Some coherent-states aspects of the electron nuclear dynamics theory: Past and present

Past and present coherent-states (CS) efforts with the electron nuclear dynamics (END) theory at its simplest level (SL-END) are reviewed. END is a time-dependent, variational, non-adiabatic, direct-dynamics method that describes simultaneously the nuclei and electrons of a molecular system. Within that characterization, SL-END adopts a classical-mechanics description for the nuclei and a quantum single-determinantal representation for the electrons. From its very inception, SL-END has been associated with the CS theory. CS sets are continuous and over-complete sets that satisfy the resolution of identity with a positive measure. Different CS sets can play an astonishing number of roles within SL-END that have several practical consequences. Originally, SL-END utilized the canonical and Thouless CS sets to correctly represent the nuclear and electronic parts of the SL-END wavefunction, respectively, thus defining a proper phase space for the SL-END dynamical equations. Later, canonical and rotational CS sets were used for reconstructing quantum vibrational and quantum rotational descriptions from the SL-END classical nuclear dynamics. That development proved essential to calculate state-resolved properties in ion-molecule and atom-molecule collisions with SL-END. Present CS efforts include a time-dependent Kohn-Sham density-functional-theory direct-dynamic method in the END framework and a CS approach to the charge-equilibration model inter alia.