Coordinates. The word coordinate(s) is used in many senses in vibrational analysis, which may be confusing to the uninitiated. It may refer to:
1) Atomic coordinates, the components of an atom location in terms either of crystal axes (crystal coordinates or fractional coordinates) or Cartesian axes (Cartesian coordinates).
2) Internal coordinates, the bonds and angles which are used to specify the force constants or potential-energy function (more strictly, the relative motions of atoms in changing the magnitude of bonds and angles). Each internal coordinate should ideally be part of a set which is symmetrically distinct from other sets of internal coordinates. VIBRATZ does not actually use bonds and angles as a basis for the solution of the secular equation - it converts these to a Cartesian basis and solves the secular equation using Cartesian matrices.
3) Symmetry coordinates, the coefficients used to factor the overall secular equation into smaller matrices for the individual species (VIBRATZ automatically derives symmetry coordinates). The symmetry coordinates may be based on internal coordinates or on Cartesian displacement vectors, and in the latter case they are sometimes called external coordinates.
4) Normal coordinates, essentially the relative motions of the atoms in the normal modes, which together with the frequencies are the objects of the calculation.
If a prefix is not applied to the word coordinate(s), the context will hopefully make the meaning clear.
Dialog Bar. This is in effect a dialog which is attached to one edge of a window, in particular the left side of the Atoms graphics window, and the upper edge of the Spectra window. Dialog Bars contain the same type of controls (buttons, checkboxes, edit boxes, etc.) as ordinary dialogs, and these controls apply to what is shown in the window.
Force Constants. As far as input to VIBRATZ is concerned, these are the second derivatives of the potential energy with respect to individual members of each group of internal coordinates or bonds and angles; and also the products of the derivatives of the potential energy with respect to pairs of internal coordinates. In a traditional normal-coordinate calculation carried out using internal coordinates, the force constants correspond to symmetrically-distinct sets of internal coordinates, and interactions thereof. In VIBRATZ, because of the way internal coordinates are located, force constants may apply to more than one symmetrically-distinct set of internal coordinates. In many places in the output and the input dialogs, the abbreviation Fcon is used to refer to the sequence number of such groups of internal coordinates. That is, Fcon refers to a group of similar internal coordinates, all of which may or may not be equivalent by symmetry.
Primary Fcons (Force Constants). This term is used in VIBRATZ when specifying interactions, to refer to the bond or angle (internal coordinate) groups whose members (primary coordinates) may individually be involved in interactions.
S-vectors. These vectors, defined by WDC in Ch. 4, p55, are essentially vectors on each atom of a bond or angle (internal coordinate) which define the direction and relative magnitude of motion in changes of these bonds or angles. Succeeding pages in WDC define how these vectors are calculated for all the types of internal coordinates used by VIBRATZ except the out-of-plane three-atom angle coordinates (for which see the Angle Force Data dialog).
Secondary Atoms. In locating bonds and angles (internal coordinates) in crystals, VIBRATZ must search through at least part of the 26 unit cells surrounding the "primary" unit cell, to find a complete and unique set. Atoms thus identified which are outside of the "primary" unit cell are called secondary atoms. For bonds, secondary atoms are found mostly in unit cells with positive lattice translations, but secondary atoms for angles may be in any of the 26 surrounding unit cells.