Electron shell

In chemistry and atomic physics, an electron shell, or a principal energy level, may be thought of as an orbit followed by electrons around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), and so on farther and farther from the nucleus. The shells correspond with the principal quantum numbers (n = 1, 2, 3, 4 ...) or are labeled alphabetically with letters used in the X-ray notation (K, L, M, …).

Each shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the nth shell can in principle hold up to 2(n²) electrons. Since electrons are electrically attracted to the nucleus, an atom's electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons. However, this is not a strict requirement: atoms may have two or even three incomplete outer shells. (See Madelung rule for more details.) For an explanation of why electrons exist in these shells see electron configuration.

Open shell

In the context of atomic orbitals, an open shell is a valence shell which is not completely filled with electrons or that has not given all of its valence electrons through chemical bonds with other atoms or molecules during a chemical reaction. Atoms generally reach a noble gas configuration in a molecule. The noble gases (He, Ne, Ar, Kr, Xe, Rn) are less reactive and have configurations 1s² (He), 1s²2s²2p⁶ (Ne), 1s²2s²2p⁶3s²3p⁶ (Ar), etc.

For molecules it signifies that there are unpaired electrons. In molecular orbital theory, this leads to molecular orbitals that are singly occupied. In computational chemistry implementations of molecular orbital theory, open shell molecules have to be handled by either the restricted open-shell Hartree–Fock method or the unrestricted Hartree–Fock method.

Likewise a closed shell or closed shell configuration is obtained with a completely filled valence shell. This configuration is very stable. In another meaning a closed shell configuration corresponds to state with all molecular orbitals doubly occupied or empty (a singlet state). Open shell molecules are more difficult to study computationally