From: hackbard <hackbard@sage.physik.uni-augsburg.de>
Date: Wed, 11 May 2011 13:36:36 +0000 (+0200)
Subject: sec checkin, start with BO approx
X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=6b8e82e926099b05e961285bb4307711d1aa8d3e;p=lectures%2Flatex.git

sec checkin, start with BO approx
---

diff --git a/bibdb/bibdb.bib b/bibdb/bibdb.bib
index c0e9159..e21d322 100644
--- a/bibdb/bibdb.bib
+++ b/bibdb/bibdb.bib
@@ -539,6 +539,22 @@
                  entropy calculations",
 }
 
+@Article{munro99,
+  title =        "Defect migration in crystalline silicon",
+  author =       "Lindsey J. Munro and David J. Wales",
+  journal =      "Phys. Rev. B",
+  volume =       "59",
+  number =       "6",
+  pages =        "3969--3980",
+  numpages =     "11",
+  year =         "1999",
+  month =        feb,
+  doi =          "10.1103/PhysRevB.59.3969",
+  publisher =    "American Physical Society",
+  notes =        "eigenvector following method, vacancy and interstiial
+                 defect migration mechanisms",
+}
+
 @Article{colombo02,
   title =        "Tight-binding theory of native point defects in
                  silicon",
@@ -2827,6 +2843,20 @@
   notes =        "substitutional c in si by mbe",
 }
 
+@Article{born27,
+  author =       "M. Born and R. Oppenheimer",
+  title =        "Zur Quantentheorie der Molekeln",
+  journal =      "Annalen der Physik",
+  volume =       "389",
+  number =       "20",
+  publisher =    "WILEY-VCH Verlag",
+  ISSN =         "1521-3889",
+  URL =          "http://dx.doi.org/10.1002/andp.19273892002",
+  doi =          "10.1002/andp.19273892002",
+  pages =        "457--484",
+  year =         "1927",
+}
+
 @Article{hohenberg64,
   title =        "Inhomogeneous Electron Gas",
   author =       "P. Hohenberg and W. Kohn",
diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex
index 92b402c..b1beb7f 100644
--- a/posic/thesis/basics.tex
+++ b/posic/thesis/basics.tex
@@ -5,7 +5,7 @@ In the following the simulation methods used within the scope of this study are
 Enabling the investigation of the evolution of structure on the atomic scale, molecular dynamics (MD) simulations are chosen for modeling the behavior and precipitation of C introduced into an initially crystalline Si environment.
 To be able to model systems with a large amount of atoms computational efficient classical potentials to describe the interaction of the atoms are most often used in MD studies.
 For reasons of flexibility in executing this non-standard task and in order to be able to use a novel interaction potential \cite{albe_sic_pot} an appropriate MD code called {\textsc posic}\footnote{{\textsc posic} is an abbreviation for {\bf p}recipitation {\bf o}f {\bf SiC}}\footnote{Source code: http://www.physik.uni-augsburg.de/\~{}zirkelfr/posic/posic.tar.bz2} including a library collecting respective MD subroutines was developed from scratch.
-The basic ideas of MD in general and the adopted techniques as implemented in {\em posic} in particular are outlined in section \ref{section:md}, while the functional form and derivative of the employed classical potential is presented in appendix \ref{app:d_tersoff}.
+The basic ideas of MD in general and the adopted techniques as implemented in {\textsc posic} in particular are outlined in section \ref{section:md}, while the functional form and derivative of the employed classical potential is presented in appendix \ref{app:d_tersoff}.
 An overview of the most important tools within the MD package is given in appendix \ref{app:code}.
 Although classical potentials are often most successful and at the same time computationally efficient in calculating some physical properties of a particular system, not all of its properties might be described correctly due to the lack of quantum-mechanical effects.
 Thus, in order to obtain more accurate results quantum-mechanical calculations from first principles based on density functional theory (DFT) were performed.
@@ -277,9 +277,20 @@ It provides a stable algorithm that allows smooth changes of the system to new v
 \section{Denstiy functional theory}
 \label{section:dft}
 
-\subsection{Hohenberg-Kohn theorem}
+In quantum-mechanical modeling the problem of describing a many-body problem is manifested in the high-dimensional Schr\"odinger equation for the wave function $\Psi({\vec{R}},{\vec{r}})$ that depends on the coordinates of the nuclei and electrons.
+The Schr\"odinger equation contains the kinetic energy of the ions and electrons as well as the electron-ion, ion-ion and electron-electron interaction.
+This cannot be solved exactly and there are several layers of approximations to reduce the number of parameters.
+In density functional theory (DFT) the problem is recasted to the charge density $n(\vec{r})$ instead of using the description by a wave function.
+Formally DFT can be regarded as an exactification of both, the Thomas Fermi and Hartree theory.
+
+Since {\textsc vasp} \cite{kresse96} is used in this work, theory and implementation of sophisticated algorithms of DFT codes is not subject of this work.
+Thus, the content of the following sections is restricted to the very basic idea of DFT.
+
+\subsection{Born-Oppenheimer approximation}
 
-\subsection{Born-Oppenheimer (adiabatic) approximation}
+The first approximation ...
+
+\subsection{Hohenberg-Kohn theorem}
 
 \subsection{Effective potential}