Cc-pCVXZ basis sets

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.. 

Table 1.7 CCSD(T) total energies calculated with the cc-pCVXZ basis sets and compared with the corresponding experimental total energies (Eh). The last row contains the mean absolute deviations from the experimental energies. All calculations have been carried out at the optimized all-electron CCSD(T)/cc-pCVQZ geometries [25].

Table 3. The f em symmetric double dissociation of water (into 2H(ls 2S) + 0(2p4 3P) cut (ii)). The H-O-H angle is kept fixed at its equilibrium value taken from Ref. [139] (ae = 104.501 degree). R is an O-H distance and Re = 0.95785 A is the equilibrium value of R [139]. All energies E (in cm-1) are reported as E - E(Re, ae), where E(Re, ae) are the corresponding values of E at the equilibrium geometry. X is a cardinal number defining the aug-cc-pCVXZ basis sets used in the calculations. In all CC calculations, all electrons were correlated.

Table 5. The differences between CC/CR-CC energies, calculated relative to their equilibrium values (the CC/CR-CC E - E(Re, ore)] values in Table 3) and the corresponding MRCI(Q) relative energies (the MRCI(Q) [E — E(Re, ae)] values in Table 1) for the dissociation of a single O-H bond in water (into H(l.s 2S) 4- OH(X 2 n) cut (i)). X is a cardinal number defining the aug-cc-pCVXZ basis sets used in the calculations.

The magnitude of the core correlation can be evaluated by including the oxygen Is-electrons and using the cc-pCVXZ basis sets, with the results shown in Table 11.9. 

Finally, based on the data in O Table 13-5 and an experimentally derived value of AE of -39.5 kcal mol (Helgaker et al. 2000), one can see the CCSD(T) results approaching chemical accuracy for this problem. MP2 also performs very well in this case, but this is not always the case. Helgaker et al. (2000) report an extrapolated CCSD(T) result from cc-pcV5Z and cc-pcV6Z values of-39.6 kcal mol . The cc-pcVXZ basis sets include additional functions to account for core correlation effects that are not included in the cc-pVXZ sets. 

Fig. 15.11. Errors relative to experiment in all-electron calculations of atomization eneigies (kJ/mol) in the cc-pCVXZ basis sets at the MP2 level (dotted line). CCSD level (dashed line) and CCSDfT) level (full line).

In the calculations of atomization energies discussed up to now, we have correlated the full set of electrons in the cc-pCVXZ basis sets. Such calculations are rather expensive, however, and significant savings would be obtained if instead the calculations could be carried out in the smaller cc-pVXZ basis sets, correlating only the valence electrons. Unfortunately, the errors arising from the neglect of core correlation in such valence-electrrm calculations would be unacceptable, at least for quantitative work. 

In the preceding sections, we discussed the energy differences associated with atomizations and chemical reactions. In the present section, we consider the smaller differences associated with conformational changes [101 the barrier to linearity of water in Section 15.9.1, the inversion barrier of ammonia in Section 15.9.2 and the torsional barrier of ethane in Section 15.9.3. All barriers have been studied at the Hartree-Fock, MP2, CCSD, CCSD(T) and CCSDT levels of theory in the cc-pVXZ, aug-cc-pVXZ and cc-pCVXZ basis sets, with the valence electrons correlated in the valence... 

The first point to note about the correlation-consistent basis sets in Table 8.16 is that the convergence is in all cases uniform and systematic - for the energies, for the bond distances, and for the bond angle. Scrutiny of the table reveals that, with each increment in the cardinal number, all errors are reduced by a factor of at least 3 or 4. Clearly, the correlation-consistent basis sets provide a convenient framework for the quantitative study of molecular systems at the Hartree-Fock level. We also note that the results for the cc-pVXZ and cc-pCVXZ basis sets are very similar. Apparently, the molecular core orbitals are quite atom-like and unpolarized by chemical bonding. In Hartree-Fock calculations, therefore, the use of the smaller valence cc-pVXZ sets is recommended. 

Table 8.20 Errors in the calculated Hartree-Fock and correlation eneigies in mEh for the cc-pCVXZ basis sets at the experimental equilibrium geometry...

Fig. 8.19. The convergence of the MP2 correlation energy (full line) and the Hartree-Fock energy (dotted line) in mEh for N2 calculated using the cc-pCVXZ basis sets. On the left, we have plotted the correlation energies superimposed on a fit of the form (8.4.3) with the horizontal axis representing the asymptotic limit of —537 mEh. On the right, we have plotted the errors in the correlation energy superimposed on the fitted form (8.4.3) (full line) as well as the errors in the Hartree-Fock energy (dotted line) on a logarithmic scale.

Having compared the valence IPs in a small basis, let us now consider the core and valence IPs in a sequence of basis sets. In Tables 10.2 and 10.3, we have listed the core and valence IPs of H2O and N2 calculated u.sing Koopmans method and the ASCF method. For cranparison, we have also listed the vertical experimental IPs. The core-valence cc-pCVXZ basis sets have been used in order to describe the relaxation of the core orbitals accurately in the ASCF method. All calculations have been carried out at the optimized geometry of the neutral molecule in the given basis. 

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