# An Evaluation of Harmonic Vibrational Frequency Scale Factors

journal contribution

posted on 2007-11-15, 00:00 authored by Jeffrey P. Merrick, Damian Moran, Leo RadomScale factors for obtaining fundamental vibrational frequencies, low-frequency vibrational frequencies, zero-point vibrational energies (ZPVEs), and thermal contributions to enthalpy and entropy have been derived
through a least-squares approach from harmonic frequencies determined at more than 100 levels of theory.
Wave function procedures (HF, MP2, QCISD, QCISD(T), CCSD, and CCSD(T)) and a large and representative
range of density functional theory (DFT) approaches (B3-LYP, BMK, EDF2, M05-2X, MPWB1K, O3-LYP,
PBE, TPSS, etc.) have been examined in conjunction with basis sets such as 6-31G(d), 6-31+G(d,p), 6-31G(2df,p), 6-311+G(d,p), and 6-311+G(2df,p). The vibrational frequency scale factors were determined by a
comparison of theoretical harmonic frequencies with the corresponding experimental fundamentals utilizing
a standard set of 1066 individual vibrations. ZPVE scale factors were generally obtained from a comparison
of the computed ZPVEs with experimental ZPVEs for a smaller standard set of 39 molecules, though the
effect of expansion to a 48 molecule data set was also examined. In addition to evaluating the scale factors
for a wide range of levels of theory, we have also probed the effect on scale factors of varying the percentage
of incorporated exact exchange in hybrid DFT calculations using a modified B3-LYP functional. This has
revealed a near-linear relationship between the magnitude of the scale factor and the proportion of exact
exchange. Finally, we have investigated the effect of basis set size on HF, MP2, B3-LYP, and BMK scale
factors by deriving values with basis sets ranging from 6-31G(d) up to 6-311++G(3df,3pd) as well as with
basis sets in the cc-pVnZ and aug-cc-pVnZ series and with the TZV2P basis.