title: On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model.
abstract: Accurate, yet simple and efficient, formulae are presented for calculation of the electrostatic potential (ESP), electric field (EF) and electric field gradient (EFG) from the aspherical Hansen-Coppens pseudoatom model of electron density [Hansen & Coppens (1978). Acta Cryst. A34, 909-921]. They are based on the expansion of |r' - r|(-1) in spherical harmonics and the incomplete gamma function for a Slater-type function of the form R(l)(r) = r(n) exp(-alpha ). The formulae are valid for 0 < or = r < or = infinity and are easily extended to higher values of l. Special treatment of integrals is needed only for functions with n = l and n = l + 1 at r = 0. The method is tested using theoretical pseudoatom parameters of the formamide molecule obtained via reciprocal-space fitting of PBE/6-31G** densities and experimental X-ray data of Fe(CO)(5). The ESP, EF and EFG values at the nuclear positions in formamide are in very good agreement with those directly evaluated from density-functional PBE calculations with 6-31G**, aug-cc-pVDZ and aug-cc-pVTZ basis sets. The small observed discrepancies are attributed to the different behavior of Gaussian- and Slater-type functions near the nuclei and to imperfections of the reciprocal-space fit. An EF map is displayed which allows useful visualization of the lattice EF effects in the crystal structure of formamide. Analysis of experimental 100 K X-ray data of Fe(CO)(5) yields the value of the nuclear quadrupole moment Q((57)Fe(m)) = 0.12 x 10(-28) m(2) after taking into account Sternheimer shielding/antishielding effects of the core. This value is in excellent agreement with that reported by Su & Coppens [Acta Cryst. (1996), A52, 748-756] but slightly smaller than the generally accepted value of 0.16 +/- 5% x 10(-28) m(2) obtained from combined theoretical/spectroscopic studies [Dufek, Blaha & Schwarz (1995). Phys. Rev. Lett. 25, 3545-3548].
authors.affiliation: Department of Chemistry, University at Buffalo, State University of New York, Buffalo, NY 14260-3000, USA. volkov@chem.buffalo.edu
authors.forename: Anatoliy
authors.initials: A
authors.lastname: Volkov
authors.forename: Harry F
authors.initials: HF
authors.lastname: King
authors.forename: Philip
authors.initials: P
authors.lastname: Coppens
authors.forename: Louis J
authors.initials: LJ
authors.lastname: Farrugia