Quantum delocalization of nuclei and electrons: cyclobutadiene

A Feynman path integral method for evaluating the quantum delocalization of atomic nuclei is combined with a scheme for calculating electronic delocalization parameters in the correlated electronic ground state. As model system we have selected the cyclobutadiene molecule whose π-electronic structure is discussed in the Pariser-Parr-Pople and Hubbard approaches. The dynamics of the electrons are described by the charge fluctuations as well as by the probabilities P(n) of finding n = 0, 1, 2 π-electrons at the respective atomic site. For both Hamiltonians we have compared the π-electron delocalization properties in the fermionic state |Ψfe〉 with those realized in the so-called hard core bosonic state |Ψhcb〉. The negative sign in |Ψfe〉 leads to a suppression of the charge fluctuations in comparison to their |Ψhcb〉 va dynamics of the electrons are attenuated by the quantum delocalization of the atomic nuclei. Details of this overall effect depend both on the nature of the π-Hamiltonian and on the nature of the electronic wavefunction.