Subject: SUMMARY: g98: excited state densities via TDDFT ?

From: Johannes Weber <[email-masked]>
Date: Wed, 21 Aug 2002 10:02:22 +0200 (MET DST)

Dear CCL members, 

a week ago I posted a question concerning excited state densities via the
TDDFT method in g98. Thanks to Doug Fox, Peter W. Thulstrup, Kiniu
Wong and Jens Spanget-Larsen for answers! Here is the
summary (detailed answers are collected below): 

The output after "Total CI Rho(1) Density" gives the density of the
excited state X which was specified in the route section with TD(Root=X). 
However, this is the "unrelaxed" density, i.e. a more or less crude
approximation, see the paper of Wiberg et al, JPC 96, 671 (1992) and Dougs
mail.  Therefore, the numbers cannot be considered as very reliable.  They
should (hopefully) show the correct trend in most cases, however.

Despite of the fact that it is technically possible to calculate the
densities in the KS-formalism, it still remains unclear to me, if this can
be justified from a theoretical point of view. The transition density is a
quantity between two different electronic states. Two wavefunctions are
needed for its calculation. DFT is, in general, restricted to a single
state (ground state) and a wavefunction does formally not exist. 

with kind regards, :-)ohannes.

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The original question was :
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Dear CCL members,   

I have a general question:

Is it possible to calculate electron densities of excited states
and/or excited state spin densities 
and/or transition densities with the TDDFT method ?

With respect to the TDDFT implementation in g98 this general question
splits up into several concrete questions:   

Which density (ground state or excited state) will be written to the
checkpoint file if I specify the DENSITY keyword in the route section
together with TD(Root=1) ? -- 
The g98 manual is not very explicit about this point.  If I look at the
formatted checkpoint file I find two densities, named the "Total SCF
Density" and "Total CI Rho(1) Density". What densities are given here? 
I was not able to extract the Total CI Rho(1) Density with the cubegen
utility. Is this possible? 

Thanks in advance for all answers. If there is interest I will summarize
them, of course.

With kind regards, :-)ohannes
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reply of Doug Fox:
=====================================================================
  Dr. Weber,

   Gaussian 98 does not properly deliver densities for excited
states using the TD-DFT methods.  So if you specify DENSITY you
should get an error message.  The manual incorrectly suggests that
this combination is valid and it is on the wish list but won't
be there in G98.

   The issue is that to get reliable properties, density, dipole,
gradients, frequencies, you need to do better than just a first
order density matrix and need to consider the change in the 
HF density due to the excitation.  This is solved in the CIS
method with a small CPCI step but the corresponding code is not
implemented for TDDFT or TDHF.  

  The field labeled Total CI Rho(1) is a density formed from the
weights of the excited KS determinants.  The proper CI density
would be labeled Total CI Density and it would correspond to the
root specified on the route, i.e. CIS(Root=2) Density would compute the
correction using the second root of the CIS, use that density for
properties listed in the output and store that density as the
Total CI Density if you make a formatted checkpoint file.

   There is no easy way to recover the CI Rho(1) but if you modify
the formatted checkpoint file and shorten this to Total CI Density
cubegen will pick it up.
=====================================================================

reply of Peter Waaben Thulstrup:
=====================================================================
Dear Johannes,

I have asked a similar question to the help at Gaussian. I got a reply
> from Doug Fox, included (in part) below:

>  Peter,
>
>   The problem with assigning spin for excited states starting from
>   an open shell system is not a solved problem.  Since the UHF or UDFT
>   reference will generally be spin contaminated it is not easy to sort
>   out the spin.  From an RHF reference the sign flips between alpha and
>   beta components but there is no simple relation for the spin
>   unrestricted reference.
>...
>   The Density options for TDDFT are not correct for Rev. A.7 and we have
>   actually turned them off with A.11 because at present even the one
>   particle RhoCI type density is not correct.  It is on the list of
>   things to do right but we lost the person who was going to do it to an
>   academic position and they have not surfaced from trying to set up a
>   group/lab etc.  So in short I would not put any credence in trying to
>   analyze the densities reported there.

So, unfortunately bad news. 
==========================================================================

reply of Kiniu Wong:
==========================================================================
Dear Johannes,

    I also have the same problem about TDDFT.  For TDHF and CIS, I am able
to generate the excited state density by either "Density = CI" or
"Density=Current".  However, for TDDFT, if I specify "Density = CI", it
shows the error.  But "Density = Current", the density is just SCF (ground
state). 

    Moreover, "Density = RhoCI" and "Density(CIS=1)" work properly for
TDDFT, TDHF as well as CIS.  Although I am not so sure what do they mean
or what is the difference between them and "Density = CI" or "Density =
Current", however, from Chapter 9 Exploring Chemistry with Electronic
Structure Methods, they don't prefer "Density = RhoCI" and
"Density(CIS=1)". 

    Anyway, if there are any useful or interesting replies, may you
forward them to me as well?  Thanks! 

Regards,
Kiniu

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| Johannes Weber                    | Email:                        |
| Universitaet zu Koeln             | [email-masked]   |
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