Subject: Summary:HOMO-LUMO gap in Pt(II)

From: [email-masked] (JirKa Kozelka)
Date: Tue, 27 Apr 1999 15:40:24 +0200 (MET DST)

Some days ago, I sent to CCL a question concerning the HOMO-LUMO gap in Pt(II)
complexes. I should perhaps have specified that I was not primarily interested
in excitation energies (at least for the moment), but wanted to use the
HOMO-LUMO-gap as a check whether the calculations were reasonable.
I have obtained a series of quick responses which are given below.
I would like to express my thanks to all contributors for their interesting
comments.

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Initial Question:

Dear CCL-members,

I have carried out a number of SCF calculations on Pt(II) complexes with
chloride, amine, and phosphine ligands, using Gaussian 94 and 98, with
different basis sets, and find consistently HOMO-LUMO gaps of 0.3-0.4
Hartrees, i.e., 65000-90000 cm-1. This is roughly 3 times the excitation
energies of spin-allowed d-d bands seen in
solutions of these species. The difference seems too big to me to be
explained by electron relaxation. I would very much appreciate comments
and/or explications on/of this apparent discrepancy.
We have seen that the bond lengths and dipole moment coming from HF
calculations are quite wrong for these compounds, and one has to apply 
correlated methods to get these quantities right. But can it be that the
difference in energies of the HF HOMO/LUMO one-electron orbitals is so
far from the excitation energy?

I shall summarize the answers.

Thanks,

Jirka Kozelka
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Answers:
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Hello, Jirka.

Recently we have been involved in the theoretical calculation of band gaps of
ionic crystals. They are certainly a type of materials different from those you
are considering, but perhaps the main findings could be relevant to you. We
have found that inclusion of electron relaxation (by means of a DeltaSCF
procedure, that is separate calculations on the ground and excited states an
difference of total energies) changes the magnitude of the band gap by more
than 3 eV in some cases (aprox. 0.1 hartrees). The effect of correlation on
the band gap was also accusated (2-3 eV), and crucial in order to achieve a
good agreement with experimental results.

If you are interested, you can download copies of our works from
http://xxx.lanl.gov/abs/cond-mat/9809176/
http://xxx.lanl.gov/abs/cond-mat/9901145/

best wishes,

        Andres Aguado.

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I would be very much surprised if you (for Pt compounds) would obtain 
better results. Generally, the IP's (Excitation energies and EA's) in heavy 
metal compounds are very much influenced by relativistic effects. You 
probably used RECP's which include the mass-velocity and Darwin
terms (being derived on DHF atomic calculations) and thus you could 
argue that the relativistic effects are partially included. However, the 
correlation energy in Heavy-Metal systems is by far more important as
it is for "regular" organic systems. Especially, the correlation contribution 
to the relativistic (de)stabilization is usually responsible for more than 50% 
of the energy (IP, E(ex), BDE, etc.). If you are interested in qualitative 
numbers and if you are willing to accept errors of ~0.5 eV you may try
some of the DFT methods, which are in connection with a proper RECP 
quite "cheap" and were proven to offer reasonable results. The Kohn-Sham
orbitals will give you an estimate (not theoretically justified) for the numbers
 you are looking for. On the other hand you may suffer from the inappropriate
description of the "exchange-correlation" which quite often leads to larger
errors (wrong ground states of the atoms) and for sure you miss the 
important spin-orbit effect. 
 
Best regards 
Jan Hrusak
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If one examines excited states using CI theory one sees that  the
diagonal of the CI matrix is E(lumo)-E(homo) - [exchange and coulombic
terms expressed in an Molecular Orbital basis]...  A decent theory book
would probably tell you exactly what the correction terms are.

John McKelvey
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Hi !
 
I just read your message on the CCL-list.
Unfortunately I am no expert in HOMO-LUMO gaps, but I would
be curious if you also tried to use completely uncontracted
basis functions for you calculations too ?

If your compounds are closed shell systems, we could try to
recompute it with my own HF-code for comparitive purposes only.

Best greetings
Siegfried
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Jirka,
   With any SCF method, the LUMO energy of a gas phase molecule will always
be exactly 0.0 hartree at the basis set limit.  Thus, in effect, you can
obtain the LUMO energy that you desire by "wisely" choosing your basis set.
Only the total energies (kinetic, e-N, N-N, e-e) have physical significance.

Preston MacDougall
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Dear Jirka, the HOMO/LUMO gap can not be directly correlated with the
excitation energies!

In case of close shell molecule, the excitation energy E* from HOMO to
LUMO  is expressed by

E*= E(LUMO) - E(HOMO) - J(HOMO,LUMO) + 2 K(HOMO,LUMO)

where J and K are coulomb and exchange integrals and E's are eigenvalues.
(no CI is also assumed)

Since for d orbitals J(HOMO,LUMO) is quite large (~10 eV), the excitation
energies are significantly lower than HOMO/LUMO gap.

Serge Gorelsky
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Hi Jirka,

as a method I would recommend LDA (SVWN) rather than HF or MP2. LDA 
(no gradient corrections) gives much better geometries.

Concerning the HOMO-LUMO gap, I assume you will get very good and 
sound comments to it - much better than I can give. But I recall that 
HOMO-LUMO gap does correspond to transitions and the HOMO-LUMO gap is 
by a factor of about 2 larger. 

If you do not get other answers I will look up the reference for you.

Generally I am very interested in what kind of Pt complexes you are 
interested in and what properties you investigate.

Our homepage is just under constructions, but do give you a feel of 
what we doing you might want to have a look at our test-version.

http://nitrogen.cem.uct.ac.za/achim/indexpgm.htm (no WWW !!)

Best regards

Achim
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I'm not sure if this helps much, but HF theory tends to yeild a HOMO-LUMO
which is too big.  LDA on the other hand yeilds a HOMO-LUMO which is too small.
And B3LYP tends to yeild a HOMO-LUMO which is just right.  I'd give it a try.   

All the best, Matt
Matt Challacombe
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Jirka:

Many years ago I did all the excitation energies for the chloride systems by
appropriatly populating the d orbitals and the excitation energies are in
reasonable accord with the experiments.

Mo Krauss
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Dear Jirka,

modeling a complex in solution by SCF calculations in the gas phase 
contains two errors: You neglect correlation and solvent effects.

Normally reaction energies are more sensitive to correlation than the 
geometry. I would not be surprised if this holds for HOMO-LUMO gaps too. 
By the way, DFT methods include correlation effects and are only slightly 
more expensive than HF calculations.

The HOMO -> LUMO transition is accompanied by a change of the charge 
distribution. Since the solvent can be polarized by the solute, your 
ground and excited state energies are lowered (by different amounts) 
in the presence of a solvent. 

There are two methods for inclusion of solvents, explicitly including 
the solvent molecules into the calculation (expensive!) and using a 
polarizable continuum as a model for the solvent (cheaper). 

Stefan
______________________________________________________________________
Dr. Stefan Fau
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Dear Jirka
The HOMO-LUMO gap calculated with the HF method, is almost allways far from the
observed excitation energy.. There are several other methods which are suitable
for  this kind of calculations  e.g CIS (C.I. sinnglets calculations).
Even semiempirical methods (suitably parametrized) usually give  HOMO-LUMO gaps
which are closer to the observed ones.

C. Garoufalis
University of Patras, Dept of Physics
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   Dear Jirka,

   Have you compared the experimental excitation energies 
to those came from CIS calculations? They should be much 
more precise since CIS is developed for this aim, and in fact,
this is the cheepest ab initio tool to perform such a calculation. 
Using Gaussian, you may even take the solvent effects into account.
I would suggest to try this.

Also, in the former days of spectroscopy, semiempirical methods 
were used for predicting electron excitation and ionisation energies.
If everything else fails, i would -at least- try some of them.
Most of them is parametrized on experimental data (IPs, etc.)
Many programs that are dealing with semiempirical calculations
allows you to carry out CIS calculations on semiempirical SCF, as well.
For very large systems -in my opinion- this is the only way.

Hope this helps.
Best wishes,

Tamas Karpati
Technical University of Budapest, Hungary
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I sent a reply to Serge:

Dear Serge,

>From Jorgensen's book "Absorption Spectra and Chemical Bonding in
Complexes", I once calculated the change in interelectron repulsion for
the d-d transitions in square-planar complexes. For the spin-allowed dz2
to dx2-y2 transition, for instance, I obtained 
E* = E(LUMO) - E(HOMO) - 4B -C.
Taking for the Racah parameter B Jorgensen's value of 600 cm-1 and C =
4B, I get a correction term 4B + C = 4800 cm-1 which is somewhat more
than 0.5 eV. Even if I take larger estimates for B, like , e.g., 822
cm-1 obtained by Vanquickenborne & Ceulemans (Inorg.Chem.,20, 796,1981),
I do not obtain more than 1 eV. That is why I neglected the
interelectron repulsion while posing my question. Your estimate is
perhaps valid for some metal ions with more contracted orbitals? I would
like to know how you have obtained it. Thank you anyway for responding
so quickly.

Greetings,

Jirka
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...and got the following comment back:

well, this expression is not valid if E(LUMO) and E(HOMO) are "true"
HF eigenvalues.

Racah papameters are small because they characterize "nonspherical"
effects in interelectronic repulsion.

J(d,d) integral is much bigger than B and C and in 8-15 eV for practically
all transition metals.
Serge Gorelsky
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