  An alternative, the VW transformation, is proposed to replace the Wilson GF
method for calculating molecular vibration frequencies and normal modes. The VW
transformation yields precisely the same eigenmodes and and eigenfrequencies
that are found with the GF method. The transformation proceeds entirely in the
mass-normalized Cartesian coordinates of the individual atoms, with no
transformations to internal coordinates. The VW transformation thus offers an
enormous computational simplification over the GF method, namely the
mathematical apparatus needed to transform to internal coordinates is
eliminated. All need for new researchers to understand the complex matrix
transformations underlying the GF method is thus also removed. The VW
transformation is not a projection method; the internal vibrations remain
dispersed over all 3N atomic coordinates. In the VW method, the 3N x 3N force
constant matrix V is replaced with a new 3N x 3N matrix W. The replacement is
physically transparent. The matrix W has the same internal normal modes and
vibration frequencies that V does. However, unlike V, W is not singular, so the
normal modes and normal mode frequencies can be obtained using conventional
matrix techniques.
