Our familiar model of covalent bonding is largely based on the Lewis model, with atoms sharing pairs of bonding electrons and everyone obeying the octet rule. It is often very successful in explaining the structures of molecules, and the bonding that gives rise to those structures, but there are many exceptions.
Try drawing out a dot and cross diagram for nitrogen monoxide. Either you can go for a double bond, in which case nitrogen has only 7 electrons, or you can try a triple bond, but then oxygen has 9 electrons. In phosphorus pentafluoride, the phosphorus has 5 bonding pairs of electrons surrounding it (we explained this earlier by invoking the idea of an expanded octet). Or take oxygen. The Lewis structure says that there is a double bond between the two oxygen atoms and each atom also has two lone pairs of electrons. The trouble is that liquid oxygen is paramagnetic, which can only be if there are unpaired electrons in the structure.
There are two modern theories of bonding – valence bond theory and molecular orbital theory. Each has its strengths and weaknesses and, like the Lewis model, is useful in different situations.
Both are based on the idea that atomic orbitals interact with each other when a covalent bond is formed between the two atoms, but in order to overcome the problem that we can’t solve Schrรถdinger equation for atoms other than hydrogen, the two theories make differing approximations and assumptions.
This is extension work – unless you are following the Cambridge Pre-U specification – but an overview of the two theories and will give you a more complete understanding of how the concept of bonding has developed in modern times. If you are thinking about studying Chemistry, Natural Science or a related degree at university, then I strongly recommend you take a look.
Valence bond theory
Valence bond theory is particularly useful for describing bonding in organic carbon-based molecules, but let’s start with the simplest of examples …
Hydrogen e.g. H2
- the 1s orbital on each hydrogen atom overlap or interact to form a ๐-bonding (sigma) orbital, positioned between the two hydrogen atoms and the shared pair of bonding electrons are placed in this new orbital
- in valence bond theory the bonds have both ionic (H+ H–) and covalent character – how each is weighted depends on the molecule. The real structure is a mixture of the different forms
Carbon – making single bonds e.g. CH4, methane
If we look at the electron configuration for carbon it would seem that carbon has only two electrons available for bonding but we know that carbon always makes four bonds in stable molecules.
- in valence bond theory the atoms in molecules can change the shape and energy of their atomic orbitals in a way that maximises the opportunities for bonding – this is known as hybridisation
- carbon hybridises the 2s and 2p orbitals to form four sp3 hybrid orbitals which have the same energy as the original s and p orbitals had between them
- in methane each sp3 hybrid orbital interacts with a 1s orbital from a hydrogen atom to form a new ๐-bonding (sigma bonding) orbital and the bonding pairs of electrons (one from carbon and one from hydrogen in each bond) are placed in these new orbitals forming sigma bonds which we know as single C-H bonds.
- you should be aware that when ๐-bonding orbitals are formed, ๐*-antibonding orbitals are also formed which are higher energy and unoccupied – this is a consequence of the way the wavefunctions of the original atomic orbitals overlap and we definitely don’t need to go down that rabbit hole ๐
Carbon – making a double bond e.g. C2H4, ethene
- a C=C double bond is actually composed of sigma bond and a pi bond
- in ethene the 2s, 2px and 2py orbitals on each carbon atom hybridise to give three sp2 hybrid orbitals which will be used to make single / sigma bonds to carbon and to hydrogen
- one of these sp2 hybrid orbitals interacts with an sp2 hybrid orbital from another carbon atom, and the other two sp2 hybrid orbitals interact with 1s orbitals from hydrogen atoms – we now have three ๐-bonding orbitals each holding a pair of bonding electrons and we have formed three single or sigma bonds (one C-C and two C-H)
- the unhybridised 2pz atomic orbitals on each carbon atom interact / overlap to give a โ-bonding (pi bonding) orbital containing a pair of electrons, with electron density extending above and below the plane of the ๐ bonds
- the electrons that make up this pi bond are delocalised within the region of the new pi orbital
- the nature of this pi bond is that firstly there is restricted rotation about a C=C double bond (leading to E/Z isomerism in alkenes) and secondly the pi electrons can be used to make bonds to other atoms in a chemical reaction (alkenes very reactive)