Dimerization enhancement in one-dimensional Hubbard and Pariser-Parr-Pople models

Abstract

The Su-Schrieffer-Heeger model for polyacetylene (PA) is generalized to electron-electron (e-e) contributions in Hubbard and Pariser-Parr-Pople (PPP) models. The equilibrium dimerization δ is found via the Hellmann-Feynman theorem. Exact results, computed by a valence-bond method, are presented for N≤14 site systems. N=4n+2 rings are lower bounds on the dimerization, due to a finite-size gap at δ=0, while N=2n chains give upper bounds, thereby facilitating N→∞ extrapolations. Enhanced dimerization is demonstrated in the PA regime of δ∼0.05–0.10, although the enhancement is less than previous estimates. Dimerization is suppressed for δ>0.40 in Hubbard models, as understood in terms of competing effects involving the band gap and bandwidth. Additional enhancement is found in PPP models due to the distance dependence of the potential V(R), primarily through the gradient V’($R_0$) at the spacing of the regular array. Molecular PPP parameters are then consistent with the PA ground state, including the dimerization, optical gap, and backbone vibrational frequencies.