Subject: summary: TDDFT - MO's

From: [email-masked]
Date: Mon, 15 Oct 2001 09:21:41 +0200

Dear CCL'ers,

as promised I will give a summary of the comments I received. From work of
Baerends and Gritsenko
it seems that :" "The Kohn-Sham orbitals are physically
sound and may be expected to be more suitable for use in qualitative
molecular orbital theory than either Hartree-Fock or semiempirical
orbitals". And even the linear combinations of these DFT MO's, which are
needed to describe the electron excitations, are claimed to give quite
good results.
Another suggestion was the use of "Natural Transition Orbitals", i.e., to
diagonalize independeently the sets of occupied and virtual MO's.

______________________________________________________________________________
JENS SPANGET-LARSEN:

I am not quite sure that I really understand your question. What do
you mean by "real AO's"? And do you consider AO's and MO's as basis
functions? - But maybe you will find some answers in the following
publications:

E.J. Baerends, O.V. Gritsenko: "A Quantum Chemical View of Density
Functional Theory", J. Phys. Chem. A 101, 5383-5403 (1997)

R. Stowasser, R. Hoffmann: "What Do the Kohn-Sham Orbitals and
Eigenvalues Mean", J. Am. Chem. Soc. 121, 3414-3420 (1999).

P. Bour: "Configuration interaction with Kohn-Sham orbitals and their
relation to excited electronic states", Chem. Phys. Letters 345,
331-337 (2001)

Baerends and Gritsenko state: "The Kohn-Sham orbitals are physically
sound and may be expected to be more suitable for use in qualitative
molecular orbital theory than either Hartree-Fock or semiempirical
orbitals". This point of view is supported by Stowasser and Hoffmann:
" - these seem to be the orbitals a qualitative, chemical analysis
needs". Bour finds that a ".. Slater determinant with the KS orbitals
is more suitable for construction of electronic states" [than a
Slater determinant based on HF orbitals].

Yours, Jens >--<
_____________________________________________________________________________________
Fedor Goumans:

Dear Mr. Goeller,

The 'physical interpration' of KS-MOs has been much debated indeed. As argued by
Baerends and Gritsenko (J. Phys. Chem. A, 101, 5383), the KS-orbitals may be
even more suitable for qualitave MO theory as they include correlation effects
inherently because the Hamiltonian already incorporates them through the Vxc.
Assuming this being so, the KS-orbital picture should be applicable to TD-DFT as
well.
 From the TD-DFT output it is already apparent that the classical one-orbital
excitation picture is incorrect: the one-electron excitation is not to a pure
virtual orbital but to a state which is a linear combination of those. Analysis
of the photochemistry based on the composition of the KS-orbitals for the
1-electron excitations have been applied in the following articles:
J.Phys.Chem.A, 103, 6835
J.Am.Chem.Soc., 121, 10356
 From the same authors a number of studies using Ziegler's Delta-SCF method for
calculation of the excited state surfaces have also been published.
I hope this helps,
Kind regards,
Fedor Goumans
___________________________________________________________________________
Geoff Hutchison:

> can we then really interpret these orbitals as the ones from and to
> which electrons are excited? Is this model stable and can it be
> interpreted photochemically? I am not aware of any publication dealing
> with this.

Dr. Richard Martin of Los Alamos National Lab gave a talk on this subject
at a conference there this summer. He called these "Natural Transition
Orbitals" and said while he wasn't sure it hadn't already been done, he
was thinking of writing it up.

In short, he defined new orbitals, the occupied orbitals by T(T+) and the
virtual orbitals by (T+)T--diagonalizing each set.

I don't know how good an explanation that is, but it didn't seem to hard
and he seemed willing to share the method.

--
-Geoff Hutchison                <[email-masked]>
Marks/Ratner Groups             (847) 491-3295
Northwestern Chemistry          <http://www.chem.nwu.edu>
___________________________________________________________________________
Stefan Grimme:

Dear Andreas,
If you interpret the KS orbitals as solutions to some
mean-field eigenvalue equation with an effective (XC)-potential
and use them as "MOs" in the usual sense, its also valid
to interpret the "excitations" from TDDFT in the usual manner,
i.e. for bonding/anti-bonding discussions and so on. My main
argument for this is that the TDDFT properties like oscillator
strengths are calculated exactly as in TDHF e.g. by taking
the transition densities and multiply with the one-electron integrals
over the KS orbitals. However, in practice I strongly recommend to
restrict all of these discussions to KS orbitals with negative
eigenvalues (bound one-particle states) because everything else
suffers from the wrong asymtotic behaviour of most functionals used
(take e.g. a Neon atom with a basis set containg a large number of the
proper Rydberg functions and calculated the 2p-ns Rydberg series:
everything except the first one is garbage showing not the correct
series behaviour for e.g. <r>, <r^2> expectation values).
Stefan

Prof. Dr. Stefan Grimme
_______________________________________________________________________________
Hi,

> There is a lot of discussion if the basis set (which even in HF theory is only
a
> model for the real AO's), which
> represents the real electron density of the whole state, can be used for
> interpretation as MO's.

I thought it could NOT

Cordially,
George
_________________________________________________________________________________