Integration of 6-12 Lennard Jones Potential to obtain the 3-9 one.

In summary, the speaker is researching the interactions of carbon atoms using the Lennard-Jones potential and needs to understand the theory behind converting the 6-12 potential to the 3-9 one. They found a useful deduction on a webpage but are unsure about the limits of the integral in relation to "z". They later discovered the answer was stated on the webpage, explaining that a molecule is located at a distance of "x" from a diffuse solid in the region of x < 0.
  • #1
Kjiel
2
0
Hi people,

I'm researching about the interactions of two carbon atoms using the Lennard-Jones potential and I need to know the theory behind some equations.

I need to know how to get from the 6-12 potential the 3-9 one. I've found in this link ( http://www.sklogwiki.org/SklogWiki/index.php/9-3_Lennard-Jones_potential ) a brilliant deduction of what I want applying triple integrals. I understand everything except the limits of the integral respect to z.

From -x to -∞? Why's that?

If someone could throw some light to this issue I would be really grateful.

Thank you in advanced.

Kind regards!
 
Last edited:
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  • #2
I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?
 
  • #3
Hi! Thanks for your concern. I got the answer several days ago and it was in front on my eyes. In the very webpage it can be read that a molecule is located at an "x" distance from a diffuse solid in the region x < 0... so there's the answer.

Thanks again!
 

1. What is the Lennard Jones Potential?

The Lennard Jones Potential is a mathematical model used to describe the interactions between two neutral atoms or molecules. It takes into account both attractive and repulsive forces between the particles.

2. Why is the Lennard Jones Potential important in scientific research?

The Lennard Jones Potential is important because it is widely used in molecular simulations to study the behavior of atoms and molecules. It is also used in various fields such as chemistry, physics, and materials science to understand the properties and interactions of particles.

3. What is the significance of integrating the 6-12 Lennard Jones Potential to obtain the 3-9 one?

The 6-12 Lennard Jones Potential is a simplified version of the original potential that is often used in simulations. However, it has limitations in accurately describing the behavior of particles at shorter distances. By integrating the potential to obtain the 3-9 form, we can improve the accuracy of the model and better understand the interactions between particles at both short and long distances.

4. How is the integration of the 6-12 Lennard Jones Potential to the 3-9 one achieved?

The integration is achieved by using a mathematical transformation to convert the parameters of the 6-12 potential (epsilon and sigma) to the parameters of the 3-9 potential (A and B). This allows for a more accurate representation of the potential energy between particles at different distances.

5. What are the potential applications of using the 3-9 Lennard Jones Potential?

The 3-9 Lennard Jones Potential can be used in various fields such as molecular dynamics simulations, protein folding studies, and drug discovery. It can also be applied to study the behavior of materials at the atomic level, leading to advancements in areas such as nanotechnology and materials design.

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