A new state-selective multireference (MR) coupled-cluster (CC) method exploiting the single-reference (SR) particle-hole formalism is described. It is an extension of a simple two-reference formalism, which we presented in our earlier paper [N. Oliphant and L. Adamowicz, J. Chem. Phys. 94, 1229 (1991)], and a rigorous formulation of another method of ours, which we obtained as an approximation of the SRCC approach truncated at triple excitations (SRCCSDT) [N. Oliphant and L. Adamowicz, J. Chem. Phys. 96, 3739 (1992)]. The size extensivity of the resulting correlation energies is achieved by employing a SRCC-like ansatz for the multideterminantal wave function. General considerations are supplemented by suggesting a hierarchy of approximate schemes, with the MRCCSD approach (MRCC approach truncated at double excitations from the reference determinants) representing the most important one. Our state-selective MRCCSD theory emerges through a suitable selection of the most essential cluster components appearing in the full SRCCSDTQ method (SRCC method truncated at quadruple excitations), when the latter is applied to quasidegenerate states. The complete set of equations describing our MRCCSD formalism is presented and the possibility of the recursive intermediate factorization [S. A. Kucharski and R. J. Bartlett, Theor. Chim. Acta 80, 387 (1991)] of our approach, leading to an efficient computer algorithm, is discussed.

A multireference coupled-cluster singles and doubles method utilizing two reference determinants which differ by a two electron excitation is proposed. One of these determinants is selected as the formal reference determinant. The proposed method includes single-reference coupled-cluster equations truncated after quadruples. These equations are graphically derived using Feynman diagrams. The appropriate restrictions are then placed on the triple and quadruple amplitudes to allow only those amplitudes which correspond to single and double excitations from the second reference determinant.

We present results of a systematic study of the theoretical determination of equilibrium geometries, harmonic frequencies, total atomization energies, and dipole moments using Hartree–Fock, a hybrid Hartree–Fock density-functional-theory, and coupled-cluster methods in conjunction with a triple zeta basis set for a large set of molecules. This allows a direct comparison of the three theoretical methods applied to a range of chemical systems. The average errors (‖experimental value-theoretical value‖) for the Hartree–Fock, hybrid Hartree–Fock density-functional-theory, and coupled-cluster methods, respectively, are bond length (Å) 0.022, 0.005, 0.005; bond angle (degrees) 2.7, 1.7, 1.9; harmonic frequencies (cm−1) 144, 40, 30; atomization energies (kcal/mol) 81.9, 3.6, 11.5; and dipole moments (debye) 0.29, 0.14, 0.10. This clearly demonstrates that the relatively inexpensive hybrid Hartree–Fock density-functional-theory method yields results which represent a reliable, significant improvement over those obtained with the Hartree–Fock method. The results obtained using the hybrid Hartree–Fock density-functional-theory method are, in fact, quite comparable with the corresponding results obtained using the high level, ab initio coupled-cluster method. For certain difficult open shell examples, the hybrid Hartree–Fock density-functional theory using a spin restricted open shell Hartree–Fock density is much improved over the corresponding hybrid Hartree–Fock density-functional-theory results obtained using a spin unrestricted Hartree–Fock density.

The coupled-cluster (CC) equations including single, double, triple, and quadruple excitation amplitudes (CCSDTQ) are derived diagramatically, and the complete set of CCSDTQ equations are presented. These equations have been programmed and an iterative reduced linear equation method is used to solve these equations. The potential curves for the dissociation of a model system with a single bond (Li2 and LiH) is 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 single, double, triple, and quadruple excitation amplitudes to the stretching of a chemical bond.

A generalized version of the multireference coupled-cluster method using a single-reference formalism, which we presented in an earlier paper, has been implemented. Any number of determinants, that differ from the formal reference determinant by single or double excitations, can now be included in the reference space. In the present implementation, the single and double excitations from the secondary reference determinants have been truncated to include only those that correspond to triple excitations from the formal reference determinant. Calculations are done on a few model systems, LiH, BH, and H2O, at equilibrium and stretched geometries. Comparisons are made with full configuration interaction (CI) treatment for the single bond stretch in LiH and BH, and the results are quite promising. For the water molecule, comparisons are made with the results obtained with the coupled cluster method truncated at triple excitations (CCSDT), as well as with the full CI results. While the multireference method did not do as well for the simultaneous two-bond stretch in H2O as it did for the single bond cases, it did at least as well as the CCSDT at representing the points on the full CI potential curve.