ANALYTICAL ENERGY GRADIENTS FOR DYNAMIC SIMULATIONS OF TRANS POLYACETYLENE CHAINS WITHIN THE PARISER-PARR-POPLE HAMILTONIAN

Exact analytical energy gradients for the Pariser-Parr-Pople (PPP) Hamiltonian are derived. A comparison of computer times for dynamical simulations of trans-Polyacetylene (t-PA) using analytical and numerical gradients is given. The numerical method is shown to lead to serious difficulties both computationally and from the point of view of numerical accuracy. Using the analytical method, it turned out that the computational effort for the gradient calculation is negligible compared to that for the SCF iteration in each time step of a simulation. Using the numerical method the gradient calculation is the time consuming bottleneck of a simulation. A previously presented method for the gradient calculation in the Huckel type Su-Shrieffer-Heeger (SSH) Hamiltonian, which was thought to be approximative, is shown to be exact.