Minimum distance measurements, molecular

Intermolecular repulsion forces will define a hard-sphere diameter for the molecules allowing the calculation and/or measurement of the density fluctuation as one moves away from the surface. As shown in Figure 4.86, the result is a damped density curve (density distribution versus distance in molecular diameters from the surface). For a liquid between two surfaces at short separation distances, the two effects will overlap producing an interference pattern as illustrated in Figure 4.9. When the distance of separation is some integral multiple of the hard sphere diameter, nAhs, reinforcement occurs producing a local free energy minimum. For separations that correspond to fractional... 

The change from a viscous to a molecular flow regime occurs when the mean free path L of the gas molecules in the system exceeds the minimum physical dimensions of the system. The mean free path is a measure of the average distance a molecule travels between collisions. The derivation of L involves a number of assumptions about the ideality of the gas and the nature of the collisions and by definition some 63.2% of the molecules in a particular gas collide with other molecules within the distance L. The mean free path for any gas can be calculated from Equation (1.1)... 

The USR (Ultrafast Shape Recognition) Method. This method was reported by Ballester and Richards (53) for compound database search on the basis of molecular shape similarity. It was reportedly capable of screening billions of compounds for similar shapes on a single computer. The method is based on the notion that the relative position of the atoms in a molecule is completely determined by inter-atomic distances. Instead of using all inter-atomic distances, USR uses a subset of distances, reducing the computational costs. Specifically, the distances between all atoms of a molecule to each of four strategic points are calculated. Each set of distances forms a distribution, and the three moments (mean, variance, and skewness) of the four distributions are calculated. Thus, for each molecule, 12 USR descriptors are calculated. The inverse of the translated and scaled Manhattan distance between two shape descriptors is used to measure the similarity between the two molecules. A value of 1 corresponds to maximum similarity and a value of 0 corresponds to minimum similarity. 

Figure 12.7 presents the molecular graph of CLOH—HBeH complex where the intermolecular O-H—H-Be DHB exists. It was found that this structure corresponds to the stable energetic minimum [35], This is the shortest ever found theoretically intermolecular contact (H—H) since it amounts to only 1.049 A. On the other hand, such a short contact represents the proton-acceptor distance.9 It is worth mentioning that the other shortest contact was revealed for bifluoride (FHF)-ion. For this system, the H—F equivalent distances amount to 1.1—1.2 A. The exact value depends on the type of experimental measurements or the applied method of calculations [36]. 

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