# [PoM] Lennard-Jones potential parameters

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1. Nov 24, 2016

### BRN

Hi guys! I need your help!

1. The problem statement, all variables and given/known data

Use the function of Lennard-Jones V (R) = ε [(σ / R)12 - (σ / R)6] as model for the adiabatic potential energy in function of the separation between the 11B boron and nitrogen nuclei 14N. You determine the parameters ε and σ to reproduce the spectroscopic values of the vibrational quantum, ν = 1514.6 cm-1, and the separation of 1,666 cm-1 between the lines of rotational BN molecule.

3. The attempt at a solution

I have

ΔErot2/I=1.666 cm-1=3.3091*10-23 J I=ħ2/ΔErot=3.3603*10-46 Kgm2

and

R0=√(I/μ)=1.8125*10-10 m

At this point, I calculating the minimum oh the potential:

V(0)=∂V(R)/∂R =0 ⇒ R06=2σ6 ⇒ σ=6√(R06/2)=1.6147*10-10 m

For ε, I calculating k by:

k=∂2V(R)/∂R2=6σ6εR-14(26σ6-7R6)

but here I'm lost...

2. Nov 24, 2016

### Staff: Mentor

You need an equation to relate k to $\nu$, then the only unknown in there will be ε.

3. Nov 24, 2016

### BRN

the only equation i know to relate k to ν is:

ν=1/(2πc)√(k/μ)

so, i have (using R=R0):

ε=[μ(2πcν)2σ7(6√2)14]/(72σ6)

but is dimensional incorrect...

4. Nov 24, 2016

### TSny

When you let R = Ro, you should then be able to simplify to get a nice expression relating $k$ to $\varepsilon$ and $\sigma$. This might make it a little easier to get the correct expression for $\varepsilon$ in terms of $\nu$.

Last edited: Nov 24, 2016
5. Nov 24, 2016

### TSny

I think your expression for $\varepsilon$ is correct except that you appear to be off by a factor of $\sigma$. Try to simplify the expression as much as possible.

6. Nov 24, 2016

### BRN

Oh Damn!
yes, the equation is correct (apart the simplifications), but υ must be convert to m-1 and not to J!

So:

ε=[μ(2πcν)2σ2(6√2)14]/72=1.5192*10-18 J

Now it's ok!

Tanks at all!