# Problem with spin orbitals analysis and state identification

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Posted by Mariusz Radon on March 13, 2006 at 13:39:36:

Dear all,

I have a problem with natural and spin orbital analysis that give inconsistent interpretation of CASSCF results.

In my example natural orbitals and spin orbitals were extracted for each state from state-average RASSCF JOBIPH file using RASREAD. For some states it turns out that spin orbital carrying excessive spin corresponds wery well (by its shape) to natural orbital being almost doubly occupied, not to the one with single occupation. At the same time there is another natural orbital with occupation close to 1.0, but no similar spin-orbital exists with non-zero eigenvalue. So the distribution of spin (defined by spin orbitals) is clearly inconsistent with the distribution of unpaired electrons (defined by natural orbitals) -- unpaired electron does not hold spin density but electronic pair does! However, the spurious spin density distribution according to spin-orbitals agrees well with Mulliken spin populations from RASSCF.

This issue with spin analysis emerged from another problem: results for state-average of 3 states are clearly inconsistent with results for state-average of 2 states (within the same active space). This problem will be described below.

Tree states A,B,C are under consideration (states are selected by overlap with reference configurations using CISELECT option). The states of interest differ clearly in distribution of unpaired electrons, so I identify them looking at natural orbitals, spin orbitals and Mulliken spin populations.

The first calculation is the state-average of A and B. C was computed also but was not taken into average energy. The order of states was: A, B, C.

When the third state was added to state-average I obtain A', B' and C' which -- according to Mulliken spin populations and spin orbitals has the following correspondence to A, B, C:

A' -> A
B' -> C
C' -> B

Thus (by spin populations and spin orbitals) it seems that state B and C has changed their relative order. To verify this the overlap integrals were computed using RASSI and it turned out that actual correspondence is as follows:

A' -> A
B' -> B
C' -> C

because =0.9810, =0.924, =0.178, =-0.163, so it means that states B and C did not swap, only mixed a bit. The same states identification can be done by inspecting natural orbitals.

My question is how it can be possible that identification of states depends so much on the criteria applied. Moreover, the results of some analysis (natural vs. spin orbitals) seems to be in clear contadiction.

PS: the version of MOLCAS is 5.4, patch level 116

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