Talk:Resonance (chemistry)

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[edit] Random comments at the top

At the end of the article, it says that resonance diagrams are soon to come. That was 6 months ago. Is anybody going to be adding resonance diagrams soon here? H Padleckas 16:17, 25 Jan 2005 (UTC)

You can steal some from Benzene_ring. - Omegatron 16:47, Jan 25, 2005 (UTC)

They don't really switch between the two possible states constantly, do they? Then the electrons would be net going in a circle and would create a magnetic field. Rather, they exist in a less-than particle state or a "cloud" or something, right? - Omegatron 16:47, Jan 25, 2005 (UTC)

No, resonance structures are not compounds that switch between the two (or more) possible forms constantly. Those two kinds of forms of a compound which readily switch back and forth are called tautomers. Nuclear magnetic resonance studies have provided a lot of information on various tautomer pairs, including how fast they switch back and forth depending on temperature. In a compound whose chemical structure can be represented by two or more resonance structures, the actual "constant" structure or condition of the molecule can be thought of as an "average" or hybrid of the its resonance structures, although this average is not always evenly weighted among its resonance structures. I have never heard and I have no reason to believe that the electrons in aromatic molecules move around in a circle creating a magnetic field. Most likely, whatever motions the electrons in an aromatic molecule engage in are more likely to be random, or random to the extent that we do not understand their order. Maybe these aromatic electrons do exist in a less-than particle state or a "cloud" or something as perhaps suggested by the Heisenberg uncertainty principle. However, if you're a scientific guy, maybe you design an experiment to look for these kinds of magnetic fields in aromatic molecules or compounds.  :-)
H Padleckas 10:42, 26 Jan 2005 (UTC)
Well, on a large scale they would swamp each other out, as they are all facing different random directions. I didn't think they really circulated around like that, but I wonder what effect it does have on the magnetic properties of these materials... I know that carbon nanofoam exhibits weak ferromagnetism. I wonder if they're related. I wish there was enough time to learn every subject in depth... - Omegatron 15:00, Jan 26, 2005 (UTC)
Actually if you apply magnetic field (such as in the aforementioned NMR), you can experience Aromatic ring current. Cubbi 22:09, 20 April 2007 (UTC)
The word I've always used for electrons in a resonant system is delocalised. ben.c.roberts

[edit] Resonant bonds

Has anyone actually heard of the term "resonant bonds"? I've look in texts before, and while I've definately heard of resonance structures, "resonant bonds" just doesn't seem standard.

[edit] Merge

There's a merge tag over at benzene. That section on resonance would look mighty good here. Isopropyl 21:08, 11 April 2006 (UTC)

I agree that some of that material should be added here, but it should also be retained in the benzene article. Resonance is a crucial part of the benzene story and readers should not have to come over here to read about it. --Bduke 21:27, 11 April 2006 (UTC)

Maintain separate articles, sharing whichever sections would improve the other. They are sufficiently separate entities. -Ayeroxor 21:41, 1 May 2006 (UTC)

[edit] Sigma bonds

The article states that sigma bonds are meaningless in MO theory for benzene. This is strictly accurate but goes against useage. Pi orbitals in benzene are also meaningless strictly. The terms sigms and pi strictly apply only to linear molecules giving the spectroscopic terms for angular momentum about the molecular axis. We can talk therefore about sigma and pi molecular orbitals even in long linear molecules where the MOs are delocalised. For planar congugated systems such as benzene the useage has come to mean how the MOs change on reflection in the molecular plane. If it changes sign, it is pi. If it does not change sign it is sigma. The term "sigma-pi separation" is very common in both MO and VB discussions of benzene, so the current wording could serious confuse people. I'm not clear how to rewrite the section. The section is:-

"Often when describing benzene the VB picture and the MO picture are intermixed, talking both about sigma 'bonds' (a meaningless concept in MO) and 'delocalized' pi electrons (a meaningless concept in VB). This is not a good practice, because mathematically the models are incompatible."

Any body got any ideas? --Bduke 22:24, 18 December 2006 (UTC)

MO has sigma orbitals, but no sigma bonds. A bond implies that an electron pair belongs to two and only two nucleus, whereas in MO the electron state vectors are calculated with the )approximate) potential of the entire molecule and not any two particular atoms. That is why in MO it does not make sense to say that every carbon has 1 sigma bond with each of its neighbours. At best we could say that these electrons are in highly localised orbitals. As is indicated in the article, sigma-pi in VB is somewhat different from sigma-pi in MO. Loom91 07:07, 19 December 2006 (UTC)

The problem is that sigma orbitals and sigma bonds do not appear that different and indeed they are not as the delocalised MOs can be transformed into localised orbitals. This means that sigma bonds are not a meaningless concept in MO although I agree that sigma in MO is not exactly the same as sigma in VB. I note also that most quantitative VB treatments of benzene such as the famous spin coupled calculations of Gerratt, Cooper and Raimondi use VB only for the pi electrons and treat the sigma as MOs. It is true that MOs are calculated with the potential of the entire molecule, but so are the VB wave functions. It is the orbitals that are delocalised or localised. The potential is always the whole molecule included the repulsion of all other electrons. We are not too far apart but I think the current wording will lead to misunderstandings and there is already too much misunderstanding in the MO/VB debate. --Bduke 07:46, 19 December 2006 (UTC)

The point made in the article is that VB and MO are two different mathematical models with different approaches to solving a problem. The sigma-orbital approach in MO and the sigma-bond approach in VB give the same predicted expectation of observables (otherwise one theory would be more 'wrong' than the other), but that doesn't mean that the theories are the same and you can go around taking a slice from VB and a scoop from MO. Also, MO is a more 'natural' theory than VB. The postulates or methodology of MO are closer to the actual quantum mechanical picture, which exists exactly only for the simplest molecules like H2+. Loom91 09:51, 20 December 2006 (UTC)

There are two major problems with what you say. (1) MO and VB do NOT give the same predicted expectation values of observables and indeed one is more wrong than the other. I never said they are the same. They are different. (2) MO is not more natural than VB. Just because the exact solution of H2+ (a one electron problem) is a MO does not mean that MO treats electron repulsion in cases with more than one electron correctly. Both are approximations. MO is much easier to do and is very popular. Computationally a lot of methods build on it or add to it. However in fact simple VB energies almost always lie below simple MO energies (and hence are better) and MO does not dissociate homonulcear diatomic molecules correctly. VB is less wrong. I would also add that it may seems odd to take "a slice from VB and a scoop from MO" but that is exactly what a lot of people do, including as I said above, some of the best VB calculations on benzene. Have you studied quantum chemistry to any depth? Of course this article is not the place for advanced quantum chemistry, but we must try to avoid too many "lies for children" as we simplify the quantum chemistry. --Bduke 10:16, 20 December 2006 (UTC)

I think the confusion is resulting from talking about VB and MO as theories in the ordinary sense. I haven't studied VB in detail, but as far as I know they are two different approaches to approximating the solution, not methods of approximation as such. As you say, computational methods build on them. There are different levels of approximation in VB and different levels of approximation in MO (you could start with Huckel and proceed to DFT). If a certain level of approximation in VB gives a result, MO will also give similar or better results at some level of approximation. You say simple VB energies lie below simple MO energies, but we can't decide superiority between the two simply by looking at the 'simple' limit.

The framework provided by MO (or VB) can not be identified with any particular method or level of approximation in either. The MO road is closer to what a physicist will do if asked to solve a system, but that does not mean the VB road will not give the same results at sufficient approximation. The converse is also true. You claim "MO does not dissociate homonuclear diatomic molecules correctly"-I've never read this, but VB fails to predict that hybridisation in CH4 does not produce equivalent orbitals. VB is not more correct than MO.

As for mixing MO and VB, you are talking about mathematical calculations where we have quantitative ways of verifying whether we are mixing in a valid manner. The article however talks about mixing the two in qualitative descriptions ("lies for children"), where there is no way to know (without having actually done the calculations) whether the pictorial descriptions reflect the actual mathematics. It is such situations that trying to mix the two models is dangerous. Also, I don't think that this article is not a place for advanced quantum chemistry. Wikipedia is a specialised as well as general purpose encyclopedia, so feel free to add a section on the detailed mathematics behind the two-headed arrows. It will be best if you cite references. Loom91 07:48, 21 December 2006 (UTC)

You state that you have not studied VB in detail. Sorry, but I'm afraid that is pretty clear. Let us take the dissociation of MO theory for homonuclear diatomics first. The simple MO wavefunction is an equal mixture at all values of the bond length of the simple VB covalent and ionic terms, so it dissociates into an equal mixture of 2 H atoms and (H+ + H-). The energy is the mean at infinite bond length of these two and thus very much higher in energy than 2 H atoms which H2 experimentally dissociates into. VB dissociates correctly. The predicted MO dissociation energy is too large. The predicted VB dissocaiation energy is closer to experiment but two small because the two atoms at large distance are exact and the VB energy lies above the exact energy at the predicted bond length. The MO energy lies even higher. These facts matter because both methods are variational - they lie above the exact result. The simple Heitler-London VB lies below the simple MO energy curve and is thus better. The similar case of F2 is so bad that the MO energy lies higher than the correct dissociation of 2 F atoms. This is in many texts. By MO I mean for H2 a single molecular orbital built as a linear combination of atomic orbitals (with simple MO using just the two 1s orbitals). Of course one can add configuration interaction and do as well as VB. Adding all possible excited configurations to MO and all possible VB structures to the simple VB gives identical results but such calculations, called full configuration interaction, are only possible for fairly small molecules with fairly small basis sets. "VB fails to predict that hybridisation in CH4 does not produce equivalent orbitals" - please explain more carefully or give a source. Hybridisation is not a physical think. It is an artifact of VB theory and the hybrids can and are closen to be equivalent. DFT is not MO although I grant you it looks like it. VB can easily do better than the best MO wavefunction - called the Hartree-Fock limit. It does exactly because it get bond breaking better.

The bottom line is that the simple pictures grew out of calculations. Pauling would have done nothing without the Heitler-London calculation on H2 and some extensions of it. We forget this at our peril. Qualitative ideas did not grow out of the air. "Also, I don't think that this article is not a place for advanced quantum chemistry". I think you meant "Also, I do think that this article is not a place for advanced quantum chemistry". I agree. It is about the simple pictures but we must not mislead. I'll think about it more after the holiday period which is going to be very busy for me. --Bduke 08:42, 21 December 2006 (UTC)

What you are saying is not that VB is a more accurate theory than MO, but that VB is computationally less intensive. As for hybridisation, the 4 CH bonds are not exactly equivalent as calculated in VB. As predicted by MO, one of the bonding pairs have a different energy from the other three. The photoelectron spectra shows two characteristic bands [1]. Also, why are you excluding post-Hartree-Fock methods from the umbrella of MO? And I meant exactly what I said: "Also, I don't think that this article is not a place for advanced quantum chemistry." That is, this article IS a place for advanced quantum chemistry. An accurate section on what exactly is mathematically meant by resonance will add greatly to the article. It may even become a GA. So feel free to add such a section. Loom91 07:12, 22 December 2006 (UTC)

No, I am saying that VB is more accurate at equivalent levels than MO, but that MO is computationally less intensive. The orbitals in MO are orthogonal and that simplifies things. In VB they are not orthogonal and it has taken a long time to get code that competes with MO. Why am I excluding post-Hartree-Fock (HF) methods? Because while based on a MO reference function they are not MO. Configuration interaction at the full level is entirely equivalent to full VB, so no comparision is fruitfull. Bond breaking is still badly handled by post-HF that uses a single determinant reference. To handle bond breaking correctly the MO guys use multi-configuration SCF where you can no longer say that 2n electrons are in n MOs for a closed shell singlet. Also it can be shown that these methods are very similar and in some cases identical to some spin-coupled VB methods, so again comparision is not fruitfull. The only meaningfull comparision is between the methods Pauling and Mulliken and their respective supporters fought about in the 1930s, for example simple MO for H2 - (a + b)(1)(a + b)(2) and Heitler London for H2 - a(1)b(2) + b(1)a(2) where a and b are the 2 is orbitals on the 2 H atoms. In passing note that expanding out the MO function, you get a(1)b(2) + b(1)a(2) + a(1)a(2) + b(1)b(2). The first 2 terms are the Heitler London terms and the last 2 are ionic terms - H- H+ and H+ H- so as I said earlier MO is a mixture of the VB covalent term that dissociates in 2 H atoms and the VB ionic terms that dissociate into two ions at a higher energy.

I have no idea where you have got the idea that the 4 CH bonds are not equivalent in VB. They are. The photoelectron spectrum with 2 peaks is best explained by the fact that there are only 2 energy-distinct MOs - 1 triply degenerate group and a single degenerate one for the 4 pairs of valence electrons. Ionisation is certainly best explained by MO theory because the electron does not leave one bond but the whole molecule. A VB description of CH4+ would have to include resonance between the 4 structures each with 3 two electron bonds and 1 one electron bond. In this way the ion would come out symmetric and there are indeed 2 solutions just as in MO theory. Yes, MO theory is simpler to describe ionisation and spectroscopy. VB can be simpler to describe bonding and generally gives better numbers. Getting numbers to agree with your PE spectra from MO theory is not easy, but the simple picture is. The orbital energies, for example, will only predict the position of your peaks well, using Koopman's approximation, if the massive correlation energy corrections and relaxation energy corrections are of opposite sign and similar magnitude which they often are for organic molecules but rarely are for metal complexes. --Bduke 08:12, 22 December 2006 (UTC)

What do you mean by equivalent levels? How would you say a particular VB method is equivalent to a particular MO method? Loom91 18:07, 23 December 2006 (UTC)

I assume you are asking about my statement that, for example, full CI is equivalent to full VB. OK, let us take the classic example of H2. The simple MO is (a + b)(1)(a + b)(2) which expands to:-

(a + b)(1)(a + b)(2) = a(1)b(2) + b(1)a(2) + a(1)a(2) + b(1)b(2) as above.

The excited state with both electrons in the antibonding orbital is:-

(a - b)(1)(a - b)(2) = a(1)b(2) + b(1)a(2) - a(1)a(2) - b(1)b(2)

Now mix these and collect terms (K is the mixing weight):-

(a + b)(1)(a + b)(2) + K {(a - b)(1)(a - b)(2)} =
(1+K){a(1)b(2) + b(1)a(2)} + {1-K){a(1)a(2) + b(1)b(2)}

The above is the full CI result for this small basis set of 2 1s orbitals. The full VB is ionic - covalent resonance, which is (C is the mixing coefficient):-

{a(1)b(2) + b(1)a(2)} + C{a(1)a(2) + b(1)b(2)}

Neither of these are normalised. In both cases the mixing coefficent is determined by finding the value that minimises the energy. Since both allow any proportion of the covalent - {a(1)b(2) + b(1)a(2)} - and ionic terms - {a(1)a(2) + b(1)b(2)}, the final results will be the same. This result is general. If we take a simple MO and mix in all possible excitatations that mix with the ground state, and then take all possible VB structures from the same set of atomic orbitals, the results are equivalent. The general result is perhaps surprising - approximations that look very different and start from different ideas, can actually be completely identical.

To our other readers, I apologise. This is getting over complicated and technical. Loom91, if you want to continue this, please move it to e-mail. I have e-mail set from my user page. I am happy to continue helping you to learn about VB theory, but I think the discussion is getting beyond relevence to this article. --Bduke 21:42, 23 December 2006 (UTC)

You misunderstand me. I know VB == MO in the high accuracy limit. I was asking in lower accuracy levels how you say that VB is more accurate than 'equivalent' MO. As for the article, what changes do you propose? Loom91 07:02, 27 December 2006 (UTC)

Let us take H2. The simplest MO approach just using the two hydrogen atom like 1s orbitals is as above. The simplest VB using the same orbitals is the Heitler-London. These are at an equivalent level, yet give different results. The latter lies lower in energy than the former at all interatomic distances and particularly at large distance and so is better. We can then optimise the orbital exponent of the 2s orbital in both cases. These are at equivalent levels. Again VB is better. That is what I mean by equivalent - same basis set and simplest possible MO or VB approach or comparable improvements to simplest approach.

I have made the changes to the article that I think should be made. My reasons are many. First, it is quite common to mix MO and VB ideas. Coulson in both "Valence" and in McWeeny's "Coulson's Valence" says this about the sigma bonds in benzene, "These bonds can be described either in MO or VB language; their essential character is the same in either case". I know of no book that criticises this statement. He goes on to give the VB and MO approaches. This mixing of language is commonly done in simple qualitative explanations and a mixing of methods is commonly done in quantitative calculations as I mention above. I do not think sigma is "meaningless in MO" or delocalised is "meaningless in VB". I do agree it is best to use "delocalisation energy" in MO descriptions, but note that somewhere on WP is a reference to a Journal of Chemical Education article that recommends delocalisation rather than resonance for VB descriptions. I also suggest it is stretching it to say about the two methods that "mathematically the models are incompatible". Different, yes, but not incompatible. To say, for example that MO for H2 is entirely identical to VB resonance between the covalent and ionic structures, but with equal weights, demonstrates this lack of incompatability. The article is best made simpler at this point. The wording was confusing and not clarifying matters, so is best removed. --Bduke 02:10, 28 December 2006 (UTC)

[edit] Reasonance diagrams for heteroaromtic compounds?

Reasonance diagrams for heteroaromtic compounds would be nice -- Quantockgoblin 23:47, 20 March 2007 (UTC)

It is requested that a diagram be included here to improve the readability of this article.
For more information, refer to the discussion below or on Wikiproject Chemistry Image Request. Please also see the image style guide before uploading images.
It does not seem useful to clutter the article with more examples. Heteroaromatic compounds present no particular challenge in drawing resonance diagrams. For example in furan, you simply move the lone pair on the O atom through the other 4 carbon atoms. Resonance diagrams for homoaromatic compounds would be more interesting. Loom91 08:35, 21 March 2007 (UTC)

[edit] Strange definition in introduction

Just out of interest, why is resonance referred to as "a tool used (predominantly in organic chemistry) to represent certain types of molecular structures."? , it's a bit of a LARGE generalisation; aside from being referred to as canonical forms, Miessler refers to it as when there is "more than one possible way in which valence electrons can be placed in a lewis[-based] structure.", Chambers refers to it as "when [a] true structure of .. [a molecule or compound] cannot be accurately represented by a single structure, ... several resonance structures are suggested." ♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ slurp me! 10:40, 6 April 2007 (UTC)

The sentence you refer to simply identifies what sort of thing we propose to discuss. It does not try to give a definition of resonance. Loom91 19:11, 8 April 2007 (UTC)
Well, with that said -- wiki articles aren't for proposing anything, but rather reporting it impartially. For instance;
"It is also not right to say that resonance occurs because electrons "flow" or change their place within the molecules. Such a thing would produce a magnetic field that is not observed in reality."
Although correct, it has a more "teaching" than "telling" approach. ♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ slurp me! 13:15, 9 April 2007 (UTC)
Referencing that statement is rather trivial, any chemistry textbook will do. An actual definition of resonance is neither useful nor easy to give. Would you like a sentence in the introduction saying "Resonance in the context of chemical structure may be defined as the method of approximating an actual state vector of a molecule as a linear combination of (not necessarily complete) basis state vectors representing states where the molecule only contains localised bonds, where bond is taken in the meaning of Valence Bond Theory"? Loom91 06:53, 10 April 2007 (UTC)
No, but i'll surmise what i mean. I'll withdraw my objection to the introduction so long as a generic definition of resonance structures is there. ♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ slurp me! 10:23, 11 April 2007 (UTC)

[edit] Resonance hybrid stability

To clarify this point "Resonance hybrids are always more stable than any of the canonical structures", the wave function Ψ is given by:

Ψ = a1C1 + a2C2 + a3C3 + ..

where Ψ is the resonance hybrid function and C1, C2, .. are the canonical structure functions. a1, a2 , a3, .. are coefficients chosen to minimise the energy. It follows from the variation theorem that the energy of Ψ is less than or equal to the energy of all of C1, C2, .. taken separately. It would be equal if one of the a1, a2, .. was 1 and all the others zero, and lower otherwise. Loom91 is correct and he gives a good simple reference. In antiaromaticity, the geometry changes to a more stable form. A good discussion is chapter 4 of "Facts and Theories of Aromaticity" by David Lewis and David Peters, Macmillan, 1975. --Bduke 13:37, 12 April 2007 (UTC)

[edit] Convoluted statement in section "Writing resonance structures" should be rewritten

Quotation:
When separating charge (giving rise to ions), usually structures where negative charges are on less electronegative elements have little contribution, but this may not be true if additional bonds are gained.

I believe this statement should be rewritten. Not being a native english speaker, my opinion may be misguided; anyway, to me it looks convoluted and is nearly uncomprehensible. A statement like this, being a list item, should speak for itself. It remains unclear however, to what phelomenon contribution should contribute.
Bertus van Heusden 10:53, 4 September 2007 (UTC)

[edit] kcal vs kJ

I see someone changed the units under "resonance energy" to kcal/mol without changing the numeric values. These should definitely stay as SI units, but someone should now check the correct values. Unfortunately I don't have time right now. --Slashme 06:53, 10 October 2007 (UTC)

The numbers are correct in kcal/mol (the resonance energy of benzene from this type of analysis is closer to 36 kcal/mol, not to 36 kJ/mol, which would be less than 9 kcal/mol, way too low). I don't think that the units should be converted to SI exclusively, although I would recommend giving the numbers in both systems. In my experience, kcal/mol are used more often in physical organic chemistry than kJ/mol, although both systems are commonly seen, and there is some regional variation. --Itub 10:02, 10 October 2007 (UTC)

You have a point, it's probably a good idea to keep the kcals, but a quick browse through the literature shows that kJ is gaining ground. I can't yet find a good ref. for the values quoted, because my chem. books are at the lab. If I get around to it, I'll sort it out, but I might not... --Slashme 13:21, 10 October 2007 (UTC)

The original estimates were in kcal, probably in the era of Pauling, but kJ are now preferred. So yes, we need both units, so I have now inserted kJ values. I just multiplied the kcal values by 4.184 and rounded off to two figures. Dirac66 13:33, 10 October 2007 (UTC)

[edit] terminology, physical reason

To me, as a physicist, there are a couple of problems with this article. One is that the article never really explains the reason for the term "resonance," and there is no obvious (to me) physical phenomenon going on that is in any way (that's obvious to me) analogous to resonance. The section near the end about Pauling's introduction of the term doesn't really explain anything very clearly: why the quantum-mechanical treatment of H2+ was relevant to Pauling, or why he used the word "resonance." The other problem IMO is that the article never gives any very transparent physical explanation of what's going on. Although I understand the general argument made above on the talk page that a superposition of trial wavefunctions can be optimized variationally to lower its energy, that argument is so generic that it really has nothing in particular to do with chemical bonds, or even chemistry. If I had to take a stab at it, I would guess that the general physical mechanism is that, compared to a structure made of single and double bonds, the actual structure delocalizes the electrons, which means that they have a larger wavelength, thus a lower momentum and kinetic energy. In the case of an ion like CH3CO2-, I can also imagine that the delocalization would lead to a lower Coulomb energy.--207.233.87.196 (talk) 23:56, 11 December 2007 (UTC)

Hmm...okay, I think I understand the reason for the term now. See http://www.nap.edu/readingroom/books/biomems/lpauling.html . The paragraph beginning "Resonance: In attempting to explain ..." seems to be saying clearly what the WP article is saying unclearly. I'd take a whack at it myself, but I'm not a chemist, so I don't want to get this wrong.--207.233.87.196 (talk) 00:08, 12 December 2007 (UTC)