THE PARISER-PARR-POPLE MODEL FOR TRANS-POLYENES .3. DERIVATION OF EQUATIONS OF MOTION FOR EXCITED-STATE DYNAMICS USING 2-DETERMINANTAL AND MCSCF TYPE ELECTRONIC WAVE-FUNCTIONS

An SCF treatment for excited two-determinantal states and for multicon figuration SCF (MCSCF), including single excitations within the framew ork of the semiempirical Pariser-Parr-Pople (PPP) Hamiltonian is deriv ed. It is shown how analytical gradients of the electronic energy with respect to the geometrical variables can be calculated and the formal ism for the two-determinantal state is applied to the dynamics of sing let and triplet excited B(u) states of polyenes. It is shown that due to technical difficulties concerning orbital ordering the inclusion of all single excitations in the excited state wave functions via an MCS CF treatment is necessary. The use of an MCSCF procedure is important because in a Cl treatment the gradients of the energy needed for the t ime simulations cannot be computed analytically. The necessary equatio ns are derived.