Molecular Force Fields and Valency

Abstract

The study of intramolecular force fields for small nuclear displacements provides a means of extending our knowledge and understanding of valency. For the chemist, the most useful expression for the force field is in terms of bond-length changes and bond-angle changes. The quadratic form for small displacements is then

$$ 2V = \sum\limits_i {{k_i}\Delta r_i^2 + \sum\limits_{ij} {{k_{ij}}\Delta r{}_i\Delta {r_j} + \sum\limits_p {{k_p}\Delta \alpha _p^2 + \sum\limits_{pq} {{k_{pq}}\Delta {\alpha _p}\Delta {\alpha _q} + \sum\limits_{ip} {{k_{ip}}\Delta {r_i}\Delta {\alpha _p}} } } } } $$

((1.1))

where the summation is over all bonds and all interbond angles; Δr _i = r _i - r _ei , where r _ei is the equilibrium length of the ith bond, and Δα _p = α _p - α _ep , where α _ep is the equilibrium value of the pth angle. There are two types of constants in equation (1.1): the main constants k _i (bond) and k _p (angle), and the interaction constants k _ij (bond-bond), k _pq (angle-angle) and k _ip (bond-angle).