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Bounds for semiempirical resonance integral approximations
Author(s) -
Cusachs Louis Chopin
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560010646
Subject(s) - antibonding molecular orbital , slater type orbital , molecular orbital , molecular orbital diagram , molecular orbital theory , non bonding orbital , atomic orbital , orbital overlap , physics , linear combination of atomic orbitals , valence bond theory , quantum mechanics , atomic physics , electron , chemistry , molecule
A lower bound to the absolute magnitude of the off‐diagonal matrix elements of the effective one‐electron Hamiltonian follows from the requirement that molecular‐orbital energies, within a symmetry class, should fall in the order of the number of nodes, i.e. that antibonding orbitals in general may not occur at lower energies than the corresponding bonding ones. An upper bound can be derived from the observation that the antibonding orbital in the homopolar two‐center case lies below the ionization limit, as for example, the ethylene π* transition. As the atomic orbitals become more dissimilar, the antibonding molecular orbital formed from two atomic orbitals will be found between the upper atomic orbital and the continuum. These requirements are used to reveal the conditions under which critical tests of the more popular approximations to these matrix elements may be developed.