94
K. B. Be´ c et al.
semi-empirical methods remain continuously evolving with newer variants developed, e.g., PM6, PM7, or new concepts introduced such as self-consistent change
density-functional tight binding (SCC DFTB).
5.3.2.5 Molecular Mechanics
An alternative to QM-based approaches is the description of interatomic potentials
in an entirely empirical way. These methods are typically referred to as molecular mechanics (MM) or force fields (FF) [9–11]. In this approach, the potential
energy is calculated as a function of the nuclear coordinates using empirical (i.e.,
pre-parametrized) interaction potentials. Accordingly, MM uses classical mechanics
to describe the forces acting between the atoms in a molecule. In the most fundamental
approach, the interatomic potential energy is described as a sum of non-covalent pairwise interactions resulting from electrostatic (Coulomb) and van-der-Waals (e.g.,
Lennard-Jones) contributions, while covalent contributions such as bond and valence
angle interactions are often represented via harmonic potentials centered on preoptimized equilibria. These pair-wise additive approaches comprise the simplest possible
description of the systems and are typically applied in the regime of (bio)organic
chemistry (e.g., peptide/protein systems, nucleic acids, organic polymer materials)
as well as for the treatment of simple solid-state systems such as oxide materials.
In order to improve the accuracy of these approaches over the pair-wise additive
character, a variety of improved MM methods have been developed. One of the
simplest approaches to improve the pair-wise additive character is the inclusion of
explicit coupling terms for bonded interactions with the Urey–Bradly angular term
and the Axilrod–Teller three-body potential being typical examples. More advanced
frameworks comprise the inclusion of polarization effects, which can for example
be achieved using charge-on-spring/shell models, explicit polarization approaches
as well as charge equilibration schemes. While these approaches are essentially
linked to the Coulombic character of the interaction, many-body potentials such
as the Finnis–Sinclair and embedded-atom models (EAMs) attempt to improve the
description of the non-Coulombic contributions with typical applications being in
the area of metals, alloys, and semiconductors. A comparably challenging yet highly
intriguing development enjoying increased success in recent years is the formulation
of dissociative/reactive force field approaches, capable of adequately describing the
formation and cleavage of chemical bonds along the calculation.
The approximate nature of the interatomic forces described this way implies that
force fields need to be heavily parametrized to yield an accurate description of the
potential energy surface of a molecular system. The practical concept of MM is
based on the assumption that a force field parametrized on the basis of a small-scale
model, for which more accurate QM methods may be used, is reasonably well transferrable to larger systems. The parametrization may be also based on experimental
data, if available. This fundamentally different approach has a significant consequence in the terms of accuracy versus complexity factor. Consequently, MM is applicable to extensively complex molecular systems counting up to millions of atoms.
K. B. Be´ c et al.
semi-empirical methods remain continuously evolving with newer variants developed, e.g., PM6, PM7, or new concepts introduced such as self-consistent change
density-functional tight binding (SCC DFTB).
5.3.2.5 Molecular Mechanics
An alternative to QM-based approaches is the description of interatomic potentials
in an entirely empirical way. These methods are typically referred to as molecular mechanics (MM) or force fields (FF) [9–11]. In this approach, the potential
energy is calculated as a function of the nuclear coordinates using empirical (i.e.,
pre-parametrized) interaction potentials. Accordingly, MM uses classical mechanics
to describe the forces acting between the atoms in a molecule. In the most fundamental
approach, the interatomic potential energy is described as a sum of non-covalent pairwise interactions resulting from electrostatic (Coulomb) and van-der-Waals (e.g.,
Lennard-Jones) contributions, while covalent contributions such as bond and valence
angle interactions are often represented via harmonic potentials centered on preoptimized equilibria. These pair-wise additive approaches comprise the simplest possible
description of the systems and are typically applied in the regime of (bio)organic
chemistry (e.g., peptide/protein systems, nucleic acids, organic polymer materials)
as well as for the treatment of simple solid-state systems such as oxide materials.
In order to improve the accuracy of these approaches over the pair-wise additive
character, a variety of improved MM methods have been developed. One of the
simplest approaches to improve the pair-wise additive character is the inclusion of
explicit coupling terms for bonded interactions with the Urey–Bradly angular term
and the Axilrod–Teller three-body potential being typical examples. More advanced
frameworks comprise the inclusion of polarization effects, which can for example
be achieved using charge-on-spring/shell models, explicit polarization approaches
as well as charge equilibration schemes. While these approaches are essentially
linked to the Coulombic character of the interaction, many-body potentials such
as the Finnis–Sinclair and embedded-atom models (EAMs) attempt to improve the
description of the non-Coulombic contributions with typical applications being in
the area of metals, alloys, and semiconductors. A comparably challenging yet highly
intriguing development enjoying increased success in recent years is the formulation
of dissociative/reactive force field approaches, capable of adequately describing the
formation and cleavage of chemical bonds along the calculation.
The approximate nature of the interatomic forces described this way implies that
force fields need to be heavily parametrized to yield an accurate description of the
potential energy surface of a molecular system. The practical concept of MM is
based on the assumption that a force field parametrized on the basis of a small-scale
model, for which more accurate QM methods may be used, is reasonably well transferrable to larger systems. The parametrization may be also based on experimental
data, if available. This fundamentally different approach has a significant consequence in the terms of accuracy versus complexity factor. Consequently, MM is applicable to extensively complex molecular systems counting up to millions of atoms.