text: Rather than internal displacement coordinates, an alternative approach to write the potential energy of a molecule as explained by Decius is to write it as a quadratic form in terms of generalized displacement forces (negative gradient) .
  :    (eq. 5)
  This gradient  is the first derivative of the potential energy with respect to the displacement coordinates, which can be expressed as shown:
  :    (eq. 6)
  By substituting the expression of  in eq. 5 into equation 5, equation 7 is obtained.
  :    (eq. 7)
  Thus, with the knowledge that  is positive definite, the only possible value of  which is the compliance matrix then must be:
  :    (eq. 8)
  Equation 7 offers a surrogate formulation of the potential energy which proves to be significantly advantageous in defining chemical bonds. Specially, this method is independent on coordinate selection and also eliminates such issue with redundant Hessian that the common force constant calculation method suffers with. Intriguingly, compliance constants calculation can be employed regardless of the redundancy of the coordinates.