Correlation consistent basis sets CCSD coupled cluster singles

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... 

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. 

Figure 1. The shape of the potential curve for nitrogen in a correlation-consistent polarized double-zeta basis set is presented for the variational 2-RDM method as well as (a) single-reference coupled cluster, (b) multireference second-order perturbation theory (MRPT) and single-double configuration interaction (MRCl), and full configuration interaction (FCl) wavefunction methods. The symbol 2-RDM indicates that the potential curve was shifted by the difference between the 2-RDM and CCSD(T) energies at equilibrium.

A different study provides some further information coneeming the effects of electron correlation upon calculated intensities. In addition to SCF and MPn type methods, these authors considered also the coupled-cluster model which is an infinite-order generalization of MR Coupled-cluster, limited to single and double excitations (CCSD), was considered, as well as CCSD + T which includes the effects of connected triple excitations. The doubleharmonic approximation was made, consistent with most calculations of H-bonded systems. The [5s3pld/3slp] basis set is of the polarized double- variety, within reach of most workers. 

Along the ordinate, a sequence of correlation-consistent cc-pVXZ basis sets with X > 2 is depicted. Along the abscissa, the FCI limit is approached—beginning with Hartree-Fock theory and followed by the first correlated level, at which the single and double excitations are described by MP2 perturbation theory. The same excitations are subsequently treated by coupled-cluster theory at the CCSD level, which is then further improved upon by a perturbation treatment of the triple excitations at the CCSD(T) level. At the CCSDT level, the triple excitations are fully treated by coupled-cluster theory, and so on. In this manner, the hierarchy Hartree-Fock -> MP2 — CCSD -> CCSD(T) > CCSDT —---------------> FCI is established. 

Excitation energies were calculated with the equation of motion coupled cluster theory with single and double excitations (EOM-CCSD) [87] and the Dunning s correlation-consistent d-aug-cc-pVDZ and aug-cc-pVTZ basis-sets [88]. 

A detailed description for the CCSD(T)/CBS approach is found elsewhere [26, 59-61]. Briefly, the single-point electronic energies are calculated by using the restricted/ unrestricted coupled-cluster R/UCCSD(T) formalism [62-64] and extrapolated to the complete basis set limit (CBS) based on the correlation-consistent aug-cc-pVnZ n = D, T, and Q) basis sets [65, 66]. The CCSD(T) energies are then extrapolated to the CBS limit energies using expression (1) [67] ... 

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