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.

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.

It is observed that, for molecular crystals, during phase transitions the Raman intensities of the vibrational modes obey the power law |T-Tc|β. The exponent bcontains much critical information and is mode dependent. The scaling properties of the doped materials are imbedded in bwhich is found to be very sensitive to very small degrees of doping. One of the eminent phenomena is the so-called crossover point where bof the totally symmetric ν1 mode equals the nonsymmetric ν4 mode of the nitrate ion. The scaling is expressed through the scaled coordinate d/M1/2 where d is the averaged interdoped-cationic distance and Mis the mass of the cation. β of the ν1 mode behaves as (d/M1/2)γ with exponent γ rather independent of the transitions and the kinds of doping. Resonant modes due to doped cations are employed to explain the origin of the scaling.

Formal quantum numbers retrieved via diabatic correlation to the zero-order states where all inter-mode couplings are switched off can be assigned to the eigenstates of the molecular highly excited vibration. These formal quantum numbers help the classification and assignment of the highly excited vibrational states. They are shown as the approximate constants of motion. A classical approach in a coset phase space is employed to show that the trajectories corresponding to the formal quantum numbers have zero or least Lyapunov exponents and that formal quantum numbers correspond to significant phase space density.

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.

An algebraic Hamiltonian for H2O, D2O, H2S, CH2 of CH2Br2 and CD2 of CD2Br2 containing anharmonicities and resonances is proposed with coefficients elucidated from the fit with the experimentally observed levels. It is demonstrated that most often the anharmonic parts show clues of action energy localization. Resonances are shown full of periodic, quasiperiodic and chaotic motion, while the intersection of the various resonances is full of chaotic motion. The barrier in intramolecular vibrational relaxation with extreme mutual irrational ratios of resonance frequencies is shown full of periodic or quasiperiodic motion, leading to the dynamical bottlenecks.

The classical characters of the highly excited bend dynamics of acetylene are analyzed in terms of two coupled SU(2)/U(1) coset spaces corresponding to the right and left circular motion of the two C-H bends. The vibrational modes show a wide variety of behaviors that are not observed in the simple SU(2)/U(1) coset case which deals with, e. g., two coupled stretches, in which case the vibrational modes can be characterized as (low-lying) local and (high-lying) normal modes with a so-called local-normal transition in between. For the two coupled SU(2)/U(1) cosets of acetylene, the general trend is that most modes are perturbed local or normal modes, with distinct characters that are not found in the SU (2) dynamics. Details of their classical characters and the dynamical action flow between the two C-H bends were deduced. When the total action number Nb is small (less than 14), normal mode motions dominate, i. e., trans bend modes at the bottom of each polyad and cis bend at the top. At higher Nb, the vibrational modes are more or less of local character though they, individually, do possess very unique characters. Specifically, as Nb ranges from 12 to 22, the characters of the low-lying levels change from the trans character with action asymmetrically distributed in the two C-H bonds to one hydrogen bending, while those of the high-lying levels change from well concerted cis to local counter rotation. These results are consistent with recent quantal and semiclassical results. [M. P. Jacobson, R. J. Silbey, and R. W. Field, J. Chem. Phys. 110, 845 (1999); M. P. Jacobson, C. Jung, H. S. Taylor, and R. W. Field, ibid. 111, 600 (1999)].

For simple molecules such as H2O, D2O, H2S, and DCN of three and two degrees of freedom, respectively, the diabatic correlation technique is employed to reconstruct the broken constants of motion by switching off the individual resonances. These constants of motion are shown suitable for the classification and assignment of their highly excited vibrational manifolds.