From: hackbard <hackbard@hackdaworld.org>
Date: Fri, 9 Sep 2011 11:25:15 +0000 (+0200)
Subject: |
X-Git-Url: https://hackdaworld.org/gitweb/?a=commitdiff_plain;h=6ff9691bfd15ba165c609de924ae7f12889776f4;p=lectures%2Flatex.git

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diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex
index b095d71..d80a4d0 100644
--- a/posic/thesis/basics.tex
+++ b/posic/thesis/basics.tex
@@ -526,7 +526,7 @@ Mathematically, a non-local PP, which depends on the angular momentum, has the f
 V_{\text{nl}}(\vec{r}) = \sum_{lm} | lm \rangle V_l(\vec{r}) \langle lm |
 \text{ .}
 \end{equation}
-Applying of the operator $V_{\text{nl}}(\vec{r})$ decomposes the electronic wave functions into spherical harmonics $\mid lm \rangle$, i.e.\ the orbitals with azimuthal angular momentum $l$ and magnetic number $m$, which are then multiplied by the respective pseudopotential $V_l(\vec{r})$ for angular momentum $l$.
+Applying of the operator $V_{\text{nl}}(\vec{r})$ decomposes the electronic wave functions into spherical harmonics $| lm \rangle$, i.e.\ the orbitals with azimuthal angular momentum $l$ and magnetic number $m$, which are then multiplied by the respective pseudopotential $V_l(\vec{r})$ for angular momentum $l$.
 The standard generation procedure of pseudopotentials proceeds by varying its parameters until the pseudo eigenvalues are equal to the all-electron valence eigenvalues and the pseudo wave functions match the all-electron valence wave functions beyond a certain cut-off radius determining the core region.
 Modified methods to generate ultra-soft pseudopotentials were proposed, which address the rapid convergence with respect to the size of the plane wave basis set \cite{vanderbilt90,troullier91}.