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QCM: Qantitative Chirality Measure of a conformer


References:

M. Petitjean, On the Root Mean Square Quantitative Chirality and
Quantitative Symmetry Measures, J.Math.Phys. 1999, 40[9], 4587-4595

M. Petitjean, Chiral Mixtures,
J. Math. Phys., 2002, 43[8], 4147-4157.
 
Author email: petitjean.chiral@gmail.com

QCM reads the cartesian coordinates of a conformer.
It computes both the chiral index CHI and the direct symmetry index DSI.
The connex components of molecules are treated separately.
The automorphisms of the graph associated to each connex component
are enumerated.
The automorphisms are called "correspondences", or "permutations".



Input data and parameters:
-------------------------

INPUT  FORMAT:
  BIO : Biosym (MSI) files
        /* The graph associated to the structural formula has no edges */
  CAS : Reserved for internal purposes
  HIN : Hyperchem-type files
  ISU : Reserved for internal purposes
  MDL : Cambridge Crystallographic Model files
  ML2 : SYBYL Mol2 files
  PDB : Protein Data Bank or Nucleic Acid Data Bank files
        (only HEADER, ATOM, ENDMDL and END records are recognized)
        /* The graph associated to the structural formula has no edges */
  SDF : Symyx Mol/SDF files
        (data between 'M  END' and '$$$$' are treated as comments)
  XYZ : n+2 lines. Line 1: n; line 2: free comment,
        Next n lines: label or atomic symbol, x, y, z
        (separator: spaces; no tabulation allowed).
        /* The graph associated to the structural formula has no edges */

INPUT  MOLEC FILE NAME: name of the input file containing the molecules

IMOL1: Sequential position number of the first molecule to be
       read in the input file

IMOL2: Sequential position number of the last molecule to be
       read in the input file

DELETE H:
 Entering Y will delete automatically hydrogen atoms.
 Entering N leaves all hydrogen atoms.
            This is the default option.

ONLYC:
 Entering Y will generate only the graph automorphisms enumerations,
            and suppresses the calculation of CHI and DSI.
 Entering N will generate both the graph automorphisms enumerations and
            the calculations of CHI and DSI.
            This is the default option.

ELIST:
 When ELIST<0, only the (-ELIST) first enumerated correspondences
               are output.
 When ELIST=0, the output of the enumerated correspondences is suppressed,
               and the output of the 2 optimal correspondences is suppressed.
               This is the default option.
 When ELIST>0, the enumerated correspondences are output from 1 with
               an increment equal to ELIST (i.e.: 1, 1+ELIST, 1+2*ELIST, ...)
 CAUTION : A small positive value of ELIST may somtimes cause a huge of output,
           even for small molecules.


Output results:
--------------

For each enumerated correspondence (graph automorphism):
    I: local minima of CHI associated to the automorphism
       (followed by its square root inside parenthesis)
    D: local minima of DSI associated to the automorphism
       (followed by its square root inside parenthesis)
    quatop: the two locally optimal quaternions, respectively
            associated to CHI and DSI
    The correspondence itself is output after the values of quatop.
    CAUTION: This correspondence is related to the molecule renumbered in
             concentric layers, and not to the sequential numbering 1,2,3,...
             The concentric numbering is the first enumerated correspondence.

T: geometric inertia of the conformer (atomic weights ignored)

CHI: Chiral Index
     (followed by its square root inside parenthesis)

DSI: Direct Symmetry Index
     (followed by its square root inside parenthesis)

COR: The total number of correspondences, followed by the two
     sequential numbers of the optimal correspondences associated
     respectively to CHI and DSI. These two sequential numbers are
     suppressed when ONLYC="Y".
     COR is followed by the two optimal correspondences.

PROFEX: number of iterations accomplished by the branch and bound algorithm
        enumerating the correspondences.


Remarks:
-------

The number of atoms is currently limited to 50000 and the number of bonds
to 60000 for each molecule.
The source has to be recompiled to read larger molecules.

The computing time is related to the value of PROFEX, which depends on
the number of graph automorphisms rather than the size of the molecule.
E.g., the graph associated to H2O has 2 automorphisms, and the graph
associated to NH3 has 6 automorphisms.

The computing time is drastically reduced when the hydrogens are suppressed.
In this situation, the returned DSI and CHI values differ from those of the
non-hydrogen suppressed molecule, although the output results are still
informative about the molecular symmetry group.

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