Subject: Summary of MO LCAO with FC

From: "Isaac B. Bersuker" <[email-masked]>
Date: Thu, 2 Mar 95 15:06:55 CST

Dear 
	Frank Jensen, Stefan Fau, Ross Underhill, Gustavo Mercier, 
Mayer Istvan, Dennis L. Lichtenberger, David Heisterber, Alain St-Amant,
Shridhar Gadre, Thomas Bally, R.L.W.M. Erens, Bingze Wang, Ole Swang,
and Gennady Gutsev:
	
	First of all, many thanks for your replies to my question about
the MO LCAO method with fractional charges.  Many answers refer to the
Density Function Theory (DFT).  We knew, of course, about this possibility,
but it does not suit us.  Our electronic transparent interface between
QM and MM calculated fragments is worked out in the semiempirical MO LCAO
approach; DFT is not sufficiently good for geometry optimization, and we
have no appropriate programs for the Fenske-Hall method with geometry
optimization.  

	The suggestions of David Heisterberg is just what we are now
doing to solve the problem, but a question remains open: how to define
the multiplicity of an open shell state with frational charges.

	Below follows my original question and the replies received so
far.

--------------------------------------------------------------------------------

ORIGINAL QUESTION

Dear Netters:

        We have a non-trivial problem.  Developing a method of semiempirical
fragmentary MO LCAO calculations, we encounter the necessity to calculate the
electronic structure of molecular systems with FRACTIONAL CHARGES.  So
far, we couldn't find any existing method which can be easily adapted to
include fractional charges; to our knowledge, all the known methods are
reasonably assuming that the number of electron is integer.  Could anybody
help us with suggestions or hints?  We promise to generalize the replies for
the CCL.

--------------------------------------------------------------------------------
From: Frank Jensen <[email-masked]>

for the electrons or the nuclei. I have played with the latter in
        Two possible solutions: introduce fractional charges either
another connection. Modifying existing code is trivial. What the
"physical" implications are I'm not sure.
        Frank

------------------------------------------------------------------------------

From: "Stefan Fau"  <[email-masked]>

Hi,
There is a paper on fractional particle numbers in DFT,
maybe it's of use:

J. P. Perdew, R. G. Parr, M. Levy in:
Phys. Rev. Lett. 49 (23), 1691 (1982)

Good luck!

Stefan Fau,               [email-masked]

FB Chemie der Philipps-Universitaet Marburg,
Hans-Meerwein-Str.
D-35032 Marburg

[email-masked]

------------------------------------------------------------------------------

From: [email-masked] (Ross Underhill)

A tough problem.  The way Hyperchem deals with the fragments and the only
way that I think will work is to break the molecule at a single bond and
then parameterize the missing part of the system with a single s orbital
suitably parameterized to represent the missing system.  In this way you
deal with an integer number of electrons but come up with a fractional
charge on the fragment in a natural way because charge transferred to the
pseudo atom can be consisdered as lost (or gained) to the system.  Obviously
some care has to be taken at where you break and how you can parameterize
the pseudo orbitals.

Dr. Ross Underhill
Royal Military College of Canada
Kingston, Ontario
(613) 541-6000 X6175

------------------------------------------------------------------------------

From: Gustavo Mercier <[email-masked]>

Hi!

Although not exactly in the spirit of semiempirical HF like methods,
DFT methods using the K-S equations allow you to specify fractional
occupation numbers. In fact, Slater's transition state method originally
described within the X-alpha approximation uses a fractional occupation.
Nothing stops you from making the sum of the fractions less than an
integer.
ADF can take fractional occupation numbers, although I don't
know if the program checks to make sure they add to a whole number. From
a computational point of view (and may be even theoretical point of view)
you should not have a problem.

Gustavo A. Mercier, Jr.
[email-masked]

------------------------------------------------------------------------------

From: Mayer Istvan <[email-masked]>

Dear Dr. Bersuker,

I suppose, you might calculate systems with fractional charges
by introducing explitly some orbitals and assigning to them
fractional occupation numbers when building the density
matrix.

Yours,
Prof. Istvan Mayer
Budapest

------------------------------------------------------------------------------

From: [email-masked] (DENNIS L. LICHTENBERGER)

Isaac,
        Fenske-Hall calculations easily do fractional charges.  You probably
know Mike Hall at Texas A&M and can contact him directly about it.
Dennis Lichtenberger

------------------------------------------------------------------------------

From: David Heisterberg <[email-masked]>

Can you write an energy expression in the form

    E = SUM_i {q_i h_ii + SUM_j {a_ij (ii|jj) - b_ij (ij|ij)}}

for one of these fractional systems?  The a_ij and b_ij are the
appropriate coupling coefficients with occupation numbers included.
If so, you might look into the way Cadpac does it's generalized SCF.
--
David J. Heisterberg ([email-masked])      Gee, it's so beautiful, I gotta
The Ohio Supercomputer Center           give somebody a sock in the jaw.
Columbus, Ohio                          -- Little Skippy (Percy Crosby)

------------------------------------------------------------------------------

From: [email-masked] (Alain St-Amant)

Hi,

With regards to your post, you might want to consider DFT.  The occupation
numbers for the KS orbitals can be fractional.  In fact, for ionization
energies, you sometimes perform SCF calculations on a system with half an
electron removed.

I had all of this working in my old code deMon.  I have no idea if it's
still supported or not.  In my new code DeFT, I had plans to implement it
in the next few months.

Alain St-Amant

------------------------------------------------------------------------------

From: [email-masked]

You may consider using DFT-bvased methods. Fractional charge poses
no formal problem there..............Shridhar Gadre..22.2.95.

------------------------------------------------------------------------------

From: [email-masked] (Thomas Bally)

Dear Dr. Bersuker,

  quite a while ago, during my PhD thesis, I did something which sounds
  similar to what you wish to do. I was at the time (and, in fact, still
  quite a while ago, during my PhD thesis, I did something which sounds
  similar to what you wish to do. I was at the time (and, in fact, still
  am!) interested in the electronic structure and potential energy surfa-
  ces of radical ions which I calculated by MINDO/3. Often I ran into con-
  vergence problems and I developed a bag full of tricks to beat those
  (they are described in Helv. Chim. Acta 62, 583 (1979), more precisely
  on pp 585/586, I can senc you a reprint if you have no access to this
  journal). One of these tricks consisted in starting out with a closed-
  shell configuration (neutral or dication) and arrive at the desired
  radical cation by "dropwise" population (from dication) or depopulation
  (from neutral) of a given MO. For this I had to do SCF calculations
  with fractional occupation numbers (and hence fractional charges). I
  actually developed and "interactive" version of the MINDO/3 program
  where I would put a "drop" of charge into the target MO and watch the SCF
  calculations converge. If it diverged, I stopped it, went back and put
  "half a drop" of charge into the MO and so on until I found conditions
  where it converged. Taken together with the other tricks (symmetrization
  of the MO's or the F-matrix after every iteration etc.) I often managed
  to achieve convergence in "impossible" cases and arrive at a set of
  potential energy curves (cf. Fig. 2 in the above paper) which made sense,
  although the "stepping stones" used to arrive at states with integral
  charge were of course entirely unphysical.

  Unfortunately, I am afraid that I no longer have the code which I used
  for these calculations. I keep a copy of MOPAC with the MO-filter and
  the symmetrization (which are also described in the above paper), but
  the fractional occupation existed only in the "interactive" version
  which was discarded when I left the University of Basel in 1979.

  Perhaps it is important to know that the fractional occupation was
  implemented in a program which used Dewar's "half electron" method
  to calculated open-shell systems. Thus, I actually always put *pairs
  of fractional alpha and beta electrons into my target MO. Conceptually,$
  it should also be possible to do the same in a UHF way.

   Feel free to contact me if you have more questions, perhaps I remember
  some important details whic I forgot to mention here.

  Sincerely

  thomas bally

*-------------------------------------------------------------------------*

*-------------------------------------------------------------------------*
|  Prof. Thomas Bally                 |  E-mail:  [email-masked]   |
|  Institute for Physical Chemistry   |  WWW page:                        |
|  University of Fribourg             |  http://sgich1.unifr.ch/pc.html   |
|  Perolles                           |                                   |
|  CH-1700 FRIBOURG                   |  Tel:     011-41-37 29 8705       |
|  Switzerland                        |  FAX:     011-41-37 29 9737       |
*-------------------------------------------------------------------------*

------------------------------------------------------------------------------

From: [email-masked] (R.L.W.M. Erens)

Dear Dr. Bersuker,

In the DFT-based program DGAUSS you can enter a non-integer occupation
number of alpha and beta electrons, using the keyword OCCUP.

Best regards,
Roger Erens

Laboratorium voor Chemische Fysika
Nijenborgh 4
9747 AG  Groningen
The Netherlands

tel. +31 50 63 43 77
e-mail [email-masked]
WWW URL http://rugch5.chem.rug.nl/~erens/

------------------------------------------------------------------------------

From: [email-masked]

Hi Isaac,

Assuming you want an intermdiate 'tool' rather than a
physical reality, you may get these numbers by playing
the trick of ESP-fitting. Just need a little bit more math
on the top of the current approaches:

  Sum_q(i) = Q(A), atom i is from fragment A.
  Sum_Q(A) = Qt,   Qt is the total charge of the molecule.

It might be irrelevant if your question is misunderstood.

Bingze Wang

------------------------------------------------------------------------------

From: [email-masked]

If you don't mind using DFT, the program system ADF (Amsterdam Density
Functional) can calculate the electronic structure for molecular
systems with fractional charges.  I haven't tried it myself, but the
manual says it's possible. The program is sold at a reasonable price
(we paid about 1000$) to academic users.  Contact Bert te Velde
([email-masked]) for additional information.

Good luck,
              Ole Swang

------------------------------------------------------------------------------

From: [email-masked]

Dear Isaak Borisovich,
   I really happy to hear from You. Some answer about fractional
charges may come from the density functional. Actually, I was
trying to fix fractional charge in my DVM-X(alpha) program in
order to calculate the core energy shifts in molecules like
SF6. The input has to contain the imlicitly defined occupation
numbers (with accounting for the MO symmetry, if exists).
In this way You may form "charges" on any internal MO, not
only the external one - with obvious tracing the orbital
when iterating for self-concistency - the easest way to
check the AO occupations. I had used it when calculating
Auger spectra in systems with several atoms of the same
type. It is easy to do if You trace the core orbitals, for higher
MOs the "adhesion" to the same MO is more complicated.
  With my personal regards,

  Gennady Gutsev
  Visiting scholar

-- 

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 
Isaac B. Bersuker		 | E-mail: 
Welch 3.140			 | [email-masked] (prefered)
Dept. of Chemistry	         | [email-masked]
Univeristy of Texas at Austin    | Phone: (512) 471-4671
Austin, TX 78712 	         | Fax:   (512) 471-8696
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *