Partition function lennard jones potential

[Derivator]

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

 

[Derivator]

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[Derivator]

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[mcodesmart]

 

[PJC01]

Hello,

Thank you for sharing your question about the partition function for the Lennard-Jones potential. It seems that your integral is not converging because the potential energy for the Lennard-Jones potential goes to infinity as the distance between the particles approaches zero. This means that the particles would have infinite energy and it is not physically realistic.

To fix this, you can introduce a cutoff distance in the integral to limit the range of interaction between the particles. This will ensure that the integral converges and provides a more accurate representation of the system. Additionally, there are also alternative methods for calculating the partition function for the Lennard-Jones potential, such as using a series expansion or numerical integration techniques.

I hope this helps and good luck with your calculations!