Subject: OVERLAP INTEGRAL AND SLATER FUNNC

From: "E. Lewars" <[email-masked]>
Date: Sun, 2 Nov 1997 16:54:11 -0500 (EST)

1997 Nov 2

                          SLATER OVERLAP INTEGRALS
>From   E. Lewars
To     CCL

  Hello,

 There is some info' about overlap integrals and Slater functions that I am
finding it hard to dig out of the literature.  I should state at the outset
that _I know_:

that there are programs for calculating overlap integrals

that in most molecular quantum chem Gaussian functions, not Slater functions,
are used

that Mulliken et al published a long paper (J Chem Phys, 17 (1949) 1248-1267))
with recipes for calculating overlap integrals

that all kinds of tricks exist for "simplifying" the calculation of overlap
integrals
---------
OK, but what I want is simply this:

(1)  In the molecule H-He+ (yes, protonated helium) if the H nucleus has
     Cartesians H1(x_1, y_1, z_1) and the He nucleus He2(x_2, y_2, z_2),
     where the coordinates are in Angstroms (_not_ atomic units or Bohrs)

     and if we write

     for H:  phi_1 = a_1 exp{b_1[(x-x_1)^2 + (y-y_1)^2 + (z-z_1)^2]^1/2}
 and for He: phi_2 = a_2 exp{b_2[(x-x_2)^2 + (y-y_2)^2 + (z-z_2)^2]^1/2}

      (usually a is expressed in terms of zeta and pi, b = -zeta, and
      the variable is a radius vector r)
   QUESTION:  what are a_1 and b_1, as numbers, not Greek letters?
              what are a_2,and b_2 as  numbers, not Greek letters?
              (i.e a_1 = 0.5647 or whatever, etc etc (4 decimals).

    S_12 = the triple integral from 0--> infinity of phi_1.phi_2 dxdydz
    must = the correct overlap, if the six Cartesian coordinates are in
    Angstroms.  And of course integral of S_11 = S_22 = 1.

(2)  If (x_1, y_1, z_1) = (0, 0, 0) and (x_2, y_2, z_2) = (0, 0, 0.800),
     (0.800 Angstroms) what is S_12 (as a number, e.g 0.4273 or whatever)?

(3)  For (x_1, y_1, z_1) = (0, 0, 0) and (x_2, y_2, z_2) = (0, 0, d),
     is there a simple function S_12 = f(d) ? (for H, He?  for any two
     1s orbitals)?  Of course f will depend parametrically on the a's and b's.
-------------
  Thanks     E. Lewars
===============

>From [email-masked] Thu Oct 23 14:22 EDT 1997
Date: Thu, 23 Oct 1997 19:23:33 +0100 (BST)
From: Peter Sarre <[email-masked]>
Reply-To: Peter Sarre <[email-masked]>
To: [email-masked]
Subject: 98.04.15 CHEMISTRY AND PHYSICS OF MOLECULES AND GRAINS IN SPACE

Royal Society of Chemistry Faraday Discussion 109,=20
The University of Nottingham, UK, 15-17 April 1998

"CHEMISTRY AND PHYSICS OF MOLECULES AND GRAINS IN SPACE"

The preliminary programme and other information are now available:

* on the WWW at http://www.nottingham.ac.uk/faraday.html, or....
* by ftp from brian.chem.nottingham.ac.uk, log on as ftp,
  use your E-mail address as the password to get faraday.txt, or....
* by post; please write requesting the First Circular to:
  Ms S Riaz, The Royal Society of Chemistry, Burlington House, Piccadilly,
  London W1V 0BN

        This Faraday Discussion of the Royal Society of Chemistry
        is sponsored by the Astrophysical Chemistry Group which is
        affiliated to the Royal Astronomical Society. It is limited  =20

Faraday Discussion no. 109
CHEMISTRY AND PHYSICS OF MOLECULES AND GRAINS IN SPACE

Preliminary Programme

INTRODUCTORY LECTURE: Frontiers of Astrochemistry
D A Williams, University College London

Chemical Processes in Astrophysical Radiation Fields
A Dalgarno, Harvard-Smithsonian Center for Astrophysics, Cambridge, USA,=20
and P C Stancil, Oak Ridge National Laboratory, USA

Chemical Models of Hot Molecular Cores
T J Millar and J Hatchell, UMIST, UK

Molecules in Harsh Environments
J H Black, Onsala Space Observatory, Sweden

Observational and Theoretical Constraints on the Chemistry of Pre-Stellar=
=20
Nebulae
R Plume, E A Bergin, P Myers and J Williams, Harvard-Smithsonian Center=20
for Astrophysics, Cambridge, USA  =20

The Calculation of Molecular Opacities for Stellar Atmospheres
D W Schwenke, NASA Ames Research Center, California, USA

Inorganic Dust Formation in Astrophysical Environments
H-P Gail, University of Heidelberg, Germany, and E Sedlmayr, TU Berlin,=20
Germany

The Role of Molecules and Dust in Shells Around Carbon Stars
B Gustafsson and K Eriksson, Uppsala Astronomical Observatory, and H=20
Olofsson, Stockholm Observatory, Sweden

Neutral-neutral reactions at the temperatures of interstellar clouds:=20
rate coefficients for reactions of C2H and C atoms
D Chastaing, P L James, I R Sims and I W M Smith, University of=20
Birmingham, UK

Low Temperature Electron Attachment to Polycyclic Aromatic Hydrocarbons
T Moustefaoui, C Rebrion-Rowe, J L Le Garrec, B R Rowe and J B A=20
Mitchell, Universit=E9 de Rennes, France

Circumstellar Molecular Absorption Lines from the Ultraviolet to the Infrar=
ed
E J Bakker and D L Lambert, University of Texas, Austin, USA

New Carbon Chains in the Laboratory and in Interstellar Space
P Thaddeus, Harvard-Smithsonian Center for Astrophysics, Cambridge, USA

Crossed Molecular Beam Investigations on the Formation of Carbon-bearing=20
Molecules in the ISM via Neutral-Neutral Reactions
R I Kaiser, D Stranges, C Ochsenfeld, M Head-Gordon and Y T Lee,=20
University of California, Berkeley, USA

What ISO tells us about Gas-Grain Chemistry
E F van Dishoeck, Leiden Observatory, The Netherlands

Some Striking New Spectral Evidence Supporting the H2 DIBs Theory
P P Sorokin and J H Glownia, IBM Research Division, Yorktown Heights, USA

Electronic Spectroscopy of Carbon Chains and Relevance to Astrophysics
J P Maier, University of Basel, Switzerland=20

Excitation Processes for the Emission of UIR Bands
O Guillois, G Ledoux, I Nenner, R Papoular and C Reynaud, SPAM CE Saclay,=
=20
France

Infrared Molecular Astronomy
P F Bernath, University of Waterloo, Canada

Apolar Ices
P Ehrenfreund, Leiden Observatory, The Netherlands, A C A Boogert,=20
Kapteyn Astronomical Institute, The Netherlands, P A Gerakines,=20
Rensselaer Polytechnic, USA, and A G G M Tielens, NASA Ames Research=20
Center, USA

Probing the Connection between PAH's and Carbonaceous Grains
C Joblin, CESR, Toulouse, France

From=20the Interstellar Medium to Planetary Atmospheres via Comets=20
T Owen, Institute for Astronomy, Hawaii, USA=20

Molecular Evolution in Planet-forming Circumstellar Disks
Y Aikawa and S M Miyama, National Astronomical Observatory of Japan, T=20
Nakano, Nobeyama Radio Observatory, and T Umebayashi, Yamagata=20
University, Japan

Evidence for Extraterrestrial Origin of PAHs in the Martian  Meteorite=20
ALH84001
S J Clemett, X D F Chillier, J S Gillette and R N Zare, Stanford=20
University, USA

Exploring Grains and Molecules on Earth Using Stable Isotope Techniques
C T Pillinger, The Open University, UK

Interstellar and Cometary Ices: Molecular Emission From Recent Comets'
W M Irvine, C H DeVries, J E Dickens, A J Lovell, F P Schloerb and M=20
Senay, University of Massachusetts, Amherst, D Jewitt, Institute for=20
Astronomy, Hawaii, and H E Matthews, Joint Astronomy Centre, Hilo,=20
USA    =20

Physics and Chemistry of Comets: Recent Results From Comets Hyakutake and=
=20
Hale-Bopp
J Crovisier, Observatoire de Paris-Meudon, France