Hybridisation and Shapes of Molecules

Principles of Molecular Orbital Theory:

In molecules, atomic orbitals combine to form molecular orbitals which surround the molecule.

Similar to atomic orbitals, molecular orbitals are wave functions giving the probability of finding an electron in certain regions of a molecule.

Each molecular orbital can only have 2 electrons, each with an opposite spin.

Each molecular orbital can only have 2 electrons, each with an opposite spin.

Once you have the molecular orbitals and their energy ordering the ground state configuration is found by applying the Pauli principle, the aufbau principle and Hund's rule just as with atoms.

The principles to apply when forming pictorial molecular orbitals from atomic orbitals are summarized in the table below:

Principle Details/Examples
Total number of molecular orbitals is equal to the total number of atomic orbitals used to make them. The molecule H2 is composed of two H atoms. Both H atoms have a 1s orbital, so when bonded together, there are therefore two molecular orbitals.
Bonding molecular orbitals are lower energy than the atomic orbitals from which they were formed. Electrons in Bonding molecular orbitals help stabilize a system of atoms since less energy is associated with bonded atoms as opposed to a system of unbound atoms. Bonding orbitals are formed by in-phase combinations of atomic orbitals and increase the electron density between the atoms (see figure 2 below)
AntiBonding molecular orbitals are higher energy than the atomic orbitals from which they were formed. Electrons in AntiBonding molecular orbitals cause a system to be destabilized since more energy is associated with bonded atoms than that of a system of unbound atoms. Antibonding orbitals are formed by out-of-phase combinations of atomic orbitals and decrease the electron density between atoms (see figure 2 below).
Following both the Pauli exclusion principle and Hund's rule, electrons fill in orbitals of increasing energy. Electrons fill orbitals with the lowest energy first. No more than 2 electrons can occupy 1 molecular orbital at a time. Furthermore, all orbitals at an energy level must be filled with one electron before they can be paired. (see figure 3 below)
Molecular orbitals are best formed when composed of Atomic orbitals of like energies. When Li2 forms the two lowest energy orbitals are the pair of bonding and antibonding orbitals formed from the two possible combinations of the 1s on each atom. The 2s orbitals combine primarily with each other to form another pair of bonding and antibonding orbitals at a higher energy.

Bonding and antibonding σ orbitals can be formed by combining s orbitals in-phase (bonding, bottom) and out-of-phase (antibonding, top).

If the atomic orbitals are combined with the same phase they interfere constructively and a bonding orbital is formed.

Bonding molecular orbitals have lower energy than the atomic orbitals from which they were formed. The lowering of the energy is attributed to the increase in shielding of the nuclear repulsion because of the increase in electron density between the nuclei.

If the atomic orbitals are combined with different phases, they interfere destructively and an antibonding molecular orbital is formed.

Antibonding molecular orbitals have a higher energy than the atomic orbitals from which they were formed.

The higher energy is attributed to the reduced shielding of the nuclear repulsion because of the lower electron probability density between the nuclei.

Combining hydrogen-like s orbitals to generate bonding (bottom) and antibonding (top) orbitals.

The dark dot represents the location of the nucleus.

Note the decrease in electron density between the nuclei in the antibonding orbital.

σ Bonds

Molecular orbitals that are symmetrical about the axis of the bond are called sigma molecular orbitals, often abbreviated by the Greek letter σ.

There are two types of sigma orbitals formed : a) AntiBonding Sigma Orbitals (abbreviated σ∗) , b) Bonding Sigma Orbitals (abbreviated σ).

In Sigma Bonding Orbitals, the in phase atomic orbitals overlap causing an increase in electron density along the bond axis.

Where the atomic orbitals overlap, there is an increase in electron density and therefore an increase in the intensity of the negative charge. This increase in negative charge causes the nuclei to be drawn closer together.

In Sigma AntiBonding orbitals (σ∗ˆ—), the out of phase 1s orbitals interfere destructively which results in a low electron density between the nuclei as seen on the top of the diagram.

Π Bonds:

The Π bonding is a side to side overlap of orbitals, which then causes there to be no electron density along the axis, but there is density above and below the axis.

The diagram below shows a Π antibonding molecular orbital and a Π bonding molecular orbital.

The two 2pz orbitals overlap to create another pair of Π 2p and Π *2p molecular orbitals. The 2pz-2pz overlap is similar to the 2py-2py overlap because it is just the orbitals of the 2pz rotated 90 degrees about the axis. The new molecular orbitals have the same potential energies as those from the 2py-2py overlap.

Drawing Molecular Orbital Diagrams

- Determine how many valence electrons you have on each atom (you can ignore the core electrons as core orbitals contribute little to molecular orbitals). This gives you the total number of electrons you will have to distribute among the molecular orbitals you form.

RULES FOR LINEAR COMBINATION OF ATOMIC ORBITALS

In deciding which atomic orbitals may be combined to form molecular orbitals, three rules must be considered:

The atomic orbitals must be roughly of the same energy.

The orbitals must overlap one another as much as possible.

In order to produce bonding and antibonding MOs, either the symmetry of the two atomic orbitals must remain unchanged when rotated about the internuclear line, or both atomic orbitals must change symmetry in an identical manner.

It is used to find the bond order and it explains the nature of magnetic properties.

It is used to find bond energy, bond length and bond strength.

If e- are removed from BMO then bond order decreases.

If e- are removed from ABMO then bond order decreases.

The order of energy level of molecular orbitals for homonuclear diatomic molecules of second row element is shown below.

For 14 e- or less than 14 e- molecule increasing energy order

σ 1s2 < σ*1s2 < σ 2s2 < σ*2s2 < Π2Py2 ≃ Π2Pz2 < σ2PX2< Π*2Py2 Π*2Pz2 < σ*2PX2

For more than 14 e- increasing energy order

σ 1s2 < σ*1s2 < σ 2s2 < σ*2s2 < σ2PX2 < Π2Py2 ≃ Π2Pz2 < Π*2Py2 Π*2Pz2 < σ*2PX2

Bond Order = (Nb - Na) / 2

Nb = no. of bonding e-

Na = no. of anti-bonding e-

For example consider B2 (each atom has an electron configuration of [He]2s22p), which has a total of 6 valence electrons

- Draw a cartoon energy level diagram with lines for the valence atomic energy levels (orbitals) of each atom. Put one atom's levels on the left and one on the right. Include the electrons. Leave space in the middle for your molecular energy levels (orbitals). It can help to include cartoons of the atomic orbitals as well

- Combine each pair of orbitals of similar energy in-phase and out-of-phase to create molecular orbitals as shown for diboron s in the figure following step

- Move the electrons from the atoms into the molecule to determine the molecular electron configuration

- Note that the σ and Π orbitals formed from the p's are not always in the order Π energy less than σ energy.

- For first row diatomics the ordering shown above is valid for Z ≤ 7.

- Thus for oxygen and fluorine the σ is below the Π orbitals.

Bond Order:

The bond order for a molecule can be determined as follows:

Bond Order = 1/2 (Bonding Electrons - AntiBonding Electrons).

Therefore, the H2 molecule has a bond order of 1/2(2 - 0) = 1.

In other words, there is a single bond connecting the two H atoms in the H2.

In the case of He2, on the other hand, the bond order is 1/2 (2 - 2) = 0. This means that He2 is not a stable molecule.

Bond Order indicates the strength of the bond with the greater the bond order, the stronger the bond.

Bond Order = (1/2)(a - b)

a is the number of electrons in bonding molecular orbitals and

b is the number of electrons in antibondng molecular orbitals.

- If the bond order is zero, then no bonds are produced and the molecule is not stable (for example He2).

- If the Bond Order is 1, then it is a single covalent bond.

The higher the Bond Order, the more stable the molecule is.

An advantage of Molecular Orbital Theory when it comes to Bond Order is that it can more accurately describe partial bonds (for example in H2+, where the Bond Order = 1/2), than Lewis Structures.

Examples:

Bond order α Bond energy α 1/(Bond Length)

Example 5:

Find the Bond Order of N2 Molecule by using MOT.

Explanation:

A nitrogen atom has 2 + 5 = 7 electrons. Thus the N2 molecule contains 14 electrons. The bond order of N2 is three.

Electrons are arranged in MOs:

σ 1s2 < σ*1s2 < σ 2s2 < σ*2s2 < σ2PX2 < Π2Py2 ≃ Π2Pz2

Example 6:

Find the Bond Order of O2 Molecule by using MOT.

Explanation:

Each oxygen atom has 2 + 6 = 8 electrons. Thus the 02 molecule contains a total of 16 electrons.

These are arranged in MOs:

σ 1s2 < σ*1s2 < σ 2s2 < σ*2s2 < Π2Py2 ≃ Π2Pz2 < σ2PX2< Π*2Py1 Π*2Pz1

Bond order of Oxygen Ions:

O 2-2 < O2- < O2 < O2+

Table is used to calculate the Bond Order:

With the increase in the bond order, the degree of overlapping of orbitals brings the atoms near to each other and hence the bond length decrease.

If C0 is ionized to give CO+ by removal pf one electron from the σ2PX. orbital then the bond order should be reduced to 2.5 and the bond length increased.

In fact, the bond length in CO is 1.128 A0 and in CO+ it is l.115A0. Thus, the bond length decreases when we expected it to increase, and it. indicates that the electron must have been removed from an antibonding orbital.

Explanation of the bond shortening when CO is changed to CO+ is that the σ 2s2 and σ*2s2 molecular orbitals differ in energy.

σ 1s2 < σ*1s2 < σ 2s2 < σ*2s2 < Π2Py2 ≃ Π2Pz2 < σ2PX2

H2 molecule having more dissociation energy than Li2 molecule due to screening effect weak overlapping takes place between two Li atoms so H2 more stable than Li2 .

Examples of MOT's diagram:

HF Molecule:

Molecular orbital diagram of CH4:

Molecular orbital diagram of SF6: