Chemistry Reference
In-Depth Information
The reaction field addition does not account for the polarisation effects in the
medium beyond the cut-off due to charges rather than dipoles, and they are not
satisfactory in inhomogeneous systems and systems with a long-range correlation.
Ways out are, for example, the smooth-particle mesh-Ewald (SPME) approach of
Essmann et al. [
89
] and the continuum correction methods by Wood [
90
]. The
dominant and most relevant omission in the usual force fields is the incorporation of
electronic polarizability, which is a non-additive electrical interaction. The electron
distribution around a given nuclear configuration depends on the presence of
external electric field. A comprehensive review of approaches including polariz-
abilities is given for the simulation of water by Guillot [
91
]. A strategy of a
systematic development of force fields based on quantum calculations is described
by Saint-Martin et al. [
92
,
93
]. After obtaining the average values of certain
molecular properties from short simulations with a fully flexible model, those
average values can be kept fixed and the simulations continued. This is a self-
consistent alternative to construct potentials based on ab initio calculations and
single molecule properties, without reparametrising for each different set of ther-
mophysical conditions, and with the advantage that even the simpler models will
reflect the improvement in quality of the ab initio data used as the learning set. This
is particularly important for a variety of molecular systems for which the experi-
mental data of condensed phases are rather scarce. Different types of force fields
were developed over the last few years, among them being MM3 [
94
], MM4 [
95
],
Dreiding [
96
], SHAPES [
97
], VALBON [
98
], UFF [
99
], CFF95 [
100
], AMBER
[
101
], CHARMM [
102
], OPLS [
103
], MMFF [
104
], GROMOS [
105
] and MAR-
TINI [
106
]. Many other force fields and their respective citations are given by Jalaie
and Lipkowitz [
107
]. Coarse-grained force fields like, e.g. MARTINI are typically
parametrised based on comparison to detailed atomistic simulations, using inverted
MC schemes [
108
,
109
] or force matching approaches [
110
].
Fitting complex PES is a highly non-trivial task. Many optimisation algorithms
for this purpose have been described by Schlick [
111
] and Leach [
112
]. The
functional form has to be sufficiently flexible to adapt to the reference points with
high accuracy. The obtained PES should have continuous derivatives for applica-
tions in MD simulations. The choice of the functional form requires great care,
because otherwise unphysical artefacts may be introduced. In connection with the
description of molecule-surface interactions, the modified Shepard method [
113
,
114
] turned out to be useful. It is based on a Taylor expansion of the energy around
the reference points. In recent years artificial neural networks (NN) [
115
] have
become a promising new tool for the representation of PES. Due to their flexibility
they are able to reproduce accurately a given set of electronic structure data, while
the resulting continuous NN-PES can be evaluated several orders of magnitude
faster than the underlying electronic structure calculations. Examples of NN-PES
are given by Lorenz and Scheffler [
116
] for the dissociation of H
2
on Pd(100)
surfaces, and by Behler et al. [
117
] for the dissociation of oxygen molecules on
Al(111).
Enabling dynamical simulations on large reacting systems (
1,000 atoms),
so-called reactive force fields have been introduced. An example of such force
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