Molecular Orbital Builder

Molecular orbital theory is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms but are treated as moving under the influence of the nuclei in the whole molecule.

Atomic Orbitals

Atomic orbitals are mathematical functions that describe the wave-like behavior of electrons in an atom. The most common types are:

• s orbitals: Spherical in shape, with the electron density decreasing with distance from the nucleus.
• p orbitals: Dumbbell-shaped, with three possible orientations (px, py, pz) along the three coordinate axes.
• d orbitals: More complex shapes, with five possible orientations (dz², dx²-y², dxy, dxz, dyz).

Molecular Orbital Formation

When atoms come together to form molecules, their atomic orbitals combine to form molecular orbitals. This combination can be:

• Bonding: When atomic orbitals combine in phase, resulting in increased electron density between nuclei and lower energy.
• Antibonding: When atomic orbitals combine out of phase, resulting in a node (zero electron density) between nuclei and higher energy.
• Non-bonding: When atomic orbitals do not significantly interact, resulting in an energy similar to the original atomic orbital.

Types of Molecular Orbitals

Sigma (σ) orbitals: Formed by head-to-head overlap of atomic orbitals along the internuclear axis. They can be bonding (σ) or antibonding (σ*).

Pi (π) orbitals: Formed by side-by-side overlap of p orbitals perpendicular to the internuclear axis. They can be bonding (π) or antibonding (π*).

Delta (δ) orbitals: Formed by side-by-side overlap of d orbitals. They are less common and typically found in transition metal complexes.

Bond Order and Stability

The bond order is calculated as:

A higher bond order indicates a stronger and shorter bond. A bond order of zero indicates no net bonding, while negative bond orders are unstable.

Applications in Chemistry

Molecular orbital theory helps explain:

• The paramagnetism of O₂ (which cannot be explained by Lewis structures)
• The stability of molecules like N₂ with triple bonds
• The reactivity of molecules based on their HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital)
• The colors of coordination compounds based on d-orbital splitting

Use this simulator to explore how different atomic orbitals combine to form molecular orbitals, and how these affect the properties and behavior of molecules.