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Apologies in advance if this is the wrong StackExchange to ask this question in... if it is not, please don't just down-vote, let me know where else to go and I will gladly. I'm just trying to learn. I'm trying to build a 3D representation of an Atoms (and Molecules) with accurate electron placement. (AKA not the Bohr's Model, instead, electron orbitals) So, is there any formula I can use in order to generate a random 3D point within any of the different electron orbitals? Or, more possibly, is there a formula I can use to create 3D models of all the electron orbital configurations? Or maybe there are already 3D models of this created that I can use in my own project?

If I can manage to generate or get a 3D model of these orbital configurations, I think I can just pick a random point within the orbitals corresponding to an element in order to place the electrons in a somewhat accurate fashion.

I appreciate any help, and send thanks in advance for any insight you may have!

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    $\begingroup$ The answer to your question is (at least superficially) obvious to me which is why I initially downvoted: Find the position wavefunctions of electrons in an atom. However, I found that googling for such wavefunctions isn't as easy as I assumed it would be. $\endgroup$ – PiKindOfGuy Mar 4 at 15:48
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    $\begingroup$ For anything beyond hydrogen, I suspect it will be quite difficult to find simple equations to give you the shapes of your oribitals (and to utilize those, you will need clouds rather than spheres for the electrons). I wouldn't be surprised if orbitals for heavier atoms aren't even described by analytically solvable solutions. And if you want to do organic, molecules, it should get even fancier with hybridization. $\endgroup$ – user191954 Mar 4 at 15:56
  • $\begingroup$ Furthermore, I think "is there any formula I can use in order to generate a random 3D point within any of the different electron orbitals?" won't exactly work because you can't exactly say that 'the electron jumps to a different random point every instant, and I will put a white sphere in each of those positions": $\endgroup$ – user191954 Mar 4 at 16:02
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    $\begingroup$ Would a DFT solution be acceptable? That does mean running the DFT for each situation of interest and validating it though... $\endgroup$ – Jon Custer Mar 4 at 19:41
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    $\begingroup$ Have a look at DFT softwares. Some are open source. With this, you can calculate the electronic density of atoms, molecules and full bodies. $\endgroup$ – thermomagnetic condensed boson Mar 4 at 19:59
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"Accurate electron placement". As far as I know, electrons are just probability clouds so placing them accurately is not possible. Your best bet would be to use Bohr's model if you want to place them.

What you can also do is to show them as orbitals. These are essentially probability clouds where you can find the electron most of the time. This would be a more accurate model.

By the way, your website is beautiful.

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  • $\begingroup$ By accurate electron placement, I mean that I would like to place them randomly within their corresponding orbital probability cloud. However, in order to do that, I need to either be able to generate or receive the 3D model for all the different orbital cloud configurations. Thanks by the way! I've put a lot of effort into it and am trying to expand it further. :) $\endgroup$ – Darryl Huffman Mar 4 at 15:50
  • $\begingroup$ The s-orbital is very easy. It's just a sphere which you can generate easily. $\endgroup$ – harshit54 Mar 4 at 15:52
  • $\begingroup$ Can't you manually write the expressions using this as reference. $\endgroup$ – harshit54 Mar 4 at 15:56
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    $\begingroup$ "Your best bet would be to use Bohr's model if you want to place them." that's probably the most important bit in this answer. Atomic orbitals just don't logically give you a new random point for each instant. $\endgroup$ – user191954 Mar 4 at 16:03
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    $\begingroup$ @Chair I think he he is talking about randomly generating the electron within the orbital every second. $\endgroup$ – harshit54 Mar 4 at 16:06
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I suggest the use of a DFT package such as QUANTUM ESPRESSO or other similar open source or free softwares. I think there are tutorials to be found easily on the Internet. With this, you can calculate the electronic density of atoms, molecules and even complex solids.

Then, as you say, once you have the electronic density, it is easy to pick a random point from the given density.

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