# Atomic velocities from forces and MgO simulation

1. Jul 12, 2012

### Hypatio

I've attached a graph of the pair potential between Mg and O. The peak attractive force experienced between the atoms is 1.6 eV, or 10^-19 Joules. From F=ma, with an O mass of 2.66*10^-26 kg the acceleration experienced by the atom is about 9650000 m/s^2, or 9.65 nm/fs (nanometers per femtosecond).

Is this right?

I know that molecular dynamics simulations of MgO are able to be performed with timesteps on the order of 0.5 fs, but from my calculations the atom may displace by on the order of 5 nm for this time, more than 10 unit cells for MgO. This either means that I have overestimated the acceleration by 1-2 orders of magnitude, or that atomic displacements from vibrations and such occur over less than 0.1 nm.

Also, I am testing an MgO simulation. I've attached an animation of atomic vibrations which occur in a 20x20 lattice due to the momentum of a contraction from an initial "equilibrium" position (black dots)--the displacement occurs because of long range coulombic forces bending the lattice from an ideal spacing. Each frame is a timestep of 0.1 fs, and I've had to use 0.01 fs as the model timestep. Absolute and relative atomic velocities are on the order of 100-900 km/s, which seems high to me.

I feel like I am doing something wrong.

 Sorry, apparently my animated gif is too big (800kb) or are not allowed.

[edit 2] The pair potential, including coulombic potential, is: 926.69*EXP(-r/0.3)+k*(1*-1)/r

where k=10*(2.31*10^-19)/(1.602*10^-19)=14.417888
or k=299792458^2*10^-7*(1.60217646*10^-19)*10^10=14.417888

and r is in Angstroms.

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• ###### MgO.jpg
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Last edited: Jul 12, 2012
2. Jul 13, 2012

### Hypatio

Maybe my coulomb potential is much too large? Is my force constant correct?

k=10*(2.31*10^-19)/(1.602*10^-19)=14.417888
or k=299792458^2*10^-7*(1.60217646*10^-19)*10^10=14.417888

correct?

The dimensions should be Joules and Angstroms...

3. Jul 13, 2012

### Staff: Mentor

I think you messed up several units.

eV and Joule are units of energy, not force. Looking at the graph, is it $\frac{eV}{\mathring{A}}$?

nm/fs is a velocity, not an acceleration. Expressed in nm/fs^2, the corresponding value is extremely small (10^-14).

4. Jul 14, 2012

### Hypatio

Thanks, I did mess up the units and I think I now have a working model.