Ground state and excited state properties of ethylene isomers studied by a combined Feynman path integral-ab initio approach

Abstract

Ground state and excited state properties of ethylene, C2H4, and several ethylene isomers have been studied by Feynman path integral Monte Carlo (PIMC) simulations. The PIMC treatment of the atomic nuclei has been combined with different electronic Hamiltonians in order to analyse the influence of the nuclear degrees of freedom on electronic quantities. Electronic expectation values at the minimum of the potential energy surface (PES) have been compared with PIMC based ensemble averaged values. Ensemble averaged quantities have been derived by Hamiltonians of the ab initio type and a tight-binding (TB) one-electron model. The combined influence of anharmonicities in the interatomic potential and the quantum fluctuations of the atomic nuclei lead to ensemble averaged bondlengths r g which are significantly larger than the parameters r e, at the minimum of the PES. The implications of this bond length elongation for the electronic properties of ethylene are discussed. The occupied canonical molecular orbitals (CMOs) of ethylene are destabilized under the influence of the nuclear degrees of freedom while virtual CMOs are stabilized. These shifts of one-electron energies suggest a comparison of electronic excitation energies at the minimum of the PES with PIMC based ensemble averages. The quantum fluctuations of the nuclei cause a strong redistribution in the intensities of electronic transitions. Transitions, which are dipole allowed in the planar D2h geometry of ethylene, lose intensity under the influence of nuclear quantum effects, and vice versa for electronic excitations that are dipole forbidden under D2h symmetry. This ‘vibrational borrowing’ is enhanced with decreasing atomic masses. The Feynman centroid density has been used to calculate the anharmonic vibrational wavenumbers of C2H4 and C2D4. The results of the present PIMC simulations have been employed to emphasize general problems of electronic structure calculations based on a single nuclear configuration (i.e. the configuration at the minimum of the PES).