## Daniel Shoemaker ## Reza Toghraee ## MSE 485/PHYS 466 - Spring 2006
**Objective** ## Write a MC liquid water simulation program from scratch which yields observables that are consistent with those found in the literature.
**Potentials** ## Many potentials exist for 2- 3- 4- and 5-site models of water. ## We chose a 3-site NVT model to maintain simplicity while keeping good agreement with physical parameters. ## TIP3P potential: - rOH = 0.96 Å
- HOH angle = 104.52°
- qO = -2qH = -0.834, charges located directly on atoms
- LJA = 582x103 kcal Å12/mol, LJC = 595 kcal Å6/mol
**Code Layout** ## Headers ## Source - Main.cxx
- Coordinates.cxx
- Energy.cxx
- GofR.cxx
- MC.cxx
- MCMove.cxx
- RandGen.cxx
**Algorithm** ## Metropolis Monte Carlo algorithm: - Move random particle by a random distance
- Calculate ∆E
- Accept or reject move based on -1/kT
- Update position
## Our maximum movement length is 0.15Å to achieve an acceptance ratio between 43% and 64%, depending on the number of iterations. ## Energy data is output every 1K-10K iterations, with g(r) data recorded about as often.
**Optimization** ## Defining H positions without trig functions - Use linear algebra with properly generated random numbers to position the H atoms based on O
- No lookup tables (trig functions) are used
- Setting up a 3x3x3 matrix of boxes that surround the core box is a quick way to find the shortest distance between to particles in PBC.
- Much faster than subtracting nint(distance/box)*box from the distances
**Energy Trends** ## Simulations were run with 10K initialization steps to ensure that the energy had settled.
**Radial Distribution Function**
**2-D Matlab Simulations** ## 2-D simulations show that water molecules cluster together. ## In this simulation, all molecules are moved after every step.
**Conclusions** ## Our program is a fast and intuitive way to simulate water using Monte Carlo. ## This code can easily handle a 3-site potential, and minor modifications would allow 4-sites. ## Our Lennard-Jones interactions are a little too strong, but the potentials behave as expected. ## The g(r) normalization should be examined to correct its scale.
**References** ## Berendsen, H. J. C. et al, *Intermolecular Forces*, (D. Reidel Co., Holland 1983), 331. ## Frenkel, D. and B. Smit, *Understanding Molecular Simulation*, (2nd Ed., Academic Press 2002). ## Jorgensen, W. L., *J. Am. Chem. Soc.* **103**, 1981, 335. ## Jorgensen, W. L. et al, *J. Chem. Phys.* **79** (2), 12 July 1983, 926. ## McDonald, I. R., *Mol. Phys.* **23**, 1972, 41.
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