computational medicinal chemistry for drug discovery - p. bultinck, et al., (marcel dekker, 2004)

Computational
Medicinal
Chemistry
for
Drug
Discovery
edited
by
Patrick Bultinck
Ghent University
Ghent, Belgium
Hans De Winter
Wi
If
ried Langenaeker
Johnson
&
Johnson Pharmaceutical Research and Development
A
Division
of
Janssen Pharmaceutica
N.
V:
Beerse, Belgium
Jan
P.
Tollenaere
Utrecht University
Utrecht, The Netherlands

MARCEL
MARCEL
DEKKER,
INC.
m
DEKKER
NEW
YORK:
BASEL
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Preface
Computational approaches to medicinal chemical problems have developed rapidly
over the last 40 years or so. In the late 1950s and early 1960s, gigantic mainframe
computers were used to perform simple HMO (Huckel molec ular orbital) and PPP
(Pariser-Parr-Pople) calculations on aromatic compounds such as substituted ben-
zenes, naphthalenes, anthracenes, etc., to explain their UV spectral properties. In the
early 1960s, stand-alone programs became available to simulate NMR spectra. With
the advent of Hansch-type analysis of structure-activity relationships (SAR), com-
puters were used to solve multiple regression equations. In 1963 the Quantum Chem -
istry Program Exchange (QCPE) started distribution of programs such as Extended
Huckel Theory (EHT) and early versions of Complete Neglect of Differential Overlap
(CNDO), which to the delight of theoretical chemists eventually made it possible to
perform conformational analyses on nonaromatic molecules. However scientifically
exciting, all these computations involved quite some expertise in mastering the
computer’s operating system as well as manual labor punching cards and hauling
boxes of punched cards to and from the mainframe computer center. Of greater
concern, however, was the fact that real-life molecules such as those routinely
synthesized by medicinal chemists were most often too big to be treated theoretically
using the computers of those days. This resulted in a situation in which the
contribution of a theoretical chemist was, at best, politely tolerated but in general

considered irrelevant to the work of a classically trained medicinal chemist.
All this changed, although slowly, in the 1970s, with improvements in the speed,
manageability, and availability of computer technology. A considerable impediment
in the late 1970s and early 1980s was the lack of proper visualization of the theoretical
results. Indeed, it was discouraging to discuss theoretical results with a suspicious
chemist on the basis of pages and pages of computer output. This obstacle was
dramatically removed with the advent of graphics computers able to depict HOMOs,
LUMOs, MEPs (molecular electrostatic potential), dipole moment vectors, etc,
superimposed on a 3D repres entation of the molecule(s) of interest. By the early
1990s graphics workstations linked to multiprocessor machines were power ful enough
to perform reliable calculations on real-life molecules in a time frame sufficiently small
to keep the interest of the medic inal chemist alive and to show the results in an
understandable and appealing way.
iii
Nowadays, one can safely state that the computational chemist has become a
respectable member of a drug (ligand) design team, standing on an equal footing with
the synthetic chemists, pharmacologists, and others at the beginning of the long and
arduous path of ligand creation aimed toward bringing a medicine to the market.
The title of this book refers to two topics, namely, Computational Medicinal
Chemistry and Drug Design. It unites these topics by giving an overview of the main
methods at the disposal of the computational chemist and to highlight some
applications of these methods in drug design. Although drug and ligand appear to
be synonymous in this volume, they most definitely are not. Notwithstanding ‘‘drug
design’’ in the title, this volume essentially deals with methods that can be applied to
molecules that may possibly become drugs. Whether, when, and how a molecule may
acquire the status of a drug or a medicine is investigated and decided by, among others,
toxicologists, pharmacists, and clinicians and is therefore explicitly outside the scope
of this volume.
Similarly, a choice had to be made regarding the topics covered in this volume.
For example, molecular dynamics (MD) based free-energy changes in solution calcu-

lations are not treated, because these are not yet a day-to-day practice in actual ligand
design due to the very high computational demands for the long MD simulations
required.
This book starts with seven chapters devoted to methods for the computation of
molecular structure: molecular mechani cs, semiempirical methods, wave fun ction–
based quantum chemistry, density-functiona l theory methods, hybrid methods, an
assessment of the accuracy and applicability of these methods, and fina lly 3D structure
generation and conformational analysis.
In the next chapters, one or several of those formalisms are used to describe some
aspects of molecular behavior toward other molecules in terms of properties such as
electrostatic potential, nonbonded interactions, behavior in solvents, reactivity and
behavior during interaction with other molecules, and finally similarity on the basis of
nonquantum and quantum properties.
Before addressing some aspects of, broadly speaking, ligand-receptor interac-
tions, a critical evaluation of protein structure determination was felt in order. This is
then followed by accounts of docking and scoring, pharmacophore identification 3D
searching, substructure searching, and molecular descriptors.
The following chapters address 2D and 3D models using classical molecular and
quantum-based descriptors and models derived from data mining techniques as well as
library design.
Given the increasing demand for enantiomerically pure drugs, vibrational
circular dichroism (VCD) will become a standard techn ique in the medicinal chemical
laboratory. The VCD chapter illustrates the use of high-level quantum chemical
calculations and conformational analysis discussed in previous chapters. Similarly, the
chapter on neuraminidase highlights the combined use of pro tein crystallography,
ligand receptor interaction theory, and computational methods. Finally, this volume
ends with a concise glossary.
Thanks are due to Anita Lekhwani, who initially suggested this project, and to
Lila Harris, who helped in realizing the project. Each individual chapter was reviewed
by at least three editors. During monthly editor ial meetings reviews were critically

compared.
Prefaceiv
The editors are grateful to those authors who strictly adhered to the time
schedule.
Finally, it is hoped that this volume may give the reader a useful overview of the
main computational techniques that are currently in use on a day-to-day basis in
modern ligand (drug) design, both in academia and in an industrial pharmaceutical
environment.
Johnson & Johnson Pharmaceutical Research and Development–Beerse (Bel-
gium) is gratefully acknowledged for financial and logistic support for this project.
Patrick Bultinck
Hans De Winter
Wilfried Langenaeker
Jan P. Tollenaere
Preface v

Contents
Preface iii
Contributors xi
1. Molecular Mechanics and Comparison of Force Fields 1
Tommy Liljefors, Klaus Gundertofte, Per-Ola Norrby, and Ingrid
Pettersson
2. Semiempirical Methods 29
Thomas Bredow
3. Wave Function–Based Quantum Chemistry 57
Trygve Helgaker, Poul Jørgensen, Jeppe Olsen, and Wim Klopper
4. Density-Functional Theory 89
Paul W. Ayers and Weitao Yang
5. Hybrid Quantum Mechanical/Mol ecular Mechanical Methods 119
Jean-Louis Rivail

6. Accuracy and Applicability of Quantum Chemical Methods in
Computational Medicinal Chemistry 133
Christopher J. Barden and Henry F. Schaefer III
7. 3D Structure Generation and Conformational Searching 151
Jens Sadowski, Christof H. Schwab, and Johann Gasteiger
8. Molecular Electrostatic Potentials 213
Peter Politzer and Jane S. Murray
9. Nonbonded Interactions 235
Steve Scheiner
vii
10. Solvent Simulation 259
Peter L. Cummins, Andrey A. Bliznyuk, and Jill E. Gready
11. Reactivity Descriptors 295
P. K. Chattaraj, S. Nath, and B. Maiti
12. Transition States and Transition Structures 323
Orlando Acevedo and Jeffrey D. Evanseck
13. Molecular Similarity, Quantum Topology, and Shape 345
Paul G. Mezey
14. Quantum Similarity and Quantitative Structure–Activity
Relationships 365
Ramon Carbo
´
-Dorca and Xavier Girone
´
s
15. Protein Structures: What Good Is Beauty If It Cannot
Be Seen? 387
Sander B. Nabuurs, Chris A. E. M. Spr onk, Elmar Krieger, Rob
W. W. Hooft, and Gert Vriend
16. Docking and Scoring 405

Ingo Muegge and Istvan Enyedy
17. Pharmacophore Discovery: A Critical Review 437
John H. Van Drie
18. Use of 3D Pharmacophore Models in 3D Database Searching 461
Re
´
my D. Hoffmann, Sonja Meddeb, and Thierry Langer
19. Substructure and Maximal Common Substructure Searching 483
Lingran Chen
20. Molecular Descriptors 515
Geoff M. Downs
21. 2D QSAR Models: Hansch and Free–Wilson Analyses 539
Hugo Kubinyi
22. 3D QSAR Modeling in Drug Design 571
Tudor I. Oprea
23. Computational Aspects of Library Design and Combinatorial
Chemistry 617
Valerie J. Gillet
24. Quantum-Chemical Descriptors in QSA R 641
Mati Karelson
Contentsviii
25. Data Mining Applications in Drug Discovery 669
Michael F. M. Engels and Theo H. Reijmers
26. Vibrational Circular Dichroism Spectroscopy: A New Tool for
the Sterochemical Characterization of Chiral Molecul es 699
Philip J. Stephens
27. Sialidases: Targets for Rational Drug Design 727
Jeffrey C. Dyason, Jennifer C. Wilson, and Mark von Itzstein
Glossary Ed E. Moret and Jan P. Tollenaere 747
Index 769

Contents ix

Contributors
Orlando Acevedo Center for Computational Studies and Department of Chem istry
and Biochemistry, Duquesne University, Pittsburgh, Pennsylvania, U.S.A.
Paul W. Ayers Department of Chemistry, McMaster University, Hamilton,
Ontario, Canada
Christopher J. Barden Departmen t of Chemistry, Dalhousie University, Halifax,
Nova Scotia, Canada
John M. Barnard Barnard Chemical Information Ltd., Stannington, Sheffield, S.
Yorks, United Kingdom
Andrey A. Bliznynk ANU Supercomputer Facility, Australian National University,
Canberra, Australian Capital Territory, Australia
Thomas Bredow Theoretical Chemistry, University of Hannover, Hannover, Ger-
many
Ramon Carbo
´
-Dorca Institute of Computational Chemistry, University of Girona,
Campus Montilivi, Catalonia, Spain
P. K. Chattaraj Department of Chemistry, Indian Institute of Technology, Khar-
agpur, India
Lingran Chen MDL Information Systems, Inc., San Leandro, California, U.S.A.
Peter L. Cummins Division of Molecular Bioscience, John Curtin School of Medical
Research, Australian National University, Canberra, Australian Capital Territory,
Australia
Geoff M. Downs Barnard Chemical Information Ltd., Stannington, Sheffield,
United Kingdom
xi
Jeffrey C. Dyason Griffith University (Gold Coast), Bundall, Queensland, Australia
Michael F. M. Engels Johnson & Johnson Pharmaceutical Research and Develop-

ment, A Division of Janssen Pharmaceutica N.V., Beerse, Belgium
Istvan Enyedy Bayer Research Center, West Haven, Connecticut, U.S.A.
Jeffrey D. Evanseck Department of Chemistry and Biochemistry, Duquesne Uni-
versity, Pittsburgh, Pennsylvania, U.S.A.
Johann Gasteiger Computer-Chemie-Centrum, Institute for Organic Chemistry,
Erlangen-Nuernberg University, Erlangen, Germany
Valerie J. Gillet Department of Information Studies, University of Sheffield,
Sheffield, United Kingdom
Xavier Girone
´
s Institute of Computational Chemistry, University of Girona, Cam-
pus Montilivi, Catalonia, Spain
Jill E. Gready Division of Molecular Bioscience, John Curtin School of Medical
Research, Australian National University, Canberra, Australian Capital Territory,
Australia
Klaus Gundertofte Department of Computational Chemistry, H. Lundbeck A/S
Copenhagen-Valby, Denmark
Trygve Helgaker Department of Chemistry, University of Oslo, Oslo, Norway
Re
´
my D. Hoffmann Accelrys SARL, Parc Club Orsay Universite
´
, Orsay, France
Rob W. W. Hooft Bruker Nonius BV, Delft, The Netherlands
Mark von Itzstein Institute for Glycomics, Griffith University (Gold Coast Campus),
Queensland, Australia
Poul Jørgensen Department of Chemistry, University of Aarhus, Aarhus, Denmark
Mati Karelson Centre of Strategic Competence, University of Tartu, Tartu, Estonia
Wim Klopper Institute of Physical Chemistry, University of Karlsruhe (TH), Karls-
ruhe, Germany

Elmar Krieger Centre for Molecular and Biomolecular Informatics, University of
Nijmegen, Nijmegen, The Netherlands
Hugo Kubinyi Molecular Modelling and Combinatorial Chemistry, BASF AG,
Ludwigshafen, Germany (retired)
Contributorsxii
Thierry Langer Department of Pharmaceutical Chemistry, University of Innsbruck,
Innsbruck, Austria
Tommy Liljefors Department of Medicinal Chemistry, The Danish University of
Pharmaceutical Sciences, Copenhagen, Denmark
B. Maiti Department of Chemistry, Indian Institute of Technology, Kharagpur,
India
Sonja Meddeb Accelrys SARL, Parc Club Orsay Universite
´
, Orsay, France
Paul G. Mezey Scientific Modeling and Simulation Laboratory, Memorial Univer-
sity of Newfoundland, St. John’s, Newfoundland, Canada
Ed E. Moret Department of Medicinal Chemistry, Utrecht Institute for Pharma-
ceutical Sciences, Utrecht University, Utrecht, The Netherlands
Ingo Muegge Boehringer Ingelheim Pharmaceuticals, Inc., Ridgefield, Connecticut,
U.S.A.
Jane S. Murray Department of Chemistry, University of New Orleans, New
Orleans, Louisiana, U.S.A.
Sander B. Nabuurs Centre for Molecular and Biomolecular Informatics, University
of Nijmegen, Nijmegen, The Netherlands
S. Nath Chemistry Department, Indian Institute of Technology, Kharagpur, India
Per-Ola Norrby Department of Chemistry, Technical University of Denmark,
Lyngby, Denmark
Jeppe Olsen Department of Chemistry, University of Aarhus, Aarhus, Denmark
Tudor I. Oprea EST Chemical Computing, AstraZeneca R&D Mo
¨

lndal, Mo
¨
lndal,
Sweden
Ingrid Pettersson Novo Nordisk A/S, Ma
˚
løv, Denmark
Peter Politzer Department of Chemistry, University of New Orleans, New Orleans,
Louisiana, U.S.A.
Theo H. Reijmers Johnson & Johnson Pharmaceutical Research and Development,
A Division of Janssen Pharmaceutica N.V., Beerse, Belgium
Jean-Louis Rivail Groupe de Chimie the
´
orique, ‘‘Structure et Re
´
activite
´
des Sys-
te
`
mes Mole
´
culaires Complexes,’’ Henri Poincare
´
University, Nancy-Vandoeuvre,
France
Contributors xiii
Jens Sadowski Structural Chemistry Laboratory, AstraZeneca R&D Mo
¨
lndal,

Mo
¨
lndal, Sweden
Henry F. Schaefer III Center for Computational Quantum Chemistry, University of
Georgia, Athens, Georgia, U.S.A.
Steve Scheiner Department of Chemistry and Biochemistry, Utah State University,
Logan, Utah, U.S.A.
Christof H. Schwab Molecular Networks GmBH, Erlangen, Germany
Chris A. E. M. Spronk Centre for Molecular and Biomolecular Informatics, Uni-
versity of Nijmegen, Nijmegen, The Netherlands
Philip J. Stephens Department of Chemistry, University of Southern California, Los
Angeles, California, U.S.A.
Jan P. Tollenaere Department of Medicinal Chemistry, Utrecht Institute for Phar-
maceutical Sciences, Utrecht University, Utrecht, The Netherlands
John H. Van Drie Vertex Pharmaceuticals, Cambridge, Massachusetts, U.S.A.
Gert Vriend Centre for Molecular and Biomolecular Inform atics, University of
Nijmegen, Nijmegen, The Netherlands
Jennifer C. Wilson Griffith University (Gold Coast), Bundall, Queensland, Australia
Weitao Yang Department of Chemistry, Duke University, Durham, North Caro-
lina, U.S.A.
Contributorsxiv
1
Molecular Mechanics and Comparison
of Force Fields
TOMMY LILJEFORS
The Danish University of Pharmaceutical Sciences, Copenhagen, Denmark
KLAUS GUNDERTOFTE
H. Lundbeck A/S, Copenhagen-Valby, Denmark
PER-OLA NORRBY
Technical University of Denmark, Lyngby, Denmark

INGRID PETTERSSON
Novo Nordisk A/S, Ma
˚
løv, Denmark
1. INTRODUCTION
Molecular mechanics (force field) calculation is the most commonly used type of cal-
culation in computational medicinal chemistry, and a large number of different force
fields have been developed over the years. The results of a molecular mechanics (MM)
calculation are highly dependent on the functional forms of the potential energy
functions of the force field and of the quality of their parameterization. Thus in order
to obtain reliable computational results it is crucial that the merits and limitations
of the various available force fields are taken into account. In this chapter, the basic
principles of force-field calculations are reviewed, and a comparison of calculated and
experimental conformational energies for a wide range of commonly used force fields
is presented. As quantum mechanical (QM) methods have undergone a rapid develop-
ment in the last decade, we have also undertaken a comparison of these force fields
with some commonly employed QM methods. The chapter also includes a review
of force fields with respect to their abilities to calculate intermolecular interactions.
1
Finally, as solvent effects play an impor tant role in computational medicinal chem-
istry, a discussion of force-field calculations including solvation is also included in
this chapter.
2. BASIC PRINCIPLES OF MOLECULAR MECHANICS
Empirical force-field methodology is based on classical mechanics and on the
fundamental assumption that the total ‘‘ steric’’ energy of a structure can be expressed
as a sum of contributions from many interaction types [1–3]. Another important
assumption is that the force field and its parameters, which have been determined from
a set of molecules, are transferable to other molecules.
Molecular mechanics methods are several orders of magnitude faster than QM
methods, and for problems where MM methods are well defined, the accuracy may be

as good as or better than QM calculations at a relatively high level (see Sec. 4). The
main drawback of MM is that the method and the quality of the calculations are
extremely dependent on empirical parameters. Such parameters are generally deter-
mined by experimental studies or high-level ab initio calculations, and the parameter-
ization is often based on a small number of model systems.
2.1. Atom Types, Bonds, and Angles
The fundamental unit o f most force fie lds i s the atom type, determining what
parameters to apply for all interactions involving the same constituent atom types.
The various interaction types include bond lengths, angles, distances, etc. (see Fig. 1).
In theory, every combination of atom types needs to be specifically parameterized. In
practice, however, only the relevant combinations of these will ever be determined. For
Figure 1 Definition of basic parameters in force fields. Bond lengths (l ), angles (h), torsion
angles (x), and nonbonded distances (r) are exemplified in n-propanol.
Liljefors et al.2
example, force fields with a carbonyl oxygen atom type will include bonds from this to
carbon, but rarely to anything else. Thus the number of bond types in most force fields
is only a few times higher than the number of atom types. In most force fields the
parameters are further differentiated, based on the particular structural surroundings
such as bond orders or the like.
Each bond in a structure will contribute a stretch term to the total energy. Bonds
are normally described as harmonic bonds, and like springs, are characterized by a
preferred length. The resistance to change from the optimum value is then defined by a
‘‘force constant,’’ and each bond type is thus described by at least two parameters and
the energies calculated by Hooke’s law (Eq. (1)). Here the reference bond length is l
0
(Fig. 1).
E
s
¼ k
s

ðl À l
0
Þ
2
ð1Þ
Hooke’s law can represent the energy increase on small distortions from the reference
value and is applied in the CHARMm force field [4] and is default in the Dreiding [5]
and UFF force fields [6]. However, for larger distortions, the energy of a true bond is
normally represented by a Morse function (Eq. (2)) that can describe the process of
dissociation energy correctly. In CVFF [7], a Morse potential is default, but a Hooke
potential may be applied. The Morse potential requires one more parameter and,
therefore, a wider range of reference data is needed for the parameterization. The
potential is given in Eq. (2), where D is the dissociation energy and a is a parameter
which, together with D, determines the curvature at the minimum.
E
s
¼ Dð1 À e
ÀaðlÀl
0
Þ
Þ
2
ð2Þ
This representation is normally not needed for organic structures of a reasonable input
quality with small distortions and the difference between the two functions is then
negligible. A harmonic potential or a higher-order derivative of such is normally used
in the initial optimization phase. Additional accuracy gained from a well-determined
Morse fun ction, at the cost of increase in complexity, may be important when studying
more complex systems.
Modified Hooke’s law corrected with cubic (as in the MM2-based force fields [8])

and further extensions to quartic terms (as in MM3 [9], CFF [10], and MMFF [11]
force fields; see Eq. (3) [9]) or other expansions [12] have been developed to mimic the
Morse potential and are used to speed up convergence in very distorted starting
geometries, while keeping a proper description of the potential energy.
E
s
¼ k
s
ðl À l
0
Þ
2
½1 þ c
s
ðl À l
0
Þþq
s
ðl À lÞ
2
ð3Þ
The simplest approach to obta ining optimized bond angles close to the reference value
h
0
(Fig. 1) is to introduce a quadratic energy penalty, the harmonic approximation,
similar to the representation of bond energies (Eq. (4)), although some methods use
nonbonded interactions to model angle forces [3].
E
b
¼ k

b
ðh À h
0
Þ
2
ð4Þ
This simple representation is used in, e.g., the CVFF and CHARMm force fields. As
for bonds, two parameters are needed, a reference angle and a force constant, and only
a fraction of all the possible combinations of atom types are represented in real
chemical structures. In certain cases, generalized parameters are used because of lack
Molecular Mechanics and Comparison of Force Fields 3
of accurate reference data, e.g., using a reference value close to 109.5j for all unknown
angles around an sp3 carbon. To avoid losing the convergence properties for very
large distortions, expansions to higher order terms, similar to those in bond energies
discussed above, are applied in most force fields. Expansions to the power of four
(MMFF) and even six (MM2 and MM3) are used.
Special care has to be taken in the representations of angles of 180j, which are
wrongly represented as a cusp. To correct this problem with the slope going to zero,
trigonometric functions as exemplified in Eq. (5) can be applied [13–15]. Close to a
maximum this correction may lead to convergence problems, but this price is worth
paying in most cases.
E
b
¼ k½1 þ cosðnh þ wÞ ð5Þ
2.2. Nonbonded Interactions
Interactions between atoms that are not transmitted through bonds are referred to as
nonbonded interactions. Most interactions are between centers of atoms, while some
force fields use through-space interactions between points that are not centered on
nuclei, such as lone pairs and bond-center dipoles. Interactions between atoms sepa-
rated by only one or two bonds are normally not calculated, whereas atoms in the 1,

4-position with three intervening bonds interact both via torsional and nonbonded
potentials. Thus these interactions become partially dependent. Introduction of scal-
able parameters for nonbonded 1,4-interactions can reduce this interdependence.
2.3. Electrostatic Interactions
Calculation of electrostatic interaction energies can be done simply by using Cou-
lomb’s law, Eq. (6), providing charges q centered on each nucleus.
E
el
¼
q
i
q
j
er
ð6Þ
Most force fields except those derived from the native MM2 and MM3 implemen-
tations apply the Coulomb potentials. Charge assignment can be done using a variety
of schemes, including fragment matching [16] and contributions through bonds [10,
17]. Furthermore, there is currently an increasing interest in polarizable force fields
incorporating electrostatics dependent on the surroundings [18]. A major problem
lies in the fact that atomic charges are statistical properties rather than observable
items, and it is not always possible to find one set of charges that will reproduce all
properties of interest. For most major force fields, one charge determination scheme
has been adopted and used in the further development of new parameter sets securing
internal consistency. Quantum mechanical calculations are generally a good source
of data for electrostatic parameters and derived charges. Inclusion of the dielectric
constant e in Eq. (6) opens the possibility of developing simple solvation models
by raising the value from 1 in the gas phase. More elaborate models are described in
Sec. 6.
Eq. (7) describes a charge model primarily based on bond-center dipoles as

applied by Allinger in MM2 and MM3 [3]. Such parameterization requires dipoles to
be determined for each bond type independent of the surroundings. v and a
i
, a
j
are the
Liljefors et al.4
angle between the dipoles and the angles between each dipole and the connecting
vector, respectively.
E
el
¼
l
i
l
j
er
3
ðcos v À 3 cos a
i
cos a
j
Þð7Þ
2.4. Van der Waals Interactions
Short-range repulsions and London dispersion attractions are balanced by a shallow
energy minimum at the van der Waals distance (Eq. (8)), describing the Lennard–
Jones’ potential, used by most force fields. Here the parameters A and B are calculated
based on atomic radii and the minimum found at the sum of the two radii.
E
vdW

¼
A
r
12
À
B
r
6
ð8Þ
Most force fields use the Lennard–Jones functional form or close derivatives (9-6 or
14-7 functional forms as opposed to the standard 12-6 form). To compensate for the
too hard repulsive component, M M2 and MM3 use the Buckingham potential shown
in Eq. (9).
E
vdW
¼ Ae
Àar
À
B
r
6
ð9Þ
2.5. Hydrogen Bonding
The simplest way to handle hydrogen bonding is to rely on the other nonbonded
potentials to reproduce hydrogen bonds. Some methods include specific pair param-
eters [19] while others use special potentials for the nonbonded interactions between
hydrogen bond donors and acceptors [20,21].
2.6. Torsional Angles
Four consecutive atoms defin e the torsional bond (see Fig. 1). A large number of
different torsional types therefore exist, and general parameters for the central bond

are often used. Whereas certain preferred values for bond lengths and angles exist,
torsions are even softer than bond angles and all possible values can be found in real
structures. Thus the energy function must be valid over the entire range and,
furthermore, be periodic. For symmetry reasons, the function should have stationary
points at 0j and 180j. A simple cosine function as exemplified in Eq. (10) has been used
in the CVFF, CHARMm, and Dreiding force fields.
E
t
¼ v cos nx ð10Þ
where the periodicity n is the number of minima for the potential, usually 3 for an sp
3
–
sp
3
bond and 2 for a conjugated bond, and v is proportional to the rotational barrier.
The Fourier expansion described in Eq. (11) allows the flexibility to model more
complex torsional profiles and is used in most force fields today, including the MM2
and MM3 suite of programs. The form depicted in Eq. (11) also allows setting the
minimum contribution to zero.
E
t
¼ v
1
ð1 þ cos xÞþv
2
ð1 À cos 2xÞþv
3
ð1 þ cos 3xÞð11Þ
Molecular Mechanics and Comparison of Force Fields 5
2.7. Out-of-Plane Bending

Special parameterization is needed to prevent atoms bound to sp
2
carbons with three
substituents to deviate from planarity. Many implementations apply an energy term
E
oop
that increases the energy when one of the atoms deviates from the plane defined
by the three others. Several functions have been implemented, e.g., improper torsions
or Hooke’s law functions [22,23].
2.8. Modifications
Several force fields apply various modifiers and additional terms to address specific
problems with the reduced set of standard terms. Allinger’s electronegativity effect
corrects the problem with substituents reducing the preferred bond lengths [24].
Adaptation of bond orders in conjugated systems is done by a simplified QM
interpolation scheme [25–27], and cross terms can be used to, e.g., correct for the
elongation of bonds when angles are compressed as shown in Eq. (12) [23].
E
sb
¼ k
sb
ðh À h
0
Þðl À l
0
Þð12Þ
3. COMPARISON OF CALCULATED CONFORMATIONAL
ENERGIES
The comparison of force fields presented in this section focuses on the ability of dif-
ferent force fields to rep roduce conformational energies. The relative performance
of the ability to reproduce geometries is not included as this is done reasonably well

by most force fields. The force fields included in the comparison are AMBER* [20,
28], CFF91 [10,29], CFF99 [10,29], CHARMm2.3 [4,29,30], CVFF [7,29], Dreiding
2.21 [5,29], MM2* [28], MM3*[28], MMFF [11,28], OPLS_AA [28,31], Sybyl5.21 [32,
33], and UFF1.1 [6,29]. These force fields have been selected as they are widely dis-
tributed as summarized in Table 1 and commonly used by computa tional and medic-
Table 1 A Summary of Different Force Fields Native to and Available in Different Software Packages
a
Cerius 2
(Accelrys Inc.)
InsightII
(Accelrys Inc.)
MacroModel
(Schro
¨
dinger Inc.)
Quanta
(Accelrys Inc.)
Sybyl5.21
(Tripos Inc.)
AMBER*/AMBER
Â
x
Â
CFF91
Â
x
CFF99 x
CHARMm2.3
Â
x

CVFF
Â
x
Dreiding2.21
Â
MM2* x
Â
MM3* x
MMFF
Â
x
Â
OPLS_AA x
Sybyl5.21 x
UFF1.1
Â
a
x = Native force field,
Â
= available force field.
Liljefors et al.6
inal chemists. MM2(91) [8] and MM3(92) [9] are also included in the comparison.
The comparison is an update of previously reported evaluations [34–36]. The data set
used in the evaluation is given in Appendix A and is the same as previously employed.
For further information on the dataset and the selection of experimental values, see
Refs. [34–36].
Fig. 2 summarizes the overall results obtained by the different force fields and
for different structural classes of compounds in terms of mean absolute errors. The
performance of the force fields for particular classes of compounds is discussed in the
following sections. Fig. 2 also includes the overall results for three QM methods (PM3,

HF/6-31G* and B3LYP/6-31G*). These results will be discussed in Sec. 4.
3.1. Acyclic Hydrocarbons
As can be seen in Fig. 2, the calculated errors for the hydrocarbons in the data set are
rather small for all tested force fields. The simplest hydrocarbon that can adopt two
conformers is butane. As butane represents a fragment that can occur several times in
a molecule and thus adds up errors, it is of importance that the force field can
reproduce the experimental gauche-anti energy difference. Different experimental
values for this energy difference have been reported [37–40 ]. The smallest reported
experimental energy difference is 0.67 and the largest 1.09 kcal/mol. The experimental
value 0.97 kcal/mol [37] has been used in the calculations of mean absolute errors in
Fig. 2. Fig. 3 shows that all force fields correctly calculate the anti-conformer to be the
most stable conformer and that most of the force fields can reproduce the exper-
imental value within the variation of the experimental data. The force fields showing
the largest errors are UFF 1.1, AMBER*, Sybyl5.21, and CVFF.
Figure 2 Comparison of mean absolute errors (in kcal/mol) for different structural classes of
organic compounds obtained in calculations of conformational energy differences by using
different commonly used force fields.
Molecular Mechanics and Comparison of Force Fields 7
3.2. Oxygen-Containing Compounds
Fig. 2 shows that the class of oxygen-containing compounds may give rise to larger
errors than the hydrocarbons (Dreiding2.21, Sybyl5.21, and UFF1.1). For 2-methoxy-
tetrahydropyrane (Fig. 4), the anomeric effect makes the conformer with the me-
thoxy group in an axial position the most stable one by 1.0 kcal/mol [41]. Fig. 4
shows how this conformational equilibrium is handled by the different force fields.
It can be seen that four of the force fields (UFF 1.1, Dreiding2.21, CVFF, and CFF91)
are not able to predict the correct global energy minimum. It can also be seen that the
equatorial–axial energy difference is significantly overestimated by OPLS_AA and
CHARMm 2.3.
3.3. Nitrogen-Containing Compounds
All of the evaluated force fields except UFF1.1 have rather small calculated errors

for this class of compounds (Fig. 2). In order to be able to calculate the conformational
preference for peptides and other compounds containing an amide bond, the pre-
diction of the energy difference between the E and Z conformer is important. The
ability of the force fields to calculate the energy difference between the E and Z form
in N-methylacetamide is shown in Fig. 5. The experimental value is 2.3 kcal/mol [42]
and all force fields except UFF1.1 correctly predict the Z conformer to be the most
stable one. Among the force fields predicting the Z conformer to be preferred, the
largest deviations from the experimental value are shown by CVFF, Dreiding2.21,
and Sybyl5.21.
Another common fragment in medicinal chemistry is N-methylpiperidine [43].
Fig. 6 shows the calculated energy difference between the axial and equatorial con-
formers for the different force fields. All force fields correct ly predict the equatorial
Figure 3 Calculated gauche-anti energy differences for butane in kcal/mol. The dashed hori-
zontal lines show the range of reported experimental values.
Liljefors et al.8
conformer to be the most stable one. However, the energy difference is significantly
overestimated by UFF1.1 and underestimated by more than 1 kcal/mol by AMBER*,
CVFF, Dreiding2.21, OPLS_AA, and Sybyl5.21.
3.4. Cyclohexanes
For substituted cyclohexanes, two conformational properties are of fundamental
importance. A force field should be able to predict both the correct conformation of
the ring system and the position (axial or equatorial) of a substituent. Fig. 7 sh ows the
ability of the different force fields to predict the energy difference between the twist-
boat and chair conformation of cyclohexa ne [44]. As can be seen in the figure most
of the force fields reproduce this well. However, the energy difference is overestimated
by several of the force fields, in particular by CVFF and UFF1.1.
For testing the ability of the force fields to reproduce the energy difference
between an axial and equa torial substituent, methylcyclohexane and aminocyclohex-
ane have been chosen as examp les. The experimental value for the energy difference
between the two chair conformers in methylcyclohexane is 1.75 kcal/mol [45]. All force

fields correctly calculate the equatorial conformer to be the most stabl e one as dis-
played in Fig. 8. Again, the energy difference is strongly overestimated by CVFF and
UFF1.1.
For aminocyclohexane, the experimental value for the energy difference between
the axial and equatorial conformer is 1.49 kcal/mol with the equatorial conformer
as the most stable one [46]. In Fig. 9 it is shown that AMBER* predicts the axial
Figure 4 Calculated equatorial–axial conformational energy differences in kcal/mol for 2-
methoxy-tetrahydropyran. The dashed line indicates the experimental value.
Molecular Mechanics and Comparison of Force Fields 9
Figure 5 Calculated energy differences in kcal/mol between the E and Z conformer of N-
methylacetamide. The dashed line indicates the experimental value.
Figure 6 Calculated conformational energy differences (axial–equatorial) in kcal/mol for N-
methylpiperidine. The dashed line shows the experimental value.
Liljefors et al.10