While VSEPR theory excels at predicting molecular geometry based on electron domain repulsion, it does not fully explain how atomic orbitals actually combine and overlap to form the bonds. For a more sophisticated understanding of bonding, particularly in the context of carbon compounds and magnetic properties, we turn to hybridization and molecular orbital theory.

Hybridization is a theoretical concept that involves the mixing of atomic orbitals within an atom to form new, degenerate (equal energy) hybrid orbitals. These newly formed hybrid orbitals have different shapes and orientations compared to the original atomic orbitals, but they are ideally suited for forming strong, directional sigma (σ) bonds through effective overlap.

The type of hybridization that occurs in a central atom is directly related to the number of electron domains around it (as determined by VSEPR theory):

• sp hybridization (2 electron domains): One s atomic orbital mixes with one p atomic orbital to generate two equivalent sp hybrid orbitals. These two sp orbitals are oriented linearly (180° bond angle) to minimize repulsion. The remaining two unhybridized p orbitals are perpendicular to the sp hybrids and are available to form pi (π) bonds.

Example: The carbon atoms in carbon dioxide (O=C=O) and ethyne (acetylene, H-C≡C-H) are sp hybridized.

• sp² hybridization (3 electron domains): One s atomic orbital mixes with two p atomic orbitals to create three equivalent sp² hybrid orbitals. These three sp² orbitals lie in a plane and point towards the corners of an equilateral triangle (trigonal planar arrangement, 120° bond angle). One unhybridized p orbital remains perpendicular to this plane, capable of forming a pi (π) bond.

Example: The carbon atoms in ethene (ethylene, H₂C=CH₂) and the boron atom in boron trifluoride (BF₃) are sp² hybridized.

• sp³ hybridization (4 electron domains): One s atomic orbital mixes with all three p atomic orbitals to produce four equivalent sp³ hybrid orbitals. These four sp³ orbitals are oriented towards the corners of a tetrahedron (tetrahedral arrangement, 109.5° bond angle). In this case, no unhybridized p orbitals remain, meaning sp³ hybridized atoms typically form only sigma bonds.

*Example: The carbon atom in methane (CH₄), the nitrogen atom in ammonia (NH₃), and the oxygen atom in water (H₂O) are sp³ hybridized (though lone pairs distort the bond angles from the ideal 109.5°).

Sigma (σ) and Pi (π) Bonds: These are the two fundamental types of covalent bonds based on the pattern of orbital overlap:

• Sigma (σ) bonds: Formed by the direct, head-on (end-to-end) overlap of atomic orbitals (or hybrid orbitals). Electron density is concentrated along the internuclear axis, the line connecting the two nuclei. All single covalent bonds are sigma bonds.
• Pi (π) bonds: Formed by the sideways (lateral) overlap of parallel unhybridized p orbitals. The electron density in a pi bond is located above and below the internuclear axis. Pi bonds are always found in conjunction with a sigma bond. A double bond consists of one sigma bond and one pi bond. A triple bond consists of one sigma bond and two pi bonds. While pi bonds are generally weaker than sigma bonds individually, their presence restricts rotation around the bond and is crucial for creating rigidity and explaining electron delocalization in molecules.

Molecular Orbital (MO) theory offers a more advanced and quantitative description of bonding compared to valence bond theory (which includes hybridization). In MO theory, instead of electrons occupying atomic orbitals around individual atoms, atomic orbitals combine to form new molecular orbitals that extend over the entire molecule. Electrons then fill these molecular orbitals following the same rules as filling atomic orbitals (Pauli exclusion principle, Hund's rule).

• When two atomic orbitals combine, they form two distinct molecular orbitals:
• A bonding molecular orbital (σ or π): This orbital is lower in energy than the original atomic orbitals from which it formed. Electrons occupying bonding MOs contribute to the stability of the molecule and strengthen the bond.
• An antibonding molecular orbital (σ or π): This orbital is higher in energy than the original atomic orbitals. Electrons occupying antibonding MOs destabilize the molecule and weaken the bond. The asterisk (*) denotes an antibonding orbital.

Example: Hydrogen Molecule (H₂)

• Each hydrogen atom has one 1s atomic orbital.
• These two 1s atomic orbitals combine to form two molecular orbitals: a lower-energy sigma (σ1s) bonding MO and a higher-energy sigma (σ1s) antibonding MO.
• The two valence electrons (one from each H atom) both occupy the lower-energy σ1s bonding MO.
• Bond Order = 0.5 x (2 bonding electrons - 0 antibonding electrons) = 1. This correctly predicts the single covalent bond in H₂.
• Since all electrons are paired in the σ1s orbital, H₂ is diamagnetic.

Example: Oxygen Molecule (O₂)

• Applying MO theory to the valence atomic orbitals (2s and 2p) of oxygen leads to a more complex MO diagram. However, the key outcome is that MO theory predicts that the O₂ molecule has two unpaired electrons occupying two separate, degenerate (equal energy) pi (π) antibonding orbitals.
• The overall bond order for O₂, based on the filling of all its molecular orbitals, is 0.5 x (8 bonding electrons - 4 antibonding electrons) = 2. This correctly predicts a double bond in O₂.
• Crucially, the presence of these two unpaired electrons in the π* orbitals elegantly explains why oxygen gas (O₂) is observed to be paramagnetic, a property that cannot be adequately explained by simpler valence bond models.