Rayleigh-Schrodinger perturbation second order correction

It should be apparent that the expressions for the wave functions after interaction [equations (3.38) and (3.39)] are equivalent to the Rayleigh-Schrodinger perturbation theory (RSPT) result for the perturbed wave function correct to first order [equation (A.109)]. Similarly, the parallel between the MO energies [equations (3.33) and (3.34)] and the RSPT energy correct to second order [equation (A. 110)] is obvious. The missing first-order correction emphasizes the correspondence of the first-order corrected wave function and the second-order corrected energy. Note that equations (3.33), (3.34), (3.38), and (3.39) are valid under the same conditions required for the application of perturbation theory, namely that the perturbation be weak compared to energy differences. 

CIS(D) can be rigorously derived by applying the Lowdin-type (as opposed to Rayleigh-Schrodinger) perturbation theory [70] to CIS, according to Meissner [71]. Additional off-diagonal second-order corrections to CIS have been considered by Head-Gordon et al. [72],... 

Applying standard Rayleigh-Schrodinger perturbation theory, the first-order wave function and second-order energy correction F 2 are... 

Ho is the normal electronic Harmltonian operator, and the perturbations are described by the operators Pi and P2, with A determining the strength. Based on an expansion in exact wave functions, Rayleigh-Schrodinger perturbation theory (Section 4.8) gives the first- and second-order energy corrections. 

One of the basic computational methods for the correlation energy is the MP2 method, which gives the result correct through the second order of the Rayleigh-Schrodinger perturbation theory (with respect to energy). 

M0ller-Plesset second-order perturbation theory [78,162] is the most widely used approach to the electron correlation problem in contemporary ab initio molecular electronic structure studies [163-168], For systems which are well described by a single determinantal reference function, this theory - based on the use of Rayleigh-Schrodinger perturbation theory to describe electron correlation corrections to the Hartree-Fock independent electron model - affords an approach which combines accuracy with computational efficiency. The method, which is often designated mp2 , is based on the lowest order of the many-body perturbation theory expansion to take account of correlation effects. 

The adiabatic corrections to the ground state of H2, HD, and Di we shall calculate using second-order Rayleigh-Schrodinger many-body perturbation theory (RS-... 

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