Subject: EXTENDED HUECKEL--MORE INFO AND A FINAL SUMMARY

From: "E. Lewars" <[email-masked]>
Date: Sat, 22 Nov 1997 17:30:30 -0500 (EST)

Saturday 1997 Nov 22

>From E. Lewars
To:  CCL
Subj: Extended Hueckel --another summary

I post another summary connected with my question (see below) because I have
received another helpful letter, and because I have myself summed up the
situation (below).

ORIGINAL Q:

Hello,  What do people out there in netland think of the *current* status of the
extended Hueckel method that was popularized by Roald Hoffmann, starting
ca. 1963?   It was, I think, the first generally applicable method, in the
sense that it was not limited to planar pi electron arrays and could in
principle perform geometry optimizations.  Is it the general view that it is
essentially obsolete, having been displaced by more sophisticated methods like
MNDO and its decendants AM1 and PM3?  Does it have some advantages over AM1
and PM3?

Thanks
  E. Lewars
================

Letter from Dr Carlo Mealli:

   Almost as a hobby and also thanks to the help of some enthusiastic
collaborators (first of all Dr. D.M.Proserpio), I have long worked to develop
a handy graphic interface (package CACAO) to the numerical results of
ehmo calculations (the basic programs of Roald Hoffmann at Cornell).
I am very much aware of the shortcomings of the method in terms of highly
reliable quantitative results. Mainly, the problems arise from neglecting
the inter-electronic terms. Under these circumstances it is impossible
 to trust blindly a quantitative response associated, for example, with
geometry optimization or with the energetics of an electronic transition.

  Still most of the times "the trends" are correct and there is a lot to
learn from trends! If used "cum grano salis" (i.e. always referring to the
e common concepts of chemical bonding, stereochemistry and reactivity),
the method provides a lot of quick, useful and reliable information. The
 rigourous subdivision of the MOs in terms of symmetry properties (remem-
ber the relevance of the Conservation of Orbital Symmetry ideas expressed
by Roald Hoffmann) is dense of chemical meanings. Thus, if a low symmetry
molecule is analyzed starting from the conformer with the highest
possible symmetry, the evolution of the MOs and the redistribution of the
electrons in them do almost invariably point toward the correct solution.
Moreover it is clearly seen where the electronic problems arise from in
the conformers with higher symmetry. In other words, the Perturbation
Theory works well and the ehmo method helps to interpret it beautifully.

   Nowadays with the ubiquitous PCs, it is fast and easy to perform these
calculations at will and to explore many different deformational trends
and/or reaction pathways. The graphics more than the pure numbers are the
e helpful interpretational tool and also the non-specialists (the experi-
mental chemists, the teachers, the students, etc.) can now seek a suited
 MO description of the chemical bonding in a molecule or series of molecules.
 But there is a good point to continue to exploit the ehmo method=
 also for those who perform high level theoretical studies. My viewpoint is
that ehmo cannot be substitutive but is a coadjutant of the latter methods most
of which (from AM1 on) provide no interpretational tools, no eventual insight
 to the user. As in an explorative approach, a preliminary ehmo analysis=
 sheds light in the field where the higher level computations are meant =
to be performed. Moreover, I notice myself from comparisons that the basic qua=
ntitative results are very often consistent. For example, the frontier MOs =
from the ehmo and those from accurate ab-initio methods correspond in
energy order, symmetry and composition. When this is the case, one can
strategically use the ehmo method to interpret to basic underpinnings of
 the given quantitative result. Beside the list of geometrical parameters
of an optimized geometry, the chemist needs to know the electronic factors
which affect the latter in order to understand the role, say, of some
me substituents. The ultimate goal of theory is to favour the planning of
new experiments.
Much chemistry has been interpreted in the past 20-30 years thanks to the
ehmo method because it is a powerful telescope to see Perturbation theory
at work. In my opinion ehmo cannot be dismissed as obsolete especial=
ly now that personal computers allow to construct a MO description of ch=
emical bonding almost as easily as the Valence Bond description is constructed
using paper and pencil.

Dr. Carlo Mealli

============================================================================
Dr. Carlo Mealli
ISSECC - CNR, Via Nardi 39, 50132 Firenze, Italy
Tel 0039-55-2346653, Fax 2478366
e-mail: [email-masked]
=============================================================================

Finally, _my_ ideas now; thanks to all who helped in forming them.
----
Strengths and weaknesses of the EHM

STRENGTHS
  One big advantage of the EHM over more elaborate semiempirical methods and
ab initio and DFT is that the EHM can be applied to large systems containing
almost any element.  The EHM can treat esentially all elements, since the only
element-specific parameter needed is the (valence-state) ionization potential
[1], which is generally available.  In contrast, more elaborate semiempirical
methods have not been parameterized for many elements (altho' recent parameteri-
zations of PM3 and MNDO for transition metals make these much more generally
useful than hitherto).  For ab initio and DFT methods, basis sets may not be
available for elements of interest, and besides ab initio and even DFT are
hundreds of times slower than the EHM and are limited to much smaller systems.
The applicability of the EHM to large systems and to a variety of elements is
one reason why it has been extensively applied to polymeric and solid-state
structures [2].  the EHM is faster than more elaborate semiempirical methods,
partly because the Fock matrix yields to be diagonalized only once to yield the
eigenvalues and eigenvectors (the eigenvectors must be transformed back to those
of the original nonorthogonalized matrix).  In contrast, methods like AM1 and
PM3 (as well as ab initio calculations) require repeated matrix diagonalization
because the Fock matrix must be iteratively refined in the SCF procedure.

  The spartan reliance of the EHM on a paucity of empirical parameters makes it
relatively easy (in the right hands) to interpret its results, which depend, in
the last analysis, only on geometry (which affects overlap integrals) and
ionization potentials.  With a strong dose of chemical intuition this has
enabled the method to yield powerful insights [3].

  The applicability to large systems, including polymers and solids, containing
almost any kind of atom, and the relative transparency of the physical basis
of the results, are the main advantages of the EHM.

  Surprisingly for such a conceptually simple approach, the EHM has a
theoretically-based advantage over otherwise more elaborate semiempirical
methods, in that it treats orbital overlap properly: AM1 and PM3, for example,
use the _neglect of differential overlap_ (NDO) approximation, meaning that they
take S_ij = delta_ij, as in the simple Hueckel method.  The EHM can thus give
superior results [4].
  The EHM is a very valuable teaching tool because it follows straightforwardly
from the simple Hueckel method yet uses overlap integrals and matrix
orhtogonalization in the same fashion as the mathematically more elaborate
ab initio procedure.

  Finally, the EHM, albeit more elaborately parameterized than in its original
incarnation, has recently been shown to be a serious competitor to the very
useful and popular semiempirical AM1 method for calculating molecular geometries
[5].

WEAKNESSES
  The weaknesses of the standard EHM probably arise at least in part from the
fact that it does not (contrast the ab initio method) take into account
electron spin or electron-electron repulsion, ignores the fact that molecular
geometry is partly determined by internuclear repulsions, and makes no attempt
to overcome these defects by parameterization.

  The standard EHM gives, by and large, poor geometries and energies.  Although
it predicts a CH bond length of ca. 1.0 A, it yields CC bond lengths of 1.92,
1.47 and 0.85 for ethane, ethene and ethyne, respectively, cf the actual values
of 1.53, 1.33 and 1.21 A, and although the favored conformation of an alkane is
usually correctly identified, the energy barriers and differences are only in
modest agreement with experiment [6].  Because of this inability to reliably
calculate geometries, EHM calculations are usually not used for geometry
optimizations, but rather utilize experimental bond lengths and angles.

[1]  J. Hinze, H H. Jaffe, J Am Chem Soc 84 (1962) 540; A Stockis, R. Hoffmann
     102 (1980) 2952
[2]  R. Hoffmann, "Solids and Surfaces: A Chemist's View of Bonding in Extended
     Structures", VCH publishers, 1988.
[3]  (a) The Woodward-Hoffman rules: R. B. Woodward, R. Hoffmann, "The
     Conservation of Orbital Symmetry", Academic Press, 1970.
     (b) Counterintuitive orbital mixing: J. H. Ammeter, H.-B. Buergi, J. C.
     Thibeault, R Hoffmann, J Am Chem Soc 100 (1978) 3686.
[4]  Rationalizing nonplanar CC double bonds: J. Spanget-Larsen, R Gleiter,
     Tetrahedron, 39 (1983) 3345.
[5]  S. L. Dixon, P C Jurs, J Comp Chem 15 (1994) 733.
[6]  R. Hoffmann, J Chem Phys 39 (1963) 1397.
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