Broken-Symmetry DFT calculations in Metal Complexes.

[arturosauza]

Hello Turbomole community!

Right now, I am working with a Ce(III) complex with four ligands. My intention is to compute reduction potentials for such a complex.

The neutral molecule has a doublet spin state. When reducing the molecule, I want to test three scenarios:

• When reducing the molecule, I obtain a triplet state where the unpaired electron in the Ce center has a ferromagnetic coupling with the added electron (which is delocalized in the ligands). 
• The reduced molecule is an open-shell singlet with antiferromagnetic coupling between the unpaired electron in the Ce atom and the electron delocalized in the ligands. 
• The resulting reduced molecule has a closed-shell singlet state with a Ce(II) center having a 4f^2 configuration. 

I already computed the first two points with unrestricted DFT calculations. However, I don't know how to compute the third option with broken-symmetry DFT, enforcing the two electrons to be localized in the metal center.

Is there any way to do this in Turbomole?

Thanks in advance for your time and help.

Arturo.

PS. (I have available Turbomole 7.8 and 8.0).

[turbomaster]

Hi Arturo,

Yes, you can try to prepare such a state in TURBOMOLE by manually changing the orbital occupations. This is essentially a Delta-SCF calculation: you start the SCF with the electronic configuration you want instead of the normal Aufbau configuration.

First I would converge the reduced molecule in a normal unrestricted calculation. Then inspect the orbitals and identify which virtual orbital has the Ce 4f character that you want to occupy. It is useful to do this in C1 symmetry, because then the orbital numbering is particularly simple.

Make a copy of the converged calculation and edit the occupations in the control file. For a UHF calculation TURBOMOLE uses

$uhf
$alpha shells ...
$beta shells  ...

For example, if orbital 100 is the normal highest occupied alpha orbital, orbital 101 is ligand-centered, and orbital 102 is the Ce 4f orbital you want to occupy, you can use an occupation such as

$uhf
$alpha shells 1-100,102 ( 1 )
$beta shells  1-100     ( 1 )

This creates a triplet-like Ce(II) 4f2 starting configuration while leaving orbital 101 empty. Of course, the actual orbital numbers have to be taken from your calculation. The TURBOMOLE manual explicitly allows arbitrary alpha and beta occupations in this way; the same occupations can also be prepared interactively in define using the a and b commands.

I would also add
$scfdamp start=5.000 step=0.050 min=0.500
$scforbitalshift automatic=1.0
$scfiterlimit 999

at least for obtaining the initial solution. Interestingly, these are exactly the settings recommended in the TURBOMOLE manual when preparing difficult broken-symmetry states, because strong damping and orbital shifting help to prevent the prepared state from being destroyed during the first SCF iterations.

In TURBOMOLE 8.0 you can additionally try

$mom on

which activates the Maximum Overlap Method. MOM tries to retain a state that has maximum orbital overlap with the previous iteration, rather than simply following the energetically lowest orbitals. This can therefore be useful for keeping the Ce-centered 4f orbital occupied instead of allowing the electron to fall back into a lower ligand orbital. A TURBOMOLE developer describes $mom in exactly this way, although he also points out that excited-state SCF convergence is not always straightforward.

After convergence, it is essential to check whether you really obtained Ce(II) 4f2 and not the Ce(III)-ligand-radical solution again. The TURBOMOLE manual recommends checking this with population analysis. You can add

$pop

and run

ridft -proper

(or dscf -proper if you are using dscf). You should also plot the relevant orbitals and inspect the spin density.

One important point, however: Ce(II) 4f2 is not normally a closed-shell configuration. I would first try the triplet with two alpha electrons in two different Ce 4f orbitals. If you want an S = 0 4f2 state with the electrons in two different 4f orbitals, you would instead prepare one Ce 4f orbital in the alpha set and the other in the beta set. That would be a broken-symmetry open-shell singlet, not a conventional closed-shell singlet.

So yes, TURBOMOLE can technically do what you want. I would use manual $alpha shells/$beta shells occupations, strong initial damping/orbital shifting, and possibly $mom on, and then carefully verify that the converged solution still has the desired Ce-centered 4f2 occupation.

Best wishes

Marek

[arturosauza]

Thank you so much! I will try to follow your instructions, and I'll let you know the result.


Best,