started ks system ...

diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex
index 46f871c..6c03878 100644 (file)
--- a/posic/thesis/basics.tex
+++ b/posic/thesis/basics.tex
@@ -277,7 +277,7 @@ It provides a stable algorithm that allows smooth changes of the system to new v
 \section{Denstiy functional theory}
 \label{section:dft}
 
 \section{Denstiy functional theory}
 \label{section:dft}
 

-Dirac declared that chemistry has come to an end, its content being entirely contained in the powerul equation published by Schr\"odinger in 1926 \cite{schroeder26} marking the beginning of wave mechanics.
+Dirac declared that chemistry has come to an end, its content being entirely contained in the powerul equation published by Schr\"odinger in 1926 \cite{schroedinger26} marking the beginning of wave mechanics.

 Following the path of Schr\"odinger the problem in quantum-mechanical modeling of describing the many-body problem, i.e. a system of a large amount of interacting particles, is manifested in the high-dimensional Schr\"odinger equation for the wave function $\Psi({\vec{R}},{\vec{r}})$ that depends on the coordinates of all 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 finding approximate solutions requires several layers of simplification in order to reduce the number of free parameters.
 Following the path of Schr\"odinger the problem in quantum-mechanical modeling of describing the many-body problem, i.e. a system of a large amount of interacting particles, is manifested in the high-dimensional Schr\"odinger equation for the wave function $\Psi({\vec{R}},{\vec{r}})$ that depends on the coordinates of all 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 finding approximate solutions requires several layers of simplification in order to reduce the number of free parameters.


@@ -331,11 +331,12 @@ E_0=\min_{n(\vec{r})}
  \text{ ,}
 \end{equation}
 where $F[n(\vec{r})]$ is a universal functional of the charge density $n(\vec{r})$, which is composed of the kinetic energy functional $T[n(\vec{r})]$ and the interaction energy functional $U[n(\vec{r})]$.
  \text{ ,}
 \end{equation}
 where $F[n(\vec{r})]$ is a universal functional of the charge density $n(\vec{r})$, which is composed of the kinetic energy functional $T[n(\vec{r})]$ and the interaction energy functional $U[n(\vec{r})]$.

-The challenging problem of determining the exact ground-state is now formally reduced to the determination of the $3$-dimensional function $n(\vec{r})$ via a well-defined but not explicitly known functional of the charge density.
+The challenging problem of determining the exact ground-state is now formally reduced to the determination of the $3$-dimensional function $n(\vec{r})$, which minimizes the energy functional.
+However, the complexity associated with the many-electron problem is now relocated in the task of finding the well-defined but, in contrast to the potential energy, not explicitly known functional $F[n(\vec{r})]$.

 
 

-It is worth to note, that this minimal principle may be regarded as exactification of TF theory, which is rederived by the approximations
+It is worth to note, that this minimal principle may be regarded as exactification of the TF theory, which is rederived by the approximations

 \begin{equation}
 \begin{equation}

-T=\int n(\vec{r})\frac{3}{10}k_{\text{F}}^2[n(\vec{r})]d\vec{r}
+T=\int n(\vec{r})\frac{3}{10}k_{\text{F}}^2(n(\vec{r}))d\vec{r}

 \text{ ,}
 \end{equation}
 \begin{equation}
 \text{ ,}
 \end{equation}
 \begin{equation}


@@ -347,6 +348,8 @@ U=\frac{1}{2}\int\frac{n(\vec{r})n(\vec{r}')}{|\vec{r}-\vec{r}'|}d\vec{r}d\vec{r
 
 Now find $F[n]$ ...
 
 
 Now find $F[n]$ ...
 

+As in the last section, the complex many-electron effects are relocated, this time into the exchange-correlation functional.
+

 \subsection{Approximations for exchange and correlation}
 
 \subsection{Pseudopotentials}
 \subsection{Approximations for exchange and correlation}
 
 \subsection{Pseudopotentials}