Partition function lennard jones potential

AI Thread Summary
The discussion centers on calculating the potential energy component of the partition function for two particles interacting through the Lennard-Jones potential. The integral proposed for the partition function is problematic due to its divergence at large distances, where the integrand approaches 1. Participants are prompted to identify the error in the formulation that leads to this non-convergence issue. Clarifications on the behavior of the Lennard-Jones potential and its implications for the partition function are sought. The conversation emphasizes the need for proper limits or modifications to ensure convergence in the integral calculation.
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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?
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