Full implementation and benchmark studies of Mukherjee’s state-specific multireference coupled-cluster ansatz

Abstract

The state-specific multireference coupled-cluster (SS-MRCC) ansatz developed by Mukherjee and co-workers [J. Chem. Phys. 110, 6171 (1999)] has been implemented by means of string-based techniques. The implementation is general and allows for using arbitrary complete active spaces of any spin multiplicity and arbitrarily high excitations in the cluster operators. Several test calculations have been performed for single- and multiple-bond dissociations of molecular systems. Our experience shows that convergence problems are encountered when solving the working equations of the SS-MRCC in the case the weight of one or more reference functions tends to take on very small values. This is system specific and cannot yet be handled in a black-box fashion. The problem can be obviated by either dropping all the cluster amplitudes from the corresponding model functions with coefficients below a threshold or by a regularization procedure suggested by Tikhonov or a combination of both. In the current formulation the SS-MRCC is not invariant with respect to transformation of active orbitals among themselves. This feature has been extensively explored to test the degree of accuracy of the computed energies with both pseudocanonical and localized active orbitals. The performance of the method is assessed by comparing the results with the corresponding full configuration interaction (CI) values with the same set of orbitals (correlated and frozen). Relative efficacies of CI methods such as MRCI singles and doubles with the same active space and size-extensivity corrected ones such as MR averaged coupled pair functional and MR averaged quadratic CC have also been studied. Allied full-fledged CC methods have also been employed to see their relative performance vis-à-vis the SS-MRCC. These latter methods are the complete-active-space-inspired single-reference (SR) CC based SS theory and the single-root MR Brillouin-Wigner CC. Our benchmark results indicate that the performance of the SS-MRCC is generally quite good for localized active orbitals. The performance with the pseudocanonical orbitals, however, is sometimes not as satisfactory as for the localized orbitals.

A simple approach to the state-specific MR-CC using the intermediate Hamiltonian formalism

“…The calculation is done with the cc-pVDZ basis set at five different geometries obtained from the equilibrium geometry (R e =1.84345Å, and ∠ HOH = 110.6 • ), in order to compare with the values of the literature. 43 The results appear in Table VI. The benefit of the MRCCSD with respect to the CASSDCI treatment is significant : the maximum error is 1.4 mE h , better than the 6.4 mE h given by the Mk-MRCC treatment.…”

Towards the full coupled-cluster model with triples: a retrospective after 25 years

“…Along with the progress related to molecules well represented by a single determinant reference we are witnessing a progression of CC methods applicable for more general molecules, particularly those which show some extent of quasidegeneracy. Either in the treatment via higher excitations [43,46,[67][68][69] or in the treatment via multireference approaches [12,15,[70][71][72][73]. In several of these approaches the ideas put forward in our original paper on approximations to iterative as well to noniterative triples were further extended.…”

Multireference coupled-cluster Ansatz

“…Another difficulty of the MRCC approaches relying on the Ansatz (12), is the lack of invariance to rotations of active orbitals [134,154,155] (this Ansatz and the resulting SU-CC, BW-CC, MkCC, and MRexpT approaches are, however, fully invariant to separate rotations of core and virtual orbitals). This lack of invariance is less severe if the M 1 ⊕ M 2 space is chosen as the range of all T µ operators [131], but it is to be determined how significant this lack of invariance is in practice (probably is not very significant in applications of the general model space method of Li and Paldus [92][93][94][95][96][97]).…”

“…The difficulties to converge the solutions of MRCC equations may be overcome by using better convergence acceleration or equation regularization techniques [134], or by including higher excitations in T µ , which should reduce the number of unphysical solutions [60,86] hampering convergence to the physical ones. A promising way of solving these convergence difficulty, successfully applied in the context of the Fock space CC theory [42], is to use the intermediate-Hamiltonian approach to reformulate the SU-CC equations [153].…”

“…On should add that also the analytical gradient of the MkCC energies was also developed [129]. Very recently a study of the MkCC method, based on a new string-based [132,133] implementation, has been presented [134]. This very informative study discusses also convergence problems which hamper the transformation of the MkCC method into an efficient black-box procedure.…”