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.