From:	Anik Peeters <anik()at()uia.ua.ac.be>
Date:	Tue, 23 Feb 1999 17:03:26 +0100 (MET)
Subject:	SUMMARY: colour of molecules in the solid state (fwd)

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My original question:

I am studying molecular crystals using the supermolecule approach:
a cluster of 10-15 molecules is described by the wave function
and this cluster is surrounded by point charges simulating the other
neighbours. The level of theory we are using is Hartree-Fock.

The molecule I am studying right now has been observed in three different
polymorphic forms. One has a white colour, another one is yellow and a
third one is light yellow. I have been trying to relate the yellow and
light yellow colour to the band gap between the HOMO and LUMO. However,
the energy differences I obtained are too large.

I was wondering whether there exists a cheap method (because of the size
of the system) to get a better approximation of the band gap.

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Summary:

Most people suggest to use semi-empirical methods since they are
better than Hartree-Fock in estimating the band gap.
Other suggestions include the use of a larger basis set (impossible due
to the size of my system), the use of pseudopotentials, the use of
different boundary conditions, the use of DFT and the inclusion of
excited states.

Many thanks to
Benoit Champagne, Sergio Emanuel Galembeck, Christos Garoufalis,
Richard Wheatley, Stefan Konietzny, Ernest Chamot, Jerry Perlstein,
Artem Masunov, Andres Aguado and Viorel Chihaia

Anik.
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The answers:

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From: Benoit Champagne 

The best method for such big clusters should be of
semi-empirical type like the famous ZINDO.

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From: Sergio Emanuel Galembeck 

    In my opinion the best method for study electronic
spectra of large systems is INDO 1/S. This method
reproduces very well experimental spectra for
organic compounds and it is to use point charges.
A nice implementation of this method is ArgusLab
1.0. You can found this program in:

http://www.seanet.com/~mthompson/ArgusLab/index.htm

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From: Christos Garoufalis 

It almost always happens that HF is overestimating the HOMO-LUMO gap.
in my opinion, it is preferable to use some other method for this type of
calculation
DFT will certainly give smaller gap values, but it depends stronly on the used
functional. B3-LYP is a good choise.
Even semiempirical methods such as AM1 or MNDO will give you better results.
It should also be kept in mind the if you want to the calculate the absorption
spectrum the Hartree-Fock level (i.e. the energy differences of the occupied and
unoccupied orbitals) is sufficient. In this case C.I. singlets calculation is
commonly used.

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From: Richard Wheatley 

Hello!  If you look at my paper in Chem Phys Letts 294, 487 (1998) you
will find a way to reduce your calculation to a monomer calculation,
including a pseudopotential representing the surroundings.  This is
approximate but seems to work quite well, and allows better than
Hartree-Fock accuracy.  Incidentally, you didn't say whether your method
is UHF, CIS or CHF.  I assume it's UHF; this will certainly overestimate
the band gap!

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From: Stefan Konietzny 

for my understanding the energy of a LUMO from a HF calculation is not
reliable, because the virtuals are not optimized. I think you have to
calculate the excited state to get a reliable result. If you are using
GAUSSIAN then have a look at the CIS keyword.

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From: Ernest Chamot 

Short of modeling the system with periodic boundary conditions, your
approach seems reasonable:

You didn't say whether you are using ab initio or semiempirical HF methods.
If you are doing ab initio calculations and aren't using diffuse functions
in your basis set, then I strongly suggest that you include them.  In my
experience you just can't model intermolecular interactions without them,
and they must be important here in order for there to be a difference
between polymorphs.  (But I assume you've already thought of this.)  Of
course, this would be a pretty big calculation!  Have you considered using
periodic boundary conditions, and/or DFT?

If you are using semiempirical HF methods, I would recommend using Zerner's
INDO/S Hamiltonian, as it has been specifically parameterized for
predicting electronic spectra.  Although you probably want to optimize the
geometry with a different method, and just use INDO/S for the spectrum
calculation.  The drawback with this is that the semiempirical methods are
based on minimal basis sets (ie. no diffuse functions), so they have a
problem with intermolecular interactions.

In either case, however, the crucial thing is to include some level of CI
in your calculation.  If you don't, the unoccupied orbitals don't get
calculated very well, and your band gap will be off.  I would expect this
to be the major reason that:

>I have been trying to relate the yellow and
>light yellow colour to the band gap between the HOMO and LUMO. However,
>the energy differences I obtained are too large.

(All this assumes your system really is "molecules."  If it is at all
"metallic" or ionic, there will be a BIG surface effect, even with larger
"clusters".)

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From: Jerry Perlstein 

Anik- I doubt whether the "band gap" has anything to do with the colors
you observe. More likely they are either charge transfer transitions or
possibly Davydov splittings of the exciton states.
Before you do anything fancy why don't you visually looked at the
structures to see if there are any molecular interactions which would
suggest charge transfer transitions?

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From: Artem Masunov 

On Thu, 11 Feb 1999, Jerry Perlstein wrote:
> Before you do anything fancy why don't you visually looked at the
> structures to see if there are any molecular interactions which would
> suggest charge transfer transitions?

 I wonder what kind of interactions in homomolecular crystals (except
conventional pi-pi stacking) could be considered as charge transfer?
Are there CT spectra for sigma-interactions?
 I would appreciate if Jerry Perlstein (and all CCLers) give me some
references for the examples and interpretations.

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From: Andres Aguado 

I have seen your message in the CCL. It is a well known result that HOMO-LUMO
differences in a Hartree-Fock approximation lead to too large band gaps. The
main problem is not Hartree-Fock theory, but the HOMO-LUMO approach. It gives
you the band gap energy without including electronic relaxation of the
excited state. You could obtain much better band gaps even within Hartree-Fock
by performing a separate self-consistent calculation for the excited state,
annd taking a difference between both total energies of the system (excited and
ground state). This does not involve any new geometry optimization, because
the transition is vertical in the Franck-Condon sense.

Anyway, inclusion of correlation is crucial in order to obtain quantitavely
accurate results. It changes the magnitude of the gap by approximately 1--3
eV.

We have recently studied this problem for the case of typical ionic insulating
crystals. This is the reference:
Title: Calculation of the band gap energy of ionic crystals
Authors: A. Aguado et al.
Ref: Rev. Mex. Fis. 44, 550 (1998).

It is not a well-known journal and I do not know if you can have it. I could
send to you a copy if you are interested.

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From: Viorel Chihaia 

Firstly I bag you pardon for my bad English.

If you try to simulate the molecular crystal I don't use point charges
for the rest of the crystal. The correct way to simulate these systems
it is to use a periodic condition for the boundary or periodical (like
solid state calculation). The cluster method can be used in case of some
defects in the molecular crystal.  For this you grow the cluster size
until you obtaine for the interest properties, the convergence. If you
want to simulate some dynamical phenomena you must include your cluster in
a clasical field for the rest of crystal.
On the other hand the Hartree - Fock calculation fail in the reproduction
of the limites for valence band and conduction band. Since you are
interested for this values you must use the periodic calculation. I have
the CRYSTAL 95 program and if you want to have a idea for the diferences I
can help you.




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