Theoretical studies on Lennard-Jones parameters of benzene and polycyclic aromatic hydrocarbons.

Lennard-Jones (L-J) parameters, i.e. collision diameter and well depth, of benzene and polycyclic aromatic hydrocarbons (PAHs) interacting with bath gases helium and nitrogen are studied theoretically in this work. The results of three different computing methods, called SA, σ-ε, η-ξ methods respectively, are compared with literature data. The SA method determines effective L-J parameters from the spherically averaged intermolecular potentials; the σ-ε method averages L-J parameters obtained from different relative orientations of interacting partners; and the η-ξ method uses an orientation-averaging rule on the basis of two characteristic variables η and ξ representing repulsive and attractive energy scales respectively. The σ-ε and η-ξ methods require much less computational time than the SA method due to the use of an iterative search algorithm. For validation of the L-J parameters, binary diffusion coefficients computed using L-J parameters by these three methods and those by empirical estimations are compared with experimental data from literature. Results show that while the SA method is reliable and the σ-ε method is efficient, the η-ξ method is both reliable and efficient for computing L-J parameters for benzene and PAHs, and captures the anisotropic effects of molecular structure on L-J parameters better than empirical methods.

On the determination of Lennard-Jones parameters for polyatomic molecules.

Characterizing the key length and energy scales of intermolecular interactions, Lennard-Jones parameters, i.e., collision diameter and well depth, are prerequisites for predicting transport properties and rate constants of chemical species in dilute gases. Due to anisotropy in molecular structures, Lennard-Jones parameters of many polyatomic molecules are only empirically estimated or even undetermined. This study focuses on determining the effective Lennard-Jones parameters between a polyatomic molecule and a bath gas molecule from interatomic interactions. An iterative search algorithm is developed to find orientation-dependent collision diameters and well depths on intermolecular potential energy surfaces. An orientation-averaging rule based on characteristic variables is proposed to derive the effective parameters. Cross-interaction parameters for twelve hydrocarbons with varying molecular shapes, including long-chain and planar ones, interacting with four bath gases He, Ar, N2, and O2 are predicted and reported. Three-dimensional parametric surfaces are constructed to quantitatively depict molecular anisotropy. Algorithmic complexity analysis and numerical experiments demonstrate that the iterative search algorithm is robust and efficient. By using the latest experimental diffusion data, it is found that the proposed orientation-averaging rule improves the prediction of cross-interaction Lennard-Jones parameters for polyatomic molecules, including for long-chain molecules that challenge the consistency of previous methods. By introducing characteristic variables, the present study shows a new route to determining effective Lennard-Jones parameters for polyatomic molecules.