 It is possible to write the vibrational energy solely in terms of the internal modes "q"r ("r" =1, ..., 3"N"-6) as we will now show.We write the different modes in terms of the displacements
The parenthesized expressions define a matrix B relating the internal and external modes to the displacements.The matrix B may be partitioned in an internal (3"N"-6 x 3"N") and an external (6 x 3"N") part,
We define the matrix M by
and from the relations given in the previous sections follow the matrix relations
and
We define
By using the rules for block matrix multiplication we can show that
where G−1 is of dimension (3"N"-6 x 3"N"-6) and N−1 is (6 x 6).