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One Open Shell

Given are term symbols (up to indices depending on actual case and group) and a and b coefficients. n is the number of electrons in an irrep with degeneracy nir. Note that not all cases are Roothaan cases.

All single electron cases are described by:

a = b = 0
nir=2: e (div. groups), π, δ ( C∞v, D∞h)
n f en πn δn a b
3A 3Σ 3Σ 1 2
2 1/2 1E% latex2html id marker 50259 \setcounter{footnote}{1}\fnsymbol{footnote} 1Δ 1Γ 1/2 0
1A 1Σ 1Σ 0 -2
3 3/4 2E 2Π 2Δ 8/9 8/9
1 nir=3: p (O(3)), t (T, O, I)% latex2html id marker 50277 \setcounter{footnote}{2}\fnsymbol{footnote}
n f pn a b
3P 3/4 3/2
2 1/3 1D% latex2html id marker 50288 \setcounter{footnote}{7}\fnsymbol{footnote} 9/20 -3/10
1S 0 -3
4S 1 2
3 1/2 2D% latex2html id marker 50298 \setcounter{footnote}{7}\fnsymbol{footnote} 4/5 4/5
2P 2/3 0
3P 15/16 9/8
4 2/3 1D% latex2html id marker 50308 \setcounter{footnote}{7}\fnsymbol{footnote} 69/80 27/40
1S 3/4 0
5 5/6 2P 24/25 24/25
only irrep g(I)
(mainly high spin available)
n f gn a b
1 1/8 2G 0 0
2 1/4 % latex2html id marker 50328 \setcounter{footnote}{8}\fnsymbol{footnote} 2/3 4/3
1A 0 -4
3 3/8 4G 8/9 16/9
4 1/2 5A 1 2
5 5/8 4G24/2532/25
6 3/4 % latex2html id marker 50348 \setcounter{footnote}{8}\fnsymbol{footnote}26/2728/27
1A 8/9 4/9
7 7/8 2G48/4948/49
d(O3), h(I)
(mainly high-spin cases work)
n f dn a b
1 1/10 2D 0 0
2 1/5 3F+ 3P% latex2html id marker 50371 \setcounter{footnote}{8}\fnsymbol{footnote} 5/8 5/4
1S 0 -5
3 3/10 4F+ 4P% latex2html id marker 50381 \setcounter{footnote}{8}\fnsymbol{footnote} 5/6 5/3
4 2/5 5D, 5H 15/16 15/8
5 1/2 6S, 6A 1 2
6 3/5 5D, 5H 35/36 25/18
7 7/10 4F+ 4P% latex2html id marker 50402 \setcounter{footnote}{8}\fnsymbol{footnote} 95/98 55/49
8 4/5 3F+ 3P% latex2html id marker 50408 \setcounter{footnote}{8}\fnsymbol{footnote}125/128 65/64
1S 15/16 5/8
9 9/10 2D, 2H 80/81 80/81
    % latex2html id marker 50419 \setcounter{footnote}{1}\fnsymbol{footnote}except cases (e.g. D2d or D4h) where e2 gives only one-dimensional irreps, which are not Roothaan cases.
    % latex2html id marker 50423 \setcounter{footnote}{2}\fnsymbol{footnote}only pn given, the state for groups Td etc. follows from
S → A (T,O,I) P → T (T,O,I) D → H (I), E+T (T,O)
    % latex2html id marker 50438 \setcounter{footnote}{7}\fnsymbol{footnote}This is not a CSF in T or O, (a, b) describes average of states resulting from E+T
    % latex2html id marker 50442 \setcounter{footnote}{8}\fnsymbol{footnote}(a, b) describes weighted average of high spin states, not a CSF.


Subsections
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Next: Example Up: Restricted Open-Shell Hartree-Fock Previous: Brief Description   Contents   Index
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