Deductive molecular mechanics of sp³ carbon atom

Abstract

ABSTRACT:The problem of substantiation of additive systematics such as molecular mechanics is considered. Antisymmetrized product of strictly localized geminals (APSLG) trial wavefunction is used as a starting point for this substantiation. The main force fields of molecular mechanics-those of bonding and bending-are derived for sp 3 carbon from the analysis of the total energy in semiempirical variant of the APSLG scheme. Analytically obtained constants of these force fields are in perfect coincidence with those typically used in the empirical force fields. The formulae for offdiagonal force fields are also obtained and analyzed. The application of the results for understanding the organic stereochemistry is discussed.

Deductive molecular mechanics of sp3 nitrogen atom and its application to analysis of a QM/MM interface

“…[18], the form of the HOs within the FA class of the approximations leading to the MM-like description of the four-coordinated carbon atom is ultimately defined by the two-center resonance interactions. The SO(4) group structure of the hybrid manifold significantly restricts the ability of the one-electron states residing on the atom to adjust themselves to the variations of geometry arrangement of the surrounding atoms (groups).…”

“…This problem was addressed in Refs. [18,19], where the parameterization of the SO(4) group by Jacobi angles was used. This six-parametric group can be parameterized by the angles sx A , sy A , sz A , yz A , xz A , and xy A , corresponding to rotations in two-dimensional subspaces of the whole 4-dimensional space spanned by one s-and three p-functions.…”

“…[18] to organic molecules containing sp 3 nitrogen. The next section gives a deductive MM description of the nitrogen-containing compounds with particular stress on the source of the pyramidalization potential.…”

“…We previously showed [18] that the classical force fields for the sp 3 carbon atom can be sequentially derived from the APSLG-MINDO/3 method. Here we try to extend this approach.…”

“…[18] where the linear response approximation was used for analysis of interrelations between molecular geometry and hybridization for the sp 3 carbon atom. This construct may be qualified as a deductive molecular mechanics, because each of its components has a transparent counterpart in the underlying QM description and the approximations and simplifications used can be uniquely characterized and formulated.…”