Coupled cluster

About: Coupled cluster is a research topic. Over the lifetime, 6280 publications have been published within this topic receiving 301055 citations.

Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3

Abstract: A benchmark set of 28 medium-sized organic molecules is assembled that covers the most important classes of chromophores including polyenes and other unsaturated aliphatic compounds, aromatic hydrocarbons, heterocycles, carbonyl compounds, and nucleobases. Vertical excitation energies and one-electron properties are computed for the valence excited states of these molecules using both multiconfigurational second-order perturbation theory, CASPT2, and a hierarchy of coupled cluster methods, CC2, CCSD, and CC3. The calculations are done at identical geometries (MP26-31G*) and with the same basis set (TZVP). In most cases, the CC3 results are very close to the CASPT2 results, whereas there are larger deviations with CC2 and CCSD, especially in singlet excited states that are not dominated by single excitations. Statistical evaluations of the calculated vertical excitation energies for 223 states are presented and discussed in order to assess the relative merits of the applied methods. CC2 reproduces the CC3 reference data for the singlets better than CCSD. On the basis of the current computational results and an extensive survey of the literature, we propose best estimates for the energies of 104 singlet and 63 triplet excited states.

Systematically convergent basis sets with relativistic pseudopotentials. I. Correlation consistent basis sets for the post-d group 13–15 elements

Abstract: New correlation consistent-like basis sets have been developed for the post-d group 13–15 elements (Ga–As, In–Sb, Tl–Bi) employing accurate, small-core relativistic pseudopotentials. The resulting basis sets, which are denoted cc-pVnZ-PP, are appropriate for valence electron correlation and range in size from (8s7p7d)/[4s3p2d] for the cc-pVDZ-PP to (16s13p12d3f2g1h)/[7s7p5d3f2g1h] for the cc-pV5Z-PP sets. Benchmark calculations on selected diatomic molecules (As2, Sb2, Bi2, AsN, SbN, BiN, GeO, SnO, PbO, GaCl, InCl, TlCl, GaH, InH, and TlH) are reported using these new basis sets at the coupled cluster level of theory. Much like their all-electron counterparts, the cc-pVnZ-PP basis sets yield systematic convergence of total energies and spectroscopic constants. In several cases all-electron benchmark calculations were also carried out for comparison. The results from the pseudopotential and all-electron calculations were nearly identical when scalar relativity was accurately included in the all-electron wo...

Towards a full CCSDT model for electron correlation

Abstract: Coupled cluster models for electron correlation which include the effects of single, double, and triple excitation operators are analyzed. An alternate version of the approximate CCSDT‐1 method is implemented. In this version, the full CCSDT cluster operator eT1+T2+T3 is preserved in the creation of single and double excitation coefficients, but in calculation of triple excitation coefficients only the T2 operator is used. We also present a theoretical analysis of the simplest improvement for the evaluation of the contribution of triples beyond that obtained with fourth‐order MBPT. In this approximation, an MBPT(4)‐like calculation of the triples energy is evaluated with converged CCSD T2 coefficients. This is found to offer a good approximation to the converged CCSDT‐1 results.

Energy-consistent relativistic pseudopotentials and correlation consistent basis sets for the 4d elements Y-Pd.

Abstract: Scalar-relativistic pseudopotentials and corresponding spin-orbit potentials of the energy-consistent variety have been adjusted for the simulation of the [Ar]3d(10) cores of the 4d transition metal elements Y-Pd. These potentials have been determined in a one-step procedure using numerical two-component calculations so as to reproduce atomic valence spectra from four-component all-electron calculations. The latter have been performed at the multi-configuration Dirac-Hartree-Fock level, using the Dirac-Coulomb Hamiltonian and perturbatively including the Breit interaction. The derived pseudopotentials reproduce the all-electron reference data with an average accuracy of 0.03 eV for configurational averages over nonrelativistic orbital configurations and 0.1 eV for individual relativistic states. Basis sets following a correlation consistent prescription have also been developed to accompany the new pseudopotentials. These range in size from cc-pVDZ-PP to cc-pV5Z-PP and also include sets for 4s4p correlation (cc-pwCVDZ-PP through cc-pwCV5Z-PP), as well as those with extra diffuse functions (aug-cc-pVDZ-PP, etc.). In order to accurately assess the impact of the pseudopotential approximation, all-electron basis sets of triple-zeta quality have also been developed using the Douglas-Kroll-Hess Hamiltonian (cc-pVTZ-DK, cc-pwCVTZ-DK, and aug-cc-pVTZ-DK). Benchmark calculations of atomic ionization potentials and 4d(m-2)5s(2)-->4d(m-1)5s(1) electronic excitation energies are reported at the coupled cluster level of theory with extrapolations to the complete basis set limit.

Coupled-cluster method for multideterminantal reference states

Abstract: A general coupled-cluster method valid for arbitrary multideterminantal reference states is formulated. The resulting cluster expansion for the wave function is a generalization of that introduced by Silverstone and Sinano\ifmmode \check{g}\else \v{g}\fi{}lu and applied by Sinano\ifmmode \check{g}\else \v{g}\fi{}lu and collaborators. The connected nature of the cluster operators and the effective interaction is proven in the case when the reference space is complete, i.e., is invariant under unitary transformations of partly occupied orbitals. For incomplete reference spaces the disconnected terms appearing in the effective interaction are properly generated by the coupled-cluster theory. Approximate schemes for solving coupled-cluster equations are proposed and their relation with perturbation theory is briefly discussed.