Mpller-Plesset partitioning

The partition (14) corresponds to treating the bare nuclear Hamiltonian (BNH) as unperturbed and the entire electron interaction as perturbation. It is much better (i.e. leads to better results to low orders and gives a better overall convergence pattern), to include part of the electron interaction in Hq. Again there are various possibilities, but the Mpller-Plesset partition [108, 109, 110] has turned out to be most convenient. Here... 

When using the Mpller-Plesset partitioning of the Hamiltonian, the zeroth order Hamiltonian Ho is defined by the Hartree-Fock approximation. For a nondegenerate ground state the matrix elements Vij of the one-particle part of the interaction in Eq. (44) are then given by... 

For the popular CCSD model recalling the definition of an exponential operator Eq. (3.71) and using the Mpller-Plesset partitioning of the Hamiltonian, Eq. (9.62), the expression for the energy and the amplitude equations then become... 

In the Mpller-Plesset partitioning, set up the zero-order and perturbed Hamiltonians. 

Table 1. Hierarchy of coupled cluster methods for response calculations. The table summarizes to which order in the electron fluctuation potential ground state and single excitation energies and response functions are obtained correctly at a given level of the correlation treatment. The analysis is based on a Mpller-Plesset like partitioning of the Hamiltonian as H(t, e) = F+ U + V t, e), where U is the electron fluctuation potential [58, 59]...

The ixc-MRCISD-l-s approach defined by Eqs. (8) and (9) is infinite order even though the contraction coefficients of the external functions

first order. Computationally, it scales as the sixth power of the molecular size N. To achieve an order scaling, we consider a second-order variant, denoted as SDS-MS-MRPT2. Depending on how the zeroth-order Hamiltonian Ho in Eq. (3) is defined, various variants of SDS-MS-MRPT2 can be obtained. For simplicity, we consider here a multi-partitioned (state-dependent) Mpller-Plesset-hke [60] diagonal operator... 

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