Partition function lennard jones potential

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SUMMARY

The discussion focuses on calculating the partition function for two particles interacting through the Lennard-Jones potential. The integral presented, \int_0^\infty exp(-\beta * 4((\frac{1}{r})^{12}-(\frac{1}{r})^6)) dr, fails to converge due to the integrand approaching 1 as r increases. The key mistake lies in not accounting for the behavior of the potential at large distances, which leads to divergence in the integral.

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  • Understanding of statistical mechanics and partition functions
  • Familiarity with the Lennard-Jones potential model
  • Knowledge of integral calculus, particularly improper integrals
  • Basic concepts of thermodynamic limits in physical systems
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Physicists, chemists, and researchers in statistical mechanics or molecular dynamics who are working with potential energy calculations and partition functions.

Derivator
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hi folks,

I want to calculate the potential energy part of the partition function of 2 particles interacting via the Lennard-Jones potential. This partition function should be proportional to:

\int_0^\infty exp(-\beta * 4((\frac{1}{r})^{12}-(\frac{1}{r})^6)) dr

But this integral won't converge, since the integrand is approx. equal to 1 for large r.

What is my mistake?
derivator
 
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