Rayleigh-Schrodinger equations calculations

At the same time, Meissner, Kucharski and others [56,57] developed the quadratic MR CCSD method in a spin-orbital form which does not exploit the BCH formula. The unknown cluster amplitudes are calculated from the so-called generalized Bloch equation [45-47,49,64,65] (or in our language the Bloch equation in the Rayleigh-Schrodinger form)... 

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. 

In 1997, Pakiari and Mohammadi used the FSGO basis set for a perturbation variation Rayleigh Ritz (PV = RR) calculation. We used a matrix representation Schrodinger equation for the configuration interaction calculation. 

In quantum calculations, the Rayleigh-Ritz variational method is widely used to approximate the solution of the Schrodinger equation [86], To obtain exact results, one should expand the exact wave function in a complete basis set... 

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