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Application Of Geometric Probability Techniques To The Evaluation Of Interaction Energies Arising From A General Radial Potential, David Schleef, Michelle Parry, Shu-Ju Tu, Brian Woodahl, Ephraim Fischbach

Chemistry & Physics Faculty Publications

A formalism is developed for using geometric probability techniques to evaluate interaction energies arising from a general radial potential V(r₁₂), where r₁₂ = ∣r₂−r₁∣. The integrals that arise in calculating these energies can be separated into a radial piece that depends on r₁₂ and a nonradial piece that describes the geometry of the system, including the density distribution. We show that all geometric information can be encoded into a “radial density function” G(r₁₂;ρ₁,ρ₂), which depends on r_{12 …}