Basis sets harmonic frequencies

Table 11.13 H2O HF harmonic frequencies (cm ) as a function of basis set experimental values are 3943 cm 3832 cmand 1649 cm...

The MP2 treatment recovers the majority of the correlation effect, and the CCSD(T) results with the cc-pVQZ basis sets are in good agreement with the experimental values. The remaining discrepancies of 9cm , 13cm and lOcm are mainly due to basis set inadequacies, as indicated by the MP2/cc-pV5Z results. The MP2 values are in respectable agreement with the experimental harmonic frequencies, but of course still overestimate the experimental fundamental ones by the anharmonicity. For this reason, calculated MP2 harmonic frequencies are often scaled by 0.97 for comparison with experimental results. ... 

H2O CCSD(T) harmonic frequencies as a function of basis set (valence electrons only)... 

Table 11.16 H2O MP2 harmonic frequencies (cm function of basis set (all electrons) " ) as a...

For comparison with experimental frequencies (which necessarily are anharmonic), there is normally little point in improving the theoretical level beyond MP2 with a TZ(2df,2pd) type basis set unless anharmonicity constants are calculated explicitly. Although anharmonicity can be approximately accounted for by scaling the harmonic frequencies by 0.97, the remaining errors in the harmonic force constants at this level are normally smaller than the corresponding errors due to variations in anharmonicity. 

The harmonic frequencies calculated with different DFT functionals as a function of basis set are shown in Tables 11.17-11.19. The convergence as a function of basis set is similar to that observed for the HF method. The B3PW91 functional again shows the best performance. With the cc-pV5Z basis set the deviations from the experimental harmonic frequencies are only 0cm", 9 cm" and 17 cm", substantially better that the... 

Table 12-6. Harmonic frequency shifts [cm 11 of the donor O-H stretching mode and elongation of the O-H bond [A] in the water dimer computed at several levels of theory (aug-cc-pVTZ basis set). 

Martin, J. M. L., El-Yazal, J., Francois, J.-P, 1995a, Basis Set Convergence and Performance of Density Functional Theory Including Exact Exchange Contributions for Geometries and Harmonic Frequencies , Mol. Phys., 86, 1437. 

In order to assign more IR signals of 4a, ab initio calculations on Hbdmpza (3b) and 4a were performed. It is well known for the chosen HF/6-31G basis set that calculated harmonical vibrational frequencies are typically overestimated compared to experimental data. These errors arise from the neglecting anharmonicity effects, incomplete incorporation of electron correlation and the use of finite basis sets in the theoretical treatment (89). In order to achieve a correlation with observed spectra a scaling factor (approximately 0.84-0.90) has to be applied (90). The calculations were calibrated on the asymmetric carboxylate Vasym at 1653 cm. We were especially interested in... 

Turning to the basis set dependence of the harmonic frequencies of HF, we see that the uncorrected CD s first increase, and then decrease with increasing basis set quality. Although the frequencies are improved by applying the counterpoise correction, the counterpoise-corrected results show the same general convergence behavior as the uncorrected results. Note the fortuitous cancellation of errors in the... 

As seen above, application of the counterpoise procedure or the addition of diffuse functions may result in Rg(nZ) or coAnZ) curves which are better behaved. As another example. Figure 9 shows the harmonic frequency of HCl, computed with the cc-pVnZ and aug-cc-pVnZ basis sets. As for HF, application of the counterpoise correction improves the convergence behavior of computed with the regular sets, although the convergence behavior of the corrected co, s is far from simple. Addition of the set of diffuse functions to the basis as well as use of the counterpoise correction results in a very smooth dependence of on basis set. 

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