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Size dependence of the X 1 A g →1 1 B u excitation energy in linear polyenes
Author(s) -
Li Xiangzhu,
Paldus Josef
Publication year - 1999
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/(sici)1097-461x(1999)74:2<177::aid-qua14>3.0.co;2-t
Subject(s) - hamiltonian (control theory) , coupled cluster , excitation , chemistry , polyene , ab initio , open shell , quantum mechanics , singlet state , perturbation theory (quantum mechanics) , atomic physics , physics , computational chemistry , excited state , molecule , mathematics , mathematical optimization , organic chemistry
The singlet X 1 A g →1 1 B u transition in linear polyenes C 2 n H 2 n +2 is examined using both ab initio and semiempirical model Hamiltonians. In the former case, several basis sets are examined at the Hartree–Fock (HF) as well as the post‐HF level, relying, in particular, on the recently introduced unitary group based, low‐order, open‐shell perturbation theory and coupled cluster method. The modeling at the semiempirical level is based on valence‐bond theory and a simple one‐ or two‐parameter Heisenberg Hamiltonian. For small polyenes (butadiene and hexatriene), the low‐order perturbation theory, or even HF, results are found to be as good as the higher‐level open‐shell coupled cluster results, thus justifying their use for longer polyenes. The ab initio excitation energies show a regular monotonic size dependence, steadily decreasing with the increasing polyene size and reaching a constant finite value for long polyenes. This dependence is qualitatively reproduced using a simple one‐parameter Heisenberg Hamiltonian, enabling the derivation of an explicit expression for the excitation energy, namely, $\Delta E=[1+(1/2)(\sqrt{3n+6}-\sqrt{3n+3})]$ in units of the exchange parameter of the Heisenberg Hamiltonian), providing an additional insight into the nature of the studied transition. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 177–192, 1999