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\begin{document} |
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\title{On the temperature dependent structural and transport properties of the soft sticky dipole (SSD) and related single point water models} |
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\title{On the temperature dependent properties of the soft sticky dipole (SSD) and related single point water models} |
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\author{Christopher J. Fennell and J. Daniel Gezelter{\thefootnote} |
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\footnote[1]{Corresponding author. \ Electronic mail: gezelter@nd.edu}} |
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systems, the Ewald summation and even particle-mesh Ewald become |
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computational burdens with their respective ideal $N^\frac{3}{2}$ and |
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$N\log N$ calculation scaling orders for $N$ particles.\cite{Darden99} |
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Up to this point, a detailed look at the model's structure and ion |
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solvation abilities has been performed.\cite{Ichiye96} In addition, a |
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thorough investigation of the dynamic properties of SSD was performed |
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by Chandra and Ichiye focusing on translational and orientational |
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properties at 298 K.\cite{Ichiye99} This study focuses on determining |
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the density maximum for SSD utilizing both microcanonical and |
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isobaric-isothermal ensemble molecular dynamics, while using the |
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reaction field method for handling long-ranged dipolar interactions. A |
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reaction field method has been previously implemented in Monte Carlo |
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simulations by Liu and Ichiye in order to study the static dielectric |
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constant for the model.\cite{Ichiye96b} This paper will expand the |
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scope of these original simulations to look on how the reaction field |
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affects the physical and dynamic properties of SSD systems. |
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In applying this water model in these types of systems, it would be |
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useful to know its properties and behavior with the more |
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computationally efficient reaction field (RF) technique, and even with |
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a cutoff that lacks any form of long range correction. This study |
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addresses these issues by looking at the structural and transport |
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behavior of SSD over a variety of temperatures, with the purpose of |
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utilizing the RF correction technique. Towards the end, we suggest |
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alterations to the parameters that result in more water-like |
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behavior. It should be noted that in a recent publication, some the |
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original investigators of the SSD water model have put forth |
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adjustments to the original SSD water model to address abnormal |
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density behavior (also observed here), calling the corrected model |
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SSD1.\cite{Ichiye03} This study will consider this new model's |
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behavior as well, and hopefully improve upon its depiction of water |
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under conditions without the Ewald Sum. |
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\section{Methods} |
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nine elements long as opposed to 3 or 4 elements for Euler angles and |
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quaternions respectively. System memory has become much less of an |
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issue in recent times, and this has resulted in substantial benefits |
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in energy conservation. There is still the issue of an additional 5 or |
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6 additional elements for describing the orientation of each particle, |
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which will increase dump files substantially. Simply translating the |
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rotation matrix into its component Euler angles or quaternions for |
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storage purposes relieves this burden. |
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in energy conservation. There is still the issue of 5 or 6 additional |
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elements for describing the orientation of each particle, which will |
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increase dump files substantially. Simply translating the rotation |
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matrix into its component Euler angles or quaternions for storage |
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purposes relieves this burden. |
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The symplectic splitting method allows for Verlet style integration of |
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both linear and angular motion of rigid bodies. In the integration |
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evaluations to update the rotation matrix.\cite{Dullweber1997} These |
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matrix rotations end up being more costly computationally than the |
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simpler arithmetic quaternion propagation. On average, a 1000 SSD |
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particle simulation shows a 7\% increase in simulation time using the |
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particle simulation shows a 7\% increase in computation time using the |
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symplectic step method in place of quaternions. This cost is more than |
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justified when comparing the energy conservation of the two methods as |
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illustrated in figure \ref{timestep}. |
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illustrated in figure \ref{timestep}. |
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\begin{figure} |
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\includegraphics[width=61mm, angle=-90]{timeStep.epsi} |
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with the quaternion method showing a slight energy drift over time in |
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the 0.5 fs time step simulation. At time steps of 1 and 2 fs, the |
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energy conservation benefits of the symplectic step method are clearly |
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demonstrated. |
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demonstrated. Thus, while maintaining the same degree of energy |
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conservation, one can take considerably longer time steps, leading to |
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an overall reduction in computation time. |
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Energy drift in these SSD particle simulations was unnoticeable for |
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time steps up to three femtoseconds. A slight energy drift on the |
