Subject: RELATIVITY IN COMP CHEM--SUMMARY

From: "E. Lewars" <[email-masked]>
Date: Wed, 17 Sep 1997 11:25:39 -0400 (EDT)

1997 Sept 17

On Sept 9 I posted to the CCL these questions about relativity in comp chem:
-------

1997  Sept 9

Hello,

Concerning the importance of the theory of relativity in computational
chemistry:

1)  Are there cases where the Dirac-Fock equation, rather than the Schroedinger
    equation, should be used?
2)  To what extent are the effective core potentials of ab initio
    calculations derived empirically, to fit experiment, rather than
    theoretically?
3)  Where should you start using effective core potentials to simulate
    relativistic effects --at which element does the error start becoming
    significant (somewhere around element 33 to 37, I suspect--As, Se, Br,
    Kr, Rb)?

    Thanks

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

These are the replies I received.  Thanks to all who helped.  I hope I have
not omitted any responses.

#1
>From [email-masked] Tue Sep  9 12:44:51 EDT 1997
Date: Tue, 09 Sep 1997 11:45:44 -0500
>From: Lipkowitz <[email-masked]>
Subject: RE: CCL:RELATIVITY IN COMP CHEM
To: "E. Lewars" <[email-masked]>

A good overview of this is "Relativistic Effects in Chemistry" by Almlof and
Gropen in volume 8 of Reviews in Computational Chemistry. Also in that volume
are chapters on effective core potentials.
_______________________________________________________________________________

#2
>From [email-masked] Tue Sep  9 13:10:40 EDT 1997
Date: Tue, 09 Sep 1997 12:10:22 -0600
>From: [email-masked] (Tom Cundari)
Subject: Re: CCL:RELATIVITY IN COMP CHEM
To: "E. Lewars" <[email-masked]>
Cc: [email-masked]

Hello,

Based on my experience with ECPs I can comment, most directly on questions
2) & 3)

2) ECPs are generally derived to model the potential generated by core
electrons in an atom.  If one starts with a Dirac-Fock calculation then the
ECP models a 'relativistic' field. Likewise, if one starts with a
Hartree-Fock calculation then a 'nonrelativistic' field is modeled by the
ECP.  In the ECPs developed by Stevens et al. all elements larger than Ne
are generated from Dirac-Fock calculations.  The use of relativistic
calculations to generate the ECP is employed by Hay-Wadt (Rb and higher)
and Ross et al. (Li and beyond).  To my knowledge, most ECPs are derived
empirically from atomic calculations and not adjusted to fit experimental
data.  I am not sure about the so-called "energy-adjusted ab initio
pseudopotentials" from the Stuttgart group, but their works can be
consulted for specifics.

3) Depends, of course, on what degree of accuracy you are looking for.  For
'chemical'
accuracy (prediction of geometries and some energetic quantities), my
experience suggests that you probably do not have to worry about
relativistic effects until the third transition series.  For highly
accurate 'spectroscopic' quantities (e.g., state-to-state transition
energies) your surmise about the 4th period elements is probably correct.

In my opinion, the best work on the use of ECPs to probe the importance of
relativistic effects
has been done by Schwerdtfeger & by the Stuttgart group.  In their work,
they cleverly use
a combination of 'relativistic' & 'nonrelativistic' ECPs to probe the
importance of
relativistic effects.    Some papers by Schwerdtfeger et al. are

38.     a)J. Am. Chem. Soc., 111, 15 (1989).
        b)  J. Am. Chem. Soc., 114, 7518 (1992).
        c) Organometallics, 9, 504 (1990).

In the following paper by Dolg et al. they study CeO.  An increase in bond
length is seen upon inclusion of relativistic effects as opposed to the
more common relativistic bond contraction.

J. Chem. Phys., 90, 1730 (1989).

=46or anyone interested in relativistic effects in chemistry, the reviews by
Pyykko are classic.  I think they remain the best intro to the topic for
those with a 'chemical' interest in relativity.

a) P. Pyykk=F6, Chem. Rev., 88, 563 (1988).  Relativistic Effects in
Structural Chemistry.
b) P. Pyykk=F6, Adv. Quantum Chem., 11, 353 (1978).  Relativistic Quantum
Chemistry.

Associate Professor                                The University of Memphis
e-mail:[email-masked]           Memphis, TN 38152-6060
phone: 901-678-2629
=46AX: 901-678-3447
http://www.chem.memphis.edu/umchem.html
===============================================================================

#3
>From [email-masked] Tue Sep  9 13:18:29 EDT 1997
Date: Tue, 9 Sep 1997 14:20:08 -0300 (ADT)
>From: "J. Sichel" <[email-masked]>
Subject: Re: CCL:RELATIVITY IN COMP CHEM
To: "E. Lewars" <[email-masked]>

The expert on relativistic QC is Pekka Pyykko in Finland, who has a
website with lots of references which is mentioned in a message posted
last year which I reproduce below.=20   [SEE BELOW]

Re your Q3, my impression is that relativity is important from about Z =3D =
50,
but I'm not really sure.

Best wishes,  John Sichel (Universite' de Moncton, NB)

 SEE BELOW:

Date: Fri, 5 Jul 1996 12:26:55 +0300 (EET DST)
>From: Leif Laaksonen <[email-masked]>
To: [email-masked]
Subject: CCL:Version 0.2 (alpha) of RTAM is now on line

Dear Computational Chemists,
The DATABASE RTAM, Version 0.2 alpha (July 05, 1996). (C) Pekka Pyykko=20
Pyykko, Department of Chemistry, University of Helsinki (E-mail:
[email-masked]) is now available for search at:

URL http://www.csc.fi/lul/rtam/

The database contains the bibliography part of the two books
"Relativistic Theory of Atoms and Molecules I-II" (Springer, Berlin, 1986
and 1993), (LNCh 41 and 60) as well as additional references, mainly from
1993-6. The contents of the references are analyzed in the books.=20

Yours,

        Leif Laaksonen              Pekka Pyykko

-------------------------------------------------------------------
Leif Laaksonen                     | =20
Center for Scientific Computing    | Phone:      358 0 4572378
P.O. Box 405                       | Mobile:     358 400425203
FIN-02101 Espoo                    | Telefax:    358 0 4572302
FINLAND                            | Mail:  [email-masked]
---------URL: http://laaksonen.csc.fi/leif.laaksonen.html----------

#4
>From [email-masked] Tue Sep  9 14:44:10 EDT 1997
Date: Tue, 9 Sep 1997 12:46:44 -0700
To: "E. Lewars" <[email-masked]>
>From: [email-masked] (Georg Schreckenbach)
Subject: Re: CCL:RELATIVITY IN COMP CHEM

Hi,

these are interesting question, and I would like to see your summary!
Let me try my $0.02 contribution ...

 To start, there are a number of excellent reviews on relativistic effects i=

chemistry, and there should be lots of material on your first two questions.
Check, for instance:
Pyykk=F6, P. Chem. Rev. 1988, 88, 563.
Pepper, M.; Bursten, B. E. Chem. Rev. 1991, 91, 719.
Alml=F6f, J.; Gropen, O. In Reviews in Computational Chemistry Volume 8;
Lipkowitz, K. B. and Boyd, D. B., Ed.; Verlag Chemie: New York, Weinheim,
Germany, 1996; p. 203.

>1)  Are there cases where the Dirac-Fock equation, rather than the Schroedi=
nger
>    equation, should be used?
It depends on what exactly you mean with the question. If you mean going
beyond the
non-relativistic Schrodinger equation, then yes, for sure. E.g., there are
numerous
examples given in the mentioned reviews and elsewhere. However, if you mean
using a 4-component Dirac-type equation, then I am not so sure. It seems
that for most
questions, one can get away with some approximate 2-component method
like ECPs, Pauli equation, or Douglas-Kroll. In fact, other errors
including basis set
size and correlation are often more important then the limitations of
whatever approximate relativistic method one has.

>2)  To what extent are the effective core potentials of ab initio
>    calculations derived empirically, to fit experiment, rather than
>    theoretically?
The ECPs that I know of are fitted to fully relativistic calculations on ato=
ms,
and not to experiment. This doesn't mean that another approach can't exist .=
 ..

>3)  Where should you start using effective core potentials to simulate
>    relativistic effects -- at which element does the error start becoming
>    significant (somewhere around element 33 to 37, I suspect--As, Se, Br,
>    Kr, Rb)?
Depends on what you want to calculate! Pyykko writes that you won't even=
 get the
experimental spectrum of H2 completely correct without relativity... For
geometries
and bond energies, you want to have relativity typically from the 2nd
transition row,
for absolute NMR shieldings, maybe one row earlier -- just to give a few
examples.

Regards, Georg

Dr. Georg Schreckenbach           Tel:     (USA)-505-667 7605
Theoretical Chemistry T-12        FAX:     (USA)-505-665 3909
M.S. B268, Los Alamos National      E-mail:  [email-masked]
Laboratory, Los Alamos, New Mexico, 87545, USA
Internet:    http://www.t12.lanl.gov/~schrecke/
==========

#5
>From [email-masked] Wed Sep 10 03:06:23 EDT 1997
>From: "Merethe Sjovoll" <[email-masked]>
Date: Wed, 10 Sep 1997 09:05:22 -0600
Reply-To: [email-masked]
To: "E. Lewars" <[email-masked]>
Subject: Re: CCL:RELATIVITY IN COMP CHEM

Dear E. Lewars,

I would like to give you a reference which I think will be most helpful to you:

P. Pyykko, Chem. Rev. 88 (1988) 563-594

It shows you many interesting examples of the impact of relativity on
chemistry.

In contrast to one of those who replied to you, David Kellogg, I would rather
focus on the spin-independent effects as being the most important ones in most
cases.
Although spin-orbit coupling has a striking effect on atomic spectra and
increase markedly by atomic number, the effect is very often "quenched out" in
molecules and, I think, always in solids.
The effects of spin-spin coupling do not increase by atomic number as do the
other relativistic effects, in other words; the effect will always be small.

Best regards

Merethe

-- 

********************************************************
Merethe Sjovoll, Ph.D.                      *          *
Research Scientist                          *          *
Norsk Hydro a.s Research Center             *          * 
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P.O.Box 2560                                *  HYDRO   *
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#6
>From:   IN%"[email-masked]"  "C. Brian Kellogg"
To:     IN%"[email-masked]"
CC:     
Subj:   CCL:RELATIVITY IN COMP CHEM

Dear Dr. Lewars-

        In reference to your questions about relativity in quantum chemistry

> 1)  Are there cases where the Dirac-Fock equation, rather than the
>     Schroedinger equation, should be used?
>
Any molecular system which has heavy elements or exhibits large spin-orbit
or spin-spin interactions should be more adequately described by Dirac-Fock
based methods.  Because of the significantly larger basis set requirements
of the Dirac-Fock method, however, effective core potential methods are
typically employed to estimate relativistic effects.  

> 2)  To what extent are the effective core potentials of ab initio
>     calculations derived empirically, to fit experiment, rather than
>     theoretically?

Effective core potentials are constructed solely with reference to the
theoretically derived atomic structure.  In brief, the core potentials are
derived such that when they are employed in the atomic case, they provide the
best possible reproduction of the valence atomic wavefunction obtained for
the all-electron case.  

> 3)  Where should you start using effective core potentials to simulate
>     relativistic effects --at which element does the error start becoming
>     significant (somewhere around element 33 to 37, I suspect--As, Se, Br,
>     Kr, Rb)?

Small errors in equilibrium properties can even show up in the third row,
and spin-orbit effects may be found throughout the periodic table.
Generally, ECP based methods are thought to be effective for the estimation
of relativistic effects on most molecular properties for Z = 19-36, and even
up through Z=54, but that for heavier elements, the agreement between
Dirac-Fock predictions and ECP predictions is often poor.

If you would like to see a more lengthy discussion of these topics, I have
an  on-line introduction to relativistic quantum chemistry which should
provide you with more in-depth answers as well as some references. It can be
found at:

http://zopyros.ccqc.uga.edu/~kellogg/docs/rltvt/rltvt.html

In particular, you may find the final section of that web page, "Relativistic 
Effects in Atoms", more helpful.  That section presents some graphs of the 
magnitude of relativistic effects for main group elements and discusses the 
major trends of relativity across the periodic table.

I hope this helps.

-Brian Kellogg

-- 
C. Brian Kellogg          Physics Building (221), office A367
phone: (301)975-2526      National Institute of Standards and Technology
fax:   (301)975-3670      Gaithersburg, MD 20899
=========

#7
>From [email-masked] Fri Sep 12 02:15:17 EDT 1997
Date: Fri, 12 Sep 1997 09:13:52 +0300 (GFT Daylight Time)
>From: Leif Laaksonen <[email-masked]>
To: Tom Cundari <[email-masked]>
cc: "E. Lewars" <[email-masked]>, [email-masked]
Subject: Re: CCL:Re: CCL:RELATIVITY IN COMP CHEM
X-X-Sender: [email-masked]

Hi,

Let me remind you all of the RTAM (Relativistic Theory of Atoms
and Molecule) database at:

http://www.csc.fi/lul/rtam/

  The RTAM database contains the bibliography part of the two books
  "Relativistic Theory of Atoms and Molecules I-II" (Springer, 
  Berlin, 1986 and 1993), (LNCh 41 and 60) as well as additional 
  references, mainly later ones from 1993- onwards. 
  The contents of the references are analyzed in the books. 

Regards,

-leif laaksonen

-------------------------------------------------------------------
Center for Scientific Computing    | Phone:      358 9 4572378
P.O. Box 405                       | Mobile:     358 400425203
FIN-02101 Espoo                    | Telefax:    358 9 4572302
FINLAND                            | Mail:  [email-masked]
-------- URL: http://laaksonen.csc.fi/leif.laaksonen.html ---------
============