NESC0620 GROUP2

1. NAME OR DESIGNATION OF PROGRAM:  GROUP2

3. DESCRIPTION OF PROBLEM OR FUNCTION

This  program calculates  the
symmetry  properties  of  lattice  vibrations  either  for  atomic
crystals or for external modes of molecular crystals and generates
the irreducible  multiplier representations (IMR's)  including the
effects  of  time  reversal  invariance   (TRI)  on  the  symmetry
coordinates.

4. METHOD OF SOLUTION

The invariance of the  dynamical matrix under
unitary  transformations by  matrices  in  a reducible  multiplier
representation of the  time reversal invariant point  group of the
wavevector leads  to a formula  for the symmetry-reduction  of the
dynamical  matrix.  The  projection  operator  method is  used  to
construct the  symmetry coordinates.   The projection  operator is
dependent on the reducible multiplier  representation used and the
IMR's of the  group of the wavevector.  These  IMR's are generated
in the program by the method  of orbitals from the representations
of cyclic subgroups  of the group of the wavevector  which in turn
are constructed from the roots  of unity.  The symmetry coordinate
vectors  form  a  matrix, which  transforms  the  symmetry-reduced
dynamical matrix into block-diagonalized form.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

The   program   is
dimensioned for up  to 30 degrees of freedom per  unit cell.  This
may  be 10  atoms  or 5  molecular  units per  unit  cell or  some
combination of atoms and molecular units.  Each atom has 3 degrees
of  freedom,  and  each  molecular unit  has  6.   By  changing  a
dimension statement, up to 60 degrees of freedom per unit cell may
be considered.   Because of the use  of random numbers  instead of
algebraic techniques,  the symmetry  reduction will  be incomplete
for crystals  of the  D3 or  C3 point  groups.  This  same problem
sometimes occurs for  other crystals with a large  number of atoms
per unit cell.

6. TYPICAL RUNNING TIME

10  seconds  are  required   for  all  wave
vectors of a crystal with two atoms per unit cell.

7. UNUSUAL FEATURES OF THE PROGRAM

The  program requires  only  the
three lattice vectors, the atomic  positions, and the desired wave
vectors as input.  It determines all of the symmetry properties in
one  pass.  It  will also  calculate external  modes of  molecular
crystals.  Time reversal is considered in all calculations.

8. RELATED AND AUXILIARY PROGRAMS:  ACMI/EM/IMR   was    an   earlier
version.

10. REFERENCES

- J.L. Warren and T.G. Worlton:
  Symmetry Properties of the Lattice Dynamics of Twenty-Three
  Crystals
  ANL-8053 and LA-5465-MS (December 1973)

- T.G.  Worlton and J. L. Warren:
  Group Theoretical Analysis of Lattice Vibrations
  Computer Physics Communications, Vol. 3, pp. 88-117 (1972)
- T.G. Worlton and J.L. Warren:
  Erratum
  Computer Physics Communications, Vol. 4, pp. 382-383 (1972)
- T.G. Worlton:
  External  Modes of Molecular Crystals
  Computer Physics Communications, Vol. 4, pp. 249-256 (1972)
- T.G. Worlton:
  Irreproducible Multiplier Representations
  Computer Physics Communications, Vol. 6, pp. 149-155 (1973)
- J.L. Warren  and T.G. Worlton:
  Improved Version of Group-Theoretical Analysis of Lattice Dynamics
  Computer Physics Communications, Vol. 8, pp. 71-84 (1974)

11. MACHINE REQUIREMENTS

The IBM360  version requires 240K  bytes to
compile and 230K  bytes to execute.  The  CDC6600 version requires
55,000 (octal) words to compile, 125,000 (octal) words to execute.

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:           OS/360
(IBM360) and SCOPE 3.1 (CDC6600).

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

   The
input deck  structure is  indicated on comment  cards in  the main
program.   The system  library or  user must  supply the  function
RANF(N) which  produces a  uniformly-distributed sequence  of real
random numbers.   In the IBM version,  n=-1; in the CDC,  n=0.  In
some  cases, the  phase angle  matrix  and the  block-diagonalized
dynamical matrix are not fixed  by symmetry considerations and may
differ  from the  sample  output.  Also,  other  vectors may  have
different    representations,    depending   on    the    specific
implementation of the ATAN function.

15. NAME AND ESTABLISHMENT OF AUTHORS

   6600          John L. Warren
                 Los Alamos Scientific Laboratory
                 P. O. Box 1663
                 Los Alamos, New Mexico  87544
   360           Thomas G. Worlton
                 Solid State Science Division
                 Argonne National Laboratory
                 9700 South Cass Avenue
                 Argonne, Illinois  60439

File name	File description	Records
NESC0620_02.001	SOURCE PROGRAM (F4)	2309
NESC0620_02.002	SAMPLE PROBLEM DATA	35
NESC0620_02.003	SAMPLE PROBLEM PRINTED OUTPUT	344