# lennard–jones potential energy diagrams plot the potential energy of interaction between two atoms as a function of the separation between them. use the diagram to approximate the optimum internuclear spacing and potential energy for the interaction between two ne atoms.

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Transcribed Image Text:Lennard-Jones potential energy diagrams plot the potential energy of interaction between two atoms as a function of Lennard-Jones potential diagram for Ne-Ne the separation between them. Use the diagram to approximate the optimum internuclear spacing and 1.00 - 0.50 - 0.00 potential energy for the interaction between two Ne atoms. A -0.50 - 2.00 2.50 3.00 3.50 4.00 4.50 5,00 5.50 6.00 -1.00 – -1.50 – -2.00 – internuclear spacing 2 Å -2.50 - -3.00 – -3.50- 4.00 – potential energy = x10-22 J -4.50 - -5.00 – Internuclear distance (Ã) privacy policy terms of use contact us help about us careers Potential energy (10-² J)

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## Solved Lennard–Jones potential energy diagrams plot the

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## Lennard

The Lennard-Jones Potential is a mathematical model that explains interactions between two atoms at a certain distance. It consists of two terms that describe attractive and repulsive force between …

## Lennard-Jones Potential

Last updated Aug 15, 2020

Ion - Ion Interactions

London Dispersion Interactions

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Proposed by Sir John Edward Lennard-Jones, the Lennard-Jones potential describes the potential energy of interaction between two non-bonding atoms or molecules based on their distance of separation. The potential equation accounts for the difference between attractive forces (dipole-dipole, dipole-induced dipole, and London interactions) and repulsive forces.

## Introduction

Imagine two rubber balls separated by a large distance. Both objects are far enough apart that they are not interacting. The two balls can be brought closer together with minimal energy, allowing interaction. The balls can continuously be brought closer together until they are touching. At this point, it becomes difficult to further decrease the distance between the two balls. In order to bring the balls any closer together, increasing amounts of energy must be added. This is because eventually, as the balls begin to invade each other’s space, they repel each other; the force of repulsion is far greater than the force of attraction.

This scenario is similar to that which takes place in neutral atoms and molecules and is often described by the **Lennard-Jones potential**.

## The Lennard-Jones Potential

The Lennard-Jones model consists of two 'parts'; a steep repulsive term, and smoother attractive term, representing the London dispersion forces. Apart from being an important model in itself, the Lennard-Jones potential frequently forms one of 'building blocks' of many force fields. It is worth mentioning that the 12-6 Lennard-Jones model is not the most faithful representation of the potential energy surface, but rather its use is widespread due to its computational expediency.The Lennard-Jones Potential is given by the following equation:

V(r)=4ϵ[ ( σ r ) 12 − ( σ r ) 6 ] (1)

(1)V(r)=4ϵ[(σr)12−(σr)6]

or is sometimes expressed as

V(r)= A r 12 − B r 6 (2) (2)V(r)=Ar12−Br6 where V V

is the intermolecular potential between the two atoms or molecules.

ϵ ϵ

is the well depth and a measure of how strongly the two particles attract each other.

σ σ

is the distance at which the intermolecular potential between the two particles is zero (Figure

1 1 ). σ σ

gives a measurement of how close two nonbonding particles can get and is thus referred to as the van der Waals radius. It is equal to one-half of the internuclear distance between nonbonding particles.

r r

is the distance of separation between both particles (measured from the center of one particle to the center of the other particle).

A=4ϵ σ 12 A=4ϵσ12 , B=4ϵ σ 6 B=4ϵσ6 Minimum value of Φ 12 (r) Φ12(r) at r= r min r=rmin .

Equation1 1

**:** The LJ potential describes both the attraction and repulsion between nonionic particles. The first part of the equation, (

σ σ

/r)12 describes the repulsive forces between particles while the latter part of the equation, (

σ/ r 6 σ/r6 denotes attraction. Example 1 1 The ϵ ϵ

andσ σ

values for Xenon (Xe) are found to be 1.77 kJ/mol and 4.10 angstroms, respectively. Determine the van der Waals radius for the Xenon atom.

**Solution**

Recall that the van der Waals radius is equal to one-half of the internuclear distance between nonbonding particles. Because

σ σ

gives a measure of how close two non-bonding particles can be, the van der Waals radius for Xenon (Xe) is given by:

r = σ σ

/2 = 4.10Angstroms/2 = 2.05 Angstroms

### Bonding Potential

The Lennard-Jones potential is a function of the distance between the centers of two particles. When two non-bonding particles are an infinite distance apart, the possibility of them coming together and interacting is minimal. For simplicity's sake, their bonding potential energy is considered zero. However, as the distance of separation decreases, the probability of interaction increases. The particles come closer together until they reach a region of separation where the two particles become bound; their bonding potential energy decreases from zero to a negative quantity. While the particles are bound, the distance between their centers continue to decrease until the particles reach an equilibrium, specified by the separation distance at which the minimum potential energy is reached.

If the two bound particles are further pressed together, past their equilibrium distance, repulsion begins to occur: the particles are so close together that their electrons are forced to occupy each other’s orbitals. Repulsion occurs as each particle attempts to retain the space in their respective orbitals. Despite the repulsive force between both particles, their bonding potential energy increases rapidly as the distance of separation decreases.

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