Talk:Electronic band structure/Archive 1

Archive 1

Proposed merger

Proposed merger from Energy band because that article is a stub with nothing to indicate why its topic is different from this one. Further, the history indicates that over several months, nobody has editted the stub significantly. --The Photon 02:32, 5 September 2006 (UTC)

Seems to have been done somewhere along the way, such that Energy band is a redirect here. Gah4 (talk) 20:57, 2 May 2017 (UTC)

diagram

I'm sure the diagram I've just added could use some improvement. Please comment here with your suggestions. -- The Photon 04:19, 6 September 2006 (UTC)i don't understand the band diagram .so plze explain it ??????

I believe the definition of the fermi level used here in the diagram to be less useful in terms of visualisation than the alternative definition where it is designated as the energy of the highest occupied energy level of the solid at Absolute zero. By this definition the fermi level lies within or at the top of the valence band. In conductors, overlap of valence and conduction bands are not essential as long as its fermi level is sufficiently below the top of the valence band. In semiconductors and insulators the fermi level would be very near the top of the valence band. Hence the band gap is important in these cases. 89.243.48.31 (talk) 11:35, 19 September 2009 (UTC)

Well, this is complicated by band structure being in three dimensions for most materials, but it being difficult to make drawings that way. As far as I know, for an undoped material, the fermi level is considered half way between the top of the valance band and bottom of the conduction band. Band overlap allows for partially filled bands. Also, an odd number of electrons in a unit cell allows for half full bands. Gah4 (talk) 21:04, 2 May 2017 (UTC)

suggestion

I think it would be a good ideea to replace the diagram with an example (Si for example) and also show on the diagram how the line in single atom beacoms a band in atom in crystal with high number of atoms (so that the splitting of orbitals is also shown) --Fractografie 20:26, 10 October 2006 (UTC)

What is a band?

The article talks about bands without stating explicitly what they are.

The answer is in the first sentence of the article: "ranges of energy that an electron is 'forbidden' or 'allowed' to have". However I would definitely agree the article is not totally clear that this is the definition of a band. -- The Photon 00:49, 26 November 2006 (UTC)

I edited the lead to include a definition for energy band, which is in boldface because a search on that term redirects here. Hopefully I got it right (I'm just learning this stuff by reading Wikipedia, and my understanding of the details doesn't go very deep into the article). Wbm1058 (talk) 02:26, 20 December 2011 (UTC)

What's a quantum mechanical electron wave?

http://en.wikipedia.org/w/index.php?title=Special%3ASearch&search=quantum+electron+wave&fulltext=Search

doesn't seem to be explained anywhere...

First, you've forgotten to sign properly. Second, it is related to the quantum-mechanical wave associated with every particle. I suppose you know that waves show particle-like behavior, when they interact with matter. Well, this implies that the opposite is also true, namely, particles show wave-like properties when they ancounter conditions within which they reveal their wave-like behavior, such as openings whose order of magnitude is compared to their associated wavelength. E.g., they can undergo diffraction. See also matter wave or de Broglie. BentzyCo (talk) 18:12, 13 July 2008 (UTC)

That is the way it happens, as quantum mechanics requires it, but I don't believe that it is necessarily implied. There is the story of de Broglie's thesis, which surprised its reviewers, so they asked Einstein if they should give him his degree. As I remember, Einstein said that they should give him the Nobel prize. It wasn't obvious until it was obvious. Gah4 (talk) 23:02, 7 September 2018 (UTC)

DFT

Quote article: In recent physics literature, a large majority of the electronic structures and band plots are calculated using density-functional theory (DFT), which is not a model but rather a theory, i.e., a microscopic first-principles theory of condensed matter physics that tries to cope with the electron-electron many-body problem via the introduction of an exchange-correlation term in the functional of the electronic density. DFT-calculated bands are in many cases found to be in agreement with experimentally measured bands, for example by angle-resolved photoemission spectroscopy (ARPES). In particular, the band shape is typically well reproduced by DFT. But there are also systematic errors in DFT bands when compared to experiment results. In particular, DFT seems to systematically underestimate by about 30-40% the band gap in insulators and semiconductors.

It must be said that DFT is, in principle an exact theory to reproduce and predict ground state properties (e.g., the total energy, the atomic structure, etc.). However, DFT is not a theory to address excited state properties, such as the band plot of a solid that represents the excitation energies of electrons injected or removed from the system. What in literature is quoted as a DFT band plot is a representation of the DFT Kohn-Sham energies, i.e., the energies of a fictive non-interacting system, the Kohn-Sham system, which has no physical interpretation at all. The Kohn-Sham electronic structure must not be confused with the real, quasiparticle electronic structure of a system, and there is no Koopman's theorem holding for Kohn-Sham energies, as there is for Hartree-Fock energies, which can be truly considered as an approximation for quasiparticle energies. Hence, in principle, DFT is not a band theory, i.e., not a theory suitable for calculating bands and band-plots. End quote

To begin: DFT is a theory as far as the derivation of the Kohn-Sham Equations is concerned. However, once we start with (obviously necessary) approximations to the exchange energy, it becomes a model or method. Most people use the term DFT to refer to the method/model isntead to the theory, therefore, the first sentence is misleading. Especially as DFT is relly just a rather narrow branch of many-body quantum mechanics, and not really what most people undestrand under a theory (a wide-reaching concept). The exchange-correlaton term is not relatied to the functional of the electron density, instead, the Hamiltonian is written as a function of the density and incorporates a xc-Term. The DFT Bands are (in principle) exact for all the occupied states in the ground state. What is correct is, that the eigenstates above the Fermi energy are not necessarily equivalent to exited states - however, at least in theory: If we do excite an "electron" in the real world, we do change the band structure anyway - but that is a problem of the concept of a band structure, not necessarily of DFT. Also, the Kohn-Sham system is as much "physical" as any other represantation - it's properties (which can be calculated through the density matrix) are - assuming exact exchange energy - the same as those of the "real" system, and all observables are identical with the real ones. Of course, other opinions are heartily invited, but if no one protests, I'd modify the article accordingly... —Preceding unsigned comment added by 128.200.93.188 (talk) 03:32, 13 February 2009 (UTC)

band gap as definition of semiconductor or insulator?

To my mind that is not correct. There are many materials we use as semiconductors and refer to as semiconductors that have a far higher band gap than many insulators. It is the ability of a material to be doped that makes it a useful semiconductor or just another insulator. --Adarah85 (talk) 11:33, 13 August 2010 (UTC)

This is tricky. There are some materials that can't be doped, as there are no atoms of the appropriate size, or with the right energy level. But most can. Ruby is chromium doped aluminum oxide, where the dopant gives the red color, but the gap is still large. Gah4 (talk) 17:39, 10 November 2016 (UTC)

John Clarke Slater

Prior omission of Slater is very worrisome. I have put in a place holder pending expansion by an expert. Also, OPW methods require mention. Michael P. Barnett (talk) 03:09, 22 February 2011 (UTC)

Conductivity and Probability flow

Apologies for my ignorance. I understand in classical electrodynamics conductivity means flow of electrons, now since here conductivity is understood in term of solution of Schrodinger's equation, what is conductivity then, which differs conductor from insulator. Now if one looks at the Bloch wave, as one approximation mentioned in this article, I will intuitively assume conductivity, the flow of electrons, is connected with the probability flow of electrons, that is (from the conservation of probability implied by the Schrodinger's equation)

${\vec {J}}={\frac {\hbar }{2im}}(\Psi ^{*}\nabla \Psi -\Psi \nabla \Psi ^{*})$

substituting the expression of Bloch wave, I get ${\vec {J}}={\frac {\hbar {\vec {k}}}{m}}$. So no matter where the electron is, it is moving like as a flow. Now I kinda guess, the summation of all the reciprocal vector ${\vec {k}}$ inside the Brillouin zone cancels out when the valence band is filled up. Is it true? Electrons are actually move collectively in the valance band but do not present macroscopic flow due to cancellation?

Then another question is, how to understand this in the case superconductivity? Gamebm (talk) 17:13, 27 November 2012 (UTC)

I don't think your calculation is right. With $\Psi =ue^{ikr}$, I get

$\Psi ^{*}\nabla \Psi -\Psi \nabla \Psi ^{*}=2ik|u|^{2}+u^{*}\nabla u-u\nabla u^{*}$

Can you please double-check? --Steve (talk) 23:29, 27 November 2012 (UTC)

Also as a side note, this won't help you understand superconductivity at all, since it doesn't arise from the band structure...a13ean (talk) 23:47, 27 November 2012 (UTC)

Thanks for pointing that out. I was study the topic and for some reason incorrectly assumed that u must be real. Now it seems the first term ($|u|^{2}$) will not change the conclusion since if one sums up all the k at a given spatial point, it is just a constant. However if the second term does remain, it will give a non-zero contribution to the flow (locally). Then I may understand that a filled band does present some flow locally since the charge flow calculated from QM does not vanish(? - is it measurable?). Now globally, since the second term is surface like (or due to its periodic behavior), it still may not lead to macroscopic flow, (since the length scale in our question is of lattice size.) and for the very same argument, the first term reduces to a irrelevant normalization constant.

I have no idea what superconductivity is. I was just trying to think of it following this line of thought, if all those electron pairs are in the same state (no idea what the wave function shall look like, will study it), and one is again legitimate to calculate its probability flow, but if everything is in the same state, and the resulting flow does not vanish (since it conducts not by excited to another state, but simply staying in this state?), then does this imply that there is some preferred direction in space? Gamebm (talk) 18:04, 28 November 2012 (UTC)

Electron motion is properly calculated using the formula for the group velocity of the electron wavepacket ... not the formula for probability current. They must be related ... I would not be surprised if they are identical ... but I'm not sure of the details off the top of my head.

As pointed out by A13ean, this line of thought will not lead you towards understanding superconductivity. Band structures are part of the "single-particle picture", where you by-and-large ignore the fact that electron quasiparticles interact with each other. But interactions between electron quasiparticles are the entire basis for superconductivity. --Steve (talk) 19:14, 28 November 2012 (UTC)

If you're interested in that bit, the last chapter of Ashcroft and Mermin gives an overview of how superconductivity arises from electron-electron interactions. a13ean (talk) 19:25, 28 November 2012 (UTC)

For symmetry reasons, the sum of all the velocities of the states in a band is zero. A full band, as an empty band, doesn't contribute to conductivity. A partially full band can shift some electrons to states that are going more one way than the other, and so contribute to conduction. Gah4 (talk) 04:49, 7 February 2017 (UTC)

Wording issue

In the section "why bands and band gaps occur", the article states: "If multiple atoms are brought together into a molecule, their atomic orbitals split into separate molecular orbitals...". According to the article on Linear combinations of atomic orbitals, when atoms join to form molecules, the resulting molecular orbital is a superposition of the existing atomic orbitals. The term "split" caused confusion for me when reading, "...their atomic orbitals combine to form molecular orbitals..." seems more clear. Ducksandwich (talk) 17:24, 29 October 2013 (UTC)

I suppose a link to normal modes somewhere here would make sense. You can use any complete basis to describe the system, but some bases make the explanation simpler. For two atoms coming together, it is the sum and difference of the corresponding one atom orbitals that make a convenient basis, with the right symmetry. This is easiest to see with two coupled pendula, which have normal modes with both going the same direction, or going opposite direction. In an energy diagram, the sum and difference form states with lower and higher energy than when separate. If the atomic orbitals are partially full, a lower energy, bonding, state can form. (When to H atoms come together.) If the atomic orbitals are full, then both (sum and difference) molecular orbitals are full, there is no lower energy system, and no bonding. (When two He atoms come together.) Gah4 (talk) 21:21, 2 May 2017 (UTC)

Also slightly re-worded the following few sentences to make it clear how the molecular orbitals are formed. Ducksandwich (talk) 16:50, 6 November 2013 (UTC)

The article says: The Pauli exclusion principle dictates that no two electrons can have the same quantum numbers in a molecule. So if two identical atoms combine to form a diatomic molecule, each atomic orbital splits into two molecular orbitals of different energy, allowing the electrons in the former atomic orbitals to occupy the new orbital structure without any having the same energy

This seems not quite right to me. The splitting comes from linear combinations of the atomic wave functions, where sums and differences have higher or lower energy. Pauli exclusion comes when you fill in the bands. Gah4 (talk) 05:06, 7 February 2017 (UTC)

OK, no other comments on this. Here is my confusion. First, you don't have atomic orbitals without Pauli exclusion, so it is obviously necessary for molecules, too. But the molecular orbitals energy levels aren't due to Pauli, but are the solutions to Schrodinger's equation when atoms (nuclei) come together. Pauli does come in when filling the molecular orbitals, two electrons each. What is slightly less obvious is that the width of a band stays close to constant as N increases, for a given atomic spacing. But the section is on band gaps, which are really a generalization of atomic orbital levels. Anyway, ascribing gaps to Pauli seems wrong. Gah4 (talk) 21:18, 9 April 2017 (UTC)

File:Metals and insulators, quantum difference from band structure.ogv

"Animation" not accessable without explanation. — Preceding unsigned comment added by Jangirke (talk • contribs) 20:39, 23 February 2014 (UTC)

since in many semiconductors the valence band is built out of the valence orbitals.

since in many semiconductors the valence band is built out of the valence orbitals. Isn't this true in all semiconductors, and also insulators? Gah4 (talk) 17:42, 10 November 2016 (UTC)

False invocation of Pauli exclusion principle

The Pauli exclusion principle dictates that no two electrons can have the same quantum numbers in a molecule. So if two identical atoms combine to form a diatomic molecule, each atomic orbital splits into two molecular orbitals of different energy, allowing the electrons in the former atomic orbitals to occupy the new orbital structure without any having the same energy.

No, the exclusion principle is not an energy exclusion principle, and does not explain eigenvalue splitting. 188.154.140.131 (talk) 10:02, 7 September 2018 (UTC)

Hmmm. I read that one before, and didn't decide to change it. Without exclusion, all electrons could go into the lower state. Then again, they could all go into the ground state. But it is also wrong, as pairs can have the same energy. It is convenient in chemistry, that without the details of molecular orbital theory, when two atoms with unpaired electrons come together, they usual form a two-electron bond. I think you are right that the statement is wrong, but I don't know any easy to explain statements that are more correct. Gah4 (talk) 23:09, 7 September 2018 (UTC)

To do it right, you need to go to molecular orbital theory. And at some point, band structure is the extension of molecular orbital theory to really large, macroscopic sized crystals. (Grains in polycrystalline materials.) But since LCAO is close enough, much of the time, it is probably good enough here. Gah4 (talk) 23:16, 7 September 2018 (UTC)

No recent thoughts on this. As I read it again, my first thought is that Pauli exclusion is the wrong way to say it, but then my second thought says that it is fine. I suppose it stays until someone things of a better way to say it. Gah4 (talk) 10:52, 3 December 2019 (UTC)

The statement is just false I think. There is no guarantee that the molecular system does not have degenerate energy levels (i.e., eigenvalue multiplicity). Generically you expect the interaction terms to split the energy levels but I don't think it's physically / mathematically guaranteed that this always happens. 2600:1700:52C0:9CC0:0:0:0:44 (talk) 22:01, 1 April 2021 (UTC)

Pauli exclusion still works with degeneracy. Usually when they form molecules or crystals, it breaks the degeneracy, at least partly. In MO theory, there are bonding and antibonding orbitals, which are the two levels after a split. There are also, but more rarely, non-bonding orbitals that don't split. If you take separate (far apart) atoms and put the together into a crystal, they start with quantized definite energy levels, and then split, and also widen into bands, as they come together. But otherwise, it is the split that makes bonds work. That is, the lower energy level relative to separate atoms. So, first they have to split, and second the lower levels have to be more full than the upper levels. Gah4 (talk) 11:26, 13 April 2021 (UTC)

Merger proposal - Electronic structure

I propose to merge Electronic structure into Electronic band structure. I think that the content in the Electronic structure article can easily be explained in the context of Electronic band structure, and the Electronic band structure article is of a reasonable size that the merging of Electronic structure will not cause any problems as far as article size is concerned. Electronic structure article is clearly talking about the same topic, even if from a slightly different point of view. It is also a very bad stub and it would be beneficial to readers that stumble onto that page to be pointed here instead, which can easily discuss the topic from physics and chemistry points of view. Also the references used are discussing electronic band structures, which is further evidence they are the same topic. Footlessmouse (talk) 21:36, 14 September 2020 (UTC)

• Merge to electron configuration It is more general. It doesn't just refer to electronic bands but also discrete molecules and even discrete atoms ("electronic structure of atoms" redirects here and it applies to single nuclei as well). I feel electron configuration, which is a more general overarching concept that encompasses both solids as well as molecules and atoms, is a much better merge target. I highly disagree with merger of electronic structure to electronic band structure because the former is a superset of the latter, not a subset.--Officer781 (talk) 02:21, 22 September 2020 (UTC)

• Don't Merge. The three articles are enough different. Electron configuration is about the structure of atoms (mostly). Electronic structure is about molecules, and this one about covalent bonded crystals. While one can consider crystals as very large molecules, and there are similarities between Molecular orbital theory and band theory (this article), all three deserve their own articles. Gah4 (talk) 07:08, 24 September 2020 (UTC)

• Don't Merge I agree with Gah4. Normally the term electronic structure is used by physical/computational chemists to discuss discrete molecules while band structure is used in the solid state physics world. Pelirojopajaro (talk) 08:23, 24 September 2020 (UTC)

Note: @Officer781 and Pelirojopajaro: FYI, the first line of the Electronic structure article says In quantum chemistry, electronic structure is the state of motion of electrons in an electrostatic field created by stationary nuclei. The electrostatic field created by stationary nuclei bit is basically the definition of a crystal. I see where you're coming from, though, it adds the term quantum chemistry in there in a poor attempt to disambiguate. If it is to be about the electronic structure of molecules, someone may consider adding some content to it that makes that clear, maybe say more than "it's real hard to compute"... Footlessmouse (talk) 00:28, 26 September 2020 (UTC)

@Footlessmouse: I strongly disagree with merging the two "electronic structure" pages. Either we merge somewhere else like I suggested or we don't merge at all. If no one else agrees with my suggestion we can assume my vote is don't merge. I agree that we need to better distinguish the two pages and make clear what we are referring to.--Officer781 (talk) 14:26, 10 October 2020 (UTC)

@Officer781: 2 things, you're kind of talking like you own the page and I didn't mean to respond to you. I gave up on this a long time ago and the response message was aimed at the other two voters. The entire article exists to say "it's real hard to compute..." and that is unacceptable, those who wish to impede progress with all their fancy ideas of what the article should be, should put the required effort into bringing the article up to standards.. That is fairly obvious, I mean, no one cares about that article except those who are voting here, so who else will ever fix it? Footlessmouse (talk) 17:16, 10 October 2020 (UTC)

@Officer781: As it stands, I fairly regret not nominating the article directly for AfD as a duplicate of the other topics, it would have gotten more turnout. If no one attempts any work on the article in the next couple of weeks, maybe I will propose a different merge into electron configuration and invite the physics project to join the discussion or something along those lines, as the two other voters here fall well short of a community consensus. Footlessmouse (talk) 18:18, 10 October 2020 (UTC)

@Footlessmouse: Sorry, I did not mean to come across as owning the talk page. I was just intending to state my choice if not merged into electron configuration. I am open to whatever you suggest. Thanks! Officer781 (talk) 15:27, 11 October 2020 (UTC)

Merging, again, and Molecular orbital theory

Rereading what I wrote above, I might believe in merging Electronic structure and Molecular orbital theory. Those to apply to smaller molecules. This article applies to crystals, usually assumed much larger than the atomic spacing. Mostly band structure is done ignoring surfaces, where more ordinary molecules are pretty much all surface. Gah4 (talk) 21:50, 10 October 2020 (UTC)

• @Gah4: I would definitely support this as well. I had no vested interest into merging into a particular article. My issues are laid out in the templates and discussion on that page, mainly it does not make an effort to demonstrate its notability and provides no context. It only includes two references and one is to a primary source and the whole article can be wrapped up as saying "it's hard to calculate". I believe strongly that it is unencyclopedic to include partial topics like that and they should be merged with larger ones until such time as editors fill out the content to the point where a split is appropriate, allowing for a meaningful standalone article. Footlessmouse (talk) 22:15, 10 October 2020 (UTC)

Reading Electronic structure again, I think I still agree. It mentions Valence bond theory, Molecular orbital theory, and this page. As noted, I believe that band structure is different enough, but I suppose it can be mentioned and a link here. Someone who knows it better than I do, should know how Valence bond theory and Molecular orbital theory compare, and how much should be said about them. Gah4 (talk) 22:36, 10 October 2020 (UTC)

I am okay with this decision. I think having more views would be good. Pinging @Dirac66: for comment. If there are other people you guys know maybe we can get their input as well. Officer781 (talk) 15:32, 11 October 2020 (UTC)

I would suggest merging Electronic structure into Quantum chemistry, as they both concern using approximate quantum mechanical methods to calculate the electronic wave functions of (atoms and) discrete molecules. Electronic band structure on the other hand is about solids so it is not really the same topic, despite the similarity in names Electronic structure and Electronic band structure. Dirac66 (talk) 17:39, 11 October 2020 (UTC)

I would agree with this last quantum chemistry proposal (given quantum chemistry has such a section and is more generic article) and then fix the quantum chemistry one. This band structure article belongs to the realm of solid state and is well scoped where instead the other belongs to quantum chemistry. Molecular orbital theory instead suggests something just in the middle between quantum physics and quantum chemistry. Being Molecular orbital theory a theory article I would expect for more specialized content with all types of molecular orbitals solutions. Electron configuration with atom solutions. Here I would expect band type of solutions (e.g. some more band diagrams). And finally in the quantum chemistry also there an overview of Quantum chemistry methods. A few about sections may help.

Flyredeagle (talk) 05:47, 24 December 2020 (UTC)