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Additional to Alone Programmer's answer. The Lennard-Jones Potential (LJ 12-6) is the standard, but is not unique, in some cases the factor of 6 is changed to 8 to simulate better the hydrogen bonds. Also, there is the Buckingham potential, where the repulsion part ($r^{12}$ term) is modified to the exponential term. But the attractive long-range term ($r^{... 20 You are looking for Lennard-Jones potential. Basically, the interatomic interaction is modeled by this formula: $$U(r) = 4 \epsilon \Bigg [ \Big ( \frac{\sigma}{r} \Big )^{12} - \Big ( \frac{\sigma}{r} \Big )^{6} \Bigg ]$$ Particularly the term$r^{-6}$in the above formula describes long-range attraction force based on van der Waals theory. Update: I'll ... 19 First I will try to directly answer this question: In terms of energy, how are van der Waals forces modelled (are there formulas that govern these)? The most common way to model the potential energy between two ground state (S-state) atoms that are far apart, is by the London dispersion formula: $$V(r) = -\frac{C_6}{r^6}$$ where$C_6$depends on the ... 15 Before talking about the pros and cons of ML-potentials, there is a huge conceptual difference between empirical- and ML-potential that needs to be clarified. In empirical potentials, one uses data from experiments to find the parameters of a fixed functional form that would explain the experiment. This is an inverse problem which is mathematically ill-posed ... 15 (Expanding my comment into an answer) When ML-based forcefields are compared to classical forcefield directly, I think we miss the most important points. ML-based models have several advantages: They do not need an a priori "correct" description of the system, nor are they limited by the applicability of specific theories to your system. Classical force ... 15 ForceBalance ForceBalance is one approach which aims at making it easier to create force fields from a combination of theoretical and experimental data. I believe it's within the OpenMM framework. The paper on the work can be found here https://pubs.acs.org/doi/10.1021/jz500737m From the GitHub page it says "The purpose of ForceBalance is to create ... 14 EDIT Doing what you want is hard! You will need a full quantum mechanics based simulation. This is unlikely to be something you can build yourself at the current time. Based on your new additions to the question what you need is Car-Parrinello or Born Oppenheimer MD. These essentially automate the idea of do a quantum electronic structure calculation, take ... 13 Lennard-Jones combining rules Most force fields define a single σ and ε for each atom and calculate them for combinations using Lorentz-Berthelot combining rules. These rules specify a arithmetic mean for σ and a geometric mean for ε:$\sigma_{ij} = \frac{1}{2}\left( \sigma_i + \sigma_j \right)\epsilon_{ij} = \sqrt{\epsilon_i \epsilon_j}$This reduces the ... 13 How to proceed depends on how accurate you want the outcome. Throughout my answer I will provide blue buttons which demonstrate that there's entire tags in our community to address certain aspects of the simulation. What you are describing is (essentially) what we call molecular-dynamics even though you're dealing with atoms rather than molecules. In MD (... 12 The only proper way to do it ab initio is to calculate the energy (E) for various internuclear distances (R) and then to approximate the equilibrium bond length by choosing the distance which has the lowest energy, or by fitting the E(R) points to something like a Morse potential (which is decent for short-distances), Lennard-Jones potential (which is decent ... 12 Generally speaking, most work in molecular dynamics tries to simulate how actual molecules behave (i.e. quantum mechanics) and it doesn't sound like you want to go down that rabbit hole. I completely agree, but I'll begin with a disclaimer that looking up "molecular dynamics" probably won't turn up the kind of results you want. Since your comments ... 10 In order to simulate two atom interaction, you have different path to follow. One is to use Density Functional Theory (DFT) or ab initio, make a script where the distance of the atoms is decreasing, and for each distance, you calculate the system energy. The image below is the result of such calculation but between a metal atom and a carbon nanotube1. You ... 10 My recommendation is to you look at the force-fields data from software that implement Molecular Mechanics. One example: at the Github site from the PYMATGEN project, you can get some library potentials files (in this case, used by GULP package). For the DREIDING force-field, you have a file with data with bond, torsions and Lennard-Jones parameters: (note: ... 9 The following are three important aspects of any force-field fitting workflow, Training Data: There should be DFT/experimental values that define structure, energetics, elastics or any other properties of the desired system. Optimizer: This is the heart of any force-field fitting tool/software. The parameters of force-field can be optimized against the ... 9 ForceBalance Cody is right, ForceBalance is designed for the task of generating custom force fields. Force fields have a lot of variability in their functional forms, representation of parameters (as text, XML files or objects in code), the possible values or ranges of parameters, the software that runs simulations using the force field, the experimental ... 9 In short, it is a semi-empirical approach to atom/atom interaction for periodic systems. It is based on the embedded atom method (EAM) idea where "the energy of a given atom is taken as one half the energy in two-body bonds with its neighboring atoms plus the energy to embed the atom in the electron density at its site arising from all the other atoms&... 8 The simplest possible atomic simulation: a noble gas As explained by Nike Dattani, what method you use depends on what you want to simulate and why. He gives you a good roadmap for what method to choose based on what you want to do. I wanted to take a different perspective. If you're familiar with writing code and want to program the simulation yourself, ... 8 Generally, if you want to perform simulations with some force field, you will have to search the literature for published FFs tailored for your problem. The Stillinger-Weber (SW) model is very popular to describe bulk (diamond) silicon, for which it was designed in the first place. But several reparametrizations have also been published. If you happen to ... 7 Universal Lennard-Jones In addition to the answer on combining rules, there are some "universal" Lennard-Jones parameters, published by Elliott and Akerson. The OpenKIM project is an Open Knowledgebase of Interatomic Models. It's integrated into a variety of simulation codes and allows you to pick out parameters for force field and interatomic ... 7 Unfortunately the answer to this question is much the same as your last one. What you are trying to do is hard. Very hard. Creating this would be PhD if not postdoc work and doing it well could well win you a nobel prize. From the comments you've made in this and your other question you do not appear to be a specialist in either physics or chemistry, and ... 6 I don't know why you need atom-atom interactions in a sandbox game. My only guess is that you want to simulate or visualize the movement of molecules of some kind in real time. If your system is large i.e. more than ~20 atoms, you have to resort to molecular dynamics to get reasonable speed. This has already been covered in detail in Max's answer, so I will ... 6 There is quite abit of work going on in this field right now. Take a look at what Rogers et al. are doing using MP2 to derive all aspects of a force-field. They are also working on a DFT implementation, since DFT is alot faster and computationally cheaper. I will assume that by interatomic, we are concerned with distant atoms interacting, and not near ... 5 However, I am not clear which command have to be used to optimise the structure at a certain pressure to have the constant pressure at the final step. For this you need to perform a time integration from the Isobaric Isothermal ($NPT$) ensemble. Essentially performing these dynamics, you equilibrate the systems at certain$T$and$P$. In LAMMPS ... 5 Get your parameters from an existing force field (UFF? ReaxFF?) People in the molecular dynamics world use established force fields to describe forces between different types of atoms. These force fields are mathematical functions that have parameters like bond lengths, bond angles, dihedrals, van der Waals radii, etc. Usually these parameters are obtained ... 5 I searched for the word "minimum" on the Wikipedia page for Lennard-Jones potential, and the 2nd paragraph says: "The potential minimum is at$r=r_m = 2^{1/6}\sigma$." You can obtain this by calculating the derivative of the Lennard-Jones potential with respect to$r$and finding which$r\$ value makes that derivative equal to 0.

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Got a bit too long for a comment, so I'll leave it as a semi-complete answer for now. In case the paper is inaccessible to other readers, much of the same information is in the gulp5.2 manual. In regards to the question, it does seem to elaborate a little in the sentences following your quote. From earlier in the document: Here the Coulomb interaction, and ...

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The most trivial model to estimate bond lengths between two atoms is probably a simple sum of Van-der-Waals Radii. Just load a table with Van-der-Waals Radii and take the equilibrium distance for two atoms as the sum of the Van-der-Waals Radii of both atoms. This is by no means accurate but for the intention of the poster it might suffice. If this is still ...

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Did you check that the bulk structures are stable? If they are, then the Coulomb part should be working, and the problem might be in your model. This type of problem is actually relatively common. If you use potentials that have been fit for bulk materials i.e. perfect crystals, you're only studying a small range of the possible configuration space: the ...

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