MAXIMALLY DIAGONAL FORCE-CONSTANTS IN DEPENDENT ANGLE-BENDING COORDINATES .2. IMPLICATIONS FOR THE DESIGN OF EMPIRICAL FORCE-FIELDS

The vast amount of information compiled in experimentally determined and quantum-mechanically calculated force fields for small molecules could be used to assist in the further development of empirical potentials used in molecular-mechanics and molecular-dynamics simulations of organic and biological systems. Unfortunately, most such force fields are defined in well-determined sets of internal coordinates, whereas empirical potentials use larger sets of dependent coordinates. This paper illustrates a unique “localized” representation of the angle-deformation potential in dependent coordinates which is exactly diagonal for in-plane bending at trigonal-planar centers and is nearly diagonal for angle bending at tetracoordinate centers. The transformation to this representation is accomplished by introducing “virtual force constants” which couple to the vanishing null-coordinate displacement. Four applications show how this transformation can be used to aid the development of improved empirical potentials. The first extracts localized force constants for angle bending at carbonyl groups in aldehydes, ketones, amides, acids, and esters from published force fields, and then demonstrates that these values are reasonably transferable and are well described by the empirical relationship kθ= 1.75ZaCbZc(Rab+ Rbc)−1θabc−2exp(-2D) where Z and C are atomic parameters and D = (Rab- Rbc)2/(Rab+ Rbc)2and shows that the corresponding force constants used in MM2, AMBER, VFF, and CHARMM do not exhibit the systematic trends found in the experimental data. The second compares “canonical” and localized force constants for angle bending at methylene groups in alkanes for three published force fields. The third application extends the approach to stretch-bend and bend-bend' interactions and transforms a calculated in-plane force field for ethylene to dependent coordinates to show how one can test model assumptions concerning the importance of and functional form required for specific interactions. The fourth application shows how the transformation to localized force constants can be carried out at a variety of geometries to probe the anharmonicity of the molecular energy surface. © 1990, American Chemical Society. All rights reserved.