Force Field Analysis

PGOPHER can do a traditional force field analysis, calculating vibrational frequencies, the l matrix, isotope shifts, rotational constants, centrifugal distortion constants and Coriolis coupling constants from force constants and geometry. The force constants and geometry can be derived by fitting to any combination of the calculated quantities. The calculations are similar to those done by the ASYM20/ASYM40 program of Hedberg and Mills (1993, 2000), though implemented in a more flexible way, and these papers give a good outline of the methodology and how the calculations  are performed. The VIBCA program (http://www.ifpan.edu.pl/~kisiel/vibr/vibr.htm) also performs similar calculations.

The force field can be expressed in terms of valence or symmetry coordinates. A typical analysis will include several isotopologues and might have a data file structured something like this:

Note the various single and multiple objects:

• A single Global Variables object which contains geometric variables and force constants common to all isotopologues.
  
• A z Matrix for each isotopologue, which specifies the geometry. The use of variables means this will be identical for all isotopologues,  except for the masses.
• An (optional) Internal Coordinates object for each isotopologue, which specifies the valence coordinates and force constants. The use of variables means this will be identical for all isotopologues.
• An (optional) Symmetry Coordinates object for each isotopologue, which specifies the combinations of valence coordinates to use. The use of variables means  this will only differ for isotopologues of different symmetry.

A Cartesian Coordinates object may also be present; the exact combination of objects used depends on the required calculation. Nuclear Co-ordinates and Vibrational Modes objects will also be present, automatically created and updated from the force field analysis objects listed above.

The current version of the program does not explicitly make use of symmetry for the force field analysis, but it is implicit in the way the force constants and geometry are specified. The current version of PGOPHER is restricted to harmonic terms, but the program is structured so that anhamonic terms can be added in future. The units are currently less flexible than for rotational calculations; the overall mixture units must be set to cm-1, the geometry specified in Angstroms and degrees and force constants (for stretches) in millidyne/Å = aJ/Ų (1 millidyne/Å = 1 aJ/Ų = 100 J/m² = 100 N/m). For a full discussion of the units see Hedberg and Mills (1993).