Decoupling electrons and nuclei without the Born-Oppenheimer approximation: The electron-nucleus mean-field configuration-interaction method

We introduce the electron-nucleus mean-field configuration-interaction (EN-MFCI) approach. It consists in building an effective Hamiltonian for the electrons taking into account a mean field due to the nuclear motion and, conversely, in building an effective Hamiltonian for the nuclear motion taking into account a mean field due to the electrons. The eigenvalue problems of these Hamiltonians are solved in basis sets giving partial eigensolutions for the active degrees of freedom (DOF's), that is to say, either for the electrons or for nuclear motion. The process can be iterated or electron and nuclear motion DOF's can be contracted in a CI calculation. In the EN-MFCI reduction of the molecular Schrodinger equation to an electronic and a nuclear problem, the electronic wave functions do not depend parametrically upon nuclear coordinates. So, it is different from traditional adiabatic methods. Furthermore, when contracting electronic and nuclear functions, a direct product basis set is built in contrast with methods which treat electrons and nuclei on the same footing, but where electron-nucleus explicitly correlated coordinates are used. Also, the EN-MFCI approach can make use of the partition of molecular DOF's into translational, rotational, and internal DOF's. As a result, there is no need to eliminate translations and rotations from the calculation, and the convergence of vibrational levels is facilitated by the use of appropriate internal coordinates. The method is illustrated on diatomic molecules.National Natural Science Foundation of China [21033001, 21273011, 21290192]; Beijing National Laboratory for Molecular Sciences; CARMA [ANR-12-BS01-0017]SCI(E)EIARTICLEcassam@unice.fr; liuwjbdf@gmail.com19