Triple Zeta plus Double Polarization

The more recent 1992 Maslen et al. force field for benzene (153) was computed by evaluating analytic derivatives through quartic terms at the SCF level. The DZP basis set was used in these studies. The derivatives were evaluated at the equilibrium geometry determined at the MP2 (Moller-Plesset second-order pertubation theory) level using a larger basis set, TZ2P (triple-zeta plus double polarization). It is significant that a complete ab initio force field at the quartic level has been computed for benzene. 

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. 

The full Cl is impractical except as a reference because the number of determinants is asymptotically N . That means its application is possible only for small molecules and small basis sets. In praaice, calculations using 25 x 10 determinants for H O in a double zeta plus polarization (DZP) basis have been made and —10 determinants for CH3 in a triple zeta plus polarization (TZP) basis. ... 

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). 

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. 

More recent ab initio calculations on the formation of the adduct H3P BH3 applied basis sets of double zeta [95], double zeta plus polarization [96], and 4-31G quality (including counterpoise corrections) [97]. A slightly exothermal decomposition of the adduct is predicted at the CEPA level and agrees with the observed instability of the adduct in the gas phase at ambient temperature [96]. A recent ab intio MO calculation for the 1 1 adduct H3P - BF3 at the SCF and MP2 levels with basis sets of triple zeta quality gave a very large P-B distance. The adduct can thus be considered only a weak van der Waals complex which should not easily be observable in experiments. The calculated results therefore disagree [98] with the alleged experimental observation of this adduct in the gas phase [99]. 

The calculations shown in this work have been performed using the Amsterdam Density Functional (ADF) code [20,21]. All of them are spin not polarized. The influence of the quality of the basis set on the Re value has been explored taking as a guide the case of Mn in fluoroperovskites. For this goal two types of basis sets have been employed. Firstly calculations have been carried out by means of functions of quality IV (which are implemented in the ADF code) involving triple zeta basis functions plus a polarization function. In a second step Re has also been computed using double zeta functions of quality II for F and ions. 

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. 

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.)... 

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. 

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