Variational principles for describing chemical reactions: Condensed reactivity indices

Abstract

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.

Critical analysis and extension of the Hirshfeld atoms in molecules

“…The reason why Hirshfeld charges are so small can be related to the work by Ayers who has shown that the Hirshfeld weighting factor is such that it makes the AIM as similar as possible to the isolated atom. 17,28 It is therefore not surprising that also the atomic properties of the AIM are as similar as possible to that of the isolated atom. One of these properties is the atomic population.…”

Descriptores globales y locales de la reactividad para el diseño de nuevos fármacos anticancerosos basados en cis-platino(II)

“…[16][17][18]31,[33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] Las ecuaciones básicas de la DFT, se obtienen a través de la minimización del funcional de energía de la densidad electrónica, E[ρ] con la restricción que el número de electrones (N) permanezca constante, conduciendo a la expresión mostrada en la Ecuación 1:…”

“…Descriptores globales y locales calculados al nivel mPW1PW/LANL2DZ* para los derivados propuestos acumulación o disminución de la densidad electrónica sobre un sitio particular de la molécula, aun cuando el número de electrones aumente o disminuya en uno. 75 Por otro lado, Ayres, 43 recientemente relacionó el comportamiento anteriormente expuesto con la reducción u oxidación de centros atómicos en determinada molécula. Estos valores negativos constituyen un verdadero rompecabezas a la hora de analizar los datos, así que, dentro de las estrategias para superar la complejidad asociada a dichos valores negativos para FF, Kolandaivel y colaboradores, 32 propusieron el descriptor atómico (sf ) k α , con el cual obtuvieron resultados confiables para las tendencias de reactividad de un grupo de moléculas seleccionadas.…”

Testing exchange–correlation functionals at fractional electron numbers

“…(The factor C LCC is omitted in our illustrative example tests as it is irrelevant at comparisons). Note that (C LCC ) −1 equals to one when the FF is not negative, but it is larger than one (even two) when FF is negative in some regions as in cases of redox-induced electron transfer [38,39]. This Δ LCC is the last indicator for testing the quality of functionals, proposed in this work.…”