Application of geometric algebra to theoretical molecular spectroscopy

In this thesis, the general definition of geometric algebra (Clifford algebra) and the basic principles for studying the geometric properties of this algebra are discussed. Next, geometric algebra was used to create a general and practical method for obtaining the operators of the kinetic energy of the molecular vibration-rotation of polyatomic molecules. On the other hand, these polyatomic molecules' precise intrinsic operators of the kinetic energy include a metric tensor, the elements of this metric tensor was expressed as the mass-weighted sum of measuring vector inner products vectors compatible with the molecule's nucleus. Whereas, the vibrational and rotational measuring vectors that appear in the metric tensor for any geometrically defined coordinates of the shape and frames of the body were easily determined using geometric algebra. The current method (geometric algebra) generates molecular vibration-rotation kinetic energy operators that are in perfect agreement with earlier studies.