MP2-R12 method

The MP2-R12 method can be regarded as an externally contracted MP2 method with (contracted) double excitations into a complete spin orbital basis. To illustrate this, we shall in the following discuss an externally contracted MP2 method that comprises contracted double excitations into a subspace (Pp-, which has been orthogonalized against the orbital basis (pp, ... 

It is instructive to discuss the MP2-R12 method [37] before going into more involved CC-R12. As in MP2, the wave function of MP2-R12 (IT1)) is a linear combination of the reference HF determinant ( o)) and doubly excited determinants produced by the action of a two-electron excitation operator T ... 

Toward the complete basis set limit Massively parallel implementation of MP2-R12 methods.116... 

The concept of extremal electron pairs is discussed in the context of coupled-cluster theory and the MP2-R12 method. Using extremal pairs the numerical stability of R12-methods is considerably improved, which is demonstrated for CCSD(T)-R12 calculations of the molecules F2, N2, and Be2-... 

When we first presented the MP2-R12 method [11], we did in fact choose a generalization of the ansatz (64,66)... 

Because we always use a finite, and hence, incomplete, basis set, Eq. (16.13) gives only an approximation to the MP2 quantity The aim of the MP2-R12 method is to essentially eliminate this basis-set-truncation error and give a value of that is close to the value that would be obtained with a complete basis set. The MK-R12 method starts with the variation-perturbation inequality (9.38), where is the SCF MO wave function d>o, and u (which can be any well-behaved function) is an approximation to the MP first-order ground-state wave-function correction In the MP2 method, the first-order correction to the wave function contains terms involving Slater determinants with two electrons excited from occupied to vacant orbitals. In the MP2-R12 method, the first-order correction to the wave function used as u in (9.38) contains additional terms of the form Cijrij o for all pairs of electrons (this is a bit of an oversimplification). 

For completeness, it is noted that a detailed derivation of the coupled-cluster theory with linear R12 terms has been given by Noga and Kutzelnigg, and that Gdanitz has presented a compilation of the formulas required for the implementation of multireference CI-R12 methods. The MP2-R12 method in its early form has also been investigated by Bearpark et al, ... 

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