The Benzene Molecule

[Ronald Hyde]

The Benzene Molecule

This is a description of the 'other kind of bonding' that occurs in Nature, resonance bonding. We all know about Coulomb bonding, the type that is determined by electric charge, and which holds the electrons to the nucleus.

 

Resonance bonding ( RB ) is purely quantum mechanical in its working, it has no classical equivalent. It's very important in Chemistry, but it's important in another way too, for it holds the nucleons together in an atomic nucleus.

 

The requirements for RB to occur are simple and easily met in Nature, so it is a frequent occurence. It needs:

 

Two states with nearly the same energy, which can change back and forth with time.

 

The two states have to be distinguishable,

in the quantum mechanical sense of distinguishabilty.

 

Benzene has two states with the same energy, which are distinguishable in the QM sense by being mirror images of each other. Benzene has six Hydrogen and six Carbon atoms, and it has six electronic bonds between the carbon atoms, three double and three single bonds. The single and double bonds can switch between themselves. If we make a 'naive' calculation of the binding energy of benzene we will get a certain value, let's call it the 'zero' energy because it has zero free energy by out calculation.

 

Now one thing about RB is that it doesn't care about the mechanism of how the states swap back and forth, it only cares about the rate, so it is a general mechanism, and only needs the two requirments.

 

Now the rules of QM say that if there are two states that change back and forth with time, there have to be two superpositions of those states which don't change with time, and which are superpositions of the time states, but differ in energy. So our zero of energy gets split into two new levels, by our non-naive new calculation, one above and one below our original zero. The difference in energy is equivalent to a photon well into the ultraviolet range, so that benzene absorbs strongly in UV.

 

We can 'tune' the benzene molecule into the visible range by substituting heavier molecules like Chlorine for some of the Hydrogen. If we attach ionizing radicals like amines and acidics to opposite ends of the benzene, it will have a large electric dipole moment, and be a strong absorber and reflector of visible light, and that is how most dyes are made.

 

If we place two benzene molecules close together they can also have some resonance bonding between them, so that benzene melts and vaporizes tht higher temperatures then other similar sized molecules.

 

We can make molecules with four or eight carbon atoms that are otherwise similar to benzene, but they are not mirror images of each other. They do not exhibit strong bonding.

Edited August 5, 2012 by Ronald Hyde

[mississippichem]

The Benzene Molecule

This is a description of the 'other kind of bonding' that occurs in Nature, resonance bonding. We all know about Coulomb bonding, the type that is determined by electric charge, and which holds the electrons to the nucleus.

 

Resonance bonding ( RB ) is purely quantum mechanical in its working, it has no classical equivalent. It's very important in Chemistry, but it's important in another way too, for it holds the nucleons together in an atomic nucleus.

 

The requirements for RB to occur are simple and easily met in Nature, so it is a frequent occurence. It needs:

 

Two states with nearly the same energy, which can change back and forth with time.

The two states have to be distinguishable,

in the quantum mechanical sense of distinguishabilty.

Benzene has two states with the same energy, which are distinguishable in the QM sense by being mirror images of each other. Benzene has six Hydrogen and six Carbon atoms, and it has six electronic bonds between the carbon atoms, three double and three single bonds. The single and double bonds can switch between themselves. If we make a 'naive' calculation of the binding energy of benzene we will get a certain value, let's call it the 'zero' energy because it has zero free energy by out calculation.

 

Now one thing about RB is that it doesn't care about the mechanism of how the states swap back and forth, it only cares about the rate, so it is a general mechanism, and only needs the two requirments.

Now the rules of QM say that if there are two states that change back and forth with time, there have to be two superpositions of those states which don't change with time, and which are superpositions of the time states, but differ in energy. So our zero of energy gets split into two new levels, by our non-naive new calculation, one above and one below our original zero. The difference in energy is equivalent to a photon well into the ultraviolet range, so that benzene absorbs strongly in UV.

 

We can 'tune' the benzene molecule into the visible range by substituting heavier molecules like Chlorine for some of the Hydrogen. If we attach ionizing radicals like amines and acidics to opposite ends of the benzene, it will have a large electric dipole moment, and be a strong absorber and reflector of visible light, and that is how most dyes are made.

 

If we place two benzene molecules close together they can also have some resonance bonding between them, so that benzene melts and vaporizes tht higher temperatures then other similar sized molecules.

 

We can make molecules with four or eight carbon atoms that are otherwise similar to benzene, but they are not mirror images of each other. They do not exhibit strong bonding.

 

The statements I bolded are problematic. It is known that the resonance forms of benzene do not convert back and forth in time, by definition of a resonance hybrid. Also, there is no spectroscopic evidence of two degenerate electronic states switching back and forth. All six hydrogen atom protons are equivalent on the NMR timescale meaning that they all are de-shielded equally. You can also use reactivity arguments to show that this is not true.

 

If you want to approximate the energy gap between the first excited state and the ground state of benzene (what would explain its UV absorbance) you need to solve a Schroedinger equation for a particle on a ring which has energy eigenstates [math] \frac{n^{2}\hbar ^{2}}{2mr^{2}} [/math]. That will give you an idea of where the first excited state lies. Subtract out the ground state energy and you'll get a decent number for the maximum absorbance wavelength for the [math] \pi \rightarrow \pi ^{*} [/math] transition in benzene. Also, remember that you can't neglect the sigma bonding electrons here either because they occupy the lowest states of the ring so the transition is not from the first to the second state on the hypothetical ring.

 

If you want a good calculation you'll need to setup a Slater determinant of the basis functions and feed that through the Hartree-Fock equation. For a decent calculation that is easier than the Hatree-Fock, you can evoke the variational theorem and use Huckel theory to diagonalize an easy Hamiltonian where all the non-adjacent overlap integrals are taken to be zero (a pretty good approximation...sometimes).

 

I think you may be mixing up the concept of degeneracy with aromaticity. The ground state for pi electrons in benzene is doubly degenerate, which only by coincidence corresponds to the two degenerate resonance forms that constitute the resonance hybrid. The excited states have 2n-fold degeneracy so this analogy is useless in the excited states. You can't mix valence bond theory with molecular orbital theory!

[Ronald Hyde]

The statements I bolded are problematic. It is known that the resonance forms of benzene do not convert back and forth in time, by definition of a resonance hybrid. Also, there is no spectroscopic evidence of two degenerate electronic states switching back and forth. All six hydrogen atom protons are equivalent on the NMR timescale meaning that they all are de-shielded equally. You can also use reactivity arguments to show that this is not true.

 

Notice that I said that when you make a 'naive' calculation that the two time/position states appeared. When you made a full calculation, the the two momentum/energy states appear.

So everything that is entailed is there, what are you quibling about? I'm just presenting it two steps, so that people can see what it involves.

[mississippichem]

If the switching between resonance forms is unphysical, why consider it at all? It provides no computational insight and no useful intuition.

[Ronald Hyde]

If the switching between resonance forms is unphysical, why consider it at all? It provides no computational insight and no useful intuition.

 

Sure it provides insight. It shows you when to apply the concept, when it will occur and when it will not. And it

helps other people have ( not yourself ) a way of seeing and understanding it.

 

And it may not be unphysical at all! It may well be possible to excite a benzene molecule into one or the other states.

[mississippichem]

Sure it provides insight. It shows you when to apply the concept, when it will occur and when it will not. And it

helps other people have ( not yourself ) a way of seeing and understanding it.

 

I don't see how. It explains a known phenomenon with a process that is known not to occur. There is already a different explanation available that is in line with the experimental evidence. The two resonance forms of benzene do not convert between each other. Any explanation that claims they do is of no use IMO.

 

And it may not be unphysical at all! It may well be possible to excite a benzene molecule into one or the other states.

 

So you are saying there are cyclohexatriene like excited states of benzene? Surely not. The first excited state of benzene promotes a pi electron into a pi-star orbital. That's not a sigma orbital . You'll never be able to get the symmetry of a cyclohexatriene. I can't see how any conceivable excited state of benzene would give you a C_3v structure.

[Ronald Hyde]

So you are saying there are cyclohexatriene like excited states of benzene? Surely not. The first excited state of benzene promotes a pi electron into a pi-star orbital. That's not a sigma orbital . You'll never be able to get the symmetry of a cyclohexatriene. I can't see how any conceivable excited state of benzene would give you a C_3v structure.

 

Ah, so it involves another of those 'spontaneously broken' symmetries that seem to happen all the time, e.g. as in ferromagnetism, superconductivity, etc..

There must be some kind of general rule about that? But I still wonder if there might be some way of even momentarily creating the other type of state.

 

I'm guessing that there's some similarity with the Oxygen molecule.

Edited August 6, 2012 by Ronald Hyde

[juanrga]

The Benzene Molecule

This is a description of the 'other kind of bonding' that occurs in Nature, resonance bonding. We all know about Coulomb bonding, the type that is determined by electric charge, and which holds the electrons to the nucleus.

 

What holds electrons to the nucleus is essentially Coulomb interaction. This is not any kind of bonding.

 

Resonance bonding ( RB ) is purely quantum mechanical in its working, it has no classical equivalent. It's very important in Chemistry, but it's important in another way too, for it holds the nucleons together in an atomic nucleus.

 

Nope. There is no Lewis structures in an atomic nucleus.

 

The requirements for RB to occur are simple and easily met in Nature, so it is a frequent occurence. It needs:

 

Two states with nearly the same energy, which can change back and forth with time.

 

The two states have to be distinguishable,

in the quantum mechanical sense of distinguishabilty.

 

Nope. There is only one state. This state cannot be represented with a single Lewis diagram and resonance was invented to represent the state as a combination of two Lewis structures. Each Lewis structure alone does not represent Benzene.

 

Moreover, benzene can be also represented without any appeal to resonance: the famous representation with inner circle that you can find in many chemistry textbooks.

 

Benzene has two states with the same energy, which are distinguishable in the QM sense by being mirror images of each other.

 

Nope. This is not any real form of isomerism. This is why chemist use a double head arrow instead of two arrows to represent it.

 

Benzene has six Hydrogen and six Carbon atoms, and it has six electronic bonds between the carbon atoms, three double and three single bonds.

 

Nope. All the C-C lengths are identical and in the middle between single and double bonds.

 

The single and double bonds can switch between themselves.

 

Nope. Apart from that said above the resonance representation involves a 'switch' in the pi part but not in the sigma skeleton.

 

Now one thing about RB is that it doesn't care about the mechanism of how the states swap back and forth, it only cares about the rate, so it is a general mechanism, and only needs the two requirments.

 

Nope. As stated above this is not a real process.

 

Now the rules of QM say that if there are two states that change back and forth with time, there have to be two superpositions of those states which don't change with time, and which are superpositions of the time states, but differ in energy.

 

QM does not say anything as that. The superposition principle refers to states at the same time, not to superposition at different times.

[Ronald Hyde]

Resonance Bonding

For something that doesn't exist, it sure pulls up a lot of links on a Google search. But I guess your views

are right and everyone else is wrong.

 

 

Resonance in quantum mechanics

Resonance has a deeper significance in the mathematical formalism of valence bond theory (VB). When a molecule cannot be represented by the standard tools of valence bond theory (promotion, hybridisation, orbital overlap, sigma and π bond formation) because no single structure predicted by VB can account for all the properties of the molecule, one invokes the concept of resonance.

 

Valence bond theory gives us a model for benzene where each carbon atom makes two sigma bonds with its neighbouring carbon atoms and one with a hydrogen atom. But since carbon is tetravalent, it has the ability to form one more bond. In VB it can form this extra bond with either of the neighbouring carbon atoms, giving rise to the familiar Kekulé ring structure. But this cannot account for all carbon-carbon bond lengths being equal in benzene. A solution is to write the actual wavefunction of the molecule as a linear superposition of the two possible Kekulé structures (or rather the wavefunctions representing these structures), creating a wavefunction that is neither of its components but rather a superposition of them.

 

In benzene both Kekulé structures have equal energy and are equal contributors to the overall structure—the superposition is an equally-weighted average, or a 1:1 linear combination of the two—but this need not be the case. In general, the superposition is written with undetermined coefficients, which are then variationally optimized to find the lowest possible energy for the given set of basis wavefunctions. This is taken to be the best approximation that can be made to the real structure, though a better one may be made with addition of more structures.

 

 

 

Edited August 7, 2012 by Ronald Hyde

[hypervalent_iodine]

For something that doesn't exist, it sure pulls up a lot of links on a Google search. But I guess your views

are right and everyone else is wrong.

 

What exactly was wrong about juanrga's post? Are you trying to say that juanrga is claiming resonance bonding doesn't exist? Because that's certainly not what I just read.

[Ronald Hyde]

What exactly was wrong about juanrga's post? Are you trying to say that juanrga is claiming resonance bonding doesn't exist? Because that's certainly not what I just read.

It's this comment that he made:

 

His comment: . As stated above this is not a real process.

 

My comment: Because it is in principal a possible process that RB occurs. If it were not in principal possible RB will not occur.

[juanrga]

Resonance in quantum mechanics

Resonance has a deeper significance in the mathematical formalism of valence bond theory (VB). When a molecule cannot be represented by the standard tools of valence bond theory (promotion, hybridisation, orbital overlap, sigma and π bond formation) because no single structure predicted by VB can account for all the properties of the molecule, one invokes the concept of resonance.

 

Valence bond theory gives us a model for benzene where each carbon atom makes two sigma bonds with its neighbouring carbon atoms and one with a hydrogen atom. But since carbon is tetravalent, it has the ability to form one more bond. In VB it can form this extra bond with either of the neighbouring carbon atoms, giving rise to the familiar Kekulé ring structure. But this cannot account for all carbon-carbon bond lengths being equal in benzene. A solution is to write the actual wavefunction of the molecule as a linear superposition of the two possible Kekulé structures (or rather the wavefunctions representing these structures), creating a wavefunction that is neither of its components but rather a superposition of them.

 

In benzene both Kekulé structures have equal energy and are equal contributors to the overall structure—the superposition is an equally-weighted average, or a 1:1 linear combination of the two—but this need not be the case. In general, the superposition is written with undetermined coefficients, which are then variationally optimized to find the lowest possible energy for the given set of basis wavefunctions. This is taken to be the best approximation that can be made to the real structure, though a better one may be made with addition of more structures.

 

Good that you quote verbatim from Wikipedia article on resonance:

 

http://en.wikipedia.org/wiki/Resonance_%28chemistry%29#Resonance_in_quantum_mechanics

 

Now if you read the parts that you do not quote you can find corrections to the multiple mistakes that you are making.

 

It's this comment that he made:

 

His comment: . As stated above this is not a real process.

 

My comment: Because it is in principal a possible process that RB occurs. If it were not in principal possible RB will not occur.

 

Indeed it is not a real process as you incorrectly believe. The same wikipedia page that you quoted (but in the part that you ignored) makes this clear:

 

the molecule does not oscillate back and forth between the contributing structures, as might be assumed from the word "resonance".

 

As said to you before, chemists represent resonance with a double head arrow, because this is not a real process (real processes are represented by double arrows).

 

http://masterorganicchemistry.com/2011/02/09/the-8-types-of-arrows-in-organic-chemistry-explained/

[studiot]

One thing I don't understand about this thread.

 

What was the original question, hypothesis or proposition for discussion?

 

post#1 appears more in the style of preaching to me.

[Ronald Hyde]

One thing I don't understand about this thread.

 

What was the original question, hypothesis or proposition for discussion?

 

post#1 appears more in the style of preaching to me.

 

That if there exists two states of the same energy that in principle can change among themselves in time,

and are quantum mechanically distinguishable, there will be two states that in reality are superpositions of those

states and differ in energy. And that forms the basis or Resonance Bonding. And so far nothing said falsifies

the original premise.

 

It doesn't matter if the time-changing states last a millionth of a millionth of a second, if they exist in principal

the effect occurs.

[mississippichem]

That if there exists two states of the same energy that in principle can change among themselves in time,

and are quantum mechanically distinguishable, there will be two states that in reality are superpositions of those

states and differ in energy. And that forms the basis or Resonance Bonding. And so far nothing said falsifies

the original premise.

 

It doesn't matter if the time-changing states last a millionth of a millionth of a second, if they exist in principal

the effect occurs.

 

Saying it again doesn't make it so. Assuming your original premise is true (it's not). How are the two resonance forms of benzene distinguishable?

[Ronald Hyde]

Saying it again doesn't make it so. Assuming your original premise is true (it's not). How are the two resonance forms of benzene distinguishable?

 

By being mirror images of each other. In the Feynman Lectures he has quite a long piece about the Ammonia Molecule resonance

that occurs in the microwave part of the spectrum. And he describes it in the same way. It's Chapter 9, Book 3, the entire chapter,

but the description of the QM interpretation is on the very first page.

[studiot]

I don't know who you are or what you are but I do know that you are consistently avoiding polite queries about your statements.

 

I asked what was the point of your thread, as I cannot see one.

 

I asked this with the intention of offering help since it is quite clear from your statement that you have only a rudimentary understanding of resonance in general and resonance in benzene in particular.

 

In particular do you understand your statement

 

And that forms the basis or Resonance Bonding.

 

The word 'basis' is a particular mathematical term used in the particular mathematical method employed (the LCAO method) which allows certain mathematical statements to be made.

 

Do you understand the basis theorem?

 

Secondly there are more terms than two involved in benzene. The Kekule forms you refer to are the dominant ones and referred to as the psi A terms. Ther are also psi B terms etc.

 

Are you aware of these?

Edited August 7, 2012 by studiot

[Ronald Hyde]

I don't know who you are or what you are but I do know that you are consistently avoiding polite queries about your statements.

 

I asked what was the point of your thread, as I cannot see one.

 

I asked this with the intention of offering help since it is quite clear from your statement that you have only a rudimentary understanding of resonance in general and resonance in benzene in particular.

 

In particular do you understand your statement

 

 

 

The word 'basis' is a particular mathematical term used in the particular mathematical method employed (the LCAO method) which allows certain mathematical statements to be made.

 

Do you understand the basis theorem?

 

Secondly there are more terms than two involved in benzene. The Kekule forms you refer to are the dominant ones and referred to as the psi A terms. Ther are also psi B terms etc.

 

Are you aware of these?

 

Is there a defined list of points of threads? I haven't seen it.

 

No, 'basis', was meant in the sense of a principal or underpinning, not as a QM basis of states. Confusing perhaps!

 

Benzene can have more states, and the principal still be true. I'm sure that it has a 'fine spectrum' of many states

near the lowest state, more analogous to a large nucleus than to say a Deuteron, or the Ammonia molecule.

Resonance is a very general thing in Nature, but no matter where it occurs it has certain things in common. And

you don't have to know everything about every problem to be able to recognize them.

[studiot]

So why did you start this thread?

 

What do you want to know?

Edited August 7, 2012 by studiot

[Ronald Hyde]

So why did you start this thread?

What do you want to know?

I want to know how the World works, and I want everyone who wants to know how the world works to know it too.

Isn't that the whole point of the place? I would certainly hope so.

[studiot]

I want to know how the World works

 

So when offered further more detailed information about a subject why are you not interested?

[Ronald Hyde]

So when offered further more detailed information about a subject why are you not interested?

 

No, it's not that I'm not interested, not at all. I would not in the least deny their truth. It's that they're all derivative.

If you add the fact that benzene has lots of excitations, they can all be derived from what I said in post #1. And if you

want another description of resonance, open the Feynman Lectures, Book 3, Chapter 9, where he describe resonance in the

context of the Ammonia Laser. And Feynman, one of the reasons I love the way he does things, always works from first

principals wherever he can.

 

And that's the difference between my point of view and you guys. I, like the good Dr., like to work from first principals

and to find them too.

 

And I don't know if this topic has helped anyone else but it sure has me. I can see much more clearly how the notions

in #1 are writ large in the scheme of things, all the way down to the now famous Higgs Mechanism, which is very basic

( there's that word again ) to Existence. And I've also concluded that the parity operator is very much a part of it, it is

the only thing I would add to Dr. Feynmans description to make it complete.

[juanrga]

By being mirror images of each other. In the Feynman Lectures he has quite a long piece about the Ammonia Molecule resonance

that occurs in the microwave part of the spectrum. And he describes it in the same way. It's Chapter 9, Book 3, the entire chapter,

but the description of the QM interpretation is on the very first page.

 

No. The inversion of the Ammonia molecule is a real process, with associated energy barrier and rate (frequency). This real process is completely different from quantum mechanical resonance in Benzene, which is not any real process.

 

I repeat this again: the Benzene molecule is not given by any of the resonant forms but that both resonant forms together describe the molecule. As explained to you before chemists have provided a modern representation of the Benzene molecule which does not use resonance of two Lewis structures

 

Edited August 7, 2012 by juanrga

[Ronald Hyde]

No. The inversion of the Ammonia molecule is a real process, with associated energy barrier and rate (frequency). This real process is completely different from quantum mechanical resonance in Benzene, which is not any real process.

 

I repeat this again: the Benzene molecule is not given by any of the resonant forms but that both resonant forms together describe the molecule. As explained to you before chemists have provided a modern representation of the Benzene molecule which does not use resonance of two Lewis structures

 

 

You caused me to reread the first two pages of the Feynman reference, and he's describing two states which differ in time, being

superposed to get two states that differ in energy. The simple fact that they are very long lived states compared to the benzene

states or the W boson, doesn't make the other states less 'real', people will still tell you the W boson is 'real'.

[studiot]

No, it's not that I'm not interested, not at all. I would not in the least deny their truth. It's that they're all derivative.

If you add the fact that benzene has lots of excitations, they can all be derived from what I said in post #1.

 

The problem with guessing what someone else means is that you can easily guess wrongly, as you have done here.

 

You have guessed wrongly because you have absolutely no idea what I mean and instead of the asking the simple and sensible question

 

'Please explain further?' or 'what do you mean?' or somesuch

 

You have the appalling arrogance to dimiss my comments as 'derivative' - whatever that means.

 

Do you understand the term 'delocalisation energy', which for benzene is 155 kjoules per mole.

How would you measure this ?

 

Do you know what the LCAO method is or what a basis means?

 

Do you know what the

[math]{\psi _B}[/math]

 

wavefunctions represent or what their contribution is to the resonance mechanism?

 

Finally do you know why acetoacetic acid is not a resonance structure, but a tuatomeric compound?

If you like what is the esential difference between a tautomeric substance and a resonance substance?

 

 

 

[math]C{H_3}.CO.C{H_2}.COO{C_2}{H_5}\; \Leftrightarrow \;C{H_3}.C(OH):CH.COO{C_2}{H_5}[/math]

 

Oh and by the way the correct term for what happens in ammonia or the ammonium ion is hybridisation not resonance.

Edited August 8, 2012 by studiot