One Open Shell

Given are term symbols (up to indices depending on actual case and group) and $a$ mathend000# and $b$ mathend000# coefficients. $n$ mathend000# is the number of electrons in an irrep with degeneracy $n_{ir}$ mathend000#. Note that not all cases are Roothaan cases.

All single electron cases are described by:

$a = b = 0$ mathend000#

$$n_{ir} \pi \delta C_{\infty v} D_{\infty h}$$

$$n f ^n \pi^n \delta^n a b$$

$$^3 ^3\Sigma ^3\Sigma$$ 1 2

$$1/2 ^1 ^1\Delta ^1\Gamma 1/2$$ 2 0

$$^1 ^1\Sigma ^1\Sigma -$$ 0

$$3/4 ^2 ^2\Pi ^2\Delta 8/9 8/9$$ 3

$$n_{ir} T O I$$

$$n f ^n a b$$

$$^3 3/4 3/2$$

$$1/3 ^1 9/20 - 3/10$$ 2

$$^1 - 3$$ 0

$$^4$$ 1 2

$$1/2 ^2 4/5 4/5$$ 3

$$^2 2/3$$ 0

$$^3 15/16 9/8$$

$$2/3 ^1 69/80 27/40$$ 4

$$^1 3/4$$ 0

$$5/6 ^2 24/25 24/25$$ 5

$$I$$ (mainly high spin available)

$$n f ^n a b$$

$$1/8 ^2$$ 1 0 mathend000# 0 mathend000#

$$1/4 2/3 4/3$$ 2

$$^1 - 4$$ 0 mathend000#

$$3/8 ^4 8/9 16/9$$ 3

$$1/2 ^5 1 2$$ 4

$$5/8 ^4 24/25 32/25$$ 5

$$3/4 26/27 28/27$$ 6

$$^1 8/9 4/9$$

$$7/8 ^2 48/49 48/49$$ 7

$$I$$ (mainly high-spin cases work)

$$n f ^n a b$$

$$1/10 ^2$$ 1 0 mathend000# 0 mathend000#

$$1/5 ^3 + ^3 5/8 5/4$$ 2

$$^1 - 5$$ 0 mathend000#

$$3/10 ^4 + ^4 5/6 5/3$$ 3

$$2/5 ^5 ^5 15/16 15/8$$ 4

$$1/2 ^6 ^6 1 2$$ 5

$$3/5 ^5 ^5 35/36 25/18$$ 6

$$7/10 ^4 + ^4 95/98 55/49$$ 7

$$4/5 ^3 + ^3 125/128 65/64$$ 8

$$^1 15/16 5/8$$

$$9/10 ^2 ^2 80/81 80/81$$ 9

$$D_{2d} D_{4h} \rm e^2$$

$$^n T_d \rightarrow T O I \rightarrow T O I \rightarrow I T O$$

$$T O a,b$$

$$a,b$$