GGA functionals

Table 2 shows that in the case of ratile the GGA overestimation of lattice constants is less important in the present calculation than in Ref. 3. Most likely explanation is that the GGA functional is used here only for solid state calculations and not for the pseudopotential generation from the free atom. This procedure has been shown to give more accurate structural results than with the GGA applied both in the potential generation and solid state... 

All DFT methods perform better than HF and MP2 the hybrid techniques are even better than the costly QCISD. Both GGA functionals show scaling factors close to unity which means that they can be used without scaling, but they do not perform quite as well as... 

The tensor of the static first hyperpolarizabilities P is defined as the third derivative of the energy with respect to the electric field components and hence involves one additional field differentiation compared to polarizabilities. Implementations employing analytic derivatives in the Kohn-Sham framework have been described by Colwell et al., 1993, and Lee and Colwell, 1994, for LDA and GGA functionals, respectively. If no analytic derivatives are available, some finite field approximation is used. In these cases the P tensor is preferably computed by numerically differentiating the analytically obtained polarizabilities. In this way only one non-analytical step, susceptible to numerical noise, is involved. Just as for polarizabilities, the individual tensor components are not regularly reported, but rather... 

The take home message of this section is that local and GGA functionals perform more or less similarly for IR and Raman intensities, whereas the hybrid ones offer a significant improvement, yielding results comparable or even better than MP2 for significantly less computational cost. In terms of basis sets, at least double-zeta sets augmented by flexible polarization and diffuse functions are needed. The POL basis set seems to offer a particularly good price/performance ratio. 

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