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In sulfur or any atom with an expanded octet on the 3rd row, where does the idea that they have an empty D orbital come from ?

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    $\begingroup$ The periodic table hides the existence of quantum chemistry, including allowed electron quantum states. $\endgroup$ – Poutnik Oct 10 at 4:27
  • $\begingroup$ but why? bc their energy is higher and therefore their uncertainty greater ? $\endgroup$ – Robertthebraveofnanog Oct 10 at 4:50
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    $\begingroup$ @Poutnik The octet rule hides the existence of quantum chemistry. Atoms are not taught the octet rule, they go ahead and make compounds as they please. $\ce{SF6}$ exists because we observe it experimentally, and quantum chemistry is a good model to explain why it exists. Quantum chemistry also predicts that we would not find any $\ce{OF6}$ lying around. If someone makes $\ce{OF6}$ anyway, we have to update the model. $\endgroup$ – Karsten Theis Oct 10 at 10:16
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    $\begingroup$ @KarstenTheis We should really start teaching atoms what theories they are allowed to follow and which not so that they’ll be better behaved! $\endgroup$ – Jan Oct 11 at 2:24
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    $\begingroup$ I'm voting to leave open because there is a high-quality answer. $\endgroup$ – Karsten Theis Oct 11 at 13:01
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Sulphur does not expand its octet. That was a hypothesis proposed long ago and vehemently supported by Linus Pauling. While Linus Pauling had a few very great ideas that moved chemistry forward, he also made some major blunders like the octet expansion hypothesis or seven grams of vitamin C a day. Possibly because of Pauling’s status and Nobel Prize, octet expansion remains to be present in high school textbooks to this day and even professors still believe in it.

Back in the day, a competing hypothesis to explain compounds such as $\ce{SO3}$ was proposed: charge separation. In a nutshell, the central sulphur atom does not take part in three double bonds (which would expand the octet) but rather forms two $\ce{\overset{+}{S}-\overset{-}{O}}$-type single bonds and one regular double bond for a total of eight electrons. On paper, these bonds can switch back and forth so that each oxygen gets one third of the double bond share (in reality, they do not switch; every bond has the bond order 1.333, all are equal length and so on. This is resonance, akin to what is found in benzene, and often called Y-aromaticity on this site). You can learn more about $\ce{SO3}$ in this wonderfully detailed answer.

In the case of $\ce{SF6}$, fluorine can only form single bonds to sulphur. So instead of a $\ce{\overset{+}{S}-\overset{-}{O}}$ bond we see a $\ce{\overset{+}{S}\bond{...}\overset{-}{F}}$ bond which is always opposite a ‘normal’ $\ce{S-F}$ bond, so together they form a $\ce{F-\overset{+}{S}\bond{...}\overset{-}{F}}$ 4-electron-3-centre bond with a similar resonance phenomenon; this type of bond probably won’t get introduced for a while in your curriculum.

Now what about this ‘empty d orbital’? Well, that actually ‘exists’ and can be derived from quantum mechanics. You may have heard of the $2n^2$ rule for predicting how many electrons can fit into a shell—but at the same time heard of the octet rule which means that after Ar the next electron gets added into the 4th shell although there is still space for ten more electrons in the 3rd shell. Well, quantum mechanics tells us that shells can be divided into subshells; we call these s, p, d, f, g, h, …. Quantum mechanics also tells us that the $n^\text{th}$ shell has exactly $n$ subshells in the order I have given them there (so 1st shell has only s, 2nd has s and p, 3rd has s, p, d; and so on). As sulphur’s position in the periodic table tells us that its valence shell is the 3rd shell, it follows that its 3d subshell of the third shell ‘exists’.

The term to exist is stretched a little here. Technically, these orbitals don’t exist at all, they are only ‘paths’ the electrons can ‘follow’ (also two wrong terms but they get the picture across). Only if an electron is excited to a higher energy level will a higher-level (sub)shell be observable. So without electrons, do the shells exist—does a falling tree make a sound if nobody hears it? On the other hand, the energy levels are there. They can be calculated, we can hurl energy at electrons and they can then get excited to these shells. Thus, in molecular calculations these unoccupied shells are usually called virtual: there, but not quite.

So in a lengthy discussion I have established that these empty d orbitals exist. Why can’t they be used in bonding? Well, the most obvious point is hidden in the aufbau principle. Basically, it is the more elaborate octet prediction and says that after putting all possible electrons into 3p the next electron must go into 4s because 4s has a lower energy level in the ground state than 3d. This shows the rather large energy gap between p and d orbitals of the same shell which is one reason why they do not participate in bonding to any meaningful extent.

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