Output - Printed to the file infile.VBD and shown in the Output window
This section describes the main computational output of VIBRATZ, which is written to a file called infile.VBD, if infile.VBR is the name of the input data file. If the Window radio button in the Output File group of the Control Window is checked, this output is shown on screen in a Text window (see Operation - Windows, Menus, Dialogs).
The first line contains the version and release date of VIBRATZ and the date and time of the calculation.
The file name and the title (Title/Axes dialog, Input menu) are on the next two lines.
Use lattice vectors. This shows which of the axes a, b and c (or x, y and z) have lattice translations - non-zero indicates presence of translation. Molecules should have all zeros and crystals all ones (Title/Axes dialog, Input menu).
Cell Parameters. For a molecule the axes are normally 1.0 and the angles are 90.0 (Title/Axes dialog, Input menu).
Pre-Calculation Rotations. These are the rotations on the x, y and z Cartesian axes which are required to bring the structure and symmetry matrices into proper orientation for symmetry analysis. The Final Atom List and detailed results for each mode are all given for the orientation attained after these rotations (Pre-Calculation Rotations dialog, Input menu).
Point or Factor Group. The Schoenflies symbol for the point or factor group. Whether centric or acentric is printed on the next line. If a point group is centric, only half of the symmetry operators in the next group will be given (Symmetry dialog, Input menu).
Symmetry Operators. In the case of space groups and crystallographic point groups, this gives the symmetry operations in International Tables or "xyz" form (Symmetry dialog, Input menu).
Bravais Cell Type. For a crystal, unless this is P, the unit cell which is used by VIBRATZ is not the Bravais cell but the primitive cell (Symmetry dialog, Input menu).
P-Cell Vectors. For a crystal or polymer, this gives the primitive unit-cell edges or axes in terms of the conventional or Bravais cell axes (Symmetry dialog, Input menu).
Input Atoms. This gives the label, type and coordinates for the input atoms, untransformed by the Pre-Calculation Rotations (Input Atoms dialog, Input menu).
Atom Types. This gives the atomic weights and charges for the atom types used in the input atom list (Atom Types, Input menu).
Symmetry Matrices (Cartesian). This gives the symmetry matrices in Cartesian form, which are the input matrices for non-crystallographic point groups (Symmetry dialog, Input menu).
All Atoms in Unit Cell or Molecule (Structure Coordinates). This gives all the atoms generated by symmetry, untransformed by the PreCalculation Rotations, and in the case of crystals, in fractional coordinate on the original axes.
P-Cell Vectors (Cartesian, rotated). This gives the primitive unit-cell vectors in transformed Cartesian coordinates (for crystals c = z, a* = x), rotated by the PreCalculation Rotations.
Internal Coordinate Types. This section gives the specifications for the internal coordinates and interactions thereof, or valence forces. This is basically a printout of the data entered in the dialogs of the Forces menu. Where there is more than one specification for a given internal coordinate or force constant, the specifications are simply given one after the other, with the same "Fcon" or force constant number (dialogs of Forces menu).
Internal Coordinates Located. This gives the complete list of individual bonds and angles, and interactions thereof, which have been located according to the given specifications. In each group are listed the number of the individual bond, angle, or interaction, the input force constant (Fcon) number and the actual atoms involved. Two types of atoms are listed, primary and secondary, and in the case of crystals or polymers these may be different (for molecules the secondary atoms are exactly the same as the primary atoms). The secondary atoms are those outside the unit cell which are necessary to specify a complete list of bonds and angles; they are related by lattice translation to the corresponding primary atoms. These numbers refer to the Final Atom List given below. For bonds, one or the other of the two atoms must be in the unit cell; for 3-atom angles, the central atom must be in the unit cell; for tau angles one of the two middle atoms must be in the unit cell, and for psi angles the central atom (number 2) must be in the unit cell. For interactions, the Primary Coordinate numbers refer back to the list of bonds and angles located (from which the common atoms may be determined).
Final Atom List (Cartesian) - Rotated, Translated. This gives all the atoms generated by symmetry, transformed by the PreCalculation Rotations, and for crystals and polymers, any secondary atoms outside the unit cell needed to complete the specified bonds and angles. These atom coordinates are also translated to put the center of gravity of the molecule or unit cell (primary atoms only) at the origin of coordinates. The atomic displacements listed below in the Calculated Mode section as well as the symmetry coordinates in the Symmetry Analysis section apply to this list, and to this orientation, not to the orientation of the input atoms or that of the non-rotated molecule/unit-cell list above.
Atomic Displacement Parameters. This gives the way the atomic displacements are normalized and rescaled, as specified in the Basic Parameters dialog (Setting menu).
Symmetry Analysis Section
For each species, this gives the starting parameters including the basis functions; the full-matrix representations; and the Cartesian symmetry coordinates.
The first line gives the species label, the degeneracy, the number of basis functions and total number of terms therein, and the translations and rotations present. The latter are given in the order translations on x, y and z and rotations on x, y and z.
Exponents give the exponents on the x, y and z coordinates in each term used in the basis function for this species. Each term is shown as a triplet of exponents. The Coefficient matrix then gives the coefficients on each term, in each basis function. Actually, this section gives the complete basis functions, in n lines if there are n functions, showing all m terms (the matrix uses only the leftmost n by n terms).
Representations gives the full-matrix representation derived from the original symmetry matrices (Cartesian symmetry matrices above), although of course there is only one number for A and B species.
Finally the Symmetry coordinates gives the Cartesian symmetry coordinates obtained by transforming in turn the x, y and z coordinates of each input atom. The first line of each coordinate gives the starting atom number and the x, y or z, and succeeding lines give the tranformed coordinates, in terms of x, y and z coordinates on the symmetry-derived atoms (in the All Atoms in Unit Cell or Molecule List). Several components may be given per line, with asterisks separating them.
Least-Squares Section.
The reduction factor and end criterion (Control Window) are first listed.
For each cycle, the average deviation and average squared deviation of the calculated from observed, the determinant of the least-squares matrix, and the new, derived values of the force constants are given. If the average squared deviation (not the average deviation) is worse than the last cycle, or if the change is less than the end criterion value (Control Window), the process is halted, and in the first case the force-constant values revert to those of the last cycle. The force constants are listed across the window or page in order of the "coord." number given in the Internal Coordinate Types lists above.
If Correlation Coefficients are selected in the Listings dialog, they are printed out in lower diagonal form, omitting diagonal elements:
21
31 32
41 42 43
that is 21, 31, 32, 41, 42, 43 and so on. Only the force constants selected for least-squares adjustment appear here. Normally, absolute values of correlation coefficients must be very close to 1.0 (say 0.95 or greater, very roughly) to indicate significant interdependency of the force constants.
Calculated Mode Section.
Each species is headed by the Species label followed by the number of modes. The polarization components for infrared and Raman are also given. Modes are listed within species in decreasing order of frequency.
The first line for each mode (marked by "####") gives the overall sequence number, the calculated frequency in reciprocal centimeters with observed frequency in parentheses, the infrared intensity, the Raman intensity, the Raman depolarization ratio and the NRVS fraction (not divided by frequency). The intensities are the averages, which are influenced by some parameters in the Spectra Plotting Parameters dialog, as well as the atomic-motion scaling parameters in the Basic Parameters dialog. The intensities are all weighted by the degeneracy for the species.
If least-squares is in effect, the wavenumber calculated from the energies derived from atomic displacements is given. This is a check on the process of calculating energies, on which least-squares analysis is based (see Theory and Implementation), and indeed on all aspects of the calculation of atomic displacements and changes in internal coordinates and interactions. In view of the assumptions involved, exact correspondence between this value and the wavenumber directly determined from the secular equation is not expected, but deviation by more that a few wavenumbers may indicate a bug or other problems. It may be possible to improve agreement by using the atomic displacement scale factor (Basic Parameters dialog, Setting menu) to reduce the magnitude of calculated atomic motions. This may be necessary especially if there are weak forces such as torsion which may lead to particularly large atomic motions.
Following this are some totals for internal coordinates and interactions thereof, arranged across the page in order of the input number in the dialogs of the Forces menu. That is for the "Net Bnds/Grp" item (for example), if there are three input bond force constants (Fcons), there are three corresponding numbers, which are the sum of the changes of all bonds derived from each input specification. These values may be carried over onto successive lines.
For bonds there is a "Net Bds/Gp" item, which is simply the sum of all the bond changes in each group, and also an "Av Bds/Gp", which is the sum of the absolute changes in bonds in the group. Comparison of these two can show whether the mode is mostly of the symmetric or antisymmetric stretching character, where this is not strictly determined by symmetry. For angles the net category is omitted and there is only an average or absolute sum of changes (in degrees).
For every type of force constant there is an energy ("En") category. These numbers are given in fractions of the total potential energy. This is a direct measure of the importance of the group or input coordinate force constant on the frequency of the mode in question. Again, the sum of these energies is used for the "Energy recalculated..." number above. Note that the value of individual entries in this section may be greater than one, since some may also be less than zero (realistically only interactions should be less than zero, although if other force constants are allowed to go negative their contribution will be negative).
Following these group results are the individual polarization components for Raman and infrared. For Raman, the components are xx, yy, zz, xy, xz and yz, and for infrared they are x, y, z. (see Theory and Implementation for the derivation of these numbers). The allowed infrared and Raman components are given in the header line for the species, or can be obtained from the Species dialog in the Input menu. For multidimensional species not all components are present, and it may be necessary to take sums and/or differences of the given simple Raman components to see the activity. Generally, x is preferred over y and z, xx-yy over xy, and xz over xy and yz. To make sure which component is present, in the Listings dialog (Setting menu, Control Window) select Representations of species to print out the basis functions used. The first one given should be the component which appears. However, this may depend on proper orientation of the symmetry elements with respect to the Cartesian axes (see Orientation)
If selected in the Listings dialog (Setting menu), the changes in individual bonds and angles are given. These are given in the order of the Coordinates Located lists above.
The Atomic Displacements are the displacements in the x, y and z directions of each primary atom in the Final Atom List, with two atoms per line, separated by a slash.
Finally, for each species the Average Energy Contributions... shows which force constants or groups of internal coordinates are absent from that species (since this information is not a direct outcome of the symmetry analysis).
List of Frequencies. This gives an overall list sorted in decreasing order of frequency, either by species or for all species together (Basic Parameters dialog, Setting menu). The intensities are the averages, which are influenced by some parameters in the Spectra Plotting Parameters dialog, as well as the atomic-motion scaling parameters in the Basic Parameters dialog.
Contributions of F's to modes. This lists the force constants (F's), giving the number and force-constant value for each, and then gives up to 12 modes to which this force constant is a significant contributor, ranked in decreasing order of contribution. For each mode, the frequency, the species and the energy contribution in percent is given. The contribution is exactly the same number (as percent) as the energy ("En") category discussed above for each mode.