# Is it reasonable to use natural orbitals of an unrestricted HF calculation as a basis to start a CASSCF calculation for a radical

Let's say we want to run a CASSCF calculation of a radical, for example the cation of a neutral closed-shell molecule (therefore, we calculate an open-shell radical cation). MOLCAS, as well as probably every other program package out there, needs starting orbitals when performing a CASSCF calculation. For a neutral species, these are normally assumed to be the regular old Hartree-Fock orbitals. Usually, when dealing with a cation, it seems that the Hartree-Fock-SCF calculation is performed for the neutral species or the di-cationic species to yield the necessary HF starting-orbitals. They are in these cases the result of closed-shell calculations. MOLCAS also permits the use of a UHF calculation as the basis for a subsequent CASSCF calculation. Then, the natural orbitals of the unrestricted calculation are used.

Is the usage of the natural orbitals of an unrestricted HF calculation reasonable as a basis for a subsequent CASSCF calculation? If not, why? When is it a good idea / when is it a bad idea? What are the differences in using natural UHF orbitals in contrast to the SCF orbitals of the neutral or di-cationic species? What are the pitfalls?

Edit: I am aware (or at least it is my understanding) that conceptually it is no problem to perform the CASSCF using the natural UHF orbitals, as it could for example also be performed using only the alpha orbitals of the UHF calculation. My question is therefore aimed at finding out in which cases it is generally a good or bad idea to use the natural UHF orbitals.

The best starting orbitals for a CASSCF calculation are optimised orbitals of another CASSCF (or RASSCF) calculation. That sounds a bit ridiculous, but this is probably the best way to figure out the active space.

At first you are probably choosing something quite small, like CAS(2,2) to CAS(4,4). For these calculations it barely matters what kind of starting orbitals you are choosing. The change will be negligible and probably depending heavily on the system you are using.

The advantage of calculating the cations by dismissing the radicals is often a good choice since you can run a very fast RHF calculation and the orbitals are symmetric, which is what you need for CAS.
Natural orbitals of an UHF calculation are also a quite sensible choice, because they already allow for fractional occupation and should also be symmetric. The only downside I can think of is, that this kind of start orbital generation takes a lot longer.
Similarly you can choose to run a ROHF calculation, if you are uncomfortable with too much cationic charge.
As you have said you can choose also an UHF calculation by throwing away one set. I would advise caution here. Sometimes - probably especially when CAS is necessary - spin contamination in UHF is significant. Therefore one set might not give you anything close and you could end up choosing the wrong CAS.

I am not aware of any major pitfalls except for the just mentioned choosing of a completely wrong active space.

In any case it is a good idea to give the CASSCF calculation a few cycles and see how the active space is developing. Sometimes you need to adjust the active space long before the calculation converges and then you will have already a much better guess than with your initial starting orbitals.

I personally use the following routine

R(O)HF [x+] -> CAS(x, ⌈½x⌉ +1)
-> RAS(x+2n, ⌈½x⌉ +n +1)
-> CAS(x+2n, ⌈½x⌉ +n +1)
-> RAS(...)
-> CAS(...) -> ...


to narrow down the active space and include all orbitals I want and need. In most cases I am not converging the intermediate calculations, except for the minimal CAS.
As you can see the procedure that follows after your start orbitals is much™ more time consuming, so it really does not matter.

I can't tell you when a UHF reference wave-function would be a good idea (maybe if you don't have ROHF), but I think it might be a BAD idea if UHF generates a significantly spin-contaminated wave-function (UHF wave-functions are not eigenfunctions of S^2). Orbitals in your CASSCF active space will obviously be optimized, but the non-active occupied and external spaces will forever stay, in your case, UHF natural orbitals.

Two configuration MCSCF (TCSCF) is a tiny bit more expensive than UHF but results in S^2 eigenfunctions. Also, I have had luck with MP2 natural orbitals (RHF/ROHF reference).

• Are you entirely sure that using natural orbitals from a spin-contaminated UHF calculation will yield false results? Theoretically, all needed for CI calculations is a one-determinant-basis. This is then used for building CSFs (thereby assuring that they are eigenfunctions of S^2, no matter if the UHF-WF was, right?). Of course I agree with you that working with a severely spin-contaminated WF is probably a very bad idea. I am curious about the role of the CSFs when pluggin in spin-contaminated UHF natural orbitals. – mrnicegyu11 Mar 11 '17 at 15:56
• Even if you have spin contamination in your system, natural orbitals are symmetric and provide a reasonable guess. "Orbitals in your CASSCF active space will obviously be optimized, but the non-active occupied and external spaces will forever stay, in your case, UHF natural orbitals." This is just wrong. You still need reference orbitals for TCSCF, how would you compute these? For systems with a MR character, MP2 is unreliable, expensive, and you still need a reference WF. And what's the point in the first place, you are just doubling your effort. (cc @mrnicegyu11) – Martin - マーチン Mar 13 '17 at 5:09
• For example, UHF can result in 'artifactual symmetry-broken' states, that are artificially stabilized by nonphysical symmetry-breaking (geometric distortions, the Jahn-Teller effect). This means one could potentially be starting from the incorrect point group (a lower point-group). This would be a very bad guess and require much trudging through phase space to even just get back to the correct higher-order point group. – ab initio in silico Mar 14 '17 at 9:06
• You are right, MP2 natural orbitals for a small cas is probably a waste but I am intretsed in MRCI wavefunctions. – ab initio in silico Mar 14 '17 at 9:09
• I'd like to hear if @Martin-マーチン agrees. I am aware of symmetry breaking in UHF calculations, but is this an issue for natural orbitals? – mrnicegyu11 Mar 16 '17 at 13:38