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Potential energy function based on the narcissus constant, its square and its cube. (English) Zbl 1149.80303

Summary: The narcissus constant, \(N = 2.3983843828\ldots \), is defined as a number that fulfills the narcissistic infinite nested radical equation
\[ \root N\of {N+N\times \root N\of {N+N\times \root N\of {N+\cdots}}}=N= \root N\of {N\times N+ \root N\of {N\times N+ \root N\of {N\times\cdots}}} . \]
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 \[ \frac{U_{\text{NLJ}}}{D}= \frac{1}{N-1}\left(\frac{R}{r}\right)^{N^3}- \frac{N}{N-1} \left(\frac{R}{r}\right)^{N^2}, \]
which (a) is suitable for modeling van der Waals interaction due to its agreement with the Lennard-Jones potential energy curve over long range [J. E. Lennard-Jones, On the determination of molecular fields. II: From the equation of state of a gas, Proc. R. Soc. Lond. A 106, 463–477 (1924)], and (b) forms a 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.

MSC:

80A50 Chemistry (general) in thermodynamics and heat transfer
03D80 Applications of computability and recursion theory
11Y60 Evaluation of number-theoretic constants
81V55 Molecular physics
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