closedshell

Closedshell, usually written as closed-shell, is a term used in atomic and molecular physics and quantum chemistry to describe an electronic configuration in which all occupied orbitals are fully paired with electrons of opposite spin. In atoms this corresponds to complete electron shells or subshells; in molecules it means that every occupied molecular orbital contains two electrons. The overall spin state is therefore S = 0, and the electronic multiplicity is singlet.

Closed-shell systems are typically diamagnetic and exhibit relatively large gaps between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO gap), reflecting stability. They tend to be less reactive than open-shell species, especially toward radical-type or single-occupation processes. Nevertheless, closed-shell species can engage in reactions under appropriate conditions, and excited states may involve open-shell configurations.

In computational chemistry, closed-shell systems are often treated with restricted methods, where alpha and beta electrons share the same spatial orbitals (for example, restricted Hartree–Fock or restricted Kohn–Sham density functional theory). These approaches usually converge rapidly and yield reliable results for ground-state properties. Open-shell systems, with unpaired electrons, require unrestricted or restricted open-shell methods and are typically more demanding computationally.

Examples of common closed-shell species include the noble gases (helium, neon), methane (CH4), nitrogen (N2), carbon monoxide (CO) in its ground state, and water (H2O). The concept contrasts with open-shell species such as molecular oxygen in its ground triplet state and many free radicals.