Subject: reply, semiempirical methods

From: elewars <[email-masked]>
Date: Fri, 11 Oct 2002 10:12:15 -0400

2002 Oct 11

Hello,

Regarding your question about semiempirical methods:

The tight binding method is what physicists call the simple Hueckel
method
(SHM), the simplest semiempirical method derived from the Schroedinger
eqn (with
the possible exception of the free-electron method, which doen't seem to
be used
now). The SHM, contrary to what some people think, still has its uses.
The
extended Hueckel method (EHM), popularized by Professor Roald Hoffmann,
is a
logical extension of the SHM which considers molecular geometry instead
of just
connectivity, uses all the valence orbitals on each atom, not just one
(usually
a p) orbital, and does not collapse the overlap matrix to a unit matrix.
Neither
Hueckel method will calculate frequencies (the EHM could in principle,
but the
results would not be very meaningful, I suspect).

The most popular semiempirical methods today are simplifications of the
rigorous
ab initio approach (the SHM and by implication the EHM were developed in
a different
atmosphere); these originated with, or are offshoots of, the work of M.
J. S.
Dewar's group: the AM1 and  PM3 (and the more recent SAM1 and PM5)
methods.

A good survey of SE methods, with references is: I. N. Levine, "Quantum
Chemistry", Fourth Ed., Prentice Hall, 2000; chapters 16, 17 (15 is ab
initio).

I 'm surprised that AM1 ot PM3 can't give you useful vibrational modes
(unless
you have metal atoms for which parameters are unavailable). Maybe an
STO-3G ab
initio calculation would work and be of some value.

E. Lewars
====

Connie Chang wrote:

> Hi --
>
> I am trying to find the vibrational modes of a 100 atom molecule that
> includes elements such as carbon, nitrogen, hydrogen, and cobalt (just

> one atom).  I tried using commercial software such as Gaussian and
> Hyperchem, but was having trouble getting "sensible" answers with
their
> semi-empirical methods and ab-initio methods proved to be too
> computer-intensive.
>
> I'm trying to write my own code to calculate energies (so that I can
> construct a hessian for the phonon spectra), but I'm not sure about
the
> methods out there.  Is tight-binding the same as the semi-empirical
> methods?  I know that in tight binding, one needs to find the
parameters
> for the elements in the molecule and the parameters for the particular

> atomic connectivity (so if my molecule has a carbon bonded to an
oxygen,
> I would need the parameters for a carbon-oxygen connectivity).  Is
this
> how semi-empirical methods work as well?  Or is there just a set of
> parameters for each element without taking into account the
> connectivity?  Or is there some systematic way to derive parameters
> between elements?
>
> Any advice about what method to use or resources that I can look at
> would be much appreciated.
>
> -Connie Chang
>
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