The purpose of this assignment is to use the matrix diagonalization approach to determine the vibrational eigenmodes of a system of point-like particles interacting via two-body forces.
Consider a system of N<5 particles of mass M (the same for all particles). The spherically-symmetrical two-body potential is of Lennard-Jones type:
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Modify a template FORTRAN program ljvib.f to determine the vibration frequencies and to visualize the vibration modes. The input is the number of particles N, the mass of the particles M, and the parameters s and e determining the potential. Use analytical expressions for the elements of the force constant matrix in your program.
For a given set of N, M,
s, and e,
the program should perform the following calculations:
i. Write the equilibrium geometry of the cluster
as an xyz file
(what is the equilibrium shape for N=2,3,4?);
ii. Determine the eigenfrequencies f (in Hz units);
iii. For selected eigenmodes, write 20 xyz files depicting
a sequence of geometries.
Discuss the nature of the eigenmodes for N=2,3.
Discuss the cases N=2,3,4 and present examples.
How do changes in M,
s, and e
affect the results? Post your results on the web.
Visualize individual geometries using the code xyzview. First, copy the graphics data files ~tomanek/PHY480/graphics/xyzsph.gdf and ~tomanek/PHY480/graphics/xyzwht.gdf into your own directory, where you can modify the sphere radius and other graphics attributes. To visualize a geometry presented as an xyz file, enter the command ~tomanek/PHY480/graphics/xyzview.x You will be prompted for the name of your input file, the name of the postscript output file (or enter RETURN for the default), and the graphics data file. An example file in the xyz format is ~tomanek/PHY480/graphics/bowl.xyz; the corresponding output file is ~tomanek/PHY480/graphics/bowl.eps.