Nuclear quantum effects in the electronic structure of C2H4: a combined Feynman path integral–ab initio approach

A tight-binding equipped Feynman path integral Monte Carlo formalism has been linked to a Hartree–Fock Hamiltonian to derive the electronic properties of C2H4 considering the quantum character of the nuclei. Configurationally averaged electronic quantities are compared with single-configuration results. The potential energy of the vibrational problem is caused by an energetic up-shift of the electron-nuclear interaction of the electronic Hamiltonian under the influence of nuclear quantum fluctuations. Relative to the values optimized by bare electronic Hamiltonians, calculated bond lengths are elongated by nuclear quantum effects. This elongation becomes more pronounced with decreasing atomic masses. Nuclear quantum properties are discussed via the radial distribution function, projected probability distributions and spatial fluctuations.