24 |
|
|
25 |
|
\title{The Langevin Hull: Constant pressure and temperature dynamics for non-periodic systems} |
26 |
|
|
27 |
< |
\author{Charles F. Varedeman II, Kelsey Stocker, and J. Daniel |
27 |
> |
\author{Charles F. Vardeman II, Kelsey M. Stocker, and J. Daniel |
28 |
|
Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\ |
29 |
|
Department of Chemistry and Biochemistry,\\ |
30 |
|
University of Notre Dame\\ |
65 |
|
|
66 |
|
\section{Introduction} |
67 |
|
|
68 |
< |
Affine transform methods |
68 |
> |
The most common molecular dynamics methods for sampling configurations |
69 |
> |
of an isobaric-isothermal (NPT) ensemble attempt to maintain a target |
70 |
> |
pressure in a simulation by coupling the volume of the system to an |
71 |
> |
extra degree of freedom, the {\it barostat}. These methods require |
72 |
> |
periodic boundary conditions, because when the instantaneous pressure |
73 |
> |
in the system differs from the target pressure, the volume is |
74 |
> |
typically reduced or expanded using {\it affine transforms} of the |
75 |
> |
system geometry. An affine transform scales both the box lengths as |
76 |
> |
well as the scaled particle positions (but not the sizes of the |
77 |
> |
particles). The most common constant pressure methods, including the |
78 |
> |
Melchionna modification\cite{melchionna93} to the |
79 |
> |
Nos\'e-Hoover-Andersen equations of motion, the Berendsen pressure |
80 |
> |
bath, and the Langevin Piston, all utilize coordinate transformation |
81 |
> |
to adjust the box volume. |
82 |
|
|
83 |
|
\begin{figure} |
84 |
< |
\includegraphics[width=\linewidth]{AffineScale} |
85 |
< |
\caption{Affine Scale} |
84 |
> |
\includegraphics[width=\linewidth]{AffineScale2} |
85 |
> |
\caption{Affine Scaling constant pressure methods use box-length |
86 |
> |
scaling to adjust the volume to adjust to under- or over-pressure |
87 |
> |
conditions. In a system with a uniform compressibility (e.g. bulk |
88 |
> |
fluids) these methods can work well. In systems containing |
89 |
> |
heterogeneous mixtures, the affine scaling moves required to adjust |
90 |
> |
the pressure in the high-compressibility regions can cause molecules |
91 |
> |
in low compressibility regions to collide.} |
92 |
|
\label{affineScale} |
93 |
|
\end{figure} |
94 |
|
|
95 |
|
|
77 |
– |
\begin{figure} |
78 |
– |
\includegraphics[width=\linewidth]{AffineScale2} |
79 |
– |
\caption{Affine Scale2} |
80 |
– |
\label{affineScale2} |
81 |
– |
\end{figure} |
82 |
– |
|
96 |
|
Heterogeneous mixtures of materials with different compressibilities? |
97 |
|
|
98 |
|
Explicitly non-periodic systems |