Combined Quantum Mechanical and Molecular Mechanical Methods

310 Pages·1998·28.35 MB·English

by  Jiali Gao and Mark A. Thompson (Eds.)

712
Combined Quantum
Mechanical and Molecular
Mechanical Methods
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October 2998 | doi: Mark A. Thompson, EDITOR
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In Combined Quantum Mechanical and Molecular Mechanical Methods; Gao, J., el al.;
ACS Symposium Series; American Chemical Society: Washington, DC, 1998.
Library of Congress Catalogingi­nP­ ublicatio n Data
Combined quantum mechanical and molecular mechanical methods / Jiali Gao,
Mark A. Thompson, editors.
p. cm—(ACS symposium series ; ISSN00976­ 156 ; 712)
"Developed from a symposium sponsored by the Division of Computers in
Chemistry at the 214th National Meeting of the American Chemical Society,
1 Las Vegas, Nevada, September 71­ 1, 1997."
cs.org 2.fw00 Includes bibliographical references and index.
a1
bs.07 ISBN 08­ 4123­ 590­ 2
p://pu1998- 1. Quantum chemistry—Congresses.
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6 on October 228, 1998 | doi: 5Q4D1.426'82—.A1dCc2613 1998 983­ 41C7I4P
7.7er
7.1mb The paper used in this publication meets the minimum requirements of American National Standard for
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PRINTED IN THE UNITED STATES OF AMERICA
In Combined Quantum Mechanical and Molecular Mechanical Methods; Gao, J., el al.;
ACS Symposium Series; American Chemical Society: Washington, DC, 1998.
Advisory Board
ACS Symposium Series
Mary E. Castellion Omkaram Nalamasu
AT&T Bell Laboratories
1
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bs.a071 University of Wisconsin at Madison Purdue University
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In Combined Quantum Mechanical and Molecular Mechanical Methods; Gao, J., el al.;
ACS Symposium Series; American Chemical Society: Washington, DC, 1998.
Foreword
THE ACS SYMPOSIUM SERIES was first published in 1974 to provide
a mechanism for publishing symposia quickly in book form. The pur­
pose of the series is to publish timely, comprehensive books devel­
1
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cs.2.f search. Occasionally, books are developed from symposia sponsored
bs.a071 by other organizations when the topic is of keen interest to the chem­
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6 on October 228, 1998 | doi: jWDecrhatiefotAnsn s, o aaafpn pcrdruh omlapepa,rt ineoarutnses l,cy ar riooepr vtispeg eraivenrreiae- lrp werrv eesipoeearwa rreeicdndh t irpnpor adcipouaermcr tstoeo rr aayfn- irdneca ahold arypaig cteifcnroesarp mlt aaranretec.v ei eaowdrd peraed­­.
17.7ber pers are included in the volumes. Verbatim reproductions of previ­
5.157.Decem ously published papers are not accepted.
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In Combined Quantum Mechanical and Molecular Mechanical Methods; Gao, J., el al.;
ACS Symposium Series; American Chemical Society: Washington, DC, 1998.
Preface
Quantum mechanical studies of chemical reactions in solution and in enzymes
present a great challenge in computational chemistry because of the enormous
size and complexity of these systems. Although molecular mechanical force
1
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6 on 28, 1 chanical and Molecular Mechanical Methods. Speakers from Australia, Canada,
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by 9ate: verse topics covered by this volume.
d D This book is divided into four sections, featuring a broad range of recent
ownloadeblication mone tmhoedthooldosg yf odre vtheelo tprmeaetnmtse natn odf nthoev ecl oanpnpelcictiaotnio nbse.t wCeehna pqteurasn t1u tmh roaungdh c l6a sfsoiccuasl
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dynamics. Chapters 11 through 14 feature models for the study of solvation ef­
fects. Chapters 15 through 19 highlight applications to biochemical problems.
In all, this book provides a self-contained introduction to the state of the art in
combined quantum mechanical and molecular mechanical (QM/MM) methods.
We take this opportunity to thank all of the participants of our symposium
and we look forward to future gatherings on this subject.
This book was developed from a symposium sponsored by the Division of
ix
In Combined Quantum Mechanical and Molecular Mechanical Methods; Gao, J., el al.;
ACS Symposium Series; American Chemical Society: Washington, DC, 1998.
Computers in Chemistry at the 214th National Meeting of the American Chemi­
cal Society, Las Vegas, Nevada, September 71­ 1 , 1997.
Jiali Gao
Department of Chemistry
State University of New York at Buffalo
Buffalo, NY 14260
MARK A. THOMPSON
WRQ Inc.
1 1500 Dexter Avenue North
cs.org 2.pr00 Seattle, WA 98109
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In Combined Quantum Mechanical and Molecular Mechanical Methods; Gao, J., el al.;
ACS Symposium Series; American Chemical Society: Washington, DC, 1998.
Chapter 1
Quantum MechanicalM­ olecula r Mechanical
Coupled Potentials
Kenneth M. Merz, Jr.
152 Davey Laboratory, Department of Chemistry, The Pennsylvania State
University, University Park, PA 16802
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d bDat future.(2) A greater appreciation of how protein dynamics affects protein structure
den and function has lead to extensive NMR(3) and molecular dynamics (MD)
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catalytic cycle as well as by identifying appropriate catalytic residues within a
protein using site-directed mutagenesis as well as chemical modification.(7)
Furthermore, detailed kinetic analyses provide insights into the energetic costs
associated with the conversion of an enzyme substrate into its corresponding
product(s).(7) Even with the tremendous progress that has been made in
understanding protein structure, function and dynamics using a plethora of
techniques it is safe to say that we still do not have a full appreciation of how
protein structure and dynamics affects function. Indeed, in order to effectively
accomplish this we need methodologies that can structurally and energetically
identify transient intermediates and transition states along a catalytic pathway while
simultaneously accounting for the dynamics of the surrounding environment in a
realistic manner.
Theoretical chemistry techniques - especially quantum mechanics (QM) based
methods can in principle be applied to address these issues at very high accuracy if
only the appropriate calculations could be carried out.(8) Thus, QM methods can
2 ©1998 American Chemical Society
In Combined Quantum Mechanical and Molecular Mechanical Methods; Gao, J., el al.;
ACS Symposium Series; American Chemical Society: Washington, DC, 1998.
3
accurately represent the electronic and structural changes that occur along a reaction
coordinate and, thereby, provide insights into the structure, energetics and dynamics
of a given reactive process. However, in practice we are a long way from carrying
out lengthy MD simulations (or, indeed, any other type of QM based simulations)
using an accurate and purelya  b initio Hamiltonian on a system as large as a typical
protein in aqueous solution. This is due to the fact that these methods scale formally
as O(N^) (where is the number of basis functions) or greater, making them
computationally intractable for large systems even on modern supercomputers.
Thus, approximations have been made over the years to model a protein and its
associated environment.(4,5) In particular, classical representations, (which
formally scale computationally as 0(M2) (where M is the number of atoms), which
were originally applied to organic molecules(9-ll) have found significant utility in
the study of the structure and dynamics of biomolecules.(4,5) However, classical
models, while particularly well suited to studying protein structure and dynamics,
by their very nature are not able to realistically represent activated
1 processes.(4,5,12) Thus, it has been clear for a number of years that a combination
org h00 of the accuracy and bond-breaking ability of quantum mechanics with the speed and
cs.2.c ability to model solvent and protein structure of classical methods (a.k.a., molecular
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completely quantum mechanical, HQM (QM in Scheme 1), the purely molecular
mechanical interactions, HMM (MM in Scheme 1) and the interactions between the
QM and M M portions of the system, HQM/MM (indicated by the arrow in Scheme
1).
Heff  = HQM  + HMM  + HQM/MM  (2) 
The total energy of the system can likewise be divided into three component parts.
^eff~   EQM +E    + E (3)
MM QM/MM
In Combined Quantum Mechanical and Molecular Mechanical Methods; Gao, J., el al.;
ACS Symposium Series; American Chemical Society: Washington, DC, 1998.
4
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In Combined Quantum Mechanical and Molecular Mechanical Methods; Gao, J., el al.;
ACS Symposium Series; American Chemical Society: Washington, DC, 1998.
5
These component energies can be obtained by solving either the Roothaan-Hall
equations(8) (associated with Hartree-Fock based methodologies) or the Kohn-
Sham equations(15) (associated with density functional theory based
methodologies) for H ff (equation 1). Another way to express the total energy of
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the system is as the expectation value of Heff. The purely M M term can be
removed from the integral because it is independent of the electronic positions.
Thus, the total energy of the system can be given as,
  = ( * +  H \¥) +E  (4)
mim m
In equation 4, HQM is the Hamiltonian given by either semiempirical(16), Hartree-
Fock(8) or density functional theory(15), while EMM is an energy obtained using a
classical force field of some type (see below for more discussion regarding the
choices).(9,l 1,17-19) The key remaining term is HQM/MM- This term represents the
1 interaction of the M M atom "cores" with the electron cloud of the Q M atoms, as
org h00 well as the repulsion between the M M and Q M atomic cores. Finally, it was found
cs.2.c to be necessary to add a Lennard-Jones term to the Q M atoms to obtain good
bs.a071 interaction energies as well as good geometries for intermolecular interactions.(20)
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adeon procedure and does not affect the electronic distribution of the system directly, but
ownloblicati tdhoee rse asfufletcint gth eel egcetroomneictr yen oerfg tyh eo nsy ssutebmse qthureonutg ShC tFh ec yccolmesp. uted gradients and, hence,
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clearly ahead of its time as this approach was not widely used again until the late
1980's and early 1990's when it was re-examined by several research groups using a
number of different quantum mechanical methods, including: semiempirical (S)(20-
26), density functional theory (DFT)(27-30) and Hartree-Fock (EF)ab  initio 
methods.(31-33) Warshel has also pioneered an alternative strategy to study
reactive processes in solution and in enzymes which he has termed the empirical
valence bond (EVB) method.(12) This approach has been applied to a wide range of
problems(12) and has some advantages and disadvantages relative to QM/MM
methods that use molecular orbital or density functional Q M methodologies.(12)
We will not comment on this approach further, but the interested reader is directed
towards Warshel's recent book on this subject.(12) In addition to the various
potentials a number of different sampling techniques have been used in conjunction
In Combined Quantum Mechanical and Molecular Mechanical Methods; Gao, J., el al.;
ACS Symposium Series; American Chemical Society: Washington, DC, 1998.