Electrons and nuclei of ethylene isomers; a Feynman path integral – ab initio study

Abstract

The finite temperature properties of the ethylene isomers C 2H 4, C 2D 4, C 2 13H 4 and C 2 13D 4 have been studied by a Feynman path integral quantum Monte Carlo (PIMC) approach which has been combined with different electronic Hamiltonians. The nuclear potential V ( R ) in the PIMC step of the present formalism has been modeled by an efficient tight-binding one-electron Hamiltonian. Electronic expectation values in thermal equilibrium have been evaluated by ab initio Hartree–Fock and Møller–Plesset calculations. The quantum degrees of freedom of the ethylene nuclei as well as the anharmonicities in V ( R ) cause sizable elongations of the bond lengths relative to the hypothetical vibrationless values at the minimum of the potential energy surface. The PIMC results demonstrate impressively the wave-packet character of the nuclear wave function. This effect is neglected in the crude Born–Oppenheimer approximation which forms the basis of the large majority of electronic structure calculations of molecules. The nuclear degrees of freedom have a strong influence on the expectation values of the electronic Hamiltonian. The isotope and temperature dependence of these quantities has been analyzed. The nuclear fluctuations attenuate the nuclear–nuclear and electron–electron repulsions and lower the electronic kinetic energy. These stabilizing shifts in thermal equilibrium compete with a destabilization of the electron–nuclear attraction. The analysis of the ensemble averaged electronic quantities offers insight into the modifications of covalent bonding under the conditions of thermal equilibrium. Conceptual problems of classical Monte Carlo simulations as well as the shortcomings of electronic structure calculations on the basis of a single nuclear configuration in molecules with light atoms are emphasized. It is demonstrated that the nuclear degrees of freedom up to room temperature of the ethylene isomers studied are caused by quantum tunneling. Physical implications which follow from the present PIMC – ab initio investigation are mentioned concisely.