Summary:HOMO-LUMO gap in Pt(II)

 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.
 **********************
 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
 **************************
 Answers:
 ***************************
 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.
 ****************************
 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
 ****************************
 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
 *************************
 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
 ***************************
 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
 ***************************
 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
 ******************************
 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
 ***************************
 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
 *************************
 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
 *********************
 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
 ******************************
 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
 ****************
    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
 ******************
 ...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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