Warmup exercise and example of post

Reproduce Fig. 2.1 of the book .


For this calculations the authors used a cutoff energy of 292 eV and a \(\vec{k}\) point mesh of 12x12x12. The exchange and correlation is (Perdew-Wang 91).

Example of an equation

\begin{equation}f(x)=\sum_{s=-\infty}^{+\infty}e^{-i2\pi xs}g_s\label{fourier}\end{equation}

with \(g_s\) given by

\begin{equation} g_s=\int_n^{n+1} dx f(x) e^{i2\pi sx} \label{fourier-coefficient}\;.\end{equation}

We can evaluate Eq. \eqref{fourier} at the point \(n+\gamma\) with \(\gamma\in[0,1]\) to obtain