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I Physical Dimensions of electron shells

  1. Jan 31, 2017 #1
    I want to model atoms of the periodic table using OpenGL (API for 3D graphics). I was told by a physics teacher one time that this cannot be done because it's not solvable.

    Can you guys confirm? Apparently only the shells of the hydrogen atom has been solved meaning that I can only model the lightest atoms but not any other atom?

    I want to visualize the S shell P shell etc etc and even use the shrodinger equation to simulate the probability fields of electrons.
     
  2. jcsd
  3. Feb 1, 2017 #2
    https://en.wikipedia.org/wiki/Runge–Kutta_methods

    Now if you read above it will mention k1 = f(tn.yn) as dy/dt. Does that make sense to you?
     
  4. Feb 1, 2017 #3

    Dr Transport

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    I'd listen to your physics teacher.....atoms larger than hydrogen are unsolvable without a huge computational effort.
     
  5. Feb 1, 2017 #4
    So have scientists used lots of computers to solve them and find out their actual dimensions? Maybe I can just use the numbers they got and draw the sizes and dimension accordingly instead of having the software work it out the hard way of calculating from scientific equations.
     
  6. Feb 1, 2017 #5

    Dr Transport

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    I have not seen those numbers..... Atoms are on the order of Angstroms or nano-meters, the shells are just a component and the outer shell is all that really matters.
     
  7. Feb 4, 2017 #6
    Nanno meters are not a problem at all, I can even use units of femto meters for my simulator. But I need to know the size of these P shells S shells etc so that users can appreciat the shape of the atom. Any suggestions on a compromised model? Perhaps use the bohr radius?
     
  8. Feb 4, 2017 #7

    TeethWhitener

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    Gaussian (and most other quantum chemistry programs) can calculate electron density isosurfaces from wavefunctions.
     
  9. Feb 5, 2017 #8

    blue_leaf77

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    From what the OP says about what he wants to do in his personal project, I can tell that he/she hasn't gotten sufficient background in quantum mechanics. The description of shells in atoms is actually a rather loose concept to simplify our mental image in understanding how electrons in atom move. The shell model of atom was originally invented to serve as a starting point to do much more complex and accurate computations for solving the wavefunction or electron density of the particular atom. In other words, the shell model is just a raw model before it is brought to the kitchen to make a finer model. You may have seen in different places the wavefunction of hydrogen depicted in 3D graph. It's possible because hydrogen wavefunction has three variables, all of which is associated to the only one electron it has. For atoms having more than one electron, it's impossible to illustrate the wavefunction in 3D graph as it now has 3N spatial variable with N being the number of electrons. In this case, the plot of electron density, which is a function of three spatial coordinates, gives a more useful picture.
    In the end I would like to say again to the OP that solving Schroedinger equation for multi-electron atom as it is (meaning exactly solving the differential equation) requires a significant computation time as someone has mentioned above. There are to date many approaches to do this task including density functional theory (DFT), Hartree-Fock method, configuration interaction, and many others. These non-trivial methods have already been implemented in some quantum chemistry computational routines as mentioned above. Some of them are free to get like GAMESS for example.
     
  10. Feb 5, 2017 #9

    anorlunda

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    The OP should find the Wikepedia article helpful. https://en.wikipedia.org/wiki/Atomic_orbital

    From the article this figure shows that the size and shape of orbitals is fuzzy and probabilistic. You can't express that with a single number. False-color density images of some hydrogen-like atomic orbitals
    HAtomOrbitals.png

    And this figure shows that the shape is not static.
    Drum_vibration_mode02.gif
     
  11. Feb 9, 2017 #10
    You did be wrong about your assumption that I have not got sufficient background, I have done University level Chemistry. It was back in 2008 but I know what youre talking about although I may not be familiar with things like Hartree-fock or GAMESS. I know that atoms have S shell P shell and various other shapes I understand that the shape is non trivial but there are ways around the problem of requiring super computers. You can have super computers work out the answer for you and you just use the completed 3D picture in the software. For example that gif that was supplied by the other contributor to this thread can be input into the simlation. I am aware of what a shrodinger equation is and about how elections ocupy a cloud of probability.

    My problem is I am not familiar with the unknowns. I need to know specifically what isnt known about the shells for non Hydrogen atoms. Is it the size of the electron cloud? Is it the shape? I suggested using the Bohr radius as a version 0 of my product in alpha as a starting point not as the commercial final product nor the beta version.

    I would appreciate it if you could help me with this project without injecting patronizing statements also that I fee are not nearly as accurate as you might think.

    I may be rusty but Im not ill prepared.

    From what I can tell the hydrgogen atom shells have been solved. But not the other atoms. So my question is, has work been done on the other elments using super computers and can I use their intellectual property to simply graft the completed 3D picture (animation or not) into my software? If work has not been done with super computers can I make assumptions? Where can I compromise in the best guessed 3D picture?

    S shell is a sphere P shell is a P shell regardless of which element its in so im guessing the size is only different while the shape is the same for S and P correct? Even if they interfere with each other creating a complex looking moving 3D picture that can easily be solved with animation technology. Sort of like inserting a gif file into the OpenGL software.

    I need assistence not judgement and personal attacks.
     
  12. Feb 9, 2017 #11
    I am not restricted to single number/variable software. I can in fact use these completed renderings static/moving and insert them into my software. But these are all shapes and sizes onlly for the hydrgone atom correct? What will I have to change about them for helium? Will they merely be the same shape but consistently larger?
     
  13. Feb 9, 2017 #12

    blue_leaf77

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    I am sorry if my previous statement was too judgmental but the reason why I might sound like that although it was not intentional was that what you want to do, namely picturing electronic shell of multielectron atom, is a crude assumption. You can go on by assuming that you only consider the only electron in the shell you want to plot and disregard the other ones hence making it a hydrogen-like system (which should be easy to calculate as you only need to change Z) but I am afraid this approach will not be of much helpful in visualizing what's really going on in that atom. Another way to go around this is by using Hartree-Fock (HF) method where you start from the assumption that the electrons in the atom do not interact with each other. This way the wavefunction of the electron is of Slater determinant type and the N orbital functions involved in this determinant are usually a good estimate of the shells you want to visualize. Although "good estimate" does not mean the best one, these orbitals still better visualize the shells rather than the crude, hydrogen-like assumption before. This is because in HF method, each electron moves under the effective field of the other electrons, therefore although you start from non-interacting electrons assumption the movement of one electron in an orbital already takes the repulsive effect of the other electrons into account.
    This sentence gives me the impression that in your project you just want to input the known parameters specific to a certain orbital, run the program, and get the 3D plot. Unfortunately I am afraid those "known" parameters might be nowhere to be found, may be you will find a closed form of the approximated orbital out there in the internet but I don't think such information will be available for a wide range of atoms. To get those "known" parameters so that your plot better visualize the reality, you have to calculate it yourself, and HF method is just one of the many.
    I hope this time the assistive intention of my post is not overshadowed.
     
  14. Feb 9, 2017 #13
    Lets start with very basic stuff. And then we can gradually evolve to more complex subjects, I think this is the best way to approach this as my chem is admitedly a little rusty and im actually watching some youtube videos to brush up. In the mean time I would appreciate it if you could help me with very simple questions starting with this:

    1S in hydrogen and 1S in Helium. Would they have identical radius size? Yes I know their probability clouds in sphere shape and dont actualy have a defined radius, more of an average radius like the bohr radius, but the spirit of the question is, are they identical in shape and size? And yes I know the 1S in Helium has has 2 electrons. So the probability of finding an electrion in that double density cloud would be doubled. But the same question applies, can I just render a probability cloud just like the 1s in Hydrgoen over Helium but make it twice as dense? Or is the size ofthe sphere shaped probability cloud larger? If so by how much?

    BTW have a look at this:

    This is what Im basicly trying to do but in later version I want to sum up all the elronic and magnetic forces to create electrical and magnetic fields for each atom and watch them interact with each other in a virtual lab.
     
    Last edited: Feb 9, 2017
  15. Feb 9, 2017 #14

    anorlunda

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    Not correct. Did you read the whole article?

    Orbitals can't be described by ordinary electro mechanical equations. You must use quantum mechanics.
     
  16. Feb 9, 2017 #15
    I was refering to the fact that only the hydrogen atom has been solved for these shells.

    Tell you what to avoid any further miscommunications can you have a look at the last question I posted about Helium and hydrongen's 1s shell? Could you be so kind as to compare and contrast to help me? What remains the same and what is different between 1s in hydrogen and in helium.
     
  17. Feb 9, 2017 #16

    blue_leaf77

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    By assuming non-interacting electrons, helium's 1s should be smaller since the nuclear attraction is larger.
    Yes, approximately.
    Such a question is not something that one can answer with high certainty without referring to literature or doing accurate calculation. The reason is that on one hand the nuclear attraction is larger, on the other hand the presence of the second electron provides a kind of net repulsion to the other electron. The net result is what determines the size of the probability distribution.
    No that won't work, you have to use quantum mechanics as Anorlunda said.
     
  18. Feb 10, 2017 #17
    So what is Helium's 1s exact average radius size? HAs it been worked out previously? If so is there a link you can supply?

    I'm sure it will take quantum mechanics/shrodinger equation to work out the end result of combining all the electron shells of an atom to work out the total shape of the electronic and magnnetic forces, but again has this been done before for helium and have their results been publicshed? If so where? I just want to use their fndings to model the helium.
     
  19. Feb 10, 2017 #18

    blue_leaf77

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    Are my previous messages not clear enough to imply from that shell model of an atom is not an exact description? Helium does not have exact 1s shell (and the other shells) because it's electrons are not non-interacting. The best way to get the idea about the actual size of wavefunction in He is to consider the repulsion effect of the other electron in an approximate way, that's the best scientist can do now without solving Schroedinger equation. One such approximate method which is less time consuming to understand is variational method, alone within the framework of this method there have been a couple of "sub-methods", the easiest one is probably by quantizing the effect of repulsion into the so-called effective charge of the nucleus. Doing variational method in this way, it's found that this effective charge is equal to 27/16. Now you can use this value in the hydrogen-like atom's wavefunction formula for the nucleus charge Z. More about variational method for helium, see this.
     
  20. Feb 10, 2017 #19

    blue_leaf77

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    That's another story of the theory. The major part of your project seems to be plotting the 3D graph of the orbitals where magnetic forces is the n-th relevant effect to the shape of the wavefunction. Magnetic forces is included implicitly in the formulation of quantum mechanics, the so-called spin-orbit coupling and amounts to very small correction to what you currently want to do.
     
  21. Feb 10, 2017 #20
    As you know Hydrgogen has been solved for most of its electron shells. What does that mean exactly? Does that mean that the basic lower electron probability cloud sizes and dimensions determined? What I want to do is not to recreate teh wheel for the hydrogen but graft the complete picture that has already been determined for it. Now that should be possible right? Tell me if you understand what Im saying for this part.

    Now imagine doing the same for Helium. What are my problems that you see for me to graft a 3D picture for helium vs hydrogen?

    You also said there are interactions between the electrons within the same atom , so that implies that if scientists have done their work they would have created an animation of such interactions, perhaps a gif file or something similar. Could I merely graft that on ?

    Do I have to read through all that complex maths on the link you gave or does that actually have a simple conclusion about the size and shape of Helium's 1s? Is it just a simple sphere and I just add in the radius? (Radius being the average of the probability cloud akin to the bohr radius of hydrogen).

    Tell you what, lets pretend this is your problem. You know the answer for hydrogen for 1s. Lets call this radius Rh. We need to work out Rhe. So can we express the size of Rhe in terms of Rh? ie Rhe = RhX 1.3.

    My chemistry is undergraduate level so I do not have a grasp on complex maths for Shrodinger equation only the basic concept of what it is. I realize eventually I will have to study it but I need laymen's terms on how to do a very simple model of my project for now. Its not modeling real life but a good model for it.

    So S shell P shell D shell their shapes are universal. So that makes it easy for us already right?
    But the main problem is their sizes vary between the elements. Scientists have worked out their sizes for hydrogen. Have they worked it out for helium?
     
    Last edited by a moderator: Feb 10, 2017
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