Augmented triples correction

A major achievement in the noniterative treatment of triples correction was the introduction of the so-called (T) correction, first defined for the quadratic configuration interaction (QCISD) model and later for the CCSD approach. Here, the energy correction from CCSD + T(CCSD) is augmented by an additional fifth-order term which couples single and triple excitations ... 

As for water, the Hartree-Fock model provides the dominant contribution to the barrier, with an estimated basis-set limit of 19.3 kJ/mol. The correlation contribution is small and positive at all levels but decreases with the cardinal number - see Figure 15.20. At the cc-pCV5Z level, this reduction leads to a near-zero MP2 correlation correction. By contrast, the CCSD correction of 1.7 kJ/mol is close to the CCSD(T) correction of 2.3 kJ/mol. The triples correction is quite stable, in particular for the augmented sets. Moreover, a full optimization of the triples at the CCSDT level hardly changes the CCSD(T) results. From the smallness of the triples correction, we expect the contributions from higher connected excitations to be negligible. 

Thus, triple-f MP2 energies at double-1 MP2 geometries are augmented witli a correction for doubles contributions beyond second order (line 2 on die r.h.s. of Eq. (7.61)) and a correction for basis set size increase beyond triple-f (line 3 on die r.h.s. of Eq. (7.61) where the T superscript in the first basis set implies that polarization functions from cc-pVTZ were used in conjunction with valence functions from cc-pVQZ). 

In BPW91 calculations by the ADF package, the zero-order regular approximation formalism (ZORA) without the spin-orbit effect was used [106, 107]. The ls-2p orbitals for Cu, ls-3d orbitals for Ag, Is—4f orbitals for ft and Au, and ls-2s orbitals for C and N are kept frozen, respectively, in the frozen core approximation, and the valence orbitals based on the Slater-type orbital are expanded within the triple zeta basis set augmented with two polarization functions. Frequency analyses have been used to assess the stability of the optimized structures. Calculated zero-point energy (ZPE) corrections have been incorporated into total energies in estimation of relative energies. 

For a more accurate treatment of electron correlation, coupled-cluster (CC) approaches [23] enter into play. While the full CC singles, doubles, triples (CCSDT) model [24] and augmented CCSDT approaches that feature corrections for quadruple and even higher excitations [25, 26] are currently too expensive, CC singles and doubles (CCSD) approximation [27] and CCSD augmented by a perturbative treatment of triple excitations, CCSD(T) [28], are more feasible and rather widely adopted. 

To illustrate the predictive capabilities of quantum chemistry in the field of rotational spectroscopy of open-shell species, in Table 6.11 the comparison between experimental and calculated isotropic and anisotropic hyperfine coupling constants of NH2 is reported. The computed values have been obtained at the CCSD(T) level employing the aug-cc-pCVQZ basis set augmented by additional tight functions on H [143]. Corrections due to fidl-treatment of triples and quadruples have also been... 

CCSD(T) CCSD model augmented by perturbative corrections for triple excitations... 

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