Epstein-Nesbet second-order energy

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. 

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.. 

However, even though thanks to parametrization the MNDO method partially takes account of the electron correlation energy, the common drawback of a one-determinant approximation, namely, its inability to correctly evaluate the bond-breaking reactions, is not thereby removed as was pointed out, for example, in Ref. [70] using as an illustration a number of dissociation reactions. In such cases, a more complete inclusion of the correlation energy can remedy the situation. In this connection, Thiel suggested a MNDOC scheme [71] in which the correlation corrections are calculated explicitly in the second order of perturbation from the Epstein-Nesbet formula [72, 73] ... 

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. 

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