Hybrid Atomic Orbitals & Valence Bond Theory
Introduction
Electrons are key to understanding organic chemistry. We can predict many of the properties of an organic molecule (basic physical properties and chemical reactivity) from our beloved skeletal representations. Being able to count to eight and push a curly arrow is sufficient to get surprisingly far through most organic chemistry courses. Many of my colleagues would hate me for saying this, but a knowledge molecular orbitals is not necessary and for many students is so confusing it is detrimental. But, going a little further does help especially when looking at reaction mechanisms.
Electrons are found in volumes of space known as orbitals. Each orbital can contain two electrons. Most students are happy with atomic orbitals - the electron orbitals of an individual atom but problems start emerging when we apply the same ideas to molecules.
Molecular orbital theory offers the most accurate representation of a molecule and is formed by combining all the atomic orbitals of all the atoms within the molecule. It is more complex than most chemists require. It is possible to understand the shape and reactivity of a molecule with simpler models. To understand organic chemistry it is rarely necessary to move beyond hybrid atomic orbitals and valence bond theory.1
Having said this, students still find orbitals scary, and it is hoped that this summary goes some way to alleviate these concerns. Basically, there is a limited number of orbitals you need to know.
Atomic Orbitals
To understand organic chemistry we focus on the valence, or outer, electrons. This means we only need five atomic orbitals. The 1s orbital of hydrogen and, for the elements of the second row of the periodic table (B, C, N, O & F), the 2s orbital and the three 2p orbitals.
Important atomic orbitals
Hybrid Atomic Orbitals
A covalent bond is formed when two electrons are shared between two atoms. Electrons are shared when atomic orbitals are combined, or overlapped. Organic chemists are used to looking at only the valence electrons so they want to use just the outer orbitals. Unfortunately, this intuitive approach gives the wrong answer. If we tried to determine the structure of methane by simply combining the 2s and 2p atomic orbitals of carbon with four hydrogen atoms, the resulting molecule would have three bonds at 90° to each other and another bond. Methane does not look like this. Molecular orbital theory, by combining all orbitals, does give the correct structure but in a manner that no longer resembles our line diagrams and scares most organic chemists off.
The wrong structure for methane
To get an answer that matches their skeletal diagram, organic chemists do not use atomic orbitals but hybrid atomic orbitals (HAO) instead. These magically (or maths … but it amounts to the same thing) mix two or more of the atomic orbitals together before we start making bonds. You don’t need to know where hybrid atomic orbitals come from (it is magic), you just need to know which ones we can use.
What do the hybrid atomic orbitals look like and how do we determine which hybrid atomic orbitals to use?
The hybridisation of an atom is given by adding the number of atoms it is bonded to with the number of lone pairs of electrons on the atom. This will give you a number between 2 & 4. The tables below tell you the hybridisation:
number of atoms + number of lone pairs = X
Hybrid atomic orbitals formed from the combination of a 2s orbital with 2p orbitals
Each hybrid orbital is composed of the 2s atomic orbital combined with one, two or three 2p orbitals. The number of orbitals must remain constant; we will always start with four atomic orbitals so must end with four orbitals, either hybrid atomic orbitals or atomic orbitals. The shape of the resulting orbitals and their geometry can be found in the table. The hybrid atomic orbitals are combined with other atoms to make σ bonds or house lone pairs of electrons. The left over, or non-hybridised, 2p orbitals are used to make π bonds.
Examples of hybrid atomic orbitals and the geometry of molecule
The four sp3 hybrid atomic orbitals are formed from the combination of the 2s atomic orbital with all three 2p atomic orbitals. They have the same shape and energy (are degenerate) but point in different directions (towards the corners of a tetrahedron). Combining the 2s atomic orbital with two 2p orbitals leads to three sp2 hybrid atomic orbitals. These have the same shape as the sp3 hybrid atomic orbitals but point in different directions (the corners of a triangle). They are also slightly smaller as they have more s character (but ignore this for the time being). Forming the sp2 hybrid atomic orbitals uses three out of the four valence atomic orbitals on the atom. This means one 2p atomic orbital is left unaltered. The non-hybridised orbitals are important as they will form π bonds.
Hybridisation of atomic orbitals
Combining just the 2s orbital with a single 2p atomic orbital results in two sp hybrid atomic orbitals. These are the same shape as before but point in opposite directions (180° to each other; and they are slightly smaller still). There are two non-hybridised 2p orbitals left that can be used to form two π bonds.
My gin and tonic analogy can be found HERE.
Covalent Bonds
Bonds are formed by the overlap of either hybrid atomic orbitals or atomic orbitals. There are just two kinds of covalent bond, σ (sigma) bonds and π (pi) bonds.
σ (sigma) bonds
These are formed by the head-to-head overlap of hybrid atomic orbitals or hybrid atomic orbitals and 1s atomic orbital of hydrogen. They are single bonds, or one line on our diagrams. If a hybrid atomic orbital is involved in forming a bond then it will be a σ bond.
Formation of σ (sigma) bond by head-to-head overlap of orbitals
At first year that is all you need to know but as you advance you will see that σ bonds between two carbon atoms can be formed in six ways depending on which hybrid orbitals overlap. This will change the characteristics of the bond. The more s character (sp versus sp3) in the bond the shorter and stronger the bond.
Six flavours of carbon-carbon σ bond depending on which hybrid atomic orbitals overlap
π (pi) bonds
A π (pi) bond is formed from the side-to-side overlap of non-hybridised 2p orbitals. It is the second line of a double bond (or the second and third lines of a triple bond). π bonds are weaker than σ bonds as the overlap is less effective, the atoms are held apart by the σ bond so the two 2p orbitals cannot overlap as effectively. This is why an alkene, a carbon-carbon double bond, is the first of our functional groups.
π bond formed by the side-to-side overlap of two non-hybridised 2p orbitals
There is only one flavour of C=C π bond as they can only be formed by the overlap of non-hybridised 2p orbitals.
How to draw a valence bond model of a molecule
To draw a valence bond, follow the flow diagram below:
Flow diagram to determine valence bond model of a molecule
An example is given below for allyl alcohol CH2CHCH2OH.
Alternatively, we can draw the valence bond orbitals.
Valence bond model of allyl alcohol
These diagrams start to give you an idea of the shape of the molecule. The hybridisation of each atom corresponds to the geometry of that atom. In allyl alcohol, the alkene is made of two, flat, trigonal planar carbon atoms (sp2). The third carbon atom is tetrahedral (sp3) as is the oxygen atom (sp3). As we describe a molecules shape by the atoms not the electrons, the alcohol would be called bent.
Wrinkles in a useful model
The valence bond model provides a useful explanation for the shape and reactivity of molecules formed from elements of the first two rows of the periodic table. There is an exception, a point where the model breaks down. Unfortunately, valence bond theory fails to represent molecules that display resonance, or delocalisation, unless we break the rules we have given you.
The new rule is: if an atom with a lone pair of electrons is next to a π bond it will be sp2 hybridised. Or if an orbital is delocalised it is not hybrised but a 2p orbital.
Amides are a common example of this exception. If we compare and amine and an amide, we find the hybridisation of the nitrogen is different. In the amine, the nitrogen is sp3 hybridised, it is attached to three atoms and has one lone pair of electrons (3+1 = 4 = sp3).
Hybridisation of a nitrogen atom in an amine
The amide looks like it would be the same (three atoms and a lone pair of electrons) but it is not. The lone pair is delocalised, we can draw two resonance structures. One of these resonance structures has a π bond so the lone pair is in a 2p orbital. The lone pair cannot be both in an sp3 orbital (first resonance structure) and in a 2p orbital (second structure). As all physical data informs us that the nitrogen is trigonal planar the nitrogen is assumed to be sp2 hybridised.
Hybridisation of a nitrogen atom in an amide - two resonance structures
We will look at delocalisation and resonance in more detail in another summary.
The other wrinkle in valence bond theory that we need to mention is the conservation of orbitals. What does this mean? Think back to the gin and tonic analogy of hybridisation. In that we told you that when you mix four glasses of liquid the volume of liquid stays the same. This meant that as we started with four glasses we end with four glasses or if we start with four orbitals we have to end with four orbitals. Making bonds is exactly the same. If you start with two orbitals and combine them there must still be two orbitals. One is going to be the σ bond (or π bond) we are interested in but what is the other? It is something called an antibonding orbital. Antibonding orbitals are the result of magic (maths) and are confusing. At present we suggest you ignore them. We only mention them as they are very useful when looking at reactions and those of you that take chemistry further than first year will need them.
Conclusion
The easiest way to represent a molecule is with a drawing of the skeletal structure. The most accurate way to represent a molecule is using molecular orbital theory. Somewhere in between these extremes is a useful simplification that allows organic chemists to predict the shape, reactivity and many of the properties of an organic molecule. This is valence bond theory.
Practice Worksheet can be found HERE.
Footnote
1. The chemistry education literature is full of suggestions that we shouldn’t teach valence bond theory and/or hybridisation because it is wrong. As a result we should only teach the correct molecular orbital theory. Obviously, I don’t hold with this view. There is a place useful models that allow us to understand the world in a relatively simple (ha ha) manner. Most first years taking chemistry aren’t going to become chemists. Most just need enough chemistry to understand biology and biochemistry. I think VB is a good compromise (but I’d also concede that we need less VB than I’ve included on this page!).