Valence Bond Theory and Molecular Orbitals

s orbital: A spherical orbital that can hold a maximum of two electrons.
p orbital: A dumbbell-shaped orbital consisting of three different orientations (px, py, pz).
N=N: Representation of a double bond between two nitrogen atoms (N2).
- σ bond: A type of covalent bond formed by the overlap of atomic orbitals along the bond axis.
- π bond: A type of covalent bond formed by the lateral overlap of p orbitals.
- л bond: Alternative notation for π bonds.

Valence-bond theory: Initially insufficient to explain bonding in polyatomic molecules like methane (CH4).
- Ground state of the carbon atom has two unpaired electrons in perpendicular orbitals:
- Configuration of carbon: C: [He] 2s² 2p²
  - Visual representation:
  - C2p - ↑↑
  - C2s - ↑↑
Prediction based on electron configuration: Carbon should form CH₂ with 90° bond angle, indicating misunderstanding of carbon's bonding capacity.

To explain bonding in CH₄, valence-bond theory assumes an electron promotion from the 2s to the 2p level:
- Resulting configuration: C: [He] 2s¹ 2px¹ 2py¹ 2p_z¹ leading to four unpaired electrons.
- Each bond releases energy, compensating for the promotion energy required for this process.

Hybridization: Requires an additional conceptual modification to explain methane’s tetrahedral structure.
- Interference of s and three p orbitals creates four equivalent sp³ hybrid orbitals.
- Arrangement: Point towards corners of a tetrahedron with bond angle of 109.5°.

Combining orbitals: One s and three p atomic orbitals yield four sp³ hybrid orbitals, each directed at 109.5°.
Node: Each sp³ orbital has a node near the nucleus. The nucleus resides in the small lobe or tail region.
- Node condition is formalized as:
- Node occurs when: Y(2s) = - Y(2p)

sp³ orbitals exhibit asymmetry with amplitude concentrated on one side, enhancing effective overlap and bond strength.
Tetrahedral methane structure: Supported by four equivalent 2-center-2-electron C-H bonds.

sp³ hybrid orbitals on central atom enable the formation of 4 σ-bonds or a mix of σ-bonds and lone pair orbitals.
Visual structure:
- CH₄ has four C-H bonds.
- NH₃ has three N-H bonds and one nitrogen lone pair.
- H₂O features two O-H bonds and two oxygen lone pairs.

sp² Hybridization: Three equivalent sp² hybrid orbitals arranged trigonal planar with bond angles of 120°.
- Formed by mixing one s orbital and two p orbitals.
sp Hybridization: Mixing of one s and one p orbital results in two linear sp hybrids.

Hybridization is a mathematical operation; it combines atomic orbitals to form hybrid orbitals that align with observed molecular geometries.

Ethylene (C₂H₄): Involves sp² hybridization leading to trigonal planar structure and bond angles of 120°.
- Carbon hybridization depicted with sp² orbitals.
Carbon Dioxide (CO₂): Exhibits sp hybridization conferring linear arrangement at 180°.
- Bond Description: Features one σ and two π bonds resulting in a stable molecule.

Hybridization is less prevalent in second and third row elements (e.g., OH₂, NH₃).
Bond angles in molecules like H₂S and PH₃ are close to 90°, largely indicative of p orbital character.

XeF₂ example: Traditionally framed as using dsp³ hybrids; however, higher energy d orbitals are often less relevant in nonmetals.
Discrepancy noted in chemistry literature regarding the actual role of d orbitals.

Valence bond theory struggles to explain certain molecular properties:
- Example: Predicts O₂ as diamagnetic conflicting with its observed paramagnetic behavior.
Requires hybridization to rationalize bonding geometries in CH₄ and other molecules.
Challenges with energy equivalence predictions for lone pairs and bond orbital energies in molecules such as water (H₂O).

Molecular Orbital Theory arises to account for limitations of valence-bond theory.
- Electrons are not confined between two atoms but can exist in orbitals spread over the whole molecule.
- Functions similarly to atomic orbitals, accommodating a maximum of two electrons with opposite spins.

Molecular orbitals derived from linear combinations of atomic orbitals (LCAO).
As atoms approach, orbitals interact constructively (bonding) or destructively (antibonding).

Bonding orbitals have increased electron probability density between nuclei, leading to lower energy.
Antibonding orbitals exhibit reduced electron density between nuclei and have a node, indicating higher energy.

Diagrammatic representation connects atomic orbitals to corresponding molecular orbitals, emphasizing number conservation in orbitals.
Each molecular orbital corresponds to the number of atomic orbitals contributing.

Defined as: ext{Bond order} = rac{( ext{# electrons in bonding orbitals}) - ( ext{# electrons in antibonding orbitals})}{2}
Indicates molecule stability: higher bond order correlates with stronger bonds and shorter bond distances.

Clarifying approach includes:
1. Identify valence shell orbitals.
2. Combine atomic orbitals of similar symmetry.
3. Account for atom electron counts and charge.
4. Place electrons in order of increasing energy, ensuring distinct spins before pairing.

Valence configurations involve 2s and 2p orbitals, yielding bonding and antibonding orbitals during combination.
Effective bond character for systems analyzed through molecular orbital diagrams illustrating bond types and demarcation of bonding characteristics.