# [PoM] Lennard-Jones potential parameters

• BRN
In summary, you determined 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. You also calculated the minimum oh the potential, V(0), and found that the potential energy is lowest when the boron and nitrogen nuclei are separated by 1.666 cm-1.
BRN
Hi guys! I need your help!

1. Homework Statement

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.

## The Attempt at a Solution

[/B]
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...

BRN said:
For ε, I calculating k by:

k=∂2V(R)/∂R2=6σ6εR-14(26σ6-7R6)

but here I'm lost...
You need an equation to relate k to ##\nu##, then the only unknown in there will be ε.

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...

BRN said:
For ε, I calculating k by:

k=∂2V(R)/∂R2=6σ6εR-14(26σ6-7R6)
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:
BRN said:
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...
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.

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!

## 1. What is the Lennard-Jones potential and how is it used in scientific research?

The Lennard-Jones potential is a mathematical model used in molecular simulations to describe the interactions between atoms or molecules in a system. It is used to calculate the potential energy between two particles as a function of their distance. This potential is commonly used in research to study properties of gases, liquids, and solids at the molecular level.

## 2. What are the parameters in the Lennard-Jones potential and how are they determined?

The two main parameters in the Lennard-Jones potential are the equilibrium distance between particles (sigma) and the depth of the potential well (epsilon). These parameters are determined empirically by fitting the potential to experimental data or by using theoretical calculations.

## 3. What is the significance of the Lennard-Jones potential parameters in understanding intermolecular interactions?

The parameters in the Lennard-Jones potential are important in understanding intermolecular interactions because they determine the strength and distance dependence of the interactions between particles. By adjusting these parameters, scientists can simulate different types of molecules and study their behavior in various environments.

## 4. How do Lennard-Jones potential parameters affect the stability and structure of a system?

The Lennard-Jones parameters determine the potential energy of a system, which directly affects its stability and structure. The equilibrium distance between particles (sigma) affects the distance at which particles are most stable, while the depth of the potential well (epsilon) determines the strength of the interactions between particles. These parameters play a crucial role in determining the overall stability and structure of a system.

## 5. Can the Lennard-Jones potential parameters be modified for different types of interactions?

Yes, the Lennard-Jones potential parameters can be modified to model different types of interactions between particles. For example, the parameters can be adjusted to simulate repulsive or attractive forces between particles, or to account for polar or charged interactions. This allows for the Lennard-Jones potential to be applied to a wide range of systems and research areas.

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