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

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 chara...

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Bibliographic Details
Published in:Molecules (Basel, Switzerland) Switzerland), 2021-07, Vol.26 (15), p.4524
Main Author: Nascimento, Marco Antonio Chaer
Format: Article
Language:English
Subjects:
Atomic structure
Atoms & subatomic particles
chemical bond
Chemical bonds
Chemists
Electrons
Group theory
Molecular modelling
Molecular orbitals
Molecular structure
Molybdenum
Permutations
quantum interference
Quantum physics
Quantum theory
Review
symmetric group
Symmetry
Valence-bond
Wave functions
X-rays
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Summary: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.
ISSN:1420-3049
1420-3049
DOI:10.3390/molecules26154524