Subject: CCL: Summary on DFT and Mott insulators

From: "Artem R. Oganov" <[email-masked]>
Date: Tue, 13 Mar 2001 18:19:35 -0000

Dear CCLers,
Many thanks to those who have replied to my question (see the original
question in the end of this e-mail). Here I give a summary of what the
situation seems to be like with Mott insulators and their DFT description -
both from the CCL replies and answers of my other colleagues.
The Kohn-Sham eigenvalues and DOS don't have any strict physical meaning.
The absence of the band gap in this unphysical DOS does not necessarily mean
that the material is a metal; generally, band theory (even not at the
LDA/GGA level) often gives zero band gaps for insulators. More rigorous
approaches are based on considerations in the momentum space. These might
enable the calculation of the electrical conductivity. Another possibility
is the Green's function formalism.
Yet, as practice shows, the Kohn-Sham orbitals resemble the more physical
Hartree-Fock orbitals; they often can be rationalised using the language of
chemistry. They are not completely unphysical. If we trust the Kohn-Sham
orbiatls and their energies, the band gaps obtained with LDA/GGA are usually
twice smaller than the experimental values; for Mott insulators LDA/GGA give
zero or very small band gaps (~0.4 eV) while experiments give gaps ~4 eV. If
we use B3LYP, the band gap comes out to be almost perfect, but physical
properties become worse. Exchange potential is particularly important for
the band gap. Spurious self-interaction, raising the energy of the occupied
levels, is partly responsible for the band gap being reduced. GGA describes
the properties rather well, but fails to give a band gap for FeO and gives
very small gaps for other transition metal oxides.
So far, GGA and B3LYP, though not perfect, are the best methods for Mott
insulators. Quantum Monte Carlo has a good potential of describing such
systems.
Below is the only reply I have got and the original question:

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Hello,
1) The band gap problem for solids in DFT is closely related to the
HOMO-LUMO gap problem for molecule. We had a recent discussion
about the latter problem on CCL, that you could easily retrieved
for the archives.
For molecule, hybrid functional (combining HF exchange and pure
DFT) yields much better orbital gap than pure DFT. I don't know
if these functionals are implemented in the "solid state" package.
2) there is an error ! It is a large as the real band gap !
3) I don't know, but a library search could gives you the answer...
4) HF gives band gap for the free electron case because of
"self-interaction" term. I think that HF will provide to large
band gap, then to low electrical conductivity etc..At least,
that's a good starting point.

...Xav
WARNING! NEW E-MAIL ADDRESS !
(u-nancy changed to uhp-nancy)
Ast. Pr. Xavier Assfeld [email-masked]
Laboratoire de Chimie theorique (T) 33 3 83 91 21 49
Universite Henri Poincare (F) 33 3 83 91 25 30
F-54506 Nancy BP 239 http://www.lctn.uhp-nancy.fr
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-----Original Message-----
From: Computational Chemistry List [mailto: ]On Behalf Of Artem R. Oganov
Sent: 25 February 2001 10:45 PM
To: CHEMISTRY
Subject: CCL:Mott insulators and DFT

Dear CCLers,
I have the following question:
It is known that DFT within the LDA and GGA gives no band gap for such
transition metal oxides as FeO, CoO, NiO, which in fact are insulators (Mott
insulators). Are there any ideas about how serious this error is?
I suspect that there may be no real error: I understand that Kohn-Sham
eigenvalues and electronic density of states are, strictly speaking,
meaningless. Therefore, the absence of a band gap does not mean anything -
even more it does not mean that the material is a metal. There might be
other, more rigorous, ways to calculate the electrical conductivity from
DFT - but I am not aware of any such work. On the other hand, GGA and LDA
are known to reproduce many properties (elastic constants, equation of
state, magnetic ordering, magnetic moments) of these oxides really well - at
nearly the same level as they reproduce the properties, e.g., of MgO or
NaCl.
I would like to hear your ideas on:
1. The applicability of LDA/GGA to Mott insulators: can we use DFT at all,
what we can and what we cannot calculate.
2. If there is any error at all, how serious it is.
3. How to calculate the electrical conductivity from DFT. Were such
calculations done for any of the Mott insulators?
4. What is the best way of treating Mott insulators, especially at high
pressures? LDA+U seems to be not too reliable at high pressures.
Hartree-Fock would definitely give a band gap - but it gives it even for the
free electron case! What else does exist?
I will summarise the replies on request.
Cheers,
Artem R. Oganov
-----------------------------------------------------
Artem R. Oganov
Department of Geological Sciences
University College London
Gower Street
London WC1E 6BT
tel: +44 (020)-7679-3344
fax: +44 (020)-7387-1612
email: [email-masked]
http://slamdunk.geol.ucl.ac.uk/~artem
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