4nelectron

4nelectron is a term used in theoretical chemistry and condensed-matter physics to describe a simplified quantum-system model consisting of four interacting electrons. It serves as a pedagogical and research-oriented shorthand for studying electron correlation, exchange interactions, and spin physics in a small, fully interacting set of particles.

The model can be realized in various settings, such as four electrons confined in a two-dimensional quantum dot, within a finite external potential, or as a minimal molecular fragment where four electrons participate in bonding and anti-bonding interactions. The governing Hamiltonian includes the kinetic energy of the electrons, external confinement, and Coulomb repulsion between all pairs of electrons. Because exact solutions are feasible only for limited basis sets, numerical approaches such as full configuration interaction, multi-configurational self-consistent field methods, and carefully chosen density-functional approximations are commonly employed to study 4nelectron systems.

The four-electron system exhibits multiple spin states, including singlet and triplet configurations, with energy gaps that depend on confinement strength, geometry, and interaction parameters. These features provide insight into exchange interactions, correlation effects, and the limitations of mean-field theories in small, strongly interacting systems. Researchers use 4nelectron as a benchmark for testing electronic-structure methods, exploring basis-set convergence, and illustrating concepts of quantum entanglement and correlation in a controlled setting.

See also: electron correlation, few-electron systems, quantum dot, configuration interaction, multi-reference methods.