Nature of physical problem IBM 360/195 Argonne National Laboratory The original version of the program [1] symmetry-reduced the dynamical matrix characterizing lattice vibrations of solids, Operating system: SCOPE 3.1 (LASL version) constructed symmetry coordinates which were labeled by the Programming language used: FORTRAN IV irreducible multiplier representations of the group of the wavevector, and block-diagonalized the dynamical matrix. This im-High speed store required: 137 K (octal) proved version of the program allows one to calculate the sym-No. of bits in a word: 60 metry properties of the external modes of vibration of molecular crystals [2], to generate the irreducible multiplier re-Overlay structure: None presentation (IMR's) [3], and to include the effects of time No. ofmagnetic tapes required: None reversal invariance (TRI) on the symmetry coordinates [4]. Other peripherals used: Card reader, line printer Method of solution The invariance of the dynamical matrix under unitary trans-Number of cards in combined program and test deck: 2334 formations by matrices in a reducible multiplier representa-Card punching code: BCD tion 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 * Work performed under the auspices of the U.S. Atomic is dependent on the reducible multiplier representation used Energy Commission. and the IMR's ofthe group of the wavevector. These IMR's '~This is a USAEC required collection and dissemination are generated in the program by the method of orbitals from center for unclassified codes developed within the USAEC. the representations of cyclic subgroups of the group of the CPC is not able to guarantee that the program obtainable wavevector which in turn are constructed from the roots of from this source is the same as that held in the CPC Program unity. The symmetry coordinate vectors form a matrix, which Library and described in this paper. transforms the symmetry-reduced dynamical matrix into block-diagonalized form.