Subject: CCL: TDHF

From: Ulrike Salzner <salzner^at^fen.bilkent.edu.tr>
Date: Wed, 25 Jun 2003 12:02:57 +0300

Many thanks to Stefan Grimme, Artem Masumov, and Doug Fox.

I asked whether it is possible to calculate and optimize the ground 
state of a system with TDHF. The answer is no. Like CIS, TDHF does not 
provide a correction to the ground state energy. More important I was 
warned that the TDHF geometry optimization for excited states in G98 is 
an approximation and should not be used. The option has been removed in G03.

One comment of mine to the statement that TDDFT is superior to TDHF: I 
am aware that TDDFT is quite successful in general. Unfortunately, the 
only excited state that is currently of interest to me (the 1Bu excited 
state of polyenes) is not well reproduced, especially with increasing 
size and conjugation length, which is exactly what I need to 
investigate. TDHF, in contrast, gives numbers similar to CASMP2. 
Therefore, it is bad news indeed that the geometries can not be 
optimized at this level of theory.

The original question and the answers follow below:

Hello,
> the time-dependent Hartree-Fock method is described as a method for
> calculating excited states. I would like to know whether one can also
> optimize the ground state including correlation with TDHF. In other
> words, if I use the keywords "fopt" and "nroot=0" in Gaussian what am I
> calculating? I know that CIS does not make a correction to the ground
> state because of Brillouin's theorem but I am not sure what TDHF
> includes exactly.  The reason why I am considering this is that I would
> like to compare the excitet state and the ground state geometries on
> equal footing. Would it be better to compare the excited state TDHF
> geometry to the HF ground state geometry?
> Thanks in advance,
> Ulrike Salzner

Dear Ulrike, 
in fact TDHF is not defined for the ground state but there is a close
analogy between CIS and TDHF (expanded in singles only,
CIS equations can be derived from the non-Hermitian TDHF
problem by neglecting the so-called B-matrix). 
>From that I would argue that the ground state analogue of TDHF is just HF.
Regards 
Stefan
_________________________________________________________
Prof. Dr. Stefan Grimme
Organisch-Chemisches Institut (Abt. Theoretische Chemie)
Westfaelische Wilhelms-Universitaet, Corrensstrasse 40
D-48149 Muenster, Tel (+49)-251-83 36512/33241/36515(Fax)

Ulrike,

Just like CIS, TDHF does not improve the ground state.
So correct comparison would be TDHF optimized excited state and HF
optimized ground state.

In fact, TDHF only differs from CIS in that it has nonzero V-O block in
hamiltonian (and thus, in transition density) matrix.

In g98 this block is missing from the routine evaluating gradients, so
excited state optimization with analytical gradients gives incorrect
(approximate) results. That is why in g03 this option is blocked. In
Turbomol TDHF opt. is coded fine.

To optimize the excited state at TDHF level you need to do Opt=Numer,
which is much slower.

Please keep in mind that TDHF is inferior to TDDFT at the same
computational cost.

Hope this helps,
Artem

________________________________________________________
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Dr. Salzner,

   G98/03 does not have gradients implement analytic gradients for
TDHF or TDDFT so optimizations need to be performed with only
energy values OPT=(EF,EnOnly) and a symbolic Z-matrix.  But it
can be done for medium to small systems.  Or at least a few degrees
of freedom.

   The TDHF and CIS methods both use the HF solution as the reference
and neither of them improve on the ground state description.

   In the sense that neither the Excited state or the Ground state
is really correlated it has been our experience that structures in
CIS are similar in quality to HF although often a slightly larger basis    
is needed.    To go beyond this you might want to consider SACCI
which is in G03 or CASSCF, both of which can include correlation,
dynamic vs. static, and treat ground and excited state on a equal
footing.