| 117 |
|
higher than desirable, or unreasonable system sizes to avoid this |
| 118 |
|
effect. For example, calculations using typical hydration boxes |
| 119 |
|
solvating a protein under periodic boundary conditions are quite |
| 120 |
< |
expensive. A 62 $\AA^3$ box of water solvating a moderately small |
| 120 |
> |
expensive. A 62 \AA$^3$ box of water solvating a moderately small |
| 121 |
|
protein like hen egg white lysozyme (PDB code: 1LYZ) yields an |
| 122 |
|
effective protein concentration of 100 mg/mL.\cite{Asthagiri20053300} |
| 123 |
|
|
| 124 |
< |
Typically protein concentrations in the cell are on the order of |
| 125 |
< |
160-310 mg/ml,\cite{Brown1991195} and the factor of 20 difference |
| 126 |
< |
between simulations and the cellular environment may have significant |
| 127 |
< |
effects on the structure and dynamics of simulated protein structures. |
| 124 |
> |
Typically {\it total} protein concentrations in the cell are on the |
| 125 |
> |
order of 160-310 mg/ml,\cite{Brown1991195} and individual proteins |
| 126 |
> |
have concentrations orders of magnitude lower than this in the |
| 127 |
> |
cellular environment. The effective concentrations of single proteins |
| 128 |
> |
in simulations may have significant effects on the structure and |
| 129 |
> |
dynamics of simulated structures. |
| 130 |
|
|
| 129 |
– |
|
| 131 |
|
\subsection*{Boundary Methods} |
| 132 |
|
There have been a number of approaches to handle simulations of |
| 133 |
|
explicitly non-periodic systems that focus on constant or |
| 139 |
|
fixed regions were defined relative to a central atom. Brooks and |
| 140 |
|
Karplus extended this method to include deformable stochastic |
| 141 |
|
boundaries.\cite{iii:6312} The stochastic boundary approach has been |
| 142 |
< |
used widely for protein simulations. [CITATIONS NEEDED] |
| 142 |
> |
used widely for protein simulations. |
| 143 |
|
|
| 144 |
|
The electrostatic and dispersive behavior near the boundary has long |
| 145 |
|
been a cause for concern when performing simulations of explicitly |
| 150 |
|
simulated clusters of TIPS2 water surrounded by a hydrophobic bounding |
| 151 |
|
potential. The spherical hydrophobic boundary induced dangling |
| 152 |
|
hydrogen bonds at the surface that propagated deep into the cluster, |
| 153 |
< |
affecting most of molecules in the simulation. This result echoes an |
| 154 |
< |
earlier study which showed that an extended planar hydrophobic surface |
| 155 |
< |
caused orientational preference at the surface which extended |
| 156 |
< |
relatively deep (7 \r{A}) into the liquid simulation |
| 157 |
< |
cell.\cite{Lee1984} The surface constrained all-atom solvent (SCAAS) |
| 158 |
< |
model \cite{King1989} improved upon its SCSSD predecessor. The SCAAS |
| 159 |
< |
model utilizes a polarization constraint which is applied to the |
| 160 |
< |
surface molecules to maintain bulk-like structure at the cluster |
| 161 |
< |
surface. A radial constraint is used to maintain the desired bulk |
| 162 |
< |
density of the liquid. Both constraint forces are applied only to a |
| 163 |
< |
pre-determined number of the outermost molecules. |
| 153 |
> |
affecting most of the molecules in the simulation. This result echoes |
| 154 |
> |
an earlier study which showed that an extended planar hydrophobic |
| 155 |
> |
surface caused orientational preferences at the surface which extended |
| 156 |
> |
relatively deep (7 \AA) into the liquid simulation cell.\cite{Lee1984} |
| 157 |
> |
The surface constrained all-atom solvent (SCAAS) model \cite{King1989} |
| 158 |
> |
improved upon its SCSSD predecessor. The SCAAS model utilizes a |
| 159 |
> |
polarization constraint which is applied to the surface molecules to |
| 160 |
> |
maintain bulk-like structure at the cluster surface. A radial |
| 161 |
> |
constraint is used to maintain the desired bulk density of the |
| 162 |
> |
liquid. Both constraint forces are applied only to a pre-determined |
| 163 |
> |
number of the outermost molecules. |
| 164 |
|
|
| 165 |
|
Beglov and Roux have developed a boundary model in which the hard |
| 166 |
|
sphere boundary has a radius that varies with the instantaneous |
| 167 |
|
configuration of the solute (and solvent) molecules.\cite{beglov:9050} |
| 168 |
|
This model contains a clear pressure and surface tension contribution |
| 169 |
< |
to the free energy which XXX. |
| 169 |
> |
to the free energy. |
| 170 |
|
|
| 171 |
|
\subsection*{Restraining Potentials} |
| 172 |
|
Restraining {\it potentials} introduce repulsive potentials at the |
| 181 |
|
Recently, Krilov {\it et al.} introduced a {\it flexible} boundary |
| 182 |
|
model that uses a Lennard-Jones potential between the solvent |
| 183 |
|
molecules and a boundary which is determined dynamically from the |
| 184 |
< |
position of the nearest solute atom.\cite{LiY._jp046852t,Zhu:xw} This |
| 184 |
> |
position of the nearest solute atom.\cite{LiY._jp046852t,Zhu:2008fk} This |
| 185 |
|
approach allows the confining potential to prevent solvent molecules |
| 186 |
|
from migrating too far from the solute surface, while providing a weak |
| 187 |
|
attractive force pulling the solvent molecules towards a fictitious |
| 197 |
|
into non-periodic simulations.\cite{Kohanoff:2005qm,Baltazar:2006ru} |
| 198 |
|
This method is based on standard Langevin dynamics, but the Brownian |
| 199 |
|
or random forces are allowed to act only on peripheral atoms and exert |
| 200 |
< |
force in a direction that is inward-facing relative to the facets of a |
| 201 |
< |
closed bounding surface. The statistical distribution of the random |
| 200 |
> |
forces in a direction that is inward-facing relative to the facets of |
| 201 |
> |
a closed bounding surface. The statistical distribution of the random |
| 202 |
|
forces are uniquely tied to the pressure in the external reservoir, so |
| 203 |
|
the method can be shown to sample the isobaric-isothermal ensemble. |
| 204 |
|
Kohanoff {\it et al.} used a Delaunay tessellation to generate a |
| 222 |
|
\label{sec:meth} |
| 223 |
|
|
| 224 |
|
The Langevin Hull uses an external bath at a fixed constant pressure |
| 225 |
< |
($P$) and temperature ($T$). This bath interacts only with the |
| 226 |
< |
objects on the exterior hull of the system. Defining the hull of the |
| 227 |
< |
simulation is done in a manner similar to the approach of Kohanoff, |
| 228 |
< |
Caro and Finnis.\cite{Kohanoff:2005qm} That is, any instantaneous |
| 229 |
< |
configuration of the atoms in the system is considered as a point |
| 230 |
< |
cloud in three dimensional space. Delaunay triangulation is used to |
| 231 |
< |
find all facets between coplanar |
| 232 |
< |
neighbors.\cite{delaunay,springerlink:10.1007/BF00977785} In highly |
| 225 |
> |
($P$) and temperature ($T$) with an effective solvent viscosity |
| 226 |
> |
($\eta$). This bath interacts only with the objects on the exterior |
| 227 |
> |
hull of the system. Defining the hull of the atoms in a simulation is |
| 228 |
> |
done in a manner similar to the approach of Kohanoff, Caro and |
| 229 |
> |
Finnis.\cite{Kohanoff:2005qm} That is, any instantaneous configuration |
| 230 |
> |
of the atoms in the system is considered as a point cloud in three |
| 231 |
> |
dimensional space. Delaunay triangulation is used to find all facets |
| 232 |
> |
between coplanar |
| 233 |
> |
neighbors.\cite{delaunay,springerlink:10.1007/BF00977785} In highly |
| 234 |
|
symmetric point clouds, facets can contain many atoms, but in all but |
| 235 |
< |
the most symmetric of cases the facets are simple triangles in 3-space |
| 236 |
< |
that contain exactly three atoms. |
| 235 |
> |
the most symmetric of cases, the facets are simple triangles in |
| 236 |
> |
3-space which contain exactly three atoms. |
| 237 |
|
|
| 238 |
|
The convex hull is the set of facets that have {\it no concave |
| 239 |
|
corners} at an atomic site.\cite{Barber96,EDELSBRUNNER:1994oq} This |
| 302 |
|
\end{equation} |
| 303 |
|
and $\Xi_f(t)$ is an approximate ($3 \times 3$) resistance tensor that |
| 304 |
|
depends on the geometry and surface area of facet $f$ and the |
| 305 |
< |
viscosity of the fluid. The resistance tensor is related to the |
| 305 |
> |
viscosity of the bath. The resistance tensor is related to the |
| 306 |
|
fluctuations of the random force, $\mathbf{R}(t)$, by the |
| 307 |
|
fluctuation-dissipation theorem, |
| 308 |
|
\begin{eqnarray} |
| 332 |
|
random force, ${\bf R}_{f} = {\bf S} {\bf Z}$, can be shown to |
| 333 |
|
have the correct properties required by Eq. (\ref{eq:randomForce}). |
| 334 |
|
|
| 335 |
< |
Our treatment of the resistance tensor is approximate. $\Xi$ for a |
| 335 |
> |
Our treatment of the resistance tensor is approximate. $\Xi_f$ for a |
| 336 |
|
rigid triangular plate would normally be treated as a $6 \times 6$ |
| 337 |
|
tensor that includes translational and rotational drag as well as |
| 338 |
|
translational-rotational coupling. The computation of resistance |
| 456 |
|
Spohr potential was adopted in depicting the interaction between metal |
| 457 |
|
atoms and the SPC/E water molecules.\cite{ISI:000167766600035} |
| 458 |
|
|
| 459 |
< |
\subsection{Compressibility of gold nanoparticles} |
| 459 |
> |
\subsection{Bulk Modulus of gold nanoparticles} |
| 460 |
|
|
| 461 |
|
The compressibility (and its inverse, the bulk modulus) is well-known |
| 462 |
|
for gold, and is captured well by the embedded atom method |
| 463 |
< |
(EAM)~\cite{PhysRevB.33.7983} potential |
| 464 |
< |
and related multi-body force fields. In particular, the quantum |
| 465 |
< |
Sutton-Chen potential gets nearly quantitative agreement with the |
| 466 |
< |
experimental bulk modulus values, and makes a good first test of how |
| 467 |
< |
the Langevin Hull will perform at large applied pressures. |
| 463 |
> |
(EAM)~\cite{PhysRevB.33.7983} potential and related multi-body force |
| 464 |
> |
fields. In particular, the quantum Sutton-Chen potential gets nearly |
| 465 |
> |
quantitative agreement with the experimental bulk modulus values, and |
| 466 |
> |
makes a good first test of how the Langevin Hull will perform at large |
| 467 |
> |
applied pressures. |
| 468 |
|
|
| 469 |
|
The Sutton-Chen (SC) potentials are based on a model of a metal which |
| 470 |
|
treats the nuclei and core electrons as pseudo-atoms embedded in the |
| 471 |
|
electron density due to the valence electrons on all of the other |
| 472 |
< |
atoms in the system.\cite{Chen90} The SC potential has a simple form that closely |
| 473 |
< |
resembles the Lennard Jones potential, |
| 472 |
> |
atoms in the system.\cite{Chen90} The SC potential has a simple form |
| 473 |
> |
that closely resembles the Lennard Jones potential, |
| 474 |
|
\begin{equation} |
| 475 |
|
\label{eq:SCP1} |
| 476 |
|
U_{tot}=\sum _{i}\left[ \frac{1}{2}\sum _{j\neq i}D_{ij}V^{pair}_{ij}(r_{ij})-c_{i}D_{ii}\sqrt{\rho_{i}}\right] , |
| 492 |
|
energy, and elastic moduli for FCC transition metals. The quantum |
| 493 |
|
Sutton-Chen (QSC) formulation matches these properties while including |
| 494 |
|
zero-point quantum corrections for different transition |
| 495 |
< |
metals.\cite{PhysRevB.59.3527} |
| 495 |
> |
metals.\cite{PhysRevB.59.3527,QSC} |
| 496 |
|
|
| 497 |
|
In bulk gold, the experimentally-measured value for the bulk modulus |
| 498 |
|
is 180.32 GPa, while previous calculations on the QSC potential in |
| 499 |
< |
periodic-boundary simulations of the bulk have yielded values of |
| 500 |
< |
175.53 GPa.\cite{XXX} Using the same force field, we have performed a |
| 501 |
< |
series of relatively short (200 ps) simulations on 40 \r{A} radius |
| 499 |
> |
periodic-boundary simulations of the bulk crystal have yielded values |
| 500 |
> |
of 175.53 GPa.\cite{QSC} Using the same force field, we have performed |
| 501 |
> |
a series of relatively short (200 ps) simulations on 40 \AA~ radius |
| 502 |
|
nanoparticles under the Langevin Hull at a variety of applied |
| 503 |
< |
pressures ranging from 0 GPa to XXX. We obtain a value of 177.547 GPa |
| 504 |
< |
for the bulk modulus for gold using this echnique. |
| 503 |
> |
pressures ranging from 0 -- 10 GPa. We obtain a value of 177.55 GPa |
| 504 |
> |
for the bulk modulus of gold using this technique, in close agreement |
| 505 |
> |
with both previous simulations and the experimental bulk modulus of |
| 506 |
> |
gold. |
| 507 |
|
|
| 508 |
|
\begin{figure} |
| 509 |
|
\includegraphics[width=\linewidth]{stacked} |
| 512 |
|
($T_\mathrm{bath}$ = 300K, $P_\mathrm{bath}$ = 4 GPa), starting |
| 513 |
|
from initial conditions that were far from the bath pressure and |
| 514 |
|
temperature. The pressure response is rapid (after the breathing mode oscillations in the nanoparticle die out), and the rate of thermal equilibration depends on both exposed surface area (top panel) and the viscosity of the bath (middle panel).} |
| 515 |
< |
\label{pressureResponse} |
| 515 |
> |
\label{fig:pressureResponse} |
| 516 |
|
\end{figure} |
| 517 |
|
|
| 518 |
< |
\begin{equation} |
| 519 |
< |
\kappa_T=-\frac{1}{V_{\mathrm{eq}}}\left(\frac{\partial V}{\partial |
| 520 |
< |
P}\right) |
| 521 |
< |
\end{equation} |
| 518 |
> |
We note that the Langevin Hull produces rapidly-converging behavior |
| 519 |
> |
for structures that are started far from equilibrium. In |
| 520 |
> |
Fig. \ref{fig:pressureResponse} we show how the pressure and |
| 521 |
> |
temperature respond to the Langevin Hull for nanoparticles that were |
| 522 |
> |
initialized far from the target pressure and temperature. As |
| 523 |
> |
expected, the rate at which thermal equilibrium is achieved depends on |
| 524 |
> |
the total surface area of the cluter exposed to the bath as well as |
| 525 |
> |
the bath viscosity. Pressure that is applied suddenly to a cluster |
| 526 |
> |
can excite breathing vibrations, but these rapidly damp out (on time |
| 527 |
> |
scales of 30-50 ps). |
| 528 |
|
|
| 529 |
|
\subsection{Compressibility of SPC/E water clusters} |
| 530 |
|
|
| 536 |
|
Langevin Hull simulations for pressures between 1 and 6500 atm are |
| 537 |
|
shown in Fig. \ref{fig:compWater} along with compressibility values |
| 538 |
|
obtained from both other SPC/E simulations and experiment. |
| 529 |
– |
Compressibility values from all references are for applied pressures |
| 530 |
– |
within the range 1 - 1000 atm. |
| 539 |
|
|
| 540 |
|
\begin{figure} |
| 541 |
|
\includegraphics[width=\linewidth]{new_isothermalN} |
| 545 |
|
|
| 546 |
|
Isothermal compressibility values calculated using the number density |
| 547 |
|
(Eq. \ref{eq:BMN}) expression are in good agreement with experimental |
| 548 |
< |
and previous simulation work throughout the 1 - 1000 atm pressure |
| 548 |
> |
and previous simulation work throughout the 1 -- 1000 atm pressure |
| 549 |
|
regime. Compressibilities computed using the Hull volume, however, |
| 550 |
|
deviate dramatically from the experimental values at low applied |
| 551 |
|
pressures. The reason for this deviation is quite simple; at low |
| 561 |
|
\caption{At low pressures, the liquid is in equilibrium with the vapor |
| 562 |
|
phase, and isolated molecules can detach from the liquid droplet. |
| 563 |
|
This is expected behavior, but the volume of the convex hull |
| 564 |
< |
includes large regions of empty space. For this reason, |
| 564 |
> |
includes large regions of empty space. For this reason, |
| 565 |
|
compressibilities are computed using local number densities rather |
| 566 |
|
than hull volumes.} |
| 567 |
|
\label{fig:coneOfShame} |
| 582 |
|
\begin{equation} |
| 583 |
|
\kappa_{T} = \frac{\left \langle V^{2} \right \rangle - \left \langle |
| 584 |
|
V \right \rangle ^{2}}{V \, k_{B} \, T}, |
| 585 |
+ |
\label{eq:BMVfluct} |
| 586 |
|
\end{equation} |
| 587 |
|
or, equivalently, fluctuations in the number of molecules within the |
| 588 |
|
fixed region, |
| 589 |
|
\begin{equation} |
| 590 |
|
\kappa_{T} = \frac{\left \langle N^{2} \right \rangle - \left \langle |
| 591 |
|
N \right \rangle ^{2}}{N \, k_{B} \, T}, |
| 592 |
+ |
\label{eq:BMNfluct} |
| 593 |
|
\end{equation} |
| 594 |
|
Thus, the compressibility of each simulation can be calculated |
| 595 |
< |
entirely independently from all other trajectories. However, the |
| 596 |
< |
resulting compressibilities were still as much as an order of |
| 597 |
< |
magnitude larger than the reference values. However, compressibility |
| 598 |
< |
calculation that relies on the hull volume will suffer these effects. |
| 599 |
< |
WE NEED MORE HERE. |
| 595 |
> |
entirely independently from other trajectories. Compressibility |
| 596 |
> |
calculations that rely on the hull volume will still suffer the |
| 597 |
> |
effects of the empty space due to the vapor phase; for this reason, we |
| 598 |
> |
recommend using the number density (Eq. \ref{eq:BMN}) or number |
| 599 |
> |
density fluctuations (Eq. \ref{eq:BMNfluct}) for computing |
| 600 |
> |
compressibilities. |
| 601 |
|
|
| 602 |
|
\subsection{Molecular orientation distribution at cluster boundary} |
| 603 |
|
|
| 604 |
< |
In order for non-periodic boundary conditions to be widely applicable, |
| 604 |
> |
In order for a non-periodic boundary method to be widely applicable, |
| 605 |
|
they must be constructed in such a way that they allow a finite system |
| 606 |
< |
to replicate the properties of the bulk. Early non-periodic |
| 607 |
< |
simulation methods (e.g. hydrophobic boundary potentials) induced |
| 608 |
< |
spurious orientational correlations deep within the simulated |
| 606 |
> |
to replicate the properties of the bulk. Early non-periodic simulation |
| 607 |
> |
methods (e.g. hydrophobic boundary potentials) induced spurious |
| 608 |
> |
orientational correlations deep within the simulated |
| 609 |
|
system.\cite{Lee1984,Belch1985} This behavior spawned many methods for |
| 610 |
|
fixing and characterizing the effects of artifical boundaries |
| 611 |
|
including methods which fix the orientations of a set of edge |
| 613 |
|
|
| 614 |
|
As described above, the Langevin Hull does not require that the |
| 615 |
|
orientation of molecules be fixed, nor does it utilize an explicitly |
| 616 |
< |
hydrophobic boundary, orientational constraint or radial constraint. |
| 617 |
< |
Therefore, the orientational correlations of the molecules in a water |
| 618 |
< |
cluster are of particular interest in testing this method. Ideally, |
| 619 |
< |
the water molecules on the surface of the cluster will have enough |
| 620 |
< |
mobility into and out of the center of the cluster to maintain a |
| 616 |
> |
hydrophobic boundary, or orientational or radial constraints. |
| 617 |
> |
Therefore, the orientational correlations of the molecules in water |
| 618 |
> |
clusters are of particular interest in testing this method. Ideally, |
| 619 |
> |
the water molecules on the surfaces of the clusterss will have enough |
| 620 |
> |
mobility into and out of the center of the cluster to maintain |
| 621 |
|
bulk-like orientational distribution in the absence of orientational |
| 622 |
|
and radial constraints. However, since the number of hydrogen bonding |
| 623 |
|
partners available to molecules on the exterior are limited, it is |
| 624 |
< |
likely that there will be some effective hydrophobicity of the hull. |
| 624 |
> |
likely that there will be an effective hydrophobicity of the hull. |
| 625 |
|
|
| 626 |
< |
To determine the extent of these effects demonstrated by the Langevin |
| 627 |
< |
Hull, we examined the orientationations exhibited by SPC/E water in a |
| 628 |
< |
cluster of 1372 molecules at 300 K and at pressures ranging from 1 - |
| 629 |
< |
1000 atm. The orientational angle of a water molecule is described |
| 626 |
> |
To determine the extent of these effects, we examined the |
| 627 |
> |
orientationations exhibited by SPC/E water in a cluster of 1372 |
| 628 |
> |
molecules at 300 K and at pressures ranging from 1 -- 1000 atm. The |
| 629 |
> |
orientational angle of a water molecule is described |
| 630 |
|
\begin{equation} |
| 631 |
|
\cos{\theta}=\frac{\vec{r}_i\cdot\vec{\mu}_i}{|\vec{r}_i||\vec{\mu}_i|} |
| 632 |
|
\end{equation} |
| 633 |
|
where $\vec{r}_{i}$ is the vector between molecule {\it i}'s center of |
| 634 |
< |
mass and the cluster center of mass and $\vec{\mu}_{i}$ is the vector |
| 635 |
< |
bisecting the H-O-H angle of molecule {\it i} Bulk-like distributions |
| 636 |
< |
will result in $\langle \cos \theta \rangle$ values close to zero. If |
| 637 |
< |
the hull exhibits an overabundance of externally-oriented oxygen sites |
| 638 |
< |
the average orientation will be negative, while dangling hydrogen |
| 639 |
< |
sites will result in positive average orientations. |
| 634 |
> |
mass and the cluster center of mass, and $\vec{\mu}_{i}$ is the vector |
| 635 |
> |
bisecting the H-O-H angle of molecule {\it i}. Bulk-like |
| 636 |
> |
distributions will result in $\langle \cos \theta \rangle$ values |
| 637 |
> |
close to zero. If the hull exhibits an overabundance of |
| 638 |
> |
externally-oriented oxygen sites, the average orientation will be |
| 639 |
> |
negative, while dangling hydrogen sites will result in positive |
| 640 |
> |
average orientations. |
| 641 |
|
|
| 642 |
|
Fig. \ref{fig:pAngle} shows the distribution of $\cos{\theta}$ values |
| 643 |
|
for molecules in the interior of the cluster (squares) and for |
| 683 |
|
|
| 684 |
|
\subsection{Heterogeneous nanoparticle / water mixtures} |
| 685 |
|
|
| 686 |
+ |
To further test the method, we simulated gold nanopartices ($r = 18$ |
| 687 |
+ |
\AA) solvated by explicit SPC/E water clusters using the Langevin |
| 688 |
+ |
hull. This was done at pressures of 1, 2, 5, 10, 20, 50 and 100 atm |
| 689 |
+ |
in order to observe the effects of pressure on the ordering of water |
| 690 |
+ |
ordering at the surface. In Fig. \ref{fig:RhoR} we show the density |
| 691 |
+ |
of water adjacent to the surface as a function of pressure, as well as |
| 692 |
+ |
the orientational ordering of water at the surface of the |
| 693 |
+ |
nanoparticle. |
| 694 |
+ |
|
| 695 |
+ |
\begin{figure} |
| 696 |
+ |
|
| 697 |
+ |
\caption{interesting plot showing cluster behavior} |
| 698 |
+ |
\label{fig:RhoR} |
| 699 |
+ |
\end{figure} |
| 700 |
+ |
|
| 701 |
+ |
At higher pressures, problems with the gold - water interaction |
| 702 |
+ |
potential became apparent. The model we are using (due to Spohr) was |
| 703 |
+ |
intended for relatively low pressures; it utilizes both shifted Morse |
| 704 |
+ |
and repulsive Morse potentials to model the Au/O and Au/H |
| 705 |
+ |
interactions, respectively. The repulsive wall of the Morse potential |
| 706 |
+ |
does not diverge quickly enough at short distances to prevent water |
| 707 |
+ |
from diffusing into the center of the gold nanoparticles. This |
| 708 |
+ |
behavior is likely not a realistic description of the real physics of |
| 709 |
+ |
the situation. A better model of the gold-water adsorption behavior |
| 710 |
+ |
appears to require harder repulsive walls to prevent this behavior. |
| 711 |
+ |
|
| 712 |
|
\section{Discussion} |
| 713 |
|
\label{sec:discussion} |
| 714 |
|
|
| 715 |
|
The Langevin Hull samples the isobaric-isothermal ensemble for |
| 716 |
< |
non-periodic systems by coupling the system to an bath characterized |
| 717 |
< |
by pressure, temperature, and solvent viscosity. This enables the |
| 718 |
< |
study of heterogeneous systems composed of materials of significantly |
| 719 |
< |
different compressibilities. Because the boundary is dynamically |
| 720 |
< |
determined during the simulation and the molecules interacting with |
| 721 |
< |
the boundary can change, the method and has minimal perturbations on |
| 722 |
< |
the behavior of molecules at the edges of the simulation. Further |
| 723 |
< |
work on this method will involve implicit electrostatics at the |
| 724 |
< |
boundary (which is missing in the current implementation) as well as |
| 725 |
< |
more sophisticated treatments of the surface geometry (alpha |
| 716 |
> |
non-periodic systems by coupling the system to a bath characterized by |
| 717 |
> |
pressure, temperature, and solvent viscosity. This enables the |
| 718 |
> |
simulation of heterogeneous systems composed of materials of |
| 719 |
> |
significantly different compressibilities. Because the boundary is |
| 720 |
> |
dynamically determined during the simulation and the molecules |
| 721 |
> |
interacting with the boundary can change, the method and has minimal |
| 722 |
> |
perturbations on the behavior of molecules at the edges of the |
| 723 |
> |
simulation. Further work on this method will involve implicit |
| 724 |
> |
electrostatics at the boundary (which is missing in the current |
| 725 |
> |
implementation) as well as more sophisticated treatments of the |
| 726 |
> |
surface geometry (alpha |
| 727 |
|
shapes\cite{EDELSBRUNNER:1994oq,EDELSBRUNNER:1995cj} and Tight |
| 728 |
|
Cocone\cite{Dey:2003ts}). The non-convex hull geometries are |
| 729 |
|
significantly more expensive ($\mathcal{O}(N^2)$) than the convex hull |
| 734 |
|
|
| 735 |
|
In order to use the Langevin Hull for simulations on parallel |
| 736 |
|
computers, one of the more difficult tasks is to compute the bounding |
| 737 |
< |
surface, facets, and resistance tensors when the processors have |
| 738 |
< |
incomplete information about the entire system's topology. Most |
| 737 |
> |
surface, facets, and resistance tensors when the individual processors |
| 738 |
> |
have incomplete information about the entire system's topology. Most |
| 739 |
|
parallel decomposition methods assign primary responsibility for the |
| 740 |
|
motion of an atomic site to a single processor, and we can exploit |
| 741 |
|
this to efficiently compute the convex hull for the entire system. |
