Term Symbols For An Electron Configuration
To calculate all possible term symbols for a given electron configuration the process is a bit longer.
 First, calculate the total number of possible microstates N for a given electron configuration. As before, we discard the filled (sub)shells, and keep only the partially filled ones. For a given orbital quantum number l, t is the maximum allowed number of electrons, t = 2(2l+1). If there are e electrons in a given subshell, the number of possible microstates is
 As an example, lets take the carbon electron structure: 1s22s22p2. After removing full subshells, there are 2 electrons in a plevel (l = 1), so we have
 different microstates.
 Second, draw all possible microstates. Calculate M_{L} and M_{S} for each microstate, with where m_{i} is either m_{l} or m_{s} for the ith electron, and M represents the resulting M_{L} or M_{S} respectively:

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 Third, count the number of microstates for each M_{L}—M_{S} possible combination
m_{l} +1 0 −1 M_{L} M_{S} all up ↑ ↑ 1 1 ↑ ↑ 0 1 ↑ ↑ −1 1 all down ↓ ↓ 1 −1 ↓ ↓ 0 −1 ↓ ↓ −1 −1 one up one down
↑↓ 2 0 ↑ ↓ 1 0 ↑ ↓ 0 0 ↓ ↑ 1 0 ↑↓ 0 0 ↑ ↓ −1 0 ↓ ↑ 0 0 ↓ ↑ −1 0 ↑↓ −2 0 M_{S} +1 0 −1 M_{L} +2 1 +1 1 2 1 0 1 3 1 −1 1 2 1 −2 1
 Fourth, extract smaller tables representing each possible term. Each table will have the size (2L+1) by (2S+1), and will contain only "1"s as entries. The first table extracted corresponds to M_{L} ranging from −2 to +2 (so L = 2), with a single value for M_{S} (implying S = 0). This corresponds to a 1D term. The remaining table is 3×3. Then we extract a second table, removing the entries for M_{L} and M_{S} both ranging from −1 to +1 (and so S = L = 1, a 3P term). The remaining table is a 1×1 table, with L = S = 0, i.e., a 1S term.

S=0, L=2, J=2
1D_{2}
M_{s} 0 M_{l} +2 1 +1 1 0 1 −1 1 −2 1 S=1, L=1, J=2,1,0
3P_{2}, 3P_{1}, 3P_{0}
M_{s} +1 0 −1 M_{l} +1 1 1 1 0 1 1 1 −1 1 1 1 S=0, L=0, J=0
1S_{0}
M_{s} 0 M_{l} 0 1
 Fifth, applying Hund's rules, deduce which is the ground state (or the lowest state for the configuration of interest.) Hund's rules should not be used to predict the order of states other than the lowest for a given configuration. (See examples at Hund's rules#Excited states.)
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Other articles related to "term symbols for an electron configuration, configurations, electrons, configuration":
... 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 ... The configuration 2p2 has the symmetry of the following direct product in the full rotation group Γ(1) × Γ(1) = Γ(0) + + Γ(2), which, using the familiar labels Γ(0) = S, Γ(1) = P and Γ(2) = D ... Hence the 2p2 configuration has components with the following symmetries S + D (from the symmetric square and hence having symmetric spatial wavefunctions) P (from ...
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