Matrix Differential Calculus with Applications in Statistics and Econometrics

Optimized scale factors for calculating vibrational harmonic and fundamental frequencies and zero-point energies have been determined for 145 electronic model chemistries, including 119 based on approximate functionals depending on occupied orbitals, 19 based on single-level wave function theory, three based on the neglect-of-diatomic-differential-overlap, two based on doubly hybrid density functional theory, and two based on multicoefficient correlation methods. Forty of the scale factors are obtained from large databases, which are also used to derive two universal scale factor ratios that can be used to interconvert between scale factors optimized for various properties, enabling the derivation of three key scale factors at the effort of optimizing only one of them. A reduced scale factor optimization model is formulated in order to further reduce the cost of optimizing scale factors, and the reduced model is illustrated by using it to obtain 105 additional scale factors. Using root-mean-square errors from the values in the large databases, we find that scaling reduces errors in zero-point energies by a factor of 2.3 and errors in fundamental vibrational frequencies by a factor of 3.0, but it reduces errors in harmonic vibrational frequencies by only a factor of 1.3. It is shown that, upon scaling, the balanced multicoefficient correlation method based on coupled cluster theory with single and double excitations (BMC-CCSD) can lead to very accurate predictions of vibrational frequencies. With a polarized, minimally augmented basis set, the density functionals with zero-point energy scale factors closest to unity are MPWLYP1M (1.009), τHCTHhyb (0.989), BB95 (1.012), BLYP (1.013), BP86 (1.014), B3LYP (0.986), MPW3LYP (0.986), and VSXC (0.986).

Computational Thermochemistry: Scale Factor Databases and Scale Factors for Vibrational Frequencies Obtained from Electronic Model Chemistries

Scaling of ab initio force fields by MOLVIB

Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications

We present an alternative approach to the derivation of scaled quantum mechanical (SQM) force fields involving the direct scaling of individual primitive valence force constants from a full set of redundant valence coordinates. Our approach is completely general and more flexible than previous SQM schemes. Optimal scaling factors for various primitive stretching, bending, and torsional force constants are derived from a training set of 30 molecules containing C, O, N, H, and Cl and used to scale force constants for a further 30 molecules. Calculated vibrational frequencies are compared with experimental values for over 1500 fundamentals. Using the hybrid three-parameter B3-LYP density functional with the split-valence 6-31G* basis set, our scaling procedure gives an average error of less than 8.5 cm-1 in the scaled frequencies. The average percentage error is under 1%.

Direct Scaling of Primitive Valence Force Constants: An Alternative Approach to Scaled Quantum Mechanical Force Fields

Fully optimized geometries, complete in- and out-of-plane force fields, and dipole moment derivatives have been
calculated for the title compounds at the ab initio HartreeFock level using the 4-21 Gaussian basis set. The theoretical information is combined with experimental data by fitting the calculated force constants through a few parameters to the observed frequencies to obtain the final, scaled quantum mechanical (SQM) force fields. Recommendations for a standard procedure of this type are given. The SQM force fields give excellent reproduction of the fundamental frequencies and are considered as approaching the best accuracy which can be achieved in a harmonic treatment. The infrared intensities obtained at this level of theory are only qualitative estimates, but they are still useful for making assignments more reliable.

Combination of theoretical ab initio and experimental information to obtain reliable harmonic force constants. Scaled quantum mechanical (QM) force fields for glyoxal, acrolein, butadiene, formaldehyde, and ethylene

Calcul du champ de force de vibration harmonique complet et des elements du champ de force cubique diagonal et semidiagonal pour la pyridine, au niveau Hartree-Fock 4-21

Gábor Pongor

Papers

Combination of theoretical ab initio and experimental information to obtain reliable harmonic force constants. Scaled quantum mechanical (QM) force fields for glyoxal, acrolein, butadiene, formaldehyde, and ethylene

Theoretical Prediction of Vibrational Spectra. 1. The In-Plane Force Field and Vibrational Spectra of Pyridine

Vibrational analysis of 2-nitrophenol. A joint FT-IR, FT-Raman and scaled quantum mechanical study

Extension of the density functional derived scaled quantum mechanical force field procedure.

Theoretical prediction of vibrational spectra. The a priori scaled quantum mechanical (SQM) force field and vibrational spectra of pyrimidine