Partition function lennard jones potential

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Discussion Overview

The discussion centers on the calculation of the potential energy component of the partition function for two particles interacting through the Lennard-Jones potential. The focus is on the mathematical formulation and convergence of the integral representing this partition function.

Discussion Character

  • Technical explanation

Main Points Raised

  • One participant expresses concern that the integral representing the partition function does not converge, noting that the integrand approaches 1 for large values of r.
  • The same participant questions their own understanding of the mistake in their approach to the integral.
  • Subsequent posts consist of simple prompts to keep the thread active, without introducing new content or responses to the initial query.

Areas of Agreement / Disagreement

The discussion remains unresolved, with no consensus reached regarding the convergence of the integral or the participant's mistake.

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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