N-electron Spin Eigenfunctions

As we know, given the number of electrons N and the spin quantum number S, there are (2S+1)N!/(N/2+S+1)!/(N/2-S)! eigenfunctions of S2 and each state has 2S+1 components. I list the spin eigenfunctions of N-electron system (N = 1 ~ 7) below. For each S, all functions with Sz = -S to +S are listed. For example, means that the first electron couples with the second one to obtain a singlet state (S = 0), then they couple with the third one to obtain the final doublet state (S = 1/2); means that the first, second and third electron is alpha, beta and alpha spin, respectively.

These graphs are generated with computers by group theories.

N = 1, S = 1/2

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

N = 2, S = 0

S = 0, Sz = 0:

N = 2, S = 1

S = 1, Sz = 1:

S = 1, Sz = 0:

S = 1, Sz = -1:

N = 3, S = 1/2

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

N = 3, S = 3/2

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

N = 4, S = 0

S = 0, Sz = 0:

S = 0, Sz = 0:

N = 4, S = 1

S = 1, Sz = 1:

S = 1, Sz = 0:

S = 1, Sz = -1:

S = 1, Sz = 1:

S = 1, Sz = 0:

S = 1, Sz = -1:

S = 1, Sz = 1:

S = 1, Sz = 0:

S = 1, Sz = -1:

N = 4, S = 2

S = 2, Sz = 2:

S = 2, Sz = 1:

S = 2, Sz = 0:

S = 2, Sz = -1:

S = 2, Sz = -2:

N = 5, S = 1/2

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

N = 5, S = 3/2

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

N = 5, S = 5/2

S = 5/2, Sz = 5/2:

S = 5/2, Sz = 3/2:

S = 5/2, Sz = 1/2:

S = 5/2, Sz = -1/2:

S = 5/2, Sz = -3/2:

S = 5/2, Sz = -5/2:

N = 6, S = 0

S = 0, Sz = 0:

S = 0, Sz = 0:

S = 0, Sz = 0:

S = 0, Sz = 0:

S = 0, Sz = 0:

N = 6, S = 1

S = 1, Sz = 1:

S = 1, Sz = 0:

S = 1, Sz = -1:

S = 1, Sz = 1:

S = 1, Sz = 0:

S = 1, Sz = -1:

S = 1, Sz = 1:

S = 1, Sz = 0:

S = 1, Sz = -1:

S = 1, Sz = 1:

S = 1, Sz = 0:

S = 1, Sz = -1:

S = 1, Sz = 1:

S = 1, Sz = 0:

S = 1, Sz = -1:

S = 1, Sz = 1:

S = 1, Sz = 0:

S = 1, Sz = -1:

S = 1, Sz = 1:

S = 1, Sz = 0:

S = 1, Sz = -1:

S = 1, Sz = 1:

S = 1, Sz = 0:

S = 1, Sz = -1:

S = 1, Sz = 1:

S = 1, Sz = 0:

S = 1, Sz = -1:

N = 6, S = 2

S = 2, Sz = 2:

S = 2, Sz = 1:

S = 2, Sz = 0:

S = 2, Sz = -1:

S = 2, Sz = -2:

S = 2, Sz = 2:

S = 2, Sz = 1:

S = 2, Sz = 0:

S = 2, Sz = -1:

S = 2, Sz = -2:

S = 2, Sz = 2:

S = 2, Sz = 1:

S = 2, Sz = 0:

S = 2, Sz = -1:

S = 2, Sz = -2:

S = 2, Sz = 2:

S = 2, Sz = 1:

S = 2, Sz = 0:

S = 2, Sz = -1:

S = 2, Sz = -2:

S = 2, Sz = 2:

S = 2, Sz = 1:

S = 2, Sz = 0:

S = 2, Sz = -1:

S = 2, Sz = -2:

N = 6, S = 3

S = 3, Sz = 3:

S = 3, Sz = 2:

S = 3, Sz = 1:

S = 3, Sz = 0:

S = 3, Sz = -1:

S = 3, Sz = -2:

S = 3, Sz = -3:

N = 7, S = 1/2

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

S = 1/2, Sz = 1/2:

S = 1/2, Sz = -1/2:

N = 7, S = 3/2

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

S = 3/2, Sz = 3/2:

S = 3/2, Sz = 1/2:

S = 3/2, Sz = -1/2:

S = 3/2, Sz = -3/2:

N = 7, S = 5/2

S = 5/2, Sz = 5/2:

S = 5/2, Sz = 3/2:

S = 5/2, Sz = 1/2:

S = 5/2, Sz = -1/2:

S = 5/2, Sz = -3/2:

S = 5/2, Sz = -5/2:

S = 5/2, Sz = 5/2:

S = 5/2, Sz = 3/2:

S = 5/2, Sz = 1/2:

S = 5/2, Sz = -1/2:

S = 5/2, Sz = -3/2:

S = 5/2, Sz = -5/2:

S = 5/2, Sz = 5/2:

S = 5/2, Sz = 3/2:

S = 5/2, Sz = 1/2:

S = 5/2, Sz = -1/2:

S = 5/2, Sz = -3/2:

S = 5/2, Sz = -5/2:

S = 5/2, Sz = 5/2:

S = 5/2, Sz = 3/2:

S = 5/2, Sz = 1/2:

S = 5/2, Sz = -1/2:

S = 5/2, Sz = -3/2:

S = 5/2, Sz = -5/2:

S = 5/2, Sz = 5/2:

S = 5/2, Sz = 3/2:

S = 5/2, Sz = 1/2:

S = 5/2, Sz = -1/2:

S = 5/2, Sz = -3/2:

S = 5/2, Sz = -5/2:

S = 5/2, Sz = 5/2:

S = 5/2, Sz = 3/2:

S = 5/2, Sz = 1/2:

S = 5/2, Sz = -1/2:

S = 5/2, Sz = -3/2:

S = 5/2, Sz = -5/2:

N = 7, S = 7/2

S = 7/2, Sz = 7/2:

S = 7/2, Sz = 5/2:

S = 7/2, Sz = 3/2:

S = 7/2, Sz = 1/2:

S = 7/2, Sz = -1/2:

S = 7/2, Sz = -3/2:

S = 7/2, Sz = -5/2:

S = 7/2, Sz = -7/2: