Talk:Hund's rules

writing science topics in Wikipedia

This is an atrocious page as of 21April, 2014, for learning the Hund's Rule. It was written by someone who has little idea of teaching science to others.

If you already know Hund's rule, then perhaps you can pick up some detail or nuance from the page. But the page should be rewritten so that someone who never heard of Hund's Rule can learn what it is.

Every textbook in beginning chemistry provides a easy understandable version of Hund's rule, and that is what Wikipedia should start its "Hund's Rule".

So that the first chapters should be the easy version and then take the existing write up and class it all into the advanced Hund's Rule chapters.

Many Wikipedia science entries suffer from authors who know only how to talk the subject as if they were talking to people who already know it. It is the author's who write the subject for those who know nothing about it that is the most valuable write up and should appear first, and then later on in a chapter, devoted to the advanced discussion of the topic.

So, Wikipedia needs very much to make science discussions not so atrocious.

Archimedes Plutonium wrote this review. — Preceding unsigned comment added by 198.228.228.153 (talk) 06:54, 21 April 2014 (UTC)

Excited states

I noted this on the page for Term_Symbol as well, but perhaps this is a better place. On the page for Hund's_Rules, it states that they can only be used to determine the ground state, not to order the excited states by energy. However, on the Term_Symbol page it seems to use Hund's Rules for exactly this. I don't know enough about the subject to know where the error lies, but there certainly appears to be an inconsistency at present. --Westm 07:00, 21 September 2006 (UTC)

I have now clarified this point here with examples, and also briefly at Term symbol. Hund's rules can be used to determine the lowest-energy state of any given configuration, ground or excited. They should not however be used to order the states other than the lowest for each configuration. Dirac66 (talk) 20:27, 22 June 2008 (UTC)

Half-filled shells

"For atoms with less than half-filled shells, the level with the lowest value of J \, lies lowest in energy. Otherwise, if the outermost shell is more than half-filled the term with highest value of J \, is the one with the lowest energy." This sentence is confusing me for the exactly half filled case. It says 'less than half filled shells...otherwise...more than half filled' what about half filled shells? This is made more confusing in the body, where it says 'The value of \zeta (L,S)\, changes from plus to minus for shells greater than half full.' Xaerocool 08:20, 27 October 2006 (UTC)

what about when the subshells are full

A mention perhaps about the case of Zinc, where subshells are full (Example 2?) --sigs —Preceding unsigned comment added by 82.130.14.161 (talk) 22:23, 18 October 2007 (UTC)

If all subshells are full, L=0 since orbitals with +m and -m are both occupied and cancel, and S=0 since equal numbers of electrons have spins +1/2 and -1/2. Therefore the only possible state for this electron configuration is ¹S, and the use of Hund's rules is unnecessary. Dirac66 (talk) 20:31, 22 June 2008 (UTC)

There is an error in rule 2

Surely this should say that term energy is lowest when S is maximised. At the moment it says that term energy is highest when S is maximised, which I believe to be incorrect. <

I have now changed "highest" to "lowest". Dirac66 (talk) 03:38, 9 March 2008 (UTC)

Example for rule 2 is just plain bullshit. —Preceding unsigned comment added by 91.105.213.62 (talk) 12:14, 20 February 2011 (UTC)

Confusion about rule #1, and problems with rule #2

As far as I was aware there are only 3 Hund's Rules, and these appear as 2, 3 and 4 on the page. I have no idea what rule 1 is going on about, and the explanation given for it makes little sense to me - it mentions repulsion between protons, which has nothing to do with electronic configuration.

If I was to edit the page I'd remove all mention of this phantom 1st rule that is currently there, and re-number the remaining 3 rules accordingly.

Problem with the explanation given for rule 2 (which would be rule 1 if I editied the page as suggest above) are in the 2nd paragraph; It is often stated that this is the highest energy atomic state because it forces the paired electrons to reside in different spatial orbitals, and this results in a larger average distance between the two electrons, reducing electron-electron repulsion energy. But, in fact, careful calculations have shown that this explanation can be wrong, at least for light systems

To start with, the state with maximised paired electrons is the lowest energy state, not the highest. My understanding is that this arises from the Fermi Hole in the wavefunction of paired electrons reducing electron-electron repulsion. The article appears to disagree with me here; ...in fact, careful calculations have shown that this explanation can be wrong, at least for light systems. but no citation is given for this statement. Krusader86 (talk) 15:53, 28 November 2007 (UTC)

Spurious rule #1

Yes, Hund proposed 3 rules and not 4. See for example Miessler and Tarr "Inorganic Chemistry" (2nd edn 1999), pp. 358 and 360.

The current (9 Mar 2007) "first rule" in the article is spurious and was inserted by a very confused editor (or vandal?) on 4 November 2007.

Prior to that edit, the following statement was cited as the "first rule": Full shells and subshells do not contribute to total S, the total spin angular momentum and L, the total orbital angular momentum quantum numbers. This is in fact a true statement, but is usually presented as a preliminary statement and not as the "first rule".

I will renumber the rules, and reinsert the correct version of the preliminary statement. Dirac66 (talk) 04:21, 9 March 2008 (UTC)

Screening vs. Separation

If the average separation between two orbitals is increased, the screening effect of one electron on the other will be reduced. So the two "different" explanations given for Hund 1 are really the same. That is, unless the modern explanation has voodoo which makes it so that the screening effect from inner shells is somehow enhanced when the outer electrons are in separate orbitals! I think the reason for the explanatory quibble is only because the hartree-fock method includes the interaction between electrons mainly in the form of the self-consistent potential, so that the greater distance when the electrons are in separate orbitals translates to a larger self consistent potential, and therefore to "greater screening", and this is the dominant reduction. But a greater screening is a reflection of the greater average distance between the electrons.Likebox (talk) 22:27, 21 September 2009 (UTC)

The text on this point is a simplified version of Levine's verbal argument; I will try to go further from memory (for now).

The difference between the two explanations is real and depends on calculated expectation values (for the different states) of the electron-nuclear (Vne) and electron-electron (Vee) potential energies, and also kinetic energies (Te). The simplest example is He(1s2s ³S) and (1s2s ¹S). The original explanation by Slater about 1930 assumed that the orbitals in singlet and triplet states were identical, so that Vne and Te are necessarily identical in the two states and the energy difference must be due to Vee. Slater proved that in this case, Vee = e²<1/r12> must be smaller in the triplet state. One would then normally expect <r12> will be larger too, so that the electrons are further apart (on average). Yes, that last step is hand-waving, but it was 1930 and there were no computers.

By the early 1970s, Hartree-Fock orbitals were available for the two states and it became clear that in the triplet state the orbitals are closer to the nucleus due to the screening difference, so that |Vne| is larger in the triplet state. Because the triplet orbitals are smaller, Vee is actually larger in the triplet than in the singlet, contrary to Slater's simple result, and so is the kinetic energy, but Vne is the dominant term.

I am not sure how much of this can be included at the level of the article. Before attempting to write a text, one would have to look up the references, starting with those mentioned by Levine. Dirac66 (talk) 01:20, 22 September 2009 (UTC)

Citations needed

The body of the article needs citations to specific articles in the References. If a whole paragraph can be attributed to a single source, a citation at the end of the paragraph is enough. I have added two citations as an example. RockMagnetist (talk) 01:44, 24 September 2010 (UTC)

Yes, in-line references are better, though more work to do. I have now changed the format (and the year) of your in-line reference to Levine, since clicking on your "Levine 2006" did not produce the book title and pages. I also converted the Engel-Reid and Miessler-Tarr references (which I had added some time ago) into in-line references at an approprate point in the text. Can't check the Woodgate reference since I have never seen this book. Dirac66 (talk) 02:54, 24 September 2010 (UTC)

Pauli principle

Someone should add something about the Pauli principle interfering with the second rule: for example in the carbon atom the 2p2 electrons dont have combined angular momentum 2, they have Ml=1 and Ml=0 (total 1) respectively because otherwise they would violate Pauli exclusion. 195.169.204.134 (talk) 00:53, 28 January 2011 (UTC)

Thanks for the suggestion. I have now made this point at the end of the example for Rule #2. I considered Ti(3d²) rather than C or Si(p²), because for p² Rule #2 is not needed to order triplets as there is only one. Dirac66 (talk) 01:27, 28 January 2011 (UTC)

Does it really violate the Pauli Principle? They can both have ml=1 as long as ms1=+1/2 and ms2=-1/2. The Pauli Principle is something else entirely and states that we may only choose wavefunctions that are antisymmetric with respect to electron exchange. Sirsparksalot (talk) 19:24, 9 April 2012 (UTC)

Dear Sirsparksalot, the wavefunction with M_L = 4, M_S = 1 has m_l1 = m_l2 = 2 and m_s1 = m_s2 = +1/2 and is therefore symmetric with respect to electron exchange, so that it violates the Pauli Principle.--173.228.47.88 (talk) 00:15, 10 April 2012 (UTC)

This is true, but Sirsparksalot actually considered the case m_l1=m_l2=1, m_s1=+1/2, m_s2=(-)1/2 so the argument is different. Since both electrons are in the same orbital, the overall 2-electron wave function can be factorized into a space part and a spin part. The space part is symmetric for this case, so the spin part must be antisymmetric to satisfy the Pauli principle. But for two electrons, the triplet state is symmetric and the singlet state is antisymmetric. Therefore only the singlet state (S = M_S = 0) can exist according to the Pauli principle.

As stated in the discussion of rule 1, the allowed states for a given multiplet are considered in the article on term symbols, which is written at a higher level than this article. Dirac66 (talk) 00:37, 10 April 2012 (UTC)

problems with triplet states

In the example of rule 2 it says that from rule 1 it is deduced that the two triplets are the ground state. as there are three (as the name suggests) triplets states it is completely unclear why one of them, I assume the state with no magnetization ms=0, should be ruled out. This goes back to most people thinking about hunds rule maximising Sz (the projection) and not S (the total spin). This common misconception should be mentioned in the article. I dont want to change the article though, because I dont know whether for some reason the ms=0 state cannot be the groundstate.

Drbaudan (talk) 11:50, 28 September 2018 (UTC)

The real problem is that the article currently mixes up "states" and "terms", especially in the section on Rule 2. Titanium has two triplet TERMS ³P and ³F, and Hund's second rule here implies that the ground state term is ³P. But this term corresponds to (2L+1)(2S+1) = 9 states, and Hund's second rule does not identify which is lowest. Hund's third rule here says that the ground state is the J=0 level, i.e. ³P₀. And magnetic quantum numbers only matter for states having J > 0, so not in this case.

I will edit the article to better distinguish states and terms. It should be noted that the confusion is not limited to Wikipedia. Some textbooks say "state" when it should be "term". Dirac66 (talk) 00:09, 7 October 2018 (UTC)

Rule1

The traditional explanation of Hund's rule 1 is that electrons with same correlate their motion by remaining far apart from each other and hence minimize the repulsions . Hence the term with higher multiplicity shall have lower energy. However this explanation proves wrong . It has been found, probability that the two electrons are very closer is small for triplet term than for singlet term. But at the same time using exact wavefunction, it turns out that two electrons in triplet state are very far, is also very less. Average distance between two electrons in triplet term is less comparable to singlet. So repulsions in triplet state are stronger than in singlet state, yet triplet state is lower in energy than singlet. The reason behind this strange result is that in triplet state there is more attraction of electron clouds towards nucleus compared to singlet state. The occupancy of two electrons in two orbitals with same spin lead to Paulis repulsion which causes the two electrons to make average angle between the radius vectors larger for triplet state than singlet. This reduces the shielding effect and hence stabilize triplet state more than singlet.

References: R.E.Boyd, Nature, 310, 480(1984). J.Katriel and R.Pauncz adv.Quantum Chem., 10,143 (1977). I.Shim, Theor.Chim.Acta, 48, 165(1978). Aejaz Ul Bashir (talk) 07:01, 22 June 2020 (UTC)

Yes, this is exactly the second explanation given in the article, starting with the words "However, accurate quantum-mechanical calculations ...". The version in the article is a summary of that given in Levine's book, which cites the same 3 references you have cited here. So I am not certain what you think you should be changed in the article. Dirac66 (talk) 20:26, 22 June 2020 (UTC)