Subject: Summary of HOMO-LUMO calculation suggestions Was: A Novice and HO MO-LUMO bandgap calculations

From: "Thoms, Travis" <[email-masked]>
Date: Mon, 28 Aug 2000 15:37:29 -0700

Greetings and thank you for all of your responses,

Here are the general conclusions that I have drawn from your posts; I will
have the actual posts follow.

1.  For realistic UV-Vis absorption calculations, ZINDO/s is the way to go.
(Hyperchem does have ZINDO)
2.  Most semi-empirical methods greatly overestimate the energy level of the
LUMO.
3.  Calculating the HOMO-LUMO bandgap is difficult, since the assumption by
the model is that the molecule is neutral and at its ground state.  Once an
electron was removed from the HOMO or added to the LUMO coulombic
interactions would change the energy level, and this interaction is not
taken into effect.
4.For a more accurate feeling of band gap interactions, ab-initio methods
(namely DFT, with which I am not familiar) are probably most helpful.  (Can
anyone recommend a DFT program?)
5.  Initial geometry optimization is important

Thanks again,

T.Thoms

Message 1:

pm3 and even hartree-fock methods are poor for describing virtual
(unoccupied) states. try a method with electron correlation (mpx or ci).

Message 2:
Equating a molecular orbital energy difference to an electronic excitation
energy is wrong, primarily for two reasons:

1)
The energy required to promote an electron from orbital i to orbital j (say,

>from the HOMO to the LUMO) is not at all equal to the orbital energy
difference 
e(j) - e(i). The promotion energy E(i-->j) can be expressed as  

  E(i-->j) = e(j) - e(i) - v(i,j)

where the term -v(i,j) represents the interaction between a hole in orbital
i
and an electron in orbital j.  This term may be relatively small if the two
molecular orbitals are spatially separated, but in general, v(i,j) amounts
to
several electron volts and is by no means negligible.

2)
The wavefunction |i-->j> of an excited electronic configuration is not 
in general a good approximation to an eigenfunction of the many-electronic
Hamilton operator H.  Generally, matrix elements corresponding to
<i-->j|H|k-->l> are not close to zero.  Hence, excited configurations tend
to
interact, and a proper description must include Configuration Interaction,
(CI).
 Of particular importance is the first order CI between near-degenerate
configurations of the same symmetry, f.inst. for alternant hydrocarbons
(like 
styrene) where it gives rise to "plus" and "minus" states. - Inclusion of 
multiply excited configurations (like i,k-->j,l etc.) in the CI formally 
accounts for electronic correlation effects, thus leading to a description 
going beyond the orbital picture.  However, semiempirical CI-procedures
(PPP, 
CNDO/S, INDO/S, ZINDO, etc.) usually limit the CI expansion to singly
excited 
configurations, and account for correlation effects by empirical adjustment
of 
parameters in the models.

In summary, if you want to predict electronic excitation energies for 
conjugated organic molecules with HyperChem, try ZINDO/S with CI.
Application 
of ZINDO/S should be explained in the HyperChem user's manual. - Good Luck! 

Message 3:
Try ZINDO, and especially the spectroscopic stuff.
These are generally very good.

Message 4:
HOMO-LUMO gap energies overestimate the actual excited state energies 
(and frequently by quite something).  At best the gap is useful for 
some trends, but don't expect any miracles from it.  The simplest way 
to imagine this is that both the HOMO and the LUMO change in going 
>from 2 resp. 0 electrons in it, to a situation with 1 electron in 
each, and that the interaction between the different orbitals also 
changes upon this change in occupancy (so e.g. the electron may not 
'fully' end up in the LUMO, but also 'to some degree' in higher 
orbitals).  In short: the HOMO-LUMO excitation picture is somewhat 
too simple, and this is independent of the programs used.
A recent readable review is one by B.O. Roos in Acc. Chem. Res. 
(either this or last year).

Somewhat better to significantly better (depending on the case) 
results can be obtained by either parametrized semiempirical methods 
(ZINDO is one of them, INDO/s another; isn't either of them in 
Hyperchem?), or by heavy-duty ab initio calculations (such as TD-DFT 
or CASSCF).  Depending on your aims, you will have to choose between 
them.

Message 5:

Try with MOPAC AM1 just to compare MOPAC AM1 and PM3.
I have compared these two methods on one molecular system.
In this case band-gaps very comparable with eachother, but heats of
formation
were different.

I am sure someone will tell you that QM (quantum mechanics) and/or DFT are
better methods
to use, but of course these methods are much more timeconsuming.

See if you find this web-site interesting:
9.7 Comparison of Calc'd and Observed for MNDO, AM1, and PM3 - Next: Notes
on the Table Up: 9. Accuracy of Methods Previous: 9.6 Faults and Errors 9.7
Comparison of Calc'd and Observed for MNDO, AM1, and PM3 :
http://www.psgvb.com/Mopac/html/node657.html

Have a nice day,

Message 6:

I suspect that you are running standard INDO/1S of Zerner, et.al.  Errors of
30-100
NM in Lmax are common......

Quality geometries often help correlations of Lmax(computed) against
experiment,
but the correlation does _not_ have slope of 1 and intercept of 0.
Intercept is
ofted ~ 70-100 NM, depending on the size of the molecule..

Message 7:

PM3 cannot reproduce the real band gap because PM3 can not handle exact
value of LUMO energy. Also PM3 was not parameterized to estimate the UV
spectra. You may use DFT program for evaluating HOMO/LUMO gap, and ZIDO/S
is known to be very powerful to calculate UV absorption spectra. 

Message 8:

Your problem is a common one. I encourage you to search the CCL archives for
this year and the last you to find extensive and more sophisticated
discussions of this problem. 
As you observed, HOMO-LUMO bandgaps are never a good measure of actual
excitation energies. There are many reasons why, but here is one way to look
at it. 
The HOMO energy is a measure of how hard it is to remove an electron from
the neutral molecule, and the LUMO energy (taken with a large grain of salt)
is a measure of how hard it is to add an electron to the neutral molecule. 
Excitation, by contrast, can be thought of as removal of an electron from
the neutral molecule (giving a radical cation), followed by return of the
electron to an unoccupied orbital of the RADICAL CATION. It is much easier
to add an electron to a radical cation than it is to add an electron to a
neutral molecule, so excitation energies are much smaller than HOMO-LUMO
bandgaps. 
Message 9:
A simple HOMO-LUMO picture for UV Vis spectra (especially for conjugated
species
is fundamentally incorrent).  Something liek PM3 can only be successfully
used for
ground state geometries and there to0 (PM3 being a semi-empirical method),
you
could encounter problems.

When you say band-gap I presume you are refering to excitattion energies.
What
kind of systems ar eyou using (# of heavy atoms etc)?

Fore spectra you need to use what are known as CI (configuration
interaction)
methods and for a molecule like styrene you need at least double CI.

Hyperchem should include ZINDO.  Have you tried that?

Message 10:
As far as I know, semi-empirical methods like PM3 overestimate the energy of
LUMO orbitals. There are techniques to reduce this effect but I think, since
you are dealing with small molecules, that the most effective way to get
better
results is to use some ab initio method. HyperChem 6 allows you to do that
at
some extent.