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