Theoretical Studies of Raman Scattering

Abstract: Different theoretical approaches have been presented in this thesis to study the Raman scattering effect. The first one is response theory applied up to third order of polarization, where the determination of α, β and γ is used to calculate linear Raman scattering (resonance Raman scattering (RRS) and normal Raman scattering (NRS)), hyper Raman scattering (HRS) and coherent anti-Stokes Raman scattering (CARS), respectively. The response theory refers to adiabatic time-dependent density functional theory in the complex domain with applications on RRS and NRS, and to a recently developed methodology (Thorvaldsen et al. [105, 106]) for the analytic calculation of frequency-dependentpolarizability gradients of arbitrary order, here with applications on CARSand HRS. Various systems have been studied with the response theory, such as explosive substances (DNT, TNT, RDX and H2O2), optical power limiting materials (platinum(II) acetylide molecules), DNA bases (methylguanine-methylcytosine) and other systems (Trans-1,3,5-hexatriene and Pyridine). We have explored the dependency of the calculated spectra on parametrization in terms of exchange-correlation functionals and basis sets, and on geometrica loptimization.The second approach refers to time-dependent wave packet methodology for RRS and its time-independent counterpart in the Kramers-Heisenberg equation for the scattering cross section, which reduces the calculation of the RRS amplitude to computation of matrix elements of transition dipole moments between vibrational wave functions. The time-dependent theory has been used to examine RRS as a dynamical process where particular attention is paid to the notion of fast scattering in which the choice of photon frequency controls the scattering time and the nuclear dynamics. It is shown that a detuning from resonance causes a depletion of the RRS spectrum from overtones and combination bands, a situation which is verified in experimental spectra.The cross section of NRS has been predicted for the studied molecules to be in the order of 10−30 cm2/sr. A further increase in sensitivity with a signal enhancement up to 104 to 105 is predicted for the RRS technique, while CARS conditions imply an overall increase of the intensity by several orders of magnitude over NRS. In contrast to RRS and CARS, the HRS intensity is predicted to be considerably weaker than NRS, by about four orders of magnitude. However, silent modes in NRS can be detected by HRS which in turncan provide essential spectroscopic information and become complementary to NRS scattering.With the above mention methodological development for NRS, RRS, CARS and HRS, we have at our disposal a powerful set of modelling tools for the four different Raman techniques. They have complementary merits and limitations which facilitate the use of these spectroscopes in applications of Raman scattering for practical applications, for instance stand-off detection of foreign substances.