leonard jones potential: idealisation

[tammie123]

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The part where it says that there would be no interactions is kind of confusing me. Above a certain distance wouldn't the attractive force be dominant? So how is there no interaction?

 

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The part where it says that there would be no interactions is kind of confusing me. Above a certain distance wouldn't the attractive force be dominant? So how is there no interaction?

according to the chart, the strength of the intermolecular interaction (repulsion/attraction) is decreasing as the distance increasing. You see the pointing arrows/axes ?? That should tell you about the increasing/decreasing parts.

The notes on the charts also say, at some close enough distance or separation, i.e. r < or = to 6, the intermolecular potential U would be infinitive, i.e. very very strong. Likewise, at some far enough distance, there would be no or negligible intermolecular interaction (repulsion/attraction) between the two molecules (i.e. U = 0 when r > 6).

The chart seems to indicate that at 6, repulsion would be the dominant force.

The chart does not say anything about attraction force. So I guess, all the above is all that we can get from the chart. But again, intermolecular potential/interaction would mean attraction and repulsion. In general, attraction force between two molecules is increasing as the distance between them is decreasing. So yes, at some distance the attractive force would be the dominant force BUT the chart does not say where.


are you going to pharmacy school in Canada ?? I see the "weird" spelling "idealisation" and am curious 🙂

 

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I googled a bit and found this,

"Introduction

In Module 1, the need for an intermolecular potential was discussed and the Lennard Jones potential was introduced. The Lennard-Jones potentials is undoubtedly the most widely used intermolecular potential for molecular simulation. It is a simple continuous potential that provides an adequate description of intermolecular interactions for many application. Although it is treated as a pair-0wise potential, it is more accurately described as an “effective” potential and as such it does not truly represent two-body interactions but it also incorporates influence of many-body interactions albeit in a very crude and inaccurate way.

The aim of this Module is to survey intermolecular potentials and provide an awareness of alternatives to the Lennard-Jones potential.

Intermolecular Interactions

The calculation of the potential energy inevitably involves assumptions concerning the nature of attraction and repulsion between molecules. Intermolecular interaction is the result of both short and long range effects.

Electrostatic, induction, and dispersion effects are examples of long range interactions. In these cases, the energy of interaction is proportional to some inverse power of intermolecular separation. Electrostatic interactions result from the static charge distribution between molecules. The effect can be either attractive or repulsive and it is exclusively pairwise additive. Induction effectsare always attractive, resulting from the distortions caused by the molecular fields of neighbouring molecules.

However, the most important contribution is the attractive influence of dispersion arising from instantaneous fluctuations caused by electron movement. Neither induction nor dispersion are pairwise additive.

Short range interactions are characterised by an exponential decay in the interaction energy with respect to intermolecular separation. At small intermolecular separations, there is a significant overlap of the molecular wave functions causing either intermolecular exchange or repulsion. These interaction are not pairwise additive.

In theory, it is possible to calculate the intermolecular interactions from first principles. However, in practice the first principle or ab initio approach is confined to relatively simple systems. More commonly, the influence of intermolecular interaction is expressed by some type of intermolecular potential.

The justification for the intermolecular potential is often entirely empirical, although, it is possible to determine an ab initio potential during the course of a simulation.

The nature of intermolecular forces is discussed in greater detail by Stone (1996)." page 3, 4, 5 & 6.


and


"Hard-Sphere Potential

The simplest approximation is to treat atoms as impenetrable hard spheres, i.e.,

where

(the equation we see above in the chart. I dont know why it did not get pasted here though)


σ is the hard-sphere diameter. In a molecular simulation, special procedures are required (Allen and Tildesley, 1987) to evaluate the effect of the hard-sphere potential. These problems are more easily overcome by MC than MD. The potential remains of considerably utility as a reference for the development of hard-sphere equations of state." page 9.


*R. J. Sadus, Centre for Molecular Simulation, Swinburne University of Technology

http://www.swinburne.edu.au/ict/success/cms/documents/mod5.pdf
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I guess because Hard-Sphere model is the simplest approximation/model (hence the term "idealisation"), it would estimate the intermolecular interaction (repulsion/attraction) as all or nothing. So I guess, I was wrong about the decreasing intermolecular interaction/increasing distance part in this Hard-Sphere model.


Again, the HS model/chart above says:

-at some close enough distance or separation, i.e. r < or = to 6, the intermolecular potential U would be infinitive, i.e. very very strong.

The chart seems to indicate that at 6, repulsion would be the dominant force.
(My guess is that at some distance r << 6, attractive force would be the dominant force as the notes above say "At small intermolecular separations, there is a significant overlap of the molecular wave functions causing either intermolecular exchange or repulsion.")

-Likewise, at some far enough distance, there would be no or negligible intermolecular interaction (repulsion/attraction) between the two molecules (i.e. U = 0 when r > 6).

 

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We need some pharmacy students or PharmDs to chip in.... where are @KidPharmD @BMBiology @blueheron @Jibby321 et al ??

help help SOS lol 🙂

 

[blueheron]

This is more physical chem type stuff.

Basically before sigma (at E=0), the force of repulsion between NUCLEI is too great. Between sigma and some value r (say approx between r0 and r on this graph) the magnetic attraction between nuclei and electron fields is "greater". After this, attraction is weak, virtually nonexistent. Think of two magnets far apart. They need to be relatively close to attract. And try to push same pole of a strong magnet together. You will hurt yourself before you succeed.

 

[tammie123]

according to the chart, the strength of the intermolecular interaction (repulsion/attraction) is decreasing as the distance increasing. You see the pointing arrows/axes ?? That should tell you about the increasing/decreasing parts.

The notes on the charts also say, at some close enough distance or separation, i.e. r < or = to 6, the intermolecular potential U would be infinitive, i.e. very very strong. Likewise, at some far enough distance, there would be no or negligible intermolecular interaction (repulsion/attraction) between the two molecules (i.e. U = 0 when r > 6).

The chart seems to indicate that at 6, repulsion would be the dominant force.

The chart does not say anything about attraction force. So I guess, all the above is all that we can get from the chart. But again, intermolecular potential/interaction would mean attraction and repulsion. In general, attraction force between two molecules is increasing as the distance between them is decreasing. So yes, at some distance the attractive force would be the dominant force BUT the chart does not say where.

are you going to pharmacy school in Canada ?? I see the "weird" spelling "idealisation" and am curious 🙂

Haha 'weird spelling'? 😛 I'm a pharmacy student in britain so that may be the reason

This is more physical chem type stuff.
View attachment 183774

Basically before sigma (at E=0), the force of repulsion between NUCLEI is too great. Between sigma and some value r (say approx between r0 and r on this graph) the magnetic attraction between nuclei and electron fields is "greater". After this, attraction is weak, virtually nonexistent. Think of two magnets far apart. They need to be relatively close to attract. And try to push same pole of a strong magnet together. You will hurt yourself before you succeed.

I understand this graph but I'm so confused about the one I posted, why would they not include the attractive force? I understand that it's simplified but cutting something out completely and simplifying something are two different things. But there must be a reason for this

 

[oldstock]

This is more physical chem type stuff.
View attachment 183774

Basically before sigma (at E=0), the force of repulsion between NUCLEI is too great. Between sigma and some value r (say approx between r0 and r on this graph) the magnetic attraction between nuclei and electron fields is "greater". After this, attraction is weak, virtually nonexistent. Think of two magnets far apart. They need to be relatively close to attract. And try to push same pole of a strong magnet together. You will hurt yourself before you succeed.

dang I guess I should have taken P-chem...

thanks for explanation !! I guess I was not too far off... 🙂

 

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Haha 'weird spelling'? 😛 I'm a pharmacy student in britain so that may be the reason

dang I guess the reason is more like you do not speak the right English LOL 🙂 jk

I understand this graph but I'm so confused about the one I posted, why would they not include the attractive force? I understand that it's simplified but cutting something out completely and simplifying something are two different things. But there must be a reason for this

yeah I am asking the same question here. They would note the repulsive force but not attraction ?? Can you check with your professor and let us know ??

hope @blueheron would shed a light here too... 🙂

 

[oldstock]

This is more physical chem type stuff.
View attachment 183774

Basically before sigma (at E=0), the force of repulsion between NUCLEI is too great. Between sigma and some value r (say approx between r0 and r on this graph) the magnetic attraction between nuclei and electron fields is "greater".

the HS model says that, when r > 6, the intermolecular interaction (repulsion/attraction) = 0. That is, according to the HS approximation, there is NO attraction force when r is greater than 6. Too idealiSed/simplified ?? 🙂

At r = 6, the HS approximation says repulsion is dominant. But r > 6, U = 0. So I guess, the only place that we might see attraction force becoming dominant, in the HS model, is probably when 0 < r << 6 ??

After this, attraction is weak, virtually nonexistent. Think of two magnets far apart. They need to be relatively close to attract. And try to push same pole of a strong magnet together. You will hurt yourself before you succeed.

 

[blueheron]

The reason there are no numbers is because it is relative (size of the magnet). A larger magnet (atom) is going to start to attract at a greater distance (Larger negative e cloud), and also repel at a greater distance (larger nuclei). The whole <6 thing is pretty much irrelevant. Unless you really are taking PChem, it is just a generic model to show you that too close will repel, too far will not attract, and in between is just right.

 

[oldstock]

The reason there are no numbers is because it is relative (size of the magnet). A larger magnet (atom) is going to start to attract at a greater distance (Larger negative e cloud), and also repel at a greater distance (larger nuclei). The whole <6 thing is pretty much irrelevant. Unless you really are taking PChem, it is just a generic model to show you that too close will repel, too far will not attract, and in between is just right.

thanks again !! 👍👍

 

[Jibby321]

Uhhhh what @blueheron said lol.

I have no idea.