Size dependence of the X1Ag→11Bu excitation energy in linear polyenes

✍ Scribed by Xiangzhu Li; Josef Paldus

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 325 KB
• Volume: 74
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(1999)74:2<177::aid-qua14>3.0.co;2-t

✦ Synopsis

The singlet

examined using both ab initio and semiempirical model Hamiltonians. In the former Ž . 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 Ž . 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, ' ' w Ž .Ž .x Ž namely, ⌬ E s 1 q 1r2 3n q 6 y 3n q 3 in units of the exchange parameter of . the Heisenberg Hamiltonian , providing an additional insight into the nature of the studied transition.