What VIBRATZ Does
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VIBRATZ is a program for modeling the fundamental optical vibrations of any compound, using valence forces (interatomic bonds and angles). VIBRATZ calculates only fundamental frequencies, not overtones and combinations (which are usually much weaker in spectra). In a molecule, there are 3n-6 fundamental vibrations, where n is the number of atoms.

In crystals, optical vibrations (or more strictly limit optical vibrations) are defined as those in which the wavevector kappa is zero. In such vibrations, all unit cells behave identically, whereas in non-optical vibrations, atoms in different unit cells have different motions. There is only a limited number of optical vibrational modes, namely 3n-3 for crystals, where n is the number of atoms in the unit cell, whereas the number of non-optical modes depends on the total number of atoms in the actual crystal. The capability to calculate all crystal vibrations and phonon dispersion curves may be added to VIBRATZ in the future.

VIBRATZ requires input of 1) unit cell axis lengths and interaxial angles for crystals; 2) selection or input of the point-or space-group symmetry; 3) the atomic coordinates; and 4) specifications for locating the bonds and angles involved in the valence forces, and a force constant for each specification.

The bonds and angles in category 4) are the internal coordinates (or groups thereof) of a traditional normal-coordinate analysis. Because VIBRATZ converts all forces to Cartesian, and carries out the symmetry analysis and solution of the secular equation using Cartesian matrices, there is no limit to the number of internal coordinates which may be used, nor is it necessary to consider explicitly any redundancy relations among them.

Bond and angle specifications can be given in either of two ways: automatically, by specifying the atom types involved and limits on bond lengths and angle values, or manually, by specifying the individual atoms. Atom types are normally chemical species (atomic number), although they can also be symmetrically distinct input atoms for more precise definition of bonds and angles. Angles include 4-atom torsion and bond-plane bending as well as 3-atom valence angles. Interactions between any pairs of internal coordinates may be specified.

Given this information, VIBRATZ then analyzes the symmetry and calculates the frequencies, classified into symmetry species. It provides the atomic displacements involved in each vibration and the fraction of the total energy of the vibrations contributed by each bond or angle (and interactions thereof). An interatomic force matrix in terms of Cartesian displacements of the individual atoms is a by-product of the calculation, and may be exported for other purposes, such as calculating elastic properties.

Least-squares adjustment of the force constants may be done, with selection of both force constants and symmetry species.

Synthetic infrared and Raman spectra may be drawn, using simple models of intensities. Individual polarization components or average spectra may be shown. The atomic motions may be shown graphically.