A state-specific partially internally contracted multireference coupled cluster approach

Abstract

A state-specific partially internally contracted multireference coupled cluster approach is presented for general complete active spaces with arbitrary number of active electrons. The dominant dynamical correlation is included via an exponential parametrization of internally contracted cluster operators ( ̂T) which excite electrons from a multideterminantal reference function. The remaining dynamical correlation and relaxation effects are included via a diagonalization of the transformed Hamiltonian ̅Ĥ =e(- ̂T)Ĥe( ̂T) in the multireference configuration interaction singles space in an uncontracted fashion. A new set of residual equations for determining the internally contracted cluster amplitudes is proposed. The second quantized matrix elements of ̅Ĥ , expressed using the extended normal ordering of Kutzelnigg and Mukherjee, are used as the residual equations without projection onto the excited configurations. These residual equations, referred to as the many-body residuals, do not have any near-singularity and thus, should allow one to solve all the amplitudes without discarding any. There are some relatively minor remaining convergence issues that may arise from an attempt to solve all the amplitudes and an initial analysis is provided in this paper. Applications to the bond-stretching potential energy surfaces for N(2), CO, and the low-lying electronic states of C(2) indicate clear improvements of the results using the many-body residuals over the conventional projected residual equations.

Similarity transformed equation of motion coupled cluster theory revisited: a benchmark study of valence excited states

“…The original work on STEOM-CC was done in the group of Rodney J. Bartlett, and the library of ACES II subroutines developed then is still in active use today (see for example references [71,72]). M. N. is grateful to Rodney J. Bartlett for providing such a stimulating environment, when he was a postdoctoral associate in his group (1993)(1994)(1995)(1996)(1997).…”

“…More than a decade ago Mukherjee and Kutzelnigg [60,61] defined a generalization of the concept of normal ordering to the multireference situation (see also references [62,63]), and this has led to a very rich set of developments (canonical transformation theory [64][65][66], antihermitian contracted Schrödinger equation [67,68], internally contracted multireference coupled cluster [69,70]). This generalization has also allowed the development of a promising multireference equation of motion coupled cluster theory [71,72], which uses both the many-body transformation concept, and the generalized normal ordering. For an early paper that forecasts some of these developments we refer to ref.…”

A transformed framework for dynamic correlation in multireference problems

“…[21][22][23] Analogues of these methods for multireference problems, such as multireference perturbation theory, [24][25][26][27][28][29] multireference configuration interaction, [30][31][32][33] and multireference coupled cluster and canonical transformation [34][35][36][37][38][39][40][41][42][43][44] theories have also been formulated. However, all of these multireference formulations are algebraically more opaque and computationally much more expensive than their singlereference counterparts.…”

Extended implementation of canonical transformation theory: parallelization and a new level-shifted condition

“…This reduced reference treatment is alternatively referred to as the internally-contracted (IC) multireference algorithm, which was first introduced by Meyer,36 was practically used in IC-MRCI by Werner et al 45,46 (with partial uncontraction) as well as CASPT2 by Roos et al, [1][2][3] and was recently investigated for the developments of IC-MRCC. [68][69][70][71] The CT theory exhibits accuracy on a par with the best MRCI approaches, but shares the same favorable sixth-power computational scaling as the singlereference coupled cluster theory. The quantum chemical applications of the joint CT and DMRG theory were shown in the copper-oxo dimer isomerization problem, 107 as well as in the study of excited states in porphin.…”