Chemistry 120

Molecular Structure

Both atoms and molecules are quantum systems

We need a method of describing molecules in a quantum mechanical way so that we can predict structure and properties

The method we use is the

Linear Combination of Atomic Orbitals

where we can use the properties of atoms to predict the properties of molecules.

Chemistry 120

Molecular Structure

We combine atoms to form molecules by considering the phase of the atomic orbitals we are using

We represent the phase via the shading we give the orbital.

The phase represents the sign of the wavefunction

Chemistry 120

Molecular Structure

We combine atoms to form molecules by considering the phase of the atomic orbitals we are using

The phase represents the sign of the wavefunction

We represent the phase via the shading we give the orbital.

Chemistry 120

Molecular Structure

For an s orbital, the orbital has the same phase everywhere:

For a p orbital, there is a

change in the sign of the

wavefunction across the

nodal plane:2p orbital, n = 2, l = 1, ml = -1

1s orbital, n = 1, l = 0

Chemistry 120

Molecular Structure

Consider two H atoms (1s1) coming together from infinite separation.

There are two possibilities:

1 The wavefunctions are in phase

2 The wavefunctions are not in phase

Chemistry 120

Molecular Structure

Case 1: The wavefunctions are in phase

The atoms move together and the electron waves overlap with the same phase, producing constructive interference and a build up of electron density between the nuclei

The energy of the system drops and we form a bond

Chemistry 120

r = 8 Å

r = 7 Å

r = 6 Å

r = 5 År = 0.75 Å

r = 1 Å

r = 2 Å

r = 3 Å

Chemistry 120

Molecular Structure

Case 2: The wavefunctions are out of phase

The atoms move together and the electron waves have opposite phase.

The electron waves overlap producing destructive interference and electron density between the nuclei is reduced.

The energy of the system rises and we have an antibonding situation

Chemistry 120

r = 8 Å

r = 7 Å

r = 5 Å

r = 4 Å r = 0.75 Å

r = 1 Å

r = 2 Å

r = 3 Å

Chemistry 120

Bonding Antibonding

Two atoms with wavefunctions in phase overlap with constructive interference. Electron density increases between the nuclei and the overall energy decreases.

When the wavefunctions are of opposite phase, the electron density between the nuclei decreases due to destructive interference. The energy of the system rises and we have an antibonding situation

Chemistry 120

Bonding

Antibonding

Here we see 2 2s orbitals in the bonding and antibonding regimes

In the antibonding regime, there is no build-up of density between the nuclei at any separation.

How do we represent this energetically?

Chemistry 120

Bond length at the minimum energy

Bonding

Antibonding

Energies and phase

Chemistry 120

Bond length at the minimum energy

Bonding

Antibonding

Energies and phase

For the antibonding interaction, there is no minimum in energy at any distance

For the bonding interaction, there is a minimum. The distance is the bond length and the energy is the bond energy

Chemistry 120

Organic Structure and Bonding

bonds and bonds

bonds are in general stronger than bonds and can be formed from either s or p orbitals:

Chemistry 120

Organic Structure and Bonding

bonds and bonds

bonds have no nodal plane that contains the two nuclei.

The * antibonding orbital has a nodal plane between the two nuclei

Chemistry 120

Organic Structure and Bonding

bonds and bonds

bonds have a nodal plane that contains both nuclei,

The * antibonding orbital also has a plane between the nuclei

Chemistry 120

Organic Structure and Bonding

bonds and bonds

These , bonding orbitals and *, * antibonding orbitals are the orbitals that are used to bind all simple organic molecules together.

We can also describe the bonding in diatomic molecules

important models for larger organic systems

Chemistry 120

Organic Structure and Bonding

bonds and bonds

To describe the bonding in the diatomic molecules such as O2, N2 and X2 (X = F, Cl, Br and I), we use both the s orbitals and the p orbitals on the two atoms as a basis set - the palette of atomic orbitals from which we will build the molecular orbitals.

The energies of the two different l states, s and p, are slightly different in polyelectronic atoms.

Chemistry 120

Organic Structure and Bonding

bonds and bonds

The s orbitals and the p orbitals appear as follows

Chemistry 120

Organic Structure and Bonding bonds and bonds

We arrange the atoms along one of the axes for convenience and so the first pair of orbitals we construct are the s and s* orbitals from the s orbitals on the atoms.

Chemistry 120

Organic Structure and Bonding bonds and bonds

We now us the higher energy p orbitals to construct p and porbitals

Chemistry 120

Organic Structure and Bonding bonds and bonds

The complete molecular orbital diagram for all the diatomic molecules from Li2 to N2

Chemistry 120

Organic Structure and Bonding bonds and bonds

The complete molecular orbital diagram for all the diatomic molecules from Li2 to N2

As each molecule has a different number of electrons,

Li2 2 Be2 4 B2 6 C2 8

N2 10 O2 12 F2 14 Ne2 16

Chemistry 120

Organic Structure and Bonding bonds and bonds

Li2 2 Be2 4 B2 6 C2 8

N2 10 O2 12 F2 14 Ne2 16

We can write the electronic structure of each molecule by placing electron pairs into the orbitals.

Chemistry 120

Organic Structure and Bonding bonds and bonds

Li2 2 Be2 4 B2 6 C2 8

N2 10 O2 12 F2 14 Ne2 16

Something peculiar happens after N2

Recall that as the charge on the nucleus increases, the orbitals become more stabilized and the electrons become more strongly bound.

Chemistry 120

Organic Structure and Bonding bonds and bonds

Li2 2 Be2 4 B2 6 C2 8

N2 10 O2 12 F2 14 Ne2 16

This happens by different amounts, depending on the orbital.

After N2 (10 e-), the ordering of the orbitals derived from p change their order in the molecule

Chemistry 120

Organic Structure and Bonding bonds and bonds

For N2 (10 e-), the ordering is this

For O2 (12 e-), the ordering is this

Chemistry 120

Organic Structure and Bonding bonds and bonds

This is an example of configurational interaction

Each electron moves in the field of the other electrons. If the energies of the two molecular orbitals are sufficiently close and the nodal properties are correct, molecular orbitals will interact and shuffle their energies in the molecule.

This causes the orbitals to change their energetic ordering but only when the nuclear charge is high enough to force the electrons close in energy.

Chemistry 120

Organic Structure and Bonding bonds and bonds

Configurational interaction

Each electron moves in the field of the other electrons. If the energies of the two molecular orbitals are sufficiently close and the nodal properties are correct, molecular orbitals will interact and shuffle their energies in the molecule.

This causes the orbitals to change their energetic ordering but only when the nuclear charge is high enough to force the electrons close in energy.

Chemistry 120

Chemistry 120

Chemistry 120

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