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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
3 A 3Σ 3Σ 1 2
2 1/2 1 E% latex2html id marker 59600
\setcounter{footnote}{1}\fnsymbol{footnote}% latex2html id marker 59600
ootnote}{1}<IMG
 WIDTH= 1Δ 1Γ 1/2 0
1 A 1Σ 1Σ 0 - 2
3 3/4 2 E 2Π 2Δ 8/9 8/9
1 nir =3: p (O(3)), t (T , O , I )% latex2html id marker 59619
\setcounter{footnote}{2}\fnsymbol{footnote}
n f pn a b
3 P 3/4 3/2
2 1/3 1 D% latex2html id marker 59630
\setcounter{footnote}{7}\fnsymbol{footnote} 9/20 - 3/10
1 S 0 - 3
4 S 1 2
3 1/2 2 D% latex2html id marker 59640
\setcounter{footnote}{7}\fnsymbol{footnote} 4/5 4/5
2 P 2/3 0
3 P 15/16 9/8
4 2/3 1 D% latex2html id marker 59650
\setcounter{footnote}{7}\fnsymbol{footnote} 69/80 27/40
1 S 3/4 0
5 5/6 2 P 24/25 24/25
only irrep g(I )
(mainly high spin available)
n f gn a b
1 1/8 2 G 0 0
2 1/4 % latex2html id marker 59670
\setcounter{footnote}{8}\fnsymbol{footnote} 2/3 4/3
1 A 0 - 4
3 3/8 4 G 8/9 16/9
4 1/2 5 A 1 2
5 5/8 4 G24/25 32/25
6 3/4 % latex2html id marker 59690
\setcounter{footnote}{8}\fnsymbol{footnote}26/27 28/27
1 A 8/9 4/9
7 7/8 2 G48/49 48/49
d(O3), h(I )
(mainly high-spin cases work)
n f dn a b
1 1/10 2 D 0 0
2 1/5 3 F+ 3 P% latex2html id marker 59713
\setcounter{footnote}{8}\fnsymbol{footnote} 5/8 5/4
1 S 0 - 5
3 3/10 4 F+ 4 P% latex2html id marker 59723
\setcounter{footnote}{8}\fnsymbol{footnote} 5/6 5/3
4 2/5 5 D, 5 H 15/16 15/8
5 1/2 6 S, 6 A 1 2
6 3/5 5 D, 5 H 35/36 25/18
7 7/10 4 F+ 4 P% latex2html id marker 59744
\setcounter{footnote}{8}\fnsymbol{footnote} 95/98 55/49
8 4/5 3 F+ 3 P% latex2html id marker 59750
\setcounter{footnote}{8}\fnsymbol{footnote}125/128 65/64
1 S 15/16 5/8
9 9/10 2 D, 2 H 80/81 80/81
    % latex2html id marker 59761
\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 59765
\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 59780
\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 59784
\setcounter{footnote}{8}\fnsymbol{footnote}(a, b ) describes weighted average of high spin states, not a CSF.



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