Basis sets, diffuse polarization

Density functional theory calculations have shown promise in recent studies. Gradient-corrected or hybrid functionals must be used. Usually, it is necessary to employ a moderately large basis set with polarization and diffuse functions along with these functionals. 

Split Valence Basis Sets Polarized Basis Sets Diffuse Functions Pseudopotentials... 

In a previous work [1,2], we were interested in the calculation of second order hyperpolarizabilities of eonjugated systems including substituted benzenes, pyridine N-oxydes and vinyl oligomers, in relation with non linear optical activity [3]. We showed that MNDO ealeulations were in good agreement with SCF ab initio results obtained using a double zeta basis set plus polarization and diffuse orbitals. 

In order to ensure reasonably well-converged results for the optical rotation, basis sets of polarized valence double-zeta quality are required, and sets such as the aug-cc-pVDZ of Woon and Dunning (1994), or the polarized triple-zeta basis of Sadlej (1988) have been shown to perform well for calculations of optical rotation. Most importantly, diffuse p functions in the outer regions of the electron density, which in most cases is described by the electron density of hydrogen atoms, are required to ensure qualitatively correct results (Zuber and Hug 2004). 

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. 

The calculations were carried out using B3LYP with a double- basis set including polarization and diffuse functions, in gas phase and only adding ZPE to the electronic energy. Admittedly, by today s standards this may be unpublishable, but it still contains some deep qualitative insights that we can use for pedagogical purposes. 

For all calculations, the choice of AO basis set must be made carefully, keeping in mind the scaling of the two-electron integral evaluation step and the scaling of the two-electron integral transfonuation step. Of course, basis fiinctions that describe the essence of the states to be studied are essential (e.g. Rydberg or anion states require diffuse functions and strained rings require polarization fiinctions). 

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