By developing our previous method [Phys. Rev. A 46, 2337(1992; J. Chem. Phys. 98, 543 (1993)],we show how to calculate Kohn-Sham kinetic energies, orbitals, orbital energies, and exchange-correlation potentials, starting from accurate ground-state electron densities. In addition, given correct total energies, we also show how to obtain exchange-correlation energies. The scheme used is based on the Levy constrained-search method for determining the Kohn-Sham kinetic energy. In our preferred implementation, the total electron-electron repulsion is written as a Fermi-Amaldi term plus the rest, thereby assuring the correct long-range behavior of the exchange-correlation potential. Results are given for He, Be, Ne, and Ar. It is demonstrated that the exact exchange-correlation functional cannot be local.PACS number(sj: 31.20.Sy
Two recent papers [P. W. Ayers and R. G. Parr, J. Am. Chem. Soc. 122, 2010 (2000); 123, 2007 (2001)] have shown how variational principles for the energy may be used to derive and elucidate the significance of the chemical reactivity indices of density-functional theory. Here, similar ideas are applied, yielding a systematic, mathematically rigorous, and physically sound approach to condensed reactivity indices. First, we use the variational principle for the energy to derive an expression for the condensed Fukui function index in terms of the condensed hardness kernel. Next, we address an important open problem pertaining to condensed reactivity indices: when (if ever) is the condensed Fukui function for an atom in a molecule negative? In particular, our analysis confirms the observation, hitherto based only on computational evidence, that the Hirshfeld partitioning is optimal for obtaining non-negative Fukui functions. We also hypothesize that the strong diagonal dominance of the condensed hardness kernel is sufficient for the non-negativity of the Fukui function. Errors in the partitioning of molecules into atoms and inadequate treatment of correlation are pinpointed as the most likely causes of negative condensed Fukui functions. We conclude by noting that the condensed Fukui functions are, in some respects, more appropriate indicators of a molecular site’s reactivity than the Fukui function itself.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.