Modified Lennard-Jones potentials for nanoscale atoms.

A classical 6-12 Lennard-Jones (LJ) equation has been widely used to model materials and is the potential of choice in studies when the focus is on fundamental issues. Here we report a systematic study comparing the pair interaction potentials within solid-state materials (i.e., [Co6 Se8 (PEt3 )6 ][C60 ]2 , [Cr6 Te8 (PEt3 )6 ][C60 ]2 , [Ni9 Te6 (PEt3 )8 ][C60 ]) using density functional theory (DFT) calculations and LJ parametrization. Both classical (6-12 LJ) and modified LJ (mLJ) models were developed. In the mLJ approach, the exponents 6 and 12 are replaced by different integer number n and 2n, respectively, and an additional parameter (α) is introduced to describe intermolecular distance shift arising within the geometric centers' approach (instead of the shortest interatomic distance between particles). A general LJ approach reexamination reveals that in the case of nanoatoms, the attractive term decays with distance as the inverse fourth power, and the dominating at short distances repulsive term decays as the inverse eighth power. The modification of the LJ equation is even more prominent for interaction profiles, where intermolecular distance corresponds to separation between geometric centers of particles. In this approach, the attractive term decays with distance as the inverse 12th power, while the repulsive term decays rapidly (as the inverse 24th power). Thus, the mLJ models (e.g., 4-8 LJ) rather than the 6-12 classical ones seem to be a better choice for the description of binary interactions of nanoatoms. The developed mLJ models and electronic structure characteristics give an insight into the explanation of the unique physicochemical properties of superatomic-based solid-state materials.