ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
Walsh's rules correctly attribute the "bent'' structures of H2O and NH3 to the occupation of the 1πz→3a1 HOMO not occupied in linear BeH2 and planar BH3. In Walsh's molecular orbital (MO) diagram E(3a1) decreases sharply with bending angle S. This has always been attributed incorrectly to changes in the 3a1 MO, mainly due to symmetry-allowed mixing with the LUMO, 4a*1. The forbidden bending of BeH2 and BH3 has been similarly "explained.'' Using large-basis-set self-consistent field molecular orbital (SCF MO) ψs, we show that the integral Hellmann–Feynman theorem ΔEIHF(approximately-equal-to)ΔESCF much better than does the analogous second-order perturbation theory λE''(SE'=0 and λ=S2/2, ΔH(approximately-equal-to)SH'+λH''). ΔEIHF=〈ψ0||ΔNA||ψ0〉+〈ψ0|| ΔNA||Δψ˜〉+ΔNR(approximately-equal-to)Σni2Δ EIHFi+ΔNR, Δψ˜=(ψ/η)−ψ0, η=〈ψ0||ψ〉, ΔEIHFi=〈φ0i|| ΔNA||φ0i〉+〈φ0i|| ΔNA||Δφ˜i〉, Δφ˜i=(φi/ηi)−φ0i, ηi=〈φ0i||φi〉, ΔNA=ΔH−ΔNR. Both theories show a large negative 〈1πz||ΔNA||1πz〉 term and small 〈1πz||ΔNA||Δ1π˜z〉 HOMO–UMO mixing term, which is positive in ΔEIHF. The 〈1πz||SH'||3σ*g〉 HOMO–LUMO mixing term is small even when 3σ*g is optimized for the excited state. The ΔEIHFis andλE‘is give the usual Walsh diagrams for bending of H2O and NH3, with or without MO partitioning of the nuclear repulsion change (ΔNR). However "decoupling'' of the φ'is in ψ' makes the λE‘is unreliable. The 〈1πz||ΔNA||1πz〉 term acts to create a large allowed barrier to inversion for H2O and CH4, but a strong ΔNR nearly destroys an otherwise large barrier for NH3. 〈1πz||ΔNA||1πz〉 acts to bend the linear H2O, planar NH3, and planar CH4, with HOMO–LUMO mixing being "antibending.'' We show that understanding of MO correlation diagrams demands consideration of the "static'' 〈φ0i||ΔNA||φ0i〉 terms as well as the OMO–UMO mixing terms, which has not been appreciated by earlier workers so far as we are aware.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.450696
