Epstein-Nesbet perturbation theory

On the one hand, the Moller-Plesset partitioning of into and V is not unique and therefore the different orders of perturbation theory are also not uniquely defined. Various other choices of V were proposed " but they all led to different variants of the Epstein-Nesbet perturbation theory with a shifted denominator. This procedure also seems to be feasible for infinite systems, so there is hope that in the future more than 70 to 75% of the correlation energy will be obtained even in the second order. 

For single reference perturbation theory, there is a choice of reference hamil-the Moller-Plesset and Epstein-Nesbet zero-order hamiltonians were two choices considered in the early literature (see, for example, Ref. 54). 

The series of values presented in table 3a originate from CASPT2 calculations carried out in the frame of Moller-Plesset and Epstein-Nesbet second-order perturbation theories bracketing the total energy upwards and downwards by 0.02-0.05 a.u.. 

Note that if matrix D is approximated by only its diagonal part, we recover the Epstein-Nesbet second-order energy. Unlike E orrCEN), eorr(I MBPT(oo)) is exact to third order in perturbation theory. In fourth order, it is missing contributions due to single, triple, and quadruple excitations. 

Double perturbation theory using Epstein-Nesbet partition. 

Nakano, H. (1993a). MCSCF reference quasidegenerate perturbation theory with Epstein-Nesbet partitioning. The Journal of Chemical Physies, 99, 7983-7992. 

BWPT = Brillouin-Wigner perturbation theory EN = Epstein-Nesbet FCI = full Cl MBPT = many-body perturbation theory MRS PT = multireference state perturbation theory PT = perturbation theory RSPT = Rayleigh-SchrSdinger perturbation theory SRS PT = single-reference state perturbation theory. 

In addition to our earlier work (9,54), we wish to point out that we can also calculate the first-order coefficients by relying entirely on perturbation theory. Of course, the result will very much depend on the way we partition the Hamiltonian H into the unperturbed part Hq and the perturbation W, H -Hq+W. Since our zero-order wave function is assumed to represent a general multi-configurational Cl wave function, it is easier to employ the Epstein-Nesbet (EN) type perturbation theory. For this purpose we choose the unperturbed Hamiltonian Hq as follow... 

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