Multielectron

Multielectron refers to systems that contain more than one electron. In atomic physics and quantum chemistry, most atoms and ions are multielectron, in contrast to hydrogen and hydrogen-like ions which have a single electron orbiting a nucleus. The presence of multiple electrons introduces electron–electron repulsion, making the many-body Schrödinger equation substantially more complex and generally not solvable analytically.

This leads to phenomena such as screening, where inner electrons shield outer electrons from the full nuclear charge; electron correlation, the interaction among electrons beyond mean-field, and exchange effects arising from the antisymmetry of fermionic wavefunctions. As a result, energy levels are shifted and split, and degeneracies apparent in one-electron models are removed. Atomic term symbols, spin-orbit coupling, and Hund's rules reflect these multielectron effects.

Solving such systems requires approximations. The Hartree-Fock method treats electrons in a mean field and builds antisymmetric wavefunctions as Slater determinants; it neglects dynamic correlation but offers a starting point. Post-HF methods (configuration interaction, Møller–Plesset perturbation theory, coupled-cluster) include electron correlation. Density functional theory uses electron density rather than wavefunctions to approximate energies, often with good accuracy for atoms, molecules, and solids. Multiconfiguration approaches account for near-degeneracies by mixing several electron configurations.

In practice, multielectron calculations underpin chemistry, spectroscopy, and materials science; they explain chemical bonding, ionization energies, and spectra of elements beyond hydrogen. Their computational cost grows rapidly with the number of electrons, guiding choices of methods and basis sets.