## Compute collision diameter window

This window provides the possibility to compute the collision diameter of a molecule.

The collision diameters should be identified as the value from σij, from the well-known Lennard-Jones potential:

Where i=j (collision of two similar molecules).

It is considered, that the linear size of the electronic density of an atom is approximately proportional to α1/3, where α is the static polarizability of this atom [1].

The following formula was proposed in the work [2]. For collisions of atoms with other atoms, their collision diameter σij can be computed from their isotropic static polarizability:

When two atoms of similar type collide, the value σ can be computed as follows:

This hypothesis works well for atoms, but for molecules their geometrical structure should be also considered.

In the work [3] a new approach was proposed and tested: Around each atom in the molecule, a sphere is built with the radius equal to the collision radius of this atom (σii). Then, a parallelepiped is built around these spheres, so that the volume of this parallelepiped is minimal:

The collision diameter of the molecule is computed as the cubic root of A*B*C.

We have calculated the collision diameters for some molecules:

 Molecule Calculated σ Experimental σ Ref (experimental σ) C2H4 4,23906 3,971 [4] C2H5OH 5,01054 4,53 [4] C3H8 5,32233 4,982 [4] CF4 4,099 4,662 [4] CH2O 4,07284 3,59 [4] CH3OH 4,45024 3,626 [4] CH4 3,93679 3,746 [4] H2O 3,39223 2,605 [4] H2O2 3,80045 3,458 [4] H2S 4,0742 3,6 [4] HCl 3,72118 3,339 [4] HCN 3,84656 3,63 [4] HF 2,93618 3,148 [4] Benzene 5,6425 5,29 [5] Toluene 6,29687 5,68 [5] Azulene 6,41968 6,39 [5] Naphthalene 6,24269 6,18 [5] Biphenyl 6,94883 6,31 [5] Anthracene 6,74621 6,96 [5] Phenantrene 6,92642 6,96 [5] Pyrene 7,0638 7,24 [5] Chrysene 7,32167 7,64 [5] Coronene 7,82404 8,16 [5]

The correlation between calculated and experimental values is the following:

The correlation coefficient here is 0.977. We think that this this correlation is sufficient, taking into account that the experimental values of the diameters can be different with different methods of investigation (molecular beams, by viscosity, by diffusion).

References:

[1] Purcell, E. Electricity and magnetism: Berkeley physics course. Cambridge , UK : Cambridge University Press, 2011, 484

[2] Cambi, R.; Cappelletti, D.; Liuti, G. & Pirani, F. Generalized correlations in terms of polarizability for van der Waals interaction potential parameter calculations. J. Chem. Phys., 1991, 95, 1852-1862

[3] Sharipov, A. S.; Loukhovitski, B. I.; Tsai, C.-J. & Starik, A. M. Theoretical evaluation of diffusion coefficients of (Al2O3)n clusters in different bath gases Eur. Phys. J. D, 2014, 68, 99

[4] H. Wang, M. Frenklach, Combust. Flame 96, 163 (1994)

[5] R.J. Kee et al.Chemkin Collection, Release 3.6, Reaction design, Inc., San Diego, CA (2000)

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