
        User's Guide to the SHRINK program
        ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
                                               May    2002

The basic concepts underlying the procedure for taking into account 
nonlinear effects can be found in: 

  [1] V.A. Sipachev, J. Mol. Struct. (Theochem), 121 (1985) 143.
  [2] V.A. Sipachev, Vibrational Effects in Diffraction and
      Microwave Experiments: A Start on the Problem, In:
      I. Hargittai and M. Hargittai (Eds.), Advances 
      in Molecular Structure Research; JAI: Greenwich, 1999; Vol. 5, pp. 
      323-371.
  [3] V.A. Sipachev, Anharmonic Corrections to Structural Experiment 
      Data, Struct. Chem., 2/3 (2000) 167.
  [4] V.A. Sipachev, Local Centrifugal Distortions Caused by Internal 
      Motions of Molecules, J. Mol. Struct., 567-568 (2001) 67.
  [5] M. Iwasaki, K. Hedberg, J. Chem. Phys., 36 (1962) 2961.


    I. INPUT INFORMATION

To run the program for a molecule, you normally need three files. The 
fourth and fifth ones are optional.

    1. Data file of an arbitrary name ('molname') with or without an 
    extension (.dat) (required). The name 'molname' will be used for 
    creating output files with extensions .txt, .fc1, .cor, and 
    cc1.

    2. File containing information about molecular symmetry with
    a three-letter (or shorter) name and extension '.sym' 
    (required).

    3. File containing the lower triangle of the force constant matrix 
    'molname.ffc' (required if a nonempirical force field is used).  

    4. File containing anharmonic constants 'molname.ccc' (if available).

    5. File containing information for thoroughly refining anharmonic 
    force field 'molname.hss' (if available).

    I.1. FILE 'MOLNAME'

This file contains options and numerical information. The options
should precede the numerical information.

    I.1.1. Options

Options are set by several key words which are case-insensitive.  
Each key word in options should be placed in a separate line 
starting with column 1. If a line begins with ';' (semicolon), it 
is treated as a comment and skipped.  

Several key words need some data to be entered. These data should
follow in the next line after the key word in free format. The
last key word in options is 'DATA'.

If a key word line contains an error, the corresponding message is
printed in the 'molname.txt' file and the program terminates.

KEY WORDS:

    'ROTHZ' calculates rotational constants in MHz (default).

    'ROTCM' calculates rotational constants in cm-1.

    'CART'  prints vibrational Hamiltonian eigenvectors as Cartesian 
            atomic displacements from equilibrium positions.  

    'MODES' prints vibrational modes in internal basis. If this
            option is specified, a table is printed with each row
            corresponding to a vibrational mode and each column,
            to a vibrational coordinate. Modes are numbered in the
            order of increasing frequencies, and vibrational
            coordinates, as they are numbered in the DATA section.

    'DISTR' prints out potential energy distribution over groups
            of equivalent coordinates and contributions of groups
            of equivalent coordinates to vibrational modes; these
            data are calculated as follows. The contribution of a
            coordinate to the potential energy is set equal to
            the square of its value multiplied by the
            corresponding force constant. The contribution of a
            group of equivalent coordinates equals the sum of the
            contributions of the coordinates that constitute this
            group. Taken for a 100 percent is the sum of the
            contributions of all vibrational coordinates. The
            contribution of a group of coordinates to the given
            mode is calculated as its relative 'length'. The
            'length' of a group of coordinates is set equal to
            the square root of the sum of squared coordinate
            values divided by the number of coordinates in the
            group. Taken for 100 percent is the sum of all
            such 'lengths'.
            Given in parentheses are the numbers of groups of
            equivalent coordinates as they appear in the list of
            force constants in the output ('MOLNAME.TXT') file.

   'THERMO' calculates mean rotational constants at the temperature 
            specified in the 'MOLNAME' file. Otherwise, rotational 
            constants calculations correspond to 0 K.

   'CHANGE' allows using arbitrary frequencies (other than those
            found by solving the direct spectral problem) in
            amplitude and rotational constant calculations. After
            this key word, the next several lines should contain
            the following data.

            a) The first line should give the number of
               frequencies to be changed (free format, integer).
            b) The numbers of the frequencies to be changed
               (free format, integer).
            c) The required frequencies (free format, real).

            IMPORTANT! In output, degenerate vibrations are
            treated as one mode.  Under 'CHANGE' we must use
            actual frequency numbers. That is, suppose the first
            mode is triply degenerate, the second one is doubly
            degenerate, and the third one is again triply
            degenerate, and we wish to change the frequency of
            the third mode. In output, this mode appears as
            frequency no. 3.  Under 'CHANGE' we must give a) '3'
            (number of frequencies), b) '6 7 8' (frequency
            numbers) and c) 3 identical real numbers of our
            choice.

   'DEFECT' calculates the inertial defect. Only makes sense for planar 
            molecules.  

   'FIRST'  prints out mode contributions to vibrational amplitudes 
            (first-order approximation).  

   'SECOND' prints out mode contributions to shrinkage corrections 
            (second-order approximation).  

   'LOCAL'  transforms the matrix of force constants in Cartesian 
            coordinates to the matrix of force constants in 
            pseudosymmetry, or local symmetry, coordinates.  

   'SHOW'   gives detailed information about selected vibrational modes.  
            When requested from the screen, you must sequentially 
            introduce the numbers of the modes of interest, one number 
            for each request (see under 'CHANGE' about numbering). To 
            continue calculations, enter '0'.The amplitudes and 
            shrinkage corrections are then calculated for the selected 
            modes only (the other modes are ignored).  
   
   'SCALE'  requires the introduction of scale factors. The following 
            numerical data should be entered after this key word: 

            a) the number of scale factors (free format, integer), it 
               may be less than the number of diagonal force field 
               parameters if some coordinates are treated as equivalent; 

            b) array of scale factors (free format, real).

            The scaled force field is written in 'MOLNAME.FC1'.  

   'FREE'   prints out temperature starting with which selected 
            torsional mode becomes free rotation.
            Should be followed by:

            a) the number of torsional coordinates of interest

            b) the numbers of these coordinates (as printed out in 
               the .txt file or as given in the .dat file)

            For instance,

            free
            1
            26

            prints out temperature starting with which coordinate 26
            becomes free rotation

   'IGNORE' excludes from calculations certain modes (sets the 
            corresponding frequency factors to zero)
            Should be followed by:

            a) the number of frequencies to be ignored

            b) the numbers of these frequencies

            For instance,

            ignore
            1
            1

            sets the frequency factor for one frequency (frequency no. 
            1) equal to zero

   'FORM'   determines the format for reading the 'MOLNAME.FFC' file. 
            This key word should be followed by 'n' (free format, 
            integer). This file may be written in three ways.  

            a) n=0 (default): complete rows of the lower triangular part 
               of force constant matrix are given one after another; 

            b) n>0 : these rows can be given in portions, first n values 
               of all N rows of the matrix, then the next n values of 
               the last N-n rows, then the next n values of the last 
               N-2n rows, etc.; 

            c) n<0 (any negative value): the lower triangular part of a 
               force constant matrix is given as a continuous array as is 
               typical of GAUSSIAN outputs (checkpoint file).  

   'ASYM40' indicates that symmetry coordinates will be introduced 
            using the format of the program ASYM40 (see I.1.2).  

   'FREQ'   sets the threshold value 'x' in cm-1 (free format, real) 
            which must be given in the next line. The frequencies less 
            than x are treated as zero and excluded from further 
            calculations (default is x=5.0).  

   'RENUMB' if a Hartree-Fock field was calculated with a low 
            gradient convergence tolerance, the program may fail 
            to recognize degeneracy and will therefore treat all 
            modes as nondegenerate. If you nevertheless want that 
            vibrational corrections to rotational constants be 
            calculated taking into account degeneracy and using 
            the corresponding equations, you must indicate 
            explicitly which frequencies are to be treated as 
            degenerate mode components.  This can be done by 
            setting option 'renumb', which must be followed by 
            (1) the total number of vibrational modes including 
                degenerate mode components (separate line, free format); 
            (2) new frequency numbers starting with the lowest frequency 
                (one or several lines, free format): degenerate mode 
                components should be assigned the same number.  
            For instance, for a tetrahedral molecule with  frequencies 
            ordered as E < T2 < A1 < T2: 
            9 (first line)
            1 1 2 2 2 3 4 4 4 (second line).

   'NOPRFY' used to reproduce Hartree--Fock frequency calculations 
            exactly, without purifying the force field. Overrides 
            'SCALE' option. Calculations end by printing out 
            frequencies

   'GAMESS' force constant matrix from the GAMESS punch file is 
            used. The corresponding section of the punch file
            is introduced as is, without any modification.
            For instance:
           
            1  1 3.19220786E-01-3.97790142E-05 ... -3.52022802E-06
            1  2-6.62862655E-08-6.37920890E-02 ... -6.37958088E-02
            1  3-4.78373206E-02-1.97409037E-02 ...  3.94732251E-02
            .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . .
           15  1 3.94474616E-02-7.40345366E-10 ...  4.09930257E-10                                            
           15  2-1.64342805E-03-4.48998084E-03 ... -4.48998103E-03                                            
           15  3 7.17967269E-04 7.49146905E-03 ...  5.19563862E-02                                            
            $END

   'ANHARM' this option indicates that calculations according to [3] 
            should be performed with the use of a complete set of 
            anharmonic constants, such as produced in frequency 
            calculations by GAUSSIAN with option 'CUBIC'. If this key 
            word is given, cubic constants should be introduced in one of 
            the following two ways:
            a) either in a file named 'molname.ccc'
               (1) exactly as these constants are written in the 
               output from GAUSSIAN, for instance:
               
               K=  1 block:                                 
                           1                                
                 1  0.927986D+00                                                              
               K=  2 block:                                 
                           1             2              
                 1  0.000000D+00                        
                 2 -0.175437D+00  0.000000D+00          
               K=  3 block:                             
                           1             2             3
                 1 -0.384803D+00                                                              
                 2  0.000000D+00 -0.138616D+00          
                 3 -0.382231D-01  0.000000D+00  0.108782D+01
                etc.

                (2) in the same way but without numbers of blocks,
                columns, and rows, for instance:
               
                 0.927986D+00                                                              
                 0.000000D+00                        
                -0.175437D+00  0.000000D+00          
                -0.384803D+00                                                              
                 0.000000D+00 -0.138616D+00          
                -0.382231D-01  0.000000D+00  0.108782D+01
                etc.

                (3) complete blocks (square matrices) may also be 
                given; the first line should then contain word 'test'
                (without quotation marks) printed right left;

            b) or below the 'ANHARM' key word as follows:
               1. The line containing number N of different constants.
               2. The line(s) with N numerical cubic constant values.
               3. The line(s) with cubic constant multiplicities (the 
                  numbers of positions each constant should occupy).
               4. The line(s) with the first indices of a(i,j,k) 
                  constants; the number of values in this array should 
                  equal the sum of cubic constant multiplicities.
               5. The line(s) with the second indices of a(i,j,k).
               6. The line(s) with the third indices of a(i,j,k).

   'ANHAR2' this key word is used if anharmonic corrections should be 
            calculated according to [3] with diagonal cubic constants 
            for stretching coordinates different from those tabulated by 
            Kuchitsu; this key word should be followed by: 
            1) the number of cubic constants to be introduced and
            2) array of cubic constant values; the values should be given 
               in the same order as stretching coordinates (as 
               specified in the 'DATA' section).

   'DATA'   ends setting options. The numerical information
            should follow this key word as described
            in the next section.



    I.1.2. Description of the DATA part of the 'MOLNAME' file

Free format is used to enter numerical information. This means that input 
data consist of a string of values separated by one or more blanks or a 
comma. Input elements are numbered below by Arabic numerals. Each input 
element must start on a new line. Real constants may be entered with or 
without a decimal point, e.g., 99 is read as 99.0. A decimal point in an 
integer field is a fatal error and causes the job to be aborted. Equal 
values may be repeated using an asterisk, e.g., 5*0.0 3*-1.0.  String 
variables (alphanumeric data) are entered in single quotation marks, 
e.g., 'Si2', 'H10', etc.  

    1) Line with arbitrary information (80 alphanumeric
       characters) which will be printed out as a job title.

    2) NFILE LINK INFC IX IZ (free format, 1 string + 4 integers)

       NFLIE --  string of 3 characters for the name of a '*.sym'
                 file containing information about molecular
                 symmetry (see I.2). This item should be entered,
                 for example, as 'c3v' for the c3v.sym file.

       LINK --   if LINK=0, force constants in Hartree/Bohr
                 are given in the 'MOLNAME.FFC' file;
                 if LINK=1, force constants are in mdyn/A, mdyn,
                 and mdyn*A.

       INFC --   the number of groups of coordinates equivalent by
                 symmetry or treated as equivalent from other
                 considerations; if scale factors are given in
                 options, this number should be equal to the
                 number of scale factors, or the program
                 terminates.

       IX, IZ    are normally set equal to zero; they can be used
                 to specify the directions of the principal axes
                 of inertia, which is sometimes necessary with
                 high-symmetry molecules, and orient these axes
                 as is standard for a molecular symmetry group.
                 IX is then set equal to the number of the atom
                 that should lie on the OX axis, and IZ, to the
                 number of the atom that should lie on the OZ axis
                 (both assignments or either of them may be made).
                 In any event, the system of coordinates is
                 transformed to the principal axes of inertia,
                 but with high-symmetry molecules, the resulting
                 configuration will not necessarily be standard
                 without specifying IX and/or IZ.

    3) NA IDM NFC NW NEK (free format, integer)

       NA --  number of atoms
       IDM -- number of internal coordinates
       NFC -- if positive, number of force constants of an empirical 
              force field (force constants are then given under 'DATA' 
              rather than in a separate 'MOLNAME.FFC' file, see below); 
              if negative, than its magnitude equals the number of 
              independent linear combinations of internal coordinates, 
              that is, the problem is solved in pseudosymmetry 
              coordinates (Pulay). The force constants are then given in 
              'MOLNAME.FFC' in mdyn/A, mdyn, and mdyn/A; 
              if zero, the matrix of force constants is in 'MOLNAME.FFC' 
              and, if LINK=0, has dimension 3*Nx3*N and is in Hatree/Bohr 
              or, if LINK=1, has dimensions IDMxIDM and is in mdyn/A, 
              mdyn, and mdyn*A 
       NW --  number of auxiliary atoms introduced to define
              linear bends or for other purposes
       NEK -- number of Eckart coordinates, generally 6 (5 for
              linear molecules)

    4) NC(i), i = 1, 5   (free format, integer)

       NC(i)  is the number of internal coordinates of type 'i'.  
              Coordinates of five types are used: 1) stretching, 2) 
              bending, 3) wagging, 4) linear bending, and 5) torsional. 
              The sum of NC(i) must equal IDM.  

    5) (Skipped if NFC.LE.0) Array of force constants if an empirical 
       force field is used (free format, real).  Different force 
       constants, one for each group of equivalent coordinates or 
       interactions, are only given.  Force constants should be given 
       stretching first, next bending, then wagging, linear bending, and 
       torsional.  

    6) Array of force constant multiplicities, or the numbers of 
       positions that each force constant occupies the lower triangle of 
       force constant matrix (free format, integer).  The first number 
       should be zero; if NFC > 0, diagonal elements should be separated 
       from off-diagonal ones by another zero. The number of array 
       elements should be INFC + 1 (or NFC + 2 if NFC > 0). The 
       multiplicities should be given in the same order as the force 
       constants (the second number, i.e., first after zero refers to the 
       first force constant, the third one to the second force constant, 
       etc.).  

    7) (Skipped if NFC.LE.0) Two arrays determining the positions of off-
       diagonal force constants in the lower triangle of the force 
       constant matrix, the first one with row numbers and the second one 
       with column numbers (free format, integer).  

    8) NAME(i), AMASS(i), X(i), Y(i), Z(i), i=1,NA (free format,
                                             1 string + 4 reals)

       NA lines contain:
       NAME    - a label of each atom, e.g., 'H 1' or 'H1', 'Si15', etc., 
                 maximum 4 alphanumeric characters within single 
                 quotation marks; NAME should begin with the symbol of 
                 the chemical element (if the symbol is one-character, 
                 the second position can be either left blank or contain 
                 a digit); hydrogen isotopes can be introduced as 'H' 
                 (AMASS should then be set equal to 2.0 or 3.0 for 
                 deuterium and tritium, respectively, see below) or as 
                 'D' or 'T' 

       AMASS   - put it equal to zero (0.0) to perform calculations for 
                 the most abundant isotope or to the mass number of the 
                 isotope you wish to use (e.g. 6.0 for 6_Li); you can 
                 also introduce the atomic weight manually (the program 
                 distinguishes between atomic weights and mass numbers by 
                 the presence or absence of nonzero digits after the 
                 decimal point); 

       X, Y, Z - Cartesian coordinates in A. When Cartesian force field 
                 is read, Cartesian coordinates entered here must 
                 correspond to Cartesian coordinates used in the 
                 calculation. Input Cartesian coordinates (and Cartesian 
                 force field) are then transformed to the system of 
                 principal axes.  

    9) NW similar lines for auxiliary atoms if NW>0 (with arbitrary 
       masses).  

   10) Description of internal coordinates (free format, integer).

       It should be given in the order: stretching, bending, wagging, 
       linear bending, torsional and agree with the order of force 
       constants and force constant multiplicities. Coordinates included 
       in the same group of equivalent coordinates should follow one 
       another.  

       Each of the following input items must start with a new line.  

       1. Stretching: N1(i), N2(i), i=1,NC(1).  Identification of two 
          atoms in each stretching coordinate.  

       2. Bending: N1(i), N2(i), N3(i), i=1,NC(2).  Identification of 
          three atoms in each bending coordinate, the N2 atom being the 
          central atom of the angle.  

       3. Wagging: N1(i), N2(i), N3(i), N4(i), i=1,NC(3).  Identification 
          of four atoms in an out-of-plane coordinate, the central atom 
          should be given first, next the "end atom" and two "anchor 
          atoms", last. The central atom moves up if the three other ones 
          are ordered clockwise.  

          This coordinate is valid for both planar and slightly nonplanar 
          groups of four atoms.  

       4. Linear bending: N1(i), N2(i), N3(i), N4(i), i=1,NC(4).  
          Identification of the three atoms (N1, N2, N3) in each linear 
          bending coordinate, the N2 atom being the central atom of the 
          angle. The N4 atom is an auxiliary one to determine the 
          direction in which the chain bends.  
          Note: N2--N1, N2--N3, and N2--N4 should be bonds (that is, they 
          should be present in the list of stretching coordinates; this 
          is required by the procedure for calculating local centrifugal 
          distortions) 

       5. Torsional: N1(i), N2(i), N3(i), N4(i), N5(i), N6(i), N7(i), 
                     N8(i), i=1,NC(5).  
          Identification of eight atoms involved in torsional motion 
          about the N4-N5 axis. The N1, N2, and N3 atoms are attached to 
          the N4 atom, while the N6, N7, and N8 atoms are attached to the 
          N6 atom. At least four atoms (N1, N4, N5, and N6) must be 
          given. The other positions may filled by zeros.  

          Note: (a) Try not to use torsional coordinates if the bond that 
                    defines one of the rotating planes makes an angle 
                    close to 180 deg with the axis of rotation. Better 
                    replace such a torsional coordinate by a wagging one.  
                (b) N4--N1, N4--N2, N4--N3, N4--N5, N5--N6, N5--N7, and 
                    N5--N8 should be bonds (that is, they should be 
                    present in the list of stretching coordinates; this 
                    is required by the procedure for calculating local 
                    centrifugal distortions) 

          The number of coordinates described above should be
          equal to IDM; otherwise, the program terminates.

       ATTENTION! A COMPLETE SET OF INTERNAL COORDINATES SHOULD
       BE GIVEN, FOR THE TRANSFORMATION MATRIX BETWEEN INTERNAL
       COORDINATES (WHICH ARE AUTOMATICALLY AUGMENTED BY THE
       ECKART COORDINATES) AND CARTESIAN COORDINATES SHOULD HAVE
       THE FULL COLUMN RANK. OTHERWISE, AN ERROR MESSAGE IS
       WRITTEN INTO THE 'MOLNAME.TXT' FILE AND THE PROGRAM
       TERMINATES.

   11) (Skipped if NFC.GE.0) If Pulay's pseudosymmetry coordinates are 
       used, a description of 3*NA-6 (3*NA-5 for linear systems) 
       independent linear combinations of internal coordinates should 
       follow. There are two ways to introduce symmetry coordinates.  

       1. Default, when option 'ASYM40' is not used.
            a) Number of the symmetry coordinate, the number of internal 
               coordinates involved, and the list of these coordinates 
               (free format, integer);          
            b) if the number of the internal coordinates involved exceeds 
               one, the next line should contain coefficients (not 
               necessarily normalized) with which these coordinates 
               appear in the corresponding linear combination (free 
               format, real).  

          NOTE: if the 'molname.ffc' file contains force constants for 
                local symmetry coordinates generated by some other 
                program, discrepancies may arise, because different 
                programs assign different signs to torsional and wagging 
                displacements. This difficulty can be removed by changing 
                the signs of the corresponding coefficients [or, if only 
                one coordinate is involved, by putting -1 for the number 
                of coordinates, see a)] 

       2. If the 'ASYM40' option is in effect, then symmetry coordinates 
          are introduced as in the ASYM40 program.  
          For each symmetry coordinate:

          U(j), j=1,IDM; IFLAG (free format, IDM reals +1 integer)

          U(j) - one row of the U-matrix which defines the symmetry
                 coordinate. The elements need not be normalized.

          IFLAG - 0, the elements will be unchanged;
                  1, the elements will be normalized.


   12) Temperature (K) at which amplitudes and shrinkage corrections are 
       to be calculated (free format, real). Rotational constants are 
       usually calculated at T = 0, but centrifugal corrections to them 
       correspond to the temperature specified here.  

   13) A line (free format, integer) with the number of distances for 
       which amplitudes and shrinkage corrections are to be calculated 
       (NAMPL) and the number of bonded distances, for which anharmonic 
       corrections will be calculated in the diatomic approximation 
       (N_BOND) (see K.Kuchitsu et al. in I.  Hargittai and M. Hargittai 
       (Eds.), Spectrochemical Applications of Gas-Phase Electron 
       Diffraction, 1988); if you wish to use anharmonic constants other 
       than those tabulated by Kuchitsu, put N_BOND = NAMPL + N_BOND.  

   14) Numbers of atoms defining these distances; bonded distances should 
       be given first (free format, integer).  

   15) If N_BOND > NAMPL, the program assigns N_BOND = N_BOND - NAMPL and 
       requires the introduction of anharmonic constants; the anharmonic 
       constants should be introduced for all bonds (free format, real).  



    I.2. FILE '*.SYM'

This file contains information about the molecular symmetry group used 
for assigning frequencies to various symmetry types. It should have a 
three-letter or shorter name specified as 'NFILE' in 'DATA' (item 2) and 
extension '.SYM'. The same '.SYM' file can be used with all molecules of 
the same symmetry.

    REMARK. Hartree-Fock force fields are often rather 'dirty'
            and do not strictly satisfy symmetry requirements.
            With such fields, the program can make incorrect
            symmetry assignments and even report 'symmetry
            failure', which, however, has no effect on the
            further calculations. To obtain a correct assignment,
            the Hartree-Fock force field matrix should be
            symmetrized, which is easily achieved by applying all
            molecular group symmetry operations to this matrix
            (or the Hartree-Fock matrix transformed to internal
            coordinates), summing the results, and dividing the
            sum by the order of the symmetry group (the number of
            symmetry operations used).

A '*.sym' file should be organized as follows.

    1) First, several lines corresponding to different types of optically 
       active modes are given. Each line contains the number(s) of the 
       function(s) that transforms (transform) according to a certain 
       representation (8i3, integer). The functions are numbered as: 

       1 -- X**2 + Y**2 + Z**2 (totally symmetric representations)
       2 -- X**2 - Y**2
       3 -- XY
       4 -- XZ
       5 -- YZ
       6 -- X
       7 -- Y
       8 -- Z
       9 -- Z**2
       (see Tables of Characters).

       If several functions transform according to a given 
       representation, then the corresponding line should contain several 
       numbers corresponding to these functions.  IT IS VERY IMPORTANT 
       THAT THE MOLECULE HAVE THE STANDARD ORIENTATION USED IN THE 
       CORRESPONDING TABLE OF SYMMETRY GROUP REPRESENTATION CHARACTERS. 
       Otherwise, modes will be given incorrect symmetry assignments, but 
       the program will continue to work normally.  

    2) A line with zero in the third column.

    3) Seven-character entries designating mode degeneracies and 
       types (format a1,i1,a5). The degeneracy number should 
       appear in the second position. The number of entries 
       should equal the number of lines describing symmetry types 
       of optically active modes. For example, one of the entries 
       may be (2,e1g) for a doubly degenerate vibration of the 
       e1g symmetry type.  

If you are not interested in symmetry assignments, you may always
use the following 'C1.SYM' file:

  1  2  3  4  5  6  7  8
  0
(1,A)


    I.3. FILE 'MOLNAME.FFC'

Force constants may be given in Cartesian, internal, or
pseudosymmetry coordinates. If the force constants are given in
Cartesian coordinates, the program 'purifies' them using the
Moore-Penrose inverse of the transformation matrix between the
internal and Cartesian coordinates to reduce translational and
rotational frequencies to zero and simultaneously transforms the
force constant matrix to internal or psudosymmetry coordinates.
Further solution is performed as if the matrix was originally
given in internal coordinates (the matrix in internal coordinates
is scaled if scale factors are introduced and written into the
'MOLNAME.FC1' file).


    II. OUTPUT FILES

Output data will be in:
    1. File 'molname.txt' containing calculation results.
    2. File 'molname.fc1' containing transformed force field.
    4. File 'molname.cor' if option 'rothz' or 'rotcm' is used.

    II.1. FILE 'MOLNAME.TXT'

The structure of this file is fairly simple and only one small point 
should be mentioned.  

In the list of frequencies with potential energy distribution data (if 
option 'DISTR' is included) and in the summary list of frequencies 
(always given), degenerate vibrations are treated as one mode, and the 
frequencies are numbered accordingly. In all tables (in the table of 
vibrational modes in internal basis if option 'MODES' is included, and in 
the tables of frequency contributions to amplitudes and shrinkage 
corrections, options 'FIRST' and 'SECOND'), degenerate vibration 
components are treated as separate modes and assigned separate numbers.  


    II.2. FILE 'MOLNAME.FC1'

If a Hartree-Fock force filed is used, file 'MOLNAME.FC1'
contains the force field transformed to internal or
pseudosymmetry coordinates, possibly scaled if option 'SCALE' is
set. If internal or pseudosymmetry coordinates are used, scaled
force fields are written or unscaled ones rewritten (may be, in
a different format) into this file from 'MOLNAME.FFC'.


    II.3. FILE 'MOLNAME.COR'

Coriolis coupling constants and vibrational mode contributions to 
corrections to rotational constants are written into this file if
rotational constants are calculated. Degenerate vibration
components are included as separate modes.


    III. RUNNING THE PROGRAM

When started, the program prompts the user to introduce the name
of the input file which has to be prepared as described above.

If option 'SHOW' is set, the program prompts the user to
introduce the numbers of modes to be examined (degenerate
vibration components are treated as separate modes and assigned
separate numbers). The numbers should be introduced one at a
time, to introduce more numbers wait for more prompts. To skip
the 'SHOW' procedure, type '0' in response to the first prompt.
To continue calculations after the required number of frequencies
is introduced, type '0' in response to the next prompt.


    IV. EXAMPLE OF THE 'MOLNAME.CCC' FILE

It runs exactly as follows:

 K=  1 block:
             1
   1  0.927986D+00
 K=  2 block:
             1             2
   1  0.000000D+00
   2 -0.175437D+00  0.000000D+00
 K=  3 block:
             1             2             3
   1 -0.384803D+00
   2  0.000000D+00 -0.138616D+00
   3 -0.382231D-01  0.000000D+00  0.108782D+01
 K=  4 block:
             1             2             3             4
   1 -0.195168D-01
   2  0.000000D+00  0.317927D-01
   3  0.119116D+00  0.000000D+00 -0.353303D-01
   4  0.576133D-02  0.000000D+00 -0.125303D+00 -0.160697D-02
 K=  5 block:
             1             2             3             4             5
   1  0.000000D+00
   2  0.115253D-01  0.000000D+00
   3  0.000000D+00  0.165741D+00  0.000000D+00
   4  0.000000D+00 -0.166894D-01  0.000000D+00  0.000000D+00
   5  0.379042D-02  0.000000D+00 -0.153640D+00 -0.831567D-03  0.000000D+00
 K=  6 block:
             1             2             3             4             5
   1  0.149151D+00
   2  0.000000D+00  0.140090D+00
   3 -0.116010D-01  0.000000D+00 -0.994300D+00
   4 -0.129553D+00  0.000000D+00  0.259725D-01  0.117553D+00
   5  0.000000D+00 -0.148989D+00  0.000000D+00  0.000000D+00  0.155422D+00
   6  0.480215D-03  0.000000D+00  0.980830D+00 -0.471707D-03  0.000000D+00
             6
   6 -0.980792D+00
 K=  7 block:
             1             2             3             4             5
   1 -0.908471D+00
   2  0.000000D+00  0.143644D+00
   3  0.265688D+00  0.000000D+00  0.735553D-01
   4  0.137568D-01  0.000000D+00  0.618632D-02 -0.415537D-02
   5  0.000000D+00  0.516417D-02  0.000000D+00  0.000000D+00 -0.295893D-02
   6 -0.195990D-01  0.000000D+00 -0.143721D-01  0.120009D-01  0.000000D+00
   7  0.894715D+00  0.000000D+00 -0.271874D+00 -0.960181D-02  0.000000D+00
             6             7
   6 -0.819246D-05
   7  0.759822D-02 -0.885114D+00
 K=  8 block:
             1             2             3             4             5
   1  0.000000D+00
   2  0.163912D+00  0.000000D+00
   3  0.000000D+00 -0.271247D-01  0.000000D+00
   4  0.000000D+00 -0.151031D-01  0.000000D+00  0.000000D+00
   5 -0.153157D-01  0.000000D+00 -0.121012D-01  0.175208D-01  0.000000D+00
   6  0.000000D+00  0.889898D-02  0.000000D+00  0.000000D+00 -0.643230D-02
   7  0.000000D+00 -0.148809D+00  0.000000D+00  0.000000D+00 -0.220514D-02
   8 -0.148597D+00  0.000000D+00  0.392259D-01 -0.241790D-02  0.000000D+00
             6             7             8
   6  0.000000D+00
   7  0.000000D+00  0.000000D+00
   8 -0.246654D-02  0.151014D+00  0.000000D+00
 K=  9 block:
             1             2             3             4             5
   1  0.235654D+00
   2  0.000000D+00 -0.147343D-02
   3  0.498236D-01  0.000000D+00 -0.935238D-01
   4  0.104356D-01  0.000000D+00  0.935880D-02  0.775145D-02
   5  0.000000D+00 -0.167519D-01  0.000000D+00  0.000000D+00 -0.178180D-02
   6  0.111218D-01  0.000000D+00  0.134707D-01 -0.255017D-01  0.000000D+00
   7 -0.246090D+00  0.000000D+00 -0.591837D-01 -0.181869D-01  0.000000D+00
   8  0.000000D+00  0.182257D-01  0.000000D+00  0.000000D+00  0.185335D-01
   9 -0.609459D-01  0.000000D+00  0.800552D-01  0.161429D-01  0.000000D+00
             6             7             8             9
   6 -0.381165D-04
   7  0.143802D-01  0.264276D+00
   8  0.000000D+00  0.000000D+00 -0.367594D-01
   9 -0.134330D-01  0.448041D-01  0.000000D+00 -0.666237D-01

etc.

