CFOUR | Main / Symmetry Types

The post-SCF program modules of CFOUR assign an integer value to specific binary combinations of orbital types (occupied or virtual; {$\alpha$} or {$\beta$}) which is then used to determine symmetry information (see, for example, the description of the SYMPOP common block). A complete listing of the assignments for these values is given below

Symmetry Number	Distribution Type
1	{$a < b$}
2	{${\bar a}<{\bar b}$}
3	{$i< j$}
4	{${\bar i < \bar j}$}
5	{$a\leq b$}
6	{${\bar a}\leq {\bar b}$}
7	{$i\leq j$}
8	{${\bar i}\leq {\bar j}$}
9	{$ai$}
10	{${\bar a}{\bar i} $}
11	{$a{\bar i}$}
12	{${\bar a } i $}
13	{$ a {\bar b} $}
14	{$ i {\bar j} $}
15	{$ a {\bar b} $}
16	{$ ia $}
17	{$ {\bar i}{\bar a} $}
18	{$ i{\bar a} $}
19	{$ab$}
20	{$ {\bar a}{\bar b} $}
21	{$ ij $}
22	{${\bar i}{\bar j}$}

Note that entries 13 and 15 are identical, which is simply a result of carelessness in the initial coding. Although not all possible combinations are given, these are the only combinations which are used in the distributions which make up the integral lists.