Two open shells

This becomes tricky in general and we give only the most important case:

shell 1

is a Roothaan case, see 6.3.2

shell 2

is one electron in an a (s) MO $(n_{ir}=1)$ mathend000#

with parallel spin coupling of shells.

This covers e.g. the $p^5\,s^1$ mathend000# $^3$ mathend000#P states, or the $d^4s^1$ mathend000# $^6$ mathend000#D states of atoms. The coupling information is given following the keyword $rohf. The ($a,b$ mathend000#) within a shell are taken from above (6.3.2), the cross term (shell 1)-(shell 2) is in this case:

$$a = 1$$

$$b = 2 \; n \le n_{ir} \qquad b = \frac{(2n_{ir})}{n} \; n > n_{ir}$$

where $n_{ir}$ mathend000# and $n$ mathend000# refer to shell 1.