Size-extensivity correction for the state-specific multireference Brillouin–Wigner coupled-cluster theory

Abstract

We present a simple a posteriori correction for the state-specific multireference Brillouin–Wigner coupled-cluster (MR BWCCSD) theory, which eliminates its size-extensivity error. In the converged amplitudes we drop terms that were identified to be responsible for the lack of size extensivity. We performed MR BWCCSD calculations with this correction on CH2, SiH2, twisted ethylene, F2, and ozone that are all, from the computational point of view, typical representatives of two-reference problems. Comparison with rigorously size-extensive calculations and experiment shows that the size-extensivity error of the corrected MR BWCCSD is only a few tenths of kcal/mol.

Multi-reference coupled-cluster study of the ionic-neutral curve crossing LiF

“…Among these are the dressed configuration interaction (CI) based ansätze of Malrieu and coworkers [30][31][32], SUMRCC based ansätze with a certain set of sufficiency conditions applied by Li and Paldus [33,34], and reduced multi-reference (RMR)-CC ansätze by Li and Paldus [35][36][37]. State specific variants of the SUMRCC approach have been proposed by Mukherjee and coworkers [38,39] Pittner, Hubac and coworkers [40][41][42] (Brillouin-Wigner type ansätze).…”

State-specific Multi-reference Perturbation Theories with Relaxed Coefficients: Molecular Applications

“…It is however not rigorously size-extensive or size-consistent. Hubač and co-workers [37], in a later development, sought to correct for the size-inextensivity by reverting to a RS type formulation. It was observed that the intruders would not show up if the inextensivity correction is incorporated by one iteration only.…”

The State-Universal Multi-Reference Coupled-Cluster Theory: An Overview of Some Recent Advances

“…The direct use of the final energy expressions in CC calculations, as is done in our MMCC theory [7,[118][119][120][121][122][123] and its multi-reference extension discussed here and in Ref. 117, which may result in the introduction of unlinked terms, is also exploited in the Brillouin-Wigner MRCC method [32][33][34][35][36][37]. As in the approximate MMCC case, the Brillouin-Wigner MRCC approach is not size extensive.…”

“…In this paper, we focus on the genuine multi-reference CC (MRCC) theories, which are based on the concept of effective Hamiltonian acting in a multi-dimensional reference or model space [4,6,[8][9][10][11][12] and which use the exponential CC ansatz to parametrize the solutions of the generalized Bloch equation [8]. The state-specific (SS) MRCC methods [4,6], including the active-space CC approaches of Adamowicz, Piecuch, Bartlett, and their collaborators [13][14][15][16][17][18][19][20][21][22][23][24][25][26] and their more recent excited-state extensions [27][28][29], the SSMRCC approach of Mahapatra et al [30,31], and the highly promising Brillouin-Wigner MRCC approach [32][33][34][35][36][37], will not be discussed in this work, although the similarity of the wave function ansatz used in the genuine state-universal MRCC theory [4,6,, considered in this paper, and the form of the wave function exploited by the SSMRCC and Brillouin-Wigner MRCC approaches of Refs. 30, 31 and 32-37, respectively, should be noted.…”