Strictly diabatic basis

Assuming that a strictly diabatic basis exists and defining the corresponding matrix elements Ay = (( f A(r, R)l Vf)), one arrives at... 

Equation (26) expresses a smoothness of matrix elements of Hermitian operator A in a strictly diabatic basis. It is the key formula for deriving the expression of the ADT angle in terms of a given molecular property [37]. 

Exterior Complex Scaling Finite Element Calculations Based on an Adiabatic and a Strictly Diabatic Basis, J. Mol. Spectrosc. 214 (2002) 103-110. 

In general, no strictly diabatic basis exists in a finite set g of interacting electronic states.To see this, let us return to Eqs. (27b) and (32) and... 

We briefly reformulate the above necessary and sufficient condition for the existence of a strictly diabatic basis in the context of gauge theory. In contrast to the gauge potential which transforms in a relatively complicated manner via Eq. (27b), the gauge field tensor simply transforms as... 

Owing to Eq. (35), there is no reason to expect that a strictly diabatic basis exists. Nevertheless, one can construct quasidiabatic states which are extremely useful in solving and understanding many relevant problems abundantly discussed in the literature. With their help it is possible to remove a substantial part of the derivative couplings and make the group-Born-Oppenheimer Eq. (26) more transparent and better amenable to explicit numerical calculations. That part of the derivative couplings which can be removed by an unitary transformation U( (R) is called... 

Mead C A and Truhlar D G 1982 Conditions for the definition of a strictly diabatic electronic basis for molecular systems J. Chem. Rhys. 77 6090... 

Apart from special models, Eq. (14) is satisfied only when the whole space of interacting electronic states is considered in the ADT matrix S (in diatomics, with only a single nuclear degree of freedom, there is no curl-condition). This, however, is contradicting the spirit of choosing a small subset of electronic states in the ADT matrix and would lead one back to the crude adiabatic basis discussed in the previous section. Therefore strictly diabatic electronic states, satisfying rigorously Eqs. (12) and (13) do not exist in the multidimensional case. ... 

Mead, C. A. and Truhlar, D. G. Conditions for a definition of a strictly diabatic electronic basis fijr molecular S5 stems, J.Chem.Phys., 77 (1982) 6090-6098. 

The concept of a diabatic state has different definitions. Strictly speaking, a basis of diabatic states (ft, If...) should be such that Equation 10.9 is satisfied for any variation 3Q of the geometrical coordinates (Q). 

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