References 259
then simply the opposite of this, as the sum of all the interparticle forces adds up
to zero.
(a) [C] Write routines for calculating the forces on the atoms and use these in an
ordinary (microcanonical) MD simulation of the atom. To check the program,
you can put the H-atoms on the vertices of a tetrahedron with the C-atom in the
centre. If you release the molecule from this conformation with a CH-distance
slightly smaller or larger than the equilibrium distance of 2.104a 0 , the molecule
should stretch and contract isotropically in an oscillatory fashion.
(b) [C] Keep the temperature of the molecule constant by rescaling the velocities
after each time step. Determine the average total energy of the molecule.
(c) [C] Add a Langevin thermostat to the simulation, for example by rescaling the
velocities after every time step. Use the algorithm given in the last section for
solving the equations of motion with friction. Add a Langevin random force,
drawn from a Gaussian distribution with a width
σ^2 =q/h
to the interparticle force. Check that the temperature is given by
T= 1 /( 2 γ).
The temperature is determined from the kinetic energy – we haveT=
15
2
kBT.
Determine the average total energy and compare the result with the program
of (b).References
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