Evaluation of Electron Population Terms for 〈rSe−3〉4p, 〈rS−3〉3p, and 〈rO−3〉2p: How Do HOMO and LUMO Shrink or Expand Depending on Nuclear Charges?

Abstract

Electron population terms <r(-3)N> are evaluated for N=Se, S, and O. Calculations are performed on HOMO and LUMO constructed by pure atomic 4p(Se), 3p(S), and 2p(O) orbitals, employing the 6-311+G(3d) and/or 6-311(++)G(3df,3pd) basis sets at the HF, MP2, and DFT (B3 LYP) levels. Se(4+), Se(2+), Se(0), and Se(2-) with the O(h) symmetry are called G(A: Se) and HSe(+), H(2)Se, and HSe(-) with the C(infinityh) or C(2v) symmetry are named G(B: Se), here [G(A+B: Se) in all]. HOMO and LUMO in G(A+B: N) (N=Se, S, and O) satisfy the conditions of the calculations for <r(-3)N>. The <r(-3)Se>(4p), <r(-3)S>(3p), and <r(-3)O>(2p) values correlate well with the corresponding MO energies (epsilon(N)) for all calculation levels employed. Plots of <r(-3)N>(HOMO) and <r(-3)N>(LUMO) versus Q(N) (N=Se, S, and O) at the HF and MP2 levels are analyzed as two correlations. However, the plots at the DFT level can be analyzed as single correlation. A regression curve is assumed for the analysis. Behaviors of <r(-3)N> clarify how valence orbitals shrink or expand depending on Q(N). The applicability of <r(-3)N> is examined to establish a new method that enables us to analyze chemical shifts with the charge effect separately from others. A utility program derived from the Gaussian 03 (NMRANAL-NH03G) is applied to evaluate <r(-3)N> and examine the applicability to the NMR analysis.