chapter 8 part 2

Advanced Theories of Covalent Bonding

Molecular Orbital Theory (MO Theory)

Molecular Orbital Theory provides a more accurate description of electron distribution in molecules than Valence Bond Theory. In MO theory, electrons are considered to be delocalized over the entire molecule, rather than being confined to individual atoms. This approach helps explain phenomena such as the paramagnetism of O2, which cannot be accounted for by Valence Bond Theory.

• Key Concept: Electrons occupy molecular orbitals that extend over the whole molecule, not just atomic orbitals localized on individual atoms.

• Example: O2 is predicted to be diamagnetic by Valence Bond Theory, but is actually paramagnetic due to two unpaired electrons, as explained by MO Theory.

Bonding and Antibonding Molecular Orbitals

When atomic orbitals combine, they form molecular orbitals that are classified as either bonding or antibonding:

• Bonding Molecular Orbitals (MO): Lower in energy than the original atomic orbitals; electron density is concentrated between the nuclei, stabilizing the molecule.

• Antibonding Molecular Orbitals (MO): Higher in energy; electron density is minimized between the nuclei, destabilizing the molecule.

• Constructive Interference: Leads to bonding MOs.

• Destructive Interference: Leads to antibonding MOs.

Sigma (σ) Molecular Orbitals

• Formed by end-to-end overlap of atomic orbitals (e.g., two 1s orbitals in H2).

• Bonding: σ1s

• Antibonding: σ*1s

• Each MO can hold up to 2 electrons with opposite spins.

Pi (π) Molecular Orbitals

• Formed by sideways overlap of p orbitals (e.g., 2py or 2pz).

• Bonding: π

• Antibonding: π*

• Electron density is above and below the internuclear axis.

• A double bond consists of one σ and one π bond; a triple bond consists of one σ and two π bonds.

Bond Order in MO Theory

Bond order indicates the stability and strength of a bond. It is calculated as:

• Formula:

$\text{Bond order} = \frac{\text{Number of electrons in bonding MOs} - \text{Number of electrons in antibonding MOs}}{2}$

• Interpretation: Higher bond order means greater stability. A bond order of 0 means the molecule is not stable and does not exist.

• Example (H2): 2 electrons in σ1s, 0 in σ*1s: $\frac{2-0}{2} = 1$ (stable single bond)

• Example (He2): 2 electrons in σ1s, 2 in σ*1s: $\frac{2-2}{2} = 0$ (does not exist)

Rules for Molecular Orbital Configurations

• Arrange MOs in order of increasing energy. The order depends on the element (see below).

• The number of MOs formed equals the number of atomic orbitals combined.

• Bonding MOs are stabilized; corresponding antibonding MOs are destabilized.

• Electrons fill from lowest to highest energy (Aufbau principle).

• Each MO holds a maximum of 2 electrons with opposite spins (Pauli exclusion principle).

• Electrons in degenerate (equal energy) MOs fill singly before pairing (Hund’s rule).

• Total number of electrons in MOs equals the sum of electrons from all atoms in the molecule.

Energy Ordering of MOs for Second Period Diatomics

• Li2 to N2:

  • σ1s, σ*1s, σ2s, σ*2s, π2py = π2pz, σ2px, π*2py = π*2pz, σ*2px

• O2 to Ne2:

  • σ1s, σ*1s, σ2s, σ*2s, σ2px, π2py = π2pz, π*2py = π*2pz, σ*2px

Examples: MO Configurations and Bond Orders

Molecule/Ion	Total Electrons	MO Electron Configuration	Bond Order	Magnetism	Stability
H2+	1	(σ1s)1	0.5	Paramagnetic	May exist
H2	2	(σ1s)2	1	Diamagnetic	Stable
He2+	3	(σ1s)2(σ*1s)1	0.5	Paramagnetic	May exist
He2	4	(σ1s)2(σ*1s)2	0	Diamagnetic	Does not exist
Li2	6	(σ1s)2(σ*1s)2(σ2s)2	1	Diamagnetic	Stable
Be2	8	(σ1s)2(σ*1s)2(σ2s)2(σ*2s)2	0	Diamagnetic	Does not exist
B2	10	(σ1s)2(σ*1s)2(σ2s)2(σ*2s)2(π2py)1(π2pz)1	1	Paramagnetic	Stable
C2	12	(σ1s)2(σ*1s)2(σ2s)2(σ*2s)2(π2py)2(π2pz)2	2	Diamagnetic	Stable
N2	14	(σ1s)2(σ*1s)2(σ2s)2(σ*2s)2(π2py)2(π2pz)2(σ2px)2	3	Diamagnetic	Stable
O2	16	(σ1s)2(σ*1s)2(σ2s)2(σ*2s)2(σ2px)2(π2py)2(π2pz)2(π*2py)1(π*2pz)1	2	Paramagnetic	Stable
F2	18	(σ1s)2(σ*1s)2(σ2s)2(σ*2s)2(σ2px)2(π2py)2(π2pz)2(π*2py)2(π*2pz)2	1	Diamagnetic	Stable
Ne2	20	(σ1s)2(σ*1s)2(σ2s)2(σ*2s)2(σ2px)2(π2py)2(π2pz)2(π*2py)2(π*2pz)2(σ*2px)2	0	Diamagnetic	Does not exist

Summary of Key Points

• Molecular Orbital Theory explains bonding by considering electrons delocalized over the entire molecule.

• Bonding and antibonding MOs are formed by constructive and destructive interference of atomic orbitals, respectively.

• Bond order is calculated as half the difference between the number of electrons in bonding and antibonding MOs.

• Paramagnetism and diamagnetism can be predicted by the presence of unpaired electrons in MOs.

• The energy ordering of MOs changes for elements after N2 due to increased nuclear charge and orbital interactions.

Additional info:

• For ions such as H2-, N2-, N2+, F2+, and Ne2+, bond order can be calculated using the same method. A positive bond order suggests possible stability, while zero or negative bond order indicates instability.