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H. Mikosch, G. Bauer:
"Normal coordinate treatment and force constant refinement in cartesian coordinates";
Journal of Molecular Structure: THEOCHEM, 89 (1982), 3-4; S. 355 - 364.

The classical method of solving the problem of vibrational eigenvalues, the Wilson GF-matrix method, sometimes leads to problems with redundant coordinates. Most of these problems disappear when a more recent method devised by Gwinn is applied for the computation of eigenvalues and normal coordinates, based on cartesian displacement coordinates. Gwinn's method is combined here with the least-squares method for force constant refinement. Assignment of the calculated to the observed frequencies during the refinement procedure is preserved utilizing the orthogonality of the eigenvectors. New internal coordinates describing in-plane bending and ring puckering are introduced and transformation to cartesian displacement coordinates is performed. The method of damped least squares is applicable if required. The FORTRAN IV program used also takes account of isotopic data and the calculation of intermolecular force fields. The results of refinements for water, heavy water and formaldehyde show good agreement with the data from programs based on symmetry coordinates. Finally the algorithm has been tested by calculations on benzene.

Normal Coordinate Analysis

http://dx.doi.org/10.1016/0166-1280(82)80094-8