| 3085 |
|
\label{table:thermIntParams} |
| 3086 |
|
\end{longtable} |
| 3087 |
|
|
| 3088 |
< |
\chapter{\label{section:rnemd}RNEMD} |
| 3088 |
> |
\chapter{\label{section:rnemd}Reverse Non-Equilibrium Molecular Dynamics (RNEMD)} |
| 3089 |
|
|
| 3090 |
|
There are many ways to compute transport properties from molecular |
| 3091 |
|
dynamics simulations. Equilibrium Molecular Dynamics (EMD) |
| 3092 |
|
simulations can be used by computing relevant time correlation |
| 3093 |
< |
functions and assuming linear response theory holds. These approaches |
| 3094 |
< |
are generally subject to noise and poor convergence of the relevant |
| 3093 |
> |
functions and assuming linear response theory holds. For some transport properties (notably thermal conductivity), EMD approaches |
| 3094 |
> |
are subject to noise and poor convergence of the relevant |
| 3095 |
|
correlation functions. Traditional Non-equilibrium Molecular Dynamics |
| 3096 |
|
(NEMD) methods impose a gradient (e.g. thermal or momentum) on a |
| 3097 |
|
simulation. However, the resulting flux is often difficult to |
| 3120 |
|
\label{rnemdDemo} |
| 3121 |
|
\end{figure} |
| 3122 |
|
|
| 3123 |
+ |
\section{\label{section:algo}Three algorithms for carrying out RNEMD simulations} |
| 3124 |
+ |
\subsection{\label{subsection:swapping}The swapping algorithm} |
| 3125 |
|
The original ``swapping'' approaches by M\"{u}ller-Plathe {\it et |
| 3126 |
|
al.}\cite{ISI:000080382700030,MullerPlathe:1997xw} can be understood |
| 3127 |
|
as a sequence of imaginary elastic collisions between particles in |
| 3133 |
|
swapping approach perturbs the system away from ideal |
| 3134 |
|
Maxwell-Boltzmann distributions, and this may leads to undesirable |
| 3135 |
|
side-effects when the applied flux becomes large.\cite{Maginn:2010} |
| 3136 |
< |
This limits the application of the swapping algorithm, so in OpenMD, |
| 3137 |
< |
we implement two additional algorithms for RNEMD in addition to the |
| 3136 |
> |
This limits the applicability of the swapping algorithm, so in OpenMD, |
| 3137 |
> |
we have implemented two additional algorithms for RNEMD in addition to the |
| 3138 |
|
original swapping approach. |
| 3139 |
|
|
| 3140 |
< |
{\bf Non-Isotropic Velocity Scaling (NIVS):}\cite{kuang:164101} |
| 3140 |
> |
\subsection{\label{subsection:nivs}Non-Isotropic Velocity Scaling (NIVS)} |
| 3141 |
|
Instead of having momentum exchange between {\it individual particles} |
| 3142 |
|
in each slab, the NIVS algorithm applies velocity scaling to all of |
| 3143 |
< |
the selected particles in both slabs. A combination of linear |
| 3143 |
> |
the selected particles in both slabs.\cite{kuang:164101} A combination of linear |
| 3144 |
|
momentum, kinetic energy, and flux constraint equations governs the |
| 3145 |
< |
amount of velocity scaling performed at each step. Interested readers |
| 3145 |
> |
amount of velocity scaling performed at each step. Interested readers |
| 3146 |
|
should consult ref. \citealp{kuang:164101} for further details on the |
| 3147 |
|
methodology. |
| 3148 |
|
|
| 3151 |
|
heterogeneous interfaces. Although the NIVS algorithm can also be |
| 3152 |
|
applied to impose a directional momentum flux, thermal anisotropy was |
| 3153 |
|
observed in relatively high flux simulations, and the method is not |
| 3154 |
< |
suitable for imposing a shear flux. |
| 3154 |
> |
suitable for imposing a shear flux or for computing shear viscosities. |
| 3155 |
|
|
| 3156 |
< |
{\bf Velocity Shearing and Scaling (VSS)}:\cite{2012MolPh.110..691K} |
| 3156 |
> |
\subsection{\label{subsection:vss}Velocity Shearing and Scaling (VSS)} |
| 3157 |
|
The third RNEMD algorithm implemented in OpenMD utilizes a series of |
| 3158 |
|
simultaneous velocity shearing and scaling exchanges between the two |
| 3159 |
< |
slabs. This method results in a set of simpler equations to satisfy |
| 3159 |
> |
slabs.\cite{2012MolPh.110..691K} This method results in a set of simpler equations to satisfy |
| 3160 |
|
the conservation constraints while creating a desired flux between the |
| 3161 |
|
two slabs. |
| 3162 |
|
|
| 3166 |
|
distributions are minimal, and thermal anisotropy is kept to a |
| 3167 |
|
minimum. This ability to generate simultaneous thermal and shear |
| 3168 |
|
fluxes has been utilized to map out the shear viscosity of SPC/E water |
| 3169 |
< |
in a wide range of temperature (90~K) just with a single simulation. |
| 3170 |
< |
VSS-RNEMD also allows the directional momentum flux to have quite |
| 3169 |
> |
over a wide range of temperatures (90~K) just with a single simulation. |
| 3170 |
> |
VSS-RNEMD also allows the directional momentum flux to have |
| 3171 |
|
arbitary directions, which could aid in the study of anisotropic solid |
| 3172 |
|
surfaces in contact with liquid environments. |
| 3173 |
|
|
| 3174 |
< |
{\bf What the user needs to specify:} To carry out a RNEMD simulation, |
| 3174 |
> |
\section{\label{section:usingRNEMD}Using OpenMD to perform a RNEMD simulation} |
| 3175 |
> |
\subsection{\label{section:rnemdParams} What the user needs to specify} |
| 3176 |
> |
To carry out a RNEMD simulation, |
| 3177 |
|
a user must specify a number of parameters in the MetaData (.md) file. |
| 3178 |
|
Because the RNEMD methods have a large number of parameters, these |
| 3179 |
< |
must be enclosed in a {\tt RNEMD\{...\}} block. The most important |
| 3179 |
> |
must be enclosed in a {\it separate} {\tt RNEMD\{...\}} block. The most important |
| 3180 |
|
parameters to specify are the {\tt useRNEMD}, {\tt fluxType} and flux |
| 3181 |
|
parameters. Most other parameters (summarized in table |
| 3182 |
|
\ref{table:rnemd}) have reasonable default values. {\tt fluxType} |
| 3187 |
|
kinetic energy exchange, as well as {\tt momentumFlux} or {\tt |
| 3188 |
|
momentumFluxVector} for simulations with directional exchange. |
| 3189 |
|
|
| 3190 |
< |
{\bf How to process the results:} OpenMD will generate a {\tt .rnemd} |
| 3190 |
> |
\subsection{\label{section:rnemdResults} Processing the results} |
| 3191 |
> |
OpenMD will generate a {\tt .rnemd} |
| 3192 |
|
file with the same prefix as the original {\tt .md} file. This file |
| 3193 |
|
contains a running average of properties of interest computed within a |
| 3194 |
|
set of bins that divide the simulation cell along the $z$-axis. The |
| 3236 |
|
\newpage |
| 3237 |
|
|
| 3238 |
|
\begin{longtable}[c]{JKLM} |
| 3239 |
< |
\caption{The following keywords must be enclosed inside a {\tt RNEMD\{\}} block} |
| 3240 |
< |
\\ |
| 3239 |
> |
\caption{Meta-data Keywords: Parameters for RNEMD simulations}\\ |
| 3240 |
> |
\multicolumn{4}{c}{The following keywords must be enclosed inside a {\tt RNEMD\{...\}} block.} |
| 3241 |
> |
\\ \hline |
| 3242 |
|
{\bf keyword} & {\bf units} & {\bf use} & {\bf remarks} \\ \hline |
| 3243 |
|
\endhead |
| 3244 |
|
\hline |
| 3268 |
|
\label{table:rnemd} |
| 3269 |
|
\end{longtable} |
| 3270 |
|
|
| 3265 |
– |
|
| 3271 |
|
\chapter{\label{section:minimizer}Energy Minimization} |
| 3272 |
|
|
| 3273 |
< |
As one of the basic procedures of molecular modeling, energy |
| 3269 |
< |
minimization is used to identify local configurations that are stable |
| 3273 |
> |
Energy minimization is used to identify local configurations that are stable |
| 3274 |
|
points on the potential energy surface. There is a vast literature on |
| 3275 |
|
energy minimization algorithms have been developed to search for the |
| 3276 |
|
global energy minimum as well as to find local structures which are |
