Boltzmann distribution conformational analysis

To generate the molecular descriptors, by which molecular similarity is evaluated, first, the Conformation Energy Profile (CEP) of each molecule is estimated. This is indicated by the Boltzmann distribution plot of the number of conformers N(AE) at energy AE. CEP was first defined and used in the framework of 4D-QSAR Analysis. 

While it is true that large, high-energy deformations are less likely to occur (and be observed) than small, low-energy ones, there is a serious flaw in these arguments. An ensemble of structural parameters obtained from chemically different compounds in a variety of crystal structures does not even remotely resemble a closed system at thermal equilibrium and does not therefore conform to the conditions necessary for the application of the Boltzmann distribution. It is thus misleading to draw an analogy between this distribution and those derived empirically from statistical analysis of observed deformations in crystals [20]. 

The selectivities were calculated using the Boltzmann distribution, based on the energies of the most stable conformations. The authors performed a conformational analysis for each of the 12 different pathways of approaching of the olefin to the osmium tetroxide. They combined two techniques, the pseudo-systematic Monte Carlo [65] to explore the entire conformational space, and the Low Mode [66] searching to explore exhaustively a local region of the potential energy surface (Table 2). 

The Gaussian distribution is derived from the binomial distribution for large N [5]. It is important for statistics, error analysis, diffusion, conformations of polymer chains, and the Maxwell Boltzmann distribution law of gas velocities. 

---