About chemical bond potential energy and Lennard-Jones Potential

[Rodrigo]

Hi, everyone.

I'm studying about the potential energy of chemical bonds and I want to know more about the attractive and repulsive terms of Lennard-Jones potential.

What is the origin of repulsive part ? Anyone knows any material that explain that ?
For example, the equation of attractive part can be derived from van der Waals forces which has 1/r^6 dependence.

Thanks.

 

[studiot]

Good Morning, Rodrigo and welcome.

 

OK so you are studying Lennard-Jones potentials, but your question is in relation to forces.

 

So I take it you understand the process (maths) of going from forces to potentials?

 

And also why we think there are two opposing forces in action?

 

 

If we think of the molecule (this includes atoms) as having a concentrated positive centre surrounded by a negative electron cloud, this is a good start.

 

Now (considering atoms for simplicity) consider what happens as the electrically neutral atoms are brought closer and closer together.

 

At first there is an attraction (ie the attractive forces outweigh the repulsive ones)

 

Too close and there is a repulsion.

 

At the magic distance a₀ the forces balance and we have equilibrium.

 

We regard a₀ a measure of the size of an atom, but really we are talking about the effective size of the electron cloud of that atom.

 

If the centres of two interacting atoms are closer than a₀ then there is overlap of their respective clouds.

This is the source of the repulsive force, which increases rapidly as the overlap increases (ie distance decreases)

 

If the centres of two interacting atoms are more widely separated than a₀ then the repulsive force falls away rapidly with increasing distance, leaving the attractive force to predominate.

 

The interaction between the electron clouds is also responsible for the attractive force, in a slightly different way.

Again imagine two clouds approaching each other.

The repulsion is stronger on the near side of the cloud than the repulsion on the far side.

This pushes or distorts the clouds so that they are stronger (the electrons spend more time) on the far side of each nuclei.

The thinning of the clouds also weakens the shielding of the nuclei in that direction.

This slightly polarises the atom, leading to the Van der Waals type bonding you note.

 

Note that the usual graphs of the LJ potential or the forces are like a free body diagram.

That is you need to draw a (mental) dotted line around the atom as a cut line and add in the interaction force (potential) with the second atom that is not shown on the graph.

Without the second atom these forces could not act.

 

 

Does this help?

Edited August 22, 2016 by studiot

[Rodrigo]

Good Morning, Rodrigo and welcome.

 

OK so you are studying Lennard-Jones potentials, but your question is in relation to forces.

 

So I take it you understand the process (maths) of going from forces to potentials?

 

And also why we think there are two opposing forces in action?

 

 

If we think of the molecule (this includes atoms) as having a concentrated positive centre surrounded by a negative electron cloud, this is a good start.

 

Now (considering atoms for simplicity) consider what happens as the electrically neutral atoms are brought closer and closer together.

 

At first there is an attraction (ie the attractive forces outweigh the repulsive ones)

 

Too close and there is a repulsion.

 

At the magic distance a₀ the forces balance and we have equilibrium.

 

We regard a₀ a measure of the size of an atom, but really we are talking about the effective size of the electron cloud of that atom.

 

If the centres of two interacting atoms are closer than a₀ then there is overlap of their respective clouds.

This is the source of the repulsive force, which increases rapidly as the overlap increases (ie distance decreases)

 

If the centres of two interacting atoms are more widely separated than a₀ then the repulsive force falls away rapidly with increasing distance, leaving the attractive force to predominate.

 

The interaction between the electron clouds is also responsible for the attractive force, in a slightly different way.

Again imagine two clouds approaching each other.

The repulsion is stronger on the near side of the cloud than the repulsion on the far side.

This pushes or distorts the clouds so that they are stronger (the electrons spend more time) on the far side of each nuclei.

The thinning of the clouds also weakens the shielding of the nuclei in that direction.

This slightly polarises the atom, leading to the Van der Waals type bonding you note.

 

Note that the usual graphs of the LJ potential or the forces are like a free body diagram.

That is you need to draw a (mental) dotted line around the atom as a cut line and add in the interaction force (potential) with the second atom that is not shown on the graph.

Without the second atom these forces could not act.

 

 

Does this help?

studiot, thanks for the reply.

 

That really helped me. But the text that I've highlighted is not clear to me. Can you explain again ? That is not clear for me yet why repulsion has a bigger dependence with distance (r^-12) than attraction (r^-6). Mathematically is easy to see why, but I do not understand the physical meaning behind it.

 

Another question: do you know any book/paper which show these effects ?

 

Thanks.