Abstract
The generalized graph matrix is extended to consider three-dimensional (3D) interatomic distances between pairs of atoms in molecules. It is used to (re)define some topographic descriptors, such as 3D-Wiener and 3D-Harary numbers. Harary numbers are generalized to a wide set of descriptors, and they are adapted for considering only nonbonded pairs of atoms. These Harary numbers for nonboded pairs of atoms are identified as repulsion potentials of the Mie type providing a physical interpretation to these descriptors. This formalism is adopted for generalizing Lennard-Jones (LJ) potentials using topological parameters. LJ parameters of three united-atom (UA) force fields, TIPS−UA, PRF−UA, and TraPPE-UA, are redefined using vertex degrees of pseudoatoms. High correlation coefficients (>0.99) are obtained between original LJ parameters and those derived from vertex degrees for linear and branched alkanes. These results make some links between some graph theoretical parameters used in structure−property relations and well-known interatomic potentials used in computational chemistry force fields.
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