Understanding Degenerate Orbitals
In quantum chemistry, degenerate orbitals are atomic or molecular orbitals that possess identical energy levels. This means that electrons occupying any of these orbitals, when isolated, would have the same potential energy. This phenomenon of degeneracy primarily arises from the inherent symmetry of an atom or a molecule, dictating how electrons are distributed.
Key Principles and Examples
Degeneracy is a critical concept for understanding how electrons fill orbitals according to fundamental rules like Hund's Rule and the Aufbau Principle. For instance, in a hydrogen atom, all orbitals with the same principal quantum number (n), such as 2s and 2p, are degenerate. However, in multi-electron atoms, electron-electron repulsion causes a splitting of these energy levels, a process known as lifting the degeneracy, where 2s becomes lower in energy than 2p, but the three 2p orbitals (px, py, pz) remain degenerate.
Degeneracy in Multi-electron Atoms
Consider a multi-electron atom like nitrogen. It has three 2p orbitals (2px, 2py, 2pz) that are degenerate, meaning they are at the same energy level. According to Hund's Rule, when filling these orbitals, electrons will individually occupy each of the three 2p orbitals with parallel spins before any orbital is doubly occupied. This equal-energy status allows for the stable, low-energy arrangement of electrons.
Importance in Chemical Bonding
The concept of degenerate orbitals is fundamental to understanding advanced topics such as crystal field theory, ligand field theory, and molecular orbital theory. In complex systems, degenerate orbitals play a crucial role in predicting molecular properties, reactivity, and explaining phenomena like resonance and aromaticity, where electrons are delocalized over multiple equivalent positions, leading to enhanced stability.