Quantum Derivative Fitting and Biomolecular Force Fields: Functional Form, Coupling Terms, Charge Flux, Nonbond Anharmonicity, and Individual Dihedral Potentials

Computer simulations are increasingly prevalent, complementing experimental studies in all fields of biophysics, chemistry, and materials. Their utility, however, is critically dependent on the validity of the underlying force fields employed. In this Perspective we review the ability of quantum mechanics, and in particular analytical ab initio derivatives, to inform on the nature of intra- and intermolecular interactions. The power inherent in the exploitation of forces and second derivatives (Hessians) to derive force fields for a variety of compound types, including inorganic, organic, and biomolecules, is explored. We discuss the use of these quantities along with QM energies and geometries to determine force constants, including nonbond and electrostatic parameters, and to assess the functional form of the energy surface. The latter includes the optimal form of out-of-plane interactions and the necessity for anharmonicity, and terms to account for coupling between internals, to adequately represent the energy of intramolecular deformations. In addition, individual second derivatives of the energy with respect to selected interaction coordinates, such as interatomic distances or individual dihedral angles, have been shown to select out for the corresponding interactions, annihilating other interactions in the potential expression. Exploitation of these quantities allows one to probe the individual interaction and explore phenomena such as, for example, anisotropy of atom atom nonbonded interactions, charge flux, or the functional form of isolated dihedral angles, e.g., a single dihedral X-C-C-Y about a tetrahedral C-C bond.