Complex states of simple molecular systems

This chapter presents a rigorous quantum formalism for the study of dynamics of a polyatomic system (comprised of N atoms) on n electronically adiabatic states, in the absence of spin-orbit interactions. These can be introduced subsequently as pertubative corrections, if they are not too large. Section II presents the adiabatic n-electronic state coupled nuclear motion Schrödinger equations and discusses the properties of first- and second-derivative non-adiabatic couplings in this adiabatic representation. Section III deals with the adiabatic-to-diabatic transformation that produces an optimal diabatic representation, in which the nonremovable couplings are minimized. Application of this transformation to the lowest two adiabatic electronic states of H³ is also presented. Section IV introduces the full three-dimensional quantum reactive scattering formalism for a triatomic system on two adiabatic electronic potential energy surfaces capable of providing state-to-state differential and integral cross-sections. The two-electronic-state reactive scattering formalism and the associated nuclear motion hyperspherical coordinate coupled equations presented in Section IV should provide cross-sections that can be compared with those obtained from a one-electron-state formalism and yield the energy range of validity of the one-electronic-state Born-Oppenheimer approximation.