A multireference coupled-cluster method using a single-reference formalism.
AuthorOliphant, Nevin Horace
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PublisherThe University of Arizona.
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AbstractThe coupled-cluster (CC) equations including single, double, triple and quadruple excitations (CCSDTQ) are qraphically derived using Feynman diagrams. These equations are programmed and an iterative reduced linear equation method is used to solve these equations. A few points on the potential curves for the dissociation of some model systems with a single bond (LiH and Li₂) are calculated using CC doubles (CCD), singles and doubles (CCSD), singles, doubles and triples (CCSDT) and CCSDTQ. These calculations demonstrate the magnitude of the CC contributions arising from triple and quadruple excitation amplitudes to the stretching of a chemical bond. A multi-reference coupled-cluster singles and doubles (MRCCSD) method utilizing two reference determinants, which differ by a two electron excitation, is then proposed. One of these determinants is selected as the formal reference determinant. The proposed method is based on the single-reference coupled-cluster equations truncated after quadruples with appropriate restrictions placed on the triple and quadruple amplitudes to allow only those amplitudes which correspond to single and double excitations from the second reference determinant. The computational expense of this method is no more than twice that of singles and doubles from a single reference (CCSD). These equations are programmed and the potential curves for the dissociation of a few model systems with single bonds (LiH, BH, and H₂O) are calculated to demonstrate the correct bond dissociation properties of this method. These calculations also demonstrate how much of the CC energy contribution arising from the triple and quadruple excitation amplitudes can be attributed to single and double excitations from the second reference determinant.