An algorithm for generation of the spin-orbital diagrammatic representation, the corresponding algebraical formulas, and the computer code of the coupled-cluster (CC) method with an arbitrary level of the electronic excitations has been developed. The method was implemented in the general case as well as for specific application in the state-specific multireference coupled-cluster theory (SSMRCC) based on the concept of a "formal reference state." The algorithm was tested in SSMRCC calculations describing dissociation of a single bond and in calculations describing simultaneous dissociation of two single bonds--the problem requiring up to six-particle excitations in the CC operator.

A new development is presented in the framework of the state-specific multireference (MR) coupled-cluster (CC) theory (MRCC). The method is based on the CASSCF (complete active space self-consistent field) wave function and it is designed specifically for calculating excited electronic states. In the proposed approach, the cluster structure of the CC wave operator and the method to determine this operator are the key features. Since the general formulation of the CASCC method is uncontracted, i.e., allows the interaction between the nondynamic and dynamic correlation effects to affect both the CAS reference function and the CC correlation wave operator, the method is expected to perform better than contracted perturbative approaches such as the CASPT2 (second-order perturbation theory based on the CAS wave function) method. Also, the CASCC method is not a perturbative approach and is not based on selection of an unperturbed Hamiltonian, which in the case of the CASPT2 method often leads to the “intruder state” problem. CASCC calculations of the lowest totally symmetric excited state of the H8 model system using the internally contracted and uncontracted approaches reveal some interesting features of the methodology.

A new multireference coupled-cluster method which includes double excitations and is based on the complete active space ͑CAS͒ multiconfigurational reference wave function is proposed. By partitioning the CAS orbitals into active and nonactive sets a two-component, coupled-cluster wave function involving excitations into orbitals of the different sets was constructed. The first component includes all the CAS excitations and the second component, which has the exponential form, consists of double external and semi-external excitations. The coupled-cluster equations for the energy and for the amplitudes involved in the two components of the wave function were derived and illustrated using a diagrammatic formalism. Several numerical tests were performed, and the results demonstrate a very good performance of the method as compared to the full configuration interaction results.

This work reviews the state-specific multireference coupled-cluster (CC) approaches which have been developed as approximate methods for performing high-level quantum mechanical calculations on quasidegenerate ground and excited states of atomic and molecular systems. The term "quasidegenerate" refers to a state that cannot be described even in the first approximation by a single-determinant wavefunction (a Slater determinant), but requires two or more determinants for this purpose. The main challenge with applying the coupled-cluster theory to such states is in describing the electron correlation effects in the wavefunctions representing these states in a manner that is size-extensive, yet accurate and simple enough so the method can be routinely applied to small and medium-size molecular systems. We are describing how this can be accomplished within a theory that focuses on only one state of the system in a single CC calculation (the state-specific theory).

The complete-active-space coupled-cluster approach with single and double excitations (CASCCSD) based on the ansatz of Oliphant and Adamowicz [J. Chem. Phys. 94, 1229 (1991); 96, 3739 (1992)] is used to derive an approach termed XCASCCSD for calculating potential energy surfaces of ground and excited electronic states with different multiplicities and symmetries. The XCASCCSD approach explicitly includes a procedure for spin and spatial orbital-momentum symmetry adaptation of the wave function that has allowed us to consider states with degenerate formal references. The XCASCCSD method is applied to calculate potential energy surfaces of the ground and some lowest singlet and triplet excited states of the FH and C(2) molecules. Some states of C(2) are known to have a very strong "multireference" character making their description difficult with single-reference methods. The problem of the change of the formal reference determinant along the potential energy surface is discussed. Also, vertical excitation energies of formaldehyde calculated with the XCASCCSD approach are presented.