Molecular Simulations Love Newton?

We all know that one couch-potato who advertently does not tend to move out from the couch because of his exigency to binge-watch some trendy Netflix show. That’s fine, and I oftentimes make myself turn into this potato to absorb those fancies as well. Well, you know how to kickstart that person (assuming you are not the couch-potato).

So, you are applying Newton’s laws of motion, although it sounds enormously weir, to make someone move. Duh? Classical Mechanics!! You are kicking the atoms and molecules to move to a new position. They don’t move as much as they should’ve been since you are, presumably, a macho-person. But, in the atomistic framework, the atoms move in a different direction depending on the force applied to them. And, as atoms have mass, according to Newton, this kickstart will result in an acceleration (a = F/m) for which the atoms will be moved with increasing velocity.

So, until now, we have kickstarted the guy, and his atoms started jiggling, eventually experiencing an acceleration to move to a new position. You can consider this movement by thinking about the waves created in the fat-layers of the person. Wait, what? Yes, the waves of fat layers of your body can arrantly be compared to the atomistic movements (a very counter-intuitive example but you know how it looks like, surely).

So, Newton’s second law is all that is needed for molecular simulations. Joking! Yes, you do need it, and this is the most fundamental thing to start with but to understand and evaluate forces, and energies of atoms, you have to have a complex formulation (Taylor expansion of newton’s equations of motion) based on this simple, beautiful formula, F = ma. In actual molecular dynamics simulation, you need to do some calculations for velocity as well.

There are some steps to perform this kickstarting and they are as follows:

(1) Define the initial position coordinates. Atoms are to be arranged in a certain manner within a system. They must not overlap, go out of the simulation box (system) unless you are considering evaporation for your simulation property.

(2) Define an interatomic potential with which particles can interact with one another. (Optional; if you need your atoms to interact with one another)

(3) Apply an ensemble of velocity to the atoms. That is, random velocities to be given to these atoms but to keep a record of these random velocities, you need to bring them under a certain category. For example, velocities of 1, 2.5, 5.2, 2.3, 1.9, 0.5, …….. will be applied to the 1st, 2nd, 3rd, and so on, respectively. And, to use this random velocity generator again in the future so that you can compare the results using the same set of velocities, you need to make an ensemble of 1234 (say). It means whenever you use 1234 in the future, it will create random velocities of 1, 2.5, 5.2, 2.3, 1.9, 0.5, …….. (just mentioned above). So think of it as the name of a random velocity generator. You kickstarted the atoms already!

(4) Calculate the forces on each atom. For example, the attractive and repulsive forces among the atoms play a major role in simple cases. It sounds like a trifle but it is way more complex and complicated. This is where your computer has to spend most of its time on calculating forces from energy values obtained from the already-specified interaction potential.

(5) Calculate the acceleration using Newton’s second law of motion. You know the mass of the atoms and also just calculated the force in (4). So, use F = ma. Or, a = F/m.

(6) Update the positions and velocities with respect to the accelerations using Taylor’s theorem. This results in the equations of motion with which atoms are moved.

(7) Repeat the procedure for the next time step to move the atoms to a new position. Steps 1 through 6 are performed for each time step to move atoms in a new direction, and then, step 7 is used to store the final values of acceleration, forces, positions, momenta, velocities to be used in the next time step.

There you go, Newton helped you move the atoms.

You might ask if atoms are quantum mechanical, then why classical mechanics is used in determining the motion of atoms? Leave that for the next blog since I have to ponder over this topic to provide you with a scrupulous answer. I know nothing. Now, think about how have you not thought of these simple simulation steps earlier? Well, been there, done that.

Stay safe.