X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Fthesis%2Fbasics.tex;h=f6a8eda37e41458fa71099fe61ac63fe811dcbe8;hp=bc1641065e0210c09a99bfe08ca5b6e9f0cc8995;hb=8b561b21134ce68789e71a53357177540516d478;hpb=cc0556c8e0be08fcb505425c53b7e722fcef8a8f

diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex
index bc16410..f6a8eda 100644
--- a/posic/thesis/basics.tex
+++ b/posic/thesis/basics.tex
@@ -421,7 +421,7 @@ for the exchange-correlation energy, where $\epsilon_{\text{xc}}(\vec{r};[n(\til
 Expressing $n(\tilde{\vec{r}})$ in a Taylor series, $\epsilon_{\text{xc}}$ can be thought of as a function of coefficients, which correspond to the respective terms of the expansion.
 Neglecting all terms of order $\mathcal{O}(\nabla n(\vec{r}))$ results in the functional equal to LDA, which requires the function of variable $n$.
 Including the next element of the Taylor series introduces the gradient correction to the functional, which requires the function of variables $n$ and $|\nabla n|$.
-This is called the generalized gradient approximation (GGA), which expresses the exchange-correlation energy density as a function of the local density and the local gradient of the density
+This is called the generalized-gradient approximation (GGA), which expresses the exchange-correlation energy density as a function of the local density and the local gradient of the density
 \begin{equation}
 E^{\text{GGA}}_{\text{xc}}[n(\vec{r})]=\int\epsilon_{\text{xc}}(n(\vec{r}),|\nabla n(\vec{r})|)n(\vec{r}) d\vec{r}
 \text{ .}
@@ -532,6 +532,7 @@ Using PPs the rapid oscillations of the wave functions near the core of the atom
 More importantly, less accuracy is required compared to all-electron calculations to determine energy differences among ionic configurations, which almost totally appear in the energy of the valence electrons that are typically a factor $10^3$ smaller than the energy of the core electrons.
 
 \subsection{Brillouin zone sampling}
+\label{subsection:basics:bzs}
 
 Following Bloch's theorem only a finite number of electronic wave functions need to be calculated for a periodic system.
 However, to calculate quantities like the total energy or charge density, these have to be evaluated in a sum over an infinite number of $\vec{k}$ points.