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– |
\title{{\sc OpenMD}: Molecular Dynamics in the Open} |
| 49 |
|
|
| 50 |
< |
\author{Kelsey M. Stocker, Shenyu Kuang, Charles F. Vardeman II, \\ |
| 51 |
< |
Teng Lin, Christopher J. Fennell, Xiuquan Sun, \\ |
| 50 |
> |
\title{{\sc OpenMD-2}: Molecular Dynamics in the Open} |
| 51 |
> |
|
| 52 |
> |
\author{Shenyu Kuang, Joseph Michalka, Kelsey Stocker, James Marr, \\ |
| 53 |
> |
Teng Lin, Charles F. Vardeman II, Christopher J. Fennell, Xiuquan Sun, \\ |
| 54 |
|
Chunlei Li, Kyle Daily, Yang Zheng, Matthew A. Meineke, and \\ |
| 55 |
|
J. Daniel Gezelter \\ |
| 56 |
|
Department of Chemistry and Biochemistry\\ |
| 499 |
|
\endhead |
| 500 |
|
\hline |
| 501 |
|
\endfoot |
| 502 |
< |
{\tt forceField} & string & Sets the force field. & Possible force |
| 503 |
< |
fields are DUFF, WATER, LJ, EAM, SC, and CLAY. \\ |
| 502 |
> |
{\tt forceField} & string & Sets the base name for the force field file & |
| 503 |
> |
OpenMD appends a {\tt .frc} to the end of this to look for a force |
| 504 |
> |
field file.\\ |
| 505 |
|
{\tt component} & & Defines the molecular components of the system & |
| 506 |
|
Every {\tt $<$MetaData$>$} block must have a component statement. \\ |
| 507 |
|
{\tt minimizer} & string & Chooses a minimizer & Possible minimizers |
| 2630 |
|
|
| 2631 |
|
\section{Constant Pressure without periodic boundary conditions (The LangevinHull)} |
| 2632 |
|
|
| 2633 |
< |
The Langevin Hull uses an external bath at a fixed constant pressure |
| 2633 |
> |
The Langevin Hull\cite{Vardeman2011} uses an external bath at a fixed constant pressure |
| 2634 |
|
($P$) and temperature ($T$) with an effective solvent viscosity |
| 2635 |
|
($\eta$). This bath interacts only with the objects on the exterior |
| 2636 |
|
hull of the system. Defining the hull of the atoms in a simulation is |
| 2942 |
|
\label{table:zconParams} |
| 2943 |
|
\end{longtable} |
| 2944 |
|
|
| 2945 |
< |
\chapter{\label{section:restraints}Restraints} |
| 2946 |
< |
Restraints are external potentials that are added to a system to keep |
| 2947 |
< |
particular molecules or collections of particles close to some |
| 2948 |
< |
reference structure. A restraint can be a collective |
| 2945 |
> |
% \chapter{\label{section:restraints}Restraints} |
| 2946 |
> |
% Restraints are external potentials that are added to a system to |
| 2947 |
> |
% keep particular molecules or collections of particles close to some |
| 2948 |
> |
% reference structure. A restraint can be a collective |
| 2949 |
|
|
| 2950 |
|
\chapter{\label{section:thermInt}Thermodynamic Integration} |
| 2951 |
|
|
| 3084 |
|
Einstein crystal |
| 3085 |
|
\label{table:thermIntParams} |
| 3086 |
|
\end{longtable} |
| 3087 |
+ |
|
| 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. 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 |
| 3098 |
+ |
measure. Furthermore, problems arise for NEMD simulations of |
| 3099 |
+ |
heterogeneous systems, such as phase-phase boundaries or interfaces, |
| 3100 |
+ |
where the type of gradient to enforce at the boundary between |
| 3101 |
+ |
materials is unclear. |
| 3102 |
+ |
|
| 3103 |
+ |
{\it Reverse} Non-Equilibrium Molecular Dynamics (RNEMD) methods adopt |
| 3104 |
+ |
a different approach in that an unphysical {\it flux} is imposed |
| 3105 |
+ |
between different regions or ``slabs'' of the simulation box. The |
| 3106 |
+ |
response of the system is to develop a temperature or momentum {\it |
| 3107 |
+ |
gradient} between the two regions. Since the amount of the applied |
| 3108 |
+ |
flux is known exactly, and the measurement of gradient is generally |
| 3109 |
+ |
less complicated, imposed-flux methods typically take shorter |
| 3110 |
+ |
simulation times to obtain converged results for transport properties. |
| 3111 |
+ |
|
| 3112 |
+ |
\begin{figure} |
| 3113 |
+ |
\includegraphics[width=\linewidth]{rnemdDemo} |
| 3114 |
+ |
\caption{The (VSS) RNEMD approach imposes unphysical transfer of both |
| 3115 |
+ |
linear momentum and kinetic energy between a ``hot'' slab and a |
| 3116 |
+ |
``cold'' slab in the simulation box. The system responds to this |
| 3117 |
+ |
imposed flux by generating both momentum and temperature gradients. |
| 3118 |
+ |
The slope of the gradients can then be used to compute transport |
| 3119 |
+ |
properties (e.g. shear viscosity and thermal conductivity).} |
| 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 |
| 3128 |
+ |
opposite slabs. In each collision, the entire momentum vectors of |
| 3129 |
+ |
both particles may be exchanged to generate a thermal |
| 3130 |
+ |
flux. Alternatively, a single component of the momentum vectors may be |
| 3131 |
+ |
exchanged to generate a shear flux. This algorithm turns out to be |
| 3132 |
+ |
quite useful in many simulations. However, the M\"{u}ller-Plathe |
| 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 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 |
+ |
\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.\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 |
| 3146 |
+ |
should consult ref. \citealp{kuang:164101} for further details on the |
| 3147 |
+ |
methodology. |
| 3148 |
+ |
|
| 3149 |
+ |
NIVS has been shown to be very effective at producing thermal |
| 3150 |
+ |
gradients and for computing thermal conductivities, particularly for |
| 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 or for computing shear viscosities. |
| 3155 |
+ |
|
| 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.\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 |
+ |
|
| 3163 |
+ |
The VSS approach is versatile in that it may be used to implement both |
| 3164 |
+ |
thermal and shear transport either separately or simultaneously. |
| 3165 |
+ |
Perturbations of velocities away from the ideal Maxwell-Boltzmann |
| 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 |
+ |
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 |
+ |
\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 {\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} |
| 3183 |
+ |
sets up the kind of exchange that will be carried out between the two |
| 3184 |
+ |
slabs (either Kinetic Energy ({\tt KE}) or momentum ({\tt Px, Py, Pz, |
| 3185 |
+ |
Pvector}), or some combination of these). The flux is specified |
| 3186 |
+ |
with the use of three possible parameters: {\tt kineticFlux} for |
| 3187 |
+ |
kinetic energy exchange, as well as {\tt momentumFlux} or {\tt |
| 3188 |
+ |
momentumFluxVector} for simulations with directional exchange. |
| 3189 |
|
|
| 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 |
| 3195 |
+ |
first column of the {\tt .rnemd} file is the $z$ coordinate of the |
| 3196 |
+ |
center of each bin, while following columns may contain the average |
| 3197 |
+ |
temperature, velocity, or density within each bin. The output format |
| 3198 |
+ |
in the {\tt .rnemd} file can be altered with the {\tt outputFields}, |
| 3199 |
+ |
{\tt outputBins}, and {\tt outputFileName} parameters. A report at |
| 3200 |
+ |
the top of the {\tt .rnemd} file contains the current exchange totals |
| 3201 |
+ |
as well as the average flux applied during the simulation. Using the |
| 3202 |
+ |
slope of the temperature or velocity gradient obtaine from the {\tt |
| 3203 |
+ |
.rnemd} file along with the applied flux, the user can very simply |
| 3204 |
+ |
arrive at estimates of thermal conductivities ($\lambda$), |
| 3205 |
+ |
\begin{equation} |
| 3206 |
+ |
J_z = -\lambda \frac{\partial T}{\partial z}, |
| 3207 |
+ |
\end{equation} |
| 3208 |
+ |
and shear viscosities ($\eta$), |
| 3209 |
+ |
\begin{equation} |
| 3210 |
+ |
j_z(p_x) = -\eta \frac{\partial \langle v_x \rangle}{\partial z}. |
| 3211 |
+ |
\end{equation} |
| 3212 |
+ |
Here, the quantities on the left hand side are the actual flux values |
| 3213 |
+ |
(in the header of the {\tt .rnemd} file), while the slopes are |
| 3214 |
+ |
obtained from linear fits to the gradients observed in the {\tt |
| 3215 |
+ |
.rnemd} file. |
| 3216 |
+ |
|
| 3217 |
+ |
More complicated simulations (including interfaces) require a bit more |
| 3218 |
+ |
care. Here the second derivative may be required to compute the |
| 3219 |
+ |
interfacial thermal conductance, |
| 3220 |
+ |
\begin{align} |
| 3221 |
+ |
G^\prime &= \left(\nabla\lambda \cdot \mathbf{\hat{n}}\right)_{z_0} \\ |
| 3222 |
+ |
&= \frac{\partial}{\partial z}\left(-\frac{J_z}{ |
| 3223 |
+ |
\left(\frac{\partial T}{\partial z}\right)}\right)_{z_0} \\ |
| 3224 |
+ |
&= J_z\left(\frac{\partial^2 T}{\partial z^2}\right)_{z_0} \Big/ |
| 3225 |
+ |
\left(\frac{\partial T}{\partial z}\right)_{z_0}^2. |
| 3226 |
+ |
\label{derivativeG} |
| 3227 |
+ |
\end{align} |
| 3228 |
+ |
where $z_0$ is the location of the interface between two materials and |
| 3229 |
+ |
$\mathbf{\hat{n}}$ is a unit vector normal to the interface. We |
| 3230 |
+ |
suggest that users interested in interfacial conductance consult |
| 3231 |
+ |
reference \citealp{kuang:AuThl} for other approaches to computing $G$. |
| 3232 |
+ |
Users interested in {\it friction coefficients} at heterogeneous |
| 3233 |
+ |
interfaces may also find reference \citealp{2012MolPh.110..691K} |
| 3234 |
+ |
useful. |
| 3235 |
+ |
|
| 3236 |
+ |
\newpage |
| 3237 |
+ |
|
| 3238 |
+ |
\begin{longtable}[c]{JKLM} |
| 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 |
| 3245 |
+ |
\endfoot |
| 3246 |
+ |
{\tt useRNEMD} & logical & perform RNEMD? & default is ``false'' \\ |
| 3247 |
+ |
{\tt objectSelection} & string & see section \ref{section:syntax} |
| 3248 |
+ |
for selection syntax & default is ``select all'' \\ |
| 3249 |
+ |
{\tt method} & string & exchange method & one of the following: |
| 3250 |
+ |
{\tt Swap, NIVS,} or {\tt VSS} (default is {\tt VSS}) \\ |
| 3251 |
+ |
{\tt fluxType} & string & what is being exchanged between slabs? & one |
| 3252 |
+ |
of the following: {\tt KE, Px, Py, Pz, Pvector, KE+Px, KE+Py, KE+Pvector} \\ |
| 3253 |
+ |
{\tt kineticFlux} & kcal mol$^{-1}$ \AA$^{-2}$ fs$^{-1}$ & specify the kinetic energy flux & \\ |
| 3254 |
+ |
{\tt momentumFlux} & amu \AA$^{-1}$ fs$^{-2}$ & specify the momentum flux & \\ |
| 3255 |
+ |
{\tt momentumFluxVector} & amu \AA$^{-1}$ fs$^{-2}$ & specify the momentum flux when |
| 3256 |
+ |
{\tt Pvector} is part of the exchange & Vector3d input\\ |
| 3257 |
+ |
{\tt exchangeTime} & fs & how often to perform the exchange & default is 100 fs\\ |
| 3258 |
+ |
|
| 3259 |
+ |
{\tt slabWidth} & $\mbox{\AA}$ & width of the two exchange slabs & default is $\mathsf{H}_{zz} / 10.0$ \\ |
| 3260 |
+ |
{\tt slabAcenter} & $\mbox{\AA}$ & center of the end slab & default is 0 \\ |
| 3261 |
+ |
{\tt slabBcenter} & $\mbox{\AA}$ & center of the middle slab & default is $\mathsf{H}_{zz} / 2$ \\ |
| 3262 |
+ |
{\tt outputFileName} & string & file name for output histograms & default is the same prefix as the |
| 3263 |
+ |
.md file, but with the {\tt .rnemd} extension \\ |
| 3264 |
+ |
{\tt outputBins} & int & number of $z$-bins in the output histogram & |
| 3265 |
+ |
default is 20 \\ |
| 3266 |
+ |
{\tt outputFields} & string & columns to print in the {\tt .rnemd} |
| 3267 |
+ |
file where each column is separated by a pipe ($\mid$) symbol. & Allowed column names are: {\sc z, temperature, velocity, density} \\ |
| 3268 |
+ |
\label{table:rnemd} |
| 3269 |
+ |
\end{longtable} |
| 3270 |
+ |
|
| 3271 |
|
\chapter{\label{section:minimizer}Energy Minimization} |
| 3272 |
|
|
| 3273 |
< |
As one of the basic procedures of molecular modeling, energy |
| 3083 |
< |
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 |
| 3940 |
|
DMR-0079647. |
| 3941 |
|
|
| 3942 |
|
|
| 3943 |
< |
\bibliographystyle{jcc} |
| 3943 |
> |
\bibliographystyle{aip} |
| 3944 |
|
\bibliography{openmdDoc} |
| 3945 |
|
|
| 3946 |
|
\end{document} |
