Images of electron orbitals for H2, He, Li and Li2?

[Br.S]

Is there some resource on the net where I can find images of electron orbitals for dihydrogen (H2), helium (He), lithium (Li) and dilithium (Li2)? Alternatively if there is some software that can produce such images, that would be good too.

 

[Br.S]

No one knows, so I guess it doesn't exist. But how can that be, is QM not supposed to be able to produce those kind of images?

All I could find are images like these below, but of what use is that, what does that tell us about H2 molecule or Li atom for example? What does that even tell us about single hydrogen atom?


http://www.webelements.com/shop/shopimages/products/normal/POS0007-A2-orbitron-2010.jpg

 

[dlgoff]

No one knows, so I guess it doesn't exist. But how can that be, is QM not supposed to be able to produce those kind of images?

All I could find are images like these below, but of what use is that, what does that tell us about H2 molecule or Li atom for example? What does that even tell us about single hydrogen atom?


http://www.webelements.com/shop/shopimages/products/normal/POS0007-A2-orbitron-2010.jpg

[PLAIN]http://4.bp.blogspot.com/_pX_Pnr_VRXY/Sv5KtAcHJHI/AAAAAAAAACU/hmoXWuONK3Y/s400/660px-Hydrogen_Density_Plots.png[/QUOTE]

They are just pictures like these. It's the math that tells you.

[PLAIN]http://upload.wikimedia.org/wikipedia/commons/1/1f/Drum_vibration_mode23.gif[PLAIN]http://upload.wikimedia.org/wikipedia/commons/7/7a/Drum_vibration_mode02.gif

http://en.wikipedia.org/wiki/Atomic_orbital

 

[Einstein Mcfly]

Is there some resource on the net where I can find images of electron orbitals for dihydrogen (H2), helium (He), lithium (Li) and dilithium (Li2)? Alternatively if there is some software that can produce such images, that would be good too.

I think most pchem books would have representations of the approximate solutions for multi-electron atoms (the only case where "orbitals" have "meaning"), especially H2. Or, you can use any electronic structure software package (gaussian, nwchem etc) to do these calculations and look at the solutions. For systems like this, it will literally take two seconds. Of course, you'll have to use either hartree-fock theory and see the solutions for cases without correlation effects or density functional theory and see solutions with some amount of correlation and some (likely incorrect) exchange effects. Higher order methods don't really have meaningful orbitals.

 

[Br.S]

They are just pictures like these. It's the math that tells you.

http://en.wikipedia.org/wiki/Atomic_orbital

I'm trying to be specific here. So now that we know all that I still don't see any answers, not even for hydrogen atom. I see dozens of possible orbitals, but I want to know the most common one, in some normal circumstances. Which is it? And for hydrogen molecule H2, can it look like anything from those pictures? Are all those orbitals equally possible, or do electrons in H2 commonly settle at some some particular orbitals, under some normal conditions? Which is it, how does H2 electron cloud usually look like?

 

[Br.S]

I think most pchem books would have representations of the approximate solutions for multi-electron atoms (the only case where "orbitals" have "meaning"), especially H2. Or, you can use any electronic structure software package (gaussian, nwchem etc) to do these calculations and look at the solutions. For systems like this, it will literally take two seconds. Of course, you'll have to use either hartree-fock theory and see the solutions for cases without correlation effects or density functional theory and see solutions with some amount of correlation and some (likely incorrect) exchange effects. Higher order methods don't really have meaningful orbitals.

Gaussian is not free and nwchem only distribute source code. Both of that is a bit too much trouble to get a few images which I'm not really sure I could produce even if I had the spftware. Surely there should be some of those images somewhere on the net already, so at this point googling seems faster option than compiling and learning that software.

 

[Einstein Mcfly]

Gaussian is not free and nwchem only distribute source code. Both of that is a bit too much trouble to get a few images which I'm not really sure I could produce even if I had the spftware. Surely there should be some of those images somewhere on the net already, so at this point googling seems faster option than compiling and learning that software.

So...are you interested in the science or do you just want some pictures that you can say represent the orbitals of these systems for some reason? I can't imagine why anyone would want that.

 

[Br.S]

So...are you interested in the science or do you just want some pictures that you can say represent the orbitals of these systems for some reason? I can't imagine why anyone would want that.

I want to know how those orbitals look like, because I'm interested in science. Where do you see a difference between science and images of molecular orbitals, what are you trying to say?

 

[bahamagreen]

I think what he may be trying to say is that they don't "look" like anything - they don't have an appearance like large objects we see.
What they do seem to have are various measures that may be described by math, but understanding that conceptually is an abstraction.

Some texts will attempt to show the ground state by an image meant to represent a 3D diffusion of shading where the shading intensity corresponds to probability, or the image may be of a solid shell that corresponds to a particular nominal probability value, or many other ways - none of which are complete and correct.
These representations may be helpful in some ways for those that already understand the math relations of the measures, but misleading for those that don't.

 

[Br.S]

I think what he may be trying to say is that they don't "look" like anything - they don't have an appearance like large objects we see.
What they do seem to have are various measures that may be described by math, but understanding that conceptually is an abstraction.

Some texts will attempt to show the ground state by an image meant to represent a 3D diffusion of shading where the shading intensity corresponds to probability, or the image may be of a solid shell that corresponds to a particular nominal probability value, or many other ways - none of which are complete and correct.
These representations may be helpful in some ways for those that already understand the math relations of the measures, but misleading for those that don't.

Orbital diagrams are not complete or correct, how? Probability density can very well be plotted as 3-dimensional diagram. Atomic and molecular orbitals are exact representations of QM equations which are supposed to explain and predict shapes and molecular geometry. And you are saying such images don't really represent or mean anything? Makes no sense.

 

[cgk]

Orbital diagrams are not complete or correct, how? Probability density can very well be plotted as 3-dimensional diagram. Atomic and molecular orbitals are exact representations of QM equations which are supposed to explain and predict shapes and molecular geometry. And you are saying such images don't really represent or mean anything? Makes no sense.

1. Orbitals are not probability densities
2. The images represent and mean something, but unless you already know what exactly that is, you are bound to be mislead by their appearance. For example, the concept of invariance of Slater determinants to unitary rotations amongst occupied orbitals is essential for understanding what and what not orbitals are. Just plotting a picture ignores the point that you can get a *completely different looking* set of orbitals for a molecule which describes the *very same* wave function.

Also, it's not like the shapes are any secrets. As already mentioned, any molecular electronic structure package can calculate them (giving you, for example, canonical Hartree-Fock or Kohn-Sham orbitals), and most books on electronic structure or physical chemistry contain pictures. You might want to pay a visit to your favorite university library.

 

[Br.S]

1. Orbitals are not probability densities

They are.

http://en.wikipedia.org/wiki/Atomic_orbital

http://en.wikipedia.org/wiki/Molecular_orbital

2. The images represent and mean something, but unless you already know what exactly that is, you are bound to be mislead by their appearance. For example, the concept of invariance of Slater determinants to unitary rotations amongst occupied orbitals is essential for understanding what and what not orbitals are. Just plotting a picture ignores the point that you can get a *completely different looking* set of orbitals for a molecule which describes the *very same* wave function.

That doesn't worry me. Molecules, like H2O for example, have very specific geometry which does not vary under normal or uniform conditions. It's therefore to be expected electron orbitals of such stable molecules are accordingly well geometrically defined.

Also, it's not like the shapes are any secrets. As already mentioned, any molecular electronic structure package can calculate them (giving you, for example, canonical Hartree-Fock or Kohn-Sham orbitals), and most books on electronic structure or physical chemistry contain pictures. You might want to pay a visit to your favorite university library.

So books are full of those images but no one bothered to put any on the internet, that's odd. If you at least have ever seen, could you describe what H2 orbitals look like?

 

[Mandelbroth]

Chemist to the rescue!

They are.

Nope. What you mean to say is that they are probability amplitudes. The square of the modulus of the orbital is the probability density function. Orbitals are the standing wave solutions of the Schrödinger equation.

That doesn't worry me. Molecules, like H2O for example, have very specific geometry which does not vary under normal or uniform conditions. It's therefore to be expected electron orbitals of such stable molecules are accordingly well geometrically defined.

Well...not really. You are going into VSEPR theory, which really should go in the chemistry forums.

So books are full of those images but no one bothered to put any on the internet, that's odd. If you at least have ever seen, could you describe what H2 orbitals look like?

Orbitals look like this: $\Psi = [something]$. It is not well defined what it looks like.

I think the pictures you gave are spherical harmonics of the respective solutions to the Schrödinger equation, though...Given what you have said, I'm going to guess (vaguely) that you are in a high school chemistry class. How is your background in math (calculus specifically)? If you know some maths, it is easier for us to relay some physics.

 

[Einstein Mcfly]

Br.S: The things you're asking for ("Give me some pictures of few-electron orbitals!") are not useful in order to gain any actual understanding of what quantum mechanical theories have to say about actual science. Orbitals as most people think about them (independent electron solutions to the Schrödinger equation) are only rigorously meaningful for single electron systems and are (usually pretty good) approximations for multi-electron systems assuming a decent level of theory. This is all important to know if you're going to "get anything out of" looking at some pictures of them. Also, the canonical molecular orbitals are the basis that diagonalizes the hamiltonian (or more accurately, the fock matrix) and are not unique; any linear combination is also correct. Therefore, I could show you two totally different looking "orbitals" that would both be totally correct. As far as that goes, I could show you an N2 or an O2 orbital and tell you that it's H2 and I doubt you'd be able to tell the difference, hence my suggestion that you download an electronic structure program and learn to use it so that you'll always know what you're looking at and have a much better chance of understanding what it means than someone on a message board posting a picture for you to look at. Honestly, the types of questions you're asking make it seem like you don't even know enough about the topic to know what you're looking for, and suggestions by those who know enough to see that don't seem to interest you. If all you want is some representation of something someone calls "an Li2 sigma orbital" then feel free to google it or try a book like this:
https://www.amazon.com/dp/1461439507/?tag=pfamazon01-20
If (as you claim) you want to understand something of science (as opposed to picture gazing) then study hard, major in chemistry/physics and learn ideas behind the pictures you're wanting to see.

 

[Br.S]

Chemist to the rescue!

Nope. What you mean to say is that they are probability amplitudes. The square of the modulus of the orbital is the probability density function. Orbitals are the standing wave solutions of the Schrödinger equation.

That makes no difference, you are just being too literal, or maybe not enough. Anyway, I wasn't talking about mathematical phrases but what orbital images actually represent, what they are, and they are representations of probability densities, which is what describes a likelihood to find an electron in a certain area.

Well...not really. You are going into VSEPR theory, which really should go in the chemistry forums.

Where do you draw a line between quantum physics and quantum chemistry? Is a chemist really supposed to know more about Li and H2 orbitals than a physicist?

Orbitals look like this: $\Psi = [something]$. It is not well defined what it looks like.

I think the pictures you gave are spherical harmonics of the respective solutions to the Schrödinger equation, though...

Not well defined? Who told you that? How do you suppose then those same equation used to make orbital images could explain and predict chemical bonding and molecular geometries?

Orbitals look like this:

volume rendering of the molecular orbital for C4H2CH2CH2CH4

contour volume rendering of the atomic orbitals for BeO

renderings of the atomic orbitals for a molecule LiH

molecular orbitals C2H5, 3rd and 21st


http://ieeexplore.ieee.org/ieee_pilot/articles/06/ttg2009061579/article.html

Given what you have said, I'm going to guess (vaguely) that you are in a high school chemistry class. How is your background in math (calculus specifically)? If you know some maths, it is easier for us to relay some physics.

Given what you have said, I'm too now going to guess (vaguely and quite unnecessarily) that you're at least ten years younger than me. If you know about the images I'm asking for it would be easier to just show them.

 

[Br.S]

Br.S: The things you're asking for ("Give me some pictures of few-electron orbitals!") are not useful in order to gain any actual understanding of what quantum mechanical theories have to say about actual science.

They are useful to me and that's why I'm asking about it. Why are you complaining to me? Ok, when we find some of those pictures I'll explain to you what it means.

Orbitals as most people think about them (independent electron solutions to the Schrödinger equation) are only rigorously meaningful for single electron systems and are (usually pretty good) approximations for multi-electron systems assuming a decent level of theory. This is all important to know if you're going to "get anything out of" looking at some pictures of them.

Who told you that? So when there is more than one electron those equations are no good any more, is that what you're saying?

Also, the canonical molecular orbitals are the basis that diagonalizes the hamiltonian (or more accurately, the fock matrix) and are not unique; any linear combination is also correct. Therefore, I could show you two totally different looking "orbitals" that would both be totally correct. As far as that goes, I could show you an N2 or an O2 orbital and tell you that it's H2 and I doubt you'd be able to tell the difference, hence my suggestion that you download an electronic structure program and learn to use it so that you'll always know what you're looking at and have a much better chance of understanding what it means than someone on a message board posting a picture for you to look at.

Go ahead, show me.

Honestly, the types of questions you're asking make it seem like you don't even know enough about the topic to know what you're looking for, and suggestions by those who know enough to see that don't seem to interest you. If all you want is some representation of something someone calls "an Li2 sigma orbital" then feel free to google it or try a book like this:
https://www.amazon.com/dp/1461439507/?tag=pfamazon01-20
If (as you claim) you want to understand something of science (as opposed to picture gazing) then study hard, major in chemistry/physics and learn ideas behind the pictures you're wanting to see.

Honestly, the type of answers you are proposing make it seem like you've never seen any orbitals. Stop worrying about me, or complaining, whatever it is you're concerned about. And thanks, but no, I'm not going to buy a book just to find a few images of electron orbitals, not with the whole internet one click away, that would be ridiculous. Besides I don't believe I would find the images I'm looking for in that book, and I don't believe the software you suggested could produce them either. Yes, I'm going to keep goggling.

 

[Einstein Mcfly]

Who told you that? So when there is more than one electron those equations are no good any more, is that what you're saying?

Believe it or not, there are some people who know things apart from people just "telling them that". Orbitals are an approximation needed to solve the Schrödinger equation assuming independent electrons with no correlation (Hartree-Fock) or some correlation (DFT) worked in. Feel free to get a book and work through the equations of these two models to convince yourself. Don't expect people who have worked hard on research in the field to spend too much time feeding you answers if you're not going to do any work to understand things on your own, particularly if you're going to be petulant in every response.

Go ahead, show me.

No. I'm not sure what gave you the impression that the internet in general or this message board in particular is some drive through where you put in an order and get what you want a few minutes later. Making these pictures is perfectly simple with the software packages I mentioned, but I'd certainly get nothing out of making them and you'd get nothing out of looking at them with your present knowledge base. Do you really expect people to waste their time if you're not willing to spend any of yours to understand the things you're asking about?

Honestly, the type of answers you are proposing make it seem like you've never seen any orbitals. Stop worrying about me, or complaining, whatever it is you're concerned about. And thanks, but no, I'm not going to buy a book just to find a few images of electron orbitals, not with the whole internet one click away, that would be ridiculous. Besides I don't believe I would find the images I'm looking for in that book, and I don't believe the software you suggested could produce them either. Yes, I'm going to keep goggling.

Goggle away. I half hope you find what you're looking for and half hope you don't so that you'll have to resort to learning something to make them yourself. I have no idea if the book I suggested has the pictures you want. This book, by the way, can be found for free at a place called a library either in the stacks or through inter-library loan.

Regarding your last statement, you should know that any orbitals that you're going to find pictorial representations of will be made by software packages from calculations. There are no "experimental" pictures of orbitals, though some groups have decided to confuse observations of electron density with observations of orbitals and for whatever reason journal reviewers and editors have gone along with it.

 

[Br.S]

Believe it or not, there are some people who know things apart from people just "telling them that". Orbitals are an approximation needed to solve the Schrödinger equation assuming independent electrons with no correlation (Hartree-Fock) or some correlation (DFT) worked in. Feel free to get a book and work through the equations of these two models to convince yourself. Don't expect...

You either can show me the pictures I'm asking about or not. It's always best to ask.

No. I'm not sure what gave you the impression that the internet in general or this message board in particular is some drive through where you put in an order and get what you want a few minutes later. Making these pictures is perfectly simple with the software packages I mentioned, but I'd certainly get nothing out of making them and you'd get nothing out of looking at them with your present knowledge base. Do you really expect people to waste their time if you're not willing to spend any of yours to understand the things you're asking about?

With you present knowledge base you are apparently unable to show me those pictures or say anything specif or particular about them. I have no idea what are you still complaining about. Don't worry about your presumptions what I would get out of those pictures. You either can show me some, or not, where your opinions about them are irrelevant.

Goggle away. I half hope you find what you're looking for and half hope you don't so that you'll have to resort to learning something to make them yourself. I have no idea if the book I suggested has the pictures you want. This book, by the way, can be found for free at a place called a library either in the stacks or through inter-library loan.

You don't know if the book suggested has the pictures I asked about and yet for some strange reason you are still insisting I should buy it. I refuse.

Regarding your last statement, you should know that any orbitals that you're going to find pictorial representations of will be made by software packages from calculations. There are no "experimental" pictures of orbitals, though some groups have decided to confuse observations of electron density with observations of orbitals and for whatever reason journal reviewers and editors have gone along with it.

There are actually experimental pictures of orbitals, but even just 'experimental pictures' of molecular structures on a larger scale is good enough to relate the equations with the real world 3-dimensional geometry.

 

[K^2]

Br.S, you are comparing two different things. Probability densities and orbitals. See the pictures of Hydrogen orbitals you posted in your second post? Look at the d-orbitals. There are five for each energy level. Consider the 3d orbitals, for example. Any linear combination of these five orbitals is a 3d orbital. The particular choice of these five has to do with particular choice of coordinate system.

Electron densities for a ground state of a particular molecule are well defined. These can be rendered, as they are for the molecules you show. Keep in mind, however, that these are approximate solutions. Many-body quantum mechanics is not something you can solve exactly for a general problem.

 

[Br.S]

Br.S, you are comparing two different things. Probability densities and orbitals.

http://en.wikipedia.org/wiki/Molecular_orbital
"Molecular orbitals represent regions in a molecule where an electron is likely to be found."

How are orbitals different thing than probability density?

See the pictures of Hydrogen orbitals you posted in your second post? Look at the d-orbitals. There are five for each energy level. Consider the 3d orbitals, for example. Any linear combination of these five orbitals is a 3d orbital. The particular choice of these five has to do with particular choice of coordinate system.

What are you saying, it's all random? Do you think stable molecules like H2 or H2O do not have well defined regions where electrons could be found like 90% of the time? That's what orbitals are, that's what 'probability density' is.

Electron densities for a ground state of a particular molecule are well defined. These can be rendered, as they are for the molecules you show. Keep in mind, however, that these are approximate solutions. Many-body quantum mechanics is not something you can solve exactly for a general problem.

Are orbitals for Li, He, H2 and Li2 well defined? Any many-body problem can only be approximated, but that's not a problem since accuracy of that approximation can still be greater than accuracy of any practical measurements. It only has to be good enough to explain chemical bonding and molecular geometry, which it does. Doesn't it?

 

[Einstein Mcfly]

You either can show me the pictures I'm asking about or not. It's always best to ask.

Can but won't.

With you present knowledge base you are apparently unable to show me those pictures or say anything specif or particular about them. I have no idea what are you still complaining about. Don't worry about your presumptions what I would get out of those pictures. You either can show me some, or not, where your opinions about them are irrelevant.

See above.

You don't know if the book suggested has the pictures I asked about and yet for some strange reason you are still insisting I should buy it. I refuse.

Library.

There are actually experimental pictures of orbitals, but even just 'experimental pictures' of molecular structures on a larger scale is good enough to relate the equations with the real world 3-dimensional geometry.

Education.

Troll on trollette. I'm done.

 

[Nugatory]

Too bad there isn't a "reset" button for threads...

If there were, we could reset this thread back to #2 or thereabouts, and ask OP to clarify something: What's the question behind the question? How is OP planning to use the answer? It would be a lot easier to provide a helpful answer if we understood that.

 

[berkeman]

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