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Manuscript Title: Group-theoretical analysis of lattice vibrations. See erratum Comp. Phys. Commun. 4(1972)382.
Authors: T.G. Worlton, J.L. Warren
Program title: GROUP THEORY OF LATTICE DYNAMICS
Catalogue identifier: ACMI_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 3(1972)88
Programming language: Fortran.
Computer: IBM 360-75.
Operating system: IBM 360 MVT.
RAM: 36K words
Word size: 32
Keywords: Solid state physics, Lattice dynamics, Group theory, Phonons, Symmetry, Dispersion curves, Dynamical matrix, Multiplier Representation method.
Classification: 7.8.

Revision history:
Type Tit le Reference
adaptation 0001 EXTERNAL MODES See below
adaptation 0002 IMR CALCULATION See below
correction B00ACORRECTION TO 0002 04/08/74 See below

Nature of problem:
The program block-diagonalizes the dynamical matrix characterizing lattice vibrations of solids, constructs symmetry coordinates, and labels these coordinates with the irreducible representations of the symmetry group.

Solution method:
Using a reducible mutliplier representation of the point group of the wavevector, projection operators are constructed. These give symmetry coordinates which are used to block diagonalize the dynamical matrix.

Restrictions:
The program is dimensioned for up to 10 atoms per unit cell; by changing a dimension statement, it shpuld handle up to 20 atoms per unit cell. For certain low-symmetry crystals in the trigonal and hexagonal systems the symmetry reduction of the dynamical matrix will be incomplete because of complicated relations between elements.

Unusual features:
The program also constructs the point group of the crystal, determines Brillouin-Zone boundaries and optical modes exhibiting infrared and Raman activity. Effects of time-reversal invariance are included.

ADAPTATION SUMMARY
Manuscript Title: External modes of molecular crystals.
Authors: T.G. Worlton
Program title: 0001 EXTERNAL MODES
Catalogue identifier: ACMI_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 4(1972)249
Programming language: Fortran.
Classification: 7.8.

Nature of problem:
This adaptation modifies GROUP THEORY OF LATTICE DYNAMICS (CPC 3 (1972) 88) to calculate the symmetry properties of the external modes of vibration of molecular crystals.

Restrictions:
Solutions are given in terms of the cartesian axes. Redundant coordinates for linear molecules are not eliminated.

ADAPTATION SUMMARY
Manuscript Title: Irreducible multiplier representations.
Authors: T.G. Worlton
Program title: 0002 IMR CALCULATION
Catalogue identifier: ACMI_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 6(1973)149
Programming language: Fortran.
Computer: IBM 370 - 195.
Operating system: OS 370 MVT.
RAM: 50K words
Word size: 32
Classification: 7.8.

Nature of problem:
The adaption inserts a subroutine to generate irreducible multiplier representations of the group of the wave vector Go(k). In the original version of ACMI these quantities were read from cards.

Solution method:
IMR's of Go(k) are induced from those of a subgroup of prime order starting from an invariant cyclic subgroup.

Restrictions:
The program would have to be modified for double groups.

Unusual features:
Although designed to improve the program ACMI, this new subroutine together with some subroutines from ACMI can be used as an independent program to calculate IMR's. The present adaptation can be used in addition to ACMI0001 for analysis of external modes of molecular crystals.

Running time:
1 s.

CORRECTION SUMMARY
Manuscript Title: Irreducible multiplier representations. (C.P.C. 6(1973)149).
Authors: T.G. Worlton
Program title: B00ACORRECTION TO 0002 04/08/74
Catalogue identifier: ACMI_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 8(1974)141
Classification: 7.8.