Small atomic clusters: quantum chemical research of isomeric composition and physical properties

Molecular Collision Diameters and Electronic Polarizabilities: Inherent Relationship and Fast Evaluation

“…Notice also that since the polarizability of the molecule or cluster is relatively easy to measure, the existence of the σ−α el correlation is of significance for the experimental recognition of the molecular structure. 13,36,72 Comparison with Other Approaches. To complement the picture, let us confront the methods described in previous sections with some other approaches (mentioned in the Introduction) to determine the collision diameter of a molecule based on the empirical correlations with atomic composition.…”

“…The presence of an algebraic relationship in this case would open the way for an evaluation of collision diameters via the known polarizability, and, conversely, for rapid assessment of α el for large polyatomic species for which direct quantum chemical determination is too computationally expensive, through the σ evaluation using any of the traditional methods. 5,13 In the present short article, we aimed to clarify this issue.…”

“…Nevertheless, we must admit that until now, there is no generally accepted simple approach for determining the molecular collision diameter theoretically. At present, there are methods for assessing the collision diameter through only the elemental composition of the species, 5,23−26 through both spatial structure and elemental composition, 5,13,14,27 as well as via the analysis of electron density in a molecule. 11,28 Unfortunately, the approaches based on the empirical correlations of σ with atomic composition only, 23−25 which go back to the seminal works of Hirschfelder, 7 for all their simplicity, do not allow for the spatial structure of the molecules and, therefore, are applicable with confidence only for the smallest (di-and triatomic) species.…”

“…The search for correlations of σ with the number of nonhydrogen atoms for hydrogen- containing compounds within homologous series also holds some promise; 5,26 however, it lacks generality. The methods for estimating the collision diameter involving the analysis of the equilibrium molecular structure 5,13,14,27 have been developed only recently but have already proven themselves well in various applications. However, their use requires the knowledge of an optimized molecular structure (i.e., not always readily available) and the implementation of special algorithms for structure analysis.…”

“…The collision diameter σ ij that specifies the range of repulsive valence forces in the Lennard-Jones potential for a pair of colliding molecules of i and j types is an essential parameter commonly used for estimating the gas-kinetic collision frequency, transport properties (diffusion, viscosity, and thermal conductivity coefficients), the characteristic time of vibrational and rotational relaxation, and so forth. − The σ ij values can be directly obtained from molecular beam scattering experiments or derived from the measurements of such macroscopic parameters as second virial, viscosity, and diffusion coefficients. ,, However, owing to the difficulties in carrying out appropriate experiments (especially, for transient species and radicals), theoretical determination of the collision diameters is immensely important for predictive modeling of chemically reacting flows. ,,− …”