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From: pitsel@chemul.uni.lodz.pl (Piotr Seliger)
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To: chemistry@ccl.net, jlye@tx.ncsu.edu, m.t.cronin@livjm.ac.uk,
        moralega%a1@lldmpc
Subject: summary AM1 vs PM3
Date: Thu, 2 Nov 95 8:19:11 MEZ



This is the summary of the responses I got to my request about 
AM1 vs PM3 references.

Thanks for help.
----------------

*****************************************************************************

Dear Dr. Seliger,

Following is a note that I sent to the next over a year ago.  Perhaps it will 
be informative.  Our SAM1 papers also extensively documented PMs vs AM1 as 
well as SAM1.  The references for these are:

1. Dewar, M. J. S.; Jie, C.; Yu, G. Tetrahedron 1993, 23, 5003.
2. Holder, A. J.; Dennington, R. D.; Jie, C. Tetrahedron 1994, 50, 627.
3. Holder, A. J.; Evleth, E. M. in Modeling the Hydrogen Bond; 
Smith, D. A.;  American Chemical Society, Washington, DC, 
1994; pp 113.

Please let me know if I can be of further assistance

Regards, Andy Holder

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
 
UUUU  UUU MMM   MMKK KKKK   CCCC   |           ANDREW J. HOLDER
 UU    U   MM   MMK   K    CC  CC  | Assoc. Prof. of Comp./Org. Chemistry
 UU    U   MMM M MK KK    CCC      |          Dept. of Chemistry
 UU    U   M MM  MK   KK   CC  CC  |  University of Missouri-Kansas City
  UUUUU   MMM M MMKK   KK   CCCC   |         Kansas City, MO  64110
                        KK         |          aholder@cctr.umkc.edu
                          K        |  (816) 235-2293, FAX (816) 235-5502
 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
 

Netters,

   A few weeks ago, Jeffrey Nauss asked about a comparison between the AM1 and
PM3 semiempirical methods.  Both of these semiempirical methods are
included in most programs that support semiempirical calculations (AMPAC,
MOPAC, etc.).  Please note that the following discussion is MY OPINION and 
a compendium of MY EXPERIENCES.  I hope you find it somewhat useful.   

   The lead references to each method follows:

AM1: Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J.
        P. J. Am. Chem. Soc. 1985, 107, 3902.

PM3: Stewart, J. J. P. J. Comput. Chem. 1989, 10, 209.

   AM1 stands for "Austin Model 1" and PM3 stands for "Parameterization 
Method 3".  Both methods implement the same basic NDDO theory pioneered 
by Michael Dewar while at the University of Texas at Austin.  The differ-
erence is in how the parameters that the semiempirical methods utilize to 
replace portions of the full ab initio implementation of Hartree-Fock theory.
   Perhaps the most important difference between AM1 and PM3 is the
involvement of the researcher in the parameterization process.  PM3 was
developed using a largely undirected mathematical optimization process
with greatly reduced guidance from chemical knowledge or intuition,  an 
addition that the Dewar methods consider essential.  The human
researcher knows for which molecules it is necessary to obtain the best fit.
For instance, it is useless to obtain parameters for carbon and hydrogen that
describe the properties of cubane correctly if the results for benzene are
significantly different from experiment.  An attentive and knowledgeable
chemist can also guide the search into areas of the parameter hypersurface 
that make sense as far as the absolute magnitude of the parameters themselves 
are concerned.  As with many chemical properties, the parameter values should 
vary periodically.  While this should not unduly constrain the final values,
parameters should follow well-defined general trends for proper interaction
with other elements.
    In terms of the actual NDDO model, the actual parameters allowed to vary 
in the two methods are quite different.  In AM1, a large number of values we
used from spectroscopy for some of the one-center terms and the other
parameters derived with these values fixed.  (This is possible only for the
lighter elements in the Main Group.)  PM3 allowed ALL of these values to 
float, resulting in substantially more parameters.
    AM1 also had a quite different concept as to the application of the
Guassian functions introduced with AM1 to adjust the core-electron/core-
electron repulsion function.  Workers in the Dewar group and subsequently 
in my group see Gaussian functions as PATCHES to the theory, not integral 
parts.  All models fail at some point and the Gaussians were introduced 
to help with some of the systematic errors in MNDO.  Traditionally, these 
patches were applied to adjust for difficult molecular systems AFTER 
semiempirical parameters were stabilized.  PM3 includes these Gaussian 
functions (two for each element) FROM THE BEGINNING.  Our experience 
indicates that in such a situtaion, the chemistry os the element will 
very likely be very strongly effected by the presence of these functions 
and the importance of the "real", "chemical" parameters will be reduced 
and swallowed up bu the Gaussians.   In short, Gaussians should only be 
used where absolutely needed, and then viewed with askance.  
    The essence of the difference between the two philosophies is evident:
the theoretical basis for the method is either accepted or denied.  
Significant approximations are made to gain the speed advantage that 
semiempirical methods enjoy over their ab initio quantum mechanical 
brethren.  But both the ab initio and semiempirical models are based on 
the Hartree-Fock set of ideas.  These ideas possess theoretical rigor as 
regards solution of the Schrodinger Equation.  If one simply views the 
semiempirical parameters as adjustables within a curve-fit scheme rather 
than as components of a theoretical model, little faith or importance 
resides in the meaning of their final values.  Simply put, the method of 
parameterization described above and used so successfully with AM1 and 
MNDO (and now SAM1) expresses confidence in the theory.  With a firmer 
footing in chemical reality, AM1 parameters are more likely to yield 
useful results for situations not specifically included in the molecular 
basis set for parameterization (MBSP).


                      Some Practical Considerations
                      -----------------------------
   The differences in errors between the two methods as published are 
minimal, but that does not relate the real story of how the methods perform
differently.  Some key points:

  -  PM3 is clearly better for NO2 compounds as a larger number of these
      were included in the MBSP.

  -  PM3 is usually a little better for geometries, as these were also 
      heavily weighted.

  -  The molecular orbital picture with PM3 is usually different from that
      expected or that predicted by other methods.  This is a direct 
      consequence of the lack of attention paid to the absolute values of 
      Uss and Upp.  It can be seen in the lack of performance in ionization 
      potentials.

  -  PM3 charges are usually unreliable, again a result of the rather strange
      values that some of the parameters take on, even when other experimental
      data such as heats of formation and geometries are acceptable.  This
      makes PM3 essentially useless for the derivation of molecular m echanics
      force fields.  Perhaps the best known example of this is the case of 
      formamide.  The partial charges for the atoms in the molecules are 
      listed below.  The lack of any appreciable charge on N has led to a 
      reversal of the actual bond dipole between C and N in this molecule!

         Atom        AM1       PM3           HF/6-31G*
         ---------------------------------------------
          O       -0.3706    -0.3692         -0.5541
          C        0.2575     0.2141          0.5079
          N       -0.4483    -0.0311         -0.8835


                  O
                 //
               H-C
                 \
                  NH2


  -  Several papers have been published describing the performance of
      AM1 vs. PM3:

Dewar, M. J. S.; Healy, E. F.; Yuan, Y.-C.; Holder, A. J. J. Comput. Chem.
      1990, 11, 541.
Smith, D.A.  J. Fluor. Chem. 1990, 50, 427
Smith, D.A.; Ulmer, C.W.; Gilbert, M.J.  J. Comput. Chem. 1992, 13, 640.

  -  Most reserachers in my experience have stopped using PM3 and have
      returned to AM1. 
  

             An Example of Parameterization Values for Aluminum
             --------------------------------------------------
        Parameter              AM1            MNDO             PM3     

        Uss, eV            -24.353585      -23.807097      -24.845404
        Upp, eV            -18.363645      -17.519878      -22.264159
        zetas, au            1.516593                        1.70288
                                          }  1.444161
        zetap, au            1.306347                        1.073269
        betas, eV           -3.866822                       -0.594301
                                          } -2.670284
        betap, eV           -2.317146                       -0.956550
        alpha                1.976586        1.868839        1.521073

        Gaussians:
        Intensity #1, eV     0.090000          -            -0.473090
        Width #1            12.392443          -             1.915825
        Position #1          2.050394          -             1.451728
        Intensity #2, eV        -              -            -0.154051
        Width #2                -              -             6.005086
        Position #2             -              -             2.51997

    The point on the potential surface located by PM3 is significantly
different than that located by AM1.  This is immediately apparent from the 
large discrepancy between the Upp values.  These are the important one-
electron energy values and they have strong influence on the parameter 
hypersurface.  Also, the difference between Uss and Upp for both MNDO and AM1 
is about 6 eV.  This has been reduced to 2.5 eV in PM3.  The real difficulty,
however, is in the Beta values.  These parameters are the two-center/one-
electron resonance terms and are responsible for bonding interactions between 
atoms.  The PM3 values are almost zero, resulting in the conclusion that 
there is very little bonding between atoms involving aluminum!  (Note that 
the AM1 values for betas and betap spread out around the single MNDO value 
for beta.  This suggests that the MNDO values were reasonable and AM1 adds 
greater flexibility.)  PM3 regains the bonding interactions lost in the low 
beta values with two strongly attractive Gaussians spanning the bonding 
region.

*******************************************************************************

We did a short note on rotational barriers in branched alkenes: L. A. Burke et
al. J. Physical Organic Chem vol 5,614-616(1992). We were surprised at the time
that no one else seemed to have published such results.

Luke Anthony Burke              tel:609-225-6158
Department of Chemistry	        fax:609-225-6506
Rutgers University              e-mail:
Camden, NJ 08102                burke@camden.rutgers.edu
USA

******************************************************************************

The comparison of AM1 against PM3 has been quite recently
discussed on this list. You may try to search trough
archives.
My three pens to that discuss may be that AM1 absolutely
incorrectly describes interaction in small water clusters;
while it was known that it gives not correct hydrogen
bond geometry for dimers - I found that it also fails
for geometry of larger systems: tetramers, octamers etc.
The geometry is absolutely different from what we expect
for such clusters (as known from ab-initio and MD studies).
In the same time PM3 reproduces these geometries acceptably
good - difference in oxygen position between PM3 and HF/6-31G*
is ~ 0.1 A for octamers.
This is a reason that I am now using PM3 in my Molecular Dynamics
studies that use semi-empirical energy surface to derive forces
(kind of "quantum" dynamics).

Mirek
---------------------------------------------------------------
dr Miroslaw Sopek
MAKO-LAB Computer Graphics Laboratory
ul. Piotrkowska 102a
90-026 LODZ, POLAND
tel. (48)(42)332946,322346
fax. (48)(42)332937
e-mail: mako@pdi.lodz.pl, sopekmir@mitr.p.lodz.pl
---------------------------------------------------------------

*******************************************************************************

1995  Oct 28

Recently the NET was asked for refs to (1) AM1 compared to PM3, and
(2) Sigma-aromaticity.  Here are some refs:

AM1 cf. PM3

1)  Extensive comparison: J Computer-Aided Molecular Design, 4 (1990) Issue 1
    (Special issue) ; discusses PM3, AM1 and MNDO
2)  W. Thiel, Tetrahedron, 44 (1988) 7393
3)  J. J. P. Stewart, J Comp Chem 11 (1990) 543
                                  10 (1989) 209
                                  10 (1989) 221
                                  12 (1991) 320
4)  Dewar et al J Comp Chem 11 (1990) 541
5)  Smith et al J Comp Chem 13 (1992) 640
6)  In a letter to the Net (1995), Andy Holder (SemiChem) said:
        PM3 is better than AM1 for NO2 compounds and usually a little better
        for geom's.  It is not as good for MO's and is unreliable for charges.

Sigma-aromaticity

1)  M. J. S. Dewar "Chemical Implications of Sigma Conjugation"
        J Am Chem Soc 106 (1984) 669
2)  Inagaki et al  JACS 116 (1994) 5954
3)  Ichikawa et al  J Phys Chem 99 (1995) 2307
4)  Hiberty et al  JACS 117 (1995) 7760
===========
Errol Lewars  Chem Dept Trent U, Peterborough  Ontario  Canada
=====

*****************************************************************************8

Piotr-

    We have a  paper in press with Spectrochimica Acta comparing AM1 and PM3
for the prediction of carboxylate stretches.  Briefly, PM3 is much closer in
absolute terms, but AM1 represents differences between compounds more reliably.
  This is a very limited specific application, of course, and probably only
useful to spectroscopists.  I would be interested in hearing what others have
to say about more general comparisons.

Regards,  Steve Cabaniss

******************************************************************************

If you mean comparison of conformational energies you might want to have a 
look at our paper in J.Comp:Chem. 12, 200 (1991).


Kind Regards

*       Klaus Gundertofte
*       Head,  Department of Computational Chemistry
*       H.Lundbeck A/S
*       Ottiliavej 9
*       DK-2500 Valby - Denmark              Fax   +45  3630 1385
*                                            Phone +45  3644 2425-3206
*       E-mail kgu@lundbeck.dk

***************************************************************************

Hi Piotr,

The performance of this methods in relation to which property ?
If you are interested in heats of formation both are OK
with about the same results.
For minimum energy conformations PM3 has lots of problems.
I performed many calculations with PM3, AM1 and ab initio
and PM3 is qualitatively wrong in most cases.
For electronic properties I didn't tried PM3.

Best regards,

Edgardo Garcia
Cristol Chem & Biochem
University of Colorado
BOULDER CO   USA

****************************************************************************

Note:

%0 Journal Article
%A Gano, J.E.
%A Jacob, E.J.
%A Roesner, R.
%D 1991
%T Evaluation of PM3, AM1, and MNDO  for Calculation of Higher Energy
Ionization Potentials
%B J. Computat. Chem.
%V 12
%P 127-134



James E. Gano, Director
Instrumentation Center in Arts and Sciences
University of Toledo
Toledo, Ohio 43606

Instrumentation Center :  http://www.icenter.utoledo.edu
Department of Chemistry:  http://www.chem.utoledo.edu

419-530-7847
419-530-4033 (FAX)

******************************   THE END   *********************************
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  Piotr Seliger                                  PPP  I  TTT  SSS  EEE  L 
  Department of General                          P P  I   T   S    E    L
  and Inorganic Chemistry,                       PPP  I   T   SSS  EE   L
  University of Lodz,                            P    I   T     S  E    L
  Narutowicza 68,                                P    I   T   SSS  EEE  LLL
  90-136 Lodz, POLAND
                                            "The right to knowledge is like
  E-mail: pitsel@chemul.uni.lodz.pl          the right to life" (G.B.Shaw)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

From owner-chemistry@ccl.net  Thu Nov  2 06:46:47 1995
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Date: Thu, 2 Nov 95 12:41:38 -0800
From: Marek Strajbl <strajbl@silicon.karlov.mff.cuni.cz>
Message-Id: <9511022041.AA17766@silicon.karlov.mff.cuni.cz>
To: CHEMISTRY@ccl.net
Subject: turbomole and g9x


Dear CCLers,

I am looking for comparison of efficiency of Turbomole and Gaussian9x
programs. I appreciate any benchmarks and tests on diferrent platforms
for different systems and different types of calculcations.  

I'll summarize responses.

Regards
	Marek

----------------------------------
Marek Strajbl
Insitute of Physics, 
Ke Karlovu 5, 121 16, Prague, CZ
e-mail: <strajbl@karlov.mff.cuni.cz>



From p.mencarelli@caspur.it  Thu Nov  2 07:31:49 1995
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To: chemistry@www.ccl.net
From: "Dr. Paolo Mencarelli" <p.mencarelli@caspur.it>
Subject: Force Field for C-H - - - PI interactions


Hi all,
I am an organic chemist interested in carrying out molecular mechanics
calculations on complexes formed by cyclophanes, containing aromatic rings,
and alkyl ammonium ions.  
An important component of the interaction energy in the complex should be 
the C-H - - - PI interactions between the hydrogen of the alkyl groups and
the Pi electrons of the aromatic units of the host.

All the Force Fields that I know (MM2, MM3, AMBER, MM+,CHARMM) do not have 
an explicit term for taking into account the above-mentioned interactions.

Does anyone know of a force field capable of explicitly handling such
interactions?

Thanks.
                Paolo Mencarelli
=============================================
Dr. Paolo Mencarelli
Dipartimento di Chimica
Universita' La Sapienza
P.le Aldo Moro, 2
00185 Roma - ITALY
tel 06-49913697
fax 06-490631
E-Mail p.mencarelli@caspur.it 
E-Mail mencarel@xantia.caspur.it
=============================================


From kdr3@leicester.ac.uk  Thu Nov  2 09:46:50 1995
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From: "Dr K.D. Roth" <kdr3@leicester.ac.uk>
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Subject: PSI88 and transition metals
To: chemistry@www.ccl.net (ccl)
Date: Thu, 2 Nov 1995 14:36:08 +0000 (GMT)
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Dear CCL'ers,
I am looking for way to display (and plot) molecular orbitals from Gaussian94
calculations. Now, I'm aware of PSI88, but to my knowledge it is a) restricted
to atoms up to Ar and b) to a few standard basis sets coming with G94. I'm 
trying to do calculations on first and second row transition metal complexes,
and I am using non-standard basis sets like those of Ahlrichs. Since I am cer-
tainly not the first fool (?) doing this, I was wondering, if some kind soul
out there has already done the necessary work and has extended PSI88 to con-
tain transition metals (I'm almost completely illiterate in FORTRAN, so I can't
do it myself ... at least not in a reasonable time :-) ). Any help will be 
greatly appreciated, in case that there is sufficient interest I'll summarize
for the list. Many thanks in advance to all those who will respond.

	Klaus-Dieter Roth

********************************************************************************
				+
  Dr. Klaus-Dieter Roth		+	I'm trying hard to prove 
  Department of Chemistry	+	Murphy's law ....
  University of Leicester	+
  Leicester LE1 7RH		+		... but something always
  e-mail: kdr3@le.ac.uk		+		goes wrong ...
				+
********************************************************************************

From jstewart@fujitsuI.fujitsu.com  Thu Nov  2 12:16:52 1995
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From: jstewart@fujitsu.com (Dr. James Stewart)
Message-Id: <9511021713.AA06723@fujitsu1.fujitsu.com>
To: CHEMISTRY@www.ccl.net
Subject: Bug in MOPAC 93



                              BUG IN MOPAC 93

The calculation of excited state transition moments in MOPAC 93 is faulty, and 
results of such calculations should not be used.  The fault can be demonstrated 
by running the following job:

  1scf meci C.I.=2


  H    0.00000000  0    0.0000000  0    0.0000000  0    0    0    0  
  C    1.11816865  1    0.0000000  0    0.0000000  0    1    0    0  
  F    1.33613605  1  109.9107649  1    0.0000000  0    2    1    0  
 Br    1.90383829  1  104.7029401  1  119.6790291  1    2    1    3  
  I    2.05736002  1  107.2678854  1 -126.1994989  1    2    1    3  

This will give the polarization of the transitions as shown below.  Transition 
moments are calculated from state functions using integrals of the type

                           <Phi_i|x|Phi_j>

and these MUST be zero if i=j.  The output indicates that the `transition' from 
State 1 to State 1 has a non-zero polarizability.  Therefore the calculation is 
faulty.  

This bug affects MOPAC 93 only, and appears to be confined to the polarization
part of the electronic excited state calculation.

James J. P. Stewart

  STATE       ENERGY (EV)        Q.N.  SPIN   SYMMETRY     POLARIZATION
         ABSOLUTE    RELATIVE                            X       Y       Z

    1   -0.011305    0.000000     1   SINGLET     A     0.0003  0.0006  0.0019
    2    2.755365    2.766670     2   TRIPLET     A
    3    3.388682    3.399987     3   SINGLET     A     0.0542  0.1115  0.3755
    4    9.202507    9.213812     4   SINGLET     A     0.0025  0.0051  0.0172


From te_meehan@ccmail.pnl.gov  Thu Nov  2 14:46:54 1995
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Date: Thu, 02 Nov 1995 11:37 -0800 (PST)
Subject: IRC in MOPAC summary
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Zu der Liste,
   A number of people answered to my inquiry concerning IRC in MOPAC-
some nice, some hostile. I will only summarize with Jeff Gosper's input,
who covers what everyone said as well as introduces an animation program 
for the PES. Ummmmm. enticing. However, I must add that I did try this
option before I made the inquiry only to get a message that the gradient 
is too large. I was hoping the Gods of Quantum would impart divine wisdom. 
Refinement of the transition state obviously is necessary, but subsequent 
refinements have given me transition states that are ridiculous. I stress 
ridiculous. Any further comments along these lines would also be greatly 
appreciated.

Danke Schoen,
Tim Meehan
te_meehan@pnl.gov

--------------------------------------------------
Dear Tim,

In response to your question about IRC calculations, using IRC=1
will run the IRC calculation in one direction while IRC=-1 will run
it in the opposite direction.

PS I have just started looking at IRC calculations in MOPAC myself
and have developed a program that allows you to analysis the
results (produce graphs of variables and 3D models) and will produce
an animation (mpeg of flc) of the output =. The name of the program
is Re_View.

If you have any interesting reaction profiles I would be interested
in receiving them and could provide you with an animation of the
results.

original query:
>
> I've been trying to run the IRC option in MOPAC, but the
> calculation progresses on only one side of the reaction path.
> Does anyone use IRC in MOPAC and how can I get it to follow
> both sides of a transition state? Thanks for any replies.
>
> Tim Meehan
> te_meehan@pnl.gov



/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\
 Dr. Jeff Gosper
 Dept. of Chemistry
 BRUNEL University
 Uxbridge Middx UB8 3PH, UK
 voice:  01895 274000 x2187
 facsim: 01895 256844
 internet/email/work:   Jeffrey.Gosper@brunel.ac.uk
 internet/WWW: http://http2.brunel.ac.uk:8080/~castjjg
\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/

From richard@biosym.com  Thu Nov  2 16:46:55 1995
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From: Richard Macdonald <richard@biosym.com>
To: "'chemistry@www.ccl.net'" <chemistry@www.ccl.net>
Subject: Asilomar conf paper
Date: Thu, 2 Nov 1995 13:33:12 -0800
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I remember reading a write-up of the protein modeling challenge
held at Asimomar recently (I think it was in Protein Science).
But I can not find it now.

Could some kind soul point me to the reference?

Thanks,   richard


From patterson@chem.wisc.edu  Thu Nov  2 17:31:58 1995
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Date: Thu, 2 Nov 1995 16:33:38 -0600
Subject: CASSCF Tutorial
To: chemistry@www.ccl.net


Greetings,
        I am a reasonably experienced user of standard single reference
techniques in ab initio calculations, and would now like to branch out and
learn about CAS and MRCI.  I am looking for anything that might help me in
my efforts to understand the complexities of setting up these jobs, and
getting good answers.  Any leading references to "tutorial" types of
publications, as well as opinions on which packages offer the best
implementations are welcome.
        I will summarize for the list.  Thanks in advance.

Regards,
Eric

========================================================================

From the desk of:
Eric Patterson                           voice:  (608) 262-0599
Department of Chemistry                  FAX:    (608) 265-4534
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From ui22204@sunmail.lrz-muenchen.de  Thu Nov  2 18:46:57 1995
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Date: Thu, 2 Nov 1995 15:54:26 +0100 (MET)
From: Eugene Leitl <ui22204@sunmail.lrz-muenchen.de>
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To: chemistry <chemistry@www.ccl.net>
Subject: PDBLib, a C++ macromolecular class library
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This is the other OO PDB class library I spoke of.

Chang, W., et al. (1994), "Design and Application of PDBLib, a C++
Macromolecular Class Library", Oxford University Press.

I haven't checked, but documentation is purported to be available at:

   http://cuhhca.hhmi.columbia.edu

-- Eugene

From lijian@scripps.edu  Thu Nov  2 20:47:00 1995
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From: lijian@scripps.edu (Jian Li)
Message-Id: <9511030128.AA15164@pauli.Scripps.EDU>
To: CHEMISTRY@www.ccl.net
Subject: journal name?



Could sombody from Italy plaese tell me what is the full name
of the journal Rent. Lincei. Sci. Nat. ?  Thanks.

