The covalent bound is due to antiparallel magnetic spin alignment between the magnetic aspect of electrons.

The magnetic interaction between electrons obeys the inverse cube interaction law, which at short distances overpowers the Coulomb force inverse square interaction force.

Kotler et al. demonstrated the inverse cube interaction law in 2014 between two electrons forced to align in parallel spin alignment:

https://www.nature.com/articles/nature13403.epdf?referrer_access_token=yoC6RXrPyxwvQviChYrG0tRgN0jAjWel9jnR3ZoTv0PdPJ4geER1fKVR1YXH8GThqECstdb6e48mZm0qQo2OMX_XYURkzBSUZCrxM8VipvnG8FofxB39P4lc-1UIKEO1

The antiparallel spin alignment (attraction) is a least action interaction with respect to the parallel spin alignment (repulsion).

Dear Renata,

Quantum mechanics allow to have bonding and antibonding states for the electrons. The covalent bond comes when the bonding state of minimum energy is reached for the shared electrons of the two atoms. Obviously the Pauli's exclusion principle must be followed and if there are two electrons both spins have to be antiparallel each other.

Thank you, André.

Given that the antiparallel magnetic spin alignment is the driving force of molecular bonding, doesn't it imply that atoms will have preference as to with what other atom to bond?

In the older atomic models, it is usually assumed that the relations between electrons and the nucleus are governed by their charges. However, the exact internal workings are not very clear in those models. I wonder how does the antiparallel and parallel alignment of magnetic spin work for the model of atomic structure.

Thank you, Daniel.

Could you please elaborate on what you mean by a "bonding state of minimum energy"? Where does this energy come from?

A follow-up question. Would you say that the Pauli exclusion principle would apply to the entire atom as well? I assume we could see an atom as a quantum system. Does it mean that the state of every electron in the atom has to be different?

Dear Renata.

First of all I must say that the answer of André is wrong. The antiparallel spins are only given to follow the Pauli's exclusion principle, but their interaction is negligable respect to the atomic energies that we are considering here. Notice that, for instance, the diamond atoms are glued with this kind of bond and this is a huge energy respect to the one assoiciate to the exchange of spins.

Respect to my question it would be better that you could start by reading the basics of this kind of energy (although it is not a good reference) in wikipedia

https://en.wikipedia.org/wiki/Antibonding_molecular_orbital

Dear Renata,

You wrote: "Given that the antiparallel magnetic spin alignment is the driving force of molecular bonding, doesn't it imply that atoms will have preference as to with what other atom to bond?"

In a certain way, you are right. In any atom, electronic layers are filled only when electrons capture mutually by pairs in magnetic antiparallel spin alignment. For 2 atoms to join in covalent bounding, one unpaired electron from the outer layer of one atom needs to pair up with an unpaired electron from a second atom.

This means that the number of atoms with which a particular atom can join by means of covalent bounds depends on the number of unpaired electrons it possesses on its outer layer.

With reference to the relations between electrons and the elementary charged particles making up the nucleons making up atomic nuclei (protons and neutrons), they are indeed governed by the interaction between their charges, but also by the interplay of their parallel and antiparallel magnetic spins as you suspects.

It is true that up to now this mechanics has been unclear, but this recent paper may possibly shed a new light on the whole issue:

http://file.scirp.org/Html/17-7503469_84158.htm

Best Regards

André

Thank you, again, Daniel. I will take a look at the page you referred to.

Renata

Thank you, André, for the link. I will definitely think about it.

Renata

Dear André,

Your answers on the mechanism of covalent bond are absolutely wrong, because the spin never is considered in the atomic or molecular bonding (only a quantum number for filling the able molecular levels). This is very basic knowledge. But with the link (I don't want to enter with the quality of the paper and review) of the last post you do even worse because it hasn't anything to do with the question of this thread, in fact could be misleading if you mixture both things. I think that it needs to be honest accepting a mistake (that everybody can make) and never confuse people just for personal defense. Over all if the people is polite with you.

Dear Daniel,

With all due respect Daniel, my paper has been peer reviewed and accepted by professional physicists.

From past conversations with you, I observed that you are completely unfamiliar with electromagnetism and the magnetic properties of electrons. I suggest you become cognizant of this important field of physics.

I particularly suggest that you read the Kotler et al. paper that I first referred here, whose title is strangely: "Measurement of the magnetic interaction between two bound electrons of two separate ions"

I draw your attention particularly to the very first sentence of their Abstract:

"Electrons have an intrinsic, indivisible, magnetic dipole aligned with their internal angular momentum (spin). "

Other than that, I think that all readers are able to pass their own judgment on the validity of information conveyed, particularly when all proper and verifiable formal references are given.

Best Regards

André

Dear André,

The question is:

What is the mechanism behind a covalent bond?

And all your answers are very wrong because the atomic bond doesn't depend of the spin. This is a very basic knowledge.

Respect to your papers (which were out of the question ), obviouly the people can enter always in the mines and see if I am writing for fun or trying to help in the understanding.

Dear Daniel,

You write "And all your answers are very wrong because the atomic bond doesn't depend of the spin. This is a very basic knowledge."

Aren't you contradicting your very own first answer to Renata here?

You answered: "The covalent bond comes when the bonding state of minimum energy is reached for the shared electrons of the two atoms. Obviously the Pauli's exclusion principle must be followed and if there are two electrons both spins have to be antiparallel each other."

Which is exactly the same answer, except for the wording and the relation with magnetism that you obviously are unfamiliar with, that I had previously given her: "The covalent bound is due to antiparallel magnetic spin alignment between the magnetic aspect of electrons….The antiparallel spin alignment (attraction) is a least action interaction with respect to the parallel spin alignment (repulsion)."

I refered the OP to the Kotler et al. article so she could see the relation between the spin orientation and the magnetic dipole orientation analyzed by Kotler et al. in their recent paper, which, you will note was published by Nature, a journal that certainly does not publish information to mislead people.

The relation between mutual spin orientation and mutual magnetic dipole orientation of the electron is very basic knowledge indeed.

As for the reference to my paper, it was in direct answer to an interrogation from Renata to me regarding the possible function of magnetic spin alignment between electronic escorts and nuclei: "In the older atomic models, it is usually assumed that the relations between electrons and the nucleus are governed by their charges. However, the exact internal workings are not very clear in those models. I wonder how does the antiparallel and parallel alignment of magnetic spin work for the model of atomic structure. "

because it so happens that this article specifically discusses this very issue.

So I linked it so she could access the analysis if she so chose. So, contrary to a previous remark of yours: "of the last post you do even worse because it hasn't anything to do with the question of this thread," it has to do with a subquestion of the original poster directly addressed to me.

You are free of course to negate the relation between the electron magnetic dipole alignment and electron spin alignment, but such opinions cannot change the outcome of the Kotler et al. experiment nor of this historically established relation. I encourage you to read their paper to see the relation.

One last note of caution with respect to the information in Wikipedia such as you provided. It is generally valid at the general level, but it is not a formal reference and often can be incomplete and misleading by omission. True valid references are the official textbooks used in colleges and universities and the original peer-reviewed papers of the discoverers.

But speaking of wikipedia references, here is one that directly links the electron spin to its magnetic moment:

https://en.wikipedia.org/wiki/Spin_magnetic_moment

I understand that you contribute answers to help people understanding, which is fine with me.

You must accept however that other people as free as you are to contribute and may contribute information that you do not agree with.

Readers are fully capable of casting their own judgment on the validity of contributions.

Best Regards

André

Dear André,

No, didn't contradict me. No, André no. I said that the spins needed to be antiparallel always when they are in the same energy states. This is always independently of the bonding or antibonding state. Both things are different. The spin configuration is not related with the bonding but with Pauli's exclusion principle. I tried to be polite with your answer and I told it without mentioning it. But it seems that you didn't understand it.

By the way, I know very well what is the magnetic moment associated to a spin and I only can tell you that is out of the answer to the question that we have here. If you want to have a good reference of what is a bond state you can go to

https://books.google.es/books?id=HcWiAwAAQBAJ&pg=PA329&lpg=PA329&dq=bond+chemical+state&source=bl&ots=y3L1-wnRt4&sig=6ULm97DrAYn7n7W6jMYObsfxkH4&hl=es&sa=X&ved=0ahUKEwjD_K7QyOfaAhUIzRQKHbxJC24Q6AEIcjAJ#v=onepage&q=bond%20chemical%20state&f=false

A more serious answer to this bond is in

Atkins' Molecular Quantum Mechanics 5th ed., pp 262–266.

Dear Daniel,

Of course the covalent bound antiparallel magnetic spin relation is subject to Pauli's exclusion principle. There is no contradiction.

You write "I know very well what is the magnetic moment associated to a spin "

That's what I wrote in my initial answer. Then we agree.

I wonder what you beef was about then.

Best Regards

André

Dear André,

Don't try to do semantics, the covalent bond cannot be explained by the interaction of spins. That is not at all true.

Bonding and antibonding are two states calculated with Schrödinger equation (never Dirac). No spin is needed when you are not worry of the number of electrons. Because never is the interaction of the spins which produces the molecular bonding. Never !

It is bad to give one wrong answer (nobody force you to do it), but it is worse to try to confuse people by mixing things. If you want I challenge you to give a proper definition of the covariant bond. Go ahead!

Dear Daniel,

I don't know what your problem is really. I contributed my answers to the original poster with proper formal references and have nothing more to contribute to her questions, unless she inquires about my opinion on other aspects of this issue.

You were the one who addressed me on issues of semantics apparently. I answered you completely in context of this thread, and have nothing more to add in this regard.

If you don't like my answers, tough luck. I dislike discussing with agressive people, so I will waste no more of my time pandering to your ego.

You are perfectly free to disagree with me and be vocal about it as much as you want if you like wasting your time at such petty activities.

Contrary to you, I have no chip on my shoulder, and don't feel I have anything to prove to you.

If fact, the more you rant about my "wrong answers", the more attention will be drawn to electromagnetism and the more people will be curious about my pertaining analyses, trying to understand what irritates you so much. So be my guest.

Best Regards

André

Dear André,

It is not possible to answer a question on covalent bond when one doesn't know it and less try to say that this knowledge is only a question of opinion. I don't want to waste also my time and I'm not writing for you but for a possible reader, starting by Renata, who doesn't want their time too reading wrong things.

Dear Daniel and André,

thank you very much for your discussion on my question. I have gained a great deal from it. As a computer scientist, I depend on researchers in other fields, like the two of you, to clarify issues arising during my own research. I have some idea now as to the treatment of chemical bonds with quantum mechanical means and will keep an open mind in the future.

Renata

Dear Renata,

Data processing and computer languages used to be my specialty before I took interest in neural networks.

Just curious. What languages are currently in use to address these chemical bounds issues?

Best Regards

André

Dear André,

I am not very familiar with what computer languages are currently being used in bioinformatics but I gather there are many. Some time ago I came across a tool written in Python. I keep seeing Python being used frequently these days.

My research is in quantum computation and its application to protein structure prediction. We are working with quantum circuits and the description is mathematical because quantum computation is still a rather theoretical discipline.

Renata

Thanks for the lead Renata.

I have been away from the field for quite a while. This gives me a recent lead to follow.

Best Regards

André

You are welcome, André. And thank you for participating in the discussion.

Renata

Late to the discussion, but the simplest and most correct answer which is also a cop out would be that covalent bonds are just emergent phenomena. Specifically - emerging from the characteristic behaviour of the wavefunctions minimising the hamiltonian (under the set of conditions corresponding to a potential in a molecule).

You could ask; what is the 'mechanism' behind the patterns on Chladni plates? Well, the boundary conditions of the problem are. But that isn't nescessarily meaningful.

Hermitian operators in quantum mechanics account for the physical interactions that you mentioned in your question, among others, in a sophisticated mathematical framework. But even then ascribing the phenomenon to one particular feature of the underlying physics is probably never going to be entirely correct.

Thank you, Jonathan.

I am working on the issue of protein structure prediction using quantum computation. And here the usual assumption is that the native structure corresponds to the conformation with minimal energy. As you pointed out, the target is to minimize entropy but there are many ways to do it. That is why I am now putting that aside and, instead, trying to understand what is exactly happening physically in a bond formation.

Yes, it appears to me too that indeed there may be several factors involved. However, as we can consider the protein and its environment as a closed system, we should be able to limit these factors and eventually we should be able to figure out the mechanism.

Renata

Thank you, Preston. I will think about what you said.

Dear Renata, You have a simple question and you do not get a simple answer. This means we do not know. Professor Bader has studied the laplacian of the electron density (which is the same as the X-ray diffraction) of molecules for years. He has not been able to find the structures that can be assigned to a single, double or triple bond. Listen, none of the theoretical things created "ad hoc" by Pauling has experimental evidence. About the charge, the electrons participating in the bond are neutral. This means that its negative charge is neutralized by the positive charge of its atom. Therefore, there is no electric repulsion between bonding electrons.

In the laplacian of the electron density of molecules, you will see toroidal structures, just like the ones observed in the nucleus of the atom.

Dear Omar, thank you for your informative reply. Yes, simple questions in chemistry and physics often do not have simple answers despite some claims that our understanding of the physical world is almost complete and there is little in the universe that has yet to be discovered.

These toroidal structures you talk about sound interesting. Does the Laplacian for the electron density thus give us electronic orbitals? Nucleus is not believed to be stationary, so I presume neither are the protons and neutrons in it. Do they also experience orbitals?

I assume that electrons and nuclei neutralise each other at some distance. If we assume the shell model of an atom, then the electrons can be at different distances with respect to the nucleus. If we further assume that each proton has the same charge and that each electron has the same charge (which is reasonable, I think), do you think that there might be a chance that the neutralisation is not 100%, because the effect will be different for electrons located closer to the nucleus than for those farther away from it?

By the way, I was under the impression that Pauling predicted correctly the existence of alpha helices in protein structures, although he got the gamma helices wrong. This is however consistent with the idea of having physical entities modeled mathematically. Not every mathematical solution corresponds to a valid physical object. It seems to be a price we have to pay.

In this new paradigm. The orbital is the electron itself. Arthur H. Compton measured its size and shape![Article The Size and Shape of the Electron

The Laplacian of the electron density is equivalent to the XRD. Therefore, we are interpreting experimental evidence. The very same toroidal structures were discovered in the atom nucleus [Article Femtometer Toroidal Structures in Nuclei

The nucleus is stationary enough to respond to collisions (electron-deuteron elastic scattering). These collisions were the way these toroidal structures were found. I just found the same structures in the chemical bond.

You wrote:"I assume that electrons and nuclei neutralize each other at some distance. If we assume the shell model of an atom, then the electrons can be at different distances with respect to the nucleus."

If the electron occupies a larger space than the proton but has the same shape. A better model of the atom is a spherical concentric capacitor [https://pdfs.semanticscholar.org/7cd8/0579214bd512f91c9a89e5fb78c4c9e72556.pdf]. Thus, no different distances.

You wrote: "do you think that there might be a chance that the neutralisation is not 100%, because the effect will be different for electrons located closer to the nucleus than for those farther away from it?"

Yes, but that involves the deformation of the electron, not its position. Valence electrons occupy different spaces and its associated chemical energy changes.

The price we have paid already is to assume too many things:

1) The electron is a point particle in an orbital (moving charges radiate)

2) The shape of the electron is meaningless (uncertainty principle does not allow to see the shape of the electron).

3) The concept of hybridization (ad-hoc fabrication to mimix the coordination).

4) sigma, pi and anti-bonding orbitals (the only evidence you find is something resembling the sigma bond).

5) The wave equation is the only source of information about the electron.

Bader said it, no evidence of double or triple bonds.

No evidence! The evidence are these toroidal structures at the picometer scale. They are acknowledged but not explained.

Thank you, Omar. This is a lot of material to think about.

So let me ask another question. I am a little unsure about the connection between the theory of orbitals and the toroidal structures for pairs of electrons. For instance, in your paper, you say that lone pairs form a torus. I wonder whether it makes sense to argue that each of the electrons in a lone pair makes two p orbitals, which is four p orbitals in total, which in terms of shape could be combined to form a torus.

The treatment of electrons as point particles in chemistry comes from the Newtonian physics, I think, where objects are taken as point masses. Newton used this depiction to define forces in terms of vectors. This wouldn't be possible if masses were treated as continuous as it would require an infinite number of vectors. In Maxwell's theory of electromagnetism, stationary charges generate an electric field and moving charges generate a magnetic field. Do you mean, in point 1, that the orbital corresponds to the magnetic field?