SimpleMDExerciseI

SimpleMDExercise SimpleMDExerciseII SimpleMDExerciseIII SimpleMDExerciseIV

In SimpleMDExerciseI, we shall get to the level of codes for microcanonical simulation of two-atom molecules.

1 # With No Internal Structure[ | ]

Since the works of Wood & Wainwright, hard sphere systems had been throughly investigated. Several years later, Rahman solved the equations of motion for a set of LJ particles, and Verlet, Nicolas, and so on performed serious researches on LJ systems in following short period. Not in the perspective of history, but in the perspective of coding, however, the system of LJ particles is much more easier than that of hard spheres. So, we will treat LJ sphere first, then the hard sphere.

1.1 # LJ sphere[ | ]

One of the most famous and important papers on the simulation of LJ particles is the paper of Rahman (Correlations in the Motion of Atoms in Liquid Argon, Phys. Rev., vol. 136, pp.A405 ~ A411 (1964)). Partial re-presentation of his work will be our first exercise. There should be almost no difficulties, except for the calculations of correlation functions. So, just get over the correlations and make argons move anyway. Make the movie file, and see the motion of argons. One of the easiest ways of seeing molecular animation is :

  1. Download Chime ( http://www.mdl.com/chime/index.html )
  2. Install Chime for your web browser.
  3. Generate the MD trajectory in xyz file format (total number of the atoms in the first line, then the atomic symbol followed by x, y, z coordinates in Angstrom consecutively per line)
  4. Attatch the successive trajectories in the same file in queueing way, untill the end.
  5. Open the trajectory file with your web browser, and select animation option.
  6. Enjoy your self-production movie :-)

For some more details for overall coding, refer to the paper of Baker & Fisher & Watts (Liquid argon : Monte Carlo and Molecular Dynamics calculations, Mol. Phy., vol. 21, pp. 657-673 (1971))

1.2 # Hard sphere[ | ]

At this stage, we are explicitly exposed to the darn collision detection problem first time. Fortunately, collision in the hard sphere simulation can be expressed in a simple closed form. Note here, the main parameter which determines whole dynamics of the system is the collision interval, not trajectories of particles ; so do keep the trace of collision interval with computer calculation. Other geometric parameters neccessary are just followed in simple geometric considerations. Our second excercise is to implement the same thing as the above, except for the argons being represented as hard spheres.

There are many textbooks treating hard sphere MD in detail. Please refer to the book of Haile's, or of Gould & Tobochnik's. Those books provide not only detailed explanations but also beutifully programmed codes.

2 # With Internal Structure I : topologically dumbell-like[ | ]

The molecule in this section will be topologically denoted as L---R. The first nuisance may be come form the problem of maintaining the structure. Don't bother if you are to study molecules of LJ atoms. Any reasonable LJ potential will automatically keep the structure. Rigid dumbell makes the problem much more fastidious. So, the very next problem is for the linear molecules of LJ atoms.

2.1 # Non-rigid case[ | ]

Maintance of the structure is easily dissolved in the non-rigid case. Now, the main points to learn from this problem are :

  • internal motion : bond stretching
  • rotation of the molecule
  • intermolecular interactions

If the forces on the molecule are in special geomtry, then only translations and vibrations are observable. But, if the forces are arbitrary, the resultant motions will be translation, rotation, and vibration. So, let's first consider the motion without rotation, and then include the torque.

For the sprit of stepwise approach, we will consider the system of only one molecule, and then the sytem of two (and many) molecules.

2.2 # Rigid case[ | ]

3 같이 보기[ | ]

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