Quantum coherences between electronically excited molecules are a signature of entanglement and play an important role for energy transport in molecular assemblies. Here we monitor and analyze for a homologous series of molecular dimers embedded in a solid host the emergence of coherence with decreasing intermolecular distance by single-molecule spectroscopy and quantum chemistry. Coherent signatures appear as an enhancement of the purely electronic transitions in the dimers which is reflected by changes of fluorescence spectra and lifetimes. Effects that destroy the coherence are the coupling to the surroundings and to vibrational excitations. Complementary information is provided by excitation spectra from which the electronic coupling strengths were extracted and found to be in good agreement with calculated values. By revealing various signatures of intermolecular coherence, our results pave the way for the rational design of molecular systems with entangled states.

Absorption and emission spectra of perylene-3,4-dicarboximide (PMI) and perylene-3,4,9,10-tetracarboxdiimide (PDI) derivatives embedded in a thin polymer film were measured by room-temperature bulk and low-temperature single-molecule spectroscopy. In contrast to bulk line narrowing spectra, the low-temperature single-molecule data allowed to unambiguously resolve the vibrational fine structure of the emission spectra. Additionally, the emission spectra were calculated by quantum chemical methods within the Franck-Condon approximation for various N-substituted derivatives of PMI and PDI. The experimental as well as calculated emission spectra are dominated by two spectral regions of high vibronic activity, a band system ranging from the 0-0 transition (at DeltaE(0-0)) down to 600 cm(-1) below DeltaE(0-0) and a band system between approximately 1250 and 1700 cm(-1) below DeltaE(0-0). Apart from the wavenumber region close to DeltaE(0-0) (down to 100 cm(-1) below DeltaE(0-0)), good agreement is found between the calculated and experimental spectra, allowing a clear-cut assignment of the dominant vibrational modes. There are, however, discrepancies in the intensities in particular for low-frequency vibrational modes. These differences between theory and experiment are tentatively attributed to linear electron-phonon coupling which is completely neglected in the calculations and hindered internal rotation that is not properly accounted for in the harmonic approximation. Furthermore, in the experimental spectra, at the bulk as well as the single-molecule level, significant differences between PMI and PDI are observed which are attributed to stronger interactions with the matrix environment in the case of PMI due to the permanent electric dipole moment of that molecule.

We calculate the effect of a linear electron-phonon coupling on vibronic transitions of dye molecules of arbitrary complexity. With the assumption of known vibronic frequencies (for instance from quantum-chemical calculations), we give expressions for the absorption or emission lineshapes in a second-order cumulant expansion. We show that the results coincide with those obtained from generalized Redfield theory if one uses the time-local version of the theory and applies the secular approximation. Furthermore, the theory allows to go beyond the Huang-Rhys approximation and can be used to incorporate Dushinsky effects in the treatment of the temperature dependence of optical spectra. We consider both, a pure electron-phonon coupling independent of the molecular vibrations and a coupling bilinear in the molecular vibrational modes and the phonon coordinates. We discuss the behavior of the vibronic density of states for various models for the spectral density representing the coupling of the vibronic system to the harmonic bath. We recover some of the results that have been derived earlier for the spin-boson model and we show that the behavior of the spectral density at low frequencies determines the dominant features of the spectra. In case of the bilinear coupling between the molecular vibrations and the phonons we give analytical expressions for different spectral densities. The spectra are reminiscent of those obtained from the well known Brownian oscillator model and one finds a zero-phonon line and phonon-side bands located at vibrational frequencies of the dye. The intensity of the phonon-side bands diminishes with increasing vibrational frequencies and with decreasing coupling strength (Huang-Rhys factor). It vanishes completely in the Markovian limit where only a Lorentzian zero-phonon line is observed.