The Interpretation of Molecular Wave Functions: The Development and Application of Roby's Method for Electron Population Analysis

• Published in: Philosophical Transactions of the Royal Society of London, Series A: Mathematical and Physical Sciences Series A: Mathematical and Physical Sciences, 1982-04, Vol.304 (1488), p.533-565
• Main Authors: Cruickshank, Durward William John, Avramides, Elizabeth J.
• Format: Article
• Language: English
• Subjects: Atoms; Chemical bonding; Electrons; Hydrogen; Mathematical functions; Molecules; Nitrogen; Orbitals; Sulfur; Wave functions
• ISSN: 1364-503X; 0080-4614; 0962-8428; 1471-2962; 2054-0272
• DOI: 10.1098/rsta.1982.0020

An extensive investigation has been made of Roby’s (Molec. Phys. 27, 81 (1974)) projection-density method for electron population analysis, particularly as applied to extended basis molecular wave functions. In the developed method maximum possible populations are ascribed to atomic s.c.f. orbitals and minimum possible populations to polarization functions. Roby populations are reported for a range of diatomic and simple polyatomic molecules. For a given coordination number, the Roby atomic population nA reflects the electronegativities of an atom and its ligands. By equipartition of shared populations, atomic charges may also be defined. The two-centre shared populations sAB = nA + nB — are found to be coherent indicators of bond strengths. For conventional single bonds, sAB can often be roughly interpreted as SAB» 2Sab,where Sab is the overlap integral between the two hybrid atomic orbitals defined by a localized molecular orbital representing the A -B bond. Multiple bonds can be interpreted similarly. Multi-centre shared populations sABC, sABCD are helpful in descriptions o f the bonding in B2H6 and P4. The Roby projector technique is particularly useful in determining the unique effects of polarization functions. Several wave functions for NF3 and SO3are examined in detail, and the sulphur d functions are confirmed as the most important polarization functions. Various technical aspects of the Roby method are also explored, and the method is shown to have some significant advantages over the widely used Mulliken ( J. chem. Phys. 23, 1833 (1955)) method of population analysis.