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?

Electron population terms 〈${r{{- 3\hfill \atop N\hfill}}}$〉 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. Se4+, Se2+, Se0, and Se2− with the Oh symmetry are called G(A: Se) and HSe+, H2Se, and HSe− with the C∞h or C2v 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 〈${r{{- 3\hfill \atop N\hfill}}}$〉. The 〈${r{{- 3\hfill \atop {\rm Se}\hfill}}}$〉4p, 〈${r{{- 3\hfill \atop {\rm S}\hfill}}}$〉3p, and 〈${r{{- 3\hfill \atop {\rm O}\hfill}}}$〉2p values correlate well with the corresponding MO energies (εN) for all calculation levels employed. Plots of 〈${r{{- 3\hfill \atop N\hfill}}}$〉HOMO and 〈${r{{- 3\hfill \atop N\hfill}}}$〉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 〈${r{{- 3\hfill \atop N\hfill}}}$〉 clarify how valence orbitals shrink or expand depending on Q(N). The applicability of 〈${r{{- 3\hfill \atop N\hfill}}}$〉 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 〈${r{{- 3\hfill \atop N\hfill}}}$〉 and examine the applicability to the NMR analysis. Well correlated: The 〈${{{\rm r}{{- 3\hfill \atop {\rm {\rm Se}}\hfill}}}$〉 values of HOMO and LUMO constructed by the pure atomic 4p(Se) orbitals are correlated very well with Q(Se) for G(A: Se4+, Se2+, Se0, Se2−) and G(B: HSe+, H2Se, and HSe−), if calculated at the B3 LYP level (R2=0.999). The results (see figure) demonstrate that 77Se NMR chemical shifts can be analyzed separately by the charge factor from others through evaluation of 〈${{{\rm r}{{- 3\hfill \atop {\rm {\rm Se}}\hfill}}}$〉.