Zero-point and temperature dependent vibrational averaging of molecular properties
Mort, Brendan C.
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A technique for calculating the zero-point and temperature dependent vibrational averages of molecular properties is derived from a perturbation expansion of the molecular property with respect to normal coordinates. A convenient formula based on an anharmonicity correction and a property curvature correction has been implemented and adapted to a number of standard quantum chemistry software packages and computational methods. The sign and magnitude of the zero-point vibrational corrections the optical rotation for a benchmark set of chiral molecules is determined. It is found that the corrections to optical rotation average about 20% of the equilibrium specific rotations at 589.3 nm. The program is also applied to the calculation of the H-D spin-spin coupling constants for a set of transition metal hydride and hydrogen complexes. It is found that vibrational corrections to J HD are highly significant and lead to improved agreement between theory and experiment. Results from these computations are used to classify different classes of complexes where a temperature dependence of J HD may or may not exist. The temperature dependence of the vibrational averaging of optical rotation for a set of rigid organic molecules is also shown. Direct comparisons are made between theory and experiment, and it is demonstrated that for cases in which there is little effect from solvation, accurate theoretical prediction of the trends in the temperature dependence of specific rotations can be obtained. Additionally, vibrational corrections to the Verdet constant (magneto-optical rotation) of a set of molecules are compared using pure density functional theory (DFT), hybrid DFT, and coupled-cluster theory. It is found that vibrational corrections to the Verdet constant can be as large as 10% of the equilibrium value. Finally, a method for eliminating the confounding effects due to hindered rotations in vibrational averaging is described and demonstrated for a set of molecules and properties. The treatment of hindered-rotor contributions to a vibrationally averaged property can improve the accuracy of computations.