# What is Lennard-jones: Definition and 26 Discussions

Sir John Edward Lennard-Jones (27 October 1894 – 1 November 1954) was a British mathematician and professor of theoretical physics at the University of Bristol, and then of theoretical science at the University of Cambridge. He may be regarded as the initiator of modern computational chemistry.

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1. ### I Pair interaction potential with more than one mininum?

Pair interactions between atoms and molecules (in gas kinetic theory simulations or other applications) are described by empirical potential energy functions such as the Lennard-Jones potential: ##V_{LJ} (r) = 4\epsilon \left[ \left(\frac{\sigma}{r} \right)^{12} -...
2. ### A Lennard-Jones for bound/unbound atoms?

I can't find anywhere information on how people treat bound/unbound condition for atoms with Lennard-Jones simulation. Say if I have 3 oxygen atoms flying around and two of them at some point become an O2 molecule, this means their electron shells are now fully occupied - so I am guessing the...
3. ### How to determine the spring constant in a Lennard-Jones potential

Hi, First of all I hope it doesn't bother if I ask too much question.I found the values of ##u1,u2## for 2 differents posistions ##(r1,r2 )## and I now have to determine the spring constant (k).I'm thinking about using$$F= -kx$$ with ##F = -\frac{du}{dr}## then  U = \int -kr \cdot dr...
4. ### B My Third Post: Change of Intermolecular Distance?

Hello, Let us imagine a rod resting on a frictionless horizontal surface such that the rod is made up of 2 identical molecules. Let these molecules be named A and B from left to right. If we pull A to the left and B to the right with forces of equal magnitude, the rod must remain at equilibrium...
5. ### Lennard-Jones Work: Calculating Equilibrium Position

Homework Statement I need to calculate the work donde by the Lennard-Jones Law, considering: F(r)=F0 [2(σ/r)13-(σ/r)7] when approximating two atoms from infinity to the equilibrium position between both atoms Homework Equations First thing I don't know how to calculate is the equilibrium...
6. ### [PoM] Lennard-Jones potential parameters

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...
7. ### Lennard-Jones potential minimized

Homework Statement At what distance r is the Lennard Jones potential minimized? Homework Equations Typical graph of Lennard Jones potential, U(r) vs. r/σ The Attempt at a Solution I thought that from looking at the graph, r = ∞ for potential minimization. However, the answer turned out to...
8. ### MATLAB Piecewise MATLAB ode45 problem for Lennard-Jones

I could run the MATLAB codes but the main issue is that data for T1 and U1 could not be produced. I am currently trying to calculate the displacement of two particles after the collision with walls with length of 10 units. Here are the codes. If you don't understand its context, you can refer...
9. ### Is the Depth of Lennard-Jones Potential Linked to Covalent Bond Strength?

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...
10. ### Lennard-Jones Potential: Derive an expression for equilibrium constant

Edit: well this is frustrating, not sure why the itex things aren't working.. Edit2: I've attached a picture of the question at the bottom as well. Homework Statement The cohesive energy of a solid noble gas may be written as (See picture below) Derive an expression for the...
11. ### Linear compressibility Lennard-Jones potential

Homework Statement Please see attachment. The correct answer is supposed to be ##\alpha = .15 k_B/U_0##. The Attempt at a Solution The minimum of the potential is at ##x = a##. Expanded about this minimum we get ##U = -U_0 + 36\frac{U_0}{a^2}(x - a)^2 - 252\frac{U_0}{a^3}(x - a)^3 + ...##...
12. ### Checking my work on a Lennard-Jones problem

EDIT: Found a silly algebra mistake. But let me know if I got this right. Homework Statement The Lennard-Jones potential is U(r) = \left[ \left( \frac{\rho}{r} \right)^{12} - \left( \frac{\rho}{r} \right)^6 \right]. What is the equilibrium distance? And can you show that the movement...
13. ### Temperature dependence of Lennard-Jones potential

My question is not so much about the Lennard-Jones potential, although I mentioned it in the title, but of the "force field" thinking in general. So a lot of people are (were) interested in the phase transition temperature of the Ising model. How realistic is the model in the sense that it...
14. ### Lennard-Jones Potential: Equilibrium Distance and Dissociation Work

Homework Statement The Lennard-Jones equation shown below gives the potential energy of two atoms when they are separated by a distance r. U(r)=4 U_0 \left[\left(\frac{r_0}{r}\right)^{12}-\left(\frac{r_0}{r}\right)^6\right] a)What is the distance between atoms at the condition of stable...
15. ### What is the Form of the Lennard-Jones Potential Between Two Water Molecules?

Homework Statement Deduce the form of the Lennard-Jones potential between two water molecules. given/known: molar enthalpy of evaporation of water is 4.1x104J/mol density is 103kg/m3 Assume water molecule is surrounded by approximately ten nearest-neighbours. Take Mr = 18 Homework...
16. ### Lennard-Jones potential graph w/ attractive/repulsive force

Based on this and the equation F = -d\Phi/dr. I can't visualize what is positive and negative force direction (what is positive direction). So is that just mean whenever the force between 2 molecules (+), it's repulsive; and whenever it's (-), it's attractive? Thanks for checking this out.
17. ### Lennard-Jones Force Formula Python Program

I'm not looking for the answer, I just want some help with understanding the question. The main thing I'm stuck on is the characteristic binding energy and the characteristic molecular size. I've tried searching for these but I'm finding a lot of different stuff. Homework Statement All to...
18. ### Lennard-Jones parameters for silicon nitride

Hello Forum, This is my first time on this forum, so, please, forgive me if I've mistaken the right section for the following question. For my research, I need to know the values of LJ pair-potential parameters: the depth of the potential well and the distance at which the latter becomes...
19. ### Disconnect between Lennard-Jones and Heat of Vaporization

I'm trying to understanding "Heat of Vaporization" in fundamental terms. People say that processes like evaporation and boiling are endothermic because chemical bonds are being broken, but for actual cooling to occur there must a loss in translational kinetic energy of the molecules involved...
20. ### Lennard-Jones potential for 3 atoms

If I have a 3 atom lattice laid out at positions ##x_1 = 1, x_2 = 2, x_3 = 3## ##x_1## and ##x_3## are stationary, but ##x_2## interacts with ##x_1## and ##x_3## via the Lennard-Jones interatomic potential. I therefore worked out that the total acceleration for ##x_2## for ##m = \sigma =...
21. ### Lennard-Jones Potential - distance of closest approach

Here's my solution to the problem of finding the distance of closest approach for two atoms approaching each other in a Lennard-Jones potential, starting with velocities (+/-) v_0: They start with energy T0 = (1/2)m(2v02) which is conserved. Thus, E = T + V = (1/2)m(2v2) + A/r12 - B/r6 = T0...
22. ### What is the change of variables for Lennard-Jones potential?

Homework Statement http://img94.imageshack.us/img94/4287/len2.jpg Homework Equations [PLAIN][PLAIN]http://img710.imageshack.us/img710/2428/len1y.jpg The Attempt at a Solution I know my way around the Lennard-Jones potential formula, but this question stumps me. Any clues on how...
23. ### Lennard-Jones Potential V(r) (Condensed Matter)

http://www.ph.qmul.ac.uk/phy108/CM2005_week2_Lecture3_Interatomic%20Forces2.pdf Page 6, I've understood all of the notes so far. But it just randomly goes into this, what/where did these p's and q's come from? What do they mean? Can't find anything that I can understand online!
24. ### Better potential than Lennard-Jones for Carbon Carbon interactions?

Hello! I was wondering if anyone could provide me with any advice on a better interatomic potential than the Lennard-Jones (Mie 6-12) potential for carbon-carbon interactions. I know that L-J fails for metals, but I am not sure how good it would be for carbon-carbon interactions. Are there any...
25. ### Lennard-Jones model and Energy Conservation

Hi, i've been doing a simulation using LJ model, but I'm having a troublesome time on figuring out, what's happening with the energy :rolleyes: This is the LJ potencial: E = 4\epsilon\left[\left(\frac{\sigma}{R}\right)^{12} - \left(\frac{\sigma}{R}\right)^6\right] but I've been using...
26. ### Computing Lennard-Jones potentials for molecules

anyone here have knowledge on computing Lennard-Jones potentials for molecules using periodic boundaries versus doing it on the 3D surface of a hypersphere?