Valence triple-zeta basis plus polarization

These comparisons, and additional comparisons with other ab initio calculations, indicate that the harmonic frequencies for benzene have not been pinned down at the 10-20 cm 1 level by the previously mentioned ab initio calculations. In order to reduce inaccuracies in the harmonic force field, we have performed relatively large scale calculations using a valence triple zeta plus polarization basis set (pVTZ) in coupled-cluster calculations with single and double excitations (CCSD). These results, as well as comparisons with previous ab initio and recent density functional (156-157) results, are described elsewhere (108). 

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. 

Abbreviations used t(0)dzp - basis set is double-zeta polarization on all atoms except oxygen for which it is valence triple-zeta svp - basis set is split-valence plus polarization. B3LYP, BP86, and PW are all gradient-corrected density functionals. See the original papers for references. 

Ab initio density functional theory calculations were also carried out on the CH2=XH(A) and CH(A)=XH2 series of molecules. The basis set used was the CEP-TZDP+ described previously26 and is more extensive than the DZP basis set used in the CAS(4,4)-OVB calculations. In TZDP+ the valence electron wave function is expanded in a triple-zeta sp set of functions plus a double set of polarization d-type functions plus a set of diffuse sp-type functions. The B3LYP exchange-correlation functional20 as defined in the Gaussian 94 program set35 was used in all the DFT calculations. 

The basis set can be minimal (one basis function per valence shell) but can be improved systematically by going to double zeta (two per valence shell), to double zeta plus polarization, to triple zeta plus double polarization plus higher angular momentum plus diffuse functions, and finally to the complete set. Some of the improvements on minimal basis sets are described next. 

A geometry optimization of Tc2(02CCH3)2Cl4 was performed using the Tao, Perdew, Staroverov, and Scuseria hybrid functional (TPSSh) at the triple-zeta valence plus polarization (TZVPP) basis set [53]. The results show that the calculated Tc-Tc, Tc-Cl, and Tc-O bond distances are in good agreement with the experimental values (Table 7.5). The largest deviation is found for the Tc-Tc distance. 

A relatively large basis set has to be used for a reasonable description of correlation effects. Minimal basis sets or split valence basis sets are not suitable for carrying out MP or other correlation corrected ab initio calculations. One needs at least a DZ + P(VDZ -I- P) or TZ + 2P basis set to get reasonable energies, geometries and first-order properties. For second-order properties, TZ -I- 2P or QZ + 3P basis sets are needed. (DZ -I- P = double-zeta plus polarization VDZ = valence DZ TZ = triple-zeta QZ = quadruple-zeta.)... 

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