Density matrix renormalization group study of dimerization of the Pariser–Parr–Pople model of polyacetilene

We apply the density matrix renormalization group method to the Pariser–Parr–Pople Hamiltonian and investigate the onset of dimerization. We deduce the parameters of the hopping term and the contribution of the σ bonds from ab initio calculations on ethylene. Denoting by Rij the C–C distances, we perform a variational optimization of the dimerization δ=(Ri,i+1−Ri−1,i)/2 and of the average bond length R0 for chains up to N=50 sites. The critical value of N at which the transition occurs is found to be between N=14 and N=18 for the present model. The asymptotic values for large N for R0 and δ are given by 1.408(3) Å and 0.036(0) Å.