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

The narcissus constant, N = 2.3983843828..., is defined as a number that fulfills the narcissistic infinite nested radical equation

$$\sqrt[N]{N+N\times \sqrt[N]{N+N\times \sqrt[N]{N+\cdots}}}=N=\sqrt[N]{N\times N+\sqrt[N]{N\times N+\sqrt[N]{N\times \cdots}}}.$$

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

$$\frac{U_{\rm NLJ} }{D}=\frac{1}{N-1}\left( {\frac{R}{r}} \right)^{N^3}-\frac{N}{N-1}\left( {\frac{R}{r}} \right)^{N^2},$$

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.