Rule-based force fields

In Eqs. (2) and (3), % is electronegativity, n is the bond order, and A, is a parameter. Another example of a rule-based force field is VALBOND, from the Landis group. 

A widely used 3D structure generator is CONCORD [131, 132] (for a more detailed description see Chapter II, Section 7.1 in the Handbook). CONCORD is also a rule- and data-based program system and uses a simplified force field for geometry optimization, CONCORD converts structures from 2D to 3D fairly fast... 

The Universal Force Field, UFF, is one of the so-called whole periodic table force fields. It was developed by A. Rappe, W Goddard III, and others. It is a set of simple functional forms and parameters used to model the structure, movement, and interaction of molecules containing any combination of elements in the periodic table. The parameters are defined empirically or by combining atomic parameters based on certain rules. Force constants and geometry parameters depend on hybridization considerations rather than individual values for every combination of atoms in a bond, angle, or dihedral. The equilibrium bond lengths were derived from a combination of atomic radii. The parameters [22, 23], including metal ions [24], were published in several papers. 

In the first chapter several traditional types of physical models were discussed. These models rely on the physical concepts of energies and forces to guide the actions of molecules or other species, and are customarily expressed mathematically in terms of coupled sets of ordinary or partial differential equations. Most traditional models are deterministic in nature— that is, the results of simulations based on these models are completely determined by the force fields employed and the initial conditions of the simulations. In this chapter a very different approach is introduced, one in which the behaviors of the species under investigation are governed not by forces and energies, but by rules. The rules, as we shall see, can be either deterministic or probabilistic, the latter leading to important new insights and possibilities. This new approach relies on the use of cellular automata. 

A potentially much more adaptable technique is force-field vibrational modeling. In this method, the effective force constants related to distortions of a molecule (such as bond stretching) are used to estimate unknown vibrahonal frequencies. The great advantage of this approach is that it can be applied to any material, provided a suitable set of force constants is known. For small molecules and complexes, approximate force constants can often be determined using known (if incomplete) vibrational specha. These empirical force-field models, in effect, represent a more sophisticated way of exhapolating known frequencies than the rule-based method. A simple type of empirical molecular force field, the modified Urey-Bradley force field (MUBFF), is introduced below. 

This restriction rules out all discrete models exclusively based on semiempirical force fields, leaving among the discrete models the MC/QM and the MD/QM procedures, in which the second part of the acronyms indicates that the solute is described at the quantum mechanical (QM) level, as well as the full ab initio MD description, and some mixed procedures that derive the position of some solvent molecules from semiclassical simulations, replace the semiclassical description with the QM one, and repeat the calculation on these small supermolecular clusters. The final stage is to perform an average on the results obtained with these clusters. These methods can be used also to describe electronic excitation processes, but at present, their use is limited to simple cases, such as vertical excitations of organic molecules of small or moderate size. This limitation is due to the cost of computations, and there is a progressive trend toward calculations for larger systems. 

Rappe AK, Casewit CJ, Colwell KS, Goddard III WA, Skiff WM (1992) UFF, a rule based full periodic table force field for molecular mechanics and molecular dynamics simulations, J Am Chem Soc, 114 10024... 

More recently, the Landis group" has used valence bond concepts to derive new angular potential energy functions and to develop rules for parameterization. The VALBOND force field angular energy function is based on Pauling s hybrid orbital nonorthogonality functions and can be derived for any arbitrary combination of s, p, d, and f orbitals. 

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