(a) Molecular Orbitals

(i) Molecular Structure

The molecular formula tells us the number of atoms of each element in one molecule.

e.g. the molecular formula of butane is C₄H₁₀, telling us each molecule contains 4 carbon atoms and 10 hydrogen atoms.

The table below shows some molecular formulae for a few selected hydrocarbon molecules.

Name	Molecular formula
ethane	C2H6
propane	C3H8
butene	C4H8
pentene	C5H10
cyclobutane	C4H8
cyclohexane	C6H12

For molecules with functional groups such as hydroxyl (OH), amine (NH₂), carboxyl (COOH) and carbonyl (CO), the shortened structural formula shows the functional group, while the molecular formula just counts the atoms.

Name	Shortened structural formula	Molecular formula
ethanol	C2H5OH	C2H6O
ethanoic acid	CH3COOH	C2H4O2
ethylamine	C2H5NH2	C2H7N
ethanal	CH3CHO	C2H4O

Skeletal Formula

The simplest examples of skeletal formulae are those for linear alkanes.

So, a "chain link" of two carbon atoms linked together by a single covalent bond (together with the hydrogen atoms attached to them) is represented by a single line when drawn in the form of a skeletal formula.

Notice that it is not necessary to write the symbols "C" or "H" for atoms that form part of simple linear chains, as opposed to other structures such as functional groups attached to alkane-chains.

Examples of the Skeletal Formulae of a few Branched Alkanes:

Linear Amines:

Linear Carboxylic Acids:

Why draw skeletal structures of organic molecules ?

Molecular Orbital Theory

VSEPR cannot explain the bonding in all compounds. Molecular orbital theory can explain the bonding in more complex molecules.

• Molecular orbitals form when atomic orbitals combine. The number of molecular orbitals formed equals the number of atomic orbitals that combine.
• Two atomic orbitals combine to form a bonding molecular orbital and an antibonding molecular orbital. Each molecular orbital can hold a maximum of two electrons.
• The bonding molecular orbital encompasses both nuclei. The attraction of the positive nuclei for the negative electrons in the bonding molecular orbital is the basis of bonding between atoms.
• In a non-polar covalent bond the bonding molecular orbital is symmetrical about the midpoint between the two atoms. In a polar covalent bond it is asymmetric: the more electronegative atom has the greater share of the bonding electrons. Ionic compounds are the extreme case, with the bonding molecular orbital almost entirely around one atom, forming ions.
• Sigma (σ) bonds form by end-on overlap of atomic orbitals along the axis of the bond. Pi (π) bonds form by side-on overlap of parallel atomic orbitals that lie perpendicular to the axis of the bond.

(ii) Molecular Orbitals 1 - sp³ Hybridisation

Introduction

Organic compounds are organised into groups according to similarities and differences in their structure.

Groups of atoms within a molecule give the molecule specific characteristic properties.

These groups of atoms are known as FUNCTIONAL GROUPS.

Hydrocarbons - Compounds containing only carbon and hydrogen.

Subdivisions

• Alkanes
• Alkenes
• Alkynes
• Cycloalkanes

Alkanes:

• Are saturated
• Have the general formula C_nH_2n+2
• All carbon atoms form 4 single covalent bonds
• Have 4 bonding pairs of electrons round each C
• These pairs mutually repel and take up a TETRAHEDRAL arrangement

In the ground state, carbon has the electron arrangement 1s² 2s² 2p².

The 2p² electrons occupy 2 of the 3 p orbitals (Hund's Rule).

This suggests that there are only two electrons available to form covalent bonds. However, carbon forms four bonds.

This is explained by the idea of Hybrid orbitals.

Hybrid orbitals are the result of 'mixing' orbitals to produce a new set of orbitals.

The mathematical basis for this is based on the Schrodinger wave equations - not needed at this level!

Spectroscopic measurements show that all four bonds in methane are identical.

One of the 2s electrons is promoted to the third p orbital.

This produces 4 Hybrid orbitals of equal energy containing single electrons. This is known as sp³ hybridisation.

Compare the shape of the p orbital for carbon with that of the sp³ orbital.

The hybrid orbital is more directional in shape → better overlap when forming bonds + stronger bonds + forms 4 bonds.

For simplicity, the smaller lobe is often omitted from diagrams.

Methane

Overlap of a half-filled sp³ hybrid orbital with a half-filled 1s orbital of a hydrogen atom forms a new molecular orbital. The shared pair of electrons are now under the influence of both nuclei.

The new molecular orbital lies along the axis joining the two nuclei and is known as a SIGMA (σ) BOND. A sigma bond is formed by end-on overlap of atomic orbitals.

Ethane

(iii) Molecular Orbitals 2 - sp² Hybridisation

Alkenes:

• unsaturated hydrocarbons
• contain at least one double bond
• ethene molecule is flat and all bond angles are 120^o
• The C = C bond is shorter than the single bond.
• The C = C bond strength is intermediate between a single and a triple bond but not twice as strong as a single bond.
• There is restricted rotation around the C = C bond.
• There are two isomers of but-2-ene which differ only in the position of the methyl groups. In one, they are on the same side of the double bond, while in the other they are on opposite sides. (Stereoisomerism).

C = C double bonds are formed by sp² hybridisation.

On mathematically mixing these, three identical hybrid orbitals are obtained.

These lie in the same plane at 120^o to each other and at 90^o to the remaining p orbital.

This is called sp² hybridisation and the new orbitals are called sp² hybrid orbitals.

Unhybridised p orbitals are close enough to overlap above and below the plane of the sp² bonds.

This produces a new molecular orbital between the 2 carbon atoms with lobes above and below the molecular plane.

This extra bond pulls the carbon atoms closer together - bond length shortens

Sideways overlap produces a weaker bond than the end-on overlap → C=C isn't 2 x as strong as C-C

π overlap is more effective when the p orbitals are parallel. Any other position and the overlap is reduced and the bond will eventually be broken → resistance to rotation.

Benzene: sp² Hybridisation and Delocalisation

Each carbon atom in benzene is sp² hybridised. The six carbon atoms form a ring held together by σ bonds. The unhybridised p orbital on each carbon overlaps side-on with those on its neighbours, forming a π molecular system above and below the plane of the ring. This π system extends across all six carbon atoms, and its electrons are delocalised.

Alkynes: sp Hybridisation

In alkynes, the 2s orbital and one 2p orbital of each triple-bonded carbon hybridise to form two degenerate sp hybrid orbitals in a linear arrangement. These overlap end-on to form σ bonds. The two remaining 2p orbitals on each carbon lie perpendicular to each other and to the σ bond, and overlap side-on to form two π bonds. e.g. ethyne, C₂H₂, is a linear molecule.

(iv) Colour in Organic Molecules

Molecular orbital theory can be used to explain why organic molecules are colourless or coloured. Electrons fill bonding molecular orbitals, leaving higher energy antibonding orbitals unfilled. The highest bonding molecular orbital containing electrons is called the highest occupied molecular orbital (HOMO). The lowest antibonding molecular orbital is called the lowest unoccupied molecular orbital (LUMO).

Absorption of electromagnetic energy can cause electrons to be promoted from HOMO to LUMO.

Most organic molecules appear colourless because the energy difference between HOMO and LUMO is relatively large. This results in absorption of light from the ultraviolet region of the spectrum.

Some organic molecules contain chromophores. A chromophore is a group of atoms within a molecule that is responsible for absorption of light in the visible region of the spectrum. Light can be absorbed when electrons in a chromophore are promoted from the HOMO to the LUMO.

Chromophores exist in molecules containing a conjugated system - a system of adjacent unhybridised p orbitals that overlap side-on to form a molecular orbital across a number of carbon atoms. Electrons within this conjugated system are delocalised. Molecules with alternating single and double bonds, and aromatic molecules have conjugated systems.

The more atoms in the conjugated system the smaller the energy gap between HOMO and LUMO. A lower frequency of light (longer wavelength, lower energy) is absorbed by the compound. When the wavelength of light absorbed is in the visible region, the compound will exhibit the complementary colour.