Monte Carlo Simulation of Liquid Water Daniel Shoemaker

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Monte Carlo Simulation of Liquid Water

  • Daniel Shoemaker

  • Reza Toghraee

  • MSE 485/PHYS 466 - Spring 2006


  • Write a MC liquid water simulation program from scratch which yields observables that are consistent with those found in the literature.


  • 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

    • Main.h
    • MC.h
  • Source

    • Main.cxx
    • Coordinates.cxx
    • Energy.cxx
    • GofR.cxx
    • MC.cxx
    • MCMove.cxx
    • RandGen.cxx


  • 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.


  • 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
  • Periodic Boundary Conditions

    • 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.


  • 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.


  • 2-D Simulations by Jihan Kim

  • 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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