changes to basics chapter

diff --git a/posic/thesis/basics.tex b/posic/thesis/basics.tex
index 05de602faf67bfe25d9a0d81ee724d1b5d941a18..ba62d82ca738adf57a3e6e1a7750cb8da6d57d94 100644 (file)
--- a/posic/thesis/basics.tex
+++ b/posic/thesis/basics.tex
@@ -31,7 +31,7 @@ The method used to investigate migration pathways to identify the prevalent diff
 \noindent
 Pierre Simon de Laplace phrased this vision in terms of a controlling, omniscient instance - the {\em Laplace demon} - which would be able to look into the future as well as into the past due to the deterministic nature of processes, governed by the solution of differential equations.
 Although Laplace's vision is nowadays corrected by chaos theory and quantum mechanics, it expresses two main features of classical mechanics, the determinism of processes and time reversibility of the fundamental equations.
-This understanding was one of the first ideas for doing molecular dynamics simulations, considering an isolated system of particles, the behaviour of which is fully determined by the solution of the classical equations of motion.
+This understanding may be regarded as the basic principle of molecular dynamics, considering an isolated system of particles, the behaviour of which is fully determined by the solution of the classical equations of motion.
 
 \subsection{Introduction to molecular dynamics simulations}
 
@@ -39,8 +39,8 @@ Molecular dynamics (MD) simulation is a technique to compute a system of particl
 The MD method was first introduced by Alder and Wainwright in 1957 \cite{alder57,alder59} to study the interactions of hard spheres.
 The basis of the approach are Newton's equations of motion to describe classicaly the many-body system.
 MD is the numerical way of solving the $N$-body problem which cannot be solved analytically for $N>3$.
-A potential is necessary describing the interaction of the particles.
-By MD a complete description of the system in the sense of classical mechanics on the microscopic level is obtained.
+A potential is necessary to describe the interaction of the particles.
+By MD, a complete description of the system in the sense of classical mechanics on the microscopic level is obtained.
 The microscopic information can then be translated to macroscopic observables by means of statistical mechanics.
 
 The basic idea is to assume that the particles can be described classically by Newton's equations of motion, which are integrated numerically.
@@ -59,7 +59,7 @@ The forces ${\bf F}_i$ are obtained from the potential energy $U(\{{\bf r}\})$:
 {\bf F}_i = - \nabla_{{\bf r}_i} U({\{\bf r}\}) \, \textrm{.}
 \label{eq:basics:force}
 \end{equation}
-Given the initial conditions ${\bf r}_i(t_0)$ and $\dot{\bf r}_i(t_0)$ the equations can be integrated by a certain integration algorithm.
+Given the initial conditions ${\bf r}_i(t_0)$ and $\dot{\bf r}_i(t_0)$, the equations can be integrated by a certain integration algorithm.
 The solution of these equations provides the complete information of a system evolving in time.
 The following sections cover the tools of the trade necessary for the MD simulation technique.
 Three ingredients are required for a MD simulation:
@@ -671,5 +671,5 @@ Structures of maximum configurational energy do not necessarily constitute saddl
 Whether a saddle point configuration and, thus, the minimum energy path is obtained by the CRT method, needs to be verified by caculating the respective vibrational modes.
 Modifications used to add the CRT feature to the VASP code and a short instruction on how to use it can be found in appendix \ref{app:patch_vasp}.
 
-% todo - advantages of pw basis concenring hf forces + inc font in crt sketch
+% todo - advantages of pw basis concenring hf forces