Method perturbation, Rayleigh-Schrodinger

There have also been other attempts to evaluate these energy differences directly."" These methods utilize Rayleigh-Schrodinger perturbation theory to express the energies for both states with a common orbital basis. When the perturbation series for the two state energies are subtracted, it is found that there is a considerable cancellation of identical terms from the individual series. 

The mathematical procedure that we present here for solving equation (9.15) is known as Rayleigh-Schrodinger perturbation theory. There are other procedures, but they are seldom used. In the Rayleigh-Schrodinger method, the eigenfunctions tpn and the eigenvalues E are expanded as power series in A... 

E. Schrodinger, Ann. Phys. 80 (1926), 437. The quantal formalism substantially follows the classical method developed by Lord Rayleigh (Theory of Sound [1894]) and is commonly referred to as Rayleigh-Schrodinger perturbation theory. ... 

The method is based on the following procedure.33 All possible doubly excited configurations are generated from the Hartree-Fock function and their contributions to the second-order Rayleigh-Schrodinger perturbation theory energy computed. Approximately 100 of the most important are used for a Cl calculation, all singly... 

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. 

Claverie P (1971) Theory of intermolecular forces. I. On the inadequacy of the usual Rayleigh-Schrodinger perturbation method for the treatment of intermolecular forces. Int J Quantum Chem 5 273-296... 

Very recently we have formulated and tested a new coupled-cluster polarization propagator method (Geertsen and Oddershede, 1986a). We still use a perturbation expansion of the reference state but we replace the Rayleigh-Schrodinger correlation coefficients (i =1,2)... 

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