Reviews in computational chemistry, volume 27

Reviews in
Computational
Chemistry
Volume 27


Reviews in
Computational
Chemistry 27
Edited by

Kenny B. Lipkowitz

Editor Emeritus

Donald B. Boyd


Kenny B. Lipkowitz
Office of Naval Research
875 North Randolph Street
Arlington, VA 22203-1995 U.S.A.


Donald B. Boyd
Department of Chemistry and
Chemical Biology
Indiana University-Purdue
University at Indianapolis
402 North Blackford Street
Indianapolis, Indiana 46202-3274

U.S.A.


Copyright © 2011 by John Wiley & Sons, Inc. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any
form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise,
except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without
either the prior written permission of the Publisher, or authorization through payment of the
appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers,
MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests
to the Publisher for permission should be addressed to the Permissions Department, John Wiley &
Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online
at />Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best
efforts in preparing this book, they make no representations or warranties with respect to the
accuracy or completeness of the contents of this book and specifically disclaim any implied
warranties of merchantability or fitness for a particular purpose. No warranty may be created or
extended by sales representatives or written sales materials. The advice and strategies contained
herein may not be suitable for your situation. You should consult with a professional where
appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other
commercial damages, including but not limited to special, incidental, consequential, or other
damages.
For general information on our other products and services or for technical support, please
contact our Customer Care Department within the United States at (800) 762-2974, outside the
United States at (317) 572-3993 or fax (317) 572-4002.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in
print may not be available in electronic formats. For more information about Wiley products,
visit our web site at www.wiley.com.
Library of Congress Cataloging-in-Publication Data:

ISBN: 978-0470-58714-0
ISSN: 1069-3599

Printed in Singapore
10 9 8 7 6 5

4 3

2 1


Preface
Computational chemistry transcends traditional barriers separating chemistry,
physics, and mathematics. It is, de facto, a product of the “Computer Age,”
but the impetus for its success really lies in the hands of scientists who needed
to better understand how Nature works. Chemists in particular were able to
adopt computational methodology quickly, in part because there were institutions like the Quantum Chemistry Program Exchange disseminating software free of charge and websites like the Computational Chemistry Listserve making available a variety of services, but also because of books like
Reviews in Computational Chemistry providing tutorials and reviews, especially for nontheorists and novice molecular modelers. By and large, computational chemistry moved from the domain of the theorist to that of the bench
chemist, and it has moved from the realm of chemistry to other disciplines,
most notably in the biological sciences where biologists are now adopting a
molecular view of living systems.
Since this book series began, we sold more than 20,000 books covering
myriad topics of interest to chemists. Those topics were written by mathematicians, chemists, computer scientists, engineers, and physicists, and they cover a
wide swath of computing in science, engineering, and technology. One area of
research where chemists are under-represented in terms of theory and simulation, however, is in multiscale modeling. The scales typically involved here are
those in, say, a molecular dynamics protein folding study where picoseconds
are required for assessing molecular vibrations but milliseconds are needed to
understand segmental relaxation, and length scales in materials science where
angstrom-level views are needed to account for bond making and bond breaking, but micron-level and larger views are required for predicting certain bulk
behavior.

For some researchers, multiscale modeling means harnessing huge computing resources at places like Los Alamos National Laboratory where multimillion atom systems can be treated; for others it means extending simulation
times for as long as possible. But throwing “brute force” at a problem has
its limitations, and accordingly, more reasonable and more elegant approaches
to solving multiscale problems are needed. Many advances in this regard have
come to fruition and are being used by some chemists. An especially well-written
tutorial on the topic of multiscale modeling appeared in Volume 26 of this
v


vi

Preface

book series; for the novice or uninformed reader, it is a chapter that is well
worth reading because it describes what “multiscale modeling” means, what is
currently being done, and what still needs to be accomplished in this area of
theory/computation.
Many companies rely heavily on simulations of mechanical properties of
materials for engineering purposes. The mathematical basis for this (mechanics)
rests on a continuum treatment of the material. That method fails when the
granularity of the system is small (at the molecular level), so something special
needs to be done to include the small length scales of atoms and molecules.
This is true for modeling micro-cracks in bulk materials as an example, but it is
even more pressing for modeling the mechanical behavior of modern materials
composed of (or incorporating) nanoparticles, which are now being prepared
and evaluated for many uses.
There is a movement afoot to couple continuum mechanics with atomistic
models. What is most needed in this area of analysis is ensuring that the correct
atomistic information is fed back to the continuum mechanics model. A concerted effort is now being made by scientists and engineers to unify modeling in
a way where atomistic information is used, either sequentially or concurrently,

with finite element methods employed in the area of mechanics. To understand
the stress-strain relationships in polymers, composites, ceramics, and metals, for
example, requires model input at the atomic level and requires treating large
volumes of space incorporating millions of atoms. My opinion is that chemists
are missing a golden opportunity, in terms of funding opportunities at agencies
like the National Science Foundation (NSF), U.S. Department of Energy, and
the various U.S. Department of Defense agencies, but also in terms of contributing their considerable wealth of knowledge about chemical systems toward this
endeavor. The following facts validate my opinion. First, the number of publications on the topic of multiscale modeling is increasing as depicted in Figure 1.
This plot was obtained by searching SciFinder for “multiscale modeling” and
“multiscale simulation.” Omitted are search terms like “multiscale analysis,”
“multiscale approach,” and the like. The use of multiscale modeling far exceeds
the relatively small number of publications indicated in this figure, however, because many multiscale modelers work in defense agencies or in industry where
publication is not de rigueur or it is outright forbidden.
Second, the majority of these publications (∼33%) emanated from departments in engineering schools—most notably from mechanical, chemical, civil,
aerospace, and bioengineering departments. Approximately 8% were published
by researchers in chemistry departments, 8% from physicists, and only 5% from
materials science departments. Industrial organizations like Toyota, Motorola,
Samsung, 3-M, and software companies contributed ∼4%, whereas national
laboratories, worldwide, contributed 14% as one might expect. Approximately
25% of the publications came from other departments like mathematics, from
mixed departments, or could not otherwise be clearly identified. Interestingly,
less than 1% came from mechanics departments and only 2% came from metallurgy departments. This assessment does not include the many papers published


Preface

vii

180
160

140
120
100
80
60
40
20
0
1998

2003

2008

Figure 1 Number of multiscale publications between 1998 and 2008.

under the moniker QM/MM and other such publications where small and large
scales are being examined simultaneously; it includes only those papers that explicitly refer to their studies as being multiscale in scope. The point I am making
is that now is an excellent time for chemists to begin working in a developing
field of computing.
With this theme of multiscale modeling, Stefano Giordano, Alessandro
Mattoni, and Luciano Colombo present in Chapter 1 a tutorial on how to
model brittle fracture, as found in myriad materials we use everyday, including
metals, ceramics, and composites. The authors begin their tutorial by providing
an overview of continuum elasticity theory, introducing the ideas of stress and
strain, and then providing the constitutive equations for their relationship. The
governing equations of elasticity and the constitutive equation of an elastic material is described before the authors focus on the microscopic (i.e., atomistic
theory of elasticity). Here an atomic version of the elasticity theory for isotropic,
homogeneous materials is established and the need is highlighted for including
three-body interactions in force fields for a formal agreement with continuum

elasticity theory; interatomic potentials for solid mechanics and atomic-scale
stress are then described rigorously. The authors consider linear elastic mechanics by first examining stress concentration, the Griffith energy criterion (an
energy balance criterion), and then different modes of crack formation in two
and three dimensions. The elastic behavior of multifractured solids is brought
forward before a review of atomistic simulations in the literature is given. The


viii

Preface

chapter terminates with a detailed look at atomistic simulation of cubic silicon
carbide because it is the prototype of an ideally brittle material up to extreme
values of strain, strain rate, and temperature and because of its relevance in
technology. Because the need exists to understand the mechanical properties of
nanoparticles that are becoming so prevalent nowadays, relying on mechanical
phenomena at a length scale where matter is treated as a continuum is not tenable; this tutorial brings the reader up to speed in the area of mechanics, points
out potential pitfalls to avoid, and reviews the literature of brittle fracture in a
rigorous, albeit straightforward, manner.
Another approach for treating systems on the mesoscopic scale is to employ dissipative particle dynamics (DPD), which is a coarse graining method
that implements simplified potentials as well as grouping of atoms into a single
particle. In Chapter 2, Igor V. Pivkin, Bruce Caswell, and George Em Karniadakis describe how interacting clusters of molecules, subject to soft repulsions,
are simulated under Lagrange conditions. The authors begin with a basic mathematical formulation and then highlight that, unlike the steep repulsion of a
Lennard–Jones potential, which increases to infinity as the separation distance,
r, approaches zero and imposes constraints on the maximum time step that
can be used to integrate the equations of motion, DPD numerically uses a soft,
conservative potential obviating that problem. The authors compare and contrast the potentials used in traditional molecular dynamics (MD) simulations
with that of DPD keeping the mathematical rigor but with easy-to-follow explanations. The thermostat used in DPD along with integration algorithms and
boundary conditions are likewise described in a pedagogical manner. With that
formal background, the authors then introduce extensions of the DPD method,

including DPD with energy conservation, the fluid particle model, DPD for
two-phase flows, and other extensions. The final part of the chapter focuses
on applications of DPD, highlighting the simplicity of modeling complex fluids. Emphasized are polymer solutions and polymer melts, binary mixtures of
immiscible liquids like oil-in-water and water-in-oil emulsions, as well as amphiphilic systems constituting micelles, lipid bilayers, and vesicles. The authors
end the chapter with an extreme example of multiscale modeling involving
deformable red blood cells under flow resistance in capillaries.
For those of us who use atomistic MD simulation methods in chemistry,
physics, or biology, we encounter rare, yet important, transitions between longlived stable states. These transitions might involve physical or chemical transformations and can be explored with classic potential functions or by quantumbased techniques. In Chapter 3, Peter G. Bolhuis and Christoph Dellago provide
an in-depth tutorial on the statistical mechanics of trajectories for studying rare
event kinetics. After a brief introduction, the authors begin with transition state
theory (TST). Using mathematics in tandem with easy-to-follow figures that illustrate the concepts, the authors focus on statistical mechanical definitions,
rate constants, TST, and variational TST before introducing us to reactive flux
methods. Here the Bennett–Chandler procedure is described in great detail as is
the effective positive flux and the Ruiz–Montero–Frenkel–Brey method. Then,


Preface

ix

transition path sampling is described, again, with simple cartoon-like figures
for clarity of complex problems. In this section, the authors illuminate path
probability, order parameter, and sampling the path ensemble. Also covered
are the shooting move, sampling efficiency, aimless shooting, and stochastic
dynamics shooting, along with an explanation of which shooting algorithm to
use. The ensuing section of the tutorial covers the computation of rates with
path sampling. Included here are the correlation function approach, transition
interface sampling, partial path sampling, replica exchange, forward flux sampling, milestoning, and discrete path sampling. Minimizing the action comprises
the penultimate section of the tutorial. Here the nudged elastic band method
is described along with action-based sampling and the string method. The authors provide insights about how to identify the mechanism under investigation

from the computed path ensemble in the final section of the tutorial. Because
so many modelers are interested in topics beyond simple structure prediction, a
need exists for methods that can be implemented to compute low-probability,
rare events; this chapter provides the detailed mathematics of those methods.
Micro-electro-mechanical systems (MEMS) are used extensively in many
devices such as radar, disk drives, telecommunication equipment, and the like.
Metal contacts that are repetitively opened and closed lead to degradation of
those materials, and it is imperative that we understand the events leading to
this degradation so that better products can be engineered, especially as we
miniaturize such machinery down to the nanoscale. The metal surfaces making
contact are not atomically smooth; instead, they have relatively rough surfaces
with thin metal asperities through which electrical current flows. The resistance
of the electrons is a consequence of inelastic interactions between the electrons
and the phonons, which in turn leads to Ohmic (Joule) heating. As the temperature increases from this resistive heating, the ability of an electron to move
through a wire decreases. How one can model such systems is the focus of
Chapter 4 where Douglas L. Irving provides a tutorial on multiscale modeling
of metal/metal electrical contact conductance. The author begins by describing
factors that influence contact resistance. Surface roughness and local heating
are paramount in this regard, as are intermixing between different materials
used in the contacts and the dimensions of the contacting asperities. He then
introduces the computational methodology needed to model those influencing
factors, highlighting the fact that modeling metal/metal interfaces is inherently
a multiscale problem. Atomistic methods like density functional theory, tight
binding methods, and potential energy functions are described. For the treatment of systems containing hundreds of thousands to millions of metal atoms,
the embedded atom method (EAM) and variations thereof are described. The
coupling of atomistic details to finite element and finite difference techniques
used in the area of mechanics is then described using simple mathematics geared
for the novice. Applications of these hybrid multiscale techniques are then described with several case studies that focus on electric conduction through
metallic nanowires and then on the deformations of metals in contact with
compressive stresses. This journey into the realm of metallurgy is enlightening,

x

Preface

but it is also especially important because computer-aided material design has
great potential for solving many future technological problems.
Biological membranes consist of complex mixtures of lipids and other materials that perform myriad functions to sustain life. Biologists, chemists, and
biophysicists have been examining these systems for many decades by experiment and by theory. In Chapter 5, Max L. Berkowitz and James Kindt bring us
up to date on advances in the field of atomistic simulations of lipid bilayers. They
begin this tutorial/review by first addressing methodologies used for membrane
simulation. A focus is placed on force fields (especially those developed and parameterized for lipid materials), the selection of appropriate statistical ensembles for simulations, force field validation, and Monte Carlo (MC) simulation
methods where the configuration-biased MC algorithm is described. Selecting
suitable experiments with which to compare simulation results is also described.
The second part of the chapter uses all of these ideas to show how one can carry
out atomistic simulations of lipid bilayers; the authors cleverly disguise their tutorial by examining four different microscopic level models proposed for cholesterol/phospholipid interactions that can produce liquid-ordered raft domains.
Of special note for the novice modeler is the explanation of the balance between
energetics and entropy; for the more experienced modeler, the complexities, utility, and pitfalls to avoid when using the isomolar semi-grand canonical ensemble
in MC simulations of bilayers consisting of more than one type of phospholipids
is especially important reading. Although much is being done computationally
to characterize phase diagrams of ternary systems, the authors provide insights
about what must be done next in this exciting area of theory.
In 1952, David Bohm presented an interpretation of quantum mechanics
(QM) that differs in profound ways from the standard way we think of quantal systems. During the last decade there has been great interest in Bohm’s
interpretation and, in particular, in its potential to generate computational
tools for solving the time-dependent Schrödinger equation. In Chapter 6, Sophya Garashchuk, Vitaly Rassolov and Oleg Prezhdo describe the semiclassical
methodologies that are inspired by the Bohmian formulation of quantum mechanics and that are designed to represent the complex dynamics of chemical
systems. The authors introduce the Madelung de Broglie–Bohm formalism by
drawing analogy with classical mechanics and explicitly highlighting the nonclassical features of the Bohmian mechanics. The nonclassical contributions to

the momentum, energy, and force are then described. The fundamental properties of the Bohmian quantum mechanics are discussed, including the conservation and normalization of the QM probability, the computation of the QM expectation values, properties of stationary states, and behavior at nodes. Several
ways to obtain the classical limit within the Bohmian formalism are considered.
Then, mixed quantum/classical dynamics based on the Bohmian formalism is
derived and illustrated with an example involving a light and a heavy particle.
At this point, the Bohmian representation is used as a tool to couple the quantum and classical subsystems. The quantum subsystem can be evolved by either


Preface

xi

Bohmian or traditional techniques. The quantum/classical formulation starts
with the Ehrenfest approximation, which is the most straightforward and common quantum/classical approach. The Bohmian formulation of the Ehrenfest
approach is used to derive an alternative quantum/classical coupling scheme
that resolves the so-called quantum backreaction problem, also known as the
trajectory branching problem. The partial hydrodynamic moment approach to
coupling classical and quantum systems is outlined. The hydrodynamic moments provide a connection between the Bohmian and phase-space descriptions of quantum mechanics. The penultimate section of this tutorial describes
approaches based on independent Bohmian trajectories. It includes the derivative propagation method, the stability approach, and the Bohmian trajectories
with complex action. Truncation of these hierarchies at the second order reveals connection to other semiclassical methods. Next, the focus shifts toward
Bohmian dynamics with globally approximated quantum potentials. Separate
subsections are devoted to the global energy-conserving approximation for the
nonclassical momentum, approximations on subspaces and spatial domains,
and nonadiabatic dynamics. Each approach is first introduced at the formal
theoretical level, and then, it is illustrated by an example. The final section
deals with computational issues, including numerical stability, error cancellation, dynamics linearization, and long-time behavior. The numerical problems
are motivated and illustrated by considering specific quantum phenomena, such
as zero-point energy and tunneling. The review concludes with a summary of
the semiclassical and quantum/classical approaches inspired by the Bohmian
formulation of quantum mechanics. The three appendices prove the quantum
density conservation, introduce quantum trajectories in arbitrary coordinates,

and explain optimization of simulation parameters in many dimensions.
The final chapter by Dr. Donald B. Boyd is an overview of career opportunities in computational chemistry. It was written in part to examine this aspect of
our history in computational chemistry but also as an aid for students and their
advisors who are now deciding whether they should enter this particular workforce. In addition to presenting trends in employment, the author provides data
on the types of computational chemistry expertise that have been most helpful
for securing employment. After an introduction, Dr. Boyd describes how, in the
early days (1960s–1970s), computational scientists had meager support and
poor equipment with which to work; moreover, there was abundant skepticism
in those days that computing could become a credible partner with experiment.
Those hard-fought efforts in computational chemistry allowed it to stand on
an equal footing with experiment, and accordingly, there was a commensurate
spate of hiring in that field. Dr. Boyd provides a dataset of jobs available from
1983 to 2008 and then provides a detailed assessment of the kinds of jobs
they were (e.g., tenure-track positions, nontenured academic staff positions,
positions at software or hardware companies, and other such positions). He
further elaborates on the specific type of expertise employers were seeking at
different periods in time, tabulating for us the rankings of desired skill sets like


xii

Preface

“working with databases,” “library design,” and “QSAR” as well as of more
broadly defined skills like “molecular modeling” and “computational chemistry.” The author dissects all of his data in an interesting way, showing the
ebbs and flows of employment over time and weaving his story into the fabric
of social and economic changes that occurred over the years, especially in the
pharmaceutical companies.
Finally, an appendix is provided by the editor that lists the names and
e-mail addresses of ∼2500 people who regularly publish in the field of computational molecular science (their postal addresses are available from the editor

upon request). Those people are not called computational chemists, although
many are. Instead, they are referred to as computational molecular scientists,
and as you will note, many are physicists, biologists, engineers, mathematicians,
materials scientists, and so on. What they all have in common, however, is that
they either develop or use computing tools to understand how nature works at
the atomic/molecular level.
Because computational molecular science is so important in today’s laboratory setting, we know that many experimentalists want to use the theories
and the associated software developed by computational scientists for their
own needs. The theoretical underpinnings and philosophical approaches used
by theorists and software developers can sometimes be buried in terse mathematics or hidden in other ways from the view of a traditional, black-boxusing bench chemist who has little time to become truly proficient as a theorist.
Yet, those experimentalists want very much to use computational tools to rationalize their results or, in some instances, to make predictions about what
next to do along their research trajectory. Because of this need, we started
the Reviews in Computational Chemistry book series that, in hindsight, could
just as well have been called “Tutorials in Computational Chemistry.”
Because the emphasis of the material covered in this book series is directed
toward the novice bench chemist wanting to learn about a particular method
to solve their problems (or for that matter the veteran computational chemist
needing to learn a new technique with a modicum of effort), we have again
asked our authors to provide a tutorial on the topic being reviewed. As before,
they have risen to the occasion and prepared pedagogically driven chapters with
the novice in mind.
Note that our publisher now makes our most recent volumes available
in an online form through Wiley InterScience; please consult the Web (http://
www.interscience.wiley.com/onlinebooks) or contact for
the latest information. For readers who appreciate the permanence and convenience of bound books, these will, of course, continue.
I thank the authors of this and previous volumes for their excellent
chapters.
Kenny B. Lipkowitz,
Washington, DC
April 2009

Contents
1.

Brittle Fracture: From Elasticity Theory to Atomistic Simulations
Stefano Giordano, Alessandro Mattoni, and Luciano Colombo

1

Introduction
Essential Continuum Elasticity Theory
Conceptual Layout
The Concept of Strain
The Concept of Stress
The Formal Structure of Elasticity Theory
Constitutive Equations
The Isotropic and Homogeneous Elastic Body
Governing Equations of Elasticity and Border Conditions
Elastic Energy
Microscopic Theory of Elasticity
Conceptual Layout
Triangular Lattice with Central Forces Only
Triangular Lattice with Two-Body and Three-Body
Interactions
Interatomic Potentials for Solid Mechanics
Atomic-Scale Stress
Linear Elastic Fracture Mechanics
Conceptual Layout
Stress Concentration

The Griffith Energy Criterion
Opening Modes and Stress Intensity Factors
Some Three-Dimensional Configurations
Elastic Behavior of Multi Fractured Solids
Atomistic View of Fracture
Atomistic Investigations on Brittle Fracture
Conceptual Layout
Griffith Criterion for Failure
Failure in Complex Systems
Stress Shielding at Crack-Tip

1
5
5
6
10
12
13
15
18
19
21
21
22
25
28
36
47
47
48

49
51
53
58
60
64
64
64
68
75

xiii


xiv

2.

3.

Contents
Acknowledgments
Appendix: Notation
References

78
78
78

Dissipative Particle Dynamics

Igor V. Pivkin, Bruce Caswell, and George Em Karniadakis

85

Introduction
Fundamentals of DPD
Mathematical Formulation
Units in DPD
Thermostat and Schmidt Number
Integration Algorithms
Boundary Conditions
Extensions of DPD
DPD with Energy Conservation
Fluid Particle Model
DPD for Two-Phase Flows
Other Extensions
Applications
Polymer Solutions and Melts
Binary Mixtures
Amphiphilic Systems
Red Cells in Microcirculation
Summary
References

85
86
86
88
90
92

94
97
97
98
98
99
99
100
100
102
103
104
104

Trajectory-Based Rare Event Simulations
Peter G. Bolhuis and Christoph Dellago

111

Introduction
Simulation of Rare Events
Rare Event Kinetics from Transition State Theory
The Reaction Coordinate Problem
Accelerating Dynamics
Trajectory-Based Methods
Outline of the Chapter
Transition State Theory
Statistical Mechanical Definitions
Rate Constants
Rate Constants from Transition State Theory

Variational TST
The Harmonic Approximation

111
111
113
114
116
116
117
118
118
119
121
126
126


Contents
Reactive Flux Methods
The Bennett–Chandler Procedure
The Effective Positive Flux
The Ruiz–Montero–Frenkel–Brey Method
Transition Path Sampling
Path Probability
Order Parameters
Sampling the Path Ensemble
Shooting Move
Sampling Efficiency
Biasing the Shooting Point

Aimless Shooting
Stochastic Dynamics Shooting Move
Shifting Move
Flexible Time Shooting
Which Shooting Algorithm to Choose?
The Initial Pathway
The Complete Path Sampling Algorithm
Enhancement of Sampling by Parallel
Tempering
Multiple-State TPS
Transition Path Sampling Applications
Computing Rates with Path Sampling
The Correlation Function Approach
Transition Interface Sampling
Partial Path Sampling
Replica Exchange TIS or Path Swapping
Forward Flux Sampling
Milestoning
Discrete Path Sampling
Minimizing the Action
Nudged Elastic Band
Action-Based Sampling
Transition Path Theory and the String Method
Identifying the Mechanism from the Path Ensemble
Reaction Coordinate and Committor
Transition State Ensemble and Committor
Distributions
Genetic Neural Networks
Maximum Likelihood Estimation
Conclusions and outlook

Acknowledgments
References

xv
128
128
134
135
137
137
139
141
142
147
147
149
149
152
154
156
157
158
158
160
161
161
161
164
176
179

184
185
186
189
189
191
193
196
196
197
199
200
202
202
202


xvi

Contents

4.

Understanding Metal/Metal Electrical Contact Conductance
from the Atomic to Continuum Scales
Douglas L. Irving

211

Introduction

Factors That Influence Contact Resistance
Surface Roughness
Local Heating
Intermixing and Interfacial Contamination
Dimensions of Contacting Asperities
Computational Considerations
Atomistic Methods
Calculating Conductance of Nanoscale Asperities
Hybrid Multiscale Methods
Characterization of Defected Atoms
Selected Case Studies
Conduction Through Metallic Nanowires
Multiscale Methods Applied to Metal/Metal Contacts
Concluding Remarks
Acknowledgments
References

211
212
213
215
223
224
225
226
230
231
233
235
235

241
247
247
247

Molecular Detailed Simulations of Lipid Bilayers
Max L. Berkowitz and James T. Kindt

253

Introduction
Membrane Simulation Methodology
Force Fields
Choice of the Ensemble
Verification of the Force Field
Monte Carlo Simulation of Lipid Bilayers
Detailed Simulations of Bilayers Containing Lipid Mixtures
Conclusions
References

253
254
254
256
258
264
266
281
281

Semiclassical Bohmian Dynamics
Sophya Garashchuk, Vitaly Rassolov, and Oleg Prezhdo

287

Introduction
The Formalism and Its Features
The Trajectory Formulation
Features of the Bohmian Formulation

287
289
289
292

5.

6.


Contents
¨
The Classical Limit of the Schrodinger
Equation and
the Semiclassical Regime of Bohmian Trajectories
Using Quantum Trajectories in Dynamics
of Chemical Systems
Bohmian Quantum-Classical Dynamics
Mean-Field Ehrenfest Quantum-Classical Dynamics
Quantum-Classical Coupling via Bohmian Particles

Numerical Illustration of the Bohmian
Quantum-Classical Dynamics
Properties of the Bohmian Quantum-Classical
Dynamics
Hybrid Bohmian Quantum-Classical Phase–Space Dynamics
The Independent Trajectory Methods
The Derivative Propagation Method
The Bohmian Trajectory Stability Approach. Calculation
of Energy Eigenvalues by Imaginary Time Propagation
Bohmian Mechanics with Complex Action
Dynamics with the Globally Approximated Quantum
Potential (AQP)
Global Energy-Conserving Approximation of
the Nonclassical Momentum
Approximation on Subspaces or Spatial Domains
Nonadiabatic Dynamics
Toward Reactive Dynamics in Condensed Phase
Stabilization of Dynamics by Balancing
Approximation Errors
Bound Dynamics with Tunneling
Conclusions
Acknowledgments
Appendix A: Conservation of Density within a Volume Element
Appendix B: Quantum Trajectories in Arbitrary Coordinates
Appendix C: Optimal Parameters of the Linearized Momentum
on Spatial Domains in Many Dimensions
References
7.

xvii

297
299
300
301
302
305
309
311
313
313
314
316
317
318
324
328
338
340
348
353
355
355
356
359
360

Prospects for Career Opportunities in Computational Chemistry
Donald B. Boyd

369

Introduction and Overview
Methodology and Results
Proficiencies in Demand
Analysis
An Aside: Economics 101

369
371
376
381
385


xviii

Contents
Prognosis
Acknowledgments
References

389
393
393

Appendix: List of Computational Molecular Scientists

395

Subject Index

473


Contributors
Max L. Berkowitz, Department of Chemistry, Venable and Kenan Laboratories,
The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3290
U.S.A. (Electronic mail: )
Peter Bolhuis, Computational Physics and Chemistry, van’t Hoff Institute for
Molecular Sciences, University of Amsterdam, Nieuwe Achtergracht 166, 1018
WV Amsterdam, The Netherlands (Electronic mail: )
Donald B. Boyd, Department of Chemistry and Chemical Biology, Indiana
University-Purdue University at Indianapolis, 402 North Blackford Street, Indianapolis, IN 46202-3274 U.S.A. (Electronic mail: )
Bruce Caswell, Division of Applied Mathematics, Brown University, 182
George Street, Providence, RI 02912 U.S.A. (Electronic mail: caswell@dam.
brown.edu)
Luciano Colombo, Department of Physics of the University of Cagliari and
CNR-IOM (SLACS Unit), Cittadella Universitaria, I-09042 Monserrato (Ca),
Italy (Electronic mail: )
Christoph Dellago, Faculty of Physics, University of Vienna, Boltzmanngasse
5, 1090 Vienna, Austria (Electronic mail: )
Sophya Garashchuk, Department of Chemistry and Biochemistry, University
of South Carolina, 631 Sumter Street, Columbia, SC 29208 U.S.A. (Electronic
mail: )
Stefano Giordano, Department of Physics of the University of Cagliari and
CNR-IOM (SLACS Unit), Cittadella Universitaria, I-09042 Monserrato (Ca),
Italy (Electronic mail: )

xix

xx

Contributors

Douglas L. Irving, Department of Materials Science and Engineering, North
Carolina State University, Campus Box 7907, Raleigh, NC 27695-7907 U.S.A.
(Electronic mail: )
James Kindt, Department of Chemistry, Emory University, 1515 Dickey Drive,
Atlanta, GA 30322 U.S.A. (Electronic mail: )
George Em Karniadakis, Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912 U.S.A. (Electronic mail:
)
Alessandro Mattoni, Department of Physics of the University of Cagliari and
CNR-IOM (SLACS Unit), Cittadella Universitaria, I-09042 Monserrato (Ca),
Italy (Electronic mail: )
Igor V. Pivkin, Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 8-139, Cambridge, MA 02139 U.S.A. (Electronic mail: )
Oleg Prezhdo, Department of Chemistry, University of Rochester, Rochester
NY 14627 U.S.A. (Electronic mail: )
Vitaly Rassolov, Department of Chemistry and Biochemistry, University of
South Carolina, 631 Sumter Street, Columbia, SC 29208 U.S.A. (Electronic
mail: )


Contributors to
Previous Volumes
Volume 1 (1990)
David Feller and Ernest R. Davidson, Basis Sets for Ab Initio Molecular Orbital
Calculations and Intermolecular Interactions.
James J. P. Stewart, Semiempirical Molecular Orbital Methods.

Clifford E. Dykstra, Joseph D. Augspurger, Bernard Kirtman, and David J.
Malik, Properties of Molecules by Direct Calculation.
Ernest L. Plummer, The Application of Quantitative Design Strategies in Pesticide Design.
Peter C. Jurs, Chemometrics and Multivariate Analysis in Analytical Chemistry.
Yvonne C. Martin, Mark G. Bures, and Peter Willett, Searching Databases of
Three-Dimensional Structures.
Paul G. Mezey, Molecular Surfaces.
Terry P. Lybrand, Computer Simulation of Biomolecular Systems Using Molecular Dynamics and Free Energy Perturbation Methods.
Donald B. Boyd, Aspects of Molecular Modeling.
Donald B. Boyd, Successes of Computer-Assisted Molecular Design.
Ernest R. Davidson, Perspectives on Ab Initio Calculations.

xxi


xxii

Contributors to Previous Volumes

Volume 2 (1991)
Andrew R. Leach, A Survey of Methods for Searching the Conformational
Space of Small and Medium-Sized Molecules.
John M. Troyer and Fred E. Cohen, Simplified Models for Understanding and
Predicting Protein Structure.
J. Phillip Bowen and Norman L. Allinger, Molecular Mechanics: The Art and
Science of Parameterization.
Uri Dinur and Arnold T. Hagler, New Approaches to Empirical Force Fields.
Steve Scheiner, Calculating the Properties of Hydrogen Bonds by Ab Initio
Methods.
Donald E. Williams, Net Atomic Charge and Multipole Models for the Ab

Initio Molecular Electric Potential.
Peter Politzer and Jane S. Murray, Molecular Electrostatic Potentials and Chemical Reactivity.
Michael C. Zerner, Semiempirical Molecular Orbital Methods.
Lowell H. Hall and Lemont B. Kier, The Molecular Connectivity Chi Indexes
and Kappa Shape Indexes in Structure-Property Modeling.
I. B. Bersuker and A. S. Dimoglo, The Electron-Topological Approach to the
QSAR Problem.
Donald B. Boyd, The Computational Chemistry Literature.

Volume 3 (1992)
Tamar Schlick, Optimization Methods in Computational Chemistry.
Harold A. Scheraga, Predicting Three-Dimensional Structures of Oligopeptides.
Andrew E. Torda and Wilfred F. van Gunsteren, Molecular Modeling Using
NMR Data.
David F. V. Lewis, Computer-Assisted Methods in the Evaluation of Chemical
Toxicity.


Contributors to Previous Volumes

xxiii

Volume 4 (1993)
Jerzy Cioslowski, Ab Initio Calculations on Large Molecules: Methodology and
Applications.
Michael L. McKee and Michael Page, Computing Reaction Pathways on Molecular Potential Energy Surfaces.
Robert M. Whitnell and Kent R. Wilson, Computational Molecular Dynamics
of Chemical Reactions in Solution.
Roger L. DeKock, Jeffry D. Madura, Frank Rioux, and Joseph Casanova, Computational Chemistry in the Undergraduate Curriculum.

Volume 5 (1994)
John D. Bolcer and Robert B. Hermann, The Development of Computational
Chemistry in the United States.
Rodney J. Bartlett and John F. Stanton, Applications of Post-Hartree–Fock
Methods: A Tutorial.
Steven M. Bachrach, Population Analysis and Electron Densities from Quantum Mechanics.
Jeffry D. Madura, Malcolm E. Davis, Michael K. Gilson, Rebecca C. Wade,
Brock A. Luty, and J. Andrew McCammon, Biological Applications of Electrostatic Calculations and Brownian Dynamics Simulations.
K. V. Damodaran and Kenneth M. Merz Jr., Computer Simulation of Lipid
Systems.
Jeffrey M. Blaney and J. Scott Dixon, Distance Geometry in Molecular Modeling.
Lisa M. Balbes, S. Wayne Mascarella, and Donald B. Boyd, A Perspective of
Modern Methods in Computer-Aided Drug Design.

Volume 6 (1995)
Christopher J. Cramer and Donald G. Truhlar, Continuum Solvation Models:
Classical and Quantum Mechanical Implementations.


xxiv

Contributors to Previous Volumes

Clark R. Landis, Daniel M. Root, and Thomas Cleveland, Molecular Mechanics Force Fields for Modeling Inorganic and Organometallic Compounds.
Vassilios Galiatsatos, Computational Methods for Modeling Polymers: An Introduction.
Rick A. Kendall, Robert J. Harrison, Rik J. Littlefield, and Martyn F. Guest,
High Performance Computing in Computational Chemistry: Methods and Machines.
Donald B. Boyd, Molecular Modeling Software in Use: Publication Trends.
Eiji Osawa and Kenny B. Lipkowitz, Appendix: Published Force Field Parameters.

Volume 7 (1996)
Geoffrey M. Downs and Peter Willett, Similarity Searching in Databases of
Chemical Structures.
Andrew C. Good and Jonathan S. Mason, Three-Dimensional Structure
Database Searches.
Jiali Gao, Methods and Applications of Combined Quantum Mechanical and
Molecular Mechanical Potentials.
Libero J. Bartolotti and Ken Flurchick, An Introduction to Density Functional
Theory.
Alain St-Amant, Density Functional Methods in Biomolecular Modeling.
Danya Yang and Arvi Rauk, The A Priori Calculation of Vibrational Circular
Dichroism Intensities.
Donald B. Boyd, Appendix: Compendium of Software for Molecular Modeling.

Volume 8 (1996)
Zdenek Slanina, Shyi-Long Lee, and Chin-hui Yu, Computations in Treating
Fullerenes and Carbon Aggregates.


Contributors to Previous Volumes

xxv

Gernot Frenking, Iris Antes, Marlis Böhme, Stefan Dapprich, Andreas W.
Ehlers, Volker Jonas, Arndt Neuhaus, Michael Otto, Ralf Stegmann, Achim
Veldkamp, and Sergei F. Vyboishchikov, Pseudopotential Calculations of Transition Metal Compounds: Scope and Limitations.
Thomas R. Cundari, Michael T. Benson, M. Leigh Lutz, and Shaun O. Sommerer, Effective Core Potential Approaches to the Chemistry of the Heavier
Elements.
Jan Almlöf and Odd Gropen, Relativistic Effects in Chemistry.
Donald B. Chesnut, The Ab Initio Computation of Nuclear Magnetic Resonance Chemical Shielding.

Volume 9 (1996)
James R. Damewood, Jr., Peptide Mimetic Design with the Aid of Computational Chemistry.
T. P. Straatsma, Free Energy by Molecular Simulation.
Robert J. Woods, The Application of Molecular Modeling Techniques to the
Determination of Oligosaccharide Solution Conformations.
Ingrid Pettersson and Tommy Liljefors, Molecular Mechanics Calculated
Conformational Energies of Organic Molecules: A Comparison of Force
Fields.
Gustavo A. Arteca, Molecular Shape Descriptors.

Volume 10 (1997)
Richard Judson, Genetic Algorithms and Their Use in Chemistry.
Eric C. Martin, David C. Spellmeyer, Roger E. Critchlow Jr., and Jeffrey
M. Blaney, Does Combinatorial Chemistry Obviate Computer-Aided Drug
Design?
Robert Q. Topper, Visualizing Molecular Phase Space: Nonstatistical Effects
in Reaction Dynamics.


xxvi

Contributors to Previous Volumes

Raima Larter and Kenneth Showalter, Computational Studies in Nonlinear
Dynamics.
Stephen J. Smith and Brian T. Sutcliffe, The Development of Computational
Chemistry in the United Kingdom.

Volume 11 (1997)

Mark A. Murcko, Recent Advances in Ligand Design Methods.
David E. Clark, Christopher W. Murray, and Jin Li, Current Issues in De Novo
Molecular Design.
Tudor I. Oprea and Chris L. Waller, Theoretical and Practical Aspects of ThreeDimensional Quantitative Structure–Activity Relationships.
Giovanni Greco, Ettore Novellino, and Yvonne Connolly Martin, Approaches
to Three-Dimensional Quantitative Structure–Activity Relationships.
Pierre-Alain Carrupt, Bernard Testa, and Patrick Gaillard, Computational Approaches to Lipophilicity: Methods and Applications.
Ganesan Ravishanker, Pascal Auffinger, David R. Langley, Bhyravabhotla Jayaram, Matthew A. Young, and David L. Beveridge, Treatment of Counterions
in Computer Simulations of DNA.
Donald B. Boyd, Appendix: Compendium of Software and Internet Tools for
Computational Chemistry.

Volume 12 (1998)
Hagai Meirovitch, Calculation of the Free Energy and the Entropy of Macromolecular Systems by Computer Simulation.
Ramzi Kutteh and T. P. Straatsma, Molecular Dynamics with General Holonomic Constraints and Application to Internal Coordinate Constraints.
John C. Shelley and Daniel R. Bérard, Computer Simulation of Water Physisorption at Metal–Water Interfaces.
Donald W. Brenner, Olga A. Shenderova, and Denis A. Areshkin, QuantumBased Analytic Interatomic Forces and Materials Simulation.