Study of excited states of polyethylene in the Hartree-Fock, Tamm-Dancoff, and random-phase approximations

We report calculations of the excitonic spectra of all-trans polyethylene in the Hartree-Fock, Tamm-Dancoff, and random-phase approximations. For the formulation of approximations beyond Hartree-Fock level, we have used the particle-hole propagator technique. In the first case the interaction between the excited electron and hole is neglected and in the latter two cases it is taken into account at first order in electron-electron interaction. Using the 3-21G atomic basis set, the elementary gap is reduced from about 17 eV at the Hartree-Fock level to 13 eV in the Tamm-Dancoff approximation. The spectra in both approximations are also different. The difference between the results obtained in the Tamm-Dancoff and the random-phase approximations is very small. We discuss the densities of exciton states for different exciton quasi momenta (K = 0 or K = π/α), different band interactions and different spins.