Alternative single-reference coupled cluster approaches for multireference problems: The simpler, the better

We report a general implementation of alternative formulations of single-reference coupled cluster theory (extended, unitary, and variational) with arbitrary-order truncation of the cluster operator. These methods are applied to compute the energy of Ne and the equilibrium properties of HF and C-2. Potential energy curves for the dissociation of HF and the BeH2 model computed with the extended, variational, and unitary coupled cluster approaches are compared to those obtained from the multireference coupled cluster approach of Mukherjee et al. [J. Chem. Phys. 110, 6171 (1999)] and the internally contracted multireference coupled cluster approach [F. A. Evangelista and J. Gauss, J. Chem. Phys. 134, 114102 (2011)]. In the case of Ne, HF, and C-2, the alternative coupled cluster approaches yield almost identical bond length, harmonic vibrational frequency, and anharmonic constant, which are more accurate than those from traditional coupled cluster theory. For potential energy curves, the alternative coupled cluster methods are found to be more accurate than traditional coupled cluster theory, but are three to ten times less accurate than multireference coupled cluster approaches. The most challenging benchmark, the BeH2 model, highlights the strong dependence of the alternative coupled cluster theories on the choice of the Fermi vacuum. When evaluated by the accuracy to cost ratio, the alternative coupled cluster methods are not competitive with respect to traditional CC theory, in other words, the simplest theory is found to be the most effective one. (C) 2011 American Institute of Physics. [doi:10.1063/1.3598471]