Epstein-Nesbet partitioning

As was shown by Claverie et al.46) this denominator shift leads to the same expression for k0 as does the Epstein-Nesbet partitioning of the Hamiltonian. 

Alternatively, excited state energies may be chosen to obtain a generalized Epstein-Nesbet (EN) partitioning... 

Double perturbation theory using Epstein-Nesbet partition. 

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. 

Table 1 Zero-order eigenvalues within the Epstein-Nesbet partitioning in multistate MCPT variants...

Diagonal matrices E and E [ above contain zero-order energies corresponding to the model space and its complement, respectively. Zero-order energies in the Epstein-Nesbet (EN) partitioning [25, 26] are collected in Table 1 for completeness. 

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

A related perturbation scheme is based on the Epstein-Nesbet partitioning of the Hamiltonian, where the zero-order operator contains those parts of the Hamiltonian that conserve the spin-orbital occupations... 

We note that this partitioning of the Hamiltonian eorresponds to that of Epstein-Nesbet theory the M0ller-Plesset partitioning has nonzero diagonal elements also in U. 

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... 

We advocate a particular choice of Hq which is akin to the Epstein-Nesbet (EN) partitioning for all the determinants which have at least... 

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