a These authors contributed equally to the work. AbstractThe understanding of excimer formation in organic materials is of fundamental importance, since it profoundly influences their functional performance in applications such as light-harvesting, photovoltaics or organic electronics. We present a joint experimental and theoretical study of the ultrafast dynamics of excimer formation in the pyrene dimer, which is the archetype of an excimer forming system. We perform simulations of the nonadiabatic photodynamics in the frame of TDDFT that reveal two distinct excimer formation pathways in the gas-phase dimer. The first pathway involves local excited state relaxation close to the initial Frank-Condon geometry that is characterized by a strong excitation of the stacking coordinate exhibiting damped oscillations with a period of 350 fs that persist for at least 5 ps. The second excimer forming pathway involves large amplitude oscillations along the parallel shift 1 coordinate with a period of ≈ 900 fs that after intramolecular vibrational energy redistribution on a 2 ps time scale leads to the formation of a perfectly stacked dimer.The electronic relaxation within the excitonic manifold is mediated by the presence of conical intersections formed between fully delocalized excitonic states. Such conical intersections may generally arise in stacked π-conjugated aggregates due to the interplay between the long-range and short-range electronic coupling. The simulations are supported by picosecond photoionization experiments in a supersonic jet that provide a time-constant for the excimer formation of around 6-8 ps, in excellent agreement with theory. Finally, in order to explore how the crystal environment influences the excimer formation dynamics we perform large scale QM/MM nonadiabatic dynamics simulations on a pyrene crystal in the framework of the tight-binding TDDFT. In contrast to the isolated dimer, the excimer formation in the crystal follows a single reaction pathway in which the initially excited parallel slip motion is strongly damped by collisions with the surrounding molecules leading to the slow excimer stabilization with a time constant of several picoseconds.2

For the rational design of new fluorophores, reliable predictions of fluorescence quantum yields from first principles would be of great help. However, efficient computational approaches for predicting transition rates usually assume that the vibrational structure is harmonic. While the harmonic approximation has been used successfully to predict vibrationally resolved spectra and radiative rates, its reliability for non-radiative rates is much more questionable. Since non-adiabatic transitions convert large amounts of electronic energy into vibrational energy, the highly excited final vibrational states deviate greatly from harmonic oscillator eigenfunctions. We employ a time-dependent formalism to compute radiative and non-radiative rates for transitions and study the dependence on model parameters. For several coumarin dyes, we compare different adiabatic and vertical harmonic models (AS, ASF, AH, VG, VGF, and VH), in order to dissect the importance of displacements, frequency changes, and Duschinsky rotations. In addition, we analyze the effect of different broadening functions (Gaussian, Lorentzian, or Voigt). Moreover, to assess the qualitative influence of anharmonicity on the internal conversion rate, we develop a simplified anharmonic model. We address the reliability of these models considering the potential errors introduced by the harmonic approximation and the phenomenological width of the broadening function.

We present an efficient method for the simulation of time-resolved photoelectron imaging (TRPEI) spectra in polyatomic molecules. Our approach combines trajectory-based molecular dynamics that account for non-adiabatic effects using surface hopping, with an approximate treatment of the photoionization process using Dyson orbitals as initial and Coulomb waves as final electron states. The method has been implemented in the frame of linear response time-dependent density functional theory. As an illustration, we simulate time- and energy-resolved anisotropy maps for the furan molecule and compare them with recent experimental data [T. Fuji, Y.-I. Suzuki, T. Horio, T. Suzuki, R. Mitrić, U. Werner, and V. Bonačić-Koutecký, J. Chem. Phys. 133, 234303 (2010)]. Our method can be generally used for the interpretation of TRPEI experiments allowing to shed light into the fundamental photochemical processes in complex molecules.

A software package, called DFTBaby, is published, which provides the electronic structure needed for running non-adiabatic molecular dynamics simulations at the level of charge-consistent tight-binding DFT. A long-range correction is incorporated to avoid spurious charge transfer states. Excited state energies, their analytic gradients and scalar non-adiabatic couplings are computed using tight-binding TD-DFT. These quantities are fed into a molecular dynamics code, which integrates Newton's equations of motion for the nuclei together with the electronic Schrödinger equation. Non-adiabatic effects are included by surface hopping. As an example, the program is applied to the optimization of excited states and nonadiabatic dynamics of polyfluorene. The python and Fortran source code is available at http://www.dftbaby.chemie.uni-wuerzburg.de.

We present two improvements to the tight-binding approximation of time-dependent density functional theory (TD-DFTB): Firstly, we add an exact Hartree-Fock exchange term, which is switched on at large distances, to the ground state Hamiltonian and similarly to the coupling matrix that enters the linear response equations for the calculation of excited electronic states. We show that the excitation energies of charge transfer states are improved relative to the standard approach without the long-range correction by testing the method on a set of molecules from the database in [J. Chem. Phys. 2008, 128, 044118] that are known to exhibit problematic charge transfer states. The degree of spatial overlap between occupied and virtual orbitals indicates where TD-DFTB and lc-TD-DFTB can be expected to produce large errors.Secondly, we improve the calculation of oscillator strengths. The transition dipoles are obtained from Slater Koster files for the dipole matrix elements between valence orbitals. In particular, excitations localized on a single atom, which appear dark when using Mulliken transition charges, in this way acquire a more realistic oscillator strength.These extensions pave the way for using long-range corrected TD-DFTB (lc-TD-DFTB) to describe the electronic structure of large chromophoric polymers, where uncorrected TD- * To whom correspondence should be addressed 1 arXiv:1503.01714v2 [physics.chem-ph] 10 Jun 2015 DFTB fails to describe the high degree of conjugation and produces spurious low-lying charge transfer states.