We present a novel approach for the calculation of vibrational (resonance) Raman optical activity (ROA) spectra based on real time propagation. The ROA linear electronic response tensors are formulated in a propagator formalism in order to treat linear response (LR-) and real time time dependent density functional theory (RT-TDDFT) on equal footing. The length, mixed, and velocity representations of these tensors are discussed with respect to the potential origin dependence of the ROA invariants in the calculations. The propagator formalism allows a straight forward extension of the optical LR tensors in a mixed or velocity representation to a coupling with nonlocal potentials, where an extra term appears in the definition of the momentum operator, in order to maintain the gauge invariance. Using RT-TDDFT paves the way for an innovative, efficient calculation of both on-and offresonance ROA spectra. Exemplary results are given for the off-resonance and (pre-)resonance spectra of (R)-methyloxirane, considering the resonance effects due to one or more electronically excited states. Moreover, the developed real time propagation approach allows us to obtain entire excitation profiles in a computationally efficient way.

Linear response theory is reviewed in a propagator formalism to treat linear response and real time (RT) time dependent density functional theory (TDDFT) in a common framework for the calculation of linear response tensors. The importance of an additional term in the definition of the momentum for a description in the velocity representation as well as an origin independent linear magnetic response in the presence of non-local pseudo potentials is discussed. The origin and meaning of the terms 'representation' and 'gauge' are explored and simulations of absorption and electronic circular dichroism spectra using RT-TDDFT are presented. The calculation of the electro-magnetic linear response functions has been implemented into the package CP2K using the gaussian and (augmented) plane wave method.

We apply the newly derived nonadiabatic golden-rule instanton theory to asymmetric models describing electron-transfer in solution. The models go beyond the usual spin-boson description and have anharmonic free-energy surfaces with different values for the reactant and product reorganization energies. The instanton method gives an excellent description of the behaviour of the rate constant with respect to asymmetry for the whole range studied. We derive a general formula for an asymmetric version of Marcus theory based on the classical limit of the instanton and find that this gives significant corrections to the standard Marcus theory. A scheme is given to compute this rate based only on equilibrium simulations. We also compare the rate constants obtained by the instanton method with its classical limit to study the effect of tunnelling and other quantum nuclear effects. These quantum effects can increase the rate constant by orders of magnitude.

We investigate approaches for the calculation of (resonance) Raman spectra in a real-time time-dependent density functional theory (RT-TDDFT) framework. Several short time approximations to the Kramers, Heisenberg, and Dirac polarizability tensor are examined with regard to the calculation of resonance Raman spectra: One relies on a Placzek type expansion of the electronic polarizability and the other one relies on the excited state gradient method. The first one is shown to be in agreement with an approach based on perturbation theory in the case of a weak-pulse perturbation. The latter is newly applied in a real time propagation framework, enabled by the use of Padé approximants to the Fourier transform which allow for a sufficient resolution in the frequency domain. An analysis of the performance of Padé approximants is given. All approaches were found to be in good agreement for uracil and R-methyloxirane. Moreover it is shown how RT-TDDFT can be used to calculate Raman excitation profiles efficiently.

Real-time time-dependent density functional theory (RT-TDDFT) and ab initio molecular dynamics (AIMD) are combined to calculate non-resonant and resonant Raman scattering cross sections of periodic systems, allowing for an explicit quantum mechanical description of condensed phase systems and environmental effects. It is shown that this approach to Raman spectroscopy corresponds to a short time approximation of Heller's time-dependent formalism for the description of Raman scattering. Two ways to calculate the frequency-dependent polarizability in a periodic system are presented: (1) via the modern theory of polarization (Berry phase) and (2) via the velocity representation. Both approaches are found to be equivalent for a system of liquid (S)-methyloxirane with the computational settings used. Resulting non-resonance and resonance Raman spectra from the dynamic AIMD/RT-TDDFT approach are compared to the spectra of one gas phase molecule in the harmonic approximation highlighting finite temperature and solvation effects. Using RT-TDDFT to calculate the full frequency-dependent Placzek-type polarizability within one set of simulations covers the non-resonance, near-resonance, and on-resonance regimes on equal footing, thus allowing the calculation of full Raman excitation profiles.