Investigating the Calculation of Anharmonic Vibrational Frequencies Using Force Fields Derived from Density Functional Theory

Abstract

The calculation of anharmonic vibrational frequencies for a set of small molecules has been examined to explore the merit of applying such computationally expensive approaches for large molecules with density functional theory. The performance of different hybrid and gradient-corrected exchange-correlation functionals has been assessed for the calculation of anharmonic vibrational frequencies using second-order vibrational perturbation theory with two-and four-mode couplings and compared to the recently developed transition optimized shifted Hermite method. A range of exchange-correlation functionals (B3LYP, BLYP, EDF1, EDF2, B97-1, B97-2, HCTH-93, HCTH-120, HCTH-147, and HCTH-407) have been evaluated with reference to a large experimental data set comprising 88 species and 655 modes as well as a smaller set of shifts in frequency because of anharmonicity derived from experimental data. The anharmonic frequencies calculated using hybrid functionals provide the best agreement with experiment, and are not significantly improved by frequency scaling factors, indicating an absence of significant systematic error. For the molecules studied, the B97-1 and B97-2 functionals give the closest overall agreement with experiment, although the improvement over the best case for pure harmonic frequencies is modest. Predictions of the experimental anharmonic shifts are closest for the B3LYP and EDF2 functionals, with B97-1 performing well because of a good description of the harmonic force field. Investigations using modified hybrid functionals with increased fractions of Hartree−Fock exchange indicate that approximately 20% Hartree−Fock exchange is optimal.

Conformational Preferences of 2-Acylpyrroles in Light of FT-IR and DFT Studies

“…Currently, modern computational chemistry yields results comparable to the most accurate experimental measurements [61]. Furthermore, the interpretation of experimental vibrational spectra is much easier and accurate owing to calculated harmonic and anharmonic [62] vibration transitions [63]. …”

Uncontracted core Pople basis sets in vibrational frequency calculations

“…30%‐40% additional Hartree‐Fock exchange, while anharmonic studies using VPT2 have shown that the B97‐1 functional outperforms B3LYP and that the optimum hybridization is ca. 20%, in line with the prediction of other molecular properties . Another method for checking the accuracy of harmonic calculations is therefore to compare the quality of the harmonic calculations with harmonic experimental frequencies that are extrapolated from vibrational spectra of small molecules.…”

“…Previous studies have shown that choice of basis set is of considerable importance when calculating accurate harmonic and anharmonic frequencies more generally . This can be such a significant source of computational cost and error, that basis sets tailored to specific vibrational coordinates are in development, and Pople basis sets are commonly used as a compromise between accuracy and computational cost, particularly during anharmonic calculations . At the same time, uncontracting the core basis functions in Pople‐type atom‐centered basis sets has been shown to improve calculations of core‐electron properties, such as core‐electron binding energies, and provides a systemic way of testing improvements in basis set quality when describing the core region of molecules as well as σ‐orbitals described by the additional s ‐functions, which are fewer in the Pople basis sets than other families of basis set …”

“…The functionals studied in this work have been chosen to reflect specific cases of interest. The B3LYP functional is known to perform particularly well for calculating scaled harmonic frequencies, and the B97‐1 functional is one of few functionals that outperforms B3LYP for calculating anharmonic frequencies . Two meta‐hybrid functionals were also chosen.…”

Calculating singlet excited states: Comparison with fast time-resolved infrared spectroscopy of coumarins

“…Harmonic frequencies were scaled using a scaling factor of 0.9682. 2,50,65 In principle it would be possible to derive scaling factors for different excited state methods. However, there is currently a lack of experimental data encompassing a wide range of functional groups to make this reliable, and we assume here that scaling factors derived for the ground state can be applied with no additional modifications following previous excited state frequency benchmarking studies.…”