Subject: ECP and PP -- summary

From: <[email-masked]>
Date: Mon, 16 Sep 1996 15:23:06 -0600 (MDT)

Hi everybody,

a few days ago, I posted an enquiry regrading the difference between
effective core potentials and pseudopotentials. Here is my summary.
First the question:

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I have just read the interesting summary by Dale Braden in the CCL on ECP's.
One of the questions he raised in his original posting was whether there is 
a difference between "effective core potentials" and "pseudopotentials". To 
my limited knowledge, there is none. But maybe one of the experts could
comment on this question? -- I couldn't find a definite answer in the mentioned
summary. So my question is, what -- if any -- is the difference between PP's
and ECP's?  Just curious ...
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I got a number of interesting responses. See also the comment by A. Ehlers
in the earlier summary on the subject. Thank you to all who took the time to
write to me.

Yours, Georg

Here are the responses:
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From: [email-masked] (Cory C. Pye)

An effective core potential includes a pseudopotential as part of its
definition, as well as including some other terms that improve the asymptotic
behaviour of the pseudopotential, like a Z/r term and l(l+1)/r^2 .
I am a little rusty on these, but there is a nice book "Pseudopotential 
Theory of atoms and molecules" which I found extremely helpful. The 
name of the author escapes me at the moment.
-Cory
   *************
 *****************  !  Cory C. Pye
***   **    **  **  !  Graduate Student and Unpaid Sys Admin
**   *  ****        !  Theoretical and Computational Chemistry
**      *  *        !  [email-masked]
**      *  *        !  http://www.ucs.mun.ca/~cory/index.html
***     *  *    **  !
 *****************  !  Les Hartree-Focks
   *************    !  (Apologies to Montreal Canadien Fans)
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From: mbdtssa <[email-masked]>

Hi Georg,
   I have mostly seen the term Pseudopotential used in connection
with plane wave basis set ab initio catlculations, and ECP used for
Gaussian basis set ab initio calculations. The reason for having two
different names could be that Pseudopotentials must give very smooth
pseudowavefunctions, to limit the size of the basis set expansion, and
so must be of a slightly differnt form to ECP's.     
         Hope this helps!
                             Simon.
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From: [email-masked] (Martin Kaupp)

The theoretical basis for all modern (atomic) pseudopotentials is the
generalized Phillips-Kleinman pseudopotential (gPK) ansatz (see
Weeks, Hazi, Rice, Adv. Chem. Phys. 1969, 16, 283). It provides the
separation of the Schroedinger equation into valence and core part
(no approximation involved up to this point, no saving either). Based
on this, there are two major schools (I neglect the solid-state
physics community for the moment, where the term pseudopotential
is sometimes used in a somewhat wider context):

a) the Huzinaga-type model-core-potentials (MCP) which include explicit
projection operators on core basis functions, i.e. they keep the radial
nodes of the pseudo-valence orbitals. The philosophy of this ansatz
involves a 'model potential' which effectively replaces the core-valence exchange
and Coulomb terms occuring when one adopts the gPK ansatz
within Hartree-Fock theory.

b) the more common semi-local pseudopotentials or ECPs (however, I have also seen the 
term ECP used for pseudopotentials of the MCP type, so things are not quite as
systematic as one would like) make use of the hermitian nature of the gPK operator.
They include projectors on spherical harmonics (the name semi-local refers to the
fact that one multiplies local radial terms with these projectors) and feature
nodeless pseudo-valence orbitals.

Both types of PPs have in common the fit of free parameters in the PP to atomic
data (usually ab initio all-electron, could also be experimental), and the frozen-core
approximation (i.e. superposition of atomic PP for molecules, solids, etc.).
Different 'sub-schools' may be distinguished by the type of data used for fitting
and the fitting procedure.

There is much more to be said about the whole business, but I hope this helps a bit.
Regards, Martin

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END OF SUMMARY
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Georg Schreckenbach                      Tel: (Canada)-403-220 8204
Department of Chemistry                  FAX: (Canada)-403-289 9488
University of Calgary                    Email: [email-masked]
2500 University Drive N.W.,  Calgary,  Alberta,  Canada,  T2N 1N4
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