Use of Low-Cost Quantum Chemistry Procedures for Geometry Optimization and Vibrational Frequency Calculations: Determination of Frequency Scale Factors and Application to Reactions of Large Systems.

We have assessed the performance of a variety of low-cost computational quantum chemistry procedures (semiempirical, pure-DFT, and screened-exchange DFT methods) for computing molecular geometries and thermochemical quantities associated with the vibrational frequencies. Frequency scale factors for zero-point vibrational energies and thermal corrections for 298 K enthalpies and 298 K entropies have been determined. In absolute terms, for small to medium-sized molecules, all procedures perform reasonably well. Semiempirical methods have mean absolute deviations (MADs) of ∼15 kJ mol-1 for total enthalpies and free energies. For DFT procedures, hybrid DFT generally performs better than pure DFT. Remarkably, the N12 pure functional shows very good performances (MADs ∼ 3 kJ mol-1) that are comparable to those for hybrid functionals. An examination of the basis set effect indicates N12/3-21G* and N12/6-31G(d) to be cost-effective for geometry optimization and vibrational frequency calculations, but the use of minimal basis sets leads to very large MADs for the calculated thermochemical quantities. Further testing with reaction energies of large systems shows that, by exploiting cancellation of systematic deviations, although the deviations can be very substantial in absolute terms (>100 kJ mol-1), those for relative energies are markedly reduced (∼10 kJ mol-1). This enables the use of even semiempirical procedures to obtain geometries and vibrational frequencies with reasonable accuracy in cases where the use of more expensive procedures is computationally prohibitive.