title: Factorized molecular wave functions: Analysis of the nuclear factor.
abstract: The exact factorization of molecular wave functions leads to nuclear factors which should be nodeless functions. We reconsider the case of vibrational perturbations in a diatomic species, a situation usually treated by combining Born-Oppenheimer products. It was shown [R. Lefebvre, J. Chem. Phys. 142, 074106 (2015)] that it is possible to derive, from the solutions of coupled equations, the form of the factorized function. By increasing artificially the interstate coupling in the usual approach, the adiabatic regime can be reached, whereby the wave function can be reduced to a single product. The nuclear factor of this product is determined by the lowest of the two potentials obtained by diagonalization of the potential matrix. By comparison with the nuclear wave function of the factorized scheme, it is shown that by a simple rectification, an agreement is obtained between the modified nodeless function and that of the adiabatic scheme.
authors.affiliation: Institut des Sciences Moléculaires d' Orsay, Bâtiment 350, UMR8214, CNRS- Université. Paris-Sud, 91405 Orsay, France and Sorbonne Universités, UPMC Univ Paris 06, UFR925, F-75005 Paris, France.
authors.forename: R
authors.initials: R
authors.lastname: Lefebvre