trunk/oopsePaper/ssd.tex

\section{\label{sec:SSD}Water Model: SSD and Derivatives}

In the interest of computational efficiency, the native solvent used
in {\sc oopse} is the Soft Sticky Dipole (SSD) water model. SSD was
developed by Ichiye \emph{et al.} as a modified form of the
hard-sphere water model proposed by Bratko, Blum, and
Luzar.\cite{Bratko85,Bratko95} It consists of a single point dipole
with a Lennard-Jones core and a sticky potential that directs the
particles to assume the proper hydrogen bond orientation in the first
solvation shell. Thus, the interaction between two SSD water molecules
\emph{i} and \emph{j} is given by the potential
\begin{equation}
u_{ij} = u_{ij}^{LJ} (r_{ij})\ + u_{ij}^{dp}
(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)\ +
u_{ij}^{sp}
(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j),
\end{equation}
where the $\mathbf{r}_{ij}$ is the position vector between molecules
\emph{i} and \emph{j} with magnitude equal to the distance $r_ij$, and
$\boldsymbol{\Omega}_i$ and $\boldsymbol{\Omega}_j$ represent the
orientations of the respective molecules. The Lennard-Jones, dipole,
and sticky parts of the potential are giving by the following
equations,
\begin{equation}
u_{ij}^{LJ}(r_{ij}) = 4\epsilon \left[\left(\frac{\sigma}{r_{ij}}\right)^{12}-\left(\frac{\sigma}{r_{ij}}\right)^{6}\right],
\end{equation}
\begin{equation}
u_{ij}^{dp} = \frac{\boldsymbol{\mu}_i\cdot\boldsymbol{\mu}_j}{r_{ij}^3}-\frac{3(\boldsymbol{\mu}_i\cdot\mathbf{r}_{ij})(\boldsymbol{\mu}_j\cdot\mathbf{r}_{ij})}{r_{ij}^5}\ ,
\end{equation}
\begin{equation}
\begin{split}
u_{ij}^{sp}
(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j) 
&=
\frac{\nu_0}{2}[s(r_{ij})w(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)\\
& \quad \ +
s^\prime(r_{ij})w^\prime(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)]\ ,
\end{split}
\end{equation}
where $\boldsymbol{\mu}_i$ and $\boldsymbol{\mu}_j$ are the dipole
unit vectors of particles \emph{i} and \emph{j} with magnitude 2.35 D,
$\nu_0$ scales the strength of the overall sticky potential, $s$ and
$s^\prime$ are cubic switching functions. The $w$ and $w^\prime$
functions take the following forms,
\begin{equation}
w(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)=\sin\theta_{ij}\sin2\theta_{ij}\cos2\phi_{ij},
\end{equation}
\begin{equation}
w^\prime(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j) = (\cos\theta_{ij}-0.6)^2(\cos\theta_{ij}+0.8)^2-w^0,
\end{equation}
where $w^0 = 0.07715$. The $w$ function is the tetrahedral attractive
term that promotes hydrogen bonding orientations within the first
solvation shell, and $w^\prime$ is a dipolar repulsion term that
repels unrealistic dipolar arrangements within the first solvation
shell. A more detailed description of the functional parts and
variables in this potential can be found in other
articles.\cite{liu96:new_model,chandra99:ssd_md}

Since SSD is a one-site point dipole model, the force calculations are
simplified significantly from a computational standpoint, in that the
number of long-range interactions is dramatically reduced. In the
original Monte Carlo simulations using this model, Ichiye \emph{et
al.} reported a calculation speed up of up to an order of magnitude
over other comparable models while maintaining the structural behavior
of water.\cite{liu96:new_model} In the original molecular dynamics studies of
SSD, it was shown that it actually improves upon the prediction of
water's dynamical properties over TIP3P and SPC/E.\cite{chandra99:ssd_md}

Recent constant pressure simulations revealed issues in the original
SSD model that led to lower than expected densities at all target
pressures.\cite{Ichiye03,Gezelter04} Reparameterizations of the
original SSD have resulted in improved density behavior, as well as
alterations in the water structure and transport behavior. {\sc oopse} is
easily modified to impliment these new potential parameter sets for
the derivative water models: SSD1, SSD/E, and SSD/RF. All of the
variable parameters are listed in the accompanying BASS file, and
these parameters simply need to be changed to the updated values.
Revision:	818
Committed:	Fri Oct 24 21:27:59 2003 UTC (21 years, 8 months ago) by gezelter
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#	User	Rev	Content
1	chrisfen	765	\section{\label{sec:SSD}Water Model: SSD and Derivatives}
2
3			In the interest of computational efficiency, the native solvent used
4	gezelter	818	in {\sc oopse} is the Soft Sticky Dipole (SSD) water model. SSD was
5	chrisfen	765	developed by Ichiye \emph{et al.} as a modified form of the
6			hard-sphere water model proposed by Bratko, Blum, and
7			Luzar.\cite{Bratko85,Bratko95} It consists of a single point dipole
8			with a Lennard-Jones core and a sticky potential that directs the
9			particles to assume the proper hydrogen bond orientation in the first
10			solvation shell. Thus, the interaction between two SSD water molecules
11			\emph{i} and \emph{j} is given by the potential
12			\begin{equation}
13			u_{ij} = u_{ij}^{LJ} (r_{ij})\ + u_{ij}^{dp}
14			(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)\ +
15			u_{ij}^{sp}
16			(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j),
17			\end{equation}
18			where the $\mathbf{r}_{ij}$ is the position vector between molecules
19			\emph{i} and \emph{j} with magnitude equal to the distance $r_ij$, and
20			$\boldsymbol{\Omega}_i$ and $\boldsymbol{\Omega}_j$ represent the
21			orientations of the respective molecules. The Lennard-Jones, dipole,
22			and sticky parts of the potential are giving by the following
23			equations,
24			\begin{equation}
25			u_{ij}^{LJ}(r_{ij}) = 4\epsilon \left[\left(\frac{\sigma}{r_{ij}}\right)^{12}-\left(\frac{\sigma}{r_{ij}}\right)^{6}\right],
26			\end{equation}
27			\begin{equation}
28			u_{ij}^{dp} = \frac{\boldsymbol{\mu}_i\cdot\boldsymbol{\mu}_j}{r_{ij}^3}-\frac{3(\boldsymbol{\mu}_i\cdot\mathbf{r}_{ij})(\boldsymbol{\mu}_j\cdot\mathbf{r}_{ij})}{r_{ij}^5}\ ,
29			\end{equation}
30			\begin{equation}
31			\begin{split}
32			u_{ij}^{sp}
33			(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)
34			&=
35			\frac{\nu_0}{2}[s(r_{ij})w(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)\\
36			& \quad \ +
37			s^\prime(r_{ij})w^\prime(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)]\ ,
38			\end{split}
39			\end{equation}
40			where $\boldsymbol{\mu}_i$ and $\boldsymbol{\mu}_j$ are the dipole
41			unit vectors of particles \emph{i} and \emph{j} with magnitude 2.35 D,
42			$\nu_0$ scales the strength of the overall sticky potential, $s$ and
43			$s^\prime$ are cubic switching functions. The $w$ and $w^\prime$
44			functions take the following forms,
45			\begin{equation}
46			w(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)=\sin\theta_{ij}\sin2\theta_{ij}\cos2\phi_{ij},
47			\end{equation}
48			\begin{equation}
49			w^\prime(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j) = (\cos\theta_{ij}-0.6)^2(\cos\theta_{ij}+0.8)^2-w^0,
50			\end{equation}
51			where $w^0 = 0.07715$. The $w$ function is the tetrahedral attractive
52			term that promotes hydrogen bonding orientations within the first
53			solvation shell, and $w^\prime$ is a dipolar repulsion term that
54			repels unrealistic dipolar arrangements within the first solvation
55			shell. A more detailed description of the functional parts and
56			variables in this potential can be found in other
57			articles.\cite{liu96:new_model,chandra99:ssd_md}
58
59			Since SSD is a one-site point dipole model, the force calculations are
60			simplified significantly from a computational standpoint, in that the
61			number of long-range interactions is dramatically reduced. In the
62			original Monte Carlo simulations using this model, Ichiye \emph{et
63			al.} reported a calculation speed up of up to an order of magnitude
64			over other comparable models while maintaining the structural behavior
65			of water.\cite{liu96:new_model} In the original molecular dynamics studies of
66			SSD, it was shown that it actually improves upon the prediction of
67			water's dynamical properties over TIP3P and SPC/E.\cite{chandra99:ssd_md}
68
69			Recent constant pressure simulations revealed issues in the original
70			SSD model that led to lower than expected densities at all target
71			pressures.\cite{Ichiye03,Gezelter04} Reparameterizations of the
72			original SSD have resulted in improved density behavior, as well as
73	gezelter	818	alterations in the water structure and transport behavior. {\sc oopse} is
74	chrisfen	765	easily modified to impliment these new potential parameter sets for
75			the derivative water models: SSD1, SSD/E, and SSD/RF. All of the
76			variable parameters are listed in the accompanying BASS file, and
77			these parameters simply need to be changed to the updated values.