(5/5)

Imagine we have N atoms of the same type with coordinates (x,y,z). These coordinates can be saved in a file similar to the example "coordinates.txt". Please write a python script which:

1. Reads the coordinates of all atoms from such a file into a numpy array and plots them on a 3D plot.

2. Creates a cubic lattice of N atoms with a given density (N/V), or reduced density. Based on the density you will need to choose the size of cube and place the atoms on the lattice. Save this file in the format, similar to "coordinates.txt" and plot these configuration as well.

3. Write the script which calculates a definite integral with trapezoidal method and Monte Carlo method with uniform sampling

4. Test this script on the integrals $\int\lim_0^{\infinity} dx \exp(-x)$ and $\int\lim_0^{\infinity} dx \exp(-x^2)$. Compare the results of the two methods.

5-Update your MC script so that it can:

- read and save coordinates

- move atoms at random (taking into account PBC, minimum image convention and checking if there no overlap as a result of moves)

- calculate the g(r) -- see Section 8.2 in Allen & Tildesley for details

(5/5)

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