Abstract
The influence of electron-electron correlations on the ground-state energy and the elastic properties of a one-dimensional polymer chain is studied in a perturbation expansion up to second order in U/w as a function of the gap energy in single-site approximation. It is shown that the correlation energy depends strongly on the gap width. An exact and an approximate analytical formula (considering only one-electron excitations) are derived and compared with other calculations. The obtained minimum of second-order correlation energy agrees well with other determinations. At zero gap the second-order term diverges logarithmically. The elastic constant shows also a similar behavior and increases with decreasing gap width. Its variation with gap energy is calculated explicitly for trans-polyacetylene.
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