Calculation of the entropy caused by hindered internal rotation—a mechanistic tool to explore the steric influence on the entropy of activation

Calculation of rotational partition functions by an efficient Monte Carlo importance sampling technique

The evaluation of the classical rotational partition function represented by a configuration integral over all external and internal rotational degrees of freedom of nonrigid chain polyatomic molecules is described. The method of Pitzer and Gwinn is used to correct the classical partition function for quantum mechanical effects at low temperatures. The internal rotor hindrance and all coupling arising from the external and internal rotational degrees of freedom are explicitly taken into account. Importance sampling Monte Carlo based on the adaptive VEGAS algorithm to perform multidimensional integration is implemented within the TINKER program package. A multidimensional potential energy hypersurface is calculated with the MM3(2000) molecular mechanics force field. Numerical tests are performed on a number of small n-alkanes (from ethane to octane), for which the absolute entropies calculated at three different temperatures are compared both with the experimental values and with the previous theoretical results. The application of a more efficient importance sampling technique developed here results in a substantial reduction of statistical errors in the evaluation of the configuration integral for a given number of Monte Carlo steps. Error estimates for the calculated entropies are given, and possible sources of systematic errors, and their importance for a reliable prediction of the absolute entropy, are discussed.

Solvent dependence of rotational energetics and formyl-proton long-range spin-spin coupling behavior of 2,6-dichloro- and 2,6-dinitrobenzaldehydes using dipolar couplings and temperature dependence of long-range couplings

The formyl rotational energetics, solvent effects on the energetics and formyl-proton spin-spin coupling behavior of 2,6-dichlorobenzaldehyde were studied by using dipolar couplings analysis and the temperature dependence of the spin-spin couplings. The general form of the rotational potential was taken from molecular mechanics and the conjugative sin2 Θ-type component (where Θ is the formyl-ring dihedral angle) was then optimized using the dipolar couplings obtained by analyzing 1H NMR and 13C proton satellite spectra in a liquid crystal solvent. The optimization based on the dipolar couplings gave the following rotational free energy potential: V(Θ) = 4.5 cos6 Θ + 10.7 (± 2.0) sin2 Θ, in kJ/mol. The analysis based on the temperature dependence of 6J data allowed estimation of solvent effects on the potential. For example, the potentials in acetone and in acetonitrile differ by a 1.0 sin2 2Θ (in kJ/mol). The chloroform solvent effect can be described by term of -1.0 cos6 Θ. When the formyl-proton six-bond coupling data was fit, assuming it obeyed the expression 6J(Θ) = 6J90 sin2 Θ + 6J0 and assuming 6J0 = 0.015 Hz, the analysis yielded 6J90 of -0.48 (± 0.03) Hz. The scalar coupling temperature dependence method was applied also to the conformational analysis of 2,6-dinitrobenzaldehyde.Key words: spin-spin coupling, dipolar coupling, solvent effect, rotational barrier, benzaldehyde.