Linear transformation of anharmonic molecular force constants between normal and Cartesian coordinates

Area of Science:

• Computational Chemistry
• Molecular Spectroscopy

Background:

• Accurate calculation of molecular force constants is crucial for understanding molecular vibrations and spectra.
• Previous methods for transforming force constants between coordinate systems were complex and non-linear.

Purpose of the Study:

• To derive a simple, linear analytic transformation for quadratic, cubic, and quartic force constants.
• To present a new method for transforming force constants from normal coordinates to Cartesian coordinates.

Main Methods:

• Derivation of an analytic linear transformation.
• Development of two distinct computational approaches.
• One approach bypasses the need for translation-rotation eigenvectors.

Main Results:

• A straightforward linear transformation for force constants is achieved.
• The new method is validated on water (H2O) and protonated cyclopropane (c-C3H2D+).
• The presented method offers a more efficient alternative to existing non-linear transformations.

Conclusions:

• The developed linear transformation simplifies the calculation of molecular force constants.
• This work provides a valuable tool for computational chemists and spectroscopists.
• The method's efficiency is demonstrated through successful application to test molecules.