The Valence-Bond (VB) Model and Its Intimate Relationship to the Symmetric or Permutation Group

Abstract

VB and molecular orbital (MO) models are normally distinguished by the fact the first looks at molecules as a collection of atoms held together by chemical bonds while the latter adopts the view that each molecule should be regarded as an independent entity built up of electrons and nuclei and characterized by its molecular structure. Nevertheless, there is a much more fundamental difference between these two models which is only revealed when the symmetries of the many-electron Hamiltonian are fully taken into account: while the VB and MO wave functions exhibit the point-group symmetry, whenever present in the many-electron Hamiltonian, only VB wave functions exhibit the permutation symmetry, which is always present in the many-electron Hamiltonian. Practically all the conflicts among the practitioners of the two models can be traced down to the lack of permutation symmetry in the MO wave functions. Moreover, when examined from the permutation group perspective, it becomes clear that the concepts introduced by Pauling to deal with molecules can be equally applied to the study of the atomic structure. In other words, as strange as it may sound, VB can be extended to the study of atoms and, therefore, is a much more general model than MO.

Theoretical cross sections for electron collisions relevant for ammonia discharges part 1: NH3, NH2, and NH

“…No experimental polarizability data was available for NH 2 . For NH, the experimental value of Scarl and Dalby [23] is considered to be underestimated, while our calculated dipole moment is in good agreement with other calculated values and with a 5% deviation compared to the experimental value given by Nascimento [24]. No experimental polarizability data was available for NH.…”

“…MOLPRO [13] was used to optimize the molecular geometries of NH 3 , NH 2 , and NH, using the Dunning's Gaussian type orbital cc-pVQZ basis set at the Hartree-Fock level. The symmetries obtained for the optimized geometries of NH [24] (0.5980-0.6374) [30] a RHF: restricted Hartree Fock; MCSCF: multi-configuration self-consistent field.…”