Coulombterm

CoulombTerm is a term used to denote the electrostatic repulsion between electric charges in a system. Named after Charles-Augustin de Coulomb, it appears in classical electrostatics and in quantum-mechanical models of many-electron systems as the energy contribution and the corresponding interaction operator.

In quantum chemistry and physics, the Coulomb term refers to the electron-electron repulsion component of the Hamiltonian. It is often represented by the Hartree energy, which for a continuous charge density ρ(r) is given by E_H = (1/2) ∫∫ ρ(r) ρ(r') / |r − r'| dr dr'. In a basis of one-electron functions, the direct Coulomb interaction between occupied orbitals is described by two-electron integrals (pp|qq) = ∫∫ φ_p*(r1) φ_p(r1) (1/|r1 − r2|) φ_q*(r2) φ_q(r2) dr1 dr2. This direct term is often called the Coulomb or J term, and it is complemented in many theories by an exchange term K that arises from antisymmetry of the electronic wavefunction.

In density functional theory, the Coulomb contribution is encapsulated in the Hartree potential, V_H(r) = ∫ ρ(r') / |r − r'| dr', representing the classical electrostatic interaction of the electron density with itself. The total energy then includes the Hartree term along with exchange-correlation contributions that account for quantum effects beyond the classical Coulomb interaction.

CoulombTerm, therefore, is central to the description of electrostatic interactions in both analytical expressions and computational implementations, influencing energy calculations, Fock matrices, and self-consistent field procedures across many-body theories.