Coupled cluster singles and doubles CCSD method

In this section we construct working equations for the coupled cluster singles and doubles (CCSD) method. Beginning from the approximation 7 = 7 + T2, we use algebraic and diagrammatic techniques to obtain programmable... 

For higher fluoro derivatives, namely di- and 1,2,3-trifluoro derivatives we have also employed the coupled-clusters singles and doubles (CCSD) method with TZ2P... 

The coupled cluster method is the Cl method based on this wavefunction. One of the noain advantages of this method is to ensure size consistency (see Sect. 3.3) in the selection of electron configurations. In coupled cluster methods, the coupled-cluster singles and doubles (CCSD) method terminates f up to the double excitation... 

It is clear from this equation, that the explicitly-correlated terms do only describe pair-correlation effects. This means that only for pair correlation contributions, we can expect an improved basis set convergence. As pair correlation covers the greatest part of the correlation energy, this seems sufficient for the time being, see also Section 3.6. In the following, we will focus on the coupled-cluster singles and doubles (CCSD) method and its F12 variant CCSD-F12, i.e. f = fi + fz -f fy-The usual projection technique is employed to obtain the energy expression (projection on o))... 

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. 

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]. 

The PCM coupled-cluster theory has been presented at the coupled-cluster single and double (CCSD) excitation level approximation [9, 11], at the Brueckner doubles (BD) coupled-cluster level [12], and within the symmetry adapted cluster (SAC) method [10]. 

The EOM-CCSD method has been shown to be an accurate approach for calculating excitation energies (EE-) (29,30), electron affinities (EA-) (31), and ionization potentials (IP-) (32) of closed-shell systems. For the computations presented here, a coupled-cluster singles and doubles (CCSD) calculation is first performed on the closed-shell NO3" anion system. The Hamiltonian is similarity... 

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... 

However, until today no systematic comparison of methods based on MpUer-Plesset perturbation (MP) and Coupled Cluster theory, the SOPPA or multiconfigurational linear response theory has been presented. The present study is a first attempt to remedy this situation. Calculations of the rotational g factor of HF, H2O, NH3 and CH4 were carried out at the level of Hartree-Fock (SCF) and multiconfigurational Hartree-Fock (MCSCF) linear response theory, the SOPPA and SOPPA(CCSD) [40], MpUer-Plesset perturbation theory to second (MP2), third (MP3) and fourth order without the triples contributions (MP4SDQ) and finally coupled cluster singles and doubles theory. The same basis sets and geometries were employed in all calculations for a given molecule. The results obtained with the different methods are therefore for the first time direct comparable and consistent conclusions about the performance of the different methods can be made. 

Harmonic and cubic force fields of Sis were calculated using coupled-cluster (CC) theory (25) and a correlation-consistent basis set. Specifically, the CC singles and doubles (CCSD) method (24) was used in conjunction with the cc-pVTZ basis set (25) developed by Dunning and co-workers. The force... 

S. R. Gwaltney and M. Head-Gordon, A second-order perturbation correction to the coupled-cluster singles and doubles method CCSD(2). J. Chem. Phys. 115, 2014 (2001). 

Valeev, E.F., Crawford, T.D. Simple coupled-cluster singles and doubles method with perturbative inclusion of triples and explicitly correlated geminals the CCSD(T)ri2 model. J. Chem. Phys. 2008, 128, 244113. 

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