Abstract
The approximate pseudorotation symmetry of linear polyenes CnHn+2 [D.R. Herrick, J. Chem. Phys. 74, 1239 (1981)] is investigated using seniority labels from irreducible representations of subgroup chains of the unitary group U2n. Seniority labels from the spin-dependent symplectic group Sp2n(n = odd) and the rotation group R2n(n = even) are found to quantize completely the alternacy particle–hole symmetry of neutral radicals and molecules in a Pariser–Parr–Pople (PPP) model of valence states. Tables of molecular seniority labels are constructed by a new approach based upon a reduction of the difference character of R2n according to R2n→spin×Spn. Lie algebra generators for subgroups Rn(n = odd) or Spn(n = even) of the spin-free group Un are linked to bond orders between different atoms in the polyene. Details are presented for a new multipole tensor expansion of the PPP Hamiltonian, and certain terms which otherwise break the pseudorotational symmetry are found to vanish identically in the special case of all-trans linear polyenes. Numerical results are presented for the remaining tensor expansion coefficients of several model interactions and suggest a further, approximate simplification of the electron correlation, due to a fortuitous cancellation of terms originating in the long-range and short-range parts of the Coulomb repulsion integral.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call