Principle and formal background

In the master formula for the analysis of the pseudo-Jahn-Teller effect, the total curvature of the adiabatic potential surface, K, is partitioned in a so-called non vibronic part K0 and the vibronic one Kv, namely K = K0 + Kv, with 

In the above formula, Q is the nuclear coordinate, p, and I/r are the ground state and excited electronic terms. Here Kv is provided through the traditional Rayleigh-Schrodinger perturbation formula and K0 have an electrostatic meaning. This expression will be called traditional approach, which has, in principle, quantum correctness, but requires some amendments when different particular approaches of electronic structure calculation are employed (see the Bersuker s work in this volume). In the traditional formalism the vibronic constants P0 dH/dQ Pr) can be tackled with the electric field integrals at nuclei, while the K0 is ultimately related with electric field gradients. Computationally, these are easy to evaluate but the literally use of equations (1) and (2) definitions does not recover the total curvature computed by the ab initio method at hand. 

The reason for such problems is contained in the following quotation from Pulay [7] Nuclear coordinates as perturbation parameters are different from other common perturbations, e.g. weak external fields. The reason for this is the deep and singular potential well at the nucleus which leads to large charge density near the nucleus . The key is suggested by a further quotation from the same source ... the 

The use of floating basis turns the vibronic curvature to the following form  

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