personal connections to each:
Ken was my Ph.D. advisor, Roald was my postdoc advisor (and the
first person I remember hearing use the term “applied theoretical
chemistry”) and Paul and I collaborated briefly before he passed
away. I learned many important lessons from working directly with
all three and from reading their many (there are very very many)
published works. Two of the most important lessons are relevant
here:
(1) Results obtained by employing a “high level of theory” do not

equate to insight. Corollary: Deep insight can be derived from
“low level” results + chemical intuition. Ken, Roald and Paul all
derived models of chemical structure and reactivity that are still
useful today despite originally arising from results using theoretical methods that are no longer considered “sufficient” or even
“valid.” I tell anyone who will listen about these successes to
drive home that computational chemistry is not automated, it’s
not done by computers — it’s done by chemists! Computers just
compute.
(2) Experimentalists are the perfect audience. Most of Ken’s, Roald’s
and Paul’s papers were not written for physical/theoretical/
computational chemists. Instead, they were written for experimentalists: synthetic organic chemists, bioorganic chemists and
v

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Preface

enzymologists, materials scientists, spectroscopists, etc. This
book has been constructed with the same audience in mind. It
is a book that will hopefully find use by theoreticians wanting
to help and inspire experimentalists and experimentalists whose
research may be enhanced by theoretical models.
This book is dedicated to Ken, Roald and Paul. I am grateful to
all of this book’s contributors, many of whom are “descendants” of
Ken, Roald and Paul (some of more than one), to my students and
collaborators for their encouragement and inspiration, and to my wife
and son for support and distraction!

Dean Tantillo
Davis, CA, USA
2017

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About the Editor

Dean Tantillo applies the tools of theoretical chemistry to problems
in mechanistic bioorganic chemistry, chemical biology, organic and
organometallic reactions of synthetic relevance, and natural products
biosynthesis and structure elucidation. He is also working to help
make Applied Theoretical Chemistry research accessible to blind and
visually impaired students.
Dean received an A.B. degree in Chemistry in 1995 from Harvard
University and a Ph.D. in 2000 from UCLA. After receiving his
Ph.D., he moved to Cornell University, where he carried out postdoctoral research. He joined the faculty at UC Davis in 2003, where
he is now a Professor of Chemistry.

vii

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Contents

Preface

v

About the Editor
Chapter 1.

vii

Modeling Organic Reactions —
General Approaches, Caveats,
and Concerns

1


Stephanie R. Hare, Brandi M. Hudson
and Dean J. Tantillo
Chapter 2.

Overview of Computational
Methods for Organic Chemists

31

Edyta M. Greer and Kitae Kwon
Chapter 3.

Brief History of Applied
Theoretical Organic Chemistry

69

Steven M. Bachrach
Chapter 4.

Solvation

97

Carlos Silva L´
opez and Olalla Nieto Faza

ix

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Chapter 5.

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Contents

Conformational Searching for
Complex, Flexible Molecules

147

Alexander C. Brueckner, O. Maduka Ogba,
Kevin M. Snyder, H. Camille Richardson
and Paul Ha-Yeon Cheong
Chapter 6.


NMR Prediction

165

Kelvin E. Jackson and Robert S. Paton
Chapter 7.

Energy Decomposition Analysis
and Related Methods

191

Israel Fern´
andez
Chapter 8.

Systems with Extensive Delocalization

227

L. Zoppi and K. K. Baldridge
Chapter 9.

Modern Treatments of Aromaticity

273

Judy I-Chia Wu
Chapter 10. Weak Intermolecular Interactions


289

Rajat Maji and Steven E. Wheeler
Chapter 11. Predicting Reaction Pathways
from Reactants

321

Romain Ramozzi, W. M. C. Sameera
and Keiji Morokuma
Chapter 12. Unusual Potential Energy Surfaces
and Nonstatistical Dynamic Effects

351

Charles Doubleday
Chapter 13. The Distortion/Interaction Model
for Analysis of Activation Energies
of Organic Reactions
K. N. Houk, Fang Liu, Yun-Fang Yang
and Xin Hong

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Contents

Chapter 14. Spreadsheet-Based Computational
Predictions of Isotope Effects

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403

O. Maduka Ogba, John D. Thoburn
and Daniel J. O’Leary
Chapter 15. Stereoelectronic Effects:
Analysis by Computational
and Theoretical Methods

451

Gabriel dos Passos Gomes and Igor Alabugin
Chapter 16. pKa Prediction

503


Yijie Niu and Jeehiun K. Lee
Chapter 17. Issues Particular to
Organometallic Reactions

519

Gang Lu, Huiling Shao, Humair Omer
and Peng Liu
Chapter 18. Computationally Modeling
Nonadiabatic Dynamics
and Surface Crossings in Organic
Photoreactions

541

Arthur Winter
Chapter 19. Challenges in Predicting
Stereoselectivity

583

Elizabeth H. Krenske
Index

605

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Chapter 1

Modeling Organic Reactions —
General Approaches, Caveats,
and Concerns
Stephanie R. Hare, Brandi M. Hudson and Dean J. Tantillo
Department of Chemistry, University of California — Davis,
Davis, CA, USA

1.1 Introduction
Computational chemistry is unique in that the researcher who uses
it as a tool is not bound by the confines of reality. This freedom has
both benefits and drawbacks because it not only allows the researcher
to be boundlessly creative in determining how to answer chemical
questions but also requires an understanding of all the assumptions
being made in the analysis (which is often nontrivial). This chapter aims to describe the basics of applying quantum chemistry to
organic structures and reactions and to highlight “everything that
can go wrong” in quantum chemical calculations — that is, when

the assumptions break down or are incorrectly applied.
1.1.1 What can the Schră
odinger equation
do for YOU?
The primary goal of any quantum chemical computation is to associate an energy value with a particular distribution of electrons
around nuclei in particular positions. This goal is achieved using
the Schră
odinger equation, shown below in its least threatening form
1

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(physically oriented chemists, please forgive):

HΨ = EΨ

(1.1)

In this equation, a distribution of electrons/electron density,
expressed as a wave function (Ψ) is associated with an energy (E)
by a Hamiltonian operator (H; an operator is a function that acts on
another function). The Hamiltonian (for short), also the “functional”
in density functional theory (DFT), is a function that contains terms
associating energy values with the relative positions of electrons and
nuclei (see Chapter 2 for a survey of different Hamiltonians). The
Hamiltonian is also referred to as the model chemistry.
1.1.2 Putting the Schră
odinger equation to work
How is the Schră
odinger equation used to predict a distribution of
electrons/electron density? Generally, a prediction is arrived at by
using the following procedure. (1) A basis set of atomic orbitals
(usually Gaussian functions) is used by the quantum chemistry software of choice to construct guesses at the shapes (mathematical
forms) of molecular orbitals (MOs). This step corresponds to the
famous linear combination of atomic orbitals (LCAO) technique. In
this step, electrons localized on individual atoms are transformed
into electrons delocalized over molecules (or portions thereof). Note
that basis sets are not restricted to one 1s, one 2s, three 2p orbitals,
etc.; for example, many p-orbitals of differing “shapes” (e.g., short
and squat, tall and diffuse) are generally used. By doing so, electrons are allowed to more freely explore larger regions of the space
around the nuclei, thereby increasing their chances of finding ideal
positions/distributions. While this all sounds rosy, the user is limited
by the computational time required to perform such sampling, which
is proportional (generally not linearly) to the number of basis functions used. (2) Once one has a guess at the MOs, the Hamiltonian

then operates on the corresponding wave function that describes this
orbital arrangement to calculate its energy. (3) Steps 1 and 2 are then
repeated, changing the coefficients in the LCAO each time to produce
different MOs and associated wave function, and correspondingly, a

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different energy. This iterative procedure (called the self-consistent
field (SCF) procedure) continues until the energy is minimized (given
particular convergence criteria built into the quantum chemistry software or set by the user). At the end, one has the “best” (lowest
energy) distribution of electrons/electron density (wave function) for
the given set of atomic/nuclear coordinates. From the wave function,
myriad useful properties can be derived, e.g., spin densities, charge

distributions, and NMR chemical shifts. As a whole, this calculation
is called a single point calculation, since only one molecular geometry
was considered.
1.1.3 But what is the shape of the molecule?
If the user would also like to optimize relative atomic positions for
the structure in question, i.e., derive ideal bond lengths, angles,
and dihedral angles, then geometry optimization is carried out. This
procedure involves a series of single point calculations. After carrying out the single point calculation on the initial geometry, the
relative atomic (i.e., nuclear) coordinates are varied slightly, a new
single point calculation is carried out and the energies associated
with the old and new structures are compared. This goes on and on
until a geometry is found with the lowest possible energy (Fig. 1.1).
Thus, the optimization of electron positions/distributions is decoupled from the optimization of nuclear positions — which is allowed
by the Born–Oppenheimer approximation, which notes that electrons move/adjust their positions much more quickly than do nuclei,
because the former have much smaller masses than do the latter.
What control does the user possess over this process? First, the
user must specify the Hamiltonian, e.g., HF, MP2, B3LYP, etc.
(see Chapter 2). The Hamiltonian to be used in a particular calculation is generally determined on the basis of: (1) past experience
(of the user or others, as reported in the literature) in applying particular Hamiltonians to molecules with particular functional groups
and particular types of reactions and/or (2) test calculations in which
the performance of particular Hamiltonians is assessed against experimental data or data from “high level” calculations (on small model

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Figure 1.1. A flowchart showing the process by which quantum chemical software calculates the electronic structure and optimizes the geometry of a molecule.
The SCF procedure occurs at each iteration of a geometry optimization to
calculate the energy of the electronic structure of each nuclear geometry.

systems, since such “high levels” are usually prohibitively expensive
for organic molecules of sizes relevant to organic synthesis, bioorganic
chemistry, etc.). Second, the user must specify the basis set. Again,
this choice is generally made on the basis of precedent or model calculations. Some functional/basis set combinations are better than others for calculating the geometry of a molecule, while some are better
than others for calculating the energy of a molecule. Third, the user
must specify the initial atomic (nuclear) coordinates of the system
to be studied. These coordinates are generally obtained from X-ray
structures (on the off-chance that one is available) or result from
the user’s chemical intuition piped through (nowadays) a graphical
user interface attached to the quantum chemistry software of choice.
If one is performing a geometry optimization, then the closer the
initial geometry is to the optimized geometry the faster the calculation will be, i.e., there is a direct pay-off for having well-developed
chemical intuition.
1.2 Energy
Let us talk about the energy that is calculated in the procedure

described above. Arguments regarding the reactivity of organic

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5

molecules almost always boil down to energy. There are various forms
of energy that can be calculated using computational methods, with
each step of a calculation bearing its own assumptions. Here we
will briefly discuss how each type of energy is calculated and what
major assumptions an applied theoretical chemist should know about
to make valid arguments about a molecule’s reactivity. For a more
detailed mathematical description of these calculations, specifically
as they are implemented in the Gaussian program package, see the
white papers by Frisch et al. and Ochterski et al.1 on quantum chemistry and thermochemistry in Gaussian.

1.2.1 Potential energy surfaces and stationary points
We will focus first on geometry optimization. The electronic
energy (E), also called the potential energy, is the only type of energy
calculated in a simple geometry optimization. This is the energy
of all nuclei and electrons combined into a molecule (or complex)
compared to the energy of all nuclei and electrons at infinite separation. Optimized molecular geometries correspond to points on a
calculated potential energy surface (PES; Fig. 1.2). A PES describes
how the energy of a molecule changes with changes in its geometry
(i.e., nuclear positions and accompanying electron distribution). A
molecular structure can be optimized to either a minimum (corresponding to a reactant, intermediate, or product) or first-order saddle point (a minimum with respect to all geometric changes except
those that occur along the intrinsic reaction coordinate [IRC, vide
infra], corresponding to a transition state structure [TSS]). Both
minima and TSSs are “stationary points” on the PES, because the
slope of the tangent to the surface at these points is zero. There
has been some debate over the years about the terms “transition
state,” “transition structure,” and “transition state structure.” We
employ the convention that “transition structure” and “transition
state structure” are synonyms, meaning a first-order saddle point
on the PES, i.e., the high energy point along a particular optimized
reaction coordinate. However, we reserve the term “transition state”
for describing an ensemble of structures around a TSS, i.e., it is a

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saddle point
(e.g., transition
state structure)
minimum
(e.g., product)
Energy

minimum
(e.g., reactant)

transition state
structure

intrinsic reaction
coordinate (IRC) or
minimum energy path
(MEP)

E

frequency
calculation
to get G

reactant
product

Intrinsic Reaction Coordinate (IRC)
G = activation free energy
k = rate constant
kB = Boltzmann's constant
T = temperature
h = Planck's constant
R= gas constant

Eyring equation:

k=

- G
kB T RT
e
h

Figure 1.2. A theoretical 3D PES (left) showing two minima and the TSS
connecting them. The minimum energy pathway (MEP) between two minima is
called the IRC, which has the 2D form shown on the right. A frequency calculation
at each stationary point (minima and TSS) leads to calculation of the free energy
barrier, which can be used in the Eyring equation2 to calculate the rate constant
of the reaction.


state not a single structure. Transition states are particularly relevant
in dynamics calculations (see Chapter 12).
No matter how many separate molecules are included in an input
file for a quantum chemical calculation, the software will treat the
entire system as a single electronic structure. This means that the
basis functions for each individual molecule are “accessible” to all
other molecules in the calculation, which artificially lowers the total
energy of a complex vs. separated species by giving the electrons of
each component molecule more space to sample. This phenomenon
is called basis set superposition error (BSSE).3 There are a couple
of methods to mitigate this error, namely, the counterpoise (CP)
method4 and the chemical Hamiltonian approach (CHA).5 This error
is often not corrected for, because its effect is small (especially with
large basis sets), but nonetheless should be considered in the case of
modeling complexes or bimolecular reactions.
Let us talk about PESs in more detail. If we have a molecule
constructed of N atoms, in 3D there will be three ways all N
atoms are moving in the same direction (along the x-, y-, and zaxes) and three ways all N atoms are rotating in the same direction

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(around the x-, y-, and z-axes), leaving 3N − 6 ways the nuclei can
move with respect to one another to affect the internal potential
energy of the molecule. While it is straightforward for a computer
to do this calculation, in order to be able to visualize a PES, one
would need to be able to see in (3N − 6) + 1-dimensions (where
the additional dimension is the energy), which is impossible for
even small organic molecules and exceptional humans. What can
easily be visualized, however, is the variation in energy along the
IRC.6 The IRC is the MEP between a TSS and its flanking minima, calculated by determining the path of steepest descent along
either phase of the reaction coordinate (i.e., toward reactants or
products).
The foundational assumption of transition state theory (TST)7
and Rice–Ramsperger–Kassel–Marcus (RRKM) theory8 is that the
activation barrier for a reaction is related directly to the rate constant. This corresponds to the assumption that a molecule remains
on the PES throughout the course of a reaction. These conditions
are sometimes referred to as “quasi-equilibrium” because there is no
time-dependence of the rate and rate constant.
IRCs provide evidence of the connection between minima and
TSSs along a reaction pathway and the assumptions of TST and
RRKM theory are often reasonable enough to reproduce experimental data. Additionally, the shapes of IRCs can give valuable
insight into the nature of a mechanism. For example, a “shoulder” along an IRC is often indicative of a concerted reaction with

asynchronous events (see Sec. 1.4.1), which may possess a so-called
“hidden intermediate”.9 However, unique features of certain PESs
can preclude the quasi-equilibrium assumption. In fact, shoulders in
IRCs are also sometimes indicative of post-transition state bifurcations (PTSBs, Fig. 1.3; see Chapter 12 and Refs. [10, 11]). A PTSB
would not be visible in the 2D TST model. PTSBs occur in systems with two products that are directly connected to the reactant
through the same TSS. Such a PES exhibits a “valley-ridge inflection (VRI) point,” where the exit channels leading to the two products diverge. If the product distribution shows anything except equal

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intrinsic reaction
coordinate (IRC) or
minimum energy
pathway (MEP)


transition state
structure

valley-ridge
inflection point
(VRI)

minimum
(e.g., product 1)
exit channels
minimum
(e.g., product 2)

Figure 1.3. A theoretical 3D PES showing the features of a PTSB. A single
TSS connects two possible products, though only one of these products is along
the IRC path.

amounts of the two products following the PTSB, traditional TST
will fail to accurately model the system.11,12 Molecular dynamics
(MD) simulations, which incorporate kinetic energy and thus do
not assume quasi-equilibrium conditions, are helpful for these more
complex systems (see Chapter 12). In MD simulations, instead of
assuming that the energy of activation is the sole indicator of reaction outcome, many (often hundreds or thousands of) trajectories
are run in order to get a statistical distribution of pathways to
products.
Another important caveat is that IRCs lead to minima that are
in conformations that are productive but are not necessarily the lowest energy conformations (Fig. 1.4). This issue is important because,
for example, only the lowest energy conformations generally will be
detectable by spectroscopic techniques (vide infra). Neglecting this

fact can lead to a severe underestimation of the barrier of a reaction.
Conformational searching is critical in determining the energy of a
molecule of interest, and as such, Chapter 5 details many methods by
which one can conduct a conformational search. In short, there are
two major approaches: (1) calculating the energy of each possible

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saddle point
(e.g., transition
state structure)

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intrinsic reaction

coordinate (IRC) or
minimum energy path
(MEP)
minimum
(lower energy
conformer)

minimum
(higher energy
conformer)

Figure 1.4. This 3D PES qualitatively depicts the consequences of an IRC
leading to a productive conformation of the molecule, which is a minimum on the
PES, but not the lowest energy conformation.

conformation, or a Monte Carlo sampling13 of conformations if a
systematic search is prohibitively large, using a molecular mechanics
(MM) force field and (2) running MD simulations at high temperature. Once the relevant conformations are located, their energies can
be calculated with a quantum chemical method and ranked. Most
flexible organic molecules will require only a conformational search,
but some molecules, particularly metal–ligand complexes, will require
additional sampling of different configurations (i.e., the different ways
the ligands can be coordinated around a central metal atom). These
issues apply not only to minima but also to TSSs.14
Conformational searching also is particularly important in the
calculation of spectral data, particularly nuclear magnetic resonance
(NMR) spectra (see Chapter 6). If several of the lowest energy conformations are close in energy (typically within a few kcal/mol or
so of one another, depending on reaction conditions), all of these
conformations are likely present in some measurable quantity. This
means the NMR spectrum obtained for this molecule will contain


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contributions from all low energy conformations, and calculating the
spectrum of only the single lowest energy conformation would not
reproduce the experimental spectrum. The proportion of molecules in
each conformation can be calculated using the Maxwell–Boltzmann
distribution, which relates the probability of finding the molecule in a
particular conformation to the relative energy of that conformation.
The probability calculated is the percentage of molecules in the total
ensemble of molecules that are in that conformation. Then, multiplying the calculated probability with the corresponding spectrum
and summing all of the spectra generates a “Boltzmann-weighted
average” spectrum. This approach should provide the best estimate

of the experimental spectrum, assuming that the relative energies
used for each conformer are close to correct.
1.2.2 Frequency calculations and fretting
about free energy
After a geometry optimization, the final energy calculated is the electronic energy (E), which is only the energy of the electronic structure
for a single (although optimized) nuclear configuration. In order to
calculate the zero-point energy, internal energy, enthalpy, and free
energy of a molecule, an applied theoretical chemist will conduct a
frequency calculation on the optimized structure. A frequency calculation will determine the frequencies of all 3N − 6 vibrational modes
(again, these correspond to the degrees of freedom, or the ways the
atoms can move with respect to one another, that affect the internal energy of the molecule). Doing so amounts to computing the IR
spectrum of the molecule (or complex) in question, which can be
useful in the identification of, for example, reactive species isolated
in frozen matrices.15 An approximation that quantum chemical programs generally make is that the frequencies calculated are for a
quantum harmonic oscillator (QHO). This approximation is usually
decent, because, unless significant changes are made to the bonding structure of a molecule during a reaction, the anharmonic corrections would mostly cancel out when looking at the difference in
energy between, say, a TSS and a reactant. Anharmonic corrections

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are usually only computed in practice if an extremely high-level
calculation of frequencies is necessary.16
The software uses these frequencies to determine thermodynamic
properties of one mole of the molecule at a certain temperature
(usually 298 K, unless otherwise specified). The most important
approximation to remember in the calculation of these thermodynamic properties is that they are all usually calculated, at least initially, for an ideal gas. Modeling of a solution-phase reaction can be
done in a variety of ways (vide infra), but additional corrections to
the calculated energies need to be considered. A correction to the
energy that is made for all types and phases of molecules is the zeropoint energy correction. QHOs can never have exactly zero energy
as a consequence of the Heisenberg uncertainty principle. The lowest
possible energy of a QHO is called its zero-point energy, which is very
straightforward to calculate for each QHO and can be summed over
the molecule to get the total zero-point correction. The molecule’s
partition function, which determines how the energy of the system
is partitioned between different translational, rotational, vibrational,
and electronic states, can then be used to calculate thermodynamic
quantities. The internal thermal energy (U) is the kinetic + potential
energy associated with motion of the nuclei. The enthalpy (H), which
is just H = U+PV where P is pressure and V is volume, also includes,
in a sense, the energy that was necessary to get the system into
its current “state.” The Gibbs free energy (G), the most commonly
used quantity to compare computational with experimental results,
takes the enthalpy and subtracts a factor of entropy multiplied by

temperature (G = H − TS). It is important to remember that TSSs
are found by determining the location of a saddle point on the PES,
but such points are only necessarily saddle points with respect to the
electronic energy. A subsequent frequency calculation determines the
free energy barrier to get to that TSS. The activation free energy is
then used to calculate the rate constant via the Eyring equation2
(Fig. 1.2). In some cases, the TSS on a PES differs significantly in
structure from the TSS on a free energy surface. In fact, it is not
always the case that a barrier on the free energy surface would be

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detectable on the PES, thus there are methods of locating a TSS on

the free energy surface if necessary.17
Frequency calculations are also used to confirm whether an optimized structure is a PES minimum, TSS, or neither. A fully optimized structure with zero imaginary frequencies is a PES minimum.
A fully optimized structure with a single imaginary frequency is a
TSS. The vibration associated with this imaginary frequency (which
can be animated and viewed using most quantum chemistry software
packages) will correspond to movement along the reaction coordinate.
A structure with more than one imaginary frequency is generally
not relevant to a reaction (although some such structures have been
proposed as relevant from time to time18 ).
1.2.3 Issues with entropy
Because the entropy correction calculated for an individual molecule
is only due to the relative motion of nuclei within the molecule,
there are additional entropic factors that need to be considered when
looking at ensembles of molecules. In order to obtain a more accurate
entropy value to compare to experiment, there are several corrections
that can be easily applied to the calculated entropy that are specific
to particular experimental systems. First, if a calculation is performed for an ideal gas when the experimental system is in solution,
the standard state of the molecule needs to be changed from a pressure of 1 atm to a concentration of 1 M. This correction is necessary
only if the number of molecules changes along the reaction path (e.g.,
two molecules reacting to form one molecule or vice versa) in the solution phase. If the reaction is unimolecular, or the number of molecules
never changes along the reaction path, this correction would cancel at
each stationary point along the reaction path. If the reaction is in the
gas phase, then a 1 atm standard state applies and there is no need
to apply this correction. If one of the reagents is a solvent molecule
that comes from neat solvent, the standard state correction for only
that solvent molecule needs to include an additional correction for
the concentration of the solvent in its neat form. This treats the standard state for that solvent as neat solvent, rather than 1 M. If the

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Modeling Organic Reactions

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reaction pathway involves a mixture of structures at any stationary
point, an entropy correction must also be included to account for the
mixture. There are two components to this correction, and either
just one or both could be applied depending on the system. The first
is a correction for an intermediate or product that exists as a chiral
species (assuming both stereoisomers are in solution). The second is
for a molecule that could adopt multiple low-energy conformations in
solution. A Boltzmann-weighted average is used to account for this
mixture of conformers (vide supra). Lastly, if the symmetry number
of a reactive species changes over the course of a reaction, there is
an additional entropic factor. The symmetry number is the number of different, but indistinguishable, arrangements of a molecule.
For example, water would have a symmetry number of 2 because
its C2 axis allows for two indistinguishable arrangements of the

molecule.
These corrections are often neglected because they tend to
amount to a free energy correction on the order of 1 kcal/mol, which
corresponds to a higher degree of accuracy than is called for in many
research studies. However, this is not always the case, and there are
scenarios where accurate calculation of entropic factors is required.
For example, in 2015, Kazemi and ˚
Aqvist19 studied the deamination
reaction of cytidine to uridine that occurs within the enzyme cytidine deaminase. This enzyme is purported to catalyze the reaction by
significantly decreasing the entropy of activation by decreasing the
entropy of the substrate on binding. This concept is referred to as
Jencks’ “Circe effect”20 : if the substrate’s configurational entropy is
significantly reduced on binding, the entropy loss associated with
reaching the TSS can be eliminated. Kazemi and ˚
Aqvist wanted
to develop a way to model this effect on the cytidine deamination
reaction by computing the activation entropy in solution, which is
beyond the scope of the corrections outlined above. To do this, they
made computational Arrhenius plots from MD and empirical valence
bond (EVB)21 simulations, which do extensive configurational sampling of arrangements of the substrate and a number of explicit
solvent molecules. The Arrhenius plots showed the temperature

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