dc.creator Shimanouchi, Takehiko en_US dc.creator Tsuhoi, Masamichi en_US dc.creator Miyazawa, Tatsuo en_US dc.date.accessioned 2006-06-15T13:08:23Z dc.date.available 2006-06-15T13:08:23Z dc.date.issued 1961 en_US dc.identifier 1961-D-2 en_US dc.identifier.uri http://hdl.handle.net/1811/8057 dc.description $^{1}$E. B. Wilson, J. Chem. Phys., 7, 1047 (1939); 9. 76 (1941). en_US dc.description Author Institution: Department of Chemistry, Faculty of Science, Tokyo University; Institute for Protein Research, Osaka University en_US dc.description.abstract A general description is given of an application of the Wilson’s GF-matrix $method^{1}$ to the treatment of optically active lattice vibrations. Wilson’s way to obtain the normal frequencies and the normal coordinates of any system (group of atoms) is to obtain eigenvalues and eigenvectors of the matrix, GF, where G is the inverse kinetic energy matrix and F the potential energy matrix of the system in question. When the system is composed of an infinite number of atoms, the order of the G or F matrix is infinite, since an infinite number of coordinates are to be taken into account. If the system has some translational symmetry, as does any crystal lattice, however, the G or F matrix of infinite order is a mere repetition of sub-matrices of a finite size. The G or F matrix of a certain species of vibrations of a crystal can be constructed by summing these sub-matrices which have been multiplied by a proper set of phase factors. In the lattice vibrations that are active in the infrared absorption and/or Raman effect, the motion of all the Bravais cells takes place in phase. For such vibrations, all of the phase factors mentioned above are unity. The G or F matrix for these optically active vibrations can be obtained by adding the G or F matrix for a Bravais cell to the sum of all the G or F matrices representing the interactions between the Bravais cells. The coordinate system in the above treatment may be either that of the internal coordinates or that of Cartesian coordinates. As examples, formulas are derived for the calculation of the frequencies of the lattice vibrations of a one-dimensional, the diamond, the zinc-blende, the wurtzite, and fluorite lattices. en_US dc.description.abstract As examples, formulas are derived for the calculation of the frequencies of the lattice vibrations of a one-dimensional, the diamond, the zinc-blende, the wurtzite, and fluorite lattices. en_US dc.format.extent 154182 bytes dc.format.mimetype image/jpeg dc.language.iso English en_US dc.publisher Ohio State University en_US dc.title OPTICALLY ACTIVE LATTICE VIBRATIONS AS TREATED BY THE GF-MATRIX METHOD. en_US dc.type article en_US
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