Subject: RESPONSE TO EHM REF REQUEST

From: "E. Lewars" <[email-masked]>
Date: Sun, 22 Mar 1998 14:30:48 -0500 (EST)

1998 March 22

 Regarding the request for a review of the extended Hueckel method:
 This is a brief summary of its features; ref 2 is a review.

    SUMMARY OF FEATURES OF EHM    ca. Jan 1998
---------------

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 needs 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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