EXPLAINING MOLECULAR GEOMETRY

Molecular Orbital TheoryA Quantum Mechanical Theory of Electronic

Structure and Chemical Bonding

Part I: Diatomic Molecules

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• As atoms approach one another, their atomic orbitals (AO's) overlap and form molecular orbitals (MO's).

• Molecular orbitals concentrated in regions between nuclei are called bonding orbitals.

• Molecular orbitals having zero values in regions between nuclei and therefore concentrated in other regions are called antibonding orbitals.

• MO's may involve more than two atoms • MO's may spread over several atoms or the entire molecule.• To form an effective MO, the energies of the atomic orbitals must

be approximately equal and the overlap must be large.

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Molecular orbital theory explains the structure of molecules in terms of molecular orbitals.

• Two 1s orbitals are added and subtracted to form two molecular orbitals

• 1s + 1s yields a bonding orbital named s1s• 1s - 1s yields a antibonding orbital named s1s*• Antibonding orbitals have higher energy than bonding

orbitals

• The ground-state electron configuration of H2 is (σ1s)2.

Molecular Orbitals for the H2 Molecule

The bond order indicates the number of bonds that exist between two atoms.

Bond order is calculated with the equation

nb = number of electrons in bonding orbitals na = number of electrons in antibonding orbitals

For H2,

A bond order of 1 indicates H2 contains a single bond.

( )b a1Bondorder2n n= -

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( – )1Bond order = 2 0 = 12

Molecular Orbitals for the He2 Molecule

• Two He atoms – 4 valence e's• Place the electrons of He2 into molecular orbitals• Use the aufbau principle

• The ground-state electron configuration is (σ1s)2(σ*1s)2.• The bond order for He2 is 0 • MO theory predicts no bond forms

( – )1Bond order = 2 2 = 02

Bonding and Antibondong Molecular Orbitals

• Electrons in bonding orbitals hold atoms together in molecules by increasing the electron density between nuclei.

• Electrons in antibonding orbitals in a molecule destabilize the molecule because they do not increase the the electron density between nuclei.

1s1s

s1s

s*1s

Overlap AO's of similar energy to make more MO's

• Two Li atoms – 6 e's• The configuration of Li2 is

Li2 (σ1s)2(σ*1s)2(σ2s)2

• (σ 1s)2(σ *1s)2 are abbreviated KK, so we can write

Li2 KK (σ *2s)2

• The 1s orbitals do not overlap appreciably because of their small size, so their MO's are filled but not helping with bonding:

1s

2s

Molecular Orbitals for the Li2 Molecule

Excited states are possible in MO theory.

• If an electron in a H2molecule absorbs the precise amount of energy for a transition to a higher orbital to occur, it will be in an excited state

• For example, the electron could absorb energy and be described by the configuration

(σ1s)1 (σ*1s)1

Electron Configurations of Some Diatomic Molecules

MO Diagrams for N2 and O2

Electron

configuration for

N2:

KK s2s2s2s

*2p2p4s2p

2

Bond order:

1/2 (8 - 2) = 3

Triple bond

No unpaired

electrons

Electron

configuration for

O2:

KK(s2s)2(s*2s)

2(p2p)4(s

2p)4 (p*2p)

2

Bond order:

1/2 (8 - 4) = 2

Double bond

Unpaired

electrons:

The molecule is

paramagnetic.

Paramagnetism and Diamagnetism

• Paramagnetism - atoms or molecules having unpaired electrons are attracted to magnetic fields

• Diamagnetism - atoms or molecules having all paired electrons are repelled by magnetic fields

Electron Configurations and Magnetic Properties of Some Diatomic Molecules

The energies of MO's are not the same for all elements.

• MO's are stabilizedas the nuclearcharge increases

• Some MO's are stabilized more than others

• The energy ranking of MO's changes between nitrogen and oxygen

Heteronuclear Diatomic Molecules

• Recall that atomic orbitals also have energies that decreaseas nuclear chargeincreases

• N and O can still form MO's because the energies are not too different

MO Guidelines

1. The total number of MO formed equals the number of atomic orbitals used in the mixing process

2. Orbitals with similar energy and shape mix effectively

3. Atomic orbitals of different principal quantum numbers (n) have different sizes and energies and don't form MO's effectively

4. A MO can accommodate two electrons with opposite spin

5. Electrons are placed in MO's according to Hund’s rule

6. Electrons are placed in MO's according to the aufbauprinciple

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Bond orders and magnetic predictions made with MO theory agree with experimental data.

Summary - Bonding Theories

• Lewis structure and valence bond theory are simple, but they help us understand the bonding ability of elements.

• VSEPR and valence bond theories account for the observed molecular geometries of many molecules.

• None of these models enables us to explain why O2 is attracted to a magnetic field while N2 is repelled slighty.

• MO theory explains magnetic properties

• MO theory is the most complete picture of covalent bonding to date