Potential energy function based on the narcissus constant, its square and its cube

Abstract

The narcissus constant, N = 2.3983843828..., is defined as a number that fulfills the narcissistic infinite nested radical equation N√ N+N× N√N+N× N√N+...=N=N√N× N+N√N× N+ N√N×.... Incorporation of this constant, its square and its cube into the generalized version of the Lennard-Jones potential function gives the narcissus constant potential function UNLJ/D= 1/N-1(R/r) N3}-N/N-1 (R/r)N2 which (a) is suitable for modeling van der Waals interaction due to its agreement with the Lennard-Jones (12-6) potential energy curve over long range, and (b) forms simple generalized hybrid interatomic-intermolecular potential energy function due to its correlation with the averaged form of Lennard-Jones, Morse, Buckingham and Linnett potential energy curve near the minimum well-depth. © 2006 Springer Science+Business Media, LLC.