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\title{{\sc OpenMD}: Molecular Dynamics in the Open} |
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|
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\author{Shenyu Kuang, Chunlei Li, Charles F. Vardeman II, \\ |
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Teng Lin, Christopher J. Fennell, Xiuquan Sun, \\ |
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Kyle Daily, Yang Zheng, Matthew A. Meineke, and J. Daniel Gezelter\\ |
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Department of Chemistry and Biochemistry\\ |
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University of Notre Dame\\ |
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Notre Dame, Indiana 46556} |
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\author{Kelsey M. Stocker, Shenyu Kuang, Charles F. Vardeman II, \\ |
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Teng Lin, Christopher J. Fennell, Xiuquan Sun, \\ |
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Chunlei Li, Kyle Daily, Yang Zheng, Matthew A. Meineke, and \\ |
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J. Daniel Gezelter \\ |
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Department of Chemistry and Biochemistry\\ |
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University of Notre Dame\\ |
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Notre Dame, Indiana 46556} |
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\maketitle |
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|
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{\tt minimizer} & string & Chooses a minimizer & Possible minimizers |
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are SD and CG. Either {\tt ensemble} or {\tt minimizer} must be specified. \\ |
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{\tt ensemble} & string & Sets the ensemble. & Possible ensembles are |
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NVE, NVT, NPTi, NPAT, NPTf, NPTxyz, LD and LHull. Either {\tt ensemble} |
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NVE, NVT, NPTi, NPAT, NPTf, NPTxyz, LD and LangevinHull. Either {\tt ensemble} |
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or {\tt minimizer} must be specified. \\ |
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{\tt dt} & fs & Sets the time step. & Selection of {\tt dt} should be |
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small enough to sample the fastest motion of the simulation. ({\tt |
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<MetaData> |
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molecule{ |
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name = "I2"; |
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atom[0]{ |
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type = "I"; |
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} |
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atom[1]{ |
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type = "I"; |
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} |
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bond{ |
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members( 0, 1); |
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} |
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atom[0]{ type = "I"; } |
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atom[1]{ type = "I"; } |
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bond{ members( 0, 1); } |
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} |
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molecule{ |
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name = "HCl" |
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atom[0]{ |
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type = "H"; |
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} |
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atom[1]{ |
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type = "Cl"; |
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} |
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bond{ |
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members( 0, 1); |
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} |
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atom[0]{ type = "H";} |
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atom[1]{ type = "Cl";} |
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bond{ members( 0, 1); } |
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} |
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component{ |
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type = "HCl"; |
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& (with separate barostats on each box dimension) & \\ |
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LD & Langevin Dynamics & {\tt ensemble = LD;} \\ |
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& (approximates the effects of an implicit solvent) & \\ |
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LangevinHull & Non-periodic Langevin Dynamics & {\tt ensemble = LHull;} \\ |
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LangevinHull & Non-periodic Langevin Dynamics & {\tt ensemble = LangevinHull;} \\ |
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& (Langevin Dynamics for molecules on convex hull;\\ |
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& Newtonian for interior molecules) & \\ |
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\end{tabular} |
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\label{table:ldParameters} |
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\end{longtable} |
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\section{Langevin Hull Dynamics (LHull)} |
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\section{Constant Pressure without periodic boundary conditions (The LangevinHull)} |
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|
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The Langevin Hull uses an external bath at a fixed constant pressure |
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($P$) and temperature ($T$) with an effective solvent viscosity |
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depends on the geometry and surface area of facet $f$ and the |
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viscosity of the bath. The resistance tensor is related to the |
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fluctuations of the random force, $\mathbf{R}(t)$, by the |
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fluctuation-dissipation theorem, |
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\begin{eqnarray} |
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\left< {\mathbf R}_f(t) \right> & = & 0 \\ |
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\left<{\mathbf R}_f(t) {\mathbf R}_f^T(t^\prime)\right> & = & 2 k_B T\ |
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\Xi_f(t)\delta(t-t^\prime). |
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\label{eq:randomForce} |
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\end{eqnarray} |
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fluctuation-dissipation theorem (see Eq. \ref{eq:randomForce}). |
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Once the resistance tensor is known for a given facet, a stochastic |
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vector that has the properties in Eq. (\ref{eq:randomForce}) can be |
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calculated efficiently by carrying out a Cholesky decomposition to |
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obtain the square root matrix of the resistance tensor, |
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\begin{equation} |
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\Xi_f = {\bf S} {\bf S}^{T}, |
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\label{eq:Cholesky} |
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\end{equation} |
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where ${\bf S}$ is a lower triangular matrix.\cite{Schlick2002} A |
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vector with the statistics required for the random force can then be |
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obtained by multiplying ${\bf S}$ onto a random 3-vector ${\bf Z}$ which |
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has elements chosen from a Gaussian distribution, such that: |
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\begin{equation} |
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\langle {\bf Z}_i \rangle = 0, \hspace{1in} \langle {\bf Z}_i \cdot |
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{\bf Z}_j \rangle = \frac{2 k_B T}{\delta t} \delta_{ij}, |
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\end{equation} |
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where $\delta t$ is the timestep in use during the simulation. The |
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random force, ${\bf R}_{f} = {\bf S} {\bf Z}$, can be shown to |
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have the correct properties required by Eq. (\ref{eq:randomForce}). |
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obtain the square root matrix of the resistance tensor (see |
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Eq. \ref{eq:Cholesky}). |
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|
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Our treatment of the resistance tensor is approximate. $\Xi_f$ for a |
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rigid triangular plate would normally be treated as a $6 \times 6$ |
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tensor that includes translational and rotational drag as well as |
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translational-rotational coupling. The computation of resistance |
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tensors for rigid bodies has been detailed |
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Our treatment of the resistance tensor for the Langevin Hull facets is |
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approximate. $\Xi_f$ for a rigid triangular plate would normally be |
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treated as a $6 \times 6$ tensor that includes translational and |
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rotational drag as well as translational-rotational coupling. The |
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computation of resistance tensors for rigid bodies has been detailed |
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elsewhere,\cite{JoseGarciadelaTorre02012000,Garcia-de-la-Torre:2001wd,GarciadelaTorreJ2002,Sun:2008fk} |
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but the standard approach involving bead approximations would be |
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prohibitively expensive if it were recomputed at each step in a |
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\item Atomic positions and velocities are propagated. |
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\end{enumerate} |
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The Delaunay triangulation and computation of the convex hull are done |
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using calls to the qhull library.\cite{Qhull} There is a minimal |
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penalty for computing the convex hull and resistance tensors at each |
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step in the molecular dynamics simulation (roughly 0.02 $\times$ cost |
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of a single force evaluation), and the convex hull is remarkably easy |
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to parallelize on distributed memory machines. |
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|
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using calls to the qhull library,\cite{Qhull} and for this reason, if |
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qhull is not detected during the build, the Langevin Hull integrator |
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will not be available. There is a minimal penalty for computing the |
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convex hull and resistance tensors at each step in the molecular |
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dynamics simulation (roughly 0.02 $\times$ cost of a single force |
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evaluation). |
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|
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\begin{longtable}[c]{GBF} |
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\caption{Meta-data Keywords: Required parameters for the Langevin Hull integrator} |
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This parameter must be specified to use Langevin Hull dynamics. \\ |
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{\tt targetPressure} & atm & Sets the target pressure of the system. |
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This parameter must be specified to use Langevin Hull dynamics. \\ |
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{\tt usePeriodicBoundaryConditions = false} & logical & Turns off periodic boundary conditions. |
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{\tt usePeriodicBoundaryConditions} & logical & Turns off periodic boundary conditions. |
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This parameter must be set to \tt false \\ |
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\label{table:lhullParameters} |
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\end{longtable} |
