Frequency and Zero-Point Vibrational Energy Scale Factors for Double-Hybrid Density Functionals (and Other Selected Methods): Can Anharmonic Force Fields Be Avoided?

Abstract

We have obtained uniform frequency scaling factors λ(harm) (for harmonic frequencies), λ(fund) (for fundamentals), and λ(ZPVE) (for zero-point vibrational energies (ZPVEs)) for the Weigend-Ahlrichs and other selected basis sets for MP2, SCS-MP2, and a variety of DFT functionals including double hybrids. For selected levels of theory, we have also obtained scaling factors for true anharmonic fundamentals and ZPVEs obtained from quartic force fields. For harmonic frequencies, the double hybrids B2PLYP, B2GP-PLYP, and DSD-PBEP86 clearly yield the best performance at RMSD = 10-12 cm(-1) for def2-TZVP and larger basis sets, compared to 5 cm(-1) at the CCSD(T) basis set limit. For ZPVEs, again, the double hybrids are the best performers, reaching root-mean-square deviations (RMSDs) as low as 0.05 kcal/mol, but even mainstream functionals like B3LYP can get down to 0.10 kcal/mol. Explicitly anharmonic ZPVEs only are marginally more accurate. For fundamentals, however, simple uniform scaling is clearly inadequate.

Revealing Disparate Chemistries of Protactinium and Uranium. Synthesis of the Molecular Uranium Tetroxide Anion, UO4–

“…While the calculated frequency for the hydroxide structure is too high, it is well-known that with the chosen PBE0 or B3LYP functional frequencies are overestimated and need to be scaled to lower values. 56 Energetically, the hydroxide structure is predicted to be 114 kJ/mol lower in energy than the hydrate (Table 1). In addition, the computed spectrum for the alternative hydrate structure has two intense absorption features split by about 50 cm −1 , instead of the single peak observed in the experiment (see Figure S5).…”

An Evaluation of Gas Phase Enthalpies of Formation for Hydrogen-Oxygen (HxOy) Species

“…In some cases anharmonic ZPEs were computed (more accurately) using the vibrational configuration interaction (VCI) [188] or second-order vibrational perturbation theory (VPT2) [189] methods. Some discussion regarding uncertainties in computed ZPEs can be found in work by Barone (2004) [190], [195], Kesharwanti et al (2015) [191], and references contained therein.…”

VIBRATIONAL SCALING FACTORS FOR Rh(I) CARBONYL COMPOUNDS IN HOMOGENEOUS CATALYSIS

“…This makes it possible to correct ab initio frequencies by a scaling factor to compensate for the approximations so that they match the experimental outcome. Deriving scaling factors for harmonic frequencies has received a much of attention in the literature [10][11][12][13][14]. Derived scaling factors are specific to each level of theory used, but they also depend on the test set of molecules.…”