Molecular quantum theory: Separable electronuclear wave functions and vibronic states—A generalized diabatic approach

The linear superposition principle is used to represent chemical and physical processes. A quantum state representation is obtained for model molecular systems. An exact Hamiltonian is first introduced and thereafter approximated by a sum of Coulomb Hamiltonian, electron–phonon (e–ph), relativistic effects, and coupling to external fields. A sharp separability ansatz is used to study the Coulomb Hamiltonian first; the electronic part is fully represented in Hilbert space (q space); a background of positive charge replaces nuclei in real space (ξ space). This QC model leads to diabatic electronic functions and diabatic potential energy (DPE) surfaces in real space. Next, the nuclear masses are introduced via a kinetic energy operator and added to the DPEs. The attractor property of the diabatic electronic functions is used to study mass fluctuation regimes. Fluctuations, if quantized, lead to the Q²C model; mass dynamics takes place in real space. The set of product functions {ϕ_j(q)ζ_jl(ξ)} provides a base to represent arbitrary electronic states. In this context, the linear superposition principle is naturally introduced. The formulation of chemical reactions, pump–probe experiments and a detailed study of H are topics examined from the present perspective. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004