| 90 |
|
One recently developed model that largely succeeds in retaining the |
| 91 |
|
accuracy of bulk properties while greatly reducing the computational |
| 92 |
|
cost is the Soft Sticky Dipole (SSD) water |
| 93 |
< |
model.\cite{Ichiye96,Ichiye96b,Ichiye99,Ichiye03} The SSD model was |
| 94 |
< |
developed by Ichiye \emph{et al.} as a modified form of the |
| 93 |
> |
model.\cite{Ichiye96,Ichiye96b,Ichiye99,Ichiye03} The SSD model |
| 94 |
> |
was developed by Ichiye \emph{et al.} as a modified form of the |
| 95 |
|
hard-sphere water model proposed by Bratko, Blum, and |
| 96 |
< |
Luzar.\cite{Bratko85,Bratko95} SSD is a {\it single point} model which |
| 97 |
< |
has an interaction site that is both a point dipole along with a |
| 96 |
> |
Luzar.\cite{Bratko85,Bratko95} SSD is a {\it single point} model |
| 97 |
> |
which has an interaction site that is both a point dipole along with a |
| 98 |
|
Lennard-Jones core. However, since the normal aligned and |
| 99 |
|
anti-aligned geometries favored by point dipoles are poor mimics of |
| 100 |
|
local structure in liquid water, a short ranged ``sticky'' potential |
| 101 |
|
is also added. The sticky potential directs the molecules to assume |
| 102 |
< |
the proper hydrogen bond orientation in the first solvation |
| 103 |
< |
shell. |
| 102 |
> |
the proper hydrogen bond orientation in the first solvation shell. |
| 103 |
|
|
| 104 |
|
The interaction between two SSD water molecules \emph{i} and \emph{j} |
| 105 |
|
is given by the potential |
| 168 |
|
SSD decreased computer time by a factor of 6-7 compared to other |
| 169 |
|
models.\cite{Ichiye96} What is most impressive is that this savings |
| 170 |
|
did not come at the expense of accurate depiction of the liquid state |
| 171 |
< |
properties. Indeed, SSD maintains reasonable agreement with the Soper |
| 172 |
< |
data for the structural features of liquid |
| 171 |
> |
properties. Indeed, SSD maintains reasonable agreement with the |
| 172 |
> |
Soper data for the structural features of liquid |
| 173 |
|
water.\cite{Soper86,Ichiye96} Additionally, the dynamical properties |
| 174 |
|
exhibited by SSD agree with experiment better than those of more |
| 175 |
|
computationally expensive models (like TIP3P and |
| 177 |
|
of solvent properties makes SSD a very attractive model for the |
| 178 |
|
simulation of large scale biochemical simulations. |
| 179 |
|
|
| 180 |
< |
One feature of the SSD model is that it was parameterized for use with |
| 181 |
< |
the Ewald sum to handle long-range interactions. This would normally |
| 182 |
< |
be the best way of handling long-range interactions in systems that |
| 183 |
< |
contain other point charges. However, our group has recently become |
| 184 |
< |
interested in systems with point dipoles as mimics for neutral, but |
| 185 |
< |
polarized regions on molecules (e.g. the zwitterionic head group |
| 186 |
< |
regions of phospholipids). If the system of interest does not contain |
| 187 |
< |
point charges, the Ewald sum and even particle-mesh Ewald become |
| 188 |
< |
computational bottlenecks. Their respective ideal $N^\frac{3}{2}$ and |
| 189 |
< |
$N\log N$ calculation scaling orders for $N$ particles can become |
| 190 |
< |
prohibitive when $N$ becomes large.\cite{Darden99} In applying this |
| 191 |
< |
water model in these types of systems, it would be useful to know its |
| 192 |
< |
properties and behavior under the more computationally efficient |
| 193 |
< |
reaction field (RF) technique, or even with a simple cutoff. This |
| 194 |
< |
study addresses these issues by looking at the structural and |
| 195 |
< |
transport behavior of SSD over a variety of temperatures with the |
| 196 |
< |
purpose of utilizing the RF correction technique. We then suggest |
| 197 |
< |
modifications to the parameters that result in more realistic bulk |
| 198 |
< |
phase behavior. It should be noted that in a recent publication, some |
| 199 |
< |
of the original investigators of the SSD water model have suggested |
| 200 |
< |
adjustments to the SSD water model to address abnormal density |
| 201 |
< |
behavior (also observed here), calling the corrected model |
| 202 |
< |
SSD1.\cite{Ichiye03} In what follows, we compare our |
| 203 |
< |
reparamaterization of SSD with both the original SSD and SSD1 models |
| 204 |
< |
with the goal of improving the bulk phase behavior of an SSD-derived |
| 205 |
< |
model in simulations utilizing the Reaction Field. |
| 180 |
> |
One feature of the SSD model is that it was parameterized for |
| 181 |
> |
use with the Ewald sum to handle long-range interactions. This would |
| 182 |
> |
normally be the best way of handling long-range interactions in |
| 183 |
> |
systems that contain other point charges. However, our group has |
| 184 |
> |
recently become interested in systems with point dipoles as mimics for |
| 185 |
> |
neutral, but polarized regions on molecules (e.g. the zwitterionic |
| 186 |
> |
head group regions of phospholipids). If the system of interest does |
| 187 |
> |
not contain point charges, the Ewald sum and even particle-mesh Ewald |
| 188 |
> |
become computational bottlenecks. Their respective ideal |
| 189 |
> |
$N^\frac{3}{2}$ and $N\log N$ calculation scaling orders for $N$ |
| 190 |
> |
particles can become prohibitive when $N$ becomes |
| 191 |
> |
large.\cite{Darden99} In applying this water model in these types of |
| 192 |
> |
systems, it would be useful to know its properties and behavior under |
| 193 |
> |
the more computationally efficient reaction field (RF) technique, or |
| 194 |
> |
even with a simple cutoff. This study addresses these issues by |
| 195 |
> |
looking at the structural and transport behavior of SSD over a |
| 196 |
> |
variety of temperatures with the purpose of utilizing the RF |
| 197 |
> |
correction technique. We then suggest modifications to the parameters |
| 198 |
> |
that result in more realistic bulk phase behavior. It should be noted |
| 199 |
> |
that in a recent publication, some of the original investigators of |
| 200 |
> |
the SSD water model have suggested adjustments to the SSD |
| 201 |
> |
water model to address abnormal density behavior (also observed here), |
| 202 |
> |
calling the corrected model SSD1.\cite{Ichiye03} In what |
| 203 |
> |
follows, we compare our reparamaterization of SSD with both the |
| 204 |
> |
original SSD and SSD1 models with the goal of improving |
| 205 |
> |
the bulk phase behavior of an SSD-derived model in simulations |
| 206 |
> |
utilizing the Reaction Field. |
| 207 |
|
|
| 208 |
|
\section{Methods} |
| 209 |
|
|
| 215 |
|
field acting on dipole $i$ is |
| 216 |
|
\begin{equation} |
| 217 |
|
\mathcal{E}_{i} = \frac{2(\varepsilon_{s} - 1)}{2\varepsilon_{s} + 1} |
| 218 |
< |
\frac{1}{r_{c}^{3}} \sum_{j\in{\mathcal{R}}} {\bf \mu}_{j} f(r_{ij})\ , |
| 218 |
> |
\frac{1}{r_{c}^{3}} \sum_{j\in{\mathcal{R}}} {\bf \mu}_{j} s(r_{ij}), |
| 219 |
|
\label{rfequation} |
| 220 |
|
\end{equation} |
| 221 |
|
where $\mathcal{R}$ is the cavity defined by the cutoff radius |
| 222 |
|
($r_{c}$), $\varepsilon_{s}$ is the dielectric constant imposed on the |
| 223 |
|
system (80 in the case of liquid water), ${\bf \mu}_{j}$ is the dipole |
| 224 |
< |
moment vector of particle $j$ and $f(r_{ij})$ is a cubic switching |
| 224 |
> |
moment vector of particle $j$, and $s(r_{ij})$ is a cubic switching |
| 225 |
|
function.\cite{AllenTildesley} The reaction field contribution to the |
| 226 |
|
total energy by particle $i$ is given by $-\frac{1}{2}{\bf |
| 227 |
|
\mu}_{i}\cdot\mathcal{E}_{i}$ and the torque on dipole $i$ by ${\bf |
| 235 |
|
|
| 236 |
|
We have also performed a companion set of simulations {\it without} a |
| 237 |
|
surrounding dielectric (i.e. using a simple cubic switching function |
| 238 |
< |
at the cutoff radius) and as a result we have two reparamaterizations |
| 239 |
< |
of SSD which could be used either with or without the Reaction Field |
| 240 |
< |
turned on. |
| 238 |
> |
at the cutoff radius), and as a result we have two reparamaterizations |
| 239 |
> |
of SSD which could be used either with or without the reaction |
| 240 |
> |
field turned on. |
| 241 |
|
|
| 242 |
< |
Simulations to obtain the preferred density were performed in the |
| 243 |
< |
isobaric-isothermal (NPT) ensemble, while all dynamical properties |
| 244 |
< |
were obtained from microcanonical (NVE) simulations done at densities |
| 245 |
< |
matching the NPT density for a particular target temperature. The |
| 246 |
< |
constant pressure simulations were implemented using an integral |
| 247 |
< |
thermostat and barostat as outlined by Hoover.\cite{Hoover85,Hoover86} |
| 248 |
< |
All molecules were treated as non-linear rigid bodies. Vibrational |
| 249 |
< |
constraints are not necessary in simulations of SSD, because there are |
| 250 |
< |
no explicit hydrogen atoms, and thus no molecular vibrational modes |
| 251 |
< |
need to be considered. |
| 242 |
> |
Simulations to obtain the preferred densities of the models were |
| 243 |
> |
performed in the isobaric-isothermal (NPT) ensemble, while all |
| 244 |
> |
dynamical properties were obtained from microcanonical (NVE) |
| 245 |
> |
simulations done at densities matching the NPT density for a |
| 246 |
> |
particular target temperature. The constant pressure simulations were |
| 247 |
> |
implemented using an integral thermostat and barostat as outlined by |
| 248 |
> |
Hoover.\cite{Hoover85,Hoover86} All molecules were treated as |
| 249 |
> |
non-linear rigid bodies. Vibrational constraints are not necessary in |
| 250 |
> |
simulations of SSD, because there are no explicit hydrogen |
| 251 |
> |
atoms, and thus no molecular vibrational modes need to be considered. |
| 252 |
|
|
| 253 |
|
Integration of the equations of motion was carried out using the |
| 254 |
< |
symplectic splitting method proposed by Dullweber {\it et |
| 255 |
< |
al.}\cite{Dullweber1997} Our reason for selecting this integrator |
| 256 |
< |
centers on poor energy conservation of rigid body dynamics using |
| 257 |
< |
traditional quaternion integration.\cite{Evans77,Evans77b} While quaternions |
| 258 |
< |
may work well for orientational motion under NVT or NPT integrators, |
| 259 |
< |
our limits on energy drift in the microcanonical ensemble were quite |
| 260 |
< |
strict, and the drift under quaternions was substantially greater than |
| 261 |
< |
in the symplectic splitting method. This steady drift in the total |
| 262 |
< |
energy has also been observed by Kol {\it et al.}\cite{Laird97} |
| 254 |
> |
symplectic splitting method proposed by Dullweber, Leimkuhler, and |
| 255 |
> |
McLachlan ({\sc dlm}).\cite{Dullweber1997} Our reason for selecting |
| 256 |
> |
this integrator centers on poor energy conservation of rigid body |
| 257 |
> |
dynamics using traditional quaternion |
| 258 |
> |
integration.\cite{Evans77,Evans77b} In typical microcanonical ensemble |
| 259 |
> |
simulations, the energy drift when using quaternions was substantially |
| 260 |
> |
greater than when using the {\sc dlm} method (fig. \ref{timestep}). |
| 261 |
> |
This steady drift in the total energy has also been observed by Kol |
| 262 |
> |
{\it et al.}\cite{Laird97} |
| 263 |
|
|
| 264 |
|
The key difference in the integration method proposed by Dullweber |
| 265 |
|
\emph{et al.} is that the entire rotation matrix is propagated from |
| 268 |
|
rotation matrix into quaternions for storage purposes makes trajectory |
| 269 |
|
data quite compact. |
| 270 |
|
|
| 271 |
< |
The symplectic splitting method allows for Verlet style integration of |
| 272 |
< |
both translational and orientational motion of rigid bodies. In this |
| 271 |
> |
The {\sc dlm} method allows for Verlet style integration of both |
| 272 |
> |
translational and orientational motion of rigid bodies. In this |
| 273 |
|
integration method, the orientational propagation involves a sequence |
| 274 |
|
of matrix evaluations to update the rotation |
| 275 |
|
matrix.\cite{Dullweber1997} These matrix rotations are more costly |
| 276 |
|
than the simpler arithmetic quaternion propagation. With the same time |
| 277 |
< |
step, a 1000 SSD particle simulation shows an average 7\% increase in |
| 278 |
< |
computation time using the symplectic step method in place of |
| 277 |
> |
step, a 1000 SSD particle simulation shows an average 7\% |
| 278 |
> |
increase in computation time using the {\sc dlm} method in place of |
| 279 |
|
quaternions. The additional expense per step is justified when one |
| 280 |
|
considers the ability to use time steps that are nearly twice as large |
| 281 |
< |
under symplectic splitting than would be usable under quaternion |
| 282 |
< |
dynamics. The energy conservation of the two methods using a number |
| 283 |
< |
of different time steps is illustrated in figure |
| 281 |
> |
under {\sc dlm} than would be usable under quaternion dynamics. The |
| 282 |
> |
energy conservation of the two methods using a number of different |
| 283 |
> |
time steps is illustrated in figure |
| 284 |
|
\ref{timestep}. |
| 285 |
|
|
| 286 |
|
\begin{figure} |
| 287 |
|
\begin{center} |
| 288 |
|
\epsfxsize=6in |
| 289 |
|
\epsfbox{timeStep.epsi} |
| 290 |
< |
\caption{Energy conservation using both quaternion based integration and |
| 291 |
< |
the symplectic step method proposed by Dullweber \emph{et al.} with |
| 292 |
< |
increasing time step. The larger time step plots are shifted from the |
| 293 |
< |
true energy baseline (that of $\Delta t$ = 0.1 fs) for clarity.} |
| 290 |
> |
\caption{Energy conservation using both quaternion-based integration and |
| 291 |
> |
the {\sc dlm} method with increasing time step. The larger time step plots |
| 292 |
> |
are shifted from the true energy baseline (that of $\Delta t$ = 0.1 |
| 293 |
> |
fs) for clarity.} |
| 294 |
|
\label{timestep} |
| 295 |
|
\end{center} |
| 296 |
|
\end{figure} |
| 297 |
|
|
| 298 |
|
In figure \ref{timestep}, the resulting energy drift at various time |
| 299 |
< |
steps for both the symplectic step and quaternion integration schemes |
| 300 |
< |
is compared. All of the 1000 SSD particle simulations started with |
| 299 |
> |
steps for both the {\sc dlm} and quaternion integration schemes is |
| 300 |
> |
compared. All of the 1000 SSD particle simulations started with |
| 301 |
|
the same configuration, and the only difference was the method used to |
| 302 |
|
handle orientational motion. At time steps of 0.1 and 0.5 fs, both |
| 303 |
|
methods for propagating the orientational degrees of freedom conserve |
| 304 |
|
energy fairly well, with the quaternion method showing a slight energy |
| 305 |
|
drift over time in the 0.5 fs time step simulation. At time steps of 1 |
| 306 |
< |
and 2 fs, the energy conservation benefits of the symplectic step |
| 307 |
< |
method are clearly demonstrated. Thus, while maintaining the same |
| 308 |
< |
degree of energy conservation, one can take considerably longer time |
| 309 |
< |
steps, leading to an overall reduction in computation time. |
| 306 |
> |
and 2 fs, the energy conservation benefits of the {\sc dlm} method are |
| 307 |
> |
clearly demonstrated. Thus, while maintaining the same degree of |
| 308 |
> |
energy conservation, one can take considerably longer time steps, |
| 309 |
> |
leading to an overall reduction in computation time. |
| 310 |
|
|
| 311 |
< |
Energy drift in the symplectic step simulations was unnoticeable for |
| 312 |
< |
time steps up to 3 fs. A slight energy drift on the |
| 311 |
> |
Energy drift in the simulations using {\sc dlm} integration was |
| 312 |
> |
unnoticeable for time steps up to 3 fs. A slight energy drift on the |
| 313 |
|
order of 0.012 kcal/mol per nanosecond was observed at a time step of |
| 314 |
< |
4 fs, and as expected, this drift increases dramatically |
| 315 |
< |
with increasing time step. To insure accuracy in our microcanonical |
| 314 |
> |
4 fs, and as expected, this drift increases dramatically with |
| 315 |
> |
increasing time step. To insure accuracy in our microcanonical |
| 316 |
|
simulations, time steps were set at 2 fs and kept at this value for |
| 317 |
|
constant pressure simulations as well. |
| 318 |
|
|
| 319 |
|
Proton-disordered ice crystals in both the $I_h$ and $I_c$ lattices |
| 320 |
|
were generated as starting points for all simulations. The $I_h$ |
| 321 |
< |
crystals were formed by first arranging the centers of mass of the SSD |
| 322 |
< |
particles into a ``hexagonal'' ice lattice of 1024 particles. Because |
| 323 |
< |
of the crystal structure of $I_h$ ice, the simulation box assumed an |
| 324 |
< |
orthorhombic shape with an edge length ratio of approximately |
| 325 |
< |
1.00$\times$1.06$\times$1.23. The particles were then allowed to |
| 326 |
< |
orient freely about fixed positions with angular momenta randomized at |
| 327 |
< |
400 K for varying times. The rotational temperature was then scaled |
| 328 |
< |
down in stages to slowly cool the crystals to 25 K. The particles were |
| 329 |
< |
then allowed to translate with fixed orientations at a constant |
| 330 |
< |
pressure of 1 atm for 50 ps at 25 K. Finally, all constraints were |
| 331 |
< |
removed and the ice crystals were allowed to equilibrate for 50 ps at |
| 332 |
< |
25 K and a constant pressure of 1 atm. This procedure resulted in |
| 333 |
< |
structurally stable $I_h$ ice crystals that obey the Bernal-Fowler |
| 321 |
> |
crystals were formed by first arranging the centers of mass of the |
| 322 |
> |
SSD particles into a ``hexagonal'' ice lattice of 1024 |
| 323 |
> |
particles. Because of the crystal structure of $I_h$ ice, the |
| 324 |
> |
simulation box assumed an orthorhombic shape with an edge length ratio |
| 325 |
> |
of approximately 1.00$\times$1.06$\times$1.23. The particles were then |
| 326 |
> |
allowed to orient freely about fixed positions with angular momenta |
| 327 |
> |
randomized at 400 K for varying times. The rotational temperature was |
| 328 |
> |
then scaled down in stages to slowly cool the crystals to 25 K. The |
| 329 |
> |
particles were then allowed to translate with fixed orientations at a |
| 330 |
> |
constant pressure of 1 atm for 50 ps at 25 K. Finally, all constraints |
| 331 |
> |
were removed and the ice crystals were allowed to equilibrate for 50 |
| 332 |
> |
ps at 25 K and a constant pressure of 1 atm. This procedure resulted |
| 333 |
> |
in structurally stable $I_h$ ice crystals that obey the Bernal-Fowler |
| 334 |
|
rules.\cite{Bernal33,Rahman72} This method was also utilized in the |
| 335 |
|
making of diamond lattice $I_c$ ice crystals, with each cubic |
| 336 |
|
simulation box consisting of either 512 or 1000 particles. Only |
| 357 |
|
|
| 358 |
|
\subsection{Density Behavior} |
| 359 |
|
|
| 360 |
< |
Our initial simulations focused on the original SSD water model, and |
| 361 |
< |
an average density versus temperature plot is shown in figure |
| 360 |
> |
Our initial simulations focused on the original SSD water model, |
| 361 |
> |
and an average density versus temperature plot is shown in figure |
| 362 |
|
\ref{dense1}. Note that the density maximum when using a reaction |
| 363 |
|
field appears between 255 and 265 K. There were smaller fluctuations |
| 364 |
|
in the density at 260 K than at either 255 or 265, so we report this |
| 371 |
|
\begin{figure} |
| 372 |
|
\begin{center} |
| 373 |
|
\epsfxsize=6in |
| 374 |
< |
\epsfbox{denseSSD.eps} |
| 374 |
> |
\epsfbox{denseSSDnew.eps} |
| 375 |
|
\caption{Density versus temperature for TIP4P [Ref. \citen{Jorgensen98b}], |
| 376 |
|
TIP3P [Ref. \citen{Jorgensen98b}], SPC/E [Ref. \citen{Clancy94}], SSD |
| 377 |
|
without Reaction Field, SSD, and experiment [Ref. \citen{CRC80}]. The |
| 383 |
|
\end{center} |
| 384 |
|
\end{figure} |
| 385 |
|
|
| 386 |
< |
The density maximum for SSD compares quite favorably to other simple |
| 387 |
< |
water models. Figure \ref{dense1} also shows calculated densities of |
| 388 |
< |
several other models and experiment obtained from other |
| 386 |
> |
The density maximum for SSD compares quite favorably to other |
| 387 |
> |
simple water models. Figure \ref{dense1} also shows calculated |
| 388 |
> |
densities of several other models and experiment obtained from other |
| 389 |
|
sources.\cite{Jorgensen98b,Clancy94,CRC80} Of the listed simple water |
| 390 |
< |
models, SSD has a temperature closest to the experimentally observed |
| 391 |
< |
density maximum. Of the {\it charge-based} models in |
| 390 |
> |
models, SSD has a temperature closest to the experimentally |
| 391 |
> |
observed density maximum. Of the {\it charge-based} models in |
| 392 |
|
Fig. \ref{dense1}, TIP4P has a density maximum behavior most like that |
| 393 |
< |
seen in SSD. Though not included in this plot, it is useful |
| 394 |
< |
to note that TIP5P has a density maximum nearly identical to the |
| 393 |
> |
seen in SSD. Though not included in this plot, it is useful to |
| 394 |
> |
note that TIP5P has a density maximum nearly identical to the |
| 395 |
|
experimentally measured temperature. |
| 396 |
|
|
| 397 |
|
It has been observed that liquid state densities in water are |
| 398 |
|
dependent on the cutoff radius used both with and without the use of |
| 399 |
|
reaction field.\cite{Berendsen98} In order to address the possible |
| 400 |
|
effect of cutoff radius, simulations were performed with a dipolar |
| 401 |
< |
cutoff radius of 12.0 \AA\ to complement the previous SSD simulations, |
| 402 |
< |
all performed with a cutoff of 9.0 \AA. All of the resulting densities |
| 403 |
< |
overlapped within error and showed no significant trend toward lower |
| 404 |
< |
or higher densities as a function of cutoff radius, for simulations |
| 405 |
< |
both with and without reaction field. These results indicate that |
| 406 |
< |
there is no major benefit in choosing a longer cutoff radius in |
| 407 |
< |
simulations using SSD. This is advantageous in that the use of a |
| 408 |
< |
longer cutoff radius results in a significant increase in the time |
| 409 |
< |
required to obtain a single trajectory. |
| 401 |
> |
cutoff radius of 12.0 \AA\ to complement the previous SSD |
| 402 |
> |
simulations, all performed with a cutoff of 9.0 \AA. All of the |
| 403 |
> |
resulting densities overlapped within error and showed no significant |
| 404 |
> |
trend toward lower or higher densities as a function of cutoff radius, |
| 405 |
> |
for simulations both with and without reaction field. These results |
| 406 |
> |
indicate that there is no major benefit in choosing a longer cutoff |
| 407 |
> |
radius in simulations using SSD. This is advantageous in that |
| 408 |
> |
the use of a longer cutoff radius results in a significant increase in |
| 409 |
> |
the time required to obtain a single trajectory. |
| 410 |
|
|
| 411 |
|
The key feature to recognize in figure \ref{dense1} is the density |
| 412 |
|
scaling of SSD relative to other common models at any given |
| 413 |
< |
temperature. SSD assumes a lower density than any of the other listed |
| 414 |
< |
models at the same pressure, behavior which is especially apparent at |
| 415 |
< |
temperatures greater than 300 K. Lower than expected densities have |
| 416 |
< |
been observed for other systems using a reaction field for long-range |
| 417 |
< |
electrostatic interactions, so the most likely reason for the |
| 418 |
< |
significantly lower densities seen in these simulations is the |
| 413 |
> |
temperature. SSD assumes a lower density than any of the other |
| 414 |
> |
listed models at the same pressure, behavior which is especially |
| 415 |
> |
apparent at temperatures greater than 300 K. Lower than expected |
| 416 |
> |
densities have been observed for other systems using a reaction field |
| 417 |
> |
for long-range electrostatic interactions, so the most likely reason |
| 418 |
> |
for the significantly lower densities seen in these simulations is the |
| 419 |
|
presence of the reaction field.\cite{Berendsen98,Nezbeda02} In order |
| 420 |
|
to test the effect of the reaction field on the density of the |
| 421 |
|
systems, the simulations were repeated without a reaction field |
| 431 |
|
simulations.\cite{Clancy94,Jorgensen98b} However, even without the |
| 432 |
|
reaction field, the density around 300 K is still significantly lower |
| 433 |
|
than experiment and comparable water models. This anomalous behavior |
| 434 |
< |
was what lead Ichiye {\it et al.} to recently reparameterize |
| 434 |
> |
was what lead Tan {\it et al.} to recently reparameterize |
| 435 |
|
SSD.\cite{Ichiye03} Throughout the remainder of the paper our |
| 436 |
< |
reparamaterizations of SSD will be compared with the newer SSD1 model. |
| 436 |
> |
reparamaterizations of SSD will be compared with their newer SSD1 |
| 437 |
> |
model. |
| 438 |
|
|
| 439 |
|
\subsection{Transport Behavior} |
| 440 |
|
|
| 450 |
|
mean-square displacement as a function of time. The averaged results |
| 451 |
|
from five sets of NVE simulations are displayed in figure |
| 452 |
|
\ref{diffuse}, alongside experimental, SPC/E, and TIP5P |
| 453 |
< |
results.\cite{Gillen72,Mills73,Clancy94,Jorgensen01} |
| 453 |
> |
results.\cite{Gillen72,Holz00,Clancy94,Jorgensen01} |
| 454 |
|
|
| 455 |
|
\begin{figure} |
| 456 |
|
\begin{center} |
| 457 |
|
\epsfxsize=6in |
| 458 |
|
\epsfbox{betterDiffuse.epsi} |
| 459 |
|
\caption{Average self-diffusion constant as a function of temperature for |
| 460 |
< |
SSD, SPC/E [Ref. \citen{Clancy94}], TIP5P [Ref. \citen{Jorgensen01}], |
| 461 |
< |
and Experimental data [Refs. \citen{Gillen72} and \citen{Mills73}]. Of |
| 462 |
< |
the three water models shown, SSD has the least deviation from the |
| 463 |
< |
experimental values. The rapidly increasing diffusion constants for |
| 464 |
< |
TIP5P and SSD correspond to significant decrease in density at the |
| 465 |
< |
higher temperatures.} |
| 460 |
> |
SSD, SPC/E [Ref. \citen{Clancy94}], and TIP5P |
| 461 |
> |
[Ref. \citen{Jorgensen01}] compared with experimental data |
| 462 |
> |
[Refs. \citen{Gillen72} and \citen{Holz00}]. Of the three water models |
| 463 |
> |
shown, SSD has the least deviation from the experimental values. The |
| 464 |
> |
rapidly increasing diffusion constants for TIP5P and SSD correspond to |
| 465 |
> |
significant decreases in density at the higher temperatures.} |
| 466 |
|
\label{diffuse} |
| 467 |
|
\end{center} |
| 468 |
|
\end{figure} |
| 478 |
|
This behavior at higher temperatures is not particularly surprising |
| 479 |
|
since the densities of both TIP5P and SSD are lower than experimental |
| 480 |
|
water densities at higher temperatures. When calculating the |
| 481 |
< |
diffusion coefficients for SSD at experimental densities (instead of |
| 482 |
< |
the densities from the NPT simulations), the resulting values fall |
| 483 |
< |
more in line with experiment at these temperatures. |
| 481 |
> |
diffusion coefficients for SSD at experimental densities |
| 482 |
> |
(instead of the densities from the NPT simulations), the resulting |
| 483 |
> |
values fall more in line with experiment at these temperatures. |
| 484 |
|
|
| 485 |
|
\subsection{Structural Changes and Characterization} |
| 486 |
|
|
| 499 |
|
\begin{center} |
| 500 |
|
\epsfxsize=6in |
| 501 |
|
\epsfbox{corrDiag.eps} |
| 502 |
< |
\caption{Two dimensional illustration of angles involved in the |
| 502 |
< |
correlations observed in Fig. \ref{contour}.} |
| 502 |
> |
\caption{An illustration of angles involved in the correlations observed in Fig. \ref{contour}.} |
| 503 |
|
\label{corrAngle} |
| 504 |
|
\end{center} |
| 505 |
|
\end{figure} |
| 508 |
|
\begin{center} |
| 509 |
|
\epsfxsize=6in |
| 510 |
|
\epsfbox{fullContours.eps} |
| 511 |
< |
\caption{Contour plots of 2D angular g($r$)'s for 512 SSD systems at |
| 512 |
< |
100 K (A \& B) and 300 K (C \& D). Contour colors are inverted for |
| 513 |
< |
clarity: dark areas signify peaks while light areas signify |
| 514 |
< |
depressions. White areas have $g(r)$ values below 0.5 and black |
| 515 |
< |
areas have values above 1.5.} |
| 511 |
> |
\caption{Contour plots of 2D angular pair correlation functions for |
| 512 |
> |
512 SSD molecules at 100 K (A \& B) and 300 K (C \& D). Dark areas |
| 513 |
> |
signify regions of enhanced density while light areas signify |
| 514 |
> |
depletion relative to the bulk density. White areas have pair |
| 515 |
> |
correlation values below 0.5 and black areas have values above 1.5.} |
| 516 |
|
\label{contour} |
| 517 |
|
\end{center} |
| 518 |
|
\end{figure} |
| 551 |
|
|
| 552 |
|
This complex interplay between dipole and sticky interactions was |
| 553 |
|
remarked upon as a possible reason for the split second peak in the |
| 554 |
< |
oxygen-oxygen $g_\mathrm{OO}(r)$.\cite{Ichiye96} At low temperatures, |
| 555 |
< |
the second solvation shell peak appears to have two distinct |
| 556 |
< |
components that blend together to form one observable peak. At higher |
| 557 |
< |
temperatures, this split character alters to show the leading 4 \AA\ |
| 558 |
< |
peak dominated by equatorial anti-parallel dipole orientations. There |
| 559 |
< |
is also a tightly bunched group of axially arranged dipoles that most |
| 560 |
< |
likely consist of the smaller fraction of aligned dipole pairs. The |
| 561 |
< |
trailing component of the split peak at 5 \AA\ is dominated by aligned |
| 562 |
< |
dipoles that assume hydrogen bond arrangements similar to those seen |
| 563 |
< |
in the first solvation shell. This evidence indicates that the dipole |
| 564 |
< |
pair interaction begins to dominate outside of the range of the |
| 565 |
< |
dipolar repulsion term. The energetically favorable dipole |
| 566 |
< |
arrangements populate the region immediately outside this repulsion |
| 567 |
< |
region (around 4 \AA), while arrangements that seek to satisfy both |
| 568 |
< |
the sticky and dipole forces locate themselves just beyond this |
| 569 |
< |
initial buildup (around 5 \AA). |
| 554 |
> |
oxygen-oxygen pair correlation function, |
| 555 |
> |
$g_\mathrm{OO}(r)$.\cite{Ichiye96} At low temperatures, the second |
| 556 |
> |
solvation shell peak appears to have two distinct components that |
| 557 |
> |
blend together to form one observable peak. At higher temperatures, |
| 558 |
> |
this split character alters to show the leading 4 \AA\ peak dominated |
| 559 |
> |
by equatorial anti-parallel dipole orientations. There is also a |
| 560 |
> |
tightly bunched group of axially arranged dipoles that most likely |
| 561 |
> |
consist of the smaller fraction of aligned dipole pairs. The trailing |
| 562 |
> |
component of the split peak at 5 \AA\ is dominated by aligned dipoles |
| 563 |
> |
that assume hydrogen bond arrangements similar to those seen in the |
| 564 |
> |
first solvation shell. This evidence indicates that the dipole pair |
| 565 |
> |
interaction begins to dominate outside of the range of the dipolar |
| 566 |
> |
repulsion term. The energetically favorable dipole arrangements |
| 567 |
> |
populate the region immediately outside this repulsion region (around |
| 568 |
> |
4 \AA), while arrangements that seek to satisfy both the sticky and |
| 569 |
> |
dipole forces locate themselves just beyond this initial buildup |
| 570 |
> |
(around 5 \AA). |
| 571 |
|
|
| 572 |
|
From these findings, the split second peak is primarily the product of |
| 573 |
|
the dipolar repulsion term of the sticky potential. In fact, the inner |
| 578 |
|
since the second solvation shell would still be shifted too far |
| 579 |
|
out. In addition, this would have an even more detrimental effect on |
| 580 |
|
the system densities, leading to a liquid with a more open structure |
| 581 |
< |
and a density considerably lower than the already low SSD density. A |
| 582 |
< |
better correction would be to include the quadrupole-quadrupole |
| 583 |
< |
interactions for the water particles outside of the first solvation |
| 584 |
< |
shell, but this would remove the simplicity and speed advantage of |
| 585 |
< |
SSD. |
| 581 |
> |
and a density considerably lower than the already low SSD |
| 582 |
> |
density. A better correction would be to include the |
| 583 |
> |
quadrupole-quadrupole interactions for the water particles outside of |
| 584 |
> |
the first solvation shell, but this would remove the simplicity and |
| 585 |
> |
speed advantage of SSD. |
| 586 |
|
|
| 587 |
|
\subsection{Adjusted Potentials: SSD/RF and SSD/E} |
| 588 |
|
|
| 597 |
|
|
| 598 |
|
The parameters available for tuning include the $\sigma$ and |
| 599 |
|
$\epsilon$ Lennard-Jones parameters, the dipole strength ($\mu$), the |
| 600 |
< |
strength of the sticky potential ($\nu_0$), and the sticky attractive |
| 601 |
< |
and dipole repulsive cubic switching function cutoffs ($r_l$, $r_u$ |
| 602 |
< |
and $r_l^\prime$, $r_u^\prime$ respectively). The results of the |
| 603 |
< |
reparameterizations are shown in table \ref{params}. We are calling |
| 604 |
< |
these reparameterizations the Soft Sticky Dipole / Reaction Field |
| 605 |
< |
(SSD/RF - for use with a reaction field) and Soft Sticky Dipole |
| 606 |
< |
Extended (SSD/E - an attempt to improve the liquid structure in |
| 607 |
< |
simulations without a long-range correction). |
| 600 |
> |
strength of the sticky potential ($\nu_0$), and the cutoff distances |
| 601 |
> |
for the sticky attractive and dipole repulsive cubic switching |
| 602 |
> |
function cutoffs ($r_l$, $r_u$ and $r_l^\prime$, $r_u^\prime$ |
| 603 |
> |
respectively). The results of the reparameterizations are shown in |
| 604 |
> |
table \ref{params}. We are calling these reparameterizations the Soft |
| 605 |
> |
Sticky Dipole / Reaction Field (SSD/RF - for use with a reaction |
| 606 |
> |
field) and Soft Sticky Dipole Extended (SSD/E - an attempt to improve |
| 607 |
> |
the liquid structure in simulations without a long-range correction). |
| 608 |
|
|
| 609 |
|
\begin{table} |
| 610 |
|
\begin{center} |
| 632 |
|
\begin{center} |
| 633 |
|
\epsfxsize=5in |
| 634 |
|
\epsfbox{GofRCompare.epsi} |
| 635 |
< |
\caption{Plots comparing experiment [Ref. \citen{Head-Gordon00_1}] with SSD/E |
| 636 |
< |
and SSD1 without reaction field (top), as well as SSD/RF and SSD1 with |
| 637 |
< |
reaction field turned on (bottom). The insets show the respective |
| 638 |
< |
first peaks in detail. Note how the changes in parameters have lowered |
| 639 |
< |
and broadened the first peak of SSD/E and SSD/RF.} |
| 635 |
> |
\caption{Plots comparing experiment [Ref. \citen{Head-Gordon00_1}] with |
| 636 |
> |
SSD/E and SSD1 without reaction field (top), as well as |
| 637 |
> |
SSD/RF and SSD1 with reaction field turned on |
| 638 |
> |
(bottom). The insets show the respective first peaks in detail. Note |
| 639 |
> |
how the changes in parameters have lowered and broadened the first |
| 640 |
> |
peak of SSD/E and SSD/RF.} |
| 641 |
|
\label{grcompare} |
| 642 |
|
\end{center} |
| 643 |
|
\end{figure} |
| 645 |
|
\begin{figure} |
| 646 |
|
\begin{center} |
| 647 |
|
\epsfxsize=6in |
| 648 |
< |
\epsfbox{dualsticky.ps} |
| 649 |
< |
\caption{Isosurfaces of the sticky potential for SSD1 (left) and SSD/E \& |
| 650 |
< |
SSD/RF (right). Light areas correspond to the tetrahedral attractive |
| 651 |
< |
component, and darker areas correspond to the dipolar repulsive |
| 652 |
< |
component.} |
| 648 |
> |
\epsfbox{dualsticky_bw.eps} |
| 649 |
> |
\caption{Positive and negative isosurfaces of the sticky potential for |
| 650 |
> |
SSD1 (left) and SSD/E \& SSD/RF (right). Light areas |
| 651 |
> |
correspond to the tetrahedral attractive component, and darker areas |
| 652 |
> |
correspond to the dipolar repulsive component.} |
| 653 |
|
\label{isosurface} |
| 654 |
|
\end{center} |
| 655 |
|
\end{figure} |
| 662 |
|
Phillips.\cite{Ichiye96,Soper86} New experimental x-ray scattering |
| 663 |
|
data from the Head-Gordon lab indicates a slightly lower and shifted |
| 664 |
|
first peak in the g$_\mathrm{OO}(r)$, so our adjustments to SSD were |
| 665 |
< |
made while taking into consideration the new experimental |
| 665 |
> |
made after taking into consideration the new experimental |
| 666 |
|
findings.\cite{Head-Gordon00_1} Figure \ref{grcompare} shows the |
| 667 |
|
relocation of the first peak of the oxygen-oxygen $g(r)$ by comparing |
| 668 |
|
the revised SSD model (SSD1), SSD/E, and SSD/RF to the new |
| 678 |
|
see how altering the cutoffs changes the repulsive and attractive |
| 679 |
|
character of the particles. With a reduced repulsive surface (darker |
| 680 |
|
region), the particles can move closer to one another, increasing the |
| 681 |
< |
density for the overall system. This change in interaction cutoff also |
| 682 |
< |
results in a more gradual orientational motion by allowing the |
| 681 |
> |
density for the overall system. This change in interaction cutoff |
| 682 |
> |
also results in a more gradual orientational motion by allowing the |
| 683 |
|
particles to maintain preferred dipolar arrangements before they begin |
| 684 |
|
to feel the pull of the tetrahedral restructuring. As the particles |
| 685 |
|
move closer together, the dipolar repulsion term becomes active and |
| 695 |
|
improves the densities, these changes alone are insufficient to bring |
| 696 |
|
the system densities up to the values observed experimentally. To |
| 697 |
|
further increase the densities, the dipole moments were increased in |
| 698 |
< |
both of our adjusted models. Since SSD is a dipole based model, the |
| 699 |
< |
structure and transport are very sensitive to changes in the dipole |
| 700 |
< |
moment. The original SSD simply used the dipole moment calculated from |
| 701 |
< |
the TIP3P water model, which at 2.35 D is significantly greater than |
| 702 |
< |
the experimental gas phase value of 1.84 D. The larger dipole moment |
| 703 |
< |
is a more realistic value and improves the dielectric properties of |
| 704 |
< |
the fluid. Both theoretical and experimental measurements indicate a |
| 705 |
< |
liquid phase dipole moment ranging from 2.4 D to values as high as |
| 706 |
< |
3.11 D, providing a substantial range of reasonable values for a |
| 707 |
< |
dipole moment.\cite{Sprik91,Kusalik02,Badyal00,Barriol64} Moderately |
| 708 |
< |
increasing the dipole moments to 2.42 and 2.48 D for SSD/E and SSD/RF, |
| 709 |
< |
respectively, leads to significant changes in the density and |
| 710 |
< |
transport of the water models. |
| 698 |
> |
both of our adjusted models. Since SSD is a dipole based model, |
| 699 |
> |
the structure and transport are very sensitive to changes in the |
| 700 |
> |
dipole moment. The original SSD simply used the dipole moment |
| 701 |
> |
calculated from the TIP3P water model, which at 2.35 D is |
| 702 |
> |
significantly greater than the experimental gas phase value of 1.84 |
| 703 |
> |
D. The larger dipole moment is a more realistic value and improves the |
| 704 |
> |
dielectric properties of the fluid. Both theoretical and experimental |
| 705 |
> |
measurements indicate a liquid phase dipole moment ranging from 2.4 D |
| 706 |
> |
to values as high as 3.11 D, providing a substantial range of |
| 707 |
> |
reasonable values for a dipole |
| 708 |
> |
moment.\cite{Sprik91,Kusalik02,Badyal00,Barriol64} Moderately |
| 709 |
> |
increasing the dipole moments to 2.42 and 2.48 D for SSD/E and |
| 710 |
> |
SSD/RF, respectively, leads to significant changes in the |
| 711 |
> |
density and transport of the water models. |
| 712 |
|
|
| 713 |
|
In order to demonstrate the benefits of these reparameterizations, a |
| 714 |
|
series of NPT and NVE simulations were performed to probe the density |
| 729 |
|
\begin{center} |
| 730 |
|
\epsfxsize=6in |
| 731 |
|
\epsfbox{ssdeDense.epsi} |
| 732 |
< |
\caption{Comparison of densities calculated with SSD/E to SSD1 without a |
| 733 |
< |
reaction field, TIP3P [Ref. \citen{Jorgensen98b}], TIP5P |
| 734 |
< |
[Ref. \citen{Jorgensen00}], SPC/E [Ref. \citen{Clancy94}] and |
| 732 |
> |
\caption{Comparison of densities calculated with SSD/E to |
| 733 |
> |
SSD1 without a reaction field, TIP3P [Ref. \citen{Jorgensen98b}], |
| 734 |
> |
TIP5P [Ref. \citen{Jorgensen00}], SPC/E [Ref. \citen{Clancy94}] and |
| 735 |
|
experiment [Ref. \citen{CRC80}]. The window shows a expansion around |
| 736 |
|
300 K with error bars included to clarify this region of |
| 737 |
|
interest. Note that both SSD1 and SSD/E show good agreement with |
| 740 |
|
\end{center} |
| 741 |
|
\end{figure} |
| 742 |
|
|
| 743 |
< |
Fig. \ref{ssdedense} shows the density profile for the SSD/E model |
| 744 |
< |
in comparison to SSD1 without a reaction field, other common water |
| 745 |
< |
models, and experimental results. The calculated densities for both |
| 746 |
< |
SSD/E and SSD1 have increased significantly over the original SSD |
| 747 |
< |
model (see fig. \ref{dense1}) and are in better agreement with the |
| 748 |
< |
experimental values. At 298 K, the densities of SSD/E and SSD1 without |
| 743 |
> |
Fig. \ref{ssdedense} shows the density profile for the SSD/E |
| 744 |
> |
model in comparison to SSD1 without a reaction field, other |
| 745 |
> |
common water models, and experimental results. The calculated |
| 746 |
> |
densities for both SSD/E and SSD1 have increased |
| 747 |
> |
significantly over the original SSD model (see |
| 748 |
> |
fig. \ref{dense1}) and are in better agreement with the experimental |
| 749 |
> |
values. At 298 K, the densities of SSD/E and SSD1 without |
| 750 |
|
a long-range correction are 0.996$\pm$0.001 g/cm$^3$ and |
| 751 |
|
0.999$\pm$0.001 g/cm$^3$ respectively. These both compare well with |
| 752 |
|
the experimental value of 0.997 g/cm$^3$, and they are considerably |
| 753 |
< |
better than the SSD value of 0.967$\pm$0.003 g/cm$^3$. The changes to |
| 754 |
< |
the dipole moment and sticky switching functions have improved the |
| 755 |
< |
structuring of the liquid (as seen in figure \ref{grcompare}, but they |
| 756 |
< |
have shifted the density maximum to much lower temperatures. This |
| 757 |
< |
comes about via an increase in the liquid disorder through the |
| 758 |
< |
weakening of the sticky potential and strengthening of the dipolar |
| 759 |
< |
character. However, this increasing disorder in the SSD/E model has |
| 760 |
< |
little effect on the melting transition. By monitoring $C_p$ |
| 761 |
< |
throughout these simulations, the melting transition for SSD/E was |
| 762 |
< |
shown to occur at 235 K. The same transition temperature observed |
| 763 |
< |
with SSD and SSD1. |
| 753 |
> |
better than the SSD value of 0.967$\pm$0.003 g/cm$^3$. The |
| 754 |
> |
changes to the dipole moment and sticky switching functions have |
| 755 |
> |
improved the structuring of the liquid (as seen in figure |
| 756 |
> |
\ref{grcompare}, but they have shifted the density maximum to much |
| 757 |
> |
lower temperatures. This comes about via an increase in the liquid |
| 758 |
> |
disorder through the weakening of the sticky potential and |
| 759 |
> |
strengthening of the dipolar character. However, this increasing |
| 760 |
> |
disorder in the SSD/E model has little effect on the melting |
| 761 |
> |
transition. By monitoring $C_p$ throughout these simulations, the |
| 762 |
> |
melting transition for SSD/E was shown to occur at 235 K. The |
| 763 |
> |
same transition temperature observed with SSD and SSD1. |
| 764 |
|
|
| 765 |
|
\begin{figure} |
| 766 |
|
\begin{center} |
| 767 |
|
\epsfxsize=6in |
| 768 |
|
\epsfbox{ssdrfDense.epsi} |
| 769 |
< |
\caption{Comparison of densities calculated with SSD/RF to SSD1 with a |
| 770 |
< |
reaction field, TIP3P [Ref. \citen{Jorgensen98b}], TIP5P |
| 771 |
< |
[Ref. \citen{Jorgensen00}], SPC/E [Ref. \citen{Clancy94}], and |
| 769 |
> |
\caption{Comparison of densities calculated with SSD/RF to |
| 770 |
> |
SSD1 with a reaction field, TIP3P [Ref. \citen{Jorgensen98b}], |
| 771 |
> |
TIP5P [Ref. \citen{Jorgensen00}], SPC/E [Ref. \citen{Clancy94}], and |
| 772 |
|
experiment [Ref. \citen{CRC80}]. The inset shows the necessity of |
| 773 |
|
reparameterization when utilizing a reaction field long-ranged |
| 774 |
< |
correction - SSD/RF provides significantly more accurate densities |
| 775 |
< |
than SSD1 when performing room temperature simulations.} |
| 774 |
> |
correction - SSD/RF provides significantly more accurate |
| 775 |
> |
densities than SSD1 when performing room temperature |
| 776 |
> |
simulations.} |
| 777 |
|
\label{ssdrfdense} |
| 778 |
|
\end{center} |
| 779 |
|
\end{figure} |
| 800 |
|
\begin{center} |
| 801 |
|
\epsfxsize=6in |
| 802 |
|
\epsfbox{ssdeDiffuse.epsi} |
| 803 |
< |
\caption{The diffusion constants calculated from SSD/E and SSD1, |
| 804 |
< |
both without a reaction field, along with experimental results |
| 805 |
< |
[Refs. \citen{Gillen72} and \citen{Holz00}]. The NVE calculations |
| 806 |
< |
were performed at the average densities observed in the 1 atm NPT |
| 807 |
< |
simulations for the respective models. SSD/E is slightly more mobile |
| 808 |
< |
than experiment at all of the temperatures, but it is closer to |
| 809 |
< |
experiment at biologically relavent temperatures than SSD1 without a |
| 810 |
< |
long-range correction.} |
| 803 |
> |
\caption{The diffusion constants calculated from SSD/E and |
| 804 |
> |
SSD1 (both without a reaction field) along with experimental results |
| 805 |
> |
[Refs. \citen{Gillen72} and \citen{Holz00}]. The NVE calculations were |
| 806 |
> |
performed at the average densities observed in the 1 atm NPT |
| 807 |
> |
simulations for the respective models. SSD/E is slightly more mobile |
| 808 |
> |
than experiment at all of the temperatures, but it is closer to |
| 809 |
> |
experiment at biologically relevant temperatures than SSD1 without a |
| 810 |
> |
long-range correction.} |
| 811 |
|
\label{ssdediffuse} |
| 812 |
|
\end{center} |
| 813 |
|
\end{figure} |
| 815 |
|
The reparameterization of the SSD water model, both for use with and |
| 816 |
|
without an applied long-range correction, brought the densities up to |
| 817 |
|
what is expected for simulating liquid water. In addition to improving |
| 818 |
< |
the densities, it is important that the excellent diffusive behavior |
| 819 |
< |
of SSD be maintained or improved. Figure \ref{ssdediffuse} compares |
| 820 |
< |
the temperature dependence of the diffusion constant of SSD/E to SSD1 |
| 821 |
< |
without an active reaction field at the densities calculated from the |
| 822 |
< |
NPT simulations at 1 atm. The diffusion constant for SSD/E is |
| 823 |
< |
consistently higher than experiment, while SSD1 remains lower than |
| 824 |
< |
experiment until relatively high temperatures (around 360 K). Both |
| 825 |
< |
models follow the shape of the experimental curve well below 300 K but |
| 826 |
< |
tend to diffuse too rapidly at higher temperatures, as seen in SSD1's |
| 827 |
< |
crossing above 360 K. This increasing diffusion relative to the |
| 828 |
< |
experimental values is caused by the rapidly decreasing system density |
| 829 |
< |
with increasing temperature. Both SSD1 and SSD/E show this deviation |
| 830 |
< |
in diffusive behavior, but this trend has different implications on |
| 831 |
< |
the diffusive behavior of the models. While SSD1 shows more |
| 832 |
< |
experimentally accurate diffusive behavior in the high temperature |
| 833 |
< |
regimes, SSD/E shows more accurate behavior in the supercooled and |
| 834 |
< |
biologically relavent temperature ranges. Thus, the changes made to |
| 835 |
< |
improve the liquid structure may have had an adverse affect on the |
| 836 |
< |
density maximum, but they improve the transport behavior of SSD/E |
| 837 |
< |
relative to SSD1 under the most commonly simulated conditions. |
| 818 |
> |
the densities, it is important that the diffusive behavior of SSD be |
| 819 |
> |
maintained or improved. Figure \ref{ssdediffuse} compares the |
| 820 |
> |
temperature dependence of the diffusion constant of SSD/E to SSD1 |
| 821 |
> |
without an active reaction field at the densities calculated from |
| 822 |
> |
their respective NPT simulations at 1 atm. The diffusion constant for |
| 823 |
> |
SSD/E is consistently higher than experiment, while SSD1 remains lower |
| 824 |
> |
than experiment until relatively high temperatures (around 360 |
| 825 |
> |
K). Both models follow the shape of the experimental curve well below |
| 826 |
> |
300 K but tend to diffuse too rapidly at higher temperatures, as seen |
| 827 |
> |
in SSD1's crossing above 360 K. This increasing diffusion relative to |
| 828 |
> |
the experimental values is caused by the rapidly decreasing system |
| 829 |
> |
density with increasing temperature. Both SSD1 and SSD/E show this |
| 830 |
> |
deviation in particle mobility, but this trend has different |
| 831 |
> |
implications on the diffusive behavior of the models. While SSD1 |
| 832 |
> |
shows more experimentally accurate diffusive behavior in the high |
| 833 |
> |
temperature regimes, SSD/E shows more accurate behavior in the |
| 834 |
> |
supercooled and biologically relevant temperature ranges. Thus, the |
| 835 |
> |
changes made to improve the liquid structure may have had an adverse |
| 836 |
> |
affect on the density maximum, but they improve the transport behavior |
| 837 |
> |
of SSD/E relative to SSD1 under the most commonly simulated |
| 838 |
> |
conditions. |
| 839 |
|
|
| 840 |
|
\begin{figure} |
| 841 |
|
\begin{center} |
| 842 |
|
\epsfxsize=6in |
| 843 |
|
\epsfbox{ssdrfDiffuse.epsi} |
| 844 |
< |
\caption{The diffusion constants calculated from SSD/RF and SSD1, |
| 845 |
< |
both with an active reaction field, along with experimental results |
| 846 |
< |
[Refs. \citen{Gillen72} and \citen{Holz00}]. The NVE calculations |
| 847 |
< |
were performed at the average densities observed in the 1 atm NPT |
| 848 |
< |
simulations for both of the models. Note how accurately SSD/RF |
| 849 |
< |
simulates the diffusion of water throughout this temperature |
| 850 |
< |
range. The more rapidly increasing diffusion constants at high |
| 851 |
< |
temperatures for both models is attributed to lower calculated |
| 852 |
< |
densities than those observed in experiment.} |
| 844 |
> |
\caption{The diffusion constants calculated from SSD/RF and |
| 845 |
> |
SSD1 (both with an active reaction field) along with |
| 846 |
> |
experimental results [Refs. \citen{Gillen72} and \citen{Holz00}]. The |
| 847 |
> |
NVE calculations were performed at the average densities observed in |
| 848 |
> |
the 1 atm NPT simulations for both of the models. SSD/RF |
| 849 |
> |
simulates the diffusion of water throughout this temperature range |
| 850 |
> |
very well. The rapidly increasing diffusion constants at high |
| 851 |
> |
temperatures for both models can be attributed to lower calculated |
| 852 |
> |
densities than those observed in experiment.} |
| 853 |
|
\label{ssdrfdiffuse} |
| 854 |
|
\end{center} |
| 855 |
|
\end{figure} |
| 868 |
|
reparameterization when using an altered long-range correction. |
| 869 |
|
|
| 870 |
|
\begin{table} |
| 871 |
+ |
\begin{minipage}{\linewidth} |
| 872 |
+ |
\renewcommand{\thefootnote}{\thempfootnote} |
| 873 |
|
\begin{center} |
| 874 |
< |
\caption{Calculated and experimental properties of the single point waters and liquid water at 298 K and 1 atm. (a) Ref. [\citen{Mills73}]. (b) Calculated by integrating the data in ref. \citen{Head-Gordon00_1}. (c) Calculated by integrating the data in ref. \citen{Soper86}. (d) Ref. [\citen{Eisenberg69}]. (e) Calculated for 298 K from data in ref. \citen{Krynicki66}.} |
| 874 |
> |
\caption{Properties of the single-point water models compared with |
| 875 |
> |
experimental data at ambient conditions} |
| 876 |
|
\begin{tabular}{ l c c c c c } |
| 877 |
|
\hline \\[-3mm] |
| 878 |
|
\ \ \ \ \ \ & \ \ \ SSD1 \ \ \ & \ SSD/E \ \ \ & \ SSD1 (RF) \ \ |
| 880 |
|
\hline \\[-3mm] |
| 881 |
|
\ \ \ $\rho$ (g/cm$^3$) & 0.999 $\pm$0.001 & 0.996 $\pm$0.001 & 0.972 $\pm$0.002 & 0.997 $\pm$0.001 & 0.997 \\ |
| 882 |
|
\ \ \ $C_p$ (cal/mol K) & 28.80 $\pm$0.11 & 25.45 $\pm$0.09 & 28.28 $\pm$0.06 & 23.83 $\pm$0.16 & 17.98 \\ |
| 883 |
< |
\ \ \ $D$ ($10^{-5}$ cm$^2$/s) & 1.78 $\pm$0.07 & 2.51 $\pm$0.18 & 2.00 $\pm$0.17 & 2.32 $\pm$0.06 & 2.299$^\text{a}$ \\ |
| 884 |
< |
\ \ \ Coordination Number & 3.9 & 4.3 & 3.8 & 4.4 & 4.7$^\text{b}$ \\ |
| 885 |
< |
\ \ \ H-bonds per particle & 3.7 & 3.6 & 3.7 & 3.7 & 3.4$^\text{c}$ \\ |
| 886 |
< |
\ \ \ $\tau_1^\mu$ (ps) & 10.9 $\pm$0.6 & 7.3 $\pm$0.4 & 7.5 $\pm$0.7 & 7.2 $\pm$0.4 & 4.76$^\text{d}$ \\ |
| 887 |
< |
\ \ \ $\tau_2^\mu$ (ps) & 4.7 $\pm$0.4 & 3.1 $\pm$0.2 & 3.5 $\pm$0.3 & 3.2 $\pm$0.2 & 2.3$^\text{e}$ \\ |
| 883 |
> |
\ \ \ $D$ ($10^{-5}$ cm$^2$/s) & 1.78 $\pm$0.07 & 2.51 $\pm$0.18 & |
| 884 |
> |
2.00 $\pm$0.17 & 2.32 $\pm$0.06 & 2.299\cite{Mills73} \\ |
| 885 |
> |
\ \ \ Coordination Number ($n_C$) & 3.9 & 4.3 & 3.8 & 4.4 & |
| 886 |
> |
4.7\footnote{Calculated by integrating $g_{\text{OO}}(r)$ in |
| 887 |
> |
Ref. \citen{Head-Gordon00_1}} \\ |
| 888 |
> |
\ \ \ H-bonds per particle ($n_H$) & 3.7 & 3.6 & 3.7 & 3.7 & |
| 889 |
> |
3.5\footnote{Calculated by integrating $g_{\text{OH}}(r)$ in |
| 890 |
> |
Ref. \citen{Soper86}} \\ |
| 891 |
> |
\ \ \ $\tau_1$ (ps) & 10.9 $\pm$0.6 & 7.3 $\pm$0.4 & 7.5 $\pm$0.7 & |
| 892 |
> |
7.2 $\pm$0.4 & 5.7\footnote{Calculated for 298 K from data in Ref. \citen{Eisenberg69}} \\ |
| 893 |
> |
\ \ \ $\tau_2$ (ps) & 4.7 $\pm$0.4 & 3.1 $\pm$0.2 & 3.5 $\pm$0.3 & 3.2 |
| 894 |
> |
$\pm$0.2 & 2.3\footnote{Calculated for 298 K from data in |
| 895 |
> |
Ref. \citen{Krynicki66}} |
| 896 |
|
\end{tabular} |
| 897 |
|
\label{liquidproperties} |
| 898 |
|
\end{center} |
| 899 |
+ |
\end{minipage} |
| 900 |
|
\end{table} |
| 901 |
|
|
| 902 |
|
Table \ref{liquidproperties} gives a synopsis of the liquid state |
| 903 |
|
properties of the water models compared in this study along with the |
| 904 |
|
experimental values for liquid water at ambient conditions. The |
| 905 |
< |
coordination number and hydrogen bonds per particle were calculated by |
| 906 |
< |
integrating the following relation: |
| 905 |
> |
coordination number ($n_C$) and number of hydrogen bonds per particle |
| 906 |
> |
($n_H$) were calculated by integrating the following relations: |
| 907 |
|
\begin{equation} |
| 908 |
< |
4\pi\rho\int_{0}^{a}r^2\text{g}(r)dr, |
| 908 |
> |
n_C = 4\pi\rho_{\text{OO}}\int_{0}^{a}r^2\text{g}_{\text{OO}}(r)dr, |
| 909 |
|
\end{equation} |
| 910 |
< |
where $\rho$ is the number density of pair interactions, $a$ is the |
| 911 |
< |
radial location of the minima following the first solvation shell |
| 912 |
< |
peak, and g$(r)$ is either g$_\text{OO}(r)$ or g$_\text{OH}(r)$ for |
| 913 |
< |
calculation of the coordination number or hydrogen bonds per particle |
| 914 |
< |
respectively. The number of hydrogen bonds stays relatively constant |
| 915 |
< |
across all of the models, but the coordination numbers of SSD/E and |
| 916 |
< |
SSD/RF show an improvement over SSD1. This improvement is primarily |
| 917 |
< |
due to the widening of the first solvation shell peak, allowing the |
| 918 |
< |
first minima to push outward. Comparing the coordination number with |
| 919 |
< |
the number of hydrogen bonds can lead to more insight into the |
| 920 |
< |
structural character of the liquid. Because of the near identical |
| 921 |
< |
values for SSD1, it appears to be a little too exclusive, in that all |
| 922 |
< |
molecules in the first solvation shell are involved in forming ideal |
| 923 |
< |
hydrogen bonds. The differing numbers for the newly parameterized |
| 924 |
< |
models indicate the allowance of more fluid configurations in addition |
| 925 |
< |
to the formation of an acceptable number of ideal hydrogen bonds. |
| 910 |
> |
\begin{equation} |
| 911 |
> |
n_H = 4\pi\rho_{\text{OH}}\int_{0}^{b}r^2\text{g}_{\text{OH}}(r)dr, |
| 912 |
> |
\end{equation} |
| 913 |
> |
where $\rho$ is the number density of the specified pair interactions, |
| 914 |
> |
$a$ and $b$ are the radial locations of the minima following the first |
| 915 |
> |
peak in g$_\text{OO}(r)$ or g$_\text{OH}(r)$ respectively. The number |
| 916 |
> |
of hydrogen bonds stays relatively constant across all of the models, |
| 917 |
> |
but the coordination numbers of SSD/E and SSD/RF show an |
| 918 |
> |
improvement over SSD1. This improvement is primarily due to |
| 919 |
> |
extension of the first solvation shell in the new parameter sets. |
| 920 |
> |
Because $n_H$ and $n_C$ are nearly identical in SSD1, it appears |
| 921 |
> |
that all molecules in the first solvation shell are involved in |
| 922 |
> |
hydrogen bonds. Since $n_H$ and $n_C$ differ in the newly |
| 923 |
> |
parameterized models, the orientations in the first solvation shell |
| 924 |
> |
are a bit more ``fluid''. Therefore SSD1 overstructures the |
| 925 |
> |
first solvation shell and our reparameterizations have returned this |
| 926 |
> |
shell to more realistic liquid-like behavior. |
| 927 |
|
|
| 928 |
< |
The time constants for the self orientational autocorrelation function |
| 928 |
> |
The time constants for the orientational autocorrelation functions |
| 929 |
|
are also displayed in Table \ref{liquidproperties}. The dipolar |
| 930 |
< |
orientational time correlation function ($\Gamma_{l}$) is described |
| 930 |
> |
orientational time correlation functions ($C_{l}$) are described |
| 931 |
|
by: |
| 932 |
|
\begin{equation} |
| 933 |
< |
\Gamma_{l}(t) = \langle P_l[\mathbf{u}_j(0)\cdot\mathbf{u}_j(t)]\rangle, |
| 933 |
> |
C_{l}(t) = \langle P_l[\hat{\mathbf{u}}_j(0)\cdot\hat{\mathbf{u}}_j(t)]\rangle, |
| 934 |
|
\end{equation} |
| 935 |
< |
where $P_l$ is a Legendre polynomial of order $l$ and $\mathbf{u}_j$ |
| 936 |
< |
is the unit vector of the particle dipole.\cite{Rahman71} From these |
| 937 |
< |
correlation functions, the orientational relaxation time of the dipole |
| 938 |
< |
vector can be calculated from an exponential fit in the long-time |
| 939 |
< |
regime ($t > \tau_l^\mu$).\cite{Rothschild84} Calculation of these |
| 940 |
< |
time constants were averaged from five detailed NVE simulations |
| 941 |
< |
performed at the STP density for each of the respective models. Again, |
| 942 |
< |
SSD/E and SSD/RF show improved behavior over SSD1 both with and |
| 943 |
< |
without an active reaction field. Numbers published from the original |
| 944 |
< |
SSD dynamics studies appear closer to the experimental values, and we |
| 945 |
< |
attribute this discrepancy to the implimentation of an Ewald sum |
| 946 |
< |
versus a reaction field. |
| 935 |
> |
where $P_l$ are Legendre polynomials of order $l$ and |
| 936 |
> |
$\hat{\mathbf{u}}_j$ is the unit vector pointing along the molecular |
| 937 |
> |
dipole.\cite{Rahman71} From these correlation functions, the |
| 938 |
> |
orientational relaxation time of the dipole vector can be calculated |
| 939 |
> |
from an exponential fit in the long-time regime ($t > |
| 940 |
> |
\tau_l$).\cite{Rothschild84} Calculation of these time constants were |
| 941 |
> |
averaged over five detailed NVE simulations performed at the ambient |
| 942 |
> |
conditions for each of the respective models. It should be noted that |
| 943 |
> |
the commonly cited value of 1.9 ps for $\tau_2$ was determined from |
| 944 |
> |
the NMR data in Ref. \citen{Krynicki66} at a temperature near |
| 945 |
> |
34$^\circ$C.\cite{Rahman71} Because of the strong temperature |
| 946 |
> |
dependence of $\tau_2$, it is necessary to recalculate it at 298 K to |
| 947 |
> |
make proper comparisons. The value shown in Table |
| 948 |
> |
\ref{liquidproperties} was calculated from the same NMR data in the |
| 949 |
> |
fashion described in Ref. \citen{Krynicki66}. Similarly, $\tau_1$ was |
| 950 |
> |
recomputed for 298 K from the data in Ref. \citen{Eisenberg69}. |
| 951 |
> |
Again, SSD/E and SSD/RF show improved behavior over SSD1, both with |
| 952 |
> |
and without an active reaction field. Turning on the reaction field |
| 953 |
> |
leads to much improved time constants for SSD1; however, these results |
| 954 |
> |
also include a corresponding decrease in system density. |
| 955 |
> |
Orientational relaxation times published in the original SSD dynamics |
| 956 |
> |
papers are smaller than the values observed here, and this difference |
| 957 |
> |
can be attributed to the use of the Ewald sum.\cite{Ichiye99} |
| 958 |
|
|
| 959 |
|
\subsection{Additional Observations} |
| 960 |
|
|
| 961 |
|
\begin{figure} |
| 962 |
|
\begin{center} |
| 963 |
|
\epsfxsize=6in |
| 964 |
< |
\epsfbox{povIce.ps} |
| 965 |
< |
\caption{A water lattice built from the crystal structure assumed by |
| 966 |
< |
SSD/E when undergoing an extremely restricted temperature NPT |
| 967 |
< |
simulation. This form of ice is referred to as ice-{\it i} to |
| 968 |
< |
emphasize its simulation origins. This image was taken of the (001) |
| 939 |
< |
face of the crystal.} |
| 964 |
> |
\epsfbox{icei_bw.eps} |
| 965 |
> |
\caption{The most stable crystal structure assumed by the SSD family |
| 966 |
> |
of water models. We refer to this structure as Ice-{\it i} to |
| 967 |
> |
indicate its origins in computer simulation. This image was taken of |
| 968 |
> |
the (001) face of the crystal.} |
| 969 |
|
\label{weirdice} |
| 970 |
|
\end{center} |
| 971 |
|
\end{figure} |
| 972 |
|
|
| 973 |
|
While performing a series of melting simulations on an early iteration |
| 974 |
< |
of SSD/E not discussed in this paper, we observed recrystallization |
| 975 |
< |
into a novel structure not previously known for water. After melting |
| 976 |
< |
at 235 K, two of five systems underwent crystallization events near |
| 977 |
< |
245 K. The two systems remained crystalline up to 320 and 330 K, |
| 978 |
< |
respectively. The crystal exhibits an expanded zeolite-like structure |
| 979 |
< |
that does not correspond to any known form of ice. This appears to be |
| 980 |
< |
an artifact of the point dipolar models, so to distinguish it from the |
| 981 |
< |
experimentally observed forms of ice, we have denoted the structure |
| 982 |
< |
Ice-$\sqrt{\smash[b]{-\text{I}}}$ (ice-{\it i}). A large enough |
| 974 |
> |
of SSD/E not discussed in this paper, we observed |
| 975 |
> |
recrystallization into a novel structure not previously known for |
| 976 |
> |
water. After melting at 235 K, two of five systems underwent |
| 977 |
> |
crystallization events near 245 K. The two systems remained |
| 978 |
> |
crystalline up to 320 and 330 K, respectively. The crystal exhibits |
| 979 |
> |
an expanded zeolite-like structure that does not correspond to any |
| 980 |
> |
known form of ice. This appears to be an artifact of the point |
| 981 |
> |
dipolar models, so to distinguish it from the experimentally observed |
| 982 |
> |
forms of ice, we have denoted the structure |
| 983 |
> |
Ice-$\sqrt{\smash[b]{-\text{I}}}$ (Ice-{\it i}). A large enough |
| 984 |
|
portion of the sample crystallized that we have been able to obtain a |
| 985 |
< |
near ideal crystal structure of ice-{\it i}. Figure \ref{weirdice} |
| 985 |
> |
near ideal crystal structure of Ice-{\it i}. Figure \ref{weirdice} |
| 986 |
|
shows the repeating crystal structure of a typical crystal at 5 |
| 987 |
|
K. Each water molecule is hydrogen bonded to four others; however, the |
| 988 |
|
hydrogen bonds are bent rather than perfectly straight. This results |
| 993 |
|
configuration. Though not ideal, these flexed hydrogen bonds are |
| 994 |
|
favorable enough to stabilize an entire crystal generated around them. |
| 995 |
|
|
| 996 |
< |
Initial simulations indicated that ice-{\it i} is the preferred ice |
| 996 |
> |
Initial simulations indicated that Ice-{\it i} is the preferred ice |
| 997 |
|
structure for at least the SSD/E model. To verify this, a comparison |
| 998 |
|
was made between near ideal crystals of ice~$I_h$, ice~$I_c$, and |
| 999 |
< |
ice-{\it i} at constant pressure with SSD/E, SSD/RF, and |
| 999 |
> |
Ice-{\it i} at constant pressure with SSD/E, SSD/RF, and |
| 1000 |
|
SSD1. Near-ideal versions of the three types of crystals were cooled |
| 1001 |
< |
to 1 K, and the enthalpies of each were compared using all three water |
| 1002 |
< |
models. With every model in the SSD family, ice-{\it i} had the lowest |
| 1003 |
< |
calculated enthalpy: 5\% lower than $I_h$ with SSD1, 6.5\% lower with |
| 1004 |
< |
SSD/E, and 7.5\% lower with SSD/RF. The enthalpy data is summarized |
| 1005 |
< |
in Table \ref{iceenthalpy}. |
| 1001 |
> |
to 1 K, and enthalpies of formation of each were compared using all |
| 1002 |
> |
three water models. Enthalpies were estimated from the |
| 1003 |
> |
isobaric-isothermal simulations using $H=U+P_{\text ext}V$ where |
| 1004 |
> |
$P_{\text ext}$ is the applied pressure. A constant value of -60.158 |
| 1005 |
> |
kcal / mol has been added to place our zero for the enthalpies of |
| 1006 |
> |
formation for these systems at the traditional state (elemental forms |
| 1007 |
> |
at standard temperature and pressure). With every model in the SSD |
| 1008 |
> |
family, Ice-{\it i} had the lowest calculated enthalpy of formation. |
| 1009 |
|
|
| 1010 |
|
\begin{table} |
| 1011 |
|
\begin{center} |
| 1012 |
< |
\caption{Enthalpies (in kcal / mol) of the three crystal structures (at 1 |
| 1013 |
< |
K) exhibited by the SSD family of water models} |
| 1012 |
> |
\caption{Enthalpies of Formation (in kcal / mol) of the three crystal |
| 1013 |
> |
structures (at 1 K) exhibited by the SSD family of water models} |
| 1014 |
|
\begin{tabular}{ l c c c } |
| 1015 |
|
\hline \\[-3mm] |
| 1016 |
|
\ \ \ Water Model \ \ \ & \ \ \ Ice-$I_h$ \ \ \ & \ Ice-$I_c$\ \ & \ |
| 1017 |
|
Ice-{\it i} \\ |
| 1018 |
|
\hline \\[-3mm] |
| 1019 |
< |
\ \ \ SSD/E & -12.286 & -12.292 & -13.590 \\ |
| 1020 |
< |
\ \ \ SSD/RF & -12.935 & -12.917 & -14.022 \\ |
| 1021 |
< |
\ \ \ SSD1 & -12.496 & -12.411 & -13.417 \\ |
| 1022 |
< |
\ \ \ SSD1 (RF) & -12.504 & -12.411 & -13.134 \\ |
| 1019 |
> |
\ \ \ SSD/E & -72.444 & -72.450 & -73.748 \\ |
| 1020 |
> |
\ \ \ SSD/RF & -73.093 & -73.075 & -74.180 \\ |
| 1021 |
> |
\ \ \ SSD1 & -72.654 & -72.569 & -73.575 \\ |
| 1022 |
> |
\ \ \ SSD1 (RF) & -72.662 & -72.569 & -73.292 \\ |
| 1023 |
|
\end{tabular} |
| 1024 |
|
\label{iceenthalpy} |
| 1025 |
|
\end{center} |
| 1037 |
|
\section{Conclusions} |
| 1038 |
|
|
| 1039 |
|
The density maximum and temperature dependence of the self-diffusion |
| 1040 |
< |
constant were studied for the SSD water model, both with and without |
| 1041 |
< |
the use of reaction field, via a series of NPT and NVE |
| 1040 |
> |
constant were studied for the SSD water model, both with and |
| 1041 |
> |
without the use of reaction field, via a series of NPT and NVE |
| 1042 |
|
simulations. The constant pressure simulations showed a density |
| 1043 |
|
maximum near 260 K. In most cases, the calculated densities were |
| 1044 |
|
significantly lower than the densities obtained from other water |
| 1045 |
< |
models (and experiment). Analysis of self-diffusion showed SSD to |
| 1046 |
< |
capture the transport properties of water well in both the liquid and |
| 1047 |
< |
super-cooled liquid regimes. |
| 1045 |
> |
models (and experiment). Analysis of self-diffusion showed SSD |
| 1046 |
> |
to capture the transport properties of water well in both the liquid |
| 1047 |
> |
and supercooled liquid regimes. |
| 1048 |
|
|
| 1049 |
|
In order to correct the density behavior, the original SSD model was |
| 1050 |
|
reparameterized for use both with and without a reaction field (SSD/RF |
| 1058 |
|
simulations of biochemical systems. |
| 1059 |
|
|
| 1060 |
|
The existence of a novel low-density ice structure that is preferred |
| 1061 |
< |
by the SSD family of water models is somewhat troubling, since liquid |
| 1062 |
< |
simulations on this family of water models at room temperature are |
| 1063 |
< |
effectively simulations of super-cooled or metastable liquids. One |
| 1064 |
< |
way to de-stabilize this unphysical ice structure would be to make the |
| 1061 |
> |
by the SSD family of water models is somewhat troubling, since |
| 1062 |
> |
liquid simulations on this family of water models at room temperature |
| 1063 |
> |
are effectively simulations of supercooled or metastable liquids. One |
| 1064 |
> |
way to destabilize this unphysical ice structure would be to make the |
| 1065 |
|
range of angles preferred by the attractive part of the sticky |
| 1066 |
|
potential much narrower. This would require extensive |
| 1067 |
|
reparameterization to maintain the same level of agreement with the |
| 1068 |
|
experiments. |
| 1069 |
|
|
| 1070 |
< |
Additionally, our initial calculations show that the ice-{\it i} |
| 1070 |
> |
Additionally, our initial calculations show that the Ice-{\it i} |
| 1071 |
|
structure may also be a preferred crystal structure for at least one |
| 1072 |
|
other popular multi-point water model (TIP3P), and that much of the |
| 1073 |
|
simulation work being done using this popular model could also be at |
