Lennard-Jones potential .

In summary, the depth of a Lennard-Jones potential is strongly related to the covalent bond strength within a molecule. The 1/r6 term in the potential is due to long-range dipole-dipole interactions, while the 1/r12 term represents close-range repulsion. The parameter ε in the potential is linked to the bond energy, and is determined by finding values that best reproduce a specific molecular bond.
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terp.asessed
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Homework Statement


Just my question from looking at a table of lennard-jones parameters (molecular species and accorded ε), it seems the depth of a Lennard-jones potential is strongly related to a covalent bond? Not hw-related, but course-related anyhow, so any suggestions would be welcome.

Homework Equations


..well, I am just going to include an equation from the same section I found the table in: u(r) = ε(r*/r)12 - 2ε(r*/r)6

The Attempt at a Solution


I understand that Lennard-jones potential is contributed by dipole-dipole, induced dipole and London-dispersion attraction...and seeing how ε/kB increases dramatically from Hydrogen gas (37.0K) to CO (100K) to Carbon Dioxide (189K), I wonder dipole-dipole is the most significant in the potential? Also, the fact that including very polar atoms (for example Fluorine) plays an important role, for CF4 increases ε/kB to 152K? But, I don't understand why organic molecules, such as Methane, C2H4 and C3H8 have much higher ε/kB values?
 
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The 1/r6 term originates from dipole-dipole interaction, but when modelling a molecule with a covalent bond (as opposed to, say, the van der Waals interaction in noble gases), then the LJ potential parameters becomes simply a "best fit" to the actual potential energy curve. The depth of the potential is then related to the dissociation energy of the bond.
 
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Wait, I was sure 1/r12 was repulsion and 1/r6 was a matter of attraction and distance between molecules/atoms, but is it simply matter of bonding, as in dipole-dipole, induced dipole and covalent? Please correct me, but I am new to the subject of 1/r12 and 1/r6, so forgive me if I am wrong.
 
  • #4
terp.asessed said:
Wait, I was sure 1/r12 was repulsion and 1/r6 was a matter of attraction and distance between molecules/atoms, but is it simply matter of bonding, as in dipole-dipole, induced dipole and covalent? Please correct me, but I am new to the subject of 1/r12 and 1/r6, so forgive me if I am wrong.
You are correct. Maybe it is me who is misunderstanding what you are asking about. Are you looking at the Lennard-Jones potential to describe bonding inside a molecule, or for intermolecular interactions?
 
  • #5
I am looking at the LJ potential to describe a covalent bond strength...so, inside a molecule?
 
  • #6
Ok, so what I wrote was relevant. The origin of the 1/r6 term in the LJ potential is the long-range dipole-dipole (or better, induced dipole-induced dipole) interaction between two atoms or molecules, also known as the van der Waals interaction. This is completed by a repulsive short-range 1/r12 term that mimics the close-range interaction. One of the advantages of this potential is that it reproduces the long-range potential energy correctly.

Now you can use this potential to represent other situations, such as a covalent bond, but it is only an approximation to the real potential. Another common approximation is the Morse potential. To come back to your question, the parameter ε represents the energy scale of the potential, and so is related to the bond energy. When figuring out LJ parameters, people try to find the values of ε and r* that best reproduce a particular molecular bond, whatever "best" means (can be context specific). So yes, there is a link between ε and the strenght of covalent bonds.
 
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1. What is the Lennard-Jones potential?

The Lennard-Jones potential is a mathematical model that describes the interaction between two neutral atoms or molecules. It takes into account both attractive and repulsive forces between the particles.

2. How is the Lennard-Jones potential calculated?

The Lennard-Jones potential is calculated using the following equation: V(r) = 4ε[(σ/r)^12 - (σ/r)^6], where r is the distance between the particles, ε is the well depth of the potential, and σ is the distance at which the potential is zero.

3. What is the significance of the parameters ε and σ in the Lennard-Jones potential?

The parameters ε and σ in the Lennard-Jones potential determine the strength and range of the interaction between particles. ε represents the depth of the potential well, while σ represents the distance at which the potential is zero.

4. What types of systems can be described using the Lennard-Jones potential?

The Lennard-Jones potential is commonly used to describe the interactions between noble gases, such as argon and xenon, as well as non-polar molecules. It can also be applied to larger systems, such as biomolecules, by adjusting the parameters to account for the effects of dipole interactions.

5. What are some limitations of the Lennard-Jones potential?

One of the main limitations of the Lennard-Jones potential is that it does not account for quantum effects, which are important for describing the behavior of particles at very low temperatures. It also does not take into account the effects of charged particles or polar molecules, as it assumes neutral particles with no dipole moments.

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