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I have a question related to parameterize Lennard-Jones interaction to get sigma $\sigma$ and epsilon $\epsilon$ to include in amber force field to do the Molecular Dynamics.

I searched a lot, they always said you should do scan between two atoms and then fit with Lennard-Jones Equation, but they don't explain which atom should I select or depend on what should I select the atoms. I am a bit confused.

In my case, I have a complex where I have two transition metals (Ru, Pt), where Ru have 6 bond with Nitrogen and Pt have two bonds with Chloro and two bonds with Nitrogen. I want to get the $\sigma$ and $\epsilon$ for both. But I don't understand which distance I should select to do the scan.

Can anyone help me to understand this point?

Here is the structure. enter image description here

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  • $\begingroup$ If it is bonded, and you are using the AMBER forcefield, I doubt you should be optimizing LJ parameters. I am really curious where they say in AMBER literature, to do a potential energy scan and fit LJ to it? can you add a source? $\endgroup$
    – Wesley
    Apr 11, 2022 at 18:13
  • $\begingroup$ @Wesley Here is the link chemistry.stackexchange.com/q/127789/101338 for a question similar. In the answer, there are a lot of links about parameter fitting. here as well a link mattermodeling.stackexchange.com/a/8707/4657 for a question, I asked before and Camps answered me. $\endgroup$ Apr 11, 2022 at 19:29
  • $\begingroup$ I don't understand you well. I want to build a force field, but my complex contains transition metal. So I need to calculate the bond, angle, dihedral, van der waals parameter for the metal. $\endgroup$ Apr 11, 2022 at 19:53
  • $\begingroup$ I would trust Camps and Geoff over me since I don't have experience with transition metals. My default approach however would be to fit LJ parameters in such a way as to minimize error between forces & energies, and I would do it over many many structures. But, perhaps transition metals have their own rules. I woud be comfortable fitting bond, angle and torsion and charge parameters solely from QM, but I don't think I would want to fit LJ from a single potential energy scan. $\endgroup$
    – Wesley
    Apr 12, 2022 at 14:33
  • $\begingroup$ @Wesley what is your suggestion ? I am doing a single potential energy scan and by using the distance and energy. I am doing a code that fit the curve with LJ equation and using curve fit in python to get the best value for sigma σ and epsilon ϵ $\endgroup$ Apr 12, 2022 at 14:46

2 Answers 2

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I searched a lot, they always said you should do scan between two atoms and then fit with Lennard-Jones Equation, but they don't explain which atom should I select or depend on what should I select the atoms. I am a bit confused.

Normally, pairs of atoms connected by chemical bonds are excluded from computation of non-bonded interactions because bonded energy terms replace non-bonded interactions. Also, it is common that in biomolecular force fields all pairs of connected atoms separated by up to 2 bonds (1-2 and 1-3 pairs) are excluded from non-bonded interactions. For example, in the image below, only the atoms 1 and 4 are considered for non-bonded interactions [1]: enter image description here

But I don't understand which distance I should select to do the scan.

You create a new system with only the two atoms you want to calculate the interaction energy. You put them apart a fixed distance. Giving the x, y, z coordinates: you can select for example: $x_1=0$, $y_1=0$ and $z_1=0$ for the first atom, and $x_2=d$, $y_2=0$ and $z_2=0$ for the second one with $d$ being the distance between them. You start with $d=1$, do a single point energy, then increase $d$, do a single point energy, and so. At the end, you will have the data to plot the energy vs $d$ and then do the fitting.

Be aware that, if your atoms are not parametrized by the fore field you are interested in, you will need to obtain all the other force fields parameters as well (take a look here).

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  • $\begingroup$ @Abd-ElazeemMohamed To avoid things getting too long here, I moved the discussion to chat $\endgroup$
    – Tyberius
    Apr 11, 2022 at 20:50
  • $\begingroup$ @Tyberius Camps. Do u have any source (article ) for this part? $\endgroup$ Apr 19, 2022 at 17:16
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You linked to my answer about parameterizing force fields. For reference, this isn't my area of expertise, although a colleague's group does this frequently.

My understanding of your question is that you want to get the non-bonded interactions between the Ru and Pt atoms in the larger complex.

What you describe is going to be tricky, even with automated force field methods like I described on Chem.SE.

In your case, you don't have neutral metal ions - you have transition metals with a surrounding ligand sphere.

Ordinarily, you'd pick the relevant elements, maybe start from the initial distance between them, scan closer and scan farther until you see a full minima. (You want at least parts of the repulsive and attractive regions to fit the potential energy curve.)

For metals, it's more complicated. There are a few approaches.

I'd probably go with the "dummy atom" method - you surround the metal ions (Ru and Pt in your case) with partially charged dummy atoms, so the net charge is identical, but the ion is properly surrounded with the right coordination environment and has some charge delocalization.

enter image description here

A fairly readable article is "Force Field Independent Metal Parameters Using a Nonbonded Dummy Model".

So you'd add some dummy atoms to the Ru and Pt at the positions relevant in the complex (e.g., remove the carbon atoms and hydrogen around both, then change the nitrogen atoms around the Ru to dummy (Du) and the two nitrogen and two chlorine atoms around the Pt atom.

Then map the curve .. again starting near the distance in the complex, going shorter and longer until you've mapped out the LJ curve.

Since it looks like you're using Avogadro, you can use the "Align" tool, click on the Ru atom to make that the origin, then the Pt atom to make that along one of the axes (e.g, x-axis). Then you can select the Pt+dummy "molecule" and use the manipulate tool to translate it forward and backwards.

Moving two water molecules closer along the x-axis

Merz also has a series of articles talking about the development of parameters for water models (TIP3P, etc.). These are probably less relevant to your needs, but discuss some of the challenges.

I'm probably leaving off relevant papers.

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  • $\begingroup$ Thanks for your comment. I will take a look at the article about dummy atoms. Moreover, I included the picture for the structure in the post if it can help more. $\endgroup$ Apr 12, 2022 at 14:54
  • $\begingroup$ I have a question, "map the curve .. again starting near the distance in the complex, going shorter and longer until you've mapped out the LJ curve." What do u mean here ? Should I do the scan for the system contains Pt and Ru with dummy atoms at the same time? Or I should deal separately with both ? $\endgroup$ Apr 14, 2022 at 13:14
  • $\begingroup$ If you want the Pt-Ru parameters, then you’ll need to scan the system with both. Obviously, you’ll also need to scan them separately for Pt-C, Pt-N etc non bonded parameters as needed. $\endgroup$ Apr 14, 2022 at 17:59

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