I Physical Dimensions of electron shells

[darkdave3000]

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.

 

[darkdave3000]

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.

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?

 

[Dr Transport]

I'd listen to your physics teacher...atoms larger than hydrogen are unsolvable without a huge computational effort.

 

[darkdave3000]

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.

 

[Dr Transport]

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.

 

[darkdave3000]

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.

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?

 

[TeethWhitener]

Gaussian (and most other quantum chemistry programs) can calculate electron density isosurfaces from wavefunctions.

 

[blue_leaf77]

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.

 

[anorlunda]

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

And this figure shows that the shape is not static.

 

[darkdave3000]

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.

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 isn't 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 I am 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 I am 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.

 

[darkdave3000]

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

And this figure shows that the shape is not static.

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?

 

[blue_leaf77]

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.

My problem is I am not familiar with the unknowns. 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.

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 need assistence not judgement and personal attacks.

I hope this time the assistive intention of my post is not overshadowed.

 

[darkdave3000]

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.

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 I am 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 don't 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 I am 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.

 

[anorlunda]

But these are all shapes and sizes onlly for the hydrgone atom correct?

Not correct. Did you read the whole article?

Orbitals can't be described by ordinary electro mechanical equations. You must use quantum mechanics.

 

[darkdave3000]

Not correct. Did you read the whole article?

Orbitals can't be described by ordinary electro mechanical equations. You must use quantum mechanics.

I was referring 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.

 

[blue_leaf77]

Would they have identical radius size?

By assuming non-interacting electrons, helium's 1s should be smaller since the nuclear attraction is larger.

So the probability of finding an electrion in that double density cloud would be doubled.

Yes, approximately.

If so by how much?

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.

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.

No that won't work, you have to use quantum mechanics as Anorlunda said.

 

[darkdave3000]

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.

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.

 

[blue_leaf77]

So what is Helium's 1s exact average radius size?

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.

 

[blue_leaf77]

magnnetic forces

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.

 

[darkdave3000]

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.

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 I am 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, let's pretend this is your problem. You know the answer for hydrogen for 1s. Let's 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?

 

[darkdave3000]

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.

There are 2 main topics here:
1. Interactions: Atoms/molecules interacting with each other due to electrica and magnetic forces. ie Amonia is relatively neutral and water has a shaped charge
2. Rendering: In this case all I need to do is use dimensions of electron shells worked out by scientists and graft them onto individual elements, even if the electrons are interacting with each other inside each atom that's no problem, just use the animation files that scientists have generated and use them (with permission) in my real time simulations 3d graphics software.

Perhaps for now we should just restrict the conversation to rendering and deal with interactions later. Now based on above can I do number 2 for hydrogen ? yes/no
Can I do the same for Helium? yes/no?

Whatever I do its got to be a consistent model. So what I use for one element should have the same error % for another element. I want to use a good model.

 

[blue_leaf77]

As you know Hydrgogen has been solved for most of its electron shells.

It has been solved exactly for any of its shells, why? Because the relevant Schroedinger equation can be analitically solved. What does solving all shells for hydrogen mean? This means you can calculate the probability density for any shell.

What are my problems that you see for me to graft a 3D picture for helium vs hydrogen?

At first I thought you need to do a rigorous rendering of the wavefunctions, now I realize that you just want to plot the shells without use of too much exactness. In this case, go on with the non-interacting model of atom I have talked before. Just use the shell formula for hydrogen but change the nuclear charge.

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.

Yes, for sure some scientists out there must have done this rendering, in their own computer. May be other members can help finding such animation?

just use the animation files that scientists have generated and use them (with permission) in my real time simulations 3d graphics software.

Just a share of my experience, as far as I know people never try to animate atom, they do have animation for molecules. In molecules there is so called bonding between atoms which can vibrate, in atoms there is no bonding obviously because there is only one atom. It's this movement of bonding that is rendered for molecules, for atoms just plot the static 3D wavefunction.

just use the animation files that scientists have generated and use them (with permission) in my real time simulations 3d graphics software.

See Jmol.

 

[darkdave3000]

It has been solved exactly for any of its shells, why? Because the relevant Schroedinger equation can be analitically solved. What does solving all shells for hydrogen mean? This means you can calculate the probability density for any shell.

At first I thought you need to do a rigorous rendering of the wavefunctions, now I realize that you just want to plot the shells without use of too much exactness. In this case, go on with the non-interacting model of atom I have talked before. Just use the shell formula for hydrogen but change the nuclear charge.

Yes, for sure some scientists out there must have done this rendering, in their own computer. May be other members can help finding such animation?

Just a share of my experience, as far as I know people never try to animate atom, they do have animation for molecules. In molecules there is so called bonding between atoms which can vibrate, in atoms there is no bonding obviously because there is only one atom. It's this movement of bonding that is rendered for molecules, for atoms just plot the static 3D wavefunction.

See Jmol.

Are you suggesting I don't bother scalling sizes of the electron shells S,P,D etc and just display them on the other elements as if their the same sizes of those in hydrogen?

 

[blue_leaf77]

Are you suggesting I don't bother scalling sizes of the electron shells S,P,D etc and just display them on the other elements as if their the same sizes of those in hydrogen?

Which part of my post suggests you not to scale the sizes?

 

[darkdave3000]

Which part of my post suggests you not to scale the sizes?

I assumed that's what you ment because you didnt give a formula or a solution to scaling up the shapes for individual elements.

 

[blue_leaf77]

I assumed that's what you ment because you didnt give a formula or a solution to scaling up the shapes for individual elements.

What about reviewing your old notes about hydrogen-like atoms? It's so elementary I believe chemistry students at least have learned in introductory QM course. Furthermore, if you had noticed I have mentioned multiple times here about replacing Z in the hydrogen with Z for the atom of interest. Does this not ring anything? In case it's no longer possible to get your old notes back, there is Google to give us great deal of resources on hydrogen-like atoms. I am sorry if I may sound too stingy to share the formula, but it has been our principle in PF that everyone of us should avoid providing the final answer but instead help the asker in a way that he/she will be able to redo the problem by him/herself. Believe me, the math of hydrogen-like atoms is not difficult to grasp.

 

[DrClaude]

Closed pending moderation.

Edit: The thread will now be reopen. I ask everyone to stay on topic, discussing the science at hand.

 

[DrClaude]

I think that one difficulty with your project is that there is no simple passage from hydrogen to other atoms. Adding even a single electron completely changes the problem at hand, and makes its solution much more difficult.

You can either simply use the results of hydrogen and scale them, but this is not satisfactory as it neglects the electron-electron interaction (so there is basically no point in plotting something else than hydrogen). The other possibility is to use a computational chemistry program to calculate single-electron orbitals for multi-electron atoms, and use that to create the plots.

 

[darkdave3000]

I think that one difficulty with your project is that there is no simple passage from hydrogen to other atoms. Adding even a single electron completely changes the problem at hand, and makes its solution much more difficult.

You can either simply use the results of hydrogen and scale them, but this is not satisfactory as it neglects the electron-electron interaction (so there is basically no point in plotting something else than hydrogen). The other possibility is to use a computational chemistry program to calculate single-electron orbitals for multi-electron atoms, and use that to create the plots.

This answer is some what useful, can you give me a link to such a program that you recommend?

I understand that this is a very complex and dynamic problem to solve, can you help me to understand it discretely? You can help by allowing me to take control of the topic and steer it so that I can understand it bit by bit but under my terms this way I can understand the nature of the problem from bottom up. This is neeccssarry so that I can slowly assess to what degree of compromise my model of the atom should take as a software architect:

First discrete question I have for you: You say that I can use hydrgoen and scale them, but how do I know by how much? For example let's say we want to model Helium, I mean its easy right? It's just a S shape atom just like hydrogen so we know its going to be a sphere and no tear drop P or D shapes to do electron-electron interaction with the 1S. Unless you tell me that 2 electrions occupying the same 1S also has electron-electron interaction?. So can we safely say that in this particular Helium example the shape of the 1s will remain a sphere? That only its size will be different? And how do we calculate the helium's S shell size?

 

[Drakkith]

Unless you tell me that 2 electrions occupying the same 1S also has electron-electron interaction?

That is indeed the case.

 

[darkdave3000]

That is indeed the case.

In fact even 1 electron in 1s1 can intefere with it self.

Meaning that the 1s1 in hydrogen is not a perfect sphere. More like a cratered planet. If in 2 dimension analogy its a 2D wave that amplifies it self with constructive inteference youre going to have exaggerated peaks and drops everywhere in a 3D model like a crattered moon. Am I right?

 

[Drakkith]

In fact even 1 electron in 1s1 can intefere with it self.

Meaning that the 1s1 in hydrogen is not a perfect sphere. More like a cratered planet. If in 2 dimension analogy its a 2D wave that amplifies it self with constructive inteference youre going to have exaggerated peaks and drops everywhere in a 3D model like a crattered moon. Am I right?

I don't believe so. As far as I am aware, the electron is indeed in a perfectly spherical shell.

 

[Dr. Courtney]

The alkali metals can be solved to very good approximations by considering the inner electrons to make up a spherically symmetric filled inner shell with a given charge density that gives the proper quantum defects of the valence electron. Then the wave functions of the valence electron are likely fairly accurate. The approach is straightforward, because you can separate variables and only need to numerically integrate the radial equation.

Things are much harder when there are two or more electrons in the outer (unfilled) shell.

 

[darkdave3000]

The alkali metals can be solved to very good approximations by considering the inner electrons to make up a spherically symmetric filled inner shell with a given charge density that gives the proper quantum defects of the valence electron. Then the wave functions of the valence electron are likely fairly accurate. The approach is straightforward, because you can separate variables and only need to numerically integrate the radial equation.

Things are much harder when there are two or more electrons in the outer (unfilled) shell.

It doesn't have to be a perfect model as long as there is some consistent formula I can use to keep the errors consistent. Thanks for this, I could use this information.
I saw a youtube video about how elections can interfere with them selves as waves around the nucleus, the wavy line become constructive interference making the areas of high and low probability more contrasting. Does this happen in hydrogen? What about in Helium. I am trying to understand why its so hard to solve the shape for helium's1s. If 1 electron in hydrogen will make a sphere 2 elections in helium would not because of election election intetrerence yes? But this non sphere shape would be consistently symetrical yes?

 

[ZapperZ]

It doesn't have to be a perfect model as long as there is some consistent formula I can use to keep the errors consistent. Thanks for this, I could use this information.
I saw a youtube video about how elections can interfere with them selves as waves around the nucleus, the wavy line become constructive interference making the areas of high and low probability more contrasting. Does this happen in hydrogen? What about in Helium. I am trying to understand why its so hard to solve the shape for helium's1s. If 1 electron in hydrogen will make a sphere 2 elections in helium would not because of election election intetrerence yes? But this non sphere shape would be consistently symetrical yes?

Unfortunately, this is one of those example of let's jump into the middle of the story and see if we can make heads or tails of what has happened so far.

Electrons in an atomic orbital don't actually "interfere" with themselves, at least not in the way you are thinking. They may be in a superposition of states, but these are not the "interference" phenomenon that you are thinking of.

If you are using something to back your claim, it is a clear policy of this forum that you make an explicit reference to that source. Don't just say that you saw something on YouTube, give us the link so that we may verify if (i) it is a legitimate, correct source, (ii) it isn't crackpottery (iii) and that you understood what it said correctly. Otherwise, there's no way to know!

Electron-electron interaction in an atom isn't just a matter of "interference". Besides an added Coulombic interaction between 2 electrons (i.e. an added term in the potential of the Hamiltonian), you also have to satisfy the exclusion principle due to the spin of the individual electrons. It is why we have bonding and antibonding states that depends on how each of the spins align!

You have a lot to learn, but unfortunately, it doesn't appear that you are starting this from the very beginning, the way most of us learn this material. This is why I stated that you're jumping into the middle of the story and thinking that you can make sense out of it.

Zz.

 

[darkdave3000]

Unfortunately, this is one of those example of let's jump into the middle of the story and see if we can make heads or tails of what has happened so far.

Electrons in an atomic orbital don't actually "interfere" with themselves, at least not in the way you are thinking. They may be in a superposition of states, but these are not the "interference" phenomenon that you are thinking of.

If you are using something to back your claim, it is a clear policy of this forum that you make an explicit reference to that source. Don't just say that you saw something on YouTube, give us the link so that we may verify if (i) it is a legitimate, correct source, (ii) it isn't crackpottery (iii) and that you understood what it said correctly. Otherwise, there's no way to know!

Electron-electron interaction in an atom isn't just a matter of "interference". Besides an added Coulombic interaction between 2 electrons (i.e. an added term in the potential of the Hamiltonian), you also have to satisfy the exclusion principle due to the spin of the individual electrons. It is why we have bonding and antibonding states that depends on how each of the spins align!

You have a lot to learn, but unfortunately, it doesn't appear that you are starting this from the very beginning, the way most of us learn this material. This is why I stated that you're jumping into the middle of the story and thinking that you can make sense out of it.

Zz.

Given enough time and study I can make sense of it, I have to start from somewhere! Starting in the middle of the story is better than starting from scratch. I'll send you the link tomorrow when I am back at work. I am home now. Have a good day!

 

[ZapperZ]

Given enough time and study I can make sense of it, I have to start from somewhere! Starting in the middle of the story is better than starting from scratch.

It isn't. You may think it is "better", but look at just this thread. Every time someone tries to make one step forward, we have to then go 2 or 3 steps back, because we have to explain our explanation. There shouldn't be a reason to explain the geometry of, say, the s-orbital IF you have solved the simple Schrodinger equation.

There is no short-cut.

Zz.

 

[DrClaude]

This answer is some what useful, can you give me a link to such a program that you recommend?

Have a look at GAMESS.

I understand that this is a very complex and dynamic problem to solve, can you help me to understand it discretely?

Lets look first at how it is done for hydrogenic atoms (forgetting about spin to keep it simple):

1. Solve the Schrödinger equation for nucleus + electron in the center-of-mass frame analytically
2. This leads to a series of discrete energy states depending on three quantum numbers, n, l, and m_l
3. Take the electron to be in a single of those states, with a given spatial wave function
4. Taking an arbitrary limit (such as probability = 0.9), plot the absolute value squared of the previous wave function, and call that a visual representation of the wave function

Problem at step #1: analytical solutions exist only when one electron is present. Only numerical solutions are possible, unless big approximations are made. Considering numerical solutions, it is easy to see what the full electronic density is, but considering it electron by electron is problematic, as these solutions are not in terms of the equivalent quantum numbers mentioned in point 2.

One possible solution is to fully neglect electron-electron interaction, which is what I think is done in the video you have posted. I don't see much advantage to this approach from the point of view of individual orbitals, are they are the same as in hydrogen. Also, it leads to an incorrect result, as is plainly seen in the video: when all p orbitals are filled, the resulting electron distribution is necessarily spherical, which is not what is obtained by naively superposing dumbbell drawings of p orbitals.

It is possible to use other approaches, such as the central field approximation, to get better approximations of single-electron orbitals, but I am not sure I see the point of investing much effort in doing that with some rigor.

 

[edguy99]

.. 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.

Great question that remains unanswered. To try and help clarify the question in specific terms:

1. You often see the hydrogen atomic orbitals visualized, but most often without a distance scale. Where would a circle of 53 picometers (Bohr radius) be overlaid on a hydrogen 1s orbital?

2. Has a picture ever been drawn of helium orbitals and where would a circle of 53 picometers be overlaid?

 

[darkdave3000]

Great question that remains unanswered. To try and help clarify the question in specific terms:

View attachment 122812

1. You often see the hydrogen atomic orbitals visualized, but most often without a distance scale. Where would a circle of 53 picometers (Bohr radius) be overlaid on a hydrogen 1s orbital?

2. Has a picture ever been drawn of helium orbitals and where would a circle of 53 picometers be overlaid?

Thanks for understanding where I'm coming from! Surely there has got to be a way to explain this in laymen's terms without studying the Shrodinger equation yet.

 

[Drakkith]

Thanks for understanding where I'm coming from! Surely there has got to be a way to explain this in laymen's terms without studying the Shrodinger equation yet.

There is. It just won't be accurate. So you either choose to be accurate, which requires extremely complex calculations involving quantum mechanics, or you choose to be not accurate and just make some approximations. Either way works just fine depending on what you're going for. The "best bang for your buck" is to probably just model everything as having a single electron, like hydrogen. It's a little bit of work to understand how to use Schrodinger's Equation for a hydrogen atom, but it's far easier than trying to model multi-electron atoms using it.

 

[darkdave3000]

There is. It just won't be accurate. So you either choose to be accurate, which requires extremely complex calculations involving quantum mechanics, or you choose to be not accurate and just make some approximations. Either way works just fine depending on what you're going for. The "best bang for your buck" is to probably just model everything as having a single electron, like hydrogen. It's a little bit of work to understand how to use Schrodinger's Equation for a hydrogen atom, but it's far easier than trying to model multi-electron atoms using it.

I will try and understand the laymen's model first before resorting to more accurate means.

So can some one try and explain to me the laymen's explanation to the shape of the Helium 1s?

Is it a sphere? If not then what exactly? And how big is it? (radius) Can you sketch it?

 

[Drakkith]

I will try and understand the laymen's model first before resorting to more accurate means.

So can some one try and explain to me the laymen's explanation to the shape of the Helium 1s?

Is it a sphere? If not then what exactly? And how big is it? (radius) Can you sketch it?

You can explain things in laymen's terms, but there isn't really a laymen's model. A model inherently implies a lot of math and such that is rarely explained to laymen. Even modeling simple harmonic motion would be beyond what I would call "laymen".

But you yourself can build models of any arbitrary complexity. An extremely basic model could just model each atom as a sphere with a radius equal to the covalent radius for each element.
If you want to get more complicated than that then you're going to have to get into the details of the math. There just isn't a model anywhere close to a "laymen's model" that will give you the shapes of the different orbitals or their sizes. You cannot get the familiar lobes seen in the various subshells without computing wavefunctions, so if you're hoping to do that without quantum equations then you're simply out of luck.

 

[darkdave3000]

You can explain things in laymen's terms, but there isn't really a laymen's model. A model inherently implies a lot of math and such that is rarely explained to laymen. Even modeling simple harmonic motion would be beyond what I would call "laymen".

But you yourself can build models of any arbitrary complexity. An extremely basic model could just model each atom as a sphere with a radius equal to the covalent radius for each element.
If you want to get more complicated than that then you're going to have to get into the details of the math. There just isn't a model anywhere close to a "laymen's model" that will give you the shapes of the different orbitals or their sizes. You cannot get the familiar lobes seen in the various subshells without computing wavefunctions, so if you're hoping to do that without quantum equations then you're simply out of luck.

Once I start getting into the maths it will show that S shells are spheres and P shells are teardrops right?
But I haven't got into the maths yet and I know that P shells are teardrops. So in the same way couldn't you explain what the shape of 1S of helium really is without getting into the maths? Maybe supply me a picture on the next post?

 

[Drakkith]

Once I start getting into the maths it will show that S shells are spheres and P shells are teardrops right?
But I haven't got into the maths yet and I know that P shells are teardrops. So in the same way couldn't you explain what the shape of 1S of helium really is without getting into the maths?

You can explain it, but you can't model it.

Maybe supply me a picture on the next post?

Sorry, computational chemistry is well beyond my skills. I've barely dealt with the Schrodinger equation in one of my classes and even there we kind of just glossed over it.

 

[Khashishi]

When you have one electron, you can imagine the electron in different states which you can label 1s, 2s, 2p, etc. When you have two or more electrons, you can't separate the solution into the sum of single electron states. For example, in helium, the shape of the 1s orbital in a 1s2s state will be different than the shape of the 1s orbital in a 1s2p state. Moreover, the shape will depend on whether the electron spins are aligned or opposite. So there are two 1s2s states: 1s2s [3S1] and 1s2s [1S0]. So it does not make sense to talk about the shape of the 1s orbital by itself, unless you are talking about a helium+1 ion.

Basically, unless you want to spend years of scholarly research on this (by then you will outgrow your teachers), you will have to make some huge approximations. And you can approximately say that the 1s orbital of helium looks like the 1s orbital of hydrogen, but scaled down by slightly less than 2 because of the higher attraction of the nucleus. It's less than 2 because there is some cancellation of the nuclear charge by the other electron.

 

[Drakkith]

My question for the OP is do you know how to go about making even a very basic model of something like this? We can give you equations and modeling methods, but if you don't know how they all fit together then it's all pointless. As an example, while I was taking my first physics class I used my knowledge to make a very simple model of the Earth orbiting the Sun using the equations I learned from my class. I could have gotten those equations from anywhere. I needed to take the class to understand how to use them and when they applied. Knowing how to get the force from the gravitational force equation is useless if you don't know how to find the force vector and how to use the other kinematic equations to make the Earth move correctly. Similarly, giving you the equations used in various approximations is pointless if you have no idea how to use them.

 

[edguy99]

When you have one electron, you can imagine the electron in different states which you can label 1s, 2s, 2p, etc. When you have two or more electrons, you can't separate the solution into the sum of single electron states. For example, in helium, the shape of the 1s orbital in a 1s2s state will be different than the shape of the 1s orbital in a 1s2p state. Moreover, the shape will depend on whether the electron spins are aligned or opposite. So there are two 1s2s states: 1s2s [3S1] and 1s2s [1S0]. So it does not make sense to talk about the shape of the 1s orbital by itself, unless you are talking about a helium+1 ion.

Basically, unless you want to spend years of scholarly research on this (by then you will outgrow your teachers), you will have to make some huge approximations. And you can approximately say that the 1s orbital of helium looks like the 1s orbital of hydrogen, but scaled down by slightly less than 2 because of the higher attraction of the nucleus. It's less than 2 because there is some cancellation of the nuclear charge by the other electron.

Thank you for the approximation on the Helium 1s² orbital. Information on shapes of orbitals is very hard to find. Like the OP, I am not so much interested in the calculations (although important of course), but am looking for published results to save time (but I am also happy with your approximations). Can you approximate the other 4 you mention? 1s¹2s¹[3S1], 1s¹2s¹[1S0], 1s¹2p¹[3S1], 1s¹2p¹[1S0]

Is there a place where people can look this up?

 

[Khashishi]

I'm really not an expert at this, so I don't know.

 

[darkdave3000]

From a computer scientist point of view I can model any complex/non-trivial 3D shape. Just need the geometry/pixel instructions. For example, if you tell me render a perfect sphere, I can do that. I can also render a porcupine, a pineapple, a cratered moon, it really doesn't matter how complex the shape is, it can be rendered on a computer screen as long as it has 3 dimensions of space and I have a scale to decide how big the 3d model is.

But I don't know how a shrodinger equation works yet and I'm guessing its a lot of work to invest to understand it. So I would like a compromised laymen's 3D instruction on rendering the helium's 1s for 2 elections. So there was a very helpful man in this thread who said 1s should be a sphere 2 times closer to the nucleus for 1 election, I like to know the non ion solution to this for Helium's 2 electrion 1s if possible but a compromised approximation just like the first.

So perhaps with 2 elections interfering with each other will it be like 2 spiked balls with the spikes between each other? Or a spiked ball and a cratered moon overlapping each other?

In fact I don't understand why we were talkinga bout 2s or P shells because Helium has only 2 elections and they both should be occupying the 1s during rest. Am I right or were you talking about excited states?

My question for the OP is do you know how to go about making even a very basic model of something like this? We can give you equations and modeling methods, but if you don't know how they all fit together then it's all pointless. As an example, while I was taking my first physics class I used my knowledge to make a very simple model of the Earth orbiting the Sun using the equations I learned from my class. I could have gotten those equations from anywhere. I needed to take the class to understand how to use them and when they applied. Knowing how to get the force from the gravitational force equation is useless if you don't know how to find the force vector and how to use the other kinematic equations to make the Earth move correctly. Similarly, giving you the equations used in various approximations is pointless if you have no idea how to use them.