Liebau density vector: a new approach to characterize lone electron pairs in mullite-type materials

Abstract

The bismuth 6s2 lone electron pair (LEP) in mullite-type Bi2M4O9/10 (where M = Al, Fe, or Mn) was characterized by means of several parameters derived from experimental and theoretical calculations. The Wang-Liebau eccentricity (WLE) parameter proved to be very useful to quantify the stereochemical activity of the LEPs. Calculations of electronic distributions (three-dimensional charge density difference isosurfaces) were used as independent measurements, which validated the relevance of the WLE parameter for the characterization and quantification of LEPs. The distribution of the Bi 6s2 electrons around the nucleus was evaluated and the maximum of electron density calculated. The spatial orientation of this electron density with respect to the nucleus is expressed as “Liebau density vector”. Therefore, this vector is ascribed to be a key result of this work as a proof that the purely geometrically defined Wang-Liebau vector indeed points towards the maximum electron density of the LEP. The LEP stereochemical activity was studied in terms of the type of structure (Bi2M4O9 or Bi2M4O10) and the nature of M. The effect of exchanging bismuth by lanthanum as well as the relative stabilities of Bi2M4O9 or Bi2M4O10 structures were calculated and discussed.