ElectronElectron

Electronelectron is a term occasionally used in discussions of electronic structure to denote the interaction between electrons within a many‑electron system. It is not a standard object in mainstream physics and there is no universally accepted definition. In most contexts, electronelectron refers broadly to the pairwise Coulomb repulsion and the resulting correlation effects that go beyond independent-particle models.

In formal treatments, electronelectron interactions arise from the Coulomb term in the electronic Hamiltonian. The repulsion between electrons is written as Vee = (1/2) ∑i≠j e^2/|ri − rj| in first-quantized form, and in second quantization as (1/2) ∑pqrs ⟨pq|V|rs⟩ a†p a†q a s ar, where the matrix elements encode the strength and spatial dependence of the interaction. Accounting for electronelectron effects is essential for describing correlation energy, magnetism, and phenomena that cannot be captured by independent-electron approximations.

Practically, electronelectron interactions are treated with a range of methods, including configuration interaction, coupled-cluster techniques, GW approximations, and density functional theory with exchange-correlation functionals. The concept underscores the limits of mean-field theories and the importance of electron correlation in determining molecular spectra, solid-state properties, and chemical reactivity.

In some pedagogical or speculative contexts, the term electronelectron may be used to imagine specialized constructs or quasi‑particles that encapsulate correlated electron motion. Such usages are not part of established theory, where the focus remains on Coulomb interaction, exchange, and correlation as integrated aspects of many-electron physics.