A new implementation of the orthogonally spin-adapted open-shell (OS) coupled-cluster (CC) formalism that is based on the unitary group approach to many-electron correlation problem is described. Although the emphasis is on the so-called state specific single-reference but multiconfigurational OS CC approach, the developed algorithms as well as the actual codes are also amenable to multireference CC applications of the state-universal type. A special attention is given to simple OS doublets and OS singlet and triplet cases, the former being applicable to the ground states of radicals and the latter to the excited states of closed shell systems. The encoding of the underlying formalism is fully automated and is based on a convenient decomposition of the Hamiltonian into the effective zero-, one-, and two-orbital contributions as well as on the general strategy that focuses on the excitation operator driven evaluation of individual absolute, linear, quadratic, etc., coupled cluster coefficients, rather than on the standard molecular (spin) orbital driven algorithms. In this way unnecessary duplications are avoided and efficient codes are developed both for the general formula generation and final executable modules. A thorough testing of this procedure on a number of model cases is described and several illustrative applications at the ab initio level are provided.

Articles you may be interested inRadial correlation effects on interconfigurational excitations at the end of the lanthanide series: A restricted active space second order perturbation study of Yb2+ and SrCl2:Yb2+ J. Chem. Phys. 138, 074102 (2013); 10.1063/1.4790166Orbitally invariant internally contracted multireference unitary coupled cluster theory and its perturbative approximation: Theory and test calculations of second order approximation A sequential transformation approach to the internally contracted multireference coupled cluster method A state-specific partially internally contracted multireference coupled cluster approach Standard multireference ͑MR͒ coupled cluster ͑CC͒ approaches are based on the effective Hamiltonian formalism and generalized Bloch equation. Their implementation, relying on the valence universal or state universal cluster Ansatz, is very demanding and their practical exploitation is often plagued with intruder state and multiple solution problems. These problems are avoided in the so-called state selective or state specific ͑SS͒ MR approaches that concentrate on one state at a time. To preserve as much as possible the flexibility and generality offered by the general MR CC approaches, yet obtaining a reliable and manageable algorithm, we propose a novel SS strategy providing a size-extensive CC formalism, while exploiting the MR model space and the corresponding excited state manifold. This strategy involves three steps: ͑i͒ The construction of a variational configuration interaction ͑CI͒ wave function within the singly ͑S͒ and doubly ͑D͒ excited state manifold, ͑ii͒ the cluster analysis of this CI wave function providing the information about the higher than pair cluster amplitudes, and ͑iii͒ the exploitation of these amplitudes in the so-called externally corrected CCSD procedure. This approach is referred to as the reduced MR ͑RMR͒ SS CCSD method and is implemented at the ab initio level and applied to several model systems for which the exact full CI results are available. These include two four electron H 4 systems ͑usually referred to as the H4 and S4 models͒, an eight electron H 8 model and the singlet-triplet separation problem in CH 2 . It is shown that the RMR CCSD approach produces highly accurate results, is free from intruder state problems, is very general and effective and applicable to both closed and open shell systems.

The performance of (i) the reduced multireference (RMR) coupled-cluster (CC) method with singles and doubles (RMR CCSD) that employs a modest-size MR CISD wave function as an external source for the most important (primary) triples and quadruples in order to account for the nondynamic correlation effects in the presence of quasidegeneracy, (ii) the RMR CCSD(T) method that adds a perturbative correction for the remaining (secondary) triples to the RMR CCSD energy, and (iii) the recently developed partially linearized MR CCSD method, which determines primary triples and quadruples using a subset of linear CC equations projected onto the corresponding higher-than-doubly excited configurations, are tested by considering the singlet-triplet splitting for several diradicals, ranging from a prototypical methylene radical to trimethylenemethane, and benzyne and pyridynium cation isomers. Both RHF and multiconfigurational self-consistent field molecular orbitals are employed. The equilibrium geometries for the lowest-lying singlet and triplet states are determined using both the density functional theory (DFT) and various CC approaches, and a comparison with both the experiment and other theoretical results, wherever available, is made. The RMR CCSD(T) results provide the most satisfactory description in all cases. The dependence of the MR diradical character on a spatial separation of radical centers, as well as the artifactual DFT geometry in the case of benzyne and pyridynium meta-isomers, is also pointed out.

The reduced multireference coupled-cluster method with singles and doubles (RMR CCSD) that employs multireference configuration interaction wave function as an external source for a small subset of approximate connected triples and quadruples, is perturbatively corrected for the remaining triples along the same lines as in the standard CCSD(T) method. The performance of the resulting RMR CCSD(T) method is tested on four molecular systems, namely, the HF and F(2) molecules, the NO radical, and the F(2) (+) cation, representing distinct types of molecular structure, using up to and including a cc-pVQZ basis set. The results are compared with those obtained with the standard CCSD(T), UCCSD(T), CCSD(2), and CR CCSD(T) methods, wherever applicable or available. An emphasis is made on the quality of the computed potentials in a broad range of internuclear separations and on the computed equilibrium spectroscopic properties, in particular, harmonic frequencies omega(e). It is shown that RMR CCSD(T) outperforms other triply corrected methods and is widely applicable.

We present a new version of the state-universal (SU), multireference, coupled-cluster (CC) theory that is capable of handling completely general, incomplete model spaces. This is achieved by exploiting the concept of “locality” for the active molecular spin orbitals and by introducing the constraining conditions (C conditions) on cluster amplitudes that are associated with the internal excitations transforming one reference configuration into another one. These C conditions make it possible to represent the exact (i.e., full configuration interaction) wave function via the SU CC cluster ansatz based on an arbitrary model space. The C conditions are then taken into account together with the standard SU CC equations for the external amplitudes, thus enabling us to reach the exact result in the limit, while preserving the connectivity property and thus the size extensivity. We also present compact expressions for the matrix elements of the effective Hamiltonian as well as the explicit expressions for the most important coupling coefficients that are required at the single and double excitation level. All other expressions are the same as in the single reference CC formalism.