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Relationship between Lennard-Jones potential and physico-chemical parameters

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Abstract

We developed in this paper the used methodology to describe the Lennard-Jones potential of two atoms in rare gas. In this treatment we supposed that one atom could be described by a harmonic oscillator. The interaction potential is developed at short and long ranges. The results showed that the obtained physico-chemical parameters such as the oscillator frequency, the atom mass, and the atom charge well reproduce the Lennard-Jones potential. Then the potential well depth and the effective equilibrium diameter are expressed in function of the oscillator frequency, the atom mass and charge.

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Abbreviations

\({H}_{T}\) :

Total Hamiltonian

\({H}_{AB}\) :

Interaction Hamiltonian

k :

Stiffness of the harmonic vibrator

zi  (i = A or B):

Dipolar charges distance

\({R}_{AB}\) :

Interatomic distance

m :

Atom mass

\({\upupsilon }_{0}\) :

Vibration frequency corresponding to the lowest energy

\({{\text{E}}}_{0}\) :

Lowest energy

h :

Planck’s constant

\({E}_{0}^{c}\) :

Minimum energy of the system (after coupling)

\({{\text{V}}}_{a}\) :

Attractive energy

\({{\text{V}}}_{r}\) :

Repulsion energy

\(V\left({R}_{AB}\right)\) :

Lennard-Jones potential

\({\varepsilon }_{s}\) :

Well depth

\({\sigma }_{s}\) :

Equilibrium diameter

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  1. Laboratory of Quantum and Statistical Physics, Faculty of sciences of Monastir, Environment Street, 5019, Monastir, Tunisia

    Yosra Ben Torkia & Abdelmottaleb Ben Lamine

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  1. Yosra Ben Torkia
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Ben Torkia, Y., Ben Lamine, A. Relationship between Lennard-Jones potential and physico-chemical parameters. J Math Chem (2024). https://doi.org/10.1007/s10910-024-01598-5

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