Fukui function from a gradient expansion formula, and estimate of hardness and covalent radius for an atom

Abstract

The Fukui function for a neutral atom is expressed as its LDA approximation plus a one-parameter gradient correction, and the resultant formula is numerically tested. Expressing hardness as a density functional involving this Fukui function, global hardness values are determined for several atoms. Estimates also are made of the covalent radii of neutral atoms. Calculated Fukui functions exhibit characteristics similar to those reported in the literature. Calculated hardnesses compare favorably with experimental values, and predicted covalent radii are in agreement with existing theoretical values and experimental data. No information other than the electron densities of the neutral species enter in the calculations. An exact nuclear cusp condition on the Fukui function is derived.

Modeling the electron density kernels

“…This result has been known as the electrostatic potential of the Fukui function or the local hardness, first calculated for atoms by Chattaraj et al 6 g(r@) % g but contains only weak dependence on r@ at reasonable distances from a nucleus. As r is an arbitrary parameter only, it may be most reasonably identified for the point of maximum density, hence at r@ 5 0 assuming g(r@ 5 0) 5 g 5 I 2 A.…”

“…(9) leads to very reasonable covalent radii for atoms. 6 Torrent-Sucarrat et al applied the Thomas-Fermi model to the computationally available densities and tested the method by calculation of the global hardness. 7 They proved that this approximation [eq.…”

Perspective on "Density functional approach to the frontier-electron theory of chemical reactivity"

“…(30) and (31) where q0 is the value of the density at the nucleus and a is an empirical parameter [36,46]. Unfortunately, expansions of this type only produce one Fukui function: f r and f À r are not found [36,46]. A variational method for obtaining the Fukui function has been devised [47].…”

Fukui functions for atoms and ions: Polarizability justified approach

“…The parameter (d) can be calculated from the very basic property of the FF, identified by Parr and coworkers [9].…”

“…In 1995, Chattaraj et al [9] proposed a physical analysis that motivated a gradient expansion formula satisfying most of conditions for the FF. However, the results were satisfactory for 12 selected atoms only when tested in the most evident application of the FF, i.e., relation between the global hardness g ¼ …”