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Length dependence of the optical transition energies of the exactly solvable Hubbard model for linear polyenes
Author(s) -
Hashimoto Katsufumi
Publication year - 1985
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.560280505
Subject(s) - excited state , hubbard model , ionic bonding , excitation , eigenvalues and eigenvectors , ground state , electron , physics , wave function , atomic physics , limiting , chemistry , quantum mechanics , ion , mechanical engineering , superconductivity , engineering
Abstract Some accurate results on the length dependence of the excitation energies from the ground state to ionic excited states in the Hubbard model of linear polyenes are obtained based on the method of Lieb and Wu. To this end, it is first shown that singly ionic excited states with “plus” alternancy symmetry in the Hubbard model are described by the wave functions in which the two electron operator [∑ n =1 N (−) n C n α +C n β + ] is acted on ( N − 2)‐electron covalent eigenstates. Then by solving the Lieb‐Wu equations the exact excitation energies of the lowest ionic state, which corresponds to the E 1 +state in this model, are calculated for systems with up to 50 electrons. The result, together with a correction for the end effect, indicates that the excitation energies do not decrease as 1/ N but converge to the limiting value more rapidly when the number of electrons N becomes large.