Single-reference coupled cluster framework

It would be remiss not to mention multireference techniques for the high-level description of correlation within the coupled-cluster framework.2,3,26 Consider that double excitations from reference functions that are doubly excited relative to each other incorporate quadruple excitations (e.g., J4) from a single reference. However, further discussion of MR-CCM is beyond the scope of the present article, and we refer the interested reader to Refs. 2, 3, and 26. 

Abstract The purpose of this paper is to introduce a second-order perturbation theory derived from the mathematical framework of the quasiparticle-based multi-reference coupled-cluster approach (Rolik and Kallay in J Chem Phys 141 134112, 2014). The quasiparticles are introduced via a unitary transformation which allows us to represent a complete active space reference function and other elements of an orthonormal multi-reference basis in a determinant-like form. The quasiparticle creation and annihilation operators satisfy the fermion anti-commutation relations. As the consequence of the many-particle nature of the applied unitary transformation these quasiparticles are also many-particle objects, and the Hamilton operator in the quasiparticle basis contains higher than two-body terms. The definition of the new theory strictly follows the form of the single-reference many-body perturbation theory and retains several of its beneficial properties like the extensivity. The efficient implementation of the method is briefly discussed, and test results are also presented. 

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