Characterization of Electronic Structure in Molecules by One-Center Expansion Techniques. No Three-Center Four-Electron Bond in PF5

Abstract

The one-center expansion technique is applied to analyze the electronic structure of molecules in terms of angular momentum eigenfunctions (s, p, d, ...) of the participating atoms. That is, by scanning through a continuous set of spherical neighborhoods of a given atom, the surrounding molecular electronic structure is characterized by functions of radius from an otherwise unbiased atomic point of view. These functions include (a) radial densities/populations of angular momentum eigenfunctions, (b) their responses, e.g., to structural changes, and (c) the extent to which the one-particle density matrix can locally be described in terms of a preset number of “natural” orbitals (study of hypervalence). Covalence and delocalization, which by definition are not attributable to a single atom, are characterized by the degree of electron sharing between angular momentum eigenstates referring to different atomic neighborhoods. A concept of hybrid orbitals in chemical bonding with no other ingredients than principles of quantum mechanics and (spherical) atomic neighborhoods is outlined. The proposed approach is applicable to any approximation of electronic structure that allows the construction of a one-particle density operator in terms of an arbitrary one-particle basis set. Elementary applications to H2, ethane, F2, and benzene and a thorough analysis of the electronic structure of PF5 are presented. The main results with respect to D3h-symmetric PF5 are the following: (a) a model of (spectroscopic) sp3d hybrid orbitals at phosphorus is inappropriate; (b) a Rundle model with three two-center two-electron bonds and one three-center four-electron bond does not apply; (c) strong 3s participation at P in covalent bonding with all five fluorine atoms creates different delocalization patterns instead; (d) a description of the valence region of phosphorus by only four orbitals is unsatisfactory (octet rule violation), and is best improved by an additional orbital of local d character; (e) the corresponding d population is only weakly bound to phosphorus, and should not be considered as chemically bonding.