Wavelet Technology in Quantum Mechanics
The specific aims of interest here are centered on the solution of the molecular
Schrödinger equation, motivated by the need for large-amplitude descriptions of the vibrational
motion characteristically probed in Dissociative Resonance Raman Spectroscopy (DRRS). While a number of
algorithms exist for solving the needed stationary and time-dependent Schrödinger equations,
many either waste effort in spatial regions where not much is happening or else require considerable
human coaxing. Compact support wavelets can be used to approach a wide variety of Cartesian and
curvilinear coordinate problems with systematic accuracy, as has been shown in recent work from this
group, and also provide a rational platform for the development of automated methods. As computational
resources continually become more powerful, there will be an increasing need for software that
minimizes the amount of user intervention. An object-oriented program MultiWavePack is being
developed as a platform for these investigations.
Surface-Enhanced Raman Scattering from Metal Nanoparticles
This work aims at calculating molecular near-field response for molecules such as p-mercaptoaniline on silver nanoshells, including vibrational dynamics of multiple Raman-active modes, directionality, field polarization, and polarizability tensors derived from small molecule-metal cluster ab initio calculations. A density matrix formalism is used to include both radiative and non-radiative relaxation processes in spectral simulations of Surface-Enhanced Raman Scattering (SERS), and special attention is paid to the effects of near-resonance in the Raman processes.