In atomic physics, a term symbol is an abbreviated description of the total spin and orbital angular momentum quantum numbers of the electrons in a multi-electron atom.
So while the word symbol suggests otherwise, it represents an actual value of a physical quantity.
For a given electron configuration of an atom, its state depends also on its total angular momentum, including spin and orbital components, which are specified by the term symbol.
The usual atomic term symbols assume LS coupling (also known as Russell–Saunders coupling) in which the all-electron total quantum numbers for orbital (L), spin (S) and total (J) angular momenta are good quantum numbers.
In the terminology of atomic spectroscopy, L and S together specify a term; L, S, and J specify a level; and L, S, J and the magnetic quantum number MJ specify a state.
The conventional term symbol has the form 2S+1LJ, where J is written optionally in order to specify a level.
Term symbols apply to both neutral and charged atoms, and to their ground and excited states.
The ground state term symbol for neutral atoms is described, in most cases, by Hund's rules.
Term symbols are also used to describe angular momentum quantum numbers for atomic nuclei and for molecules.
The use of the word term for an atom's electronic state is based on the Rydberg–Ritz combination principle, an empirical observation that the wavenumbers of spectral lines can be expressed as the difference of two terms.
Tables of atomic energy levels identified by their term symbols are available for atoms and ions in ground and excited states from the National Institute of Standards and Technology (NIST).
(Russell–Saunders coupling is named after Henry Norris Russell and Frederick Albert Saunders, who described it in 1925[2]).
where The orbital symbols S, P, D and F are derived from the characteristics of the spectroscopic lines corresponding to s, p, d, and f orbitals: sharp, principal, diffuse, and fundamental; the rest are named in alphabetical order from G onwards (omitting J, S and P).
The superscript 3 indicates that the spin multiplicity 2S + 1 is 3 (it is a triplet state), so S = 1; the letter "P" is spectroscopic notation for L = 1; and the subscript 0 is the value of J (in this case J = L − S).
[1] Small letters refer to individual orbitals or one-electron quantum numbers, whereas capital letters refer to many-electron states or their quantum numbers.
In the coupled representation where total angular momentum (spin + orbital) is treated, the associated states (or eigenstates) are
, there are (2×1+1)(2×2+1) = 15 different states (= eigenstates in the uncoupled representation) corresponding to the 3D term, of which (2×3+1) = 7 belong to the 3D3 (J = 3) level.
When it is odd, the parity of the term symbol is indicated by a superscript letter "o", otherwise it is omitted: Alternatively, parity may be indicated with a subscript letter "g" or "u", standing for gerade (German for "even") or ungerade ("odd"): It is relatively easy to predict the term symbol for the ground state of an atom using Hund's rules.
It corresponds to a state with maximum S and L. As an example, in the case of fluorine, the electronic configuration is 1s22s22p5.
Thus, hydrogen and the alkali metals are all 2S1⁄2, the alkaline earth metals are 1S0, the boron column elements are 2P1⁄2, the carbon column elements are 3P0, the pnictogens are 4S3⁄2, the chalcogens are 3P2, the halogens are 2P3⁄2, and the inert gases are 1S0, per the rule for full shells and subshells stated above.
Term symbols for the ground states of most chemical elements[3] are given in the collapsed table below.
[4] In the d-block and f-block, the term symbols are not always the same for elements in the same column of the periodic table, because open shells of several d or f electrons have several closely spaced terms whose energy ordering is often perturbed by the addition of an extra complete shell to form the next element in the column.
For example, the table shows that the first pair of vertically adjacent atoms with different ground-state term symbols are V and Nb.
The process to calculate all possible term symbols for a given electron configuration is somewhat longer.
For configurations with at most two electrons (or holes) per subshell, an alternative and much quicker method of arriving at the same result can be obtained from group theory.
Hence the 2p2 configuration has components with the following symmetries: The Pauli principle and the requirement for electrons to be described by anti-symmetric wavefunctions imply that only the following combinations of spatial and spin symmetry are allowed: Then one can move to step five in the procedure above, applying Hund's rules.
The group theory method can be carried out for other such configurations, like 3d2, using the general formula The symmetric square will give rise to singlets (such as 1S, 1D, & 1G), while the anti-symmetric square gives rise to triplets (such as 3P & 3F).
More generally, one can use where, since the product is not a square, it is not split into symmetric and anti-symmetric parts.
Where two electrons come from inequivalent orbitals, both a singlet and a triplet are allowed in each case.
For an inert (noble) gas atom, usual excited states are Np5nℓ where N = 2, 3, 4, 5, 6 for Ne, Ar, Kr, Xe, Rn, respectively in order.