a review of atomic orbitals, hybridization, and bonding molecular orbitals hybridization tutor...

A review of atomic orbitals, hybridization, and bonding molecular orbitals

Hybridization Tutor

Charles AbramsAssistant Professor, Department of Physical Science and Engineering

Truman College, 1145 W. Wilson Ave, Chicago IL [email protected]

Unlimited distribution is encouraged so long as no changesare made and copyright remains with Charles Abrams.

Version 1.0 September 9, 2003Copyright 2003 Charles Abrams

1s

First, review the shapes of the hydrogen-like orbitals.

Copyright © 2003 Charles B. Abrams

2s



2px



2py



2pz



2s + 2px + 2py + 2pz

Here are all of the n=2 level orbitals. The problem: these do not point directly towards the surrounding atoms (e.g. for tetrahedral, trigonal planar, or linear molecules) so it is not easy to imagine adding these to make bonds.


C C

H

HH

HH H

Ethane

For example, consider the bonding in ethane. Each carbon atom has a tetrahedral geometry, but the orbitals s, px, py, and pz do not have a tetrahedral geometry.Copyright © 2003 Charles B. Abrams

s + px + py + pz

To to solve the problem of orbitals pointing in the wrong direction, we will hybridize: combine all four of them and get four new orbitals …


sp3 + sp3 + sp3 + sp3

Because we combined the s orbital and all three p orbitals, we call these new orbitals “sp3 orbitals”. There are four of them, each pointing towards a corner of a tetrahedron, exactly where we want them.


Each of the C-H bonds in ethane, CH3CH3, can be described as the combination of a carbon sp3 and a hydrogen 1s orbital. These are cylindrically symmetrical, and are called sigma bonds ()

=Csp3 + Hs


C1sp3 + C2sp3

The bond between the two carbon atoms can be described as the combination of an sp3 orbital on one carbon with an sp3 orbital on the other carbon.


=C1sp3 + C2sp3

The resulting combination is cylindrically symmetrical, and is therefore called a sigma () bond. Because it is cylindrically symmetrical, this bond can rotate without changing the overlap between the two sp3 orbitals


The next few slides show that rotating around the C-C bond in ethane does not change the overlap of the two C sp3 orbitals, and therefore does not change the bond in any way.


(Rotated 30 degrees)


(Rotated 120 degrees). This completes the discussion of bonding in ethane.


Ethene (Ethylene)

C C

HH

H HConsider the bonding in ethene (also known as ethylene). The carbon

atoms have a triangular planar geometry.


s + px + py + pz

Here again are the four n=2 orbitals. These orbitals are not in a triangular planar arrangment.. However, they can be hybridized by combining the s orbital with only two of the p orbitals.


sp2 + sp2 + sp2 + pz

These hybrid orbitals are called sp2 orbitals. The complete set of orbitals available for bonding now includes three sp2 orbitals and the p orbital which was not involved in the hybridization.


Each of the C-H bonds ethene, CH2=CH2, can be described as the combination of a carbon sp2 and a hydrogen 1s orbital. These are cylindrically symmetrical sigma bonds ()

=Csp2 + Hs


C1sp2 + C2sp2

There are two bonds between the carbon atoms. One of these can be described as the combination of an sp2 orbital on one carbon with an sp2 orbital on the other carbon.


=C1sp2 + C2sp2

The resulting combination is cylindrically symmetrical, and is therefore called a sigma () bond. Before we can decide if this bond can rotate, we must consider the other bond in ethene.


C1pz + C2pz

The second bond between the carbon atoms can be described as the combination of the p orbital on one carbon with the p orbital on the other carbon. These two p orbitals are parallel and therefore have good overlap.


=C1pz + C2pz

The resulting combination is not cylindrically symmetrical; instead it has a plane of symmetry. It is called a pi () bond. The p orbitals can only overlap if they are parallel. This bond can not rotate.


However, what if carbon 2 was rotated …. (step through the next three slides to see the rotation)


(rotated 45 degrees)


C1pz + C2py

(Rotated 90 degrees.) The p orbital on carbon 2 now does not overlap with the p orbital on carbon 1. Because the p orbital now points in a different direction, it is labeled with a different Cartesian coordinate. No pi bond can form.


Let’s rotate the carbon atom back to where it was, so that the p orbitals can overlap… (rotated 45 degrees)


(Rotated 0 degrees.) Again the p orbitals can overlap, and a pi bond can form.


The carbon-carbon double bond in ethene can be described as one sigma and one pi bond. The pi bond prevents the double bond from rotating. All of the atoms (H and C) are in one plane, so this is a planar molecule.


Ethyne (Acetylene)

C CH H

Now consider the bonding in ethyne (also called acetylene).


s + px + py + pz

Here again are the four n=2 orbitals. The geometry around the carbons in acetylene is linear. There is a way to hybridize these so they point in a line. We combine the s orbital with only one of the p orbitals.


sp + sp + py + pz

These hybrid orbitals are called sp orbitals. The complete set of orbitals available for bonding now includes these two sp orbitals and the two p orbital which were not involved in the hybridization.


C1sp + C2sp

One bond between the carbons is described as the combination of the carbon 1 sp orbital plus the carbon 2 sp orbital.


= C1sp + C2sp

This is called a sigma bond, as in the previous examples.


C1py + C2py

There are now two sets of p orbitals which can be combined. The py orbitals on each carbon can combine to form one pi bond…


=C1py + C2py

This is one of the pi bonds in ethyne.


C1pz + C2pz

The other set of p orbitals can also combine to form a second pi bond.


=C1pz + C2pz

Here is another pi bond in ethyne.


The triple bond in ethyne (acetylene) is described as one sigma bond and two pi bonds.


Allene

C C

H

H

C

H

H

Now consider the bonding in allene, in order to answer the question: is allene planar or twisted? The geometry around the central carbon is linear, and the geometry around the carbons on the ends is triangular planar.


The central carbon in allene is sp hybridized, while the carbons on the ends are sp2 hybridized. The sigma bonds are combinations of these hybridized orbitals.

= C1sp2 + C2sp = C2sp + C3sp2

= Hs + C1sp2


Two parallel p orbitals can combine to form a pi bond.

C1pz + C2pz


This is one pi bond in allene. However, the remaining p orbital on the central carbon is not parallel to the p orbital on the last carbon! The last carbon must be rotated so the p orbitals are parallel.

=C1pz + C2pz


(Rotated 90 degrees.) Now the remaining p orbital on the central carbon is parallel to the p orbital on the end, and a second pi bond can be made by their overlap.

C2py + C3py


This model shows the two pi bonds in allene, and makes it clear that allene is not planar; not all of the atoms of allene are in the same plane. Instead, allene is twisted.

= C2py + C3py


Allene

C C

H

H

CH

H

This diagram of allene illustrates the non-planar geometry of this molecule.


[4]Cumulene

C C

H

H

C C

H

H

Consider the bonding in [4]cumulene in order to predict whether this molecule is planar or twisted. The end carbons are triangular planar and sp2 hybridized, while the middle carbons are linear and sp hybridized.


The sigma bonds are combinations of the sp and sp2 hybrid orbitals as before. The remaining p orbitals can form pi bonds.


The first pi bond can form between the two aligned p orbitals.


The second pi bond can form between another set of p orbitals.


The third pi bond can form between the last set of p orbitals. No rotations were required to align the p orbitals in this case, so the molecule is planar.


[4]Cumulene

C C

H

H

C C

H

H

This diagram properly represents the planar shape of [4]cumulene.


AcknowledgementsThe design of this presentation was inspired by lap-dissolve techniques ofProfessor David Harpp, McGill University

Special thanks to Joy Walker, Truman College, for providing equipment and enthusiasm.

The orbital models used in this presentation are MolyorbitalsTM models MOS-901-14 (Atomic Orbital Set) and MOS-900-4 (Molecular Orbital Organic Structures). These can be purchaced from www.molymod.com.

Future versions of this tutorial will include better pictures of everything (higher contrast, better alignment), orbital descriptions of hyper-conjugation, alkene addition, E2 and SN2 reactions, and bonding in benzene. Thank you in advance for your comments and suggestions.


a review of atomic orbitals, hybridization, and bonding molecular orbitals hybridization tutor...

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