The M.O. occupancy during the SCF calculation can be defined in terms of doubly occupied, empty, and fractionally occupied M.O.s. By default, RHF SCF calculations are run using doubly occupied M.O.s, with, at most, one singly occupied M.O. For some systems, the symmetry of the M.O.s can be preserved only if two or more M.O.s have fractional occupancies. Such fractional occupancies can be defined using OPEN(n1,n2), where n1 = number of electrons in the open-shell manifold, and n2 = number of open-shell M.O.s; The ratio of n1 to n2 is restricted to 2 > n1/n2 > 0. Example: if OPEN(3,4)were used then the occupancy near the HOMO-LUMO gap would be ...2, 2, 2, 0.75, 0.75, 0.75, 0.75, 0, 0, 0, ...
The two p M.O.s in molecular oxygen would not be degenerate if a closed-shell SCF were run. In order to maintain the degeneracy, OPEN(2,2) would need to be used.
Do not use OPEN(n1,n2) for ground-state systems except for high symmetry systems with open shells, such as twisted (D2d) ethylene or molecular oxygen O2, or if there is a very small band-gap (such as in metal clusters).
Examples of OPEN(n1,n2) are given in the Table.
Notes:
Table:
Use of OPEN(n,m)|
Keywords |
Example |
Number of M.O.s |
No. of Electrons |
State |
|
OPEN(2,2) |
Twisted Ethylene |
2 |
2 |
3A2 |
|
OPEN(1,2) |
O2+ |
2 |
1 |
2Pg |
|
OPEN(5,3) |
CH4+ |
3 |
5 |
2T2 |
| OPEN(3,3) | [CrIIIF6]3- | 3 | 3 | 4A2g |
| OPEN(5,5) | [MnII(H2O)6]2+ | 5 | 5 | 6A1 |
| OPEN(5,3) | [FeIII(CN)6]3- | 3 | 5 | 2T2g |
OPEN(1,1) will be assumed for odd-electron systems unless an OPEN keyword is used. Errors introduced by use of fractional occupancy are automatically corrected [136] in a MECI calculation when OPEN(n1,n2) is used. See also C.I.=n.