Comparison of the accurate Kohn-Sham solution with the generalized gradient approximations (GGAs) for the S(N)2 reaction F-+CH3F -> FCH3+F-: A qualitative rule to predict success or failure of GGAs

Kohn-Sham solutions are constructed from ab initio densities obtained with multireference configuration interaction (MRCI) calculations for the transi tion state (TS) and for the intermediate complex (IC) of the prototype symm etrical S(N)2 reaction F- + CH3F --> FCH3 + F-. The calculated KS exchange and correlation energies, epsilon(x)(KS) and epsilon(c)(KS), as well as the exchange and exchange-correlation (xc) energy densities epsilon(x)(KS)(r) and epsilon(xc)(KS)(r), are compared with the corresponding quantities of t he standard generalized gradient approximation (GGA). GGA functionals subst antially underestimate the repulsive exchange contribution to the central b arrier of the S(N)2 reaction, thus producing a too low barrier. A similar p roblem arises in a number of other bonding situations, and a qualitative ru le is put forward to predict success or failure of standard GGAs in molecul ar calculations, depending on the type of chemical bonding. For systems wit h two-center two-electron bonds (standard covalent bonds), two-center four- electron Pauli repulsion (interacting closed shells), and three-center thre e-electron bonds, current GGAs (or minor modifications) are expected to per form successfully. In these cases the GGA exchange functional represents ex change and (if it is present) nondynamical Coulomb correlation, while the G GA correlation functional represents dynamical Coulomb correlation. Contrar y to this, for systems with three-center four-electron bonds (TS of the S(N )2 reaction), two-center three-electron bonds, and two-center one-electron bonds, for which the exchange hole is delocalized over all interacting frag ments and efficient nondynamical correlation is hampered by the unfavorable electron count, the GGA exchange functionals still yield nondynamical corr elation, which is in these cases spurious, the GGAs thus overestimating the relative stability of these systems.