Temperature Dependence of the Optical Rotation in Six Bicyclic Organic Molecules Calculated by Vibrational Averaging

Abstract

The vibrational corrections and the temperature dependence of the specific rotation of six rigid organic molecules (alpha-pinene, beta-pinene, cis-pinane, camphene, camphor, and fenchone) were calculated at three wavelengths using hybrid time-dependent density functional theory (TDDFT). A technique for calculating the temperature dependence of the vibrational average of a molecular property has been applied to obtain the specific rotation of the molecules as a function of temperature. For cases in which accurate equilibrium optical rotations can be obtained as a "base value," and for which there is little effect from solvation, accurate predictions of the trends in the temperature-dependence of the specific rotations can be calculated. For other cases, the method can be used to extract purely vibrational contributions to the overall temperature dependence of optical rotation.

Stereochemical analysis of (+)-limonene using theoretical and experimental NMR and chiroptical data

“…The calculated ORD [45]. Likewise, the incorporation of vibrational averaging for six conformational rigid molecules did not improve the prediction of the optical rotation, maybe since the calculations were performed in vacuo and the experimental data were obtained in ethylcyclohexane [46]. Therefore, typical polarization effects of the solvent were neglected.…”

“…Therefore, typical polarization effects of the solvent were neglected. In addition, Mort and Autschbach [46] concluded that the incorporation of vibrational effects on the ORD might not be sufficient to obtain accurate results as exemplified for methyloxirane and methylnorbornanone. A publication on the gas phase optical rotation of limonene demonstrated that very small amounts of analyte can be measured: a detection limit of 20 ng was determined [47].…”

Gas phase optical rotation calculated from coupled cluster theory with zero‐point vibrational corrections from density functional theory

“…Vibrational effects are generally non-neglible [21][22][23][24][25][26] and have been shown to account for as much as 20% of the optical rotation of rigid molecules. 22 In the case of methyloxirane, vibrational effects must be taken into account to reproduce the experimental gas phase optical rotation to within a few degrees.…”

A Pragmatic Recipe for the Treatment of Hindered Rotations in the Vibrational Averaging of Molecular Properties

“…[14,16] This program can be easily interfaced with a number of standard quantum chemistry packages and computational models (density functional theory, correlated ab initio, Hartree-Fock, and semi-empirical methods) as long as energy gradients and the property P are available analytically. The vibrational corrections of a molecular property P and their temperature-dependence is modeled with an expression that includes the first order effects due to the anharmonicity of the potential energy surface and the curvature of the property surface, Equation (1):…”

“…[18,19] We have recently reported a generally applicable and relatively simple protocol for calculating the temperature dependence of a molecular property based on vibrational averaging. [14] This technique has been applied to the calculation of the intrinsic vibrational temperature dependence of optical rotation in organic molecules, [15,16] H-D spin-spin coupling constants in metal complexes, [14] and the Verdet constants of small molecules. [17] Two fields of application where vibrational corrections have turned out to be important are optical activity and NMR parameters.…”