On the approximation of the similarity-transformed Hamiltonian in single-reference and multireference coupled cluster theory

We consider the recursive single commutator (RSC) approximation of the Baker-Campbell-Hausdorff expansion introduced by Yanai and Chan [T. Yanai, G. K.-L. Chan, J. Chem. Phys. 124 (2006) 194106] and apply it in order to approximate the similarity transformation of the Hamiltonian in both traditional and unitary coupled cluster theory. The equilibrium bond distance, harmonic vibrational frequency, and anharmonic constant of H-2, HF, N-2, CuH, and Cu-2 were computed using the coupled cluster approach with single and double excitations (CCSD) and CCSD with the RSC approximation of the similarity-transformed Hamiltonian (CCSD-RSC). Our results demonstrate that the RSC approximation introduces substantial errors in the estimates of molecular properties. The leading pejorative effects of the RSC approximation can be traced back to the imbalanced description of diagrams arising from the term 1/2 [[(H) over cap, (T) over cap (2)], (T) over cap (2)]. Following this analysis we consider a modified RSC scheme correct to fourth-order in the energy, which is found to reproduce CCSD results more closely. The RSC scheme is also applied in conjunction with the state-specific multireference coupled cluster approach of Mukherjee and co-workers [U. S. Mahapatra, B. Datta, D. Mukherjee, J. Chem. Phys. 110 (1999) 6171] to compute the potential energy curve of the BeH2 model, the vibrational frequencies of ozone, and the singlet-triplet splitting of p-benzyne. These examples show that the deterioration of the results caused by the RSC scheme is analogous to the one observed in the single-reference case. Implications for the formulation of approximate internally contracted multireference theories are discussed. (C) 2011 Elsevier B. V. All rights reserved.