The purpose of this assignment is to use the atomic trajectories, obtained from a molecular dynamics simulation of a Lennard-Jones Cluster, to determine its vibrational spectrum using a Fourier transformation. The input are trajectories, stored at discrete uniform time intervals and calculated in the course of Assignment #5. The eigenmode frequencies are to be compared to those determined by diagonalizing the force constant matrix in the course of Assignment #7.
As in Assignments #5 and #7, we 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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Execute the program ljmd.x to determine the trajectories of a particular Lennard-Jones cluster and save them as a sequence of "configurational snap-shots". The resulting data file ljmd.dat will contain the following information in each record, separated by blank spaces: t x(1) y(1) z(1) x(2) y(2) z(2) ... x(N) y(N) z(N) containing the time t of the snapshot and Cartesian coordinates of all atoms.
Your next task is to write a FORTRAN program ljft.f which reads in this data file. This program should read in the number of atoms from terminal input and then perform a Fourier transformation of the structure data. The output should be stored in a data file ljft.dat containing the Fourier spectrum between frequency f=0 and the Nyquist critical frequency fc. Each record should contain, in analogy to the structure of ljmd.dat, the frequency, the Fourier transform of x(1), ..., the Fourier transform of z(N). Plot the frequency spectrum using gnuplot for selected atomic coordinates. Compare the peaks in the frequency spectrum with the frequencies of the eigenmodes for this system using the code created as part of your Assignment #7, or alternatively the code ljvib.x. All the codes are to be found in the directory ~tomanek/PHY480/HW8/. Run the simulation for N=2,3,4 and use at least two different values for each of the input parameters: the mass of the particles M, and the parameters s and e determining the potential.
For a given set of N, M,
s, and e,
perform the following calculations:
i. Run a Molecular Dynamics simulation starting with
and arbitrary equilibrium geometry. How many
modes appear to be in the vibrational spectrum?
How does their frequency depend on
M?
ii. Run a Molecular Dynamics simulation
for the cluster prepared in one particular eigenmode.
Is the spectrum dominated by the frequency of this
eigenmode? Does the spectrum depend on the initial
amplitude of the distortion from equilibrium?
If yes, can this be understood in terms of anharmonic
modes?
How do changes in s, e, and the time interval between the "configurational snap-shots" affect the results? Post your results on the web.