
                    Program FUZZY, Version 1.01
                    ----------------------------

   Calculating:
   ------------

     A) Conventional (Hilbert space) bond orders and valences
        (I. Mayer, Chem. Phys.Lett. 97, 270, 1983....)

     B) Mulliken and "fuzzy atom" populations

     C) "Fuzzy atoms" bond orders and valences
        (I. Mayer and P. Salvador, Chem. Phys. Letters 383, 368, 2004)

   Cite this program as:
   ---------------------
 I. Mayer and P. Salvador, Program "FUZZY", Version 1.01, Girona, Ocober 2003.


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 The gzipped tar contains the Fortran code and the Makefile, as well as
 a small script "fuzzydimens" with the data "dimension.data" permitting
 to change in an easy way the dimensions of all routines. Parameters are
 "nmax" maximum number of basis orbitals and "maxat" maximum number
 of atoms.

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  The program has been written by using parts of the program APOST by
  I. Mayer and A. Hamza, Budapest, 2000-2003.
      

  The numerical integration utilizes the subroutines for Lebedev
  quadrature downloaded from CCL. The appropriate reference is:
      
  V.I. Lebedev, and D.N. Laikov, Doklady Mathematics, 59, No. 3, 477 (1999)


   We are extremely grateful for the possibility of using these routines!  
        
                      
           e-mails: mayer@chemres.hu, pedro.salvador@udg.es 
 
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 USAGE:

 The input of the program is the "Formatted checkpoint file" generated
 in a Gaussian run. Its name is Test.FChk. To generate it, include in the
 Gaussian input the keyword FormCheck. (It can also be generated by
 the "formchk" utility from the binary checkpoint file.)

 The default integration grid is 30 radial by 110 angular points per atom
 To change it, prepare a formatted (non-binary) fortran file "60" (fort.60 
 under Linux) with two integers: the number of the radial and angular 
 points. (As only some predetermined numbers of angular points are possible, 
 the program will take the next which is lower than or equal to the 
 selected one.)



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 Remark on
 THE POSSIBILITY OF USING DIFFERENT WEIGHT FUNCTIONS:

 The present program uses the weight functions of the different atoms in
 different points of space according to the scheme which was originally 
 proposed by Becke for doing efective numerical integrations (A. D. Becke, 
 J. Chem. Phys. 88, 2547, 1988). This function is calculated by the function 
 "wat" (see file wat.f), by using the atomic radii specified in subroutine
 "prepar" (see file numint.f) and calling different functions in wat.f.  
 
 One may replace this function "wat" by his own weight function by writing 
 an appropriate "function wat(ii,x,y,z)" instead to ours. (The first 
 argument is the atom for which the weight function is calculated, the 
 remaining ones are the Cartesian laboratory coordinates of an arbitrary 
 point in space.) This function should be non-negative, and in every point 
 of space the weight functions of the different atoms should sum to 1.

 
 (The above conditions in LaTeX notations: 
   w_A(x,y,z) \ge 0    and    \sum_A w_A(x,y,z) \equiv 1.)


 

