Comparison between the frozen core and finite differences approximations for the generalized spin-dependent global and local reactivity descriptors in small molecules

Abstract

Local and global reactivity descriptors defined within {N, N_S, υ(r)} and {N_α, N_β, υ(r)} representations provide a remedy to the problem of inadequacy of hitherto-known reactivity descriptors in {N, υ(r)} representation in the analyses of situations where spin multiplicity changes are present. The tailor-made nature of the spin-dependent representations for specific processes is highlighted and a discussion on the convenience to use each representation is included. The connection between both representations is presented as a linear transformation. Generalized Fukui functions associated with processes where the number of electrons and/or the multiplicity change are calculated for closed-shell (NH₃, H₂O, HCOOH) and open-shell molecules (CH₂) with BLYP/aug-cc-pVTZ level of theory, using both the finite differences and the frozen core approximations. Chemical processes involving spin transfer require the explicitly spin-dependent reactivity descriptors whose definitions and domain of applicability are analyzed. The method of calculation of these quantities, using finite differences and frozen core approximations, highlights that these two techniques provide similar trends, however for cases where orbital relaxation is important, the finite differences approximation should be used.