New formulations of relativistic multi-reference coupled cluster approach

Jeppe Olsen

Rahul Maitra, Debalina Sinha, Sangita Sen +2 more

Malaya Kumar Nayak, Rajat K. Chaudhuri

Hermann G. Kümmel

Zoltán Rolik, Mihály Kállay

The purpose of this paper is to introduce a quasiparticle-based multi-reference coupled-cluster (MRCC) approach. 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 (MR) basis in a determinant-like form. The quasiparticle creation and annihilation operators satisfy the fermion anti-commutation relations. On the basis of these quasiparticles, a generalization of the normal-ordered operator products for the MR case can be introduced as an alternative to the approach of Mukherjee and Kutzelnigg [Recent Prog. Many-Body Theor. 4, 127 (1995); Mukherjee and Kutzelnigg, J. Chem. Phys. 107, 432 (1997)]. Based on the new normal ordering any quasiparticle-based theory can be formulated using the well-known diagram techniques. Beyond the general quasiparticle framework we also present a possible realization of the unitary transformation. The suggested transformation has an exponential form where the parameters, holding exclusively active indices, are defined in a form similar to the wave operator of the unitary coupled-cluster approach. The definition of our quasiparticle-based MRCC approach strictly follows the form of the single-reference coupled-cluster method and retains several of its beneficial properties. Test results for small systems are presented using a pilot implementation of the new approach and compared to those obtained by other MR methods.

Piotr Piecuch B, Karol Kowalski

Some recent advances in the area of multi-reference coupled-cluster theory of the state-universal type are overviewed. An emphasis is placed on the following new developments: (i) the idea of combining the state-universal multi-reference coupled-cluster singles and doubles method (SUMRCCSD) with the multi-reference many-body perturbation theory (MRMBPT), in which cluster amplitudes of the SUMRCCSD formalism that carry only core and virtual orbital indices are replaced by their first-order MRMBPT estimates; and (ii) the idea of combining the recently proposed method of moments of coupled-cluster equations with the SUMRCC formalism. It is demonstrated that the new SUMRCCSD(1) method, obtained by approximating the SUMRCCSD cluster amplitudes carrying only core and virtual orbital indices by their first-order MRMBPT values, provides the results that are comparable to those obtained with the complete SUMRCCSD approach.