Electrons and nuclei of C 6H 6 and C 6D 6; a combined Feynman path integral – ab initio approach

Abstract

We have linked an ab initio approach of the Hartree–Fock (HF) type to the Feynman path integral quantum Monte Carlo (PIMC) formalism in order to study C 6H 6 and C 6D 6 under consideration of the quantum character of the nuclei and electrons. The combination of the statistical Monte Carlo approach with an electronic Hamiltonian offers the possibility to study the influence of the quantum and classical (=thermal) nuclear degrees of freedom on electronic expectation values. The PIMC technique has been used to derive the finite-temperature properties of the nuclei of both π rings. We discuss the temperature ( T) dependence of the energy of the C 6H 6 and C 6D 6 nuclei, their spatial delocalization properties as well as the radial and angular distribution functions. The nuclear configurations generated by the PIMC formalism have been used as input for ab initio HF calculations. Electronic expectation values have been derived as ensemble averages over 6000 different nuclear configurations which are populated in thermal equilibrium. As a result of the large quantum effects of the C 6H 6 and C 6D 6 nuclei, we derive ensemble averaged electronic expectation values which differ sizeable from the corresponding single-configuration quantities at the energy minimum. This difference is mainly caused by nuclear quantum effects; thermal degrees of freedom are of minor importance only. The electronic origin of the potential energy part of the total vibrational energy is emphasized. It is largely determined by the raise in the electron–core attraction under the influence of the spatial uncertainty of the nuclei. The all-quantum approach yields a temperature and isotope dependence of bare electronic quantities already in the framework of the Born–Oppenheimer approximation (BOA). The principal findings of the all-quantum study have been used to reconsider certain solid state problems. We mention theoretical difficulties to reproduce Compton profiles and consider metal–insulator transitions of the Mott type as well as superconductivity. On the basis of the present all-quantum results we have to emphasize, that there is no unambiguous justification to adopt an observed isotope shift in the superconducting transition temperature T c as an indicator of an electron–phonon-coupled superconducting pairing mechanism.