The adiabatic or Born-Oppenheimer approximation is often used in molecular calculations to simplify the solution to the Schrodinger equation. The basis of the approximation is the large difference in the relative motions of the nuclei and electrons in the molecule-the electrons are able to respond almost instantly to the movements of the nuclei. Thus, the nuclei may be regarded as being fixed in a certain position and the Schrodinger equation can then be solved using the potential obtained by solving the electronic problem at fixed nuclear configuration. A similar argument can be used to decouple the angular and radial motions of many van der Waals complexes because, like nuclei in molecules, the radial motions in many van der Waals complexes are strongly localized. Fixing the radial separation between the atoms and molecules in the complex to a particular value results in a Schrodinger equation that is much simpler to solve because it is only dependent on angles. van der Waals complexes containing helium atoms, however, present a dilemma because the extremely weak interactions present also lead to large amplitude radial as well as angular motions. Because the basis of the adiabatic approximation is a large difference in time scale between the angular and radial motions, the validity of the adiabatic approximation for helium complexes is uncertain. In this thesis, the adiabatic separation of angular and radial motion is shown to be accurate for extremely floppy complexes of helium by demonstrating its use on the van der Waals molecule He-HCN. A major application of this method is expected to be the quick calculation of approximate wave functions for Diffusion Monte Carlo studies of the rotation of impurity molecules inside ultra-cold droplets of helium. The method presented here is significantly faster than other methods (e.g., Variational Monte Carlo) that have been used to calculate approximate wave functions for Diffusion Monte Carlo.

Background：Aortic stenosis (AS) is the commonest valve disease in the West. Aortic valve replacement (AVR) remains the only available management for AS and results in improved symptoms and recovery of ventricular functions. In addition, it is well known that AVR results in disruption of LV function mainly in the form of reversal of septal motion as well as depression of right ventricular (RV) systolic function. The aim of this thesis was to study, in detail, the early and mid-term response of ventricular function to AVR procedures (surgical and TAVI) as well as post operative patients’ exercise capacity. Methods：We studied LV and RV function by Doppler echocardiography and speckle tracking echocardiography (STE) in the following 4 groups; (1) 30 severe AS patients (age 62±11 years, 19 male) with normal LV ejection fraction (EF) who underwent AVR, (2) 20 severe AS patients (age 79±6 years, 14 male) who underwent TAVI, (3) 30 healthy controls (age 63±11 years, 16 male), (4) 21 healthy controls (age 57±9 years, 14 male) who underwent exercise echocardiography. Results: After one week of TAVI, the septal radial motion and RV tricuspid annulus peak systolic excursion (TAPSE) were not different from before, while surgical AVR had significantly reversed septal radial motion and TAPSE dropped by 70% compared to before. The extent of the reversed septal motion correlated with that of TAPSE (r=0.78, p<0.001) in the patients as a whole after AVR and TAVI (Study I). Compared with controls, the LV twist function was increased in AS patients before and normalized after 6 months of surgical AVR. In controls, the LV twist correlated with LV fractional shortening (r=0.81, p<0.001), a relationship which became weak in patients before (r=0.52, p<0.01) and after AVR (r=0.34, p=ns) (Study II). After 6 months of surgical AVR, the reversed septal radial motion was still significantly lower than before. The septal peak displacement also decreased and its time became prolonged. In contrast, the LV lateral wall peak displacement increased and the time to peak displacement was early. The accentuated lateral wall peak displacement correlated with the septal peak displacement time delay (r=0.60, p<0.001) and septal-lateral time delay (r=0.64, p<0.001) (Study III). In 21 surgical AVR patients who performed exercise echocardiography, the LV function was normal at rest but different from controls with exercise. At peak exercise, oxygen consumption (pVO2) was lower in patients than controls. Although patients could achieve cardiac output (CO) and heart rate (HR) similar to controls at peak exercise, the LV systolic and early diastolic myocardial velocities and strain rate as well as their delta changes were significantly lower than controls. pVO2 correlated with peak exercise LV myocardial function in the patients group only, and the systolic global longitudinal strain rate (GLSRs) at peak exercise was the only independent predictor of pVO2 in multivariate regression analysis (p=0.03) (Study IV). Conclusion: Surgical AVR is an effective treatment for AS patients, but results in reversed septal radial motion and reduced TAPSE. The newly developed TAVI procedure maintains RV function which results in preservation of septal radial motion. In AS, the LV twist function is exaggerated, normalizes after AVR but loses its relationship with basal LV function. While the reversed septal motion results in decreased and delayed septal longitudinal displacement which is compensated for by the accentuated lateral wall displacement and the time early. These patients remain suffering from limited exercise capacity years after AVR.