Boltzmann-averaged conformation

The PCM/DFT model failed to predict the intrinsic rotation (i.e. the specific rotation extrapolated to infinite dilution) of (R)-3-methylcyclopentanone dissolved in carbon tetrachloride, methanol and acetonitrile [68], This molecule has been investigated because it exists in both an equatorial and an axial form, allowing researchers to investigate the interplay of solvent and conformational effects. The conformer populations used in the Boltzmann averaging were derived from IR absorption and VCD spectra. The deviation of the calculated optical rotation from experiment was found actually to be larger when IEF-PCM was used to account for direct solvent effects (and geometry relaxation) on the optical rotation than when the gas-phase values were used. 

Barone, G. Duca, D. Silvestri, A. Gomez-Paloma, L. Riccio, R. Bifulco, G. Determination of the relative stereochemistry of flexible organic compounds by ab initio methods conformational analysis and Boltzmann-averaged GIAO C NMR chanical shifts, Chenu-Eur, J. 2002, 8, 3240-3245. 

At the conclusion of the conformational search, the Boltzmann-averaged energy of the system was calcrilated using... 

Table 28-1 shows the three possible axial and equatorial conformations. Substitution in Equation 28-27 generates the calculated ratio of each conformcr. Because MMFF94 was parameterized to reproduce the quantum mechanical calculations. it is illustrative to look at the ratio calculated with MMFF94. The Boltzmann-averaged distribution may then be compared with the experimental data as well as the other force field results. 

Figure 46 (-)-Chimonantine 119 experimental CD spectrum in cyclohexane and two calculated in the velocity and length formalism. The TDDFT/B3LYP/6-31G calculated spectra were obtained as Boltzmann average upon the total six conformers taking into account the 40 lowest energy transitions and assuming a Gaussian distribution with (7i = 0.15eV. Redrawn from E. Giorgio K. Tanaka L. Verotta K. Nakanishi N. Berova C. Rosini, Chirality 2007, 19, 434-445.

Table 1.4 Nucleobase trimer formation enthalpies (kcal/ mol]. Brackets represent a Boltzmann averaging of the conformations shown above it at 298K. ...

The MM4 values are for the confotmer that is calculated to be of lower enthalpy. The experimental numbers are the Boltzmann averaged values for the conformers. 

The second rank orientational order parameters of the two conformers can be obtained by taking the Boltzmann average using the appropriate potential of mean torque. For example, for the linear conformer the order parameter for the molecular symmetry axis is... 

Different approaches to the calculation of vibrational corrections to response properties can be found in the work of Sauer and Pack (2000), Ruud et al. (2000), and Kongsted and Christiansen (2006). The Boltzmann averaging procedure for conformationally flexible molecule has been critically reviewed by Crawford and Allen (2009). Mort and Autschbach (2008) have proposed an approach based on a decoupling of hindered rotations from the remaining (high-frequency) vibrational modes, which allows for a separate calculation of the hindered rotations without invoking the harmonic approximation. 

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