A full derivation of the analytic transformation of the quadratic, cubic, and quartic force constants from normal coordinates to Cartesian coordinates is given. Previous attempts at this transformation have resulted in non-linear transformations; however, for the first time, a simple linear transformation is presented here. Two different approaches have been formulated and implemented, one of which does not require prior knowledge of the translation-rotation eigenvectors from diagonalization of the Hessian matrix. The validity of this method is tested using two molecules H2O and c-C3H2D+.
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A linear transformation is used within the code MULTIMODE14 to evaluate the potential on the n-mode grids in normal coordinates by making the transformation to Cartesian and then to internal coordinates, e.g., bond lengths, to obtain the potential.
