COHERENT-STATE APPROACH TO ELECTRON-NUCLEAR DYNAMICS WITH AN ANTISYMMETRIZED GEMINAL POWER STATE

A formulation of the complete dynamics of electrons and nuclei is pres ented. The dynamical equations are derived using the time-dependent va riational principle (TDVP). The approximate electronic state vectors a re antisymmetrized geminal power (AGP) states parameterized as project ed coherent states, while the nuclei are treated as classical point pa rticles. This leads to a formulation of time-dependent AGP theory that generalizes time-dependent Hartree-Fock (TDHF) theory and explicitly includes the dynamics of the nuclei. The linear approximation to the e volution equations (the classical harmonic approximation) which corres ponds to a generalized random phase approximation (RPA) based on an AG P electronic reference state and which explicitly includes the dynamic s of the nuclei, is studied and presented in this paper. The equations are formulated in terms of the primitive nonorthogonal electronic ato mic basis thus avoiding any transformation to orthonormal molecular or bitals during the evolution.