[redfox]

Hi, I have a question about the supposed orbit of an electron. Say we have one atom with the electron fying around it in its orbit...then another atom comes along with its electron also flying around...howdo the two create a bond between them if the atoms are continuously moving around to the back of them? Is it possible the electrons don't actually orbit as we're taught, but they *can* orbit? And because of the forces of attraction between atom A's electron with atom B's nucleus could the electron not rather go back and forth between the two nuclei? Please go easy on me, I clearly don't know much about this subject;) Thanks!

[orgopete]

This is a topic that I have to be careful with. This will assuredly increase the number of flags I can get. The questions being asked are good ones and they have existed for a very long time. Undoubtedly, some will answer that quantum theory explains it. Maybe it does, but I still don't understand it.

If you are asking for a class, I'm fairly confident the quantum theory answer is the right one. If you are asking for yourself, then you might agree with Gilbert Lewis. Lewis said that in some circumstances electrons may form pairs. If you were to require that an energy difference can only exist due to the application of a force, then if you can find an energy well, you may ask what is the force?

So, you may ask yourself, which is stronger, e-e cohesion or e²-proton or nucleus force. Let me rephrase that. Which is easier, to ionize water or homolyze it? A very small amount of pure water is ionized. If NaOH is added, a lot more can be ionized. Adding an acid to increase the pull upon a pair of electrons does not give radicals. If you heat water to 2500^oC, you can homolyze it to give hydrogen and oxygen, think Fukushima and resultant explosion.

You can see that I have not and cannot answer your question. You can find many energy wells, but I don't think you will find an explanation which uses one of the four forces of nature (or a new fifth force). The energy levels of benzene are much lower than predicted from an isolated double bond. What is the force that leads to this energy well? I think if you can answer any of these questions, you will know the answer why two atoms should become bonded together.

[zsinger]

Petes info is all correct.  Also, bonds are the result of electronegativity differences between moieties.  This is a very quantum explanation, that would likely take a P-Chem professor, and a LARGE background in the subject to answer.  I do not know enough about it.  Also, bonds which are drawn on paper ARE moving if they are single, as they can rotate, etc.  A bond, more or less, is a region of electron density.
       -Zack

[Corribus]

First, being quantum particles, electrons do not orbit nuclei in the planetary sense. Second - at least in the molecular orbital model - the stability of the chemical bond is a purely quantum effect created by electron exchange, which has no classical analog. Coulombic attraction/repulsion of charges is insufficient to explain all the bonding properties of molecules. (Although, it's certainly important.)

Honestly, to truly understand bonding requires a strong foundation in physical chemistry, which is basically physics applied to chemical systems.  If you have specific questions, the physical chemists here will undoubtedly be happy to help you understand the phenomenon at any level, but "bonding" is too broad a topic to be covered in a single post.

[AromaticAcrobatic]

Orgo,
I'm just curious but what are these "flags" your talking about?

And since I'm posting, I might as well add that Linus Pauling single handedly transformed the world of chemistry with his book "The Nature of the Chemical Bond". You can find a lot of the answers to your questions within that book.

 

[Irlanur]

There is no explanation that uses the classical formalism and still explains the experimental observations. You can tell high school students that a bond is formed because two nuclei "share" electrons. but why should they be paired? and why should the energy be quantized? Regarding the "orbit" question, I think one could say that in the end, chemists dont care. Energy and observables are the things you want to know about. (Bonding energies, NMR shifts, "structures")


However, there is no new fundamental force introduced in the QM formalism. Normally, one constructs a Hamiltonoperator, which comes from the classical Energy terms (mostly, only Kinetic and Coulomb energies of the elementary particles are taken into account). If you go deeper into the formalism and accept the Pauli-Principle, something completely new (to classical physics) happens. We cannot distinguish electrons and the Wavefunction has to adopt certains symmetry properties. This "leads" to the so-called Exchange Energy. But there are no new fundamental Energy-terms introduced.

[Enthalpy]

Redfox, you're fully right that electrons don't orbit the nuclei as planets do. The image as planets was attempted over a century ago; physicists noticed very soon that it couldn't work, because

• The electron would emit light like an antenna emits radiowaves and fall on the nucleus, obviously not the case;
• Atoms emit and absorb light at some frequencies only, which correspond to electrons changing their energy between a limited set of permitted values within an atom.

A first improvement, Bohr's model, kept point electrons on orbits almost like planets, but allowed only some permitted orbits. It explained the spectrum of light emission but the reason for permitted orbits was mysterious, unrelated with the rest of physics. This progress was important historically but is abandoned now, because since Schrödinger, we have the Rolls among the Ferraris: quantum mechanics (QM).

QM tells that electrons (and all others: protons, neutrons, light...) are waves. QM gives one single equation (Schrödinger's one) for electrons, which holds for an electron in one atom, in a molecule or a metal, in vacuum - and gives very accurate results everywhere, getting rid of the mysterious and specific assumption of permitted orbits.

With QM, electrons around a nucleus, that is atoms, have a volume because they are waves. They look like this:
http://winter.group.shef.ac.uk/orbitron/
A lone hydrogen atom would have a spherical electron of 1s (for first spherical orbital) shape:
http://winter.group.shef.ac.uk/orbitron/AOs/1s/index.html
A lone carbon atom would have two 1s electrons, two 2s, and two 2p
http://winter.group.shef.ac.uk/orbitron/AOs/2s/index.html
http://winter.group.shef.ac.uk/orbitron/AOs/2p/index.html
Keep the address in your favorites, it's always useful.

Please notice that I use the integrist wording "the electron is a wave". I believe to be absolutely orthodox with that, and renowned physicists say it the same way. Though, many people want to keep some notion of a point electron and say rather "the wave defines the probability to find the point electron at some place". Be ready for such wording as well, and avoid arguments about it.

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Among the possible wave forms, some are trapped around a nucleus because the electron is attracted by the positive charge and has lost the energy needed to escape - that's the usual situation, forming a neutral atom. Some trapped wave forms are especially interesting: the orbitals, or stationary solutions, shown by the Orbitron website. Their shape does not evolve over time (hence stationary). Such an electron is immobile, which explains why it radiates no light. This is the usual state of electrons in an atom.

Even when the shape doesn't evolve over time, an electron has a kinetic energy and possibly an angular momentum. This results from how steeply the wave function evolves over the distance - exactly like for a free electron that moves. It explains why the electron has a volume: if getting smaller, it's nearer to the attracting nucleus which is favourable, but its kinetic energy increases more quickly, which at some point more that compensates the proximity to the nucleus. This most favourable point defines the electron size (the orbital size, most people would say).

The very nature of electrons as "fermions" allows one or two of them (then with opposite spin) in each orbital, no more. That's Pauli's exclusion principle. Photons for instance, the particle of light, could be packed in any number at the same location, same shape, same size... because they're "bosons" instead. Two electrons per orbital tells you why a lone carbon atom has two 1s, two 2s electrons - and one 2p along x plus one 2p along y. 1s couldn't accept all 6 electrons. Then they use to most favourable orbitals available: 1s is full, then the second-best 2s is full, and the two remaining electrons make 2p orbitals - and because the ones along x, y and z are equally favourable and electrons repel an other for carrying the same charge, they spread among two 2p to be wider apart. Carbon permits many more orbitals (one 2p available, 3s, 3p, 3d, 4s, 4p, 4d, 4f...) which are empty since all six carbon's electrons have a place.

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Orbitals are only the stationary waves around a nucleus; maths tell that every electron bound to a nucleus, not necessarily stationary, is a combination of these orbitals - but such combinations do evolve over time. Besides being a function of the position, the wave depends on time; as a complex number however, the wave can, when it's stationary, depend on time just for being a function of the position multiplied by exp(i*2pi*t*E/h), where E is the electron's energy and h Planck's constant. This exp(i...) has a constant modulus, so that the orbital's modulus doesn't evolve over time and is immobile, but the phase does vary over time, at the frequency E/h.

Now, when the electron is a combination of several orbitals with different E, their phases evolve over time at different paces. Take again the 2p and 1s orbitals from the Orbitron website:

• 1s is spherical, positive everywhere, multiplied by an exp(i...) at frequency E₁/h
• 2p is a peacock, for instance positive at right and egative at left, multiplied by exp(i...) at frequency E₂/h

When the electron is a combination (a weighted sum) of 1s and 2p, at some times both exp(i...) have the same phase, at others the opposite phase, and this change with frequency (E₂-E₁)/h.

This means that the electron is sometimes more at right (when 1s and 2p have the same phase) and sometimes more at left (when the phases oppose). This combined wave is not stationary. The electron moves with frequency (E₂-E₁)/h. As any wobbling electron, it radiates light at the frequency (E₂-E₁)/h, or energy E₂-E₁. These energy differences are the lines observed in the emission and absorption spectrum of an atom, resulting from the E₁, E₂... energies of orbitals in atoms, and QM predicts them for hydrogen with fabulous accuracy.

The electron loses its energy by radiating it. In doing so, it combines less and less 2p with more and more 1s over time, until it rests at 1s only, which is then the "ground state", an orbital that doesn't radiate for being immobile. Many more transitions are possible (some are defavoured or said "forbidden" because they wobble badly hence can't emit light, say 2s to 1s), for instance towards 2p in a carbon atom.

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Now, a chemical bond. Atomic orbitals are computed by assuming one positively charged central nucleus and nothing else. When other influences exist, an external electric field, a second nucleus... electrons just adapt their shape. Sadly, we can't compute exactly these too complicated cases, so we tinker the maths to get an approximate solution. With two nuclei, we claim (imprecisely) that the "molecular orbitals" combine two atomic orbitals as their sum and their difference. With an external electric field, we would add a little bit of 2p to a 1s orbital. It's accurate when the nuclei a far from an other, less so with a true chemical bond.

The sum of both atomic orbitals is a "bonding" molecular orbital, the difference an "antibonding" one. One electron on the bonding orbital has more room near to the attracting nuclei, so the wave function varies less steeply, and the electron's kinetic energy is smaller, so this combination is more favourable. The antibonding molecular orbital subtracts two atomic ones, so that the wave passing from + to - varies more steeply, the kinetic energy is bigger, the combination is less favourable.

Of course, two nuclei would also attract one single electron more strongly, but a chemical bond is between two atoms, so two electrons share two nuclei. Now, remember that opposite spins permit two electrons to make the same orbital. With two hydrogen atoms, both electrons can be in the favourable bonding orbital and leave the unfavourable empty. The electron pair makes a chemical bond.

More reasons make a bonding molecular orbital favourable. As the kinetic energy decreases, the electron can rearrange a bit to be nearer to the nuclei. Far less concrete: two electrons making one orbital arrange themselves to repel an other less. This, together with the spin, is (for me) an abstract notion of QM, because these electrons are immobile, both are spread permanently over the orbital, but if some outside action localizes one electron near some position, then the other is likely away.

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Some molecules share more than two electrons between atoms. A nitrogen atom has two 2s and three 2p electrons, or 10 electrons for the atom pair - these atomic orbitals have similar sizes and energies and react all, as oppposed to the smaller 1s. The molecular orbitals are created (see the link below for oxygen):

• Sigma s, filled with two electrons, results from 2s
• Anti sigma s, filled as well, also from 2s
• Sigma p, results from 2p along x, filled
• Pi y, results from 2p along y, filled
• Pi z, results from 2p along z, filled

The unfavourable anti sigma s compensates approximately the sigma s. The real benefit is from the sigma p, pi y, pi z which are all bonding and filled. This makes the N₂ molecule very stable and unreactive.

As opposed, the oxygen molecule has two electrons more and no bonding orbital left for them. Two electrons fill antibonding orbitals, which makes the O₂ molecule very active.
http://en.wikipedia.org/wiki/File:MOO2a.svg
http://en.wikipedia.org/wiki/Triplet_oxygen

By the way, electrons are more stable on antibonding orbitals than far from the nuclei. "Antibonding" means only that these molecular orbitals alone are worse than separated atomic orbitals and would not keep the atoms together.

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More than two atoms can build a molecule. Then the molecular orbital spans over these atoms, but as this idea isn't easy to handle, we represent bonds between pairs of atoms only - except for benzene and other "aromatic" molecules, for which a special drawing aknowledges the spread of the electrons.

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Orbitals are very concrete because atomic force microscopes show them (Schrödinger didn't have this chance, and people long imagined abstract "probability waves" for the position of a point particle). Here you have the pentacene molecule:
http://physicsworld.com/cws/article/news/2009/aug/27/molecules-revealed-in-all-their-glory-by-microscope
http://www.rsc.org/chemistryworld/news/2009/August/27080902.asp
http://www.newscientist.com/article/dn17699-microscopes-zoom-in-on-molecules-at-last.html
Van der Waals bonds between molecules
http://cen.acs.org/articles/91/i51/Atomic-Force-Microscopy-Provides-Astonishing.html
Varied orbitals (Homo, Lumo) of a molecule
http://www.physik.uni-regensburg.de/forschung/repp/reresults.htm (but-last topic of that page)

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I've been longer than I wanted, sorry... Err, Redfox, you didn't tell us how much you already know about waves, complex numbers, linear algebra, so maybe some parts are less understandable for you presently. Then, I suggest to keep it somewhere and read such parts again later, when you've met these topics.

[Corribus]

Though, many people want to keep some notion of a point electron and say rather "the wave defines the probability to find the point electron at some place". Be ready for such wording as well, and avoid arguments about it.

A very nice post Enthalpy. I'd say among chemists and probably many physicists this is more common formulation. At the quantum level, though, the distinction doesn't mean very much. We might also describe a moving baseball as a wave, but from common experience it behaves more like a particle. In reality it has properties as both. In the case of an electron, both of those properties are discernable. In the case of a baseball, only the particle-like properties are observable because the wavelength is so small.

[orgopete]

Orgo,
I'm just curious but what are these "flags" your talking about?

And since I'm posting, I might as well add that Linus Pauling single handedly transformed the world of chemistry with his book "The Nature of the Chemical Bond". You can find a lot of the answers to your questions within that book.

Okay, so I'm not following the jargon. It just seemed to me that if I was at a football game and the ref through something, it felt more like a flag than a snack. As you can see, I have received a lot of negative snacks or as I call them, I've been flagged for bad answers. And now just to prove why I can get a negative snack (flag), you can see the quantum theorists have come out to defend it. Einstein said, “Quantum mechanics is very impressive. But an inner voice tells me that it is not the real thing. The theory yields a lot, but it hardly brings us any closer to the Old One.” This quote is often used for its religious connotation, but J.D. Norton continues, “There is no doubt of Einstein's principal objection. He believed that the quantum wave function of some system, the ψ-function, was not a complete description of the system. Rather, it provided some sort of statistical summary of the properties of many like systems.” I cannot speak for Einstein and I do not know precisely what he may have meant. I thought (or wish) Einstein might have been concerned with the forces acting in molecules. Measuring the energy tells us the result of the forces, but it doesn’t measure or explain the forces themselves.

Imagine that Newton discovered a way to calculate the energy of an apple as it fell from a tree, but said it was NOT due to gravity. Would we all admire the ability to calculate the energy difference and yet not ask what the force was? Clearly I am not an Einstein, but what was Einstein's problem? Didn't he know Schroedinger solved why two electrons and two protons form a bond?

I know I am in over my head on this topic, so I don't want to go too far. This is not a new problem. If two electrons are parallel, they behave normally and repel. If they are antiparallel, they result in an energy well. All one needs to do is ask how that might be possible? Oh, I think that was the original poster's question. If you think the electrons are in the center is a good answer, then you should know all you need to know.

... This, together with the spin, is (for me) an abstract notion of QM, ...

Actually, I don't want to pick on Enthalpy. I believe his post is a pretty accurate description of how bonding is perceived. If you look carefully at atomic theory, you encounter a number of inconsistencies and work arounds. For example, the notion of having an electron orbit the nucleus, gives the s, p, d, and f orbits and all of the crazy shapes being quoted. Linus Pauling created hybridization theory. What it did was to shift the center of charge away from the nucleus. That is the net effect of changing the 2s and 2p electrons into sp3 orbits was simply to shift the center of the charge from around the 1s2 electrons.

I want to draw a careful distinction. The highly accurate calculations that have been created are very likely correct and true. How we interpret them is a different matter. When the Swiss mathematician created a formula to correlate the hydrogen emissions with integers of n, he did so without knowledge of atomic structure. Rydberg extended that formula to predict additional lines. Bohr attempted to interpret the Rydberg formula into an atomic model. As it should have been noted, Bohr was not right, but the Rydberg formula is. The mathematics are correct, but how they apply to structure is not certain.

This is your homework assignment. Take an element and look up its emission spectrum. Look up the shapes in the quoted orbitron website. Prove the emissions have those shapes. I'll wait.

[Corribus]

@Orgopete

Quantum mechanics is one of the most successful scientific theories in history. For chemists it is completely sufficient to explain pretty much everything we need to know. I don't want to delve deeply into science philosophy and the true meaning of "theory", but from a practical standpoint, it is for all intents and purposes correct. That said, there are probably no serious theoretical physicists out there that regard quantum theory as absolutely "correct". (And not only for the philosophical reason that theories are never absolutely "correct", anyway.) You keep pulling back layers of that onion, and you eventually find things it can't quite explain, or things we just have to accept as axiomatic. Chemists reach that level a lot sooner than physicists do, but it's still there.

Plus, while in some sense Einstein has been elevated to demigod status, his famous (or infamous) rejection of some of the implications of quantum theory doesn't really mean anything. The theory has been changed substantially since he was involved. True, we still debate the philosophical meaning of the theory, but it's far more rigorously understood today than it was in his time.

The Rydberg formula is completely semi-empirical and we shouldn't expect it to lead to any fundamental understanding of the structure of nature. On the contrary, today's highly sophisticated quantum calculations, which can reproduce the Rydberg formula, and in many cases given even better agreement with observation, are largely based on first-principles physics (a phrase we should admittedly not scrutinize too far), which can lead to fundamental understanding of nature, at least on some level.

Hmmm.. now that I think on it, I'm not sure what we're really arguing about or how we got here. I guess that's what happens in a thread started by a very broad, open-ended question.

[Borek]

I'm not sure what we're really arguing about or how we got here. I guess that's what happens in a thread started by a very broad, open-ended question.

Which everyone interprets in his own way.

[AromaticAcrobatic]

"Okay, so I'm not following the jargon. It just seemed to me that if I was at a football game and the ref through something, it felt more like a flag than a snack. As you can see, I have received a lot of negative snacks or as I call them, I've been flagged for bad answers."

Orgo,
Thanks for clarifying this. I was just confused about what and who would be throwing the flag.