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

The finite temperature properties of the ethylene isomers C2H4, C2D4, (C2H4 )-H-13 and (C2D4)-D-13 have been studied by a Feynman path integral quantum Monte Carlo (PIMC) approach which has been combined with different electro nic Hamiltonians. The nuclear potential V(R) in the PIMC step of the presen t formalism has been modeled by an efficient tight-binding one-electron Ham iltonian. Electronic expectation values in thermal equilibrium have been ev aluated by ab initio Hartree-Fock and Moller-Plesset calculations. The quan tum degrees of freedom of the ethylene nuclei as well as the anharmonicitie s in V(R) cause sizable elongations of the bond lengths relative to the hyp othetical vibrationless values at the minimum of the potential energy surfa ce. The PIMC results demonstrate impressively the wave-packet character of the nuclear wave function. This effect is neglected in the crude Born-Oppen heimer approximation which forms the basis of the large majority of electro nic structure calculations of molecules. The nuclear degrees of freedom hav e a strong influence on the expectation values of the electronic Hamiltonia n. The isotope and temperature dependence of these quantities has been anal yzed. The nuclear fluctuations attenuate the nuclear-nuclear and electron-e lectron repulsions and lower the electronic kinetic energy. These stabilizi ng shifts in thermal equilibrium compete with a destabilization of the elec tron-nuclear attraction. The analysis of the ensemble averaged electronic q uantities offers insight into the modifications of covalent bonding under t he conditions of thermal equilibrium. Conceptual problems of classical Mont e Carlo simulations as well as the shortcomings of electronic structure cal culations 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 b y quantum tunneling. Physical implications which follow from the present PI MC - ab initio investigation are mentioned concisely. (C) 2001 Elsevier Sci ence B.V, All rights reserved.