Quasi-diabatic representation

In one dimension and with a complete set of electronic states, such a transformation is always possible. Tjv becomes diagonal, and V R) now has off-diagonal elements. The off-diagonal elements are simple functions and not operators so that they are much easier to make use of. This is the di-abatic representation, in which we now have diabatic electronic states. In the case of more than one dimension or with an incomplete set of electronic states, this transformation is not exactly possible. But frequently (or we are hoping that) a transformation which makes the off-diagonal kinetic energy operator matrix elements almost zero is possible. This is also named the diabatic representation (or the quasi-diabatic representation when we have need to make clear that the transformation is not exact). 

To this end, Truhlar and coworkers have developed the first full-dimensional quasi-diabatic representation of the coupled X f A PESs for NH3 [35, 36], More recently, Zhu, Ma, Guo, and Yarkony (ZMGY) presented a more accurate set of coupled quasi-diabatic PESs for this system [37], These PESs allowed full-dimensional QM calculations of the absorption spectra, which yielded detailed information about the tunneling dynamics in this system [37-40],... 

Zhu X, Ma J, Yarkony DR, Guo H (2012) Computational determination of the A state absorption spectrum of NH3 and of ND3 using a new quasi-diabatic representation of the X and A states and full six-dimensional quantum dynamics. J Chem Phys 136 234301... 

Zhu X, Yarkony DR (2012) Quasi-diabatic representations of adiabatic potential energy surfaces coupled by conical intersections including bond breaking a more general construction procedure and an analysis of the diabatic representation. J Chem Phys 137 22A511... 

Assuming a quasi-diabatic representation, the diabatic diagonal excited potentials Wjjiq) and the off-diagonal couplings re expanded in Taylor series with respect to the coordinates q about the ground equilibrium geometry = 0 (vertical approach) ... 

Divergent couplings ai e a nuisance for the computational treatment of the nuclear dynamics. In cases of exact or near degeneracy of electronic potential-energy surfaces it is therefore preferable to introduce an alternative electronic representation, the so-called diabatic (or quasi-diabatic) representation, which avoids singular coupling elements. The basic concept of diabatic states has been introduced in early descriptions of atomic collision processes and vibronic-coupling phenomena in molecular spectroscopy. ... 

In this section we give the relations between the nonadiabatic coupling matrix elements in the quasi-diabatic and adiabatic representations. We do not obtain simple... 

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