Chapter 2 Quantum Linear Superposition Theory for Chemical Processes: A Generalized Electronic Diabatic Approach

Abstract

Abstract Complete basis states (BSs), in abstract configuration space-projected quantum mechanics (QM), permit representations of any physical and chemical process elicited by quantum states changes. For a material 1-system, defined by n -electrons and m -nuclei, BSs including relevant fragments cover a representation of chemical species identifiable by spectral response toward electromagnetic (EM) radiations. Reactants, products, and intermediate species are expressed as specific linear superpositions where the amplitude in square modulus at a given BS controls the relative intensity to the spectrum rooted at the corresponding energy eigenstate. Moreover, there is no trace that quantum numbers characterizing BSs would be changed as a function of particular regions of nuclear or electronic configuration space. The exact Coulomb Hamiltonian generates BSs. However, in this basis set, this operator does not generate evolution measured by changes of amplitudes in time, only time phases change. This operator in semiclassical models cannot drive effective time evolution via changes of amplitudes for the electronic quantum states either. The presence of a driving external field, for example, EM fields, is a sufficient condition to produce evolution standing for the physical process. It is a matter of logics that if the exact operator and the semiclassical one do not generate time evolution, then approximate models – such as computational Born–Oppenheimer (BO) – should not do it as well. However, standard (s-)BO scheme does change basis quantum numbers as a function of nuclear configuration space leading to chemical reaction representation. This apparent contradiction and possible solutions are examined here. By introducing the concept of abstract generalized electronic diabatic (a-GED) and a-BO models, electronuclear separability models are examined. Sets of noninteracting many-I-frame fragments leading to asymptotic states descriptions are included together with sets of quantum states for the one-I-frame system providing BSs to describe dissociation/association processes in chemistry. The theory takes on a clear semiclassical flavor. This approach permits introducing nuclear fixed configuration concept and relate theoretical states to laboratory ones in a natural manner. The approach leads to a generalization of the many-state reactivity models. General semiclassic schemes are introduced in Section 6 , which permit integration of one-I-frame to many-I-frames states. Planting one-electron functions at nuclear positions is the origin of the parametric dependence of s-BO wave functions, and it explains why the method displays chemical behavior. This atomic-orbital algorithm permits connecting one-I-frame semiclassic electronic states to asymptotic ones in a continuous way. A ghost atomic-orbital model is introduced to facilitate diabatic studies and reinstate the linear superposition model. As indicated in the “Contents,” some other subjects are examined from the present perspective. This includes the Jahn–Teller effect defined in this new diabatic framework and the nature of the BO scheme.