Download Combined Quantum Mechanical and Molecular Mechanical

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Combined Quantum
Mechanical and Molecular
Mechanical Potentials
Patricia Amara and Martin J. Field
Institut de Biologie Structurale Jean-Pierre Ebel, Grenoble, France
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Introduction
Methodology
Applications
Conclusion
Related Articles
References
Abbreviations
EVB D empirical valence bond; MM D molecular mechanical; QM D quantum mechanical.
1 INTRODUCTION
Molecular systems, such as organic molecules in solution
and biological macromolecules, have been the subject of
numerous theoretical studies. Molecular dynamics and Monte
Carlo simulations are two techniques that can provide useful
insights into the structural, thermodynamic, and, for molecular
dynamics, dynamical properties of systems in the condensed
phase.1 An essential part of simulation methodology is to
have a potential energy function which is accurate enough to
model the properties of the system of interest. A number of
such functions, or force fields, have been developed for the
simulation of biomolecules and these appear to give reliable
results in many cases. However, in many standard force
fields, the arrangement of bonds between the atoms in the
system must be specified in advance and so they will not be
appropriate for modeling processes in which chemical bonds
are broken or created.2 One way to overcome this problem is
to modify the force fields in some fashion. However, this is
difficult to do consistently, particularly for atoms such as the
transition metals which show a rich electronic behavior.
Another approach is to use one of the many quantum
mechanical (QM) methods, based on the Born Oppenheimer
approximation, that have been developed to determine the
electronic structure of molecular systems. In these methods the
number of electrons and nuclei for each system is specified
and the electronic density and the energy are calculated for
each different configuration of the nuclei. Thus, it is possible
to determine the redistribution of electrons among atoms as a
reaction proceeds. The drawback with QM calculations is that
they are much more expensive than force field calculations and
can only be applied to the simulation of systems comprising
a small number of atoms. Although recent advances in
algorithmic techniques suggest that much larger systems could
be treated,3 it is clear that possible applications are still limited
by existing computational technology.
In 1976 Warshel and Levitt introduced the idea of a hybrid
QM/MM (molecular mechanical) method4 that treated a small
portion of the system using a quantum mechanical representation while the rest of the system, which did not need such
a detailed description, was represented by an empirical force
field. They used their potential to study the reaction catalyzed
by the enzyme, lysozyme. Since then, Warshel has continued
to use such hybrid methods, most notably his empirical valence
bond (EVB) approach, to study a wide variety of reactions in
solution and in enzymes. It is undoubtedly he who has made
the major contribution, both in terms of method development
and in applications, to this area. Warshel has summarized his
work on studying reactions in enzymes and interested readers
are recommended to look at that for further details.5
The next workers to use these methods were Singh and
Kollman, who devised a combined QM/MM potential6 using
an ab initio molecular orbital method and the AMBER MM
force field.7 They applied their method to studying the methyl
chloride/chloride exchange reaction in solution and to the
protonation of polyethers in the gas phase6 and, in a separate
study, to the reaction catalyzed by the serine protease, trypsin,
in solution and in the enzyme.8,9 The limitation of the potential
developed by Kollman and co-workers was that it used an
expensive ab initio QM method. While accurate, this precluded
the use of the potential in molecular dynamics and Monte
Carlo simulations and limited it to the static exploration
of the potential energy surface. To overcome this problem,
Karplus and co-workers10 developed a combined potential of
the same basic form as that of Singh and Kollman but using
the AM1/MNDO family of semiempirical QM methods11
and the CHARMM MM force field.12 Since these initial
studies, potentials with both ab initio and semiempirical QM
methods have been developed and applied by a large number
of groups to a wide range of problems in condensed phase
chemistry.
The aim of this review is to give an overview of the form
and the use of the type of hybrid QM/MM potentials mentioned
above and to describe recent developments and applications.
Section 2 discusses the methodology of the hybrid potentials,
Section 3 discusses their application, and Section 4 summarizes the scope for future developments.
2 METHODOLOGY
2.1 General Principles
The fundamental idea behind the use of hybrid potentials is
that a system is partitioned into several regions which are then
modeled with different levels of approximation. The atoms
from the residues or molecules that are participating in the
reaction process, or atoms that are rich in electrons, such
as metals, are treated quantum mechanically. The rest of the
system is described by standard molecular mechanics force
fields. Finally a boundary region is defined to account for the
finite size of the system.
Different strategies can be adopted to partition the system.
The simplest approximation is to divide the system into three
regions a QM region and an MM region surrounded by
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a boundary. However, it is possible to envisage a system
partitioned into multiple regions in which less sophisticated
potentials are used as the distance from the central core
increases (see Figure 1). Such ‘onion’ models have been
proposed by a number of groups, including Morokuma and
co-workers.13
The most important point when employing any hybrid
scheme is to test how the results of calculations change as
different partitionings are tried. In general, the aim is to have
as few atoms as possible treated with a high level of theory
(which is expensive) but enough so that the results obtained
are of the same quality as if all the system were being treated
at the highest level. In other words, the minimum number of
QM atoms should be chosen for a reasonable simulation time
without losing too much accuracy in the model.
A convenient way to describe the behavior of a system
being studied with a hybrid potential is to use a notation
O eff .10 In this formulation,
involving an effective Hamiltonian, H
the energy for the system at a given configuration of the atoms,
E, is obtained by solving the time-independent Schrödinger
equation, which has the form:
Ĥeff .ri , R˛ , RM / D E.R˛ , RM /.ri , R˛ , RM /
.1/
where ri and R˛ stand for the coordinates of the electrons and
the nuclei in the QM region and RM for the coordinates of the
atoms in the MM region, respectively. is the wavefunction
whose square gives the electron density in the system.
For the simplest case of a system partitioned into three
regions, the effective hybrid Hamiltonian is composed of four
terms:
O QM C H
O MM C H
O QM/MM C H
O boundary
Ĥeff D H
.2/
O QM , has the standard form for
The electronic Hamiltonian, H
the quantum mechanical method being used. For an ab initio
method, for example, this would be:
ĤQM D
1X 2 X 1
r C
2 i i
rij
ij
X Z˛ X Z˛ Zˇ
C
ri˛
r˛ˇ
i˛
˛ˇ
.3/
where Z˛ is the charge on nucleus ˛ and rxy is the distance
between particles x and y. The subscripts (i, j) and (˛, ˇ) refer
to electrons and nuclei, respectively.
O MM , has interactions between
The MM Hamiltonian, H
MM atoms only and can be equated directly to the standard
molecular mechanics energy, EMM . This will itself consist of
a sum of independent energies, such as the ‘bonded’ bond,
angle, and dihedral terms and the ‘nonbonded’ electrostatic
and Lennard-Jones interactions, i.e.
ĤMM D EMM D Ebond C Eangle C Edihedral
C ECoulomb C ELennard
The form of the QM/MM Hamiltonian will depend upon the
forms of the separate QM and MM Hamiltonians. However,
for the case where there are electrostatic and Lennard-Jones
interactions between the QM and MM regions, a possible
Hamiltonian is
Ĥ0QM/MM D
X qM
X Z˛ qM X A˛M
C
C
12
r
r˛M
R˛M
iM iM
˛M
˛M
B˛M
6
R˛M
.5/
There are three terms. The first two terms are electrostatic
interactions which consist of two Coulombic terms, one
between the electrons and the MM atoms and one between the
nuclei and the MM atoms. The third term is a Lennard-Jones
term which takes care of close-range exchange repulsion
terms and the longer-range dispersion contributions which cannot be explained using a pure Coulombic interaction. This term
is particularly important when the charge on an MM atom (and,
hence, its electrostatic interaction) is zero.
A number of extensions to the simple interaction Hamiltonian given above have been proposed. An example is for the
case where polarization effects on the MM atoms are important. In general, there will be some polarization of the atoms in
the QM region because the electron cloud will be distorted by
interaction with the surrounding MM charges. There are several ways to include equivalent effects on the MM atoms but
a common approach is to give to each MM atom an isotropic
dipole polarizability, ˛M , which means that a dipole, mM , can
be induced on each atom that is proportional to the electric
field at the atom, EM :
mM D ˛M EM
Figure 1 Partitioning of a system into different regions for use with
a hybrid potential. There are four regions in this representation. The
yellow region, QM1, corresponds to high-level QM calculations while
the dark green area, MM, is modeled with MM force fields. The
light green region, QM2, could be treated with a lower level of QM
theory or by a more complicated MM force field (which includes
polarization, for example). The hatched area is the boundary region
.4/
Jones
.6/
Because the electric field at an atom has contributions arising
from the charges and induced dipoles on the other MM atoms
as well as the QM electrons and nuclei, the calculations of
the QM energy and the MM electrostatic energy are coupled
when polarization is included on the MM atoms and the time
required for the evaluation of the hybrid energy is substantially
increased.
O boundary in equation (2) is the boundary Hamiltonian which
H
accounts for the truncation of the system. The same boundary
approximations that are commonly used for simulations with
MM potentials1 can be used with hybrid potentials. Typical
examples include periodic boundary conditions in which the
system is replicated in each direction in space, boundary force
methods which introduce a force in the boundary region to
constrain the atoms in the central region, and methods which
treat the neglected part of the system as a continuum dielectric.
The term in the Hamiltonian will typically consist of two
O boundary.QM/ , and an MM contribution,
terms, a QM part, H
Eboundary.MM/ .
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3
To obtain the total energy for the system, the expectation
value of the wavefunction over the effective Hamiltonian
is calculated. For the effective Hamiltonian described above
(without polarization on the MM atoms), the energy is:
O QM C H
O QM/MM C H
O boundary.QM/ /j i/h j i
Etot D h j.H
C EMM C Eboundary.MM/
.7/
Once the total energy is known, the forces on the atoms are
easily derived as derivatives of the energy with respect to the
atomic coordinates:
F˛ D
∂Etot
∂R˛
FM D
∂Etot
∂RM
.8/
The resulting energy and the associated forces can be
employed for geometry optimizations and molecular dynamics
and Monte Carlo simulations on the hybrid potential surface
in exactly the same way as for calculations with purely QM
or MM potentials.
2.2 The Junction Between the QM and MM Regions
For a reaction involving relatively small molecules in solution, the partitioning of the atoms in a system between different
regions is simple. The molecules implicated in the reaction are
put in the QM region and the solvent molecules in the MM
region. The situation is more complicated though when the
region of interest is part of a large molecule, e.g., the active
site of an enzyme. In that case, parts of the same molecule
will be in different regions and there will be covalent bonds
between the QM and MM atoms. It is not possible to simply truncate these bonds as this would leave lots of half-filled
orbitals and give an inaccurate description of the electronic
state of the QM region. Therefore, some means must be found
to terminate these bonds reliably.
In the original QM/MM study of Warshel and Levitt,4 this
problem was overcome by including only a single hybrid
sp2 orbital with a single electron for each of the QM atoms
(carbon or nitrogen) at the junction. The remaining interactions
for these atoms were treated using MM terms. A simpler,
although less rigorous approach was introduced by Singh
and Kollman6 and also used by Karplus and co-workers.10
They included ‘dummy junction’ or ‘link’ atoms in the QM
region. These were QM atoms (usually hydrogens although
other elements have been used) which were placed along the
QM MM bond at an appropriate distance. They were included
in the QM calculation but the interactions with the MM atoms
were reduced in magnitude or even neglected altogether. In
these cases, the interactions between the QM and the MM
atoms were accounted for solely using MM force field terms.
A schematic of both these types of approach is shown in
Figure 2.
Both the above schemes were not entirely satisfactory and
several modifications have been suggested. Rivail and coworkers have developed a hybrid orbital method,14 similar in
spirit to that of Warshel and Levitt, in which the QM atom at
the junction is taken to have a normal complement of orbitals
but the hybrid orbital which points towards the MM atom is
kept frozen. The form of this orbital is not optimized in the
QM calculation although it is counted in the evaluation of the
QM energy terms and its interaction with the MM atoms is
carefully parametrized. The hybrid orbital method is relatively
Figure 2 Two alternative methods to treat the junction between
the QM and MM regions. On the left, the ‘link atom’ method is
represented where the dummy atom is a QM hydrogen placed along
the QM MM bond. On the right is the ‘single hybrid orbital’ model
where there is a single hybrid orbital along the QM MM bond
easy to implement for semiempirical QM methods (as done
by Warshel and Rivail et al.) but becomes more complicated
for ab initio HF wavefunctions. An equivalent approach is
possible for DFT wavefunctions and this is to define a frozen
electron density on one of the atoms at the junction whose
form is not included in the variational QM calculation but
which interacts with the QM and MM atoms in the appropriate
fashion. This method was first introduced, but in a different
context, by Wesolowski and Warshel.15
An alternative scheme deserving mention is that devised
by Morokuma and co-workers,13 which resembles the ‘link
atom’ scheme. In their method, the system is defined as being
composed of several superposed systems each of which is
treated with a potential of a different quality. Thus, for a
system with two partitions, there is a small central QM region
and an MM region which includes all the atoms of the system,
including those of the QM region. To avoid overcounting of
atoms, the total energy for the system has to be redefined so as
to subtract out the MM energy of the QM atoms. The problem
with this method is that it is essentially steric in character
and it does not, in its present incarnation, allow interactions
between the different superposed systems.
2.3 Implementations of the QM/MM Approach
As mentioned in the introduction a number of QM/MM
methods have been implemented using different QM and MM
approximations and different QM/MM interaction schemes.
In principle, there is no restriction on the types of potential
that can be coupled. In practice, certain combinations have
proved more popular than others, in large part due to the
computational expense of using ab initio QM methods. Thus, it
is true that while combined potentials with ab initio HF or DFT
methods would be preferable due to their greater reliability
than semiempirical methods, the semiempirical methods have
proved more popular because they can be used to study
relatively large systems, with up to 100 QM atoms, using
molecular dynamics or Monte Carlo simulation techniques.
While, even for semiempirical QM methods, the QM portion will be the most time-consuming part of the calculation,
the most difficult part of the implementation of a hybrid potential is the parametrization of the QM/MM Hamiltonian which
determines the precision of the interactions between the QM
and MM regions. The parametrization has to be done for the
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nonbonded interactions between the atoms in the QM and MM
regions and also for the covalent or ‘link’ atom interactions.
For the covalent interactions it is probably true to say that no
fully satisfactory parametrization has been performed. However, for the nonbonded interactions a number of extensive
parametrization studies exist.
For hybrid potentials with ab initio methods, only the
Lennard-Jones interactions need to be parametrized as the
electrostatic interactions between the QM and MM atoms
can be evaluated exactly. For semiempirical QM methods it
is necessary also to parametrize the electrostatic interactions
as semiempirical methods, such as AM1 and MNDO, use a
modified form for the Coulomb interaction which is softer at
short range. Likewise, when polarization is included in the MM
part of the force field, no parametrization is needed with ab
initio methods but the form of the QM/MM dipole interaction
needs to be parametrized with semiempirical QM methods.
To conclude this section, it is worth mentioning the EVB
approach that has been extensively used by Warshel and his
collaborators5 and is being increasingly used by other workers
(see, for example, Ref. 16). This method is essentially similar
in conception to the types of potential described here but it
is different in that it uses a much simpler valence bond QM
model of the reacting region. The method is much faster than
standard hybrid potentials but the potential is less easy to use
as it must be conceived and parametrized for each different
problem studied.
3 APPLICATIONS
In this section we review some of the simulation studies
that have been performed using hybrid QM/MM potentials.
The most extensive set of applications has been to chemical
processes in solution. We consider these first and then studies
of reactions in biomolecules. It should be noted that the study
of a reaction in solution is often a useful adjunct to the study
of an equivalent reaction in some other environment, such as
a protein.
3.1 Chemical Processes in Solution
The study of many chemical processes in solution is relatively straightforward using hybrid potentials as the partitioning of the system into different QM and MM regions is
often obvious the atoms of the reacting molecules are in the
QM region and the solvent molecules in the MM region and
there is no necessity to divide a single molecule into separate regions. Of course, in some cases the partitioning might
not be evident, notably for reactions which involve the solvent molecules themselves (water being the most important
example).
Both Singh and Kollman5 and Karplus and co-workers17
in their early works investigated the methyl chloride/chloride
exchange reaction, CH3 Cl C Cl , which is a standard test case
for theoretical studies of reaction mechanisms in solution.
In the gas phase, stable symmetric chloride/methyl chloride
complexes are formed with complexation energies of about
36 kJ mol 1 between which there is a barrier to reaction of
about 50 kJ mol 1 . In solution, however, the profile is simpler
with no stable minima and a single barrier with a height
of about 113 kJ mol 1 . In both Refs. 5 and 16 the reaction
was studied in the gas phase with all seven atoms treated
quantum mechanically and then in solution with the water
molecules treated as the MM region. Singh and Kollman with
their ab initio potential carried out minimizations of various
structures along the reaction path and found a higher barrier to
reaction and two complexes which were less stable than in the
gas phase. Bash et al.,17 because they used a semiempirical
method, were able to perform a full calculation of the free
energies along the path and obtained results which agreed very
closely with experiment. One of the advantages of studies with
hybrid potentials and which was illustrated well here was that
full information about the charge distribution for the reacting
atoms was obtained along the reaction path with the result that
a detailed analysis of the effect of the presence of solvent on
the reaction profile was possible.
The work described in Refs. 5 and 17 indicated that hybrid
potentials could describe reaction processes in solution. However, it is only with the work of Gao that the real utility of this
approach has become apparent. He and his co-workers have
developed a hybrid potential that combines the AM1/MNDO
semiempirical method with a force field similar to the OPLS
force field of Jorgensen18 and with it they have studied a very
wide range of solution phenomena in combination with Monte
Carlo simulation techniques. As Gao has recently published
two excellent reviews of hybrid potentials which include discussion of his own work19,20 only a few brief details will be
given here.
One area in which Gao has made specific contributions to
the development of hybrid potentials is in their parametrization
and, in particular, of the Lennard-Jones interactions. The
strategy that he has adopted is to determine the LennardJones parameters for the QM atoms of the hybrid potential
that best fit the results of high-level ab initio QM calculations
(energies and geometries) on complexes between a solute and
a small number of solvent molecules. He has then shown that
these parameters can give excellent results for the solvation
free energies of a wide range of organic compounds and
he has discussed their significance in terms of the solvent
polarization effect, i.e., the energetic effect the solvent has
on the distortion of the solute’s electron density.21 Although
his initial work in this area involved the AM1 method, he and
Freindorf have recently performed the same parametrization
using solute/solvent complex data for a hybrid potential with
an ab initio molecular orbital method and have shown that
significantly better results can be obtained than with the
previous potential.22
In addition to solvation free energies, Gao has studied the
effects of solvent on the conformational equilibria of different
molecules and on the free energy profiles for various reactions,
including nucleophilic substitution and pericyclic reactions.
Another area he has studied is the effect of solvent on solute
molecules in their excited states and, in particular, the shifts
that are observed in their spectra in different solvents. The
calculations showed that, whereas the blue shifts of acetone
arising from stabilization of the ground state in polar solvents
could be successfully reproduced, the hybrid potentials could
not account for the red shifts which arise in some nonpolar
solvents. This is a limitation of the model as the red shifts are
caused by changes in the dispersion interactions between the
two states and the solvent.23
Thompson has also studied the effects of solvation on
spectra. He has calculated the spectral shifts for the ! nŁ
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COMBINED QUANTUM MECHANICAL AND MOLECULAR MECHANICAL POTENTIALS
transition for some simple carbonyl compounds.24 This work
uses an AM1 semiempirical method for the atoms in the QM
region but is unusual in that it includes polarization on the
atoms of the MM region and develops a consistent way for
calculating the interactions between the induced dipoles on
the MM atoms and the QM atom charges. Thompson and
Schenter have applied a similar model with polarizable MM
atoms to the calculation of spectra of the excited states of the
bacteriochlorophyll b dimer from the photosynthetic reaction
center of Rhodopseudomonas viridis.25 Thompson has also
studied processes without MM atom polarization, including
the association of the potassium cation, KC , with dimethyl
ether.26
Other workers who have developed or used QM/MM
semiempirical potentials include Bakowies and Thiel, who
have discussed the integration of MM polarization into hybrid
potentials and have applied their method to study a number of
reactions in the gas phase.27 Bash and co-workers have calculated the free energy profile for the proton transfer between
methanol and imidazole in solution.28,29 The different aspect
of this work was that they reparametrized the semiempirical
method to get accurate interactions between the QM and MM
portions of the system using a method originated by Rossi and
Truhlar.30
The majority of the studies in this section have been
performed with hybrid potentials that employ a semiempirical
QM method because these methods are computationally less
demanding. However, there has been considerable interest
in developing combined potentials which use a DFT model
for the QM region.31 A number of workers have developed
methods of this sort, although, as yet, their application has
been limited to the study of fairly simple systems, such as
a single QM water molecule in a bath of MM waters or the
solvation of small ions.32 34
3.2 Enzymatic Reactions
Hybrid potentials are an ideal way to study reaction processes in enzymes. Such studies are, however, more demanding than studies of the equivalent processes in solution.
Figure 3 shows a schematic of the partitioning of an enzymatic system for simulation with a hybrid potential. Atoms
constituting the active center are modeled with QM methods while the rest of the enzyme and the solvent are represented by an MM force field. A major difference to the
simulation of reaction processes in solution is that the way in
which the system has to be partitioned into different regions
may no longer be clear and it will be necessary to investigate how many atoms within the active site need to be
treated quantum mechanically. Another difference is that the
protein will be divided between QM and MM regions and
so some sort of ‘link atom’ approximation will need to be
employed.
It is probably true to say that the driving force for the
development of hybrid potentials was the desire to investigate
reactions in enzymes. Warshel and Levitt in their pioneering
paper4 studied the stability of the carbonium ion intermediate
formed in the cleavage of a glycosidic bond by lysozyme
and concluded that electrostatic stabilization by the protein
of the intermediate was an important factor in determining
the protein’s catalytic activity. Since the work on lysozyme,
Warshel has studied a large number of enzyme reactions with
5
Figure 3 The QM/MM hybrid potential approach applied to an
enzymatic reaction. The atoms in red are QM while the rest of the
atoms are MM; light blue atoms are mobile while the purple ones
are fixed and only ‘feel’ the rest of the system through nonbonded
interactions. The purple ring is the boundary region
his EVB methods, including some serine proteases and various
metalloenzymes.5
There have been a number of QM/MM studies of enzyme
reactions by other workers. They all follow basically the
same pattern outlined in the original paper by Warshel
and Levitt, but they have used the QM(ab initio)/MM or
QM(semiempirical)/MM types of hybrid potentials described
in Refs. 6 and 10. It should be noted that, up to the present,
calculations with these types of hybrid potentials on enzymes
have been limited to minimization or reaction path studies.
In contrast to the case with the EVB models, no free energy
calculations have been performed due to their expense.
Studies with ab initio types of hybrid potential include
the early work of Weiner et al. on the nature of catalysis in
trypsin8,9 and the studies of the catalytic activity of phospholipase A2 by Hillier et al.35 Investigations with semiempirical
hybrid potentials are more extensive and include calculations
of the reactions in triosephosphate isomerase by Bash et al.36
and in chorismate mutase by Lyne et al.37 and a study of
the proton jump in the catalytic triad of human neutrophil
elastase.14 The study of the chorismate mutase reaction was
especially interesting because the enzyme is the only known
one that catalyzes a pericyclic reaction that also occurs readily
in solution. The results of the hybrid study were particularly
lucid in this case because the enzyme works, not by chemically
catalyzing the reaction, but by preferentially binding a distorted form of the substrate and stabilizing the transition state.
4 CONCLUSION
It is apparent that hybrid QM/MM potentials complement
existing methods of simulation. They are very useful tools
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6 COMBINED QUANTUM MECHANICAL AND MOLECULAR MECHANICAL POTENTIALS
for studying the properties of condensed phase systems, such
as solvation effects and reaction processes, that cannot be
studied using alternative potentials, either because they are
too expensive (purely QM potentials) or because they are not
appropriate (traditional MM force fields).
Certain trends in the development and application of hybrid
potentials are evident. Up to now most studies have been done
with potentials that use semiempirical methods as the approximation. It is likely that these potentials will remain the most
widely used in the future as they are relatively inexpensive to
apply, although they will be improved, either by reparametrizing the semiempirical method for each new problem of interest or by using newer semiempirical approximations. Wider
application of potentials with ab initio methods is also likely.
Particularly promising are hybrid DFT/MM potentials as DFT
methods are one of the most inexpensive types of ab initio
methods yet they can provide results of an accuracy equivalent
to the more expensive correlated molecular orbital methods.
The other area of improvement in the potentials will be in
the description of the interactions between the QM and MM
regions. Increasing numbers of studies, such as those investigating electronic spectra, have shown that the inclusion of
polarization effects on the atoms in the MM region is important if accurate results are to be obtained. Equally, it is possible
to imagine that a more accurate and consistent representation
of the exchange repulsion and dispersion interactions between
the QM and MM atoms than that obtained by using LennardJones terms could be developed. Such methods could involve,
for example, putting pseudopotentials on the MM atoms or
using frozen densities on the MM atoms in conjunction with
a DFT method for the QM region. The other obvious area
in need of investigation is the ‘link atom’ problem, i.e., how
to represent accurately covalent interactions between QM and
MM atoms.
In addition to improvements in the potentials themselves, it
is also clear that the rapid advance in computer technologies,
such as the increasing speed of hardware components, and in
techniques such as massively parallel computing, will make
possible the application of hybrid potentials to larger numbers
of exciting chemical problems.
5 RELATED ARTICLES
AM1; Hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) Methods; Combined Quantum Mechanics
and Molecular Mechanics Approaches to Chemical and Biochemical Reactivity; Density Functional Theory, HF and
the Self-consistent Field; Divide and Conquer for Semiempirical MO Methods; Electrostatic Catalysis; Force Fields:
AMBER; Force Fields: CFF; CHARMM: The Energy Function and Its Parametrization; Force Fields: General Discussion; The GROMOS Force Field; Hybrid Methods; Mixed
Quantum-classical Methods; MNDO; MNDO/d; Molecular Dynamics: Techniques and Applications to Proteins;
OPLS Force Fields; Parameterization of Semiempirical MO
Methods; PM3; Protein Force Fields; QM/MM; Quantum Mechanical/Molecular Mechanical Coupled Potentials
Applied to Biological Systems; SINDO1: Parametrization
and Application.
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DC, 1972.
3. T.-S. Lee, D. M. York, and W. Yang, J. Chem. Phys., 1996, 105,
2744 2750.
4. A. Warshel and M. Levitt, J. Mol. Biol., 1976, 103, 227 249.
5. A. Warshel, ‘Computer Modeling of Chemical Reactions in
Enzymes and Solutions’, Wiley, New York, 1992.
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