fourcenter

Fourcenter is a term used in chemistry and quantum chemistry to describe situations, concepts, or calculations that involve four atomic centers. In bonding terminology, four-center two-electron bonds (4c-2e) refer to a bonding arrangement in which two electrons are delocalized over four atoms. This extends multicenter bonding beyond the more familiar three-center two-electron bonds and is encountered in certain electron-deficient compounds and metal clusters. The existence and strength of 4c-2e interactions depend on the geometry of the four centers and the participating atomic orbitals, and they are often investigated through structural data and spectroscopic evidence.

In computational chemistry, four-center integrals describe the Coulomb repulsion between electrons associated with four basis functions located on four centers, commonly denoted as (μν|λσ). These four-center electron repulsion integrals are a central component of ab initio methods such as Hartree–Fock and post-Hartree–Fock calculations. Their evaluation is computationally demanding because of the scale with system size. Naive evaluation typically scales roughly as the fourth power of the number of basis functions. To make calculations feasible for larger systems, a range of approximation and acceleration techniques are used, including density fitting (resolution of the identity), Cholesky decomposition, and tensor hypercontraction, among others. These methods reduce computational cost while aiming to preserve accuracy.

Overall, fourcenter concepts bridge structural chemistry and computational methods, reflecting both the physical reality of multicenter bonding and the practical challenges of calculating electron interactions in complex molecules.