Openshell

Open-shell is a term used in atomic, molecular, and solid-state physics and chemistry to describe systems that contain unpaired electrons in their electronic configuration. This contrasts with closed-shell systems, where all electrons are paired in filled orbitals. Open-shell configurations give rise to nonzero electronic spin and magnetic properties.

In practice, open-shell systems have at least one unpaired electron in the valence or near-valence region. The overall spin is described by the total spin quantum number S, and the electronic state is labeled by its spin multiplicity, 2S+1 (for example, a system with two unpaired electrons can have a triplet state, multiplicity 3). Hund’s rule governs the distribution of unpaired electrons among degenerate orbitals, often leading to higher multiplicities in radicals and many transition-metal species.

Open-shell behavior influences a range of properties, including magnetism, reactivity, and color. Open-shell species include radicals, biradicals, and many transition-metal ions in various oxidation states. These systems often exhibit altered bond strengths, unusual geometries, and multiple accessible spin states, which can affect reaction pathways and catalytic activity.

From a computational perspective, open-shell systems pose special challenges. Methods that allow unequal electron spin densities, such as unrestricted Hartree–Fock (UHF) or unrestricted DFT (UDFT), are commonly used, but they can suffer from spin contamination. Restricted open-shell approaches (ROHF) and careful method selection help maintain spin purity and reliable energetics.

Note: the term openshell can also appear in software names unrelated to chemistry; this article concentrates on the scientific meaning of open-shell systems.