Correlated coupled cluster singles and doubles

Shiozaki, T., Kamiya, M., Hirata, S., Valeev, E.F. Explicitly correlated coupled-cluster singles and doubles method based on complete diagrammatic equations. J. Chem. Phys. 2008, 129, 071101. 

The main goal of the present work is to report the implementation of the explicitly-correlated coupled-cluster singles-and-doubles method (CCSD(F12)) in Turbomole. This tool is capable of very efficient calculating the CCSD energies at the basis set limit with relatively small orbital basis sets. The implementation works with RHF, UHF and ROHF reference wave functions, which means that it can treat both closed- and open-shell species. The formulation in terms of intermediate quantities and the application of density fitting techniques make this implementation quite unique. 

The purpose of the present work is to test the efficiency and performance of the implementation of the explicitly correlated coupled-cluster singles-and-doubles, CCSD(F12), model in the Turbomole package. This model, initially proposed by Fliegl et al. [41], is the approximation to the full CCSD-F12 approach originally given by Noga et al [40]. It has been demonstrated that this method is able to recover quintuple- quality correlation energies with the orbital basis set of the size of triple- [31]. 

CCSD-F12 Full explicitly correlated coupled-cluster singles-and-doubles... 

In the SOPPA(CCSD) method [36] the Mqller-Plesset correlation coefficients and are replaced in all SOPPA matrix elements by the corresponding coupled cluster singles and doubles amplitudes and r , whereas in the earlier CCSDPPA method [52,53] only some of the Mqller-Plesset correlation coefficients were replaced. Although SOPPA(CCSD) is based on a CCSD wavefunction, it is still only correct through second order and not the linear... 

CCSD Model. Coupled Cluster Singles and Doubles. A Correlated Model. 

G. E. Scuseria, A. C. Scheiner, T. J. Lee, J. E. Rice, and H. F. Schaefer, J. Chem. Phys., 86, 2881 (1987). The Closed-Shell Coupled-Cluster Single and Double Excitation (CCSD) Model for the Description of Electron Correlation. A Comparison with Configuration Interaction (CISD) Results. 

SM calculations are broadly based on either the (i) Hartree-Fock method (ii) Post-Hartree-Fock methods like the Mpller-Plesset level of theory (MP), configuration interaction (Cl), complete active space self-consistent field (CASSCF), coupled cluster singles and doubles (CCSD) or (iii) methods based on DFT [24-27]. Since the inclusion of electron correlation is vital to obtain an accurate description of nearly all the calculated properties, it is desirable that SM calculations are carried out at either the second-order Mpller-Plesset (MP2) or the coupled cluster with single, double, and perturbative triple substitutions (CCSD(T)) levels using basis sets composed of both diffuse and polarization functions. 

In this research, the coupled-cluster single and double substitutions method with a perturbative treatment of triple excitations CCSD(T) [16-18] was adopted based on unrestricted Hartree-Fock reference wave functions. For the CCSD(T) computations, the cc-pVDZ, cc-pVTZ, and cc-pVQZ quality basis sets were used, where cc-pVnZ is an abbreviation for the correlation-consistent polarized valence basis sets of Dunning et al. [19-22]. With the coupled-cluster methods used in this research, the core orbitals are frozen. That is, the Is-like molecular orbital is frozen for O, while the Is2s2p3s3p3d-like molecular orbitals are frozen for Br. 

Spin-spin coupling constants were evaluated using the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) method in the Cl (configuration interac-tion)-like approximation [52, 53], with all electrons correlated. For these calculations, the Ahlrichs [54] qzp basis set was placed on and F, and the qz2p basis... 

Relativistic calculations of NMR properties of RgH ion (where Rg = Ne, Ar, Kr, Xe), Pt shielding in platinum complexes, and Pb shielding in solid ionic lead(II) halides have been reported in this review period. For the Rg nucleus in the RgH ions, the following methods were used and results compared with each other non-relativistic uncorrelated method (HF), relativistic uncorrelated methods, four component Dirac Hartree-Fock method (DHF) and two-component zeroth order regular approach (ZORA), non-relativistic correlated methods using second order polarization propagator approach SOPPA(CCSD), SOPPA(MP2), respectively coupled cluster singles and doubles or second order Moller-Plesset, and... 

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