In this work, we present the generalization of a time-dependent method for the calculation of intersystem crossing (ISC) rates in the Condon approximation. When ISC takes place between electronic states with the same orbital type, i.e., when the transition is forbidden according to the El-Sayed rules, it is necessary to go beyond the Condon approximation. Similar to the Herzberg-Teller expansion of the vibronic interaction, the electronic spin-orbit matrix elements are assumed to depend linearly on the nuclear coordinates. The ISC rate is then a sum of three contributions: a direct, mixed direct-vibronic, and vibronic term. The method, presented in this work, is based on the generating function formalism and the multi-mode harmonic oscillator approximation. In addition to the zero-temperature case, we implemented formulae for finite-temperature conditions assuming a Boltzmann population of vibrational levels in the initial state. Tests have been carried out for a variety of molecules for which literature data were available. We computed vibronic one-photon spectra of free-base porphyrin and free-base chlorin and calculated ISC rates for xanthone, thioxanthone, thionine, as well as free-base porphyrin and found excellent agreement with previous results. Quantitative rates for triplet formation in rhodamine A have been determined theoretically for the first time. We find the S1↝ T2 channel to be the major source of triplet rhodamine formation in the gas phase.

The photophysics of thioxanthone (TX) dissolved in methanol (MeOH) and 2,2,2,-trifluoroethanol (TFE) was studied by time-resolved fluorescence and absorption spectroscopy. The spectrally integrated stimulated emission is seen to lose amplitude within ∼5-10 ps. This is much shorter than the fluorescence lifetimes of the compound (2.7 ns for MeOH and 7.6 ns for TFE). The initial reduction in amplitude is attributed to reversible intersystem crossing between the primarily excited (1)ππ* and a triplet (3)nπ* state. The latter one is energetically slightly (∼0.02 eV) above the former one. Addition of the quencher 1-methylnaphthalene (1-MN) reduces the fluorescence lifetime and yields triplet excited 1-MN, giving further evidence for the equilibrium of singlet and triplet excitations. The depopulation of these two states on the nanosecond time scale results in the rise of the lowest triplet state, a (3)ππ* state. Temperature dependencies attribute this to an activated internal conversion process between the two triplet states. Kinetic and energetic parameters derived from the experimental data will be compared with quantum chemical results in the accompanying paper [Rai-Constapel , V. , Villnow , T. , Ryseck , G. , Gilch , P. , and Marian , C. M. J. Phys. Chem. A 2014 , DOI: 10.1021/jp5099415].

The photophysics of thioxanthone dissolved in cyclohexane was studied by femtosecond fluorescence and transient absorption spectroscopy. From these experiments two time constants of ∼400 fs and ∼4 ps were retrieved. With the aid of quantum chemically computed spectral signatures and rate constants for intersystem crossing, the time constants were assigned to the underlying processes. Ultrafast internal conversion depletes the primarily excited (1)ππ* state within ∼400 fs. The (1)nπ* state populated thereby undergoes fast intersystem crossing (∼4 ps) yielding the lowest triplet state of (3)ππ* character.

Quantum chemical methods have been employed to study the photophysics of thioxanthone in vacuum and various solvents. Structurally, the solvation leads to a lengthening of the carbonyl bond, whereas the benzene skeleton is mostly unaffected. This is mirrored by the larger blue shift of the (n(O)π*) states as compared to the red shift which the (ππ*) states undergo. For a proper understanding of the radiative and radiationless processes occurring, the excitation energy profile along a linearly interpolated path has been determined in various cases. The interesting interplay of excited states thus revealed, has been investigated to qualitatively suggest the relaxation pathways available (or dominant) in the cases under study. Rates for these processes have also been computed wherever possible.

A theoretical analysis of the chromophore xanthone has been carried out in various cases, starting from the isolated molecule and going on to the extremely polar-protic solvated chromophore. In the gas phase, we find that an El-Sayed forbidden channel with a rate constant of kISC = 2 × 10(11) s(-1) is one of the trend-setting factors in the photophysical kinetics. The fluorescence is found to be quenched in the gas phase and polar-aprotic solvents. The analysis of xanthone in aqueous solution supports the delayed fluorescence model, which has been suggested to explain the high fluorescence quantum yield observed in water. Besides, we present a detailed analysis of the photophysics of xanthone in acetonitrile and methanol.

The chimeric behavior of thioxanthone in protic solvents has been investigated employing computational chemistry methods. In particular, methanol and 2,2,2-trifluoroethanol have been chosen in this study. The solvent environment has been modeled using microsolvation in combination with a conductor-like screening model. The vertical excitation spectrum within the same solvent is seen to depend on the number of specific bonds formed between the chromophore and the solvent molecules. Two different models have been discussed in this work, namely, one and two H-bond models. In particular, the formation of the second H-bond causes the energy gap between the πHπL* and nOπL* states to increase further. Excited-state absorption spectra for the photophysically relevant electronic states have been theoretically determined for comparison with the time-resolved spectra recorded experimentally [Villnow, T.; Ryseck, G.; Rai-Constapel, V.; Marian, C. M.; Gilch, P. J. Phys. Chem. A 2014]. The equilibration of the 1(πHπL*) and 3(nOπL*) states holds responsible for the chimeric behavior. This equilibrium sets in with a calculated time constant of 23 ps in methanol and 14 ps in TFE (5 and 10 ps in experiment, respectively). The radiative decay from the optically bright 1(πHπL*) state is computed to occur with a time constant of 25 ns in both solvents (14–25 ns in experiment).

The effect of substituting the intra-cyclic sulphur of thionine by oxygen (oxonine) and selenium (selenine) on the intersystem crossing (ISC) efficiency has been studied using high level quantum mechanical methods. The ISC rate constants are considerably increased when going from O towards Se while the fluorescence rate constants remain unchanged. For the three dyes, all accessible ISC channels are driven by vibronic spin-orbit coupling (SOC) between ππ* states. The interplay between the ground and low-lying excited states has been investigated in order to determine the dominant relaxation pathways. In oxonine the relaxation to the ground state after photoexcitation in water proceeds essentially via fluorescence from the S1(πHπL*) bright state (kF = 2.10 × 10(8) s(-1)), in agreement with the high experimental fluorescence quantum yield. In aqueous solution of thionine, the ISC rate constant (kISC ∼ 1 × 10(9) s(-1)) is one order of magnitude higher than fluorescence (kF = 1.66 × 10(8) s(-1)) which is consistent with its high triplet quantum yield observed in water (ϕT = 0.53). Due to a stronger vibronic SOC in selenine, the ISC rate is very high (kISC ∼ 10(10) s(-1)) and much faster than fluorescence (kF = 1.59 × 10(8) s(-1)). This suggests selenine-based dyes as very efficient triplet photosensitizers.

High-level electronic structure methods and quantum chemistry programs have been employed for a thorough investigation of the photophysics of acridone in isolated and solvated states.