We demonstrated for the first time the observation of surface enhanced Raman scattering of thiocyanate ion on the roughened Au electrode under ultraviolet laser excitation. Its fruitful information was obtained by an algorithm which enables the elucidation of the bond polarizability (derivative) from the Raman intensity. Together with EHMO calculation, the charge transfer pathway between the adsorbed SCN and Au electrode is also proposed.

An H-function in analogy with the entropy in thermodynamics is proposed for intra-molecular ibrational energy redistribution (IVR) in an algebraic approach, which is based on an algebraic classical Hamiltonian on the coset sphere where actions are treated as continuous variables. The time rate of the H-function serves nicely as a tool for IVR and is applied to show the resonances in H2O and DCN in a compact way.

The classical Hamiltonian for which the dynamics is represented by trajectories in a multidimensional phase (coset) space is quantized via Lyapunov analysis. A system of one electron in four sites and the vibration of H2O with Fermi resonance is studied. The quantization condition is that the average Lyapunov exponents show local minima as a function of the classical energy. This means that it requests the least global chaoticity. This quantization algorithm leads to results consistent with those obtained by the quantal models.

The multifractal nature of the eigencoefficients of the eigenstates of the highly excited vibration of H2O, D2O and H2S is probed. The Hamiltonian includes the two stretches and the bend with anharmonic interaction and multiple resonances. It is shown that there are eigenstates possessing multifractal structure but not all. As the polyad number increases, larger percentages of eigenstates become multifractal. The self-similar structure that exists in the distribution of the eigencoefficients of the eigenstates as displayed on the zero-order state energy axis is also demonstrated.

The action integrals of periodic orbits of the non-integrable (chaotic) two-mode system of DCN stretch vibration were analyzed to show ample linear relations. This enables us to obtain by extrapolation all the action integrals of any periodic orbits and at any energies from very few arbitrary action integrals. Based on this property,a very simple and easy semiclassical quantization algorithm by numerical arithmetic was proposed for low excitation which is chaotic classically. The result shows less than 1% deviation from the exact quantal method.