Subject: LUMO<0: Summary

From: "Hr. Dr. S. Shapiro" <[email-masked]>
Date: Wed, 10 Sep 1997 09:42:29 +0200

Dear Colleagues;

	Many thanks for the people who cared to respond to my query re the
physical interpretation of values of LUMO<0.  Here is a very edited summary
of the responses I rec'd:

	LUMO<0 is sometimes encountered when the MOPAC calc'n falls into a shallow
well and yields a false optimal geometry.

	By Koopmans' theorem, the LUMO energy is _very_ approximately related to
the electron affinity (EA).  When LUMO<0, the molecule is
electron-deficient and stabilised through acquisition of an electron; on
the other hand, if LUMO>0 the molecule is destabilised by acquisition of an
electron.  The LUMO (and other low-lying orbitals) of cations is usually
<0.  Molecules for which LUMO<0 are good electron acceptors in redox
systems, and the LUMO energy correlates well with experimental redox
potentials.  Because of rough parallels that exist between LUMOs and
electron affinities or reduction potentials for a series of related
compounds, LUMOs can be useful in QSPR formulations.

	If LUMO<0, then it constitutes a non-bonding molecular orbital, as in the
case of aniline or phenol.  When LUMO<0, "LUMO electrons" are formally
involved in bonding, e.g., benzene in which the LUMO is a bonding
pi-orbital.  When LUMO>0, this orbital has antibonding character.

	Koopmans' theorem is not only roughly right in quantifying HOMOs and
ionisation potentials, and is mostly wrong in quantifying LUMOs and EAs.
Different Hamiltonians in semi-empirical calculations and different basis
sets in ab initio calculations can give not only different magnitudes but
different signs for LUMO energies.  It is dangerous to assign too much
significance to either signs or magnitudes of isolated orbitals; it is
better to rely on trends of orbital properties across a set of molecules
rather than on the properties of a single orbital in a single molecule.

	  One person explicitly remarked that it is sometimes assumed (from the
responspes I rec'd, that should be "usually assumed") that since Koopmans'
theorem approximately equates HOMOs with IPs, then this theorem also
approximately equates LUMOs with EAs.  According to this respondent, this
is not true; examination of the theoretical justification for Koopmans'
theorem shows that it should _not_ apply to LUMOs.

	Comments and/or criticisms of this summary should _NOT_ be directed to me,
but rather to the whole CCL readership.

Regards,

S. Shapiro
[email-masked]