Subject: CCL: question about CIS excited states calculation

From: "Mark Thompson" <mark-.at.-arguslab.com>
Date: Tue, 30 Sep 2003 16:37:14 -0700

Jeny,

The answer depends on the type of Hamiltonian you are using.  Since you also
posted this to the ArgusLab users group, I'll limit my answer to the
semi-empirical ZINDO method.

Zerner and coworkers parameterized ZINDO to reproduce low-energy singlet
excitations for organic systems containing pi-electrons.  The size of the CI
they used for small (e.g. benzene) molecules was generally ~10 occupied into
~10 virtual MOs for the CI active space. Even then, ZINDO is really only
accurate to within ~700 cm-1 - 1000 cm-1 with experiment.  As Jens
Spanget-Larsen noted, the formula for the two-electron integrals and other
parameters used to get the ZINDO ground state compensate somewhat for the
limitation of singles-only excited configurations.  For porphyrins,
bacteriochlorophylls, etc, I've used CI expansions of the order of 20 x 20
and obtained good results.

It is critical that you include all the "important" orbitals for the excited
states you want to study.  For example, the pi-pi* spectra for benzene: you
want to make sure to include the 6 pi-orbitals.  Don't split groups of
symmetry related orbitals: if you do, the excited states will have the wrong
energy splittings and relative intensities (for porphyrins you want to
include all of Gouterman's 4-pi orbitals, at the least, or you'll never get
the relative intensities of the Qy and Qx states correct).  For transition
metal systems, like ferrocene or metallo-porphyrins, you'll want to make
sure to include all the MOs that are dominated by the metal d-orbitals (or
you'll never see the d->d*, d->ligand*, and ligand->d* excitated states).

I disagree with John McKelvey's recommendation to use all single-excited
configurations.  Simple variational degrees of freedom may depress your
low-lying excited states as you make the CI expansion larger, and give the
impression of higher accuracy.  However, when one includes a single-excited
configuration that is 130,000 cm-1 in energy, why not also include double or
triple-excitations of lower energy?  Are they not perhaps more imporant to
the final result?  Its probably best to keep with as modest a CI expansion
as possible with the caveat of including all the "important" orbitals.
Zerner recommended including all single excited configurations up to an
energy of ~75,000 cm-1.  Anything above that and double-excitations start to
become important (doubles generally start to appear at ~85,000 cm-1 for
small to medium sized organic systems like benzene, etc).

Its important to remember that ZINDO has traditionally been a qualitative
tool.  It's parameterization was never rigorously refined like Jimmy
Stewart's PM3.  There are no well-defined error bars on the ZINDO method.
However, ZINDO has proven enormously useful over the years and has been
extended to include: excited states with double- and triple-excited
configurations, solvent effects, transition metal system, polarizabilities,
hyperpolarizabilities, etc.  ZINDO has also been used successfully with the
RPA treatment for excitations even though it was never parameterized for
that approach.  ZINDO-RPA describes the low-energy excited states of the
bacteriochlorophyll-b dimer from Rps. viridis reaction center quite well and
gets the correct sign for the rotational strength.

When studying a new molecule, I generally do a ZINDO SCF first and look at
the energies of the MOs.  I make sure that any CI expansion I use will not
split orbitals that are symmetry related or even those that are very close
in energy.  If there are any metals present, I try to identify the MOs that
represent the metal's valence shell. I generally start with a 10x10 CI and
ask ArgusLab to print the CI Hamiltonian matrix: which causes the energies
of the pure configurations to be output to the .out file as well.  This
allows me to examine the energies of the pure configurations.  You should
make sure you are consistent.  If you are studying a series of substituted
benzenes of similar size, a consistent treatment of the CI expansion across
the series is more imporant than fine-tuning the CI expansion for each
molecule.

The quickest off-the-cuff answer is to generally do all single-excitations
> from the highest 10 occupied into the lowest 10 virtual MOs for molecules of
the size of benzene and up to perhaps porphyrins.  Large chromophore arrays
(like the photosynthetic reaction center) or fullerenes would require a
larger CI expansion.

If you have any examples of molecules you are studying, please feel free to
send them to me and I'll take a look.

Mark

***************************
Mark Thompson, PhD
Planaria Software LLC
PO Box 55207
Seattle, WA  98155

mark-.at.-arguslab.com
http://www.arguslab.com
***************************

-----Original Message-----
From: Computational Chemistry List [mailto:chemistry-request-.at.-ccl.net]On
Behalf Of jz7-.at.-duke.edu
Sent: Monday, September 29, 2003 6:57 AM
To: chemistry-.at.-ccl.net
Subject: CCL:question about CIS excited states calculation

Dear all,

I just began to use CIS to calculate excited states properties, such as
state dipole moment, transition dipole moment and energy. But I am
confused about how many occupied and unoccupied orbitals to
choose when using CIS to calculate excited states.

I had expected that if I include more orbitals, I should get closer
result to the "true value". And when the number of orbitals is greater
than some certain number, the result should not change much. But the
calculation results showed great fluctuation when I include more and
more orbitals. So what is the problem?

Really thanks a lot!

Best,
Jeny

---

From: John McKelvey <jmmckel/at/attglobal.net>
Date: Tue, 30 Sep 2003 21:36:18 +0000

All,

I would like to disagree with Mark Thompson's  reply, at least in part.  First I
would like to point out that I have spent 25+ years working with Zerner's INDO/S
in industry and as a consultant.  I helped industry help support the development
of Zerner's ZINDO to a significant financial extent, and have used INDO/S for
practical, industrial applications since 1977.  I, along with many people, have
noticed that limited singles CI using INDO/S for molecules that absorb in the
visible region often are too short in wavelength by as much as 75 to 300 NM!
Further, Nishimoto, the author of the Nishimoto-Mataga integrals, has made the
same observation using the NM integrals [the same ones used in INDO/S] in PPP ,
or pi only, CI, exactly as has been found for INDO/S.

I have done thousands of  calculations for dyes using INDO/S, and have vitrually
always found this problem for visible transitions for dyes.  I have also found
in the last year that ~85-90% of the error for these dyes can be eliminated
using all singles CI.

Qualitative, descriptive explanations can be had with 10up/10down CIS, but not
quantitative results in the visible region.

John McKelvey
McKelvey Computational Chemistry
Carmel, IN

Mark Thompson wrote:

> mark/at/arguslab.com
> From: Computational Chemistry List [mailto:chemistry-request/at/ccl.net]On
> Behalf Of jz7/at/duke.edu
> To: chemistry/at/ccl.net