While entropy is a major driving force in many chemical changes and is a key component of the free energy of a molecule, it can be challenging to calculate with standard quantum thermochemical methods. With proper consideration in flexible molecules, we can break down the total entropy into different components, including vibrational, translational, rotational and conformational entropy. The calculation of conformational entropy is the most time-consuming as we have to sample all thermally-accessible conformers. Here, we attempt to understand the components that contribute to the conformational entropy of a molecule, and develop a physically-motivated statistical model to rapidly predict the conformational entropies of small molecules.

In our analysis, we sampled conformers for over 120,000 molecules, and showed that the number of low energy conformers increases logarithmically with the number of degrees of freedom, implying only a logarithmic increase in conformational entropy. We also showed that the formation of intramolecular interactions such as hydrogen bonds and \pi-\pi stacking reduces conformational flexibility of small molecules, and thus decreases the conformational entropy. We introduced a consistent atom numbering scheme to study the path characteristics of these intramolecular interactions, and developed rules to predict potential intramolecular interactions. Using insight into the nature of conformational disorder, our cross-validated physically-motivated statistical model can outperform common machine learning and deep learning methods, with a mean absolute error≈4.8 J/mol·K, or under 0.4 kcal/mol at 300 K.

In summary, our analysis provided a better understanding of various contributions to conformational entropies , and the proposed model can facilitate the calculation of thermodynamic properties.

References:

[1] L. Chan et al. Understanding Conformational Entropy in Small Molecules. ChemRxiv 2020