1. Implementation of the TIP5P Potential
John A. Thomas
Department of Mechanical Engineering
Carnegie Mellon University
NTPL Group Meeting
March 8, 2007

2. Introduction Background and motivation
Overview of TIP5P water potential
Geometry
Interactions
Dynamics
Integrating the equations of motion
Comparison with experimental data
Long range interactions
Ewald sum
Wolf potential
Future directions

3. Molecular dynamics of H2O
Much effort has gone into the development of water models
Relevant to many biological and engineering systems
Wealth of experimental information
But water is a complicated substance
Several energy storage mechanisms
Density maximum at 4° C
Using simplifying assumptions, several water models have been developed
TIP3P, TIP4P, TIP5P (Transferable Intermolecular Potential)
SPC, SPC/E (Simple Point Charge)
BNS, MCY, ST2 (Peoples’ Initials)

4. Overview of the TIP5P water model: Geometry
“The most popular water model in history”
The TIP5P water model is rigid
Bond angles and bond lengths do not change
This limits the maximum simulation temperature (<550K)
The charge distribution on the TIP5P water model is fixed
The positions and magnitude of the charges is fixed
Cannot model charge transfer near an oxidized interface -
Charge site, 0 amu
90°
109.47°
0.70 Å +
Hydrogen, 1 amu
104.52° Å
Oxygen, 16 amu
Tuned parameters
Measured values

5. Overview of the TIP5P water model: Interactions
Electrostatic interactions are modeled using Coulomb’s potential
Dislike charges attract and like charges repel
Responsible for long-range interactions
Oxygen-Oxygen interaction are modeled using Lennard-Jones potential
Significant only during short-range interactions
Gives the molecule a “radius” and prevents molecular overlap
All interactions cutoff at roo > 9 Å

6. Overview of the TIP5P water model: Dynamics
Atomic dynamics
Motion is purely translational
System is defined by positions and linear momentums
No basis transformation required
Molecular dynamics
Motion is both translational and rotational
System is defined by positions, orientations, angular, and linear momentum
Basis transformation required

7. Atomic versus molecular dynamics: Integration
Integrating atomic dynamics: Verlet Leapfrog Scheme
Integrating molecular dynamics: Evans Quadternion Scheme

8. The results
4096 molecules with spatial decomposition

9. Comparison with Experimental Data
Radial distribution, goo(r)
First peak of TIP5P is close to expt., and shape of both tails are similar
Our implementation reproduces the published data
Density profile, ρ(T)
Tuned to reproduce properties near 25° C
We reproduce the data point at 25° C
Self diffusion coefficient, Ds
Ds, expt = 2.30x10-9 m2/s
Ds, TIP5P, them = 2.62x10-9 m2/s
Ds, TIP5P, us = 2.63x10-9 m2/s

10. Handling long-range interactions
The original TIP5P implementation cutoff all interactions at roo > 9 Å.
What about the energy drift ?
Will autocorrelation functions be affected by the large force discontinuity?
Can we reproduce the TIP5P/experimental data using an alternative potential function?
What alterative electrostatic potential functions are available?
Ewald sum
Wolf potential
Reaction field

11. Ewald sum: An expensive alternative
The Ewald sum replaces the r-1 term with two, more quickly converging sums
Energy is conserved, but the system is assumed to be periodic.
The sum requires a loop over all k-vectors while looping over all charge sites.
Two tunable parameters: damping factor α and number of lattice vectors k
I can get PE correct, but pressure and diffusion are difficult to predict.

12. Wolf potential: A faster alternative
“An exact method for the simulation of Coulombic systems by spherically truncated, pairwise r-1 summation”
Modified form of the Ewald sum
Does not require a sum in k-space
Consists of a real-space pair interactions minus a so-called “self-energy” term
Two tunable parameters: damping factor α and cutoff radius Rc
Parameters that reproduce accepted TIP5P density, diffusion and RDF data
Rc = 9 Å, α = 0.6
Rc = 11 Å, α = 0.5
Rc = 12 Å, α = 0.5
Need to test reorientation

13. Wolf and Coulomb force comparison

14. A moment of reflection (summary)
Water is an important and relevant material
We have implemented the TIP5P water potential, which utilizes both Coulomb and Lennard-Jones interactions
The dynamics of molecular systems are more complicated than those of atomic systems, and the integration scheme is more involved
We saw a movie
The TIP5P model (both the original and our implementation) reproduces experimentally observed data
But we have questions about the long range interactions.
Can we simply truncate the slowly-decaying electrostatic energy/force?
We are tuning the parameters of the Wolf potential to reproduce accepted data
Further refinement is needed

15. Future work Construct a graphite solid
Continue to refine Wolf potential parameters
Begin exploring reaction field potential
Merge graphite solid and TIP5P water into single simulation