Is the Depth of Lennard-Jones Potential Linked to Covalent Bond Strength?

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SUMMARY

The discussion centers on the relationship between the depth of the Lennard-Jones (LJ) potential, represented by the parameter ε, and covalent bond strength. It is established that the 1/r6 term in the LJ potential corresponds to long-range dipole-dipole interactions, while the 1/r12 term accounts for short-range repulsive forces. The parameter ε is directly linked to bond energy, indicating that higher ε values correlate with stronger covalent bonds. The conversation also highlights the limitations of the LJ potential as an approximation for covalent bonding compared to other models like the Morse potential.

PREREQUISITES
  • Understanding of Lennard-Jones potential parameters (ε and r*)
  • Familiarity with intermolecular forces, including dipole-dipole and van der Waals interactions
  • Basic knowledge of covalent bonding and bond energy concepts
  • Awareness of alternative potential models, such as the Morse potential
NEXT STEPS
  • Research the mathematical derivation and applications of the Lennard-Jones potential
  • Explore the Morse potential and its advantages over the Lennard-Jones potential
  • Study the role of polar atoms in influencing ε values in molecular interactions
  • Investigate the significance of dipole-dipole interactions in various molecular species
USEFUL FOR

Chemists, physicists, and materials scientists interested in molecular interactions, computational modeling, and the relationship between intermolecular forces and covalent bond strength.

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.
 
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?
 
I am looking at the LJ potential to describe a covalent bond strength...so, inside a molecule?
 
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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