# Molpro - Simple explanation of OCC, CORE, FROZEN and CLOSED orbitals

I'm beginning with quantum chemistry and I'm supposed to do some ab initio calculations with Molpro. The problem is, I don't understand the orbital specification very well.

Let's say, I have the following computation:

 {mrci;
occ,4,2,2,0,4,2,2,0;
core,1,0,0,0,1,0,0,0;
wf,13,5,1;
state,3;
option,nstati=5;
option,maxit=200;
option,maxiti=200;
}


I don't understand much the flags OCC, CORE, CLOSED and FROZEN. I've read about them in the documentation, but I have troubles understanding it. Moreover, they possess different meaning in different methods, i.e. MCSCF and MRCI.

Could you, please, explain it in a basic way and graphically, if possible? I'm not looking for the deep understanding of methods now (I'll study them later), but I need to be able to use Molpro for some simple (di/tri-atomic) systems.

In MCSCF we have:

• occ are occupied orbitals, it refers to all orbitals that may be occupied in any configuration. For a FCI calculation this equals the total number of orbitals (per IRREP). If occ is smaller than that, the difference will be the number of virtual (unoccupied) orbitals. Virtual orbitals are never occupied in all the configurations.

• closed orbitals are doubly occupied in all configurations. This means occ - closed equals the number of active orbitals. closed orbitals are optimized in an MCSCF calculation.

• frozen is similar to closed, but they are not optimized in MCSCF, i.e. their MO coefficients will be kept fixed.

In MRCI there are:

• occ and closed being similar to MCSCF. They are used to define the reference space of configurations.
• Multi-reference means additional external configurations are created by excitations from the reference space. Here excitations from closed orbitals are considered, but not from core orbitals. In other words: closed orbitals are only doubly occupied in the reference space but may have different occupations in the external configurations, while core orbitals are doubly occupied in both, the reference space and external configurations.
• frozen is not used here, as orbitals are not optimized anyway.

The "lower" set of orbitals is always included in the "higher" set, e.g. occ includes all closed. Thus we always have core/frozen <= closed <= occ <= total number of orbitals.

Here is a graphic for the MRCI case. The curved arrows to the left indicate considered (black) and neglected (red) external excitations into the virtual orbital space. For MCSCF replace core with frozen and ignore the curved arrows.

One more note: The picture shows only excitations into the virtual space. But in principle you could also have excitations from closed to active orbitals.

• Text only answer for now, I will try to make a graphic later. – Feodoran Oct 17 '18 at 10:50
• Great! Thank you very much! And I'll be grateful for the pictures. – Eenoku Oct 17 '18 at 10:53
• @Eenoku I added an orbital diagram to show the different orbital spaces. – Feodoran Oct 17 '18 at 14:41