This PhD dissertation deals with the development and testing of methods able to evaluate internal rotor and rotational vibrational partition functions of molecules with two torsional modes. The main method discussed in the Dissertation includes both the kinetic and potential couplings and is called Two- Dimensional Non Separable (2D-NS).
Chapter 1 considers two molecular systems, one with weak coupling between rotors and the other with strong coupling. The 2D-NS partition function and several monodimensional and bidimensional partition functions were calculated and compared. The main idea was to test if the other methods are able to handle both situations as the 2D-NS does.
Chapter 2 explores the possibilities that the method provides by studying three molecules presenting two hindered internal rotors for which experimental tunneling splittings have been reported. The analysis of the wavefunctions were important tools to get insight into the tunneling mechanism. Furthermore, the calculation of the ground vibrational state energy levels by the 2D-NS method allowed us to test its accuracy for the prediction of this kind of phenomena.
The Third Chapter includes an extensive study of twenty molecules with two hindered internal rotations. The 2D-NS method is used to calculate the hindered rotation partition functions and the results are compared with several of the most popular monodimensional and bidimensional methods. During this chapter the 2D-NS method is extended to obtain the rovibrational partition function, and this leads to two diﬀerent methods, which diﬀer in the global sep- arability assumption of the torsional degrees of freedom. In the same manner, and as for the bidimensional partition functions, a comparison between several methods was also included. In order to evaluate the accuracy of the methods, rovibrational partition functions were used to calculate ideal-gas standard-state thermodynamic functions. The calculated values were compared to experimen- tal data available in the scientiﬁc literature.
Chapter 4 comprises a study of the kinetic isotope eﬀects (KIEs) for the hydrogen abstraction reaction from ethanol by atomic hydrogen in aqueous so- lution at room temperature. Multipath canonical variational transition state theory accounted for tunneling and variational eﬀects. The anarmonicity due to the torsions was incorporated through the 2D-NS method. All possible tran- sition states were incorporated to the study and their contribution to the tor- sional, rovibrational, translational, and tunneling KIEs factors was individually analyzed. The results were compared to the available experimental data.