Subject: LUMO energy summary

From: "Leo, Howard" <[email-masked]>
Date: Fri, 12 Nov 1993 12:15:05 EDT

Many thanks to everyone who responded to my question regarding
the difference between semi-empirical and ab initio LUMO energies.

--------------------------------------------------------------------
From:	MX%"[email-masked]"  8-NOV-1993 12:21:46.10

Because semiempirical methods use a very restricted basis set, they
are not good at predicting LUMO energies.

Jimmy Stewart

--------------------------------------------------------------------
From:	MX%"[email-masked]"  8-NOV-1993 13:53:06.68

I believe that this is a conseequence of the minimal basis set
employed by semi-empirical methods.  The extra orbitals in the
extended basis set of the ab initio calculation make little difference
for the occupied levels, including the HOMO, as the semi-empirical
methods are parametrized to reproduce proper behaviour for the
ground state properties.  The semi-empirical methods (AM1 and PM3
anyway) are not parameterized to reproduce excited state properties.

In the SCF procedure, the unoccupied orbitals are, to some extent,
simply the left-overs of the calculation.  The SCF optimizes the
occupied orbitals to obtain the lowest energy state, and the unoccupied
orbitals are set by orthogonality requirements.  The antibonding overlaps
in the minimal basis set are large because the basis set has little
flxibility, and the LUMO energies are high.  When you have
the d orbitals as in the 6-31G* set, the d orbitals mix in to produce
less drastically antibonding orbitals, with significantly lower energy.

You should notice that the HOMO-LUMO gap is always quite a bit bigger
than the UV absoprtion frequency anyway, for other reasons.

                        Hope this is of use.

                                Tom Slee

--
Tom Slee
Hypercube, Inc., #7-419 Phillip St., Waterloo, Ont. N2L 3X2
Internet:  [email-masked]               Tel. (519) 725-4040

-------------------------------------------------------------------
From:	MX%"[email-masked]"  8-NOV-1993 14:27:40.25

Although I don't know the codes that you are using specifically,
I think that most likely your problem is that in the Hartree-Fock
method empty orbitals see a full N electron potential instead of
the proper N-1 electron potential seen by the occupied orbitals.
This means that in a neutral system like yours, the LUMO energies
are actually estimates of the electron affinity (and probably not very
good estimates either), i.e. the LUMO energy is the Koopman's energy
of the anion. To improve this, you would need to use improved
virtual orbitals, or to do CI (or both). Improved virtual orbitals
(IVO's) have been described by Davidson and others. While the physical
process you are trying to evaluate is optical excitation, you have instead
a poor approximation to the electron affinity. Alternatively, you could try
Density Functional methods which do not suffer from this problem,
using either DELTA SCF or the Slater transition state.
I hope this is helpful.
Lou Noodleman
Molecular Biology MB1
The Scripps Research Institute
La Jolla CA 92037
[email-masked]

---------------------------------------------------------------------
From:	MX%"[email-masked]"  8-NOV-1993 15:48:08.27

Do you have also STO-3G numbers for these cases?

It would be interesting to see if they are more like 6-31G or more
like AM1.

Milan Hodoscek ([email-masked])

---------------------------------------------------------------------
From:	MX%"[email-masked]"  9-NOV-1993 07:52:24.67

Is it possible that the LUMO's of the molecules you are studying are
falling onto "continuum functions"? We have had this same trouble with
chlorides (LUMO's) and the problem stems from the diffuseness of the
chlorine orbitals (which might be expected to be a problem considering
the relatively diffuse basis sets you are using). A couple of references
I can give you that describe this problem (as well as what needs to be
done to solve it) are the following:

Falcetta, M. F.; Jordan, K. D., J. Phys. Chem., 1990, 94, 5666

Falcetta, M. F.; Jordan, K. D., J. Am. Chem. Soc., 1991, 113, 2903

Hope this helps!

Sincerely,
John Nash

--------------------------------------------------------------------------
From:  	 MX%"[email-masked]" (John E. Bloor) 9-NOV-1993 13:10:25.31

 If you look at the elements of the Fock matrix you will see that the
  charge density is only over the occupied MOS. Thus the unoccupied MOs change
only because they are forced to be orthogonal to the occupied MOs and to the Ot
   otherunoccupied MOs. Since AM1 does not include overlap and has a very diffe
rent Hamiltonian one should not expect any relationship with the ab initio
 results on an absolute scale. With respect to the difference in the ab initio
  results. When you add the * you add sets of High lying D orbitals. These
  by orthogonality repel the LUMO and it goes down!
        In order to get results which have any relationship to reality
   you have to add an electron into the LUMO. The accurate calc of electron aff
inities though is a very difficult task. (PA13808 at UTKVM1)(John E. Bloor)

--------------------------------------------------------------------------
From:	MX%"[email-masked]" 11-NOV-1993 10:58:49.80

I have noticed the same effect. In general I find that the semiempirical
methods can predict geometries OK but the energies are not good. For a
discussion of ab initio versus semiempirical energies in classical
organic ring systems, see J. Comp. Chem. 13:525-532 (1992). I hope this
helps.

Susan C. Jackels
Department of Chemistry
Wake Forest University
Winston-Salem, NC  27109
Phone: (919)759-5514     FAX: (919)759-4656
Internet: [email-masked]

On sabbatical for 1993-1994 at:
Department of Medicinal Chemistry
308 Harvard Street S.E.
University of Minnesota
Minneapolis, MN 55455
Phone: (612)626-4429

---------------------------------------------------------------------
There was one other response which I accidently lost. I apologize
to that person.
				Howard Leo