Computing resonance effects

In general, no simple, consistent set of analytical expressions for the resonance condition of all intradoublet transitions and all possible rhombicities can be derived with the perturbation theory for these systems. Therefore, the rather different approach is taken to numerically compute all effective g-values using quantum mechanics and matrix diagonalization techniques (Chapters 7-9) and to tabulate the results in the form of graphs of geff,s versus the rhombicity r = E/D. This is a useful approach because it turns out that if the zero-field interaction is sufficiently dominant over... 

Clearly the resonance effect places an upper limit on the frequency at which the capacitor can normally be used. Above resonance the reactance of a capacitor is inductive (coL), and this is significant for some applications. For example, ceramic multilayer capacitors, which are discussed later, are commonly used to decouple high-speed computer circuits, and a prime function is to eliminate noise which has frequency components above the resonance frequency. Therefore the inductive reactance must be kept to a minimum. 

The stabilizing effect of delocalization can be seen even with certain functional groups that are normally considered to be electron withdrawing. For example, computations indicate that cyano and carbonyl groups have a stabilizing resonance effect. This is opposed by a polar effect, so the net effect is destabilizing, but the resonance component is stabilizing. 

We present a new effective numerical method to compute resonances of simple but non-integrable quantum systems, based on a combination of complex coordinate rotations with the finite element and the discrete variable method. By using model potentials we were able to compute atomic data for alkali systems. As an example we show some results for the radial Stark and the Stark effect and compare our values with recent published ones. 

The gas phase basicities and pKa values of tris(phosphazeno) substituted azacalix[3](2,6) pyridine in acetonitrile and some related compounds were examined by the density functional theory (DFT) computational method. It was shown that the hexakis(phospha-zeno) derivative of azacalx[3](2,6)pyridine is a hyperstrong neutral base, as evidenced by the absolute proton affinity of 314.6kcal/mol and pKa (MeCN) of 37.3 units. It is a consequence of the very strong bifurcated hydrogen bond (32kcal/mol) and substantial cationic resonance effect [14]. 

No abnormalities were noted in any of the computer-assisted tomography scans or magnetic resonance images, nor in the blood chemistry or hematology evaluations. No systemic effects of the implants were noted on histological examination of any of the tissues exaoiined. No unexpected or untoward reactions to the treatments were observed. 

---