Electro-nuclear quantum mechanics beyond the Born-Oppenheimer approximation. Towards a quantum electronic theory of chemical reaction mechanisms

An electro-nuclear quantum theory is introduced where electronic states are represented with wave functions that are independent from the instantaneous nuclear configurations. The set of continuous and discrete symmetries, these latter related to a stationary nuclear configuration whenever it is the case, lay down the framework to bracket a Hilbert space describing the system. While the expectation value of the molecular hamiltonian (including the electronic, nuclear repulsion and electron-nuclear attraction) depends upon geometry, it is a 'universal' electronic wave function Phi, which renders the total energy functional stationary in a neighborhood of a geometry sharing the point symmetries of the system. The portion corresponding to the functional of the electronic energy, defined as the expectation value of the kinetic and electron-electron repulsion operators with respect to cp becomes a universal electronic functional. This electronic functional allows for a correlate with the density functional theory. In the context of this formalism, it is shown that a Hellmann-Feynman theorem holds. Pictorially speaking, one may think of nuclei fluctuating and having different geometric configurations while the invariant electronic wave function (seen as a field) provides the glue keeping the system bound. In the present approach the system cannot change electronic state by varying geometric parameters. As for any change of quantum electronic state, it will happen as a Franck-Condon process mediated by an electromagnetic field. The description of physical and chemical processes includes the radiation field as an integral part of the scheme. It is assumed that, at nuclear stationary points only, the Born-Oppenheimer based wave functions offer the best computational models to the Phi s. For a class of mechanisms, transition structures can be characterized by a unique electronic wave function leading to a Hessian with one (or more) negative eigenvalues and a definite stationary geometry. Thence, reactants (products) should not only collide but they must be molded into geometries overlaping such transition structures.