Cc-pVDZ Correlation-consistent Basis

Canonical ensemble 60 Cartesian components 4 Cartesian Gaussian-type orbitals 161 CASSCF (Complete Active Space Self Consistent Field) model 205 cc-pVDZ (Correlation-consistent Basis Sets) 175, 201 Centrifugal effects 276 Charge element 15 Choice of origin 297... 

To illustrate how well DFT or ab initio methods predict the dipole moments. Table 1 illustrates the comparison between theory and experiment for eight small molecules. The error statistics are summarized in Table 2. In general, the quality of the basis set plays an important role in the prediction of dipole moments. We see that the 6-3IG basis set provides poor predictions, even when applied with a QCISD level of theory. The performances of the double-zeta basis set plus polarization functions (6-3IG, DZVPD (double-zeta valence orbitals plus polarization and diffuse functions on heavy atoms), and cc-pVDZ (correlation-consistent polarized valence double-zeta)) are poorer than those from the polarized triple-zeta basis sets. The only exception is B-P/DZVPD (B-P = Becke-Perdew), from which we obtained an average absolute deviation of 0.040 debye, lower than that (0.053 debye) from B-P/TZVPD (triple-zeta valence orbitals plus polarization and diffuse functions on heavy atoms). It can be seen that the inclusion of correlation effects through either ab initio or DFT approaches significantly improves the agreement. 

An extension of this last notation is aug—cc—pVDZ. The aug denotes that this is an augmented basis (diffuse functions are included). The cc denotes that this is a correlation-consistent basis, meaning that the functions were optimized for best performance with correlated calculations. The p denotes... 

Electron correlation studies demand basis sets that are capable of very high accuracy, and the 6-31IG set I used for the examples above is not truly adequate. A number of basis sets have been carefully designed for correlation studies, for example the correlation consistent basis sets of Dunning. These go by the acronyms cc-pVDZ, cc-pVTZ, cc-pVQZ, cc-pV5Z and cc-pV6Z (double, triple, quadruple, quintuple and sextuple-zeta respectively). They include polarization functions by definition, and (for example) the cc-pV6Z set consists of 8. 6p, 4d, 3f, 2g and Ih basis functions. 

We see that only the cc-pVDZ is (roughly) comparable in size to the 6-31G (15 + 2 + 2= 19 functions) the other cc sets are much bigger. Correlation-consistent basis sets sometimes [55] but do not necessarily [56] give results superior to those with Pople sets that require about the same computational time. 

CO Peterson and Dunning [92] have made an extensive analysis of the role of basis sets and correlation treatments in the calculation of the molecular properties of CO. By carefully controlling the errors in the calculations, it was possible to compute properties of this small molecule to an accuracy that rivals the most sophisticated experimental studies. They made use of the correlation consistent basis sets (cc). The dissociation energy with icCAS+SDQ was computed 258.5 kcal/mol with the best method, and the experimental value is 259.6 0.1 kcal/mol. The CCSD(T) yielded 258.6 kcal/mol in excellent agreement with experiment. CASSCF, MP4, and CCSD yield results with errors bigger than 4 kcal/mol. The CBS limit was obtained by exponential extrapolation of the cc-pVDZ through cc-pV6Z for all methods. 

The first set of calculations (Figure 2.1) was done using Dunning s contracted correlation-consistent basis set of double-zeta quality augmented with a set of diffuse functions, aug-cc-pVDZ (10s5p2d) [4s3p2d]. Each PEC was obtained from 30-35 calculated points. 

There are two families of correlation consistent basis sets designed to recover core correlation effects, denoted cc-pCVnZ and cc-pwCVnZ [24,25]. Both add shells of functions to the standard cc-pVnZ sets in the usual correlation consistent prescription and both systematically lead to identical CBS limits. The number and type of added functions is dependent on the core definition. First-row atoms have a [He] core, so the DZ core correlation set adds a (Islp) set to the cc-pVDZ, while the TZ basis adds a (2s2pld) set, etc. In the case of the 2nd-row atoms, only 2s2p correlation is treated, i.e., the Is electrons are not correlated and the [Ne] core results in additional (Islpld), (2s2p2dlf), etc. added to the cc-pVDZ, cc-pVTZ, etc. sets to construct the core correlation basis sets. 

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