Aug-cc-pVXZ basis sets

A more sequential approach to the analysis of the systematic error of ab initio methods has been proposed in [14]. The same set of molecules as in [10] has been analyzed there. For this set the series of calculations using the basis sets aug-cc-pVxZ containing both polarization and diffuse functions with the number of exponents x in their respective radial parts up to x = 6 (single zeta x = 1, double zeta - DZ -x = 2, triple zeta - TZ - x = 3, etc.) and with the account of correlation effects in the range of methods from MP2 up to CCSD(T) had been performed and then fitted to the formulae [15-18] ... 

The correlation-consistent basis sets described in Section 8.3.3 have been designed for one particular purpose the accurate calculation of valence-correlated wave functions of ground-state neutral systems. The cc-pVXZ basis sets therefore do not have the flexibility required either for the investigation of core correlation discussed in Section 8.3.1 or for the study of anions and excited states with diffuse electron distributions. For such applications, additional AOs must be introduced. In the present subsection, we shall first discuss the correlation-consistent polarized core—valence sets cc-pCVXZ [24], where the standard cc-pVXZ sets have been extended for additional flexibility in the core region, and next the augmented correlation-consistent basis sets aug-cc-pVXZ and aug-cc-pCVXZ [25], where diffuse functions have been added so as to improve the flexibility in the outer valence region. 

We now turn our attention to the outer, diffuse regions of the electronic system. The valence and core-valence basis sets considered so far are inadequate for the description of the difiuse electron distributions characteristic of anionic systems and excited states. In addition, these sets do not have the flexibility required for a proper description of interactions with external electric fields and hence the accurate calculation of dipole moments and polarizabilities. For such calculations, additional functions must be added in the outer valence region. Within the framework of correlation-consistent basis sets, we proceed by adding primitive functions to the standard cc-pVXZ sets, with exponents adjusted so as optimize the energy of atomic anions. Diffuse functions are added in groups, with one set of functions for each angular momentum present in the root set. This procedure leads to the augmented correlation-consistent polarized valence basis sets aug-cc-pVXZ [25], the composition and size of which are listed in Table 8.13. The number of functions in the aug-cc-pVXZ sets may be calculated as... 

From the broad spectrum of atomic orbital basis sets, one type can be strongly recommended. It is the basis set library of Dunning and coworkers [5], the correlation consistent polarized valence XZ (cc-pVXZ, X = D, T, Q,. . . ) basis sets. Dunning s augmented sets of correlation consistent basis sets (aug-cc-... 

The tables below give some examples of atomic charges and bond orders calculated by various methods as a function of the basis set at the HF level of theory. It is evident that the Mulliken and Ldwdin methods do not converge as the basis set is increased, and the values in general behave unpredictably. Especially the presence of diffuse functions lead to absurd behaviours, as the aug-cc-pVXZ basis sets illustrate for CH4. Note also that... 

Table 11.10 establishes that diffuse functions are mandatory for calculating dipole moments, and only results with the aug-cc-pVXZ basis sets are shown for the DFT methods in Table 11.12. 

The experimental value for the dipole moment of CO is 0.122 D, with the polarity C 0+, for a bond length of 1.1281 A. Calculated values with the aug-cc-pVXZ basis sets are given in Table 11.21. Some other results using other basis sets are shown in Table 11.22. 

Figure 2 The valence correlation energies of Ne obtained by the CC or CC-R12 methods and the aug-cc-pVXZ basis sets (abbreviated as aXZ) [35].

For various intermolecular complexes, it has been found that KSCED interaction energies converge rather rapidly with both the number of atomic centers and the atomic basis sets. Table 3 collects the KSCED results (interaction energy and the energy of the highest occupied orbital in one of the monomers) for two series of the basis sets (CC-PVxZ and AUG-CC-PVxZ, for x=2-5) applied in the KSCED(s) or KSCED(m) schemes for the CH4-CH4 complex. 

P = Ibar, temperature T = 273.15K, electric field strength E = 2.6 x IC/ V m , magnetic induction field B = 3 T. The acronym nXZ is a shorthand notation for the correlation consistent n-aug-cc-pVXZ basis set. Wf is the wave function model employed. From [40]... 

Figure 6. Dependence of the HF and MP2 formation energy (in kcal/mol) on the basis set size. Upper row. HF for the cc-pVxZ and aug-cc-pVxZ basis sets. Lower row MP2 values for the same basis sets. Empty symbols are for formation energies whose BSSE has not been corrected, while filled circles are for BSSE-corrected values (see text).

Figure 14. Variation of the MP2 BSSE-uncorrected and BSSE-corrected interaction energies of the methane-water complex with the basis set. Circles indicate results obtained using Pople basis set, while squares indicate results obtained with the aug-cc-pVxZ basis sets. The geometry is the optimum one computed at the MP2/aug-cc-pVTZ level.

A study of atomization energies of 66 small molecules with the aug-cc-pVxZ (x = D,T, Q) basis sets gave the following average absolute errors in kcal/mol [D. Feller and K. A. Peterson, J. Chem. Phys., 108,154 (1998)], where the letters D, T, Q denote the basis set ... 

MP2 calculations with large aug-cc-pVxZ basis sets yielded an estimate of -5.0 0.1 kcal/mol for the binding energy of the water dimer in the complete basis-set limit and the effect of going to the MP4 level was found to be negligible [M. W. Feyereisen, D. Feller, and D. A. Dixon,/. Phys. Chem., 100,2993 (1996)] essentially the same result was found by a method called symmetry-adapted perturbation theory, which treats the interactions between the monomers as a perturbation [E. M. Mas and K. Szalewicz, /. Chem. Phys., 104,7606 (1996)]. 

---