Scaling of Jaguar Frequencies

Because the errors in quantum mechanical calculations of frequencies are often fairly predictable, it is sometimes desirable to scale frequencies by one or more factors. Scaling methods can also improve calculations of thermochemical properties, which use the scaled frequencies. In Jaguar, two methods are available for frequency scaling: the Pulay et al. Modified Scaled Quantum Mechanical Force Fields (SQM) method [112] for B3LYP calculations using the 6‑31G* basis set, and standard frequency scaling, in which all frequencies are simply multiplied by a single parameter.

The SQM method alters the frequencies by scaling the Hessian elements themselves (in internal coordinates), using 11 different scale factors, which depend on the type of stretch, bend, or torsion. This method was parametrized using B3LYP calculations for 30 molecules containing C, H, N, O, and Cl, using the 6‑31G* basis set. Jaguar permits the SQM scaling method to be used only for B3LYP/6‑31G* frequency jobs.

Alternatively, for any type of frequency job, you can multiply all frequencies by the same scale factor. Scale factors have been optimized for many combinations of basis set and method. Table 1 lists the recommended scale factors for various methods and basis sets. The factors in the table are from Ref. [113] and Ref. [114] and are optimized for the best agreement with experiment for the frequencies themselves. Ref. [113] also includes scale factors suitable for low-frequency vibrations, for zero-point vibrational energies, and for prediction of enthalpy and entropy. Other scale factors may be available in the literature.

^aRef. [113]

^bRef. [114]