Molecular Orbital Theory Study Notes

Overview of MO Theory
- MO Theory provides a better description of bonding than Valence Bond Theory and Lewis Structures.
- Helps explain phenomena such as why H₂ is diatomic while He is not, and why O₂ has magnetic properties.
- Although complicated, MO Theory can be understood at a general chemistry level.
Introduction to Molecular Orbitals
- In molecular hydrogen (H₂), electrons reside in overlapping orbitals (1s).
- Atomic orbitals are wave functions, solutions to the Schrödinger equation.

Understanding Atomic Orbitals
- 1s orbitals can be visualized with sine functions.
- Positive values are between 0 and π, negative values between π and 2π, with nodes (zeros) appearing at multiples of π.
- Nodes indicate zero probability of finding electrons in those regions.
Constructive and Destructive Overlap
- Constructive Overlap: When wave functions overlap positively (in-phase), leading to amplification of electron probability.
- Destructive Overlap: When wave functions overlap negatively (out-of-phase), resulting in cancellation (node created).

Molecular Orbitals (MOs)
- Formed from the combination of atomic wave functions.
- The constructive overlap results in bonding molecular orbitals (lower energy), while destructive overlap leads to antibonding molecular orbitals (higher energy).
- An example is the formation of the sigma 1s orbital and sigma 1s* (anti-bonding) orbital from 1s atomic orbitals.
- Sigma 1s orbital is lower in energy and stabilizes the molecule (bonding).
- Sigma 1s* orbital is higher in energy and destabilizes the molecule (anti-bonding).
Energy Considerations
- Electrons prefer lower energy states and will occupy the bonding molecular orbital first (Aufbau principle).
- Both types of molecular orbitals can hold a maximum of 2 electrons.

Defining Homonuclear Diatomic Molecules
- MO Theory primarily deals with homonuclear diatomics—two identical atoms.
- Both atoms contribute their atomic orbitals to form molecular orbitals.
P Orbitals and their Combination
- P orbitals can also overlap to form molecular orbitals.
- Sigma 2p and Pi 2p:
- Pz orbitals overlap end-to-end (sigma), while Px and Py overlap side-to-side (pi).
- Again, constructive overlap results in bonding molecular orbitals, and destructive overlap leads to anti-bonding molecular orbitals.

Molecular Orbital Diagrams
- Diatomic Hydrogen (H₂): 1s atomic orbitals overlap.
- Creates sigma 1s (bonding) and sigma 1s* (anti-bonding).
- Filled with 2 electrons; bond order = 1 (stable and diatomic).
Why Helium (He₂) Does Not Exist
- He has 2 electrons in 1s each.
- Forms sigma 1s and sigma 1s*.
- Two bonding and two anti-bonding electrons cancel each other out.
- Bond order = 0 (unstable; does not exist).
O₂ and Paramagnetism
- Oxygen has 2 electrons in the 2p orbitals.
- Bond order calculation reveals it has a bond order of 2 (double bond).
- O₂ is paramagnetic due to two unpaired electrons in the pi 2p* orbital, leading to attraction in magnetic fields.
Fluorine (F₂) and Diamagnetism
- Bond order equals 1 (single bond) with all electrons paired, indicating F₂ is diamagnetic.
Neon (Ne₂) Does Not Exist
- Bond order equals 0 following similar principles as He₂, hence Ne₂ also does not exist.
Nitrogen (N₂) and its Triple Bond
- N₂ exhibits a bond order of 3 (triple bond) with diamagnetism, due to fully filled orbitals and no unpaired electrons.

For homonuclear diatomics from Li₂ to N₂, MO diagrams differ:
- The sigma and pi/anti-bonding order are altered for diatomics from elements across the second period.
- Important to identify the presence of sp mixing in these elements.

A solid understanding of MO Theory enables better predictions about the nature of molecules and their properties compared to older theories.
Students should be able to:
- Construct MO diagrams for homonuclear diatomics;
- Calculate bond orders based on MO occupancy;
- Understand the relation of bond orders to molecular stability and existence.