Subject: Summary: allyl vs formate pi system

From: Douglas_Stack/CAS/UNO/[email-masked]
Date: Thu, 2 Sep 1999 11:54:19 -0500

Below are the comments (thanks to all!) that I received on the question of MO
ordering and basis sets with regard to the allyl and formate pi systems.  The
interesting thing to note, is that the Huckel level (a basis set of three
p-orbitals) the order of the MO matches HF at 3-21G and 6-31G*.  It was the
semi-empirical methods that had a sigma orbital as the HOMO for the formate
system, whereas the other methods indicate that the MO with a node at the center
carbon was the HOMO for formate.  Evidently, the basis set choice is important.
Below is first a copy of the original post ant then the responses I received.
Thanks again to all those who replied.

I have question about molecular orbitals  (MO) generated by simple Huckel
calculations involving just conjugated p-orbitals and MO generated via
semi-empirical calculations using all of the atomic valence orbitals.
Specifically, the differences in calculating the allyl pi system vs. the formate
(HCO2-) pi system.  Both systems have 3 p orbitals that combine to form the
familiar Huckel orbitals, we'll call them HMO1, HMO2, and HMO3.  Since the allyl
cation system has just two electrons, HMO1 is the HOMO and HMO2 is the LUMO.  If
one does a semi-empirical calculation using all valence obitals on the allyl
cation system (AM1 or PM3), a graphical representation of the HOMO matches the
familiar all bonded  HMO1 and the LUMO matches the HMO2.  However, with the
formate system, a semi-empirical calculation does not produce a HOMO the matches
HMO2 (with four electrons in this pi system, HMO2 is the HOMO).  The HOMO
generated by the semi-empirical method not only has significant coefficients on
both oxygens, but also has a large coefficients on the hydrogen (connected to
the middle carbon).  The HMO2 for formate matches HOMO-1 in the semi-empirical
calculation not HOMO.  The question is, why does the semi-empirical method  for
formate generate a HOMO that is different than that predicted by simple Huckel
theory?  I understand the latter has only 3 atomic orbitals as a basis set while
the former has 13 by including all valence orbitals.  Can this change the order
of MO we are accustom to when we think of  Huckel explanations of electron
delocalization?  Why would the allyl cation system match semi-empirical but not
the formate, is symmetry involved?

Douglas E. Stack

As a follow-up to the previous post, if I run a HF/6-31G* calculation on the
formate anion, the HOMO matches the Huckel HOMO and the LUMO macthes the Huckel
LUMO.

Douglas E. Stack

>>Dr. Stack,
   I have no comment on the basis set dependence of the orbital ordering,
other than to reiterate your observation that it exists.  It is curious why
this does not bother more computational chemists.  I can point you to a
paper that addresses the correspondence just between atomic charges that
are "observables" and simple Huckel theory, thus avoiding all basis set
artifacts.  If you are interested, the reference is Slee and MacDougall,
Can. J. Chem., vol. 66, p. 2961 (1988).

Sincerely,

Preston MacDougall

~~~
Preston J. MacDougall
Associate Professor
Department of Chemistry, Box X101
Middle Tennessee State University
Murfreesboro, TN 37132

Doug,
     Several answers are possible depending the type of explanation you are
looking for.

     First, you need to recognize that HMO2 of formate anion is a sigma orbital
and not a pi orbital. This can be seen by graphing the orbital isosurface. It is
also "obvious" from the fact that HMO2 contains a contribution from hydrogen;
semi-empirical methods do not put p-type orbitals on hydrogen, so hydrogen
cannot contribute to a pi-type orbital in this molecule.

     Short answer: Huckel theory ignores the sigma system. Since chemists are
trained using Huckel theory they often mistakenly assume that sigma orbitals are
always low-energy and pi orbitals are always the frontier orbitals. Not true!
     Semi-empirical methods include sigma orbitals and can (and often do) arrive
at different conclusions. Look at the HOMO of formaldehyde; it is not a pi
orbital. I think a sigma orbital also sneaks into the pi manifold of benzene.

     A longer answer: The semi-empirical HMO2 of formate anion looks like it
contains an antibonding interaction between the oxygens and hydrogen. This can't
be too strong since these atoms are fairly well separated. On the other hand,
the bonding interactions (CO and CH) in HMO2 appear to be weak. This balance of
interactions suggests that HMO2 should be a high energy orbital.
     Huckel HOMO of allyl anion, by comparison, is a pi nonbonding orbital. We
shouldn't be surprised that an orbital with sigma antibonding components has a
higher energy than a nonbonding orbital (pi or sigma).

     An even longer answer: Huckel theory completely ignores the effects of
electronegativity and electron-electron interactions. For example, Huckel theory
says that the orbital energies of allyl cation and anion are the same. This is
wrong.
     The Huckel HOMO for allyl anion is delocalized over the two end carbons.
These carbons are replaced by electronegative oxygens in formate anion, and
perturbation theory predicts a significant drop in MO energy. In fact, this
orbital appears as HOMO-1 in the semi-empirical calculation.
     In general, MO energies reflect the energies of the AOs that they are made
out of (this is a gross simplification since we also need to think about
electron-electron interactions, and whether the MO contains bonding or
antibonding orbital interactions). An MO that is composed entirely of oxygen AO
might be lower in energy than an orbital that mixes the same type of oxygen AO
with a higher energy hydrogen AO.

     Hope this hasn't confused you too much,
-Alan

------------
Alan Shusterman
Department of Chemistry
Reed College
Portland, OR
www.reed.edu/~alan

Dear Prof. Stack,

     I have checked your results for formate anion and it seems to me that
the semiempirical pi-orbitals are in agreement with the Hueckel calculations.
The pi-orbitals are HOMO-3, HOMO-1 and HOMO+1.  If I understand your question
correctly, you had an impression that semiempirical pi-orbitals are ordered
differently than Hueckel orbitals. That is, you're not concerned with the
relative positions of pi- and sigma- semiempirical orbitals but only of pi-
-orbitals.  For such a small system it would be really strange if pi-orbitals
were ordered differently than Hueckel predicts, but this does not seem to be
the case.  Maybe you mistook some of the sigma-orbitals as a pi-orbital as it
looks like from significant contributions of H-atom orbitals which you
mentioned (pi-orbitals [usually!] do not include contributions from non-p
atomic orbitals).  Pi-orbitals are not necessarilly confined to HOMO-LUMO
region, that is, they are more or less interspersed among the sigma-orbitals
and only the coefficients enable identification of the pi-orbitals.

     If you have more questions, let me know.

                         Sincerely,
                                         Darko Babic
                                   Institute "Rudjer Boskovic"
                                   HR-10001 Zagreb, P.O.B. 1016
                                           Croatia

I suppose a bunch of people told you this, but maybe not.  The MOS in
formate are degenerate because of symmetry, so any arbitrary linear
combination of these is also a solution.  Huckel thry gives you the
symmetry adapted linear combination if you do it right; computer MO
programs cannot be counted on to do this for you.  HOwever, if you add &
subtract the degenerate ones you DID get, they should give you the 2 you'd
like to see...

Irene Newhouse

Douglas E. Stack
Assistant Professor
Department of Chemistry
University of Nebraska at Omaha
Omaha, NE 68182-0109
(402) 554-3647
(402) 544-3888 (fax)
[email-masked]