|
377. Programs for the Calculation of Normal Modes and
Structure Factors for Crystals and Molecules
by Flemming Y. Hansen, The Technical University of Denmark, Lyngby, Denmark The three programs FYCOOR, FYFRE and FYADJ are used for normal mode calculations of a crystal or a molecule; besides frequencies and normal modes, the structure factor for neutron scattering of crystals may be calculated and temperature effects may be included. For practical reasons, the calculations have been divided into three parts in such a way that the results of FYCOOR are used as input for FYFRE, which again may produce input data for FYADJ. The transmission of data between the programs is done by writing on suitable units, so there will be no manual work involved. The FYCOOR Program: The purpose of the program is to generate a complete set of coordinates and force matrices to be used in a subsequent normal mode calculation for a molecule or a crystal. The program eliminates or reduces time-consuming and error- producing complexities which have handicapped the application of some computer programs for calculating normal modes. Group theory is used in the program in such a way that many (often most) of the coordinates are generated from a minimum input of so-called basis- set coordinates, which may be arbitrary. All force-constant matrices are set up by the program with very small "dummy" force constants which are easily updated in a selective manner by the user to give the desired potential. The program includes a logic, which assures that force constants which are interrelated by symmetry are given the same value. This means that no matter the complexity of the basis coordinates our procedure always generates a complete set of coordinates and force matrices so degeneracies in the normal mode calculation will be displayed correctly and the dynamical matrix will always be blocked correctly, if symmetry coordinates are used to represent the normal modes. The FYFRE Program: This program is used to calculate the normal modes of a crystal or a molecule on the basis of the complete set of coordinates (D-matrices) and force matrices generated by FYCOOR. The program may be run in three different modes: 1. Calculation of the normal modes of a crystal or a molecule for a specific set of force constants. 2. Generation of an analytical expression for the elements of the dynamical matrix in terms of the various force constants. In this mode, one force constant at a time is updated from the value zero (or rather, its dummy value ~10-10) to one, while all other force constants are practically zero. No eigenvalues are calculated. The dynamical matrix is scanned and elements about a certain input threshold value, Alimit, are printed and written on unit 1 for later use in the force constant adjuster program FYADJ. The contribution to the dynamical matrix is then found by multiplying the non-zero elements with the appropriate force constants; and in this way one may obtain an analytic expression of the various elements in terms of the force constant. 3. Calculation of the normal modes and dynamical structure factors for a given set of force constants and for a given wave vector. The dynamical structure factors are calculated both for phonon annihilation and creation processes. The polarization factors for each atom in the origin cell are also calculated. Temperature effects on the structure factors through the Debye-Waller factor may be taken into account; and for a given neutron incident wave vector |O(k,')o|, the partial differential cross sections for neutron scattering are also calculated at the given temperature. The FYADJ Program: This program may be used to find the values of a given set of force constants which give an optimal fit to a set of frequencies. The computations are based on the results of calculations with FYFRE in mode 2. Thus, it is assumed that for a suitableset ofwave vectors the analytic form of the dynamical matrix has been generated for all relevant force constants and that they are stored on unit 1 in the format described in the program documentation. The order of the data on unit 1 is immaterial because they are sorted out in this program. FORTRAN IV (IBM) Lines of Code: 4223 Recommended Citation: F. Y. Hansen, QCPE 11, 377 (1979). |