Coupled cluster

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

Large-scale calculations of excitation energies in coupled cluster theory: The singlet excited states of benzene

Abstract: Algorithms for calculating singlet excitation energies in the coupled cluster singles and doubles (CCSD) model are discussed and an implementation of an atomic‐integral direct algorithm is presented. Each excitation energy is calculated at a cost comparable to that of the CCSD ground‐state energy. Singlet excitation energies are calculated for benzene using up to 432 basis functions. Basis‐set effects of the order of 0.2 eV are observed when the basis is increased from augmented polarized valence double‐zeta (aug‐cc‐pVDZ) to augmented polarized valence triple‐zeta (aug‐cc‐pVTZ) quality. The correlation problem is examined by performing calculations in the hierarchy of coupled cluster models CCS, CC2, CCSD, and CC3, as well as by using the CCSDR(3) perturbative triples corrections. The effect of triple excitations are less than 0.2 eV for all excitations except for the 2 1E2g state. The calculated excitation energies are compared with experiment and other theoretical results.

Ab initio study of the absorption spectra of Agn (n=5–8) clusters

Abstract: The absorption spectra of Ag5–8 have been determined in the framework of the linear response equation-of-motion coupled cluster method and related techniques employing 11-electron relativistic effective core potential. In these treatments electron correlation effects for 11 electrons per atom are included, providing an accurate description of excited states of silver clusters. The calculations of transition energies and oscillator strengths have been carried out in a large energy interval for the stable structures and for the isomeric forms higher in energy. This allowed us to investigate the influence of structural properties on the spectroscopic patterns and to determine the role of d-electrons. Inclusion of d-electrons in the correlation treatment is mandatory to obtain accurate values for transition energies, but the excitations of s-electrons are primarily responsible for the spectroscopic patterns. They are characterized by the interference phenomena known in molecular spectroscopy which lead to a s...

Noniterative energy corrections through fifth-order to the coupled cluster singles and doubles method

Abstract: Perturbation corrections through fifth order in the many-body perturbation theory energy with respect to a coupled cluster singles and doubles reference have been derived and analyzed. The formulas employ the T1 and T2 amplitudes obtained as a solution of the coupled cluster singles and doubles equations. Four different energy functionals have been considered as a starting point in the derivation: the regular coupled cluster energy expression, the coupled cluster functional incorporating Λ amplitudes, the one constructed via an expectation value coupled cluster method, and that obtained on the basis of the extended coupled cluster method. The proposed corrections have been applied to several small molecules to test their performance compared to full configuration interaction. The fourth-order Λ-based formulas improve upon CCSD(T), (coupled cluster singles and doubles with noniterative triples), while the best fifth-order formulas reduce the fourth-order error by about two-thirds. We also introduce a facto...

Coupled-cluster calculations of nuclear magnetic resonance chemical shifts

Abstract: Theory and implementation of the gauge‐including atomic orbital (GIAO) ansatz for the gauge‐invariant calculation of nuclear magnetic resonance chemical shifts are described for the coupled‐cluster singles and doubles (CCSD) approach. Results for the shielding constants of the hydrides HF, H2O, NH3, and CH4 as well as for a few multiply bonded systems such as CO, N2, and HCN demonstrate the importance of higher‐order correlation corrections, as good agreement with experiment is only obtained at the CCSD level and to some extent at partial fourth‐order many‐body perturbation theory [SDQ‐MBPT(4)] with the latter slightly overestimating correlation effects due to single and double excitations. For relative chemical shifts, GIAO‐CCSD calculations provide in difficult cases (e.g., CO and CF4) more accurate results than previous GIAO‐MBPT(2) calculations. But, it seems that it is often more important to include rovibrational effects (as well as possible molecule–solvent interactions) than higher‐order correlation corrections. Despite that, GIAO‐CCSD proves to be a powerful tool for the accurate calculation of NMR chemical shifts. Its capabilities as well as its limitations are demonstrated in shielding calculations for formaldehyde, diazomethane, and ozone. At least for the latter, the description provided by the CCSD ansatz is not sufficient and even higher excitations need to be considered.

Method of moments of coupled-cluster equations: a new formalism for designing accurate electronic structure methods for ground and excited states

Abstract: The method of moments of coupled-cluster equations (MMCC), which provides a systematic way of improving the results of the standard coupled-cluster (CC) and equation-of-motion CC (EOMCC) calculations for the ground- and excited-state energies of atomic and molecular systems, is described. The MMCC theory and its generalized MMCC (GMMCC) extension that enables one to use the cluster operators resulting from the standard as well as nonstandard CC calculations, including those obtained with the extended CC (ECC) approaches, are based on rigorous mathematical relationships that define the many-body structure of the differences between the full configuration interaction (CI) and CC or EOMCC energies. These relationships can be used to design the noniterative corrections to the CC/EOMCC energies that work for chemical bond breaking and potential energy surfaces of excited electronic states, including excited states dominated by double excitations, where the standard single-reference CC/EOMCC methods fail. Several MMCC and GMMCC approximations are discussed, including the renormalized and completely renormalized CC/EOMCC methods for closed- and open-shell states, the quadratic MMCC approaches, the CI-corrected MMCC methods, and the GMMCC approaches for multiple bond breaking based on the ECC cluster amplitudes.