The implementation of the multireference coupled-cluster method based on the single-reference formalism

Abstract

A generalized version of the multireference coupled-cluster method using a single-reference formalism, which we presented in an earlier paper, has been implemented. Any number of determinants, that differ from the formal reference determinant by single or double excitations, can now be included in the reference space. In the present implementation, the single and double excitations from the secondary reference determinants have been truncated to include only those that correspond to triple excitations from the formal reference determinant. Calculations are done on a few model systems, LiH, BH, and H2O, at equilibrium and stretched geometries. Comparisons are made with full configuration interaction (CI) treatment for the single bond stretch in LiH and BH, and the results are quite promising. For the water molecule, comparisons are made with the results obtained with the coupled cluster method truncated at triple excitations (CCSDT), as well as with the full CI results. While the multireference method did not do as well for the simultaneous two-bond stretch in H2O as it did for the single bond cases, it did at least as well as the CCSDT at representing the points on the full CI potential curve.

Dynamical Electron Correlation Within Hartree-Fock Limitation

“…Thus, it is expected that if we be able to evaluate λ exactly we should get exact electronic energy of any system. [34,35,36,37,38] method for this molecule. Due to multi-reference description more computational complexities arises.…”

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

“…This is no longer the case, when cluster operators T (p) are truncated in a standard manner according to Eq. (14). Indeed, in the standard SUMRCC approximations, the system of equations (22) and (23) is replaced by a truncated system of equations for the many-body components T…”

“…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.…”

Method of Moments of Coupled-Cluster Equations: Externally Corrected Approaches Employing Configuration Interaction Wave Functions

“…It should be noted that the CISDt and CISDtq approaches, which are used to generate wave functions |Ψ for the MMCC(2,3) and MMCC(2,4) calculations, can be regarded as the CI analogs of the active-space CC approaches, such as CCSDt [19,61,62] or SSCCSD(T) [14,[51][52][53][54][55][56][57][58][59][60] and CCSDtq [61] or SSCCSD(TQ) [54][55][56][57], which are known to provide excellent description of bond breaking [14,19,57,61,62]. Although the numbers of triples and quadruples used in the CISDt and CISDtq calculations are identical to the numbers of triples and quadruples used in the CCSDt and CCSDtq calculations (provided that we use the same active space in all these calculations) and although the most expensive N o N u n In consequence, the CISDtbased MMCC(2,3) method and the CISDtq-based MMCC(2,4) approach are less expensive than their CCSDt and CCSDtq counterparts.…”

“…The representative examples include the externally corrected CC methods of Paldus and co-workers [6,10,[39][40][41][42][43][44][45][46][47][48][49] (see, also, Ref. 50), the activespace CC approaches of Adamowicz, Piecuch, Bartlett, and their collaborators [14,19,[51][52][53][54][55][56][57][58][59][60][61][62], the orbital-optimized CC methods of Head-Gordon et al [23,24], the perturbative CC approaches based on the partitioning of the similarity-transformed Hamiltonian of Gwaltney and HeadGordon [25][26][27], the state-selective MRCC approach of Mahapatra et al [63,64], the BrillouinWigner MRCC approach of Hubač and co-workers [65][66][67][68][69][70], and the method of moments of coupledcluster equations (MMCC) of Kowalski and Piecuch [7,[16][17][18]…”