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HYBRIDIZATON: Flexibility at its best

When you think of fasteners, you probably think of nuts and bolts. Surprisingly, we haven't done much improvement on fasteners for a couple of thousands of years.

The problem with our fasteners are that they aren't flexible. In other words, you can't use a 1/4 inch nut on a 1/2 inch bolt. You can't even use a 1/4 inch nut on a 1/4 inch bolt if the threads don't match (There are about 3 or more types of threads).

Another type of connector are tubing connectors. I like to use PVC tubing and connectors to make stands and other objects. Unfortunately, these kind of connectors are very limited. So that limits what you can build with them. You also have the problem of different diameters. 1/2 inch, 3/4 inch, 1.5 inch, etc.

In general all of the fasteners and connectors that engineers have built so far "stink".

We need to learn from electrons. They are the ultimate masters in knowing how to connect things together.

First of all, electrons are super flexible. Remember they are both particle and wave. As connectors, they are mostly waves. That gives them enormous advantages. Waves can travel through each other. Think of sound from an orchestra. Each instrument is generating its own sound waves, but the different sound waves all pass through each other and coexist with each other because you hear all instruments at the surface of your ear drum. Electrons are very much like that. They cross through each other as they do their job of connecting. That's quite a trick.
3d orbitals

For example, here are five d orbital electrons. Notice how they pass through each other. They can also connect at various angles.

No fastener or connector that we've ever built can pass through each other.

The real magic of electrons are their ability to change shapes depending on the needs for bonding. For example, on the left is nitrogen's 3 lobe-shaped p orbital electrons that sit along the x, y, and z axis. The s orbital is the large orange translucent sphere. In this configuration, p orbital electrons are at 90° angles. Depending on how many other atoms it needs to connect to, the electrons can rearrange themselves into different shapes to accommodate the number of bonds it needs to make. Those can have different angles. Roll cursor over image to see these 4 electrons change their shapes. Note: The p orbitals are drawn thinner than normal so you can see their orientations better.
sp hybrid

Up until now we have talked about the s, p, d, and f orbitals. That alone gives atoms all kinds of flexibility in connecting with other atoms. This tutorial is about how these orbitals can blend with each other to form new shapes, which gives even more flexibility in bonding. This blending is called hybridization. It's a good word because the final orbital is a hybrid of the original orbitals.

In my example on the left, I show an s orbital and a p orbital at the top. When they blend they make an sp orbital. You can see some of the traits of both s and p orbitals in the sp orbital.

Since organic chemistry and biochemistry rely on the carbon atom, that's the element that we put our attention on first. The diversity of carbon to make complex molecules is only possible because of the hybridization that its electrons undergo.
Carbon no bond On the left are 3 carbon atoms with their electrons in their ground state (lowest energy level). Carbon's two 2p orbital electrons (2px and 2py) are the more available for bonding than the s orbital electrons. However, those p orbital bonds would be at right angles to each other, which would make the atoms crowded. It also would only allow carbon to connect to 2 other atoms. So carbon's electrons do something that allows for more spacing and for connection to more atoms.
Carbon orbitals

Here is the ground state of carbon. The 1s electrons are small and not shown. They aren't involved in bonding. The two paired 2s electrons are spherical and are symbolized with two arrows. [↑↓]. There are 2 unpaired p orbital electrons that align on the x and y axes.

As the carbon atom nears another atom, such as hydrogen, one of the electrons in the 2s orbital gets pulled into a higher energy orbital. In this case, it goes into the unfilled 2pz orbital (see next panel).

Carbon s orbital Again, one of the electrons in the 2s orbital gets pulled into the unfilled 2pz orbital. Notice the green 2pz orbital is now present. The orange dotted arrow shows it came from the 2s orbital. The 2s orbital still has 1 electron left. So the orange sphere is still there.
Carbon sp3 hybridized

What happens next is that these four electrons blend with each other (hybridize), and they all become the same shape. The shape is two lobes with one much larger than the other. In the right image I'm showing the four larger lobes and not the small ones.

The shape is named after the number of the orbitals involved. The name "sp3" means there was one s orbital and three p orbitals that got hybridized. Warning: In the electron configuration symbols of "2s22p3", the exponents are the number of electrons. In "sp3" the exponent is number of orbitals. There can be 4 to 8 electrons in the "sp3" orbitals. Notice in the image the 4 electrons in the sp3 orbital area unpaired. If all were paired, you would have 8 electrons (the octet).

carbon sp3 orbital tetrahedron The sp3 orbital forms a tetrahedron (a pyramid with a triangular base and all equal sides) The angle formed between the bonds is 109.5°. When carbon combines with 4 other atoms, this is the shape of the molecule.

When you see the zigzag lines, those are carbon atoms connecting with the sp3 hybrid electrons. The angles are 109.5°. Even if the lines are drawn straight like the red ones in the image, they are still 109.5°.

The 3 dimensional ball-and-stick model below also shows the tetrahedral angles of 109.5 degrees due to the sp3 electrons.

sp2 Orbitals for 3 connections
Carbon orbitals

When carbon is surrounded by 2 hydrogen atoms and an oxygen atom, carbon's electrons will do something different. Remember oxygen needs 2 electrons to make an octet, so carbon needs to share two electrons with oxygen by forming a double-bond with oxygen. At the top I show the electron configuration of carbon after one of the 2s orbital electrons have been promoted to the 2pz orbital.

Three electrons are going to get hybridized. From the name of "sp2" you can deduce that it will be one s orbital electron and two p orbital electrons.

carbon sp2 orbital

This image shows the result of 3 of carbon's electrons hybridizing into sp2 electrons. Notice these three sp2 electrons spread out in a triangle with 120° between them. In the earlier tutorial on VSEPR (Valence Shell Election Pair Repulsion) we saw that when a central atom bonds with 3 other atoms and there's no lone pair on the central atom, the shape of the molecule is called planar triangular. This hybridizing is how that happens.

The one 2py electron (yellow lobes) did not get hybridized which is how carbon forms a double bond with oxygen shown next.

Formaldehyde orbitals

The image on the left is of carbon combining with 2 hydrogen atoms and one oxygen atom to make formaldehyde. The top diagram is the Lewis Dot Structure. The bottom illustration shows the orbitals as they prepare for bonding. Notice that the oxygens electrons underwent the same hybridization as did carbon's electrons. The presence of carbon triggered oxygen to also do hybridization. The difference is that oxygen has 2 more electrons than carbon, which explains why two of the sp2 orbitals are full. That's indicated by the 2 black dots, which represent the 2 paired electrons. Since these are not used for bonding, these are called lone pairs.

Now we will see how the bonded molecule looks...

Formaldehyde orbitals What happens is the two sp2 electrons that were pointing towards each other overlap and form a bond. The two vertical 2py electrons from both carbon and oxygen bend toward each other and overlap. That also forms a bond.
Sigma and Pi bonds

By the way, bonds that overlap directly between 2 atoms are called sigma bonds. The overlapped region is spherically shaped, much like the s orbital. The Greek letter for the "s" sound is σ (sigma). The sigma bonds are the strongest of the bonds.

The bond formed by the overlapping p orbital electrons is called a pi (π) bond. Note the overlapping at the top and bottom of the p orbital electrons, but it still counts as just one pi bond. In the Lewis Structure at the top, the double bond symbol (=) shows 2 lines. One is the sigma bond and the other line represents the pi bond.

sp2 orbital top
This is the same molecule as above but seen from the top. I left off the pi bond so you can see the sp2 bonds better. These bonds sit flat (planar) and form 120° angles.
Benzene sp2 orbitals
This is benzene. It is made up of 6 carbon atoms that are connected using the sp2 orbital electrons. The 120° angles between the bonds make this a hexagon. I'm not showing the pi bonds that would be above and below the sp2 sigma bonds that are showing.
Benzene Here are the skeletal formulas for benzene. You can see the hexagonal shape due to the 120 degree angles. You can also see the double bonds where one of the lines represents a pi bond. The benzene molecule is flat also due to the flat sp2 bonds.
sp Orbitals for 2 connections
Carbon sp orbital

To show its flexibility even more, carbon can connect to an element that needs 3 electrons to reach its octet. The molecule of hydrogen cyanide has carbon in the center of hydrogen and nitrogen. A triple bond is needed with nitrogen.

Like before, carbon promotes one of its 2s electrons to the 2pz orbital. Then the other 2s electron plus one of the p orbital electrons gets hybridized into an sp orbital. The two sp orbital electrons point in the opposite direction. One will bond with hydrogen and the other with nitrogen. The two 2px and 2py electrons will form the other two bonds. (Shown in next panel.)

Cyanide orbitals

Here the hydrogen, carbon, and nitrogen atoms are set to bond. The pink sp electrons point directly at the atom they will bond with. Notice that the electrons in nitrogen did the same hybridization as carbon. The only difference is that nitrogen has 1 more electron than carbon which explains why one of nitrogen's sp electrons is full (2 dots) and forms a lone pair (non-bonding pair).

The yellow lobes are the unchanged p orbital electrons as are the green lobes. They are going to bend towards each other and overlap.

Cyanide orbitals Here the sigma bond between the sp electrons have overlapped and those bonds are in place. The 2 pairs of p electrons are moving towards each other. In the next panel I show overlap of the p electrons

The yellow lobes form a single pi bond above and below the sigma bond. The green lobes form a single pi bond to the front and back of the sigma bond. So in the Lewis structure that shows the triple bond, one line represent the sigma bond and the other 2 lines represent the 2 pi bonds. The lone pair of electrons on the nitrogen atom are the 2 dots in the non-bonding sp orbital. The hydrogen atom also forms a sigma bond with carbon's second sp orbital electron.

The shape of the molecule is linear because the sp electrons are on opposite sides of carbon and nitrogen and there are no lone pairs on carbon to repel these bonds.

Here is phosphorus trichloride. It connects to 3 chlorine atoms, and phosphorus also has 1 lone pair of electrons. From the VSEPR table in the previous tutorial, it says the shape of the molecule will be tetrahedral (like methane above); however, the table nor I explained how the electrons can make that tetrahedral shape.
Phosphorus orbitals
This is the electron configuration of phosphorus plus an image of its 3s and 3p orbitals. It appears that phosphorus could share each of its 3p electrons with electrons from 3 chlorine atoms. That would give both phosphorus and chlorine the 8 electrons it needs for a stable octet. However, that would force the chlorine atoms to be at right angles to each other. That's kind of crowded, so phosphorus electrons do some hybridizing to spread out the chlorine atoms more and reduce repulsion between the bonds and atoms.

The five electrons are blended (hybridized) to make four sp3 orbitals. Because phosphorus has one more electron than carbon, one of those sp3 orbitals is filled as indicated by 2 dots on the orbital and by [↑↓] in the electron configuration. The other three sp3 orbitals have just one electron in them, so they are available to accept electrons from chlorine and donate one. In other words, these orbitals are ready for bonding.


Here I'm showing phosphorus with its sp3 orbitals, that had just one electron, sharing that electron with a p orbital electron from 3 chlorine atoms. The fourth sp3 orbital is full (a lone pair) so it can't bond, but it does repel the other bonds causing the shape of the molecule to be a trigonal pyramid.

Here I show the chlorine bonding using its only p orbital that isn't full (others have 2 dots). The textbook says the chlorine hybridizes all 7 of its outer electrons also making sp3 electrons. The literature shows it both ways. So we really don't know if chlorine leaves its electrons alone for bonding or hybridizes them. Either way, it doesn't change the angle.

Phosphorus lewis structure
In the previous tutorial I showed phosphorus pentachloride. I pointed out that it was odd because phosphorus had 5 electrons and with all being paired with an electron from 5 chlorine atoms, it gave phosphorus 10 electrons, which violates the octet rule. The final shape turns out to be a trigonal bipyramid (2 pyramids with 3 sided base) as shown in the small image here.
octahedralHow it did that was not explained. Now it's time.
Phosphorus is in the 3rd row on the Periodic Table. So its principle quantum number is n=3. At n=3, the l values available (if you remember) are 0, 1, and 2. That means s, p, and d orbitals are available. Carbon is in row 2, so it doesn't have any d orbitals available. Because d orbitals are available for phosphorus, it can promote one of its 3s electrons to a d orbital.

What you see here is that 1 of the 3s electrons got promoted to one of the d orbitals. That causes the appearance of four turquoise egg shape lobes. Those 4 lobes are just one d orbital electron that came from the 3s orbital. I picked the dxy orbital because it's easier to draw.

The beauty of this move is that phosphorus now has five electrons that are in 3 different orbitals. That allows it to hybridize all of them into 5 identically shaped orbitals. These are called sp3d orbitals because the one s orbital, three p orbitals, and one d orbital were hybridized.

After the five electrons are hybridized, they are five electrons of equal size and shape. They are five sp3d orbital electrons. Three form a triangle (120° separation) in the middle. One bond is above and one is below those 3. Here is the geometry of how it will bond with the 5 chlorine atoms.
This is what phosphorus looks like with it five sp3d orbitals (1 electron each) bonded to 5 chlorine atoms. This time with chlorine I didn't bother to show chlorine's p or sp3 orbitals that would be used for bonding to phosphorus. I just used a sphere for the chlorine atom.
I found a website that had some animations of hybridization. You can follow the link below.
If you had trouble understanding the above instructions on hybridization, be comforted in knowing that in the future this may all be tossed aside in favor of molecular bonding. Unfortunately, molecular bonding is more difficult to understand, so stick with hybridization bonding for now, because it does explain a lot of the observations regarding bonds.

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