Strictly diabatic

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... 

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]. 

In this appendix we generalise the expressions of the diabatic quantities first introduced in Sec. 2 for the ideal case of an exact two-level problem to a more realistic description. In a normal situation, the Hamiltonian has an infinite number of eigenstates, and there is no finite number of strictly diabatic states [76] that can describe a given pair of adiabatic states [77-80]. Instead, one can define a unitary transformation of the adiabatic states generating two quasidiabatic states characterised by a residual non-adiabatic coupling, as small as possible, but never zero (see, e.g., [5,24,32-35]). In practice, the electronic Hilbert space is always truncated to a finite number of configurations. In what follows, we consider the case of MCSCF wavefunctions and make use of generalised crude adiabatic states adapted to this. 

It appears that a strictly diabatic (or adiabatic) theory cannot account for the above data. The SACM has been modified by including some nondiabaticity (Dashevskaya et al., 1990, 1992), and it may be that with an appropriate mix of diabatic and nondiabatic curves, the ketene and NCNO decay rates could be accommodated. In this regard, it is interesting that some adiabaticity has recently been introduced into variational RRKM theory (Wardlaw and Marcus, 1988). However, this does not affect the predicted dis-... 

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... 

In this context, let us briefly return to the two-state case. As discussed above, strictly diabatic states exist in one dimension, e.g. for a diatomic molecule with interatomic distance R. In a typical situation, the adiabatic potentials exhibit an avoided crossing and the diabatic potentials cross each other once a function of R. Assuming that the derivative couplings vanish at infinite internuclear distance, and using Eq. (30) then gives... 

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. ... 

Strictly diabatic states are defined in order to have vanishing derivative cou-phngs [17],... 

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. 

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