Harmonic Vibrational Frequencies: An Evaluation of Hartree−Fock, Møller−Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors

1996/01/01 by Anthony P. Scott, Leo Radom · 6,709 citations
Chemistry · Materials Science · Mathematics · Physics and Astronomy · #Ab initio #Advanced Chemical Physics Studies #Anharmonicity #Atomic physics #Basis set #Chemistry #Computational chemistry #Crystallography and molecular interactions #Density functional theory #Harmonic #Hartree–Fock method #Mathematics #Molecular physics #Molecular vibration #Molecule #Møller–Plesset perturbation theory #Perturbation theory (quantum mechanics) #Physics #Quantum mechanics #Scaling #Thermal and Kinetic Analysis

paper · doi:10.1021/jp960976r

published in The Journal of Physical Chemistry 100(41), 16502-16513 (American Chemical Society)

openalex publication_date 1996/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Scaling factors for obtaining fundamental vibrational frequencies, low-frequency vibrations, zero-point vibrational energies (ZPVE), and thermal contributions to enthalpy and entropy from harmonic frequencies determined at 19 levels of theory have been derived through a least-squares approach. Semiempirical methods (AM1 and PM3), conventional uncorrelated and correlated ab initio molecular orbital procedures [Hartree−Fock (HF), Møller−Plesset (MP2), and quadratic configuration interaction including single and double substitutions (QCISD)], and several variants of density functional theory (DFT: B-LYP, B-P86, B3-LYP, B3-P86, and B3-PW91) have been examined in conjunction with the 3-21G, 6-31G(d), 6-31+G(d), 6-31G(d,p), 6-311G(d,p), and 6-311G(df,p) basis sets. The scaling factors for the theoretical harmonic vibrational frequencies were determined by a comparison with the corresponding experimental fundamentals utilizing a total of 1066 individual vibrations. Scaling factors suitable for low-frequency vibrations were obtained from least-squares fits of inverse frequencies. ZPVE scaling factors were obtained from a comparison of the computed ZPVEs (derived from theoretically determined harmonic vibrational frequencies) with ZPVEs determined from experimental harmonic frequencies and anharmonicity corrections for a set of 39 molecules. Finally, scaling factors for theoretical frequencies that are applicable for the computation of thermal contributions to enthalpy and entropy have been derived. A complete set of recommended scale factors is presented. The most successful procedures overall are B3-PW91/6-31G(d), B3-LYP/6-31G(d), and HF/6-31G(d).

Citations

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