The orbital invariance problem is analyzed from the tensor theory point of view, with an emphasis on multireference coupled cluster methods. Using the transformation properties of second-quantized operators, we discuss the orbital invariance properties of various methods by examining the tensor properties of the residual equations. A simple self-consistency-checking algorithm is proposed. We first establish the orbital invariance properties for the Hartree–Fock, single reference configuration interaction, single reference coupled cluster, complete-active-space self-consistent-field, and multireference configuration interaction methods, and then discuss the invariance properties of the complete-active-space coupled cluster and CCSDt methods. Finally, we demonstrate theoretically the lack of orbital invariance for Jeziorski–Monkhorst ansatz based methods. It appears necessary to modify the ansatz to achieve orbital invariance, and internal contraction serves as one possible solution. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010
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