converging Rydberg states in DFT

[vormar]

Dear All,

I'm trying to calculate converged TDDFT excitation energies up to 1-2 eV above the gap at the PWLDA level for simple organic molecules, eg. benzene. Though this sentence suggests that my post would be in a better place in "Escf and Egrad", I think that this is rather a problem of ground state calculations. It turns out that some of the unoccupied states not at all far away from LUMO are so much delocalized (mainly Rydberg states) that even augmented/Rydberg basis sets fail to correctly describe the shape of such orbitals, which results in an artifical 'confinement' so these states go up in energy even by several eV.

For example, I successfully used a d-aug-cc-pVQZ basis set, but the energies of the orbitals changed a lot compared to eg. aug-cc-pVTZ (of course, this is not unexpected, since the former contains more diffuse functions). Also, just by increasing the size of the basis set does not really help, since the SCF calculation fails to converge. Actually, in some of the cases it does converge but to an excited state of the system (negative HOMO-LUMO gap, since an unoccupied state ends up below HOMO).

I'm using a planewave basis set calculation as a test, and of course, there is another issue there: namely the size of the vacuum around the molecule should be enormous, still with only this parameter one may reach convergence for certain states at the expense of several day long calculations. But even without this test, energies coming from Turbomole calculations do not seem to be converged.

I have two closely connected questions regarding this issue.

1) Is there any accepted way to describe such really delocalized states in gaussian basis set calculations? I have been thinking about using ghost atoms with few diffuse basis functions on them somewhere around the molecule so that there is a larger flexibility in the orbital expansion. However, this is not really systematic. If there is an accepted way to that, how can one converge the SCF cycle without ending up with an artifical ground state?

2) Let's suppose I just keep on adding manually very diffuse states to the basis set. Since the basis set will become almost linearly dependent, the SCF will have troubles converging and it is also very time consuming, since one would diagonalize the full Hamiltonian though just the occupied states are of interest for the ground state.

Thus, it would be a very nice feature to have 'non self consistent calculations' in Turbomole: one would determine the ground state of the molecule with a small basis set (DZP-TZP, whatever) and then using the charge density of this system one would diagonalize the Hamiltonian expressed in the large basis set without being self consistent. That is, the charge density won't be updated anymore. This feature is implemented in planewave codes and it is an accepted way to calculate many unoccupied states when needed for spectral calculations. I know that this procedure is somewhat against the logique of quantum chemistry codes, but it would be nice to have something like this. Sorry, if this already exists and I just overlooked it.

As a last note, all these symptoms made me think that these orbitals just should not converge. Since many of these states are unbound, they just have infinite spread by definition... but then what is the meaning of calculating a TDDFT spectrum if all states above eg. LUMO+2 are resonance states in the continuum?

Thanks in advance for all comments and sorry for the long post.

Sincerely,
Marton Voros

[uwe]

Hi,

first of all, I'd use a reasonable functional for TDDFT like PBE or PBE0. You should not get any occupied positive orbital energies for benzene, no matter which basis function you are using.

1. negative HOMO-LUMO gap

  - did you use symmetry?

     if yes: try to reduce it
     if no: use $fermi or see next point

  - do you have degenerated orbitals around the gap?

    if yes: add $lastdiag to the control file and retry.
   

2. small basis set -> large basis set

There are a lot of things that could be written about linear dependent basis sets, but I just want to give some technical advise (or better: suggestions)...

The 'non self consistent' scheme you have described can be done by:

  a. run SCF with small basis set
  b. copy the files to a new directory, for example with
        cpc big
      cpc will copy the control file and all referenced files in there to a new directory called big
  c. run define, change basis set and go on to the molecular orbital menu
  d. in the MO menu of define, say:
       use ../control
      and accept all defaults. This will use the converged orbitals of the previous calculation and projects them to the new basis set.
  e. change the number of max. SCF iterations ($scfiterlimit) to 1
  f.  run dscf or ridft

I never tried running TDDFT on non-converged orbitals, and I assume that escf and egrad will perhaps not converge or report instabilities. But anyway, try it yourself:

  g. edit the mos file (or alpha and beta) and change
         scfdump=1
      which is the flag for non-converged MOs after 1 SCF cycle to
         scfconv=6
      to cheat the programs such that they assume to have converged mos.

  h. now run whatever you think you want to run on those projected orbitals.


I must admit that I am kind of curious if that works or not...

Regards,

Uwe

[vormar]

Hi Uwe,

Thanks for your comments and sorry for not answering earlier. Since I haven't really succeeded in solving the problem I just let the process run iny my head with low priority... Now I think I found a solution regarding my original problem. I report this, so it might be useful to other users as well.

Finally, in order to correctly describe Rydberg states I recalled that they almost transform as the irreducible representations of spherical symmetry in many electron systems. Thus, to have the (almost) spherical symmetry I put a ghost atom in the middle of the cluster with a basis set which contained only very diffuse basis functions (exponents with 10^-1-10^-2 or even lower). With this approach I could remove diffuse basis functions from other atoms, so not only the calculation became faster and easier to converge, diffuse Rydberg states are quite well described. I benchmarked the calculation with periodic plane-wave calculations, and there an insanely large cell size was needed to converge these delocalized states.

I must admit this approach may be well-known in the quantum chemistry community.

Regarding your recommendations:

1. negative HOMO-LUMO gap

I tried both options you mentioned, they didn't really work. I do use symmetry, but lowering it did not really help.

2. small basis set -> large basis set

Yes, this is exactly the procedure I tried -- unfortunately it didn't work. After projecting the old orbitals to the new ones, one scf iteration was not enough to get a reasonable electronic structure, it got totally messed up, and full convergence was needed. 

Marton