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 sigma bonds from ab initio calculations on ethylene. Denoting by R-ij the C-C distances, we perform a variational optimization of the dimerization delta=(R-i,R-i+1-R-i-1,R-i)/2 and of the average bond length Ro 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 R-0 and delta are given by 1.408(3) Angstrom and 0.036(0) Angstrom.