Quasi-diabatic states

Nakamura and Truhlar [26] have developed direct calculation techniques to obtain quasi-diabatic states. Yet, a main issue remains there is no clear quantum-mechanical interpretation as to the meaning of an electronic wave ftinction that depends parametrically on the positive charge positions [4]. The multi-electronic-state molecular dynamics approach by Martinez et al. [27] highlights the problems raised by the use of the BO scheme. The crossing points and the uncontrolled coupling of electronic states... 

In this section we survey some common methods used in the literature for computing (quasi)diabatic states. They are grouped into three classes, depending on the type of information upon which the construction is based. 

Eq. (26). All the removable derivative coupling is transformed away, which is probably the most systematic way to arrive at optimum (quasi )diabatic states in general. Of course, in a given example the smallness of the residual couphng in the (quasi)diabatic basis remains to be verified and other methods could be superior when matrix elements of the derivative couplings with nuclear wavefunctions are considered. 

The theoretical and practical limitations of an approach which aims at the exact cancellation of the derivative couplings have led several authors to propose procedures to build sets of a priori quasi-diabatic states. These are electronic states which undergo, by construction, only slow variations as functions of the nuclear coordinates. As a consequence, in this basis the derivative couplings should be small and, for many purposes, negligible however, they are not required to vanish exactly, whence the name of quasi-diabatic states. The matrix elements of all important operators (//el, the d/dQa themselves, the multipole operators, etc.) should be smooth functions of the Qa. this facilitates the interpolation or fitting of these quantities and allows a reduction of the number of ab initio calculations required to characterize portions of the hypersurfaces. We shall discuss here some general features and we shall review in the next subsections the different methods devised to build quasi-diabatic states. 

Several methods to determine quasi-diabatic states are based on the assumption that single determinants or configurations are quasi-diabatic wavefunctions in other words, their physical content should not change too much with the nuclear geometry and the matrix elements of d/dQa in this basis should be small. When this is true, the main source of variation of the adiabatic wavefunctions, and the dominant contribution to is the change of the Cl coefficients as functions of the nuclear coordinates keeping the Cl coefficients as constant as... 

These methods " aim at minimizing the variation of the quasi-diabatic states, without making use of diabatic orbitals or diabatic templates. The diabatic states are assumed to concide with the adiabatic ones at some special geometry usually in the asymptotic region for a collisional problem then, they are propagated to other geometries by impos-... 

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