deletions | additions       diff --git a/Sternheimer.tex b/Sternheimer.tex  index 85c2534..9a8349e 100644  --- a/Sternheimer.tex  +++ b/Sternheimer.tex 
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where  %  \begin{align}  \alpha_n &= {\rm max} \left( \epsilon_{\rm F} - 3 \sigma - \epsilon_n, 0 \right) \right)\ ,  \\ \beta_{n,m} &= \tilde{\theta}_{{\rm F},n} \tilde{\theta}_{n,m} + \tilde{\theta}_{{\rm F},m} \tilde{\theta}_{m,n} + \alpha_m \frac{\tilde{\theta}_{{\rm F},n} - \tilde{\theta}_{n,m}}{\epsilon_n - \epsilon_m \mp \omega} \tilde{\theta}_{m,n} \tilde{\theta}_{m,n}\ ,  \end{align}  %  $\sigma$ is the broadening energy energy,  and $\tilde{\theta}_{ij}$ is the smearing scheme's approximation to the Heaviside function $\theta \left( \left( \epsilon_i - \epsilon_j \right) / \sigma \right)$. Apart from semiconducting smearing (\textit{i.e.} the original equation above, which corresponds to the zero temperature limit),  the code offers the standard Fermi-Dirac~\cite{Mermin_1965}, Methfessel-Paxton~\cite{Methfessel_1989}, spline~\cite{Holender_1995}, and cold~\cite{Marzari_1999} smearing schemes.  Additionally, we have developed a scheme for handling arbitrary fractional occupations, which do not have to be defined by a function of the energy eigenvalues \cite{Strubbethesis}.