CCSD + T methods

We need to look at the convergence as a function of basis set and amount of electron correlation (Figure 4.2). For the former we will use the correlation consistent basis sets of double, triple, quadruple, quintuple and, when possible, sextuple quality (Section 5.4.5), while the sensitivity to electron correlation will be sampled by the HF, MP2 and CCSD(T) methods (Sections 3.2, 4.8 and 4.9). Table 11.1 shows how the geometry changes as a function of basis set at the HF level of theory. 

The variation at the CCSD(T) level is shown in Table 11.3, with the ehange relative to the MP2 level given as A values. Additional eorrelation with the CCSD(T) method gives only small changes relative to the MP2 level, and the effeet of higher-order eorrelation diminishes as the basis set is enlarged. For H2O the CCSD(T) method is virtually indistingable from CCSDT. ... 

The magnitude of the core correlation can be evaluated by including the oxygen Is-electrons and using the cc-pCVXZ basis sets the results are shown in Table 11.9. The extrapolated CCSD(T) correlation energy is —0.370 a.u. Assuming that the CCSD(T) method provides 99.7% of the full Cl value, as indicated by Table 11.7, the extrapolated correlation energy becomes —0.371 a.u., well within the error limits on the estimated experimental value. The core (and core-valence) electron correlation is thus 0.063 a.u.. 

Figures 11.9 and 11.10 compare the performance of the CCSD and CCSD(T) methods, based on either an RFIF or UHF reference wave function. Compared to the RMP plot (Figure 11.7), it is seen that the infinite nature of coupled cluster causes it to perform somewhat better as the reference wave function becomes increasingly poor. While the RMP4 energy curve follows the exact out to an elongation of 1.0A, the CCSD(T) has the same accuracy out to - 1.5 A. Eventually, however, the wrong dissociation limit of the RHF wave also makes the coupled cluster methods break down, and the energy starts to decrease.

The HF level as usual overestimates the polarity, in this case leading to an incorrect direction of the dipole moment. The MP perturbation series oscillates, and it is clear that the MP4 result is far from converged. The CCSD(T) method apparently recovers the most important part of the electron correlation, as compared to the full CCSDT result. However, even with the aug-cc-pV5Z basis sets, there is still a discrepancy of 0.01 D relative to the experimental value. 

Millefiori and Alparone calculated the dipole polarizabihties of S clusters up to m=12 using the HF, B3LYP and CCSD(T) methods [56]. They found that... 

Another standard for quality/price is defined within the coupled cluster approach. In particular, the CCSD(T) method [42] is nowadays generally accepted as the most accurate method which can be applied systematically for systems of a reasonable size. One must nevertheless be aware of the high computational cost of the method, which is often used only for energy calculations on geometries optimized with other computational methods. 

Among the various approximate methods for including the connected triple excitations, the CCSD(T) method is the most popular [19]. In this approach, the CCSD calculation is followed by the calculation of a perturbational estimate of the triple excitations. In addition to reducing the overall scaling with respect to the number of atoms K from K8 in CCSDT [see Eq. (2.5)] to K7 in CCSD(T), the CCSD(T) method avoids completely the storage of the triples amplitudes. 

Nevertheless, the formidable n3N4 (with n the number of electrons and N the number of basis functions) cost scaling of the CCSD(T) method creates a substantial barrier to applications of methods that... 

Some representative results can be found in Table 2.2. For the G2-1 set of electron affinities, W1 theory has a mean absolute error of 0.016 eV [26]. Not unexpectedly - given the slow basis set convergence of electron affinities - the extra effort invested in W2 theory pays off with a further reduction of the mean absolute error to 0.012 eV. Accuracy appears to be limited principally by imperfections in the CCSD(T) method for the atoms B-F and Al-Cl, using even larger basis sets we achieve 0.009 eV at the CCSD(T) level, which decreases to 0.001 eV if approximate full Cl energies are used. 

The errors obtained with the CCSD(T) method are, in general, smaller than 0.2 eV. There are some exceptions, however, in particular for palladium and silver. 

Our recent numerical experiments with the Cl-corrected MMCC methods indicate that in looking for the extensions of the CR-CCSD[T], CRCCSD(T), and CR-CCSIXfQ) methods that would provide an accurate description of triple bond breaking one may have to consider the approximations that use the pentuply and hextuply excited moments of the CCSD equations, M (2), k = 5 and 6, respectively (21). The CR-CCSD[T] and CR-CCSD(T) methods use only the triexcited CCSD moments M (2), whereas the CR-CCSD(TQ) approaches use the tri- and tetraexcited moments, (2) and (2),... 

The motivation behind the LMMCC approximation stems from the success of the CR-CCSD[T] and CR-CCSD(T) methods in describing single bond breaking... 

Comparisons with experimental results show that vertical NOF-EAs are better than those predicted by the CCSD(T) method within the 6-31++G basis set. 

Results of applying the CCSD(T) method to selected tin compounds are also given in Table 1. Again, there are almost no data available in the literature for comparison. However, the predicted heat of formation for SnO is in reasonable agreement with experiment. Since data for Sn - O species are so limited, it is difficult to fully validate this model chemistry. Thus, we placed relatively high uncertainties on the calculated values. Nevertheless, we are sufficiently confident of the results to use them to establish BAG parameters for Sn - OH bonds. The resulting BAC-MP4 predictions as well as the... 

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