Lennard-Jones potential .

[terp.asessed]

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/k_B 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/k_B to 152K? But, I don't understand why organic molecules, such as Methane, C₂H₄ and C₃H₈ have much higher ε/k_B values?

 

[DrClaude]

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.

 

[terp.asessed]

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.

 

[DrClaude]

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?

 

[terp.asessed]

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

 

[DrClaude]

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.