Breaking the Kasha Rule for More Efficient Photochemistry - Chemical

Review pubs.acs.org/CR

Breaking the Kasha Rule for More Efficient Photochemistry Alexander P. Demchenko,† Vladimir I. Tomin,‡ and Pi-Tai Chou*,§ †

Palladin Institute of Biochemistry, National Academy of Sciences of Ukraine, 9 Leontovicha Street, Kyiv 01030, Ukraine Institute of Physics, Pomeranian University in Słupsk, ul. Arciszewskiego, 22b, Słupsk 76-200, Poland § Department of Chemistry, National Taiwan University, 1 Roosevelt Road Section 4, Taipei 106, Taiwan ‡

ABSTRACT: This paper provides a systematic review and analysis of different phenomena that violate a basic principle, Kasha’s rule, when applied to photochemical reactions. In contrast to the classical route of ultrafast transition to the lowest energy excited state and photochemical reaction starting therein, in some cases, these reactions proceed directly from high-energy excited states. Nowadays, this phenomenon can be observed for a number of major types of excited-state reactions: harvesting product via intersystem crossing; photoisomerizations; bond-breaking; and electron, proton, and energy transfers. We show that specific conditions for their observation are determined by kinetic factors. They should be among the fastest reactions in studied systems, competing with vibrational relaxation and radiative or nonradiative processes occurring in upper excited states. The anti-Kasha effects, which provide an important element that sheds light on the mechanisms of excited-state transformations, open new possibilities of selective control of these reactions for a variety of practical applications. Efficient utilization of excess electronic energy should enhance performance in the systems of artificial photosynthesis and photovoltaic devices. The modulation of the reporting signal by the energy of excitation of light should lead to new technologies in optical sensing and imaging.

CONTENTS 1. 2. 3. 4. 5.

Introduction History of Anti-Kasha Photochemistry Problems in the Studies of Anti-Kasha Effects Impact of High-Energy Vibrations Photochemistry from Sn (or from S1m) States 5.1. Intersystem Crossing (ISC) 5.2. Photoisomerizations 5.3. Photochromic Ring Opening 5.4. Electron Transfer (ET) Reactions 5.5. Intramolecular Charge Transfer (ICT) 5.6. Excited-State Energy Transfer (EET) 5.7. Excited-State Intramolecular Proton Transfer (ESIPT) 6. Conditions for Observing Anti-Kasha Photochemistry 6.1. General Theoretical Background 6.2. SnN Excited Dual Fluorescence in Thermodynamic and Kinetic Regimes 6.3. Criteria for Observing the Anti-Kasha Effects 6.4. Evaluation of kn2 Rate from Experimental Data 7. Photophysics of High-Energy Excited States 7.1. Energy Gap Law and Conical Intersections 7.2. Role of Vibrational Relaxations 7.3. Involvement of Solvent Relaxations 8. Horizons for Efficient Applications 8.1. Photoreactivity and Photocatalysis 8.2. Artificial Photosynthesis 8.3. Organic Optoelectronics

8.4. Photonic Switches and Molecular Logic Gates 8.5. Biological Sensing and Imaging 9. Conclusions Author Information Corresponding Author ORCID Notes Biographies Acknowledgments References

A B D E F F G H H J L

V W W X X X X X X X

1. INTRODUCTION Observations of stronger photobleaching of organic dyes by UV radiation than by visible light are not uncommon.1,2 In nature, living systems have developed efficient protection mechanisms to withstand damage from UV light.3,4 In-depth analysis of these facts reveals their apparent inconsistency with a fundamental principle of photophysics and photochemistry, Kasha’s rule. This rule5 establishes the connection between two basic processes, excitation and emission, and it states that in any condensed phase, photon emission (fluorescence or phosphorescence) occurs in appreciable yield only from the lowest excited state of a given (singlet or triplet) multiplicity, irrespective of the initial photoexcited state.6 Therefore, any process involving excited states should be independent of excitation energy. Upon absorbing a photon of sufficiently high energy, a molecule residing in its electronic ground singlet state

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Received: February 23, 2017

© XXXX American Chemical Society

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on investigating the photochemical reactions occurring from S2−Sn states. During the preparation of this review article, we have scanned several hundreds to a thousand papers for making this selection of references. We hope to provide new horizon for the exploration of photophysics and photochemistry in the higher-lying excited states. Validation of Kasha’s rule and demonstrations of characteristic exceptions should shed light on the mechanisms of excitedstate reactions. In this work, we illustrate that the anti-Kasha effects can be observed in quite different photochemical reactions and that these effects follow some general regularities. The exploration of anti-Kasha photochemistry opens up an unexpectedly broad range of possibilities for selective control of these reactions. This selective control may allow reduction of the losses in energy-dissipating internal conversion processes in photonic devices that follow excitation by high-energy quanta and presently seem to be unavoidable. In different practical applications (photosensors, artificial photosynthesis, photovoltaics, etc.), the exploitation of excess photoexcitation energy can become more efficient. New possibilities may appear in sensing and imaging, particularly with the use of multiphoton excitation.

S0 and excited to any of a set of higher electronic states (denoted Sn where n > 1) after electronic and vibrational relaxation can emit light or exhibit photochemical transformation only from the lowest excited state, S1. A similar regularity must exist for the triplet manifold, emitting phosphorescence. Thus, the emission or any excited-state reaction should proceed from the lowest excited energy states S1 and T1, being independent of the electronic excitation wavelength. The physical background behind this rule lies in the congestion of states among S1 and Sn such that the energy gap law operates efficiently (vide infra). As a result, internal conversion (IC) and vibrational relaxation (VR) from higherenergy states to the S1 and T1 states, in which IC is an isoenergetic (horizontal) electronic-coupling process between two states and VR is a vertical energy dissipation process via medium perturbation, are faster than the rate of radiative and other nonradiative depopulation of these states. Essentially, this rule is strictly applicable only in the condensed phase, where the excess energy released in the VR and IC processes could be released as heat through intermolecular interactions. An analogous expression to Kasha’s rule is the Vavilov law,7,8 which states that the quantum yield of phototransformation does not depend on the excitation wavelength. Because the emission color and intensity are accessible with common instruments or even the naked eye, Kasha’s rule is prevalent among chemists. The validity of Kasha’s rule has been proven in numerous fluorescence spectroscopic experiments on different fluorophore systems, so conformance to this rule is quite common.7,8 However, a number of exceptions to this rule have become known, so this regularity was formulated as a “rule”, not a “law”. These exceptions are mostly characteristic short-wavelength bands in emission spectra at excitations to high-energy electronic states,8−10 implying that the rates of emission decay can in some cases compete with internal conversion to the S1 state. Prototypical examples are azulene and aromatic thioketones. Michael Kasha himself was among the pioneers to study these exceptions.11 Independent of the excitation energy, the relaxation processes leading to population of the S1 state via internal conversion are usually very fast; the photochemical transformations commonly start from the lowest excited S1 state. This provides grounds for extending Kasha’s rule to a broader range of excited-state events, including photochemical reactions. In such extended form, Kasha’s rule can be formulated as follows: “In the condensed phase, polyatomic molecular entities react with appreciable yield only from the lowest excited state of a given multiplicity”.12 Yet a number of exceptions have been reported, raising the issue of “anti-Kasha photochemistry”. The relevant results are scattered and nonsystematic, and it is hard, on the basis of those results, to predict the appearance of these anti-Kasha effects. Here we make an attempt to provide systematic analysis of the effects and establish the conditions in which they can be observed. The results discussed below show that the photochemical reactions from highly excited states can compete in rate with other relaxation pathways to the S1 state, so that population of this state can be avoided before the reaction proceeds. It is worth noting that many authors describing the photochemistry at higher excited states do not use the “anti-Kasha” terminology, and in some cases, the results were erroneously interpreted as “anti-Kasha”. Therefore, it was difficult to dig out from the massive world literature the results

2. HISTORY OF ANTI-KASHA PHOTOCHEMISTRY The idea that excess electronic and vibrational energy of the excited molecule not only may result in local heating but also can lead directly to chemical transformation is not new. Early review by Turro et al.13 summarized the observations and discussed basic ideas regarding the energetics and kinetics of this phenomenon. However, the findings of deviations from Kasha’s behavior in photochemical reactions, despite their long history, are much more limited than those of anomalous Sn emission.9 The reason is that the higher complexity of studied events may entail different energetic and kinetic aspects. This new level of complexity appears because the kinetics of forward and reverse reactions from multiple states have to be considered. Their rates may depend on a complicated interplay of vibrational relaxation, internal conversion, and emissive or nonemissive relaxation to the ground state. It was recognized early that photochemical reactions in solutions may occur from the higher vibrational levels or higher-energy excited states only in cases where the nonradiative decay route to the lowest energy emissive state is slower than competing radiation or photochemistry. Therefore, anti-Kasha photochemistry may be observed only due to the specific interplay of different relaxation processes that follow high-energy electronic excitation. The role of intermolecular interactions in Sn → S1 relaxations was strongly emphasized by the emission from the Sn states in the gas phase at low pressures, where molecular collisions are rare, and thus the energy removal is relatively slow (see section 4). This led to suggestions that the higher excited state photochemistry has to be most easily observed when radiationless deactivation rates are unusually slow or when radiative or photochemical rates are unusually fast. Focusing on the events of slow relaxation to the emissive S1 state, Turro13 suggested differentiating two cases in addition to the commonly observed case (a) excitation to high vibrational levels of the S1 state with the slow vibrational relaxation rate, (b) with the removal of excess energy by collisions, and (c) excitation to higher electronic states Sn with slow IC to S1 state (Figure 1). B

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to increased intersystem crossing to the triplet manifold. Of special interest were the publications of Becker (discussed in section 4), which suggested the connection of excited-state reactions with vibrational relaxations.18 Particularly, it was shown that, in reactions producing cyclic ketone, some highenergy vibrational modes promote this reaction, but some tend to suppress it. The next important steps in these studies were associated with the introduction of new experimental techniques. As the sensitivity of detectors improved and powerful laser excitation sources became generally available, many new anti-Kasha emitting fluorophores were reported. Commonly, they exhibited very short Sn lifetimes that still allowed the collection of quantitative information on the rates of nonradiative transitions between higher excited energy levels of molecules.10 Direct lifetime measurements of highly excited states using picosecond and femtosecond spectroscopy became possible. The experiments on “hole burning” in absorption spectra and line-narrowing fluorescence spectra at low temperatures allowed bandwidth measurements of structured emission spectra from higher excited levels and the acquisition of state lifetime values from homogeneous line widths.19−21 Twophoton up-conversion spectroscopy has become actively used for studies in solutions with femtosecond time resolution. Techniques for measurement of the fluorescence spectra from higher excited singlet levels populated via triplet−triplet annihilation were developed.22,23 Most of these efforts were directed at quantitative analysis of vibrational relaxations in high-energy excited molecules,24 estimations of lifetimes of the Sn states in different fluorophores and conditions,25,26 and at the quenching effects.27 The Sn lifetimes derived from these data for typical organic fluorophores were found to be at least 3 orders of magnitude shorter than the S1 lifetimes. Among the results of particular interest is the increase of the S2 lifetime in the trans-retinal on H-bond formation28 and the observation in several studies24 of two-step S2 → S1 relaxation. The faster one could be due to isoenergetic transition to S1m, and the longer one (>200 fs) to vibrational cooling to S10. A surprising finding was the independence on the band gap (from 1600 to 4800 cm−1) of rather long (∼500 fs) lifetimes of the S2 state for all-trans-α,ω-diphenylpolyenes of different lengths (N = 3−7),29 which may be due to variations of electronic factors (see eq 1) compensating for the energy gap effect. To summarize, the focus in most of these studies was on lightemitting and nonemitting transformations from high-energy electronic states, so the photochemical transformations starting from them remained vague. A new wave of interest in anti-Kasha effects in photochemistry emerged at the beginning of this century. This interest arose with the understanding that anti-Kasha observations are not just exotic cases. With high temporal resolution, they can be observed in a large range of objects. Moreover, as it will be shown below, with knowledge of the background mechanisms, they can be modulated by targeted chemical design. This opened up the possibility of operating with photochemical transformations by the energy of incident light needed in different practical applications (phototransformations, chemical sensing, bioimaging, etc.). In the presentation that follows, we analyze recent developments with reference to classical results obtained in previous decades.

Figure 1. General state diagrams for reactions from (a) S1 state, (b) higher vibrational levels of S1, and (c) higher excited state.13 Reprinted from ref 13. Copyright 1978 American Chemical Society.

With regard to the first case, the rates of vibrational relaxations, estimated to be 10−11 − 10−12 s, were considered too short to influence emission, which commonly proceeds on a much longer time scale (10−8 − 10−10 s), and this should determine the dominant emission from the zero vibrational level of the S1 state. These rates can compete, however, with the rates of ultrafast photochemical events, suggesting a difference in the conditions for anti-Kasha emission and anti-Kasha photochemistry (for more details, see section 5). In the second case, the vibrational relaxation in the Sn state may be fast, but IC to the S1 state is slow enough to allow the photochemical process to proceed. This occurs because of unfavorable conditions for IC. It follows from quantum mechanics14 that the IC rate kIC from state 2 to the manifold of m levels of state 1 should be determined by the product of two factors: 2 k ic ∝ |⟨Ψ2|J |Ψ⟩| ∑ ⟨χ20 |χ1m ⟩|2 1 m

(1)

The first term involves the electronic wave functions Ψ2 and Ψ1 of the S2 and S1 states, respectively, and the nuclear kinetic energy operator J is an electronic factor describing the coupling of these functions. The second term is the familiar Franck− Condon factor between the two states. The nuclear wave functions χ20 and χ1m represent the zero vibrational level of S2 (so vibrations in S2 are assumed to be equilibrated) and manifold of m sublevels of S1. From eq 1, it is clear that slow internal conversion may result from either a poor Franck− Condon factor, as when the energy gap between S2 and S1 is large, or a poor electronic factor, as when Ψ2 and Ψ1 are orthogonal. Analysis of experimental data suggested that both vibrational relaxation and IC to the S1 state occur at rates comparable to or slower than those of photochemical events. Experimentally, vibrational relaxation and IC are hard to distinguish due to the spectral congestion and overlaps, the combination of which is dubbed vibronic relaxation. Many corresponding studies were limited by the phenomenological description of abnormalities in excitation and emission spectra, the decrease of fluorescence quantum yield at high-energy excitations, and the temperature dependence of these effects. The first experiments of Weber,15 in which quantum yield was measured as a function of excitation wavelength, found some effects that were interpreted by complexation and tautomerism in the ground-state. Soon after that, Ferguson16 and Hochstrasser17 found the effects of quantum yield decrease at short-wavelength excitations for halogen-substituted aromatic hydrocarbons and attributed them C

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Figure 2. Resolution of vibrational bands in the spectra of photochromic molecules. (a) Flindersine (above) is an example.38 (b) Fluorescence, λexc = 340 nm (1), fluorescence excitation, λem = 410 nm (2), and absorption (3) spectra of flindersine in 3MP at 180 K.37 (c) Suggested model of phototransformations of a photochromic molecule as a function of the vibronic level (m) excited within a given sequence. Kv are the rate constants of vibrational relaxations, and Kpc are the rate constants for photochemistry involving individual vibrational levels. Adapted with permission from ref 38. Copyright 2011 Elsevier B.V. Reprinted from ref 37. Copyright 1999 American Chemical Society.

3. PROBLEMS IN THE STUDIES OF ANTI-KASHA EFFECTS Manifestation of anti-Kasha effects is seemingly very simple. What is needed is just to measure the emission spectra at different excitation wavelengths and check for the appearance of new short-wavelength bands. For photochemical reactions with both light-emitting reactant and product, it is possible to measure excitation spectra recorded at two emission bands and to compare them with the absorption spectrum. Also, the emission spectra can be measured at different excitation wavelengths with analysis of the changes in relative intensities and/or quantum yields of two emission bands. However, a lot of additional work should be done to prove these effects and exclude all possible artifacts that may appear in these studies, which can be erroneously attributed as anti-Kasha effects. The classical paper of Hochstrasser17 may serve as instructions for scientists beginning research on these effects so that they can avoid such errors. To ascertain that it is the targeted Sn state being excited and that no impurities intervene, a two-step excitation has been suggested.30 The first laser pulse transfers the system to the S1 state, and the second pulse, with energy corresponding to the S1 → Sn transition with or without delay, provides additional quanta for exciting the system to exactly the needed Sn state. This method allows determining the quantum yield of Sn emission. The observation that the spectral profile of the excitation spectrum is different from that of the absorption spectrum in the range of higher lying excited states is not enough to state anti-Kasha behavior. The commonly observed decrease in emission intensity at the short wavelengths can be due to the faster nonradiative decay process directly to the ground state; however, some photochemistry cannot be excluded. Since the emission from Sn states is usually weak, impurities may present the major problem. A typical example of dual emission as a result of impurity is of 1-piperidinoanthraquinone, for which incorrectly assigned “S2” fluorescence was confirmed by use of purified synthetic samples. 31 In concentrated solutions or on forming molecular associates,

the impurities, even in very low concentrations, may serve as excitation energy transfer acceptors, ruining the whole picture. Impurities may appear as a result of uncontrolled photochemical reaction upon intense radiation by high-energy quanta.32 Commonly, they give rise to species which have less extended ππ-conjugation and which will therefore absorb and emit light at higher energies than the parent molecule. In general, fluorescence lifetimes and fundamental anisotropies should be different for emissions from the S1 and Sn states, and they must be ascribed to different origins of photoreaction products, but similarity can also be observed in the presence of impurities. The contaminant does not need to be a different chemical species. There are many examples of the presence of groundstate forms of the same dye (conformers or dimers) producing distinct excitation and emission spectra33−35 that could be recognized erroneously as violations of Kasha’s rule. It has to be taken into account that in hydrophobic solvents that are commonly used in such studies, the formation of intermolecular H-bonding complexes can be especially strong. The literature36 contains examples of the unprecedented stability of dimers with the dimerization constant Kdimer > 5 × 108 M−1. The low-polar solvents can be also contaminated with polar and H-bonding impurities that stabilize the H-bonded and chargeseparated states, leading to excitation wavelength selective spectra. The trivial inner-filter effect may also spoil the excitation at the bands of high absorbance, and it often increases at shorter wavelengths. Moreover, the wavelength-dependent reabsorption and self-quenching of fluorescence emission may result in discrepancies between absorption and excitation spectra when the latter are recorded at different emission wavelengths. In addition, misinterpretations are possible even with one type of pure fluorophore, but when there are two, close, low-lying singlet excited states, for instance a strongly fluorescent ππ* state overlapping from the high energy side with the silent nπ* state such that fast Sππ* → Snπ* ISC is thermally accessible, the measurements of wavelength-dependent quantum yields can be erroneously recognized as an anti-Kasha phenomenon. D

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Figure 3. Electron injection from the S1 state of 6-methyl-azulene-2-carboxylic acid (shown in the inset) into the bulk conduction band and the surface defects of TiO2 nanoparticles. (a) Vibronic profile of S1 absorption band with indicated excitation wavelengths. (b) Quantum yield of electron ejection as a function of excitation energy and schematic representation of effect of “cold” and “hot” electrons.46 Reprinted from ref 46. Copyright 2013 American Chemical Society.

its rate is nearly independent of the excitation wavelength. In jets, such dependence is very pronounced.42 In the studies of aromatic molecules in gas phase and on solid surfaces, it was shown that selective excitation of different vibrational modes such as the symmetric and antisymmetric stretches lead to very different chemical reactivities.43 With regard to the C−H bond cleavage in a single collision reaction, molecules excited with the symmetric stretching vibration can be as much as 10 times more reactive than ones excited with the antisymmetric stretching vibration. The interpretation of this behavior lies in the different vibrational motion inducing a different interaction with the atomic reaction partner or the surface. The existence of such effects in solutions, however, is still open for active research and discussion. In studies of pericyclic ring-opening reaction of indolylfulgides and indolylfulgimides, the effects of excess energy supplied by electronic excitation and by the increase of temperature were compared. It was shown that excess energy supplied by optical excitation accelerates the ring-opening reaction less efficiently than thermal energy and that vibrational relaxation from highly excited modes to modes promoting the ring-opening reaction is not completed within the ∼10 ps duration of the ring-opening reaction.44 Azulene, along with its derivatives, is a convenient object of study not only due to the presence of a bright long-living S2 band together with the short-living S1 band45 but also because of the strong wavelength separation between these bands and their well-defined vibronic structures, which allow excitation of the series of high-energy vibrational levels of the S1 state. This excitation allowed the observation of exoergic electron injection to a selected acceptor from the higher vibrational levels of this state, while injection from the lower levels remains endoergic. From studying the reactivity originating from these states, one can provide correlations with the amount of supplied excess vibrational energy. Exploiting this idea, carboxyazulene was bound to the surface of colloidal TiO2, and its electron ejection reactivity was studied by exciting different vibrational bands.46 Two distinct electron injection regimes were observed: a long wavelength one, which was attributed to a low yield direct injection into trap sites, and a short wavelength one, corresponding to a much higher yield of injection into the bulk conduction band of the TiO2 nanoparticles, demonstrating a 9-fold increase of reaction quantum yield (Figure 3). The charge recombination kinetics was also different for the low-

Thus, a number of precautions are required in the studies of anti-Kasha emission and photochemistry. A healthy degree of skepticism and caution are always needed when new, unexpected features in excitation and emission spectra are detected. When analyzing the results within a particular model, one should be always aware that no extra effect that is not predicted by the model can influence the result. Therefore, scientists have to be very cautious in conducting experiments and developing their interpretations.

4. IMPACT OF HIGH-ENERGY VIBRATIONS The contour of the electronic spectrum of organic fluorophores is composed of often poorly resolved or even unresolved bands arising due to the contributions of many vibrational states. Spectral selectivity may allow focused excitation of high-energy vibrational modes (S1m or Snm, m > 0). Strong contributions to vibronic S0 → S1m or S0 → Snm transitions are given by only a few modes with high Franck−Condon factors. In a series of experiments, Becker18,37,38 and his colleagues and followers39 presented a number of examples wherein the rates of photoreaction or intersystem crossing compete with vibrational relaxation. The excitation of higher vibrational modes, in general, increases the output of these reactions, decreasing the quantum yield of emission. Interestingly, excitation of different vibrational modes produced different effects; some promoted photochemical conversion, and some did not (Figure 2). Thus, the competition must exist between internal conversion and photochemistry at each vibrational level within a vibrational manifold. Both the excess energy provided by electronic excitation of vibronic bands and the thermal energy of intermolecular collisions are known to affect photochemical reactions. This is emphasized by strong differences in the rates of the reactions occurring with and without intermolecular interactions in the gas phase. Kasha’s rule cannot even be formally applied to the reactions in conditions where collisions are rare and the energy dissipation is slow, leading to excitations from high energy states.7 There are many examples of efficient fluorescence emission from the Sn states or photoproducts derived from these states in jets or gases in collision-free conditions or in supercritical fluids, where the probability of collisions may be smaller than that of emission.9,40 Instructive in this respect are the results on photoisomerization of trans-stilbene.41 In solutions, this reaction occurs much faster than in jets, and E

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Figure 4. Steady state spectra of Os(II) complex in aerated CH2Cl2 at 298 K.54 (a) Normalized absorption and excitation spectra monitored at different emission wavelengths. The excitation spectrum monitored at 420 nm (-□-) reveals a deficiency of constitution at short wavelengths as compared to those measured at 644 nm (-○-) and steady state absorption (−). (b) Excitation-wavelength-dependent (250−400 nm) emission spectra normalized at the fluorescence peak maxima. The intensity ratio for phosphorescence (P) versus fluorescence (F) increases by about 8 times while tuning λex from 400 to 250 nm. Reprinted from ref 54. Copyright 2012 American Chemical Society.

the triplet manifold may compete with the internal conversion. The results of recent experiments, however, show that it is more likely that photocleavage of the C−Br bond is responsible for this effect.52 For pentacene incorporated into crystal, vibronically induced ISC was reported,53 but this work was not developed any further. The study of the influence of high-energy excitation on ISC can be realized in systems that exhibit both fluorescence and phosphorescence and allow switching between these two emissions. The recent experiments of Chou et al. 54 demonstrated remarkable excitation wavelength dependent changes in the intensity ratio for phosphorescence (P) versus fluorescence (F) for a series of Os(II) and Ag(I) complexes displaying solely ππ* character in the S1 state but dominant metal−ligand charge transfer (MLCT) character in the higher excited state (Sn, n ≥ 2). It was shown that upon tuning of the electronic excitation from S1 to higher lying transitions, the P/F intensity ratio can be dramatically increased (Figure 4). For Os(II) and Ag(I) complexes, the P/F intensity ratio can be as high as 8-fold upon shifting of the electronic excitation from the lowest to higher-lying transitions in solution as well as in the solid state. Accordingly, the excitation spectra recorded for the P emission show a dramatic increase over those recorded for the F emission in the far UV region. The interpretation lies in the direct involvement of the Os(II) (or Ag(I)) d orbital in the high lying state Sn possessing MLCT character, such that the Sn → Tm ISC can be very fast, which is competitive with or even faster than vibrational relaxations and IC transitions. Conversely, in the lowest energy S1 state with ππ* character, the heavy metal atom and hence d orbital is not directly involved in S1 (ππ*) → T1 (ππ*) ISC. As a result, the rate of S1 (ππ*) → T1 (ππ*) ISC is slow, and the T1 production is significantly lower than that from Sn → Tm ISC followed by Tm → T1 relaxation, resulting in the prominent excitation wavelengthdependent phosphorescence intensity. To further demonstrate the general character of these observations, a series of chain phenylpolyyne molecules were selected; their relevant charac-

energy (λ > 585 nm) and high-energy (λ < 585 nm) excitation of the donor. Thus, different trapping sites are accessible to the “cold” and “hot” electrons generated by quanta of different energies. In section 7.2 of this review, we will discuss the coupling of excitations to Sn states with the high vibrational levels of the S1 state. Internal conversion to the S1 state proceeds through population of these “hot” intermediates.

5. PHOTOCHEMISTRY FROM Sn (OR FROM S1m) STATES Possessing excess energy, the high electronic Sn and high vibrational S1m states can participate in diverse chemical transformations with different reactivity from the vibrationally relaxed S1 state, in addition to Sn → S1 internal conversion. The result of the appearance of multiple decay pathways follows from comparison of the lifetimes and the quantum yields in the systems, in which the emission occurs from both the S2 and S1 states. In this approach, the radiative lifetime of the emission can be deduced from the Strickler−Berg relationship between absorption intensity and fluorescence radiative lifetime of molecules.47 Using ultrafast fluorescence spectroscopy, it was observed that in triphenylmethane48−50 and ketocyanine51 dyes, a substantial fraction of the initially excited S2 population decays by a dark route, which does not lead to S1 fluorescence. Meanwhile, an important issue for identification is the detection and analysis of different reaction products, an overview of which is provided in the following discussion. 5.1. Intersystem Crossing (ISC)

The idea that excitation to high energy states can facilitate singlet−triplet intersystem crossing (ISC) arose from early studies of Ferguson16 and Hochstrasser,17 who showed that a variety of aromatic hydrocarbons, including dibromoanthracene, exhibit wavelength-dependent fluorescence quantum yields with their strong decrease at high excitation energies. For rationalization, it was suggested that intersystem crossing to F

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( 1) electronic excitation, for which Sn → Tm ISC involves drastic spatial flipping of the associated frontier orbitals, such as nπ* → ππ* or vice versa. As a result, the spin−orbit coupling constant can be large, and the rate of ISC is competitive with the Sn → S1 relaxation, bypassing the relatively slow S1 → T1 ISC. A recent case in point is given by a bromo-substituted naphthalenediimide dye (rNDI, see Figure 5), for which the

5.2. Photoisomerizations

Also interesting with respect to anti-Kasha behavior are the isomerization reactions that occur in the excited states with ultrafast rates. However, the obtained results must be treated with extreme caution, since the photoselection of species already isomerized in the ground-state may be involved here. For benzyl, a nonconjugated aromatic α-dicarbonyl compound, emissions from both S1 and S2 states were recorded.57,58 However, in the S1 state, the emission comes from both the relaxed skew and the unrelaxed trans-planar forms. In the S2 state, it proceeds from the skew form only. The fact that, in the photoactivated isomerization reactions, the quantum yield and lifetime of excited product may depend on the conditions of excitation to the S1 or S2 state was observed in azobenzene59,60 and its derivatives.61 The behavior of these and of more complex rotaxanes was explained by the absence of full kinetic accessibility of the S1 states.62 The presence of extended singlet/triplet degenerate regions of twisted molecular structures with significant spin−orbitcoupling values account for ultrafast (picosecond time scale) isomerizations. Recently, this system was studied in detail.63 It was shown that the key issue is the high-energy excitation to either the nπ*(S1) or the ππ*(Sn) state and the isomerization paths and kinetics are quite different at these excitations. Trans-stilbene, another molecule that easily isomerizes in the excited state, behaves quite differently from azobenzene.41 The first nontrivial result is that this reaction in solution occurs much faster than in collisionless conditions (in jets or gases). However, unlike the well-resolved λex dependence in jets, it is rather weak in solution. Therefore, it has been suggested that the isomerization reaction in solution is promoted by intermolecular collisions, which depends only weakly on excitation energy. Such a weak but noticeable λex-dependent difference (Figure 6) was attributed to the effect of vibrational cooling. In the present state of our knowledge, it is quite dangerous to generalize that in any excited-state isomerization reaction, we should always observe the effect of acceleration as a result of high-energy excitation. These reactions vary strongly in their corresponding mechanisms, and the opposite effect can be equally probable. Thus, for the trans−cis isomerization of azobenzene, the product quantum yield is lower by a factor of 2 for the emission excited at S2 (yield equals 0.1−0.15) than at the lowest excited state S1 (0.24−0.31).64 The authors attribute this difference to additional vibrational excitation caused by the

Figure 5. Absorption spectrum (red solid line) and excitation spectrum (black dashed line, monitored at 600 nm emission) for rNDI in acetonitrile. Inset: energy level scheme of rNDI with the relevant relaxation pathways and time scale.56 Note: except for Tn with nπ* character, all other excited states have a ππ* character. Reprinted from ref 56. Copyright 2015 American Chemical Society.

fluorescence quantum yield was found to decrease by a factor of ∼2, going from S0 → S1 to S0 → S2 excitation. Results of femtosecond transient absorption, together with a computational approach, indicate that rNDI undergoes an ultrafast

Figure 6. Isomerization kinetics for trans-stilbene in n-hexane at 294 K recorded with 326 and 267 nm excitations.41 For 0−0 excitation (326 nm), the decay is monoexponential, τ = 84.2 ps, whereas for λex = 267 nm, it is biexponential, τ1 = 10 ps (8%) and τ2 = 84.2 ps. Adapted with permission from ref 41. Copyright 2013 Elsevier B.V. G

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S2 → S1m transition, which can promote the nonreactive decay processes. 5.3. Photochromic Ring Opening

The photochromic ring-opening reactions can proceed as ultrafast bond-breaking events as well,31 and some of them demonstrate their sensitivity to solvent polarity and viscosity, the environment temperature, and the excitation wavelength.39 Among the various photochromic molecules, the diarylethene and fulgide derivatives undergo cyclization and cycloreversion reactions in 6π-electrocyclic systems on ultrafast time scales. In diarylethene derivatives, cycloreversion proceeds with extremely low reaction yields in the condition of one-photon absorption. This reaction was drastically enhanced by twophoton absorption, leading to higher excited states.65 The opened efficient cycloreversion channel allowed reaction yields of up to 0.3−0.5. The efficient cycloreversion reaction was also observed in fulgide derivatives in a higher excited state. It was shown that photoreaction initiated by optical excitation into the S1 (570 nm) and Sn (340 nm) absorption bands of the closed isomer leads to considerable differences in reaction dynamics and product yields.66 The photoreaction starts from the Sn state and bypasses, to a large extent, the S1 state, driving the system directly to the product ground state and back to the initially excited ground state. The low efficiency of the transient population of the S1 state is evident from decay associated spectra (Figure 7). The multiphoton absorption leading to the Sn (n > 1) states allows comparative studies of cycloreversion reaction dynamics. The studies of photochromic fulgide derivatives have shown drastic enhancement of the reaction yield upon the two-photon absorption process accessing the higher excited states.65 Thus, the nonequilibrium dynamics controls the outcome of the photochemical process, and these reactions can proceed without having to populate the S1 state. We emphasize that the role of these dynamics can be seen in comparison of the same reactions occurring in the gas phase and in solutions. They can proceed along different routes because in the gas phase the high-energy electronic and vibrational states can live longer without rapid solvent-induced radiationless deactivation. Particularly, the very distinct differences between absorption and excitation spectra and also the latter spectra recorded at different wavelengths were observed for alkylindenes67 and dihydronaphthalenes.68 The effects of high-energy excitation can be found in these reactions on the condition that their rates compete with the IC relaxations to S1 state. A special case combining photoisomerization (section 5.2) and photochromic ring opening in this section is illustrated in a recent report,69 in which the S1 for both cis and trans benzophenone-substituted cyclopropanes possesses nπ* character and undergoes ISC, followed by ring opening in T1 to form a triplet biradical 36·· in the ground state (see Figure 8). 3 ·· 6 then undergoes thermally reversible type ISC 36··⇆16·· followed by cis−trans isomerization (light-blue pathway in Figure 8). Conversely, the S2 (ππ*) excitation undergoes fast ring opening to form a singlet biradical adiabatically, giving the radical 630 nm emission that cannot be accessed by S1 excitation (see pink pathway in Figure 8). Although both S1 and S2 excitations yield the same branching ratio for the cis versus trans products, the anti-Kasha effect and combination of ring opening, cis−trans isomerization open new diversity for harnessing the higher electronically excited states.

Figure 7. Wavelength-selective ring opening in indolylfulgide.66 (a) Structure and schematic drawing of the ring-opening reaction. The reaction can be initiated by both S1 and Sn excitations of the C-isomer. (b) Comparison of decay associated (DAS) spectra related to the time constants of 1.3 ps (black, broken, SN excitation) and 2.2 ps (red, solid, S1 excitation) for the decay of the S1 state. The small amplitude observed after Sn excitation shows that only a small fraction (38%) of the molecules reaches the minimum of the S1 state of the C-isomer. The inset spectra in the upper left are normalized to show the similarity of the two DAS spectra assigned to the S1 decay. Reprinted from ref 66. Copyright 2008 American Chemical Society.

Last but not least, it is worth noting that, in the studies of some photochromic reactions, an increase of the quantum yield at the short-wavelength excitation was attributed to increased reactivity from the “hot” vibrational levels of the S1 state but not from the Sn state37 (see section 4). However, based on these experimental results, it is extremely difficult to differentiate between these pathways, especially in view of ultrafast Sn ↔S1m transitions forming conical intersections (see section 7.1) through which the nuclear coordinates may change drastically.70 5.4. Electron Transfer (ET) Reactions

The most popular objects for studying the electron transfer (ET) dynamics in high-energy excited states may be the porphyrins. They are among a small number of molecules that display an easily recordable anti-Kasha fluorescence from the S2 state.71,72 Their measurable fluorescence from both S1 (Qband) and S2 (B or Soret band) states with large separation in energy has been widely exploited as a probe of the porphyrins’ excited state ET dynamics with ultrafast time resolution. Porphyrins are able to donate electrons to a number of acceptors that are covalently bound, forming molecular complexes in solutions.73 This opens up a lot of opportunities to study the effects of excess excitation energy by selective excitation to the S2 state, followed by charge separation and recombination dynamics. Such an ET quenching process in the H

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Figure 8. Energy diagrams for photoreactions of trans- and cis-5. Energy levels are determined by using wavelengths of luminescence and the results of density functional theory calculations.69 Adapted with permission from ref 69. Copyright 2017 Wiley.

Figure 9. (a) The ET photoreaction in self-assembled 1:1 complex of zinc(II)tetrasulphonatophenyl porphyrin (ZnTPPS4−) and methylviologen (MV2+).75 (b) The states involved and the time constants for ET and IC processes of ZnTPPS4-/MV2+ in H2O. D+/A− denotes the radical ion pair state originating from S2 or S1 excitation. (c) Schematic decay scheme of the observed dynamics in ZnTPPS4−/MV2+ excited to the S1(ν = 0), S1(ν = 1), and S2 states. Reprinted from ref 75. Copyright 2010 American Chemical Society.

MV2+ with the same time constant (∼180 fs) from both electronic states. The result is rather unexpected because the back electron transfer is rapid, and the kinetics is independent of the initially excited state (∼700 fs). However, the observation of the amount of vibrationally excited ground states revealed their increase with the increases in energy of the initial excited state and this led to the unexpected conclusion that the excess excitation energy survived during a two-step electron transfer reaction in solution. In accordance with these data, the ET rate from the S2 state was faster than the S2 → S1 decay by 1 order of magnitude. Therefore, in this case, the porphyrin-acceptor coupling was strong enough to allow an ultrafast rate of electron transfer from the S2 state to compete with the internal conversion. In yet another approach, the pyromellitimide acceptor was attached to the para position of the meso-phenyl group of zincporphyrin, and competitive electron transfer was observed from the S2 and S1 states.81 The result presented in Figure 10 shows

highly excited state could be up to the femtosecond time scale, depending on the linked donor−acceptor systems.74 In this context, porphyrin rings allow many possibilities of covalent bonding with ET partners. The search for the most efficient ET acceptors for the S2 excited Zn-porphyrin donors resulted in the application of closely positioned methylviologen,75 naphthalene diimide,76,77 and amino substituted naphthalene diimide78 acceptors. Fullerenes C60 proved their role as universal electron acceptors.79 In one prototypical approach, the ET reaction rates from the S2 state and S1 state have been compared in complexes of zincmeso-tetrasulfonatophenyl-porphyrin (ZnTPPS4−) with methyl viologen (MV2+).75,80 The photoinduced electron transfer reaction in zinc(II)-tetrasulphonatophenylporphyrin (ZnTPPS4−) and methylviologen (MV2+) complex (Figure 9) was studied in aqueous solution with transient absorption spectroscopy.75 Excitation of ZnTPPS4− in the Soret (S2) band or one of the two Q-bands (S1) results in electron transfer to I

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Figure 10. Transient absorption kinetics of Zn-porphyrin−pyromellitimide (ZnTPP-PI) conjugate at S2 (excitation at 420 nm) and S1 (excitation at 550 nm) states in 2-methyltetrahydrofuran probed at (a) 720 and (b) 480 nm.81 Solid lines are exponential fits. Reprinted from ref 81. Copyright 2004 American Chemical Society.

model, which describes explicitly the hot transitions from the charge-separated state into the first excited state occurring in the course of the nuclear relaxation. Many efforts are directed toward optimizing the connecting positions of an acceptor so as to realize an efficient electron transfer system. A heterogeneous ET from the S2 state in dyes immobilized on solid surfaces is of particular interest, but this will require further development for practical applications.83 Finally, the basic question may lie in whether ET quenching proceeds similarly or differently in the S1 and Sn states. For tetraphenylporphyrin, its occurrence via the S2 state was confirmed by observing the transient absorption of radical anion in the femtosecond laser flash photolysis. Moreover, the excitation-dependent difference was found in fluorescence emission decays showing that the quenching rate via the S1 state was faster than that from the S2 state.84 The ET quenching can be coupled with some ultrafast evolution of the S2 emission spectrum, which precedes the internal conversion and the excited state photochemistry, as has been demonstrated in studies of malachite green.49

clearly that an efficient electron transfer occurs from the S2 zinc porphyrin macrocycle to the ET acceptor, bypassing the S1 state. Therefore, zinc-porphyrins are attractive objects for studying the mechanisms of photoinduced ET reactions, and the S2 excitation adds a new dimension to the reaction in the higherlying excited state. These reactions can be modulated by various factors, such as the magnitude of electronic interaction between donor and acceptor, the free energy gap between the initial and final states of the ET process, and the interactions with the environment, including solvent dynamics and coupling with intramolecular vibrations. Among them, the energy gap dependence of these reactions is especially diagnostic for testing the ET theories, and the donor−acceptor pairs constructed with Zn-porphyrin allow comparison of the band gaps on excitations to the S2 and S1 states. On this basis, the influence of different factors, particularly that of solventdependent reorganization energy, can be studied.77 Variation of the donor−acceptor composition allows probing of the electronic coupling efficiency.73 Shifting the ET dynamics from nonadiabatic to adiabatic conditions, where the solvent dynamics regulate the charge separation rate, is possible in such systems. The efforts of theoretical analysis are directed at comprehension of the obscure features of electron transfer from the S2 state.82 Of particular interest is the role of “hot” vibrational states that appear at the higher-energy excitation. Do they remain “hot” in ET reaction? Do they contribute to the ET efficiency? The suggested model incorporates four electronic states (the first and the second excited singlet, the charge separated, and the ground states) as well as their vibrational sublevels corresponding to the excitation of intramolecular high frequency vibrational modes. Electron transfer from the S2 state results in the creation of the charge separated state with a strongly nonequilibrium surrounding solvent configuration and intramolecular vibrations. The solvent motion to its equilibrium is introduced into the

5.5. Intramolecular Charge Transfer (ICT)

Electronic charge transfer between distinct regions within the same molecule often results in the appearance of fluorescent emission at different (Stokes-shifted) wavelengths, and the formed charge-separated states are commonly stabilized in polar environments. Since this reaction is coupled with solvent polarization, it may proceed slowly enough that some of the initial locally excited (LE) emission can be recorded. This is the reason why in a number of reported cases dual emission spectra were observed. Their origin gave rise to active discussion regarding the change of dye geometry upon the formation of the ICT state.85 However, regarding Kasha’s rule, in many cases (including the most studied p-aminobenzonitriles),85 the situation is rather simple. The ICT state cannot be excited directly, and it has to be populated via a locally excited state. Therefore, its excitation spectrum cannot be different from the J

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Figure 11. Spectroscopic behavior of 3-(2,2′-bipyridyl)-iminocoumarin in acetonitrile.89 (Top) Plausible dual emissive excited states in the 3-bipyiminocoumarin platform involving an electron donor (D) and two acceptors: 2-imino and 3-bipy groups. Excitation and fluorescence are shown by hollow- and solid-headed arrows, respectively. (Bottom) (a) Fluorescence spectra at indicated excitation wavelengths and (b) excitation spectra at indicated emission wavelengths. Note that the spectra were normalized at correspondent excitation/emission band maxima. Adapted with permission from ref 89. Copyright 2012 Wiley.

addition to exhibiting two emission bands, this molecule also shows two distinct absorption bands corresponding to each of the two emissions. It was found that its short wavelength emission band arises from the higher excited singlet state, S2, while the longer wavelength emission band originates from the S1ICT state. Excitation at the S2 band leads to two kinds of excited state populations. One, emitting at shorter wavelengths, resembles the π−π* transitions of the parent molecule, anthracene. The other is mirror-imaged with respect to the lowest-energy S1 band. Thus, it was suggested that the S2 excitation populates the LE state with slow transition to the ICT state, whereas the S1 excitation populates directly the ICT state, such that both states can be populated by direct excitation from the ground state. The poor electronic coupling between the S2 and S1 states that possess different geometries, reducing the rate of S2 → S1 transition, can explain this effect. The anti-Kasha effect may appear strong if the two emissive states are kinetically uncoupled or coupled to a small extent.89 In 3-(2,2′-bipyridyl)-substituted iminocoumarins, dual emission bands can be observed. Each of these molecules has one electron donor and two conjugated electron acceptors, which leads to fluorescence from two independent charge transfer states (Figure 10). Each of them is populated from either the S2 or the S1 state, but to a different extent, and the two emissions demonstrate quite independent behavior. Essentially, the rapidly formed excited ICT states do not interconvert, or they convert very slowly, competing with emission. This results in a strong difference of excitation spectra collected at variable

LE excitation band. Accordingly, the LE population is independent of the excitation wavelength; no dependence ought to be observed in the wavelength distribution of twoband intensities in emission, and the excitation spectra recorded at two emission bands should be similar and correspond to the absorption spectrum, which is a typical Kasha-rule behavior. However, in certain cases, a different situation was observed; the absorption spectrum was represented by two or more bands, so the species populated on excitation of these bands behaved kinetically independent, with a lack of correlation. This situation was described for 6-styryl-2,4-disubstituted pyrylium salts.86 On the one hand, their short-wavelength emission at 420−530 nm is due to depopulation of the S2 excited state (band maximum at 340−400 nm) localized on the pyrylium fragment. On the other hand, the long-wavelength emission arises from a charge-transfer state S1ICT delocalized over the whole molecule and depends on the electron-donating property of the styryl substituent. The two fluorescing states do not exhibit a precursor-successor type of relationship, which can virtually be ascribed to anti-Kasha behavior. The other category, composed of a carbazoleimidizolium-based cation and various hydrophobic anions, forming salts that behave as ionic liquids, demonstrates emission from both the S2 state and the ICT state due to inhibition of internal conversion from the S2 state to the S1 state. This has been well-supported by both spectral and time-resolved data.87 The dual absorption and emission behavior of a donor− acceptor substituted chromophore, 9-amino-10-cyanoanthracene, has been investigated in polar and nonpolar solvents.88 In K

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Figure 12. Cyclic S2D → S2A followed by S2A → S1A excitation energy transfer between 1,3-difluoroazulene (DFAz) and zinc tetra(4-sulfonatophenyl) porphyrin (ZnTPP).97 (a) The absorption (abs) and emission (em) spectra for DFAz and ZnTPP in CH2Cl2. The absorbances are normalized to the maximum optical density. (b) Energy levels of donor (D) and acceptor (A) chromophores and the various EET and energy relaxation pathways. Solid lines are the radiative processes, while the broken lines are the nonradiative processes. τi are the lifetimes of correspondent states. Adapted with permission from ref 97. Copyright 2003 Royal Society of Chemistry.

raises a lot of interest and stimulates its modeling on molecular complexes of different compositions.93 Experiments on chromophore dyads that mimic the energy transfer kinetics in photosynthetic systems showed that from S2 states, this process can proceed very fast, on a scale of ∼100 fs,94,95 so it can provide the high electronic coupling needed for efficient energy transfer from an extremely short-lived energy donor state existing in photosynthesis.92 Can the energy transfer be observed between the higher excited states? Regarding the S2 → S2 transfer, this effect was realized with different fluorophore pairs. On a pathway to constructing porphyrin-based supramolecular artificial photosynthetic antennas, a series of porphyrin dimers and trimers consisting of a zinc porphyrin donor and a zinc di(phenylethynyl)-porphyrin acceptor were synthesized.96 In these systems, the S2 → S2 EET from donor to acceptor was followed by back EET to the S1 state of the donor. Probably, the strong Soret-transitions of both the donor and acceptor lead to large Coulombic interactions, thereby rendering S2 → S2 energy transfer effective enough to compete with the rapid internal conversion to the donor S1 state. In another model experiment, the S2 → S2 energy transfer was realized in the following way.97 As the donor, 1,3difluoroazulene was selected. Like azulene, it exhibits bright S2 emission with S2−S1 separation so strong that a proper acceptor can be selected with the absorption spectrum overlapping the donor emission spectrum from the S2 state and with the emission spectrum overlapping its S1 absorption spectrum (Figure 12). Thus, this azulene derivative serves both as S2 donor and as S1 acceptor. With zinc porphyrin as an EET partner, a bidirectional and cyclic process of energy transfer was observed, S2D → S2A, followed by internal conversion, S2A → S1A. Then either the relaxation to the ground state from S1A generating emission occurs, or the donor is excited again via the EET pathway S1A → S1D. The extremely fast rate of energy transfer from the S2 state that allows competition with internal conversion can be explained by the involvement of the Dexter-type electronexchange mechanism of transfer.98 Therefore, very short distances need to be provided in donor−acceptor ensembles. Different kinetic schemes that depend on variation of donor and acceptor concentrations in these systems can be realized.99

emission wavelengths and also of emission spectra at different excitations (see Figure 11). The ICT can be coupled with rotations (twisting) of molecular fragments. In a system exhibiting twisted intramolecular charge-transfer (TICT), the anti-Kasha behavior was also found.90 The formation of the metal-to-ligand charge transfer (MLCT) state in (2-ferrocenyl)indene is followed by a rotation of the indene group. Notably, the fluorescence emission from this state is observed at wavelengths shorter than the position of the longest absorption band, which suggests that the preferable formation of the TICT state is not in S1 but in Sn (n > 1) states, for which the energies are higher with respect to the nonrotated situation. The emission thus occurs from this corresponding state without relaxation to the S1 state. Summarizing the above elaboration, for anti-Kasha effects to appear in ICT reactions, a specific combination of selectivity in energy and kinetic control over relaxation pathways is needed. Since these reactions commonly follow the solvent-controlled adiabatic mechanism and often are associated with conformational changes (twisting), in order to proceed in higher-lying energy states, the ICT reaction should be an ultrafast subpicosecond event coupled with molecular vibrations, rather than with solvation dynamics.91 5.6. Excited-State Energy Transfer (EET)

The study of energy transfers from S2 and higher excited states is stimulated by attempts to understand one of the key features of the biological action of light−photosynthesis.92 The ability of the light harvesting pigments, carotenes, to absorb sunlight in the 400−600 nm region is due to their S0 → S2 electronic transition, represented by three vibronic bands. This transition is strongly allowed (molar absorbance ∼105). In contrast, S1 is the symmetry forbidden state, which cannot be accessed directly from the ground state but can be populated by internal conversion from S2. With the increase in the length of the conjugated chain, these transitions move to lower energies. At around eight conjugated CC bonds appears a new feature, the emission from the S2 state competing with internal conversion S2 → S1. In natural systems, neither the emission nor the IC from the S2 state is detected because carotenoids donate their excited-state energy to closely located tetrapyrole structures, chlorophylls. That is why the EET from the S2 state L

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Figure 13. Anti-Kasha ESIPT behavior of 2-butylamino-6-methyl-4-nitropyridine N-oxide (2B6M).104 (Top) Molecular structure of 2B6M showing intramolecular H-bonding. (Bottom) (a) Emission spectra in n-octane at indicated excitation wavelengths. (b) Excitation spectra in n-octane detected at the maxima of the emission spectra: 471 nm (solid line) and 595 nm (dashed line). Reprinted from ref 104. Copyright 2007 American Chemical Society.

Figure 14. Chemical structure of various 3-hydroxychromone (3-HC) derivatives.

fluorescence quantum yields, a kinetic scheme explaining these observations was proposed. On the basis of transient absorption spectroscopy, a more recent publication of the same group suggested that it may be not the S2 state but the high-energy vibrational mode of S1 state that is involved; therefore, this issue remains open.105 3-Hydroxychromone (3HC, see Figure 14) and its derivatives are considered to be classical in the studies of excited-state reactions. They display the ESIPT reaction, in which the interplay with the excited-state intramolecular charge transfer (ICT) is involved, so the reaction rates together with the emissive, nonemissive, and ESIPT processes can be modulated in broad ranges.103 By variations of the 3HCs heterocyclic structure and addition of electron-donor and electron-acceptor substitutions in the fluorophore, switching between different kinetic regimes can be achieved.106−108 Basic ESIPT events can proceed at an ultrafast (subps) rate,109−111 being coherent with low frequency vibrational motion along the pathway of ESIPT reaction (the intramolecular H-bond). The overall ESIPT rate, however, can be retarded due to the formation of reaction barriers that can be both intramolecular and intermolecular, involving solvation dynamics and the formation of ESICT (excited state intramolecular charge transfer) states.103,107 In a series of recent works, Tomin et al.112−114 have shown that the N* band, present as a low relative contribution to intensity in 3-hydroxyflavone (3HF, Figure 14) in polar aprotic solvent acetonitrile, disappears at excitation wavelengths shorter than 250 nm, so the excitation spectra do not match the absorption ones. It was also found that the ESIPT rate, when

5.7. Excited-State Intramolecular Proton Transfer (ESIPT)

Excited-state intramolecular proton transfer (ESIPT) is a fundamental reaction in chemistry and biology. It is also one of the most rapid reactions. Thus, the ESIPT in 10hydroxybenzo-[h]quinoline occurs in 12 fs,100 which may result from the ballistic proton wave packet transfer. Though the elementary act of ESIPT reaction can be extremely fast, the two fluorescence emission bands from the reactant normal (N*) and product tautomer (T*) states can be observed in some cases. The observations on modulating ESIPT by excitation energy were made with several dyes. It was found that 2-butylamino-6methyl-4-nitropyridine N-oxide (2B6M) demonstrates the presence of the N* band in emission only in low-polar solvents, and with the increase of polarity, the fluorescence becomes represented totally by the T* band.101,102 Since it is not the N* band but the T* band that exhibits solvent polaritysensitive shifts, demonstrating the ICT character, this reaction, according to recent classification,103 belongs to the class II type of ESIPT. For 2B6M, an anti-Kasha behavior was clearly manifested: The excitation spectra did not correspond to the absorption spectra, and the excitation at the short wavelength band led to a dramatic decrease in the intensity of the “blue” N* emission band (Figure 13). The lifetimes and quantum yields differed from S1 excitations at the short-wavelength.104 In that study, no indications of the presence of variable ground-state forms or associations were found. It was concluded that the emission proceeds via two different pathways, one originating at the S1 state and the other starting at the S2 state. On the basis of the measured lifetimes and M

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measured at these wavelengths, ∼2.2 × 1011 s−1, was higher than in the case of usual long wavelength excitation.113 A model involving competition between the emission from the S2 state, IC to S1 state, and ESIPT was suggested.112 Extended to other excited-state reactions, it will be discussed in the next section. The possibility of ESIPT from Sn states in 3HF raised active discussion.114−116 For different reasons, 3HF is not the best object to demonstrate such an anti-Kasha effect. In polar media, it exhibits strong intermolecular hydrogen bond perturbation of ESIPT, and its very high rate in low polar environments does not allow observing the emission from the reactant N* state. The proton-donating and proton-accepting ability of the reactive groups103,107,110 and the distribution of electron density within the molecule117 can be modulated by targeted variations in 3HC heterocyclic structure and by the addition of electron-donor and electron-acceptor substitutions in different positions in the fluorophore. Therefore, solvent-dependent switching of emission intensities between the N* and T* bands can be provided. In this way, the kinetic regime of ESIPT reaction can be alternated between irreversible and reversible.103,106−108 In addition, in these and other electron-donor substituted 3HC dyes,117 due to rapidly established N* ↔ T* equilibrium in the S1 state leading to repopulation of the N* state from the product T* state, no anti-Kasha effects in ESIPT are expected. To verify the possibility of anti-Kasha ESIPT kinetics, systems completely different from the numerous 3HC dyes synthesized previously were designed.118 Instead of an electrondonating group being anchored to increase the proton accepting power of the hydrogen bonding base site (the carbonyl group), the electron-withdrawing substituent is appended in such a way that the proton-donating site decreases its electron density and increases its proton-donating ability. This modification yields new characteristics: (1) the chargetransfer (ICT) state in the normal form becomes energetically lower, which should make the ESIPT reaction highly exergonic; (2) the electron-withdrawing action increases the acidity of the hydroxyl group, which must facilitate ESIPT and make it a preferential relaxation route in the higher-energy excited states; (3) still, the ESIPT kinetics remains to be slow enough to observe the normal N* band in both steady-state and kinetic experiments. The 3-HC derivatives 5-(3-hydroxy-4-oxo-4Hchromen-2-yl)thiophene-2-carbaldehyde (3-HTCA) and 2-((5(3-hydroxy-4-oxo-4H-chromen-2-yl)thiophen-2-yl)methylene)malononitrile (3-HTC-DiCN) were obtained (Figure 14). For 3-HTCA and 3-HTC-DiCN, on excitation at the shortwavelength S2 band, notable anti-Kasha behavior was observed, demonstrating the increased rate of ESIPT reaction. It was observed that the normal emission N* band disappears completely in favor of the reaction product tautomer T* band. This shows that the ESIPT reaction can proceed faster than other processes of relaxation in higher excited states. Accordingly, when the fluorescence emission is monitored at the tautomer band, the excitation spectrum is dramatically enhanced at short wavelengths, deviating from the absorption spectrum (Figure 15). Moreover, a dramatic rise of the fluorescence quantum yield at the tautomer band is observed in these conditions. The picosecond time-resolved experiments demonstrate that no equilibrium between the normal form and the tautomer form is achieved during the fluorescence lifetime when 3HTCA and 3-HTC-DiCN species are excited to the S1 state. The femtosecond up-conversion experiments showed that the

Figure 15. Absorption, emission (excited at 440 nm), and excitation spectra (monitored at indicated emission wavelengths) for 3-HTCDiCN in CH2Cl2.118 Adapted with permission from ref 118. Copyright 2016 Royal Society of Chemistry.

rate of ESIPT reaction almost doubles when excited at 350 nm in comparison with 425 nm excitation. This indicates that a barrier in the ESIPT reaction from S1 state is removed or diminished in higher-energy states. Comparative studies on the series of dyes with different electron acceptor substituents in thienyl fragments (3-HTC, 3-HTCA, and 3-HTC-DiCN) demonstrated that the switching between Kasha and antiKasha behavior can be achieved by proper molecular design. Withdrawing the electronic density from the proton donor −OH group creates the barrier for ESIPT reaction in the S1 state. The barrier is removed by excitation at higher energies, and in this way, the anti-Kasha effect can be observed. Concluding this section, we have to point out that the manifestation of deviations from Kasha’s rule can be found for all major types of photochemical reactions. Therefore, it is not the reaction specificity but some general regularities that determine the appearance of this phenomenon.

6. CONDITIONS FOR OBSERVING ANTI-KASHA PHOTOCHEMISTRY An intrinsic mechanism behind Kasha’s rule is an ultrafast vibrational relaxation (VR) and internal conversion to the emissive S1 state, so the modulation of any reaction by highenergy excitation is possible only if this reaction proceeds at a comparable rate to or faster than VR and IC in the condensed phase. There were attempts to develop a model of anti-Kasha photochemical reactions based on two alternative assumptions: (1) the internal conversions Sn → S1 are unusually slow or (2) the lifetimes of Sn states are relatively short, while the photochemical reaction rates from Sn are extremely fast. If the higher electronic states are so long-lived that other reaction channels compete with the internal conversions to S1, then one of these channels could be the photochemical reaction. A model based on time-resolved studies of excited-state transformations of pyridine N-oxide derivative 2B6M exhibiting ESIPT reaction in n-octane114 is presented in Figure 16. It is based on strong acceleration of ESIPT from the S2 state occurring in competition with S2 → S1 internal conversion. Regarding the state-dependent ESIPT dynamics, Tomin113,119 presented an analytical description of a similar scheme and considered, on its basis, the competition between two possible pathways of this reaction: the S2 → S1 IC N

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Figure 16. Suggested scheme of (a) excited-state processes and (b) corresponding rate constants (in s−1) as derived for 2B6M in n-octane; room temperature.86 Reprinted from ref 86. Copyright 2006 American Chemical Society.

by absorbing the energy νex′. Then the internal conversion to the S1N proceeds with the rate constant pn2. For simplicity, it neglects the contribution of the other Sn state depopulation processes, namely, the SnN → S0N transitions, as their energy gap is larger than that for SnN → S1. Also, it is possible to show that the latter possibility does not change the relative population of N/P bands, which we will be analyzing in different conditions in this section. Simultaneously, the excitedstate photoproduct S1P can be populated starting directly from the SnN state with the rate constant kn2, and in the S1P state, vibrational relaxation takes place before its spontaneous emission. In this case, we have kinetic reaction in this channel and can neglect the reverse transitions SnN ← S1. Deactivation of the S1N and S1P states occurs also with radiative kNR *, kPR* and nonradiative kNnR*, kPn * rates, respectively. The balance equations for the populations [N*] and [P*] of the correspondent states in the steady state regime can be written as

fluorescence emission and opening a direct ESIPT channel from the S2 state. Though their experiments on 3HF113,119 did not allow a preference for either of these possibilities, this general approach can be used as a starting point in the analysis of different photoreactions demonstrating anti-Kasha behavior. 6.1. General Theoretical Background

As for the formation of fluorescing photoproduct depicted above, the photoreactions that proceed from the lowest excited state of the reactant normal form S1N to the photoproduct state pertaining to kinetic type are characterized by a considerable energy gap between these states and by a small energy barrier that separates them along the reaction potential energy surface. In such reactions, equilibrium is much shifted toward the product, so the rate constant of the reverse transition k− is considerably smaller than that of the forward reaction rate k+, and in many cases, k− can be even smaller than the sum of the radiative and nonradiative rate constants of the electronic transition. Such reactions are practically irreversible.112,120 It should be noted that the reaction product need not be in the S1P state, but rather in the S0P ground state with an adiabatic manner. Nevertheless, the kinetic derivation is essentially the same. The scheme presented in Figure 17 illustrates the basic processes starting from the S 1 N and S nN states. The fluorophores can be excited to a high-energy SnN singlet state

N* (kRN * + knR + k+)1[N*] = k −[P*] + [Nn]pn2

(2)

P* (kRP * + k nR + k −)2 [P*] = k+[N*] + k n2[Nn]

(3)

where [Nn] is the population of the SnN state. Equations 2 and 3 allow the following expression for the most important parameter of dual emission, namely the population ratio of the two emissive states, [N*]/[P*]: P* (kRP * + k nR + k −)2 + (k n2k −/pn2 ) [N*] = N* [P*] k+ + (k n2/pn2 )(kRN * + k nR + k+)1

(4)

Clearly, the population ratio [N*]/[P*] does not depend on the density of the exciting light U(v′ex); rather, it depends directly on the rates k+, k−, kNR *, kNnR*, kpR*, kPnR* and on the probability kn2 of photoproduct formation directly from the SnN state. In a typical case, when the reaction from the S1N state is very fast, N* k+ > >kRN * + k nR

(5)

the sum of deactivation rates of the S1P state may be conveniently presented as the reverse function of the lifetime τP of the S1P state that is measurable experimentally, Figure 17. Scheme of energy levels for describing the formation of fluorescing photoproduct (P) caused by excitations into the S1 and Sn absorption electronic bands of the normal (N) fluorophore form.119 Adapted with permission from ref 119. Copyright 2008 Springer.

P* kRP * + k nR + k − ≈ τP−1

(6)

Eq 4, in view of eq 5 and eq 6, can be simplified to O

DOI: 10.1021/acs.chemrev.7b00110 Chem. Rev. XXXX, XXX, XXX−XXX

Chemical Reviews [N*] = [P*]

k n2 k pn2 −

Review

[N*] k ≈ − [P*] k+

+ τP−1

⎛ k+⎜1 + ⎝

k n2 ⎞ ⎟ pn2 ⎠

(11)

In this case, the ratio for the reverse versus the forward reaction rates controls the ratio of concentrations of the two emissive forms and does not depend on excitation to the S1N or S1P states. Therefore, in the thermodynamic regime of photochemical reaction, the population ratio of excited states of the normal form and its photoproduct and, accordingly, the ratio of fluorescence intensities from these states does not depend on the absorption band to which the system is excited. This case is illustrated in Figure 18a.

(7)

This relation opens up room for simple evaluation of the efficiency of the kn2 route on the appearance of the photoreaction product. The population ratio, [N*]/[P*], k depends on n2 , which determines the contribution of the pn2

photoproduct formation via the SnN state. Clearly, this will occur if the value of the rate constant kn2 is comparable to the k value of the IC rate constant pn2, approximately when n2 ≥ 0.1. pn2

Therefore, when the higher-energy states are excited, the role played by the rate constant kn2 will lead to a relative increase in the formation of the reaction product [P*]. The product efficiency could be expressed by its quantum yield (Q). Taking the photoproduct [P*] formation from the SnN state as an example, QnP* can be defined as Q nP * =

A n0

k n2 + pn1 + p2o + k n2

(8)

where An0 and p20 are the rates of radiative and nonradiative transitions from the SnN to S0N state, respectively, and pn1 is the rate of nonradiative transition from the SnN to S1N states. QnP* depends on the competition of all rates depopulating the SnN state. It is evident that the reaction quantum yield will be maximal when the sum of the SnN state deactivation rates is less than the SnN → S1P transition rate; for instance, A n0 + pn1 + p2o < k n2

Figure 18. Three limiting cases observed for photochemical reaction started by excitation to SnN states by high-energy quanta hνa. (a) The S1N and S1P equilibrium is established rapidly. Then the excitation wavelength will not influence the distribution of emission intensities. (b) The S1N → S1P reaction is in a kinetic regime, and the internal conversion SnN → S1N is faster than the photochemical reaction from the S1N state to the S1P state. The selectivity on excitation energy is lost in the SnN → S1N step. (c) The case of anti-Kasha photochemistry. The S1P state can be populated directly from the SnN state, which can be observed due to S1N → S1P reaction proceeding in a kinetic regime. Direct fluorescence emission from the SnN state is not shown.

(9)

Thus, in some systems with parameters satisfying eq 9, QnP* may be relatively high, and theoretically, it can even reach unity if the rate constant kn2 exceeds significantly the rates of internal conversion and fluorescence from the SnN state. The derived relation 7 allows simple evaluation of the kn2 effect on the generation of the excited state product. Of particular interest is the very fast forward reaction kinetics, where the reverse reaction has minor influence, and the case of the thermodynamic reaction mode, when the reversibility changes the essential principal characteristics, such as the ratiometric dual emission bands. Here, it is important to note that we discuss the model with fluorescent product P*. This model is applicable to the excited-state reactions the products of which emit light, followed by fast, reversibly transfers to the ground state of the N form as it is typical for ESIPT. For antiKasha photochemistry with nonfluorescent products and products accumulating in the P state, it is necessary to develop other models. Below, we treat the above cases analytically and then present the results of numerical simulations.

Quite a different picture can be expected in the case of reaction occurring in the S1N state in a kinetic regime (Figure 18, panels b and c). In this case, due to the high kn2 rate, the relative population of excited states of different energies changes over time. When the rate of photoproduct formation is high enough to satisfy inequality (eq 5), but the reverse reaction is slower than the sum of radiative and nonradiative rates of the S1P → S0P electronic transitions, for instance, P* k − < 0.1.

The influence of reaction in the channel SnN−S1P on dual fluorescence differs essentially in two extreme cases, namely, thermodynamic and kinetic regimes. If the excited-state reaction is fast and reversible, such that the reverse reaction rate is faster than the sum of emissive and nonemissive rates of the excited product state, P* k − > >kRP * + k nR

(12)

pn2

(10)

pn2

Then together with inequality (eq 12), we can obtain the expression

≤ 0.1 (vide supra), eq 7 can be reduced to P

DOI: 10.1021/acs.chemrev.7b00110 Chem. Rev. XXXX, XXX, XXX−XXX

Chemical Reviews [N*] = [P*]

τP−1

⎛ k+⎜1 + ⎝

Review

k n2 ⎞ ⎟ pn2 ⎠

=

6.3. Criteria for Observing the Anti-Kasha Effects

1 ⎛ τPk+⎜1 + ⎝

k n2 ⎞ ⎟ pn2 ⎠

On the basis of the theoretical considerations and simulations presented above, the criteria for observation of anti-Kasha effects can be formulated as follows. (1) The photochemical reaction should be under kinetic control, k+ ≫ k−. If, on the contrary, the excited-state equilibrium between reactant and product species is established, resulting in dual emissions from such equilibrated states for a two-state reaction, this would exclude any excitation energy-dependent selectivity (vide supra). Here the photoproducts are the major emitters, showing considerably longer fluorescence decays than the low intensity and short decay of the N* form. (2) The rate constant of excited state reaction from the SnN state should be comparable to the rate of SnN → S1N internal conversion, k n2 > 0.1. This allows the two channels populating the excited

(14)

which shows the possibility to assess the photoproduct through the higher excited state SnN with the rate kn2. Growth of this rate is accompanied by an increase of concentration [P*] and by the correspondent drop of the ratio [N*]/[P*]. Critical for the observation of this phenomenon are the relatively long lifetimes of the SnN states, which cannot be easily predicted.10

pn2

reaction product state, SnN → S1P and SnN → S1N → S1P, to compete, increasing the P* state population. The presence of this additional pathway should result in the excitationwavelength-dependent redistribution of the fluorescence intensity between two emission bands, decreasing the quantum yield of the N* emission and increasing that of P* emission. Special cases can enhance the anti-Kasha effects. The S1N state can be inaccessible to population (forbidden) from higher excited states, as in the case of photosynthesis and for some compounds, such as azulene, carothenoids, and porphyrins, where the S2−S1 gap is large. In such cases, the competition between IC and the excited state reaction from the SnN state can be the most efficient at high-energy excitations, as we observed in previous sections. Selective quenching of the S1N state also can result in the same effect because of the relative decrease in the number of molecules starting the reaction from this state.

Figure 19. Surface of the relative [N*]/[P*] population presented as functions of k− and k n2 calculated with eq 7. The lifetime of the pn2

photoproduct fluorescence τP was taken as 1 ns; the rate of forward reaction k+ = 1012 s−1.

6.4. Evaluation of kn2 Rate from Experimental Data

Experimentally, we can measure only the intensities of emission which are proportional to the population of excited states. Therefore, our calculations should be adapted to the numerical results of these measurements. The emission intensity ratio for IN versus IP in terms of the fluorescence spectrum can be expressed, accounting for eq 14, by the following expression:111,119

Figure 19 presents a 3D graphic surface for the relative population [N*]/[P*] as functions of k‑ and kn2 calculated on pn2

the basis of relation 7. The pronounced appearance of photoproduct via the higher excited state SnN occurs only when the reverse reaction does not play any essential role in depopulation of the P* state. Thus, when the values of rate k− are lower than ∼8 × 108 s−1, upon kn2 increasing from 0.1 to

IN c k N *ν [N*] 1 = INP = N × RP * N × = C NP ⎛⎜ Ip cP [P*] kR νp τPk+ 1 + ⎝

pn2

∼5, the [N*]/[P*] ratio drops from 10−3 to 10−4. With the increase of k−, these dependences are weakening, and at k− ∼ 109 s−1, this ratio practically does not depend on the rate of SnN → S1P transition. If k− is higher than 1.2 × 109 s−1, the reaction starts shifting to the reactant side. The 3D surface also well demonstrates that the same relative populations [N*]/[P*] may exist for different combinations of kn2 and k− values (one

k n2 ⎞ ⎟ pn2 ⎠

(15)

where cN and cP are the coefficients depending on the parameters of the detection system at frequencies νN and νP, respectively, and νN and νP are the mean frequencies of the N and P emission bands. The constant CNP is defined by

pn2

C NP =

may follow the lines between the stripes of different colors). Hence, we can derive that the reaction, and accordingly the photoproduct formation, in a higher-energy state will mainly affect the population ratio [N*]/[P*] via the terms kn2 in eq 7.

cN k N *ν × RP * N cP kR νp

(16)

Expression 15 provides an evident link between the relative intensities of the dual emission bands and reactions from the higher states SnN, which obviously shows that the rate of photoreaction from these states may be simply deduced from the following equation:

pn2

The rate constant kn2 should be of comparable value to the IC rate constant pn2, starting approximately from kn2 ≥ 0.1. When pn2

the SnN states are excited, the role played by the rate constant kn2 will lead to a relative increase in the yield of the reaction product [P*].

k n2 = Q

[1 − (INP × k+τP /C NP)]pn2 [(INPk+/C NP) − k −]τp

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Figure 20. Dependences of the relative probability

k n2 p2n

on the ratio of intensities INP/CNP for different rates of the reverse reaction k−. Lifetime of the

product emission τP is taken to be 1 ns; the rate of forward reaction k+ = 1012 s−1.

The dependences of the probability kn2 versus the intensity ratio INP for different combinations of the parameters characteristic of typical organic systems (τP ∼ 1 ns) are shown in Figure 20. We choose the relative populations [N*] and [P*] normalized by parameter CNP determined by eq 16 (i.e., the INP/CNP value). The calculations are then performed as a function of the relative value kn2 and different constants k+,

emission, cN and cP, which can be different. In our simulations, for the sake of simplicity, we took the value of CNP as unity. The above general methods for estimating the contribution of the high-energy states to the photoproduct formation can be used for investigation of various physicochemical processes generating fluorescence emissive states.

7. PHOTOPHYSICS OF HIGH-ENERGY EXCITED STATES Having established the formal criteria for observing the antiKasha phenomena, we now turn to the mechanisms of their realization in real organic fluorophores. Commonly, species excited to high-energy electronic states are extremely shortliving in condensed phases, and their normal type of relaxation is fast nonradiative internal conversion to the S1 state, in accordance with Kasha’s rule. This process involves both intramolecular vibrational modes and vibrational cooling with the participation of solvent. These processes can be observed on time scales ranging from a few tens of femtoseconds up to many tens and even hundreds of picoseconds. Recent experimental evidence demonstrates that elementary acts in photochemical transformations can be extremely fast, proceeding on the femtosecon scale.110,121,122 The essential peculiarity of anti-Kasha reactions proceeding from highly excited states is their simultaneous occurrence and coupling with these ultrafast relaxation processes. These nonequilibrium dynamic effects make them mechanistically different from the reactions progressing on a slower scale from energetically equilibrated S1 states.123

pn2

7

8

where reverse reaction rates k− are specified at 0, 10 , 10 , and 5 × 108 s−1. From the plots shown in Figure 20, we can derive the following remarks. (i) All curves kn2 (INP/CNP) with a growth of pn2

k+ rate demonstrate declining trends and higher relative intensities of dual emission; the strongest dependence is observed for the lowest k+ rates and INP/CNP values. (ii) In each case, increasing the k− rate decreases its influence on the kn2 rate and hence the relative fluorescence intensities. (iii) The maximal values and sensitivity of kn2 on the INP/CNP ratio are pn2

observed in the range of lower values of INP/CNP. Using the plots presented in Figure 20, we can estimate the relative rates kn2 , characterizing the reaction efficiency from the pn2

SnN level if the rates of k+, k−, τP, and INP/CNP for molecular systems under study are known. The rates kn2 can be estimated from the intensity ratio of the two fluorescence bands. In eq 17, we take into account the spectral sensitivity of the registration equipment at the correspondent wavelengths of the N* and P* R

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photochemical reactivity. Strong coupling due to “accessible conical intersections” between S1 and S0 was suggested for describing the observed ultrafast decay of the S1 state of azulene.45,128 Conical intersections (CI) are the crossing points between potential energy surfaces, at which these surfaces are degenerate (intersect). In the vicinity of these points, the principle of adiabaticity (the Born−Oppenheimer approximation) breaks down, and nonadiabatic processes such as transitions between electronic and vibrational states can take place. CI is an important concept in theoretical treatments of ultrafast electronic dynamics in polyatomic molecules.129 It allows description of the efficient coupling between electronic states that are mediated by motions along the degrees of freedom of the atomic nuclei, mainly vibrational coordinates. On the basis of this concept, the coupling between the Sn states and the high-energy vibrational substates of S1 can be understood. In the development of physical theory,130 this concept has recently gained support from experiments.131,132 By using an ultrashort pump pulse (∼10 fs) in an up-conversion experiment, it is possible to generate coherent vibrational wavepackets in all Franck−Condon active modes and to show that the vibrational coherence can be retained after internal conversion. A pending detailed understanding of the CI region and the factors connecting chemical reactivity with electronic transformations in this region may become resolvable in the analysis of antiKasha effects.

The photochemical pathway in the S1 state is commonly associated with an appreciable barrier, and this barrier may be removed or reduced in Sn (n > 1) states; thus, these states can play an active role not only in emission but also in photochemical transformations. This becomes possible when the coupling between the Sn state and the high vibrational levels of the S1 state allows “hot” photochemical reactions.82 Such coupling can be realized via conical intersection (see below). Moreover, strong spin−orbit coupling may exist between the Sn and triplet states, resulting in their enhanced nonemissive decays.71 In any respect, many variables are involved in the mechanisms of anti-Kasha photochemistry. 7.1. Energy Gap Law and Conical Intersections

The general requirement for photochemical anti-Kasha effects is clear: the reactions of interest in the Sn states have to be faster than or comparable in rate to the sum of all other processes responsible for the Sn depopulation. Therefore, the factors that govern the Sn → S1 conversion deserve focused analysis. As mentioned earlier (see eq 1 and the corresponding discussion), the facts of anti-Kasha high-energy emission are commonly attributed to a large energy gap between the S1 and S2 states, which leads to a decrease in the IC rate owing to a poor Franck−Condon factor. According to time-dependent perturbation theory, the rate of irreversible radiationless decay depends strongly on the interstate coupling energy and the density-of-state weighted Franck−Condon factor (Fermi’s golden rule),14 so these parameters are important for the lifetime of the Sn state. On the basis of theoretical description in terms of the energygap law,124 it was estimated that in cases of a relatively small energy gap between excited electronic states and the manifold of vibrational modes, the IC rate constants can be as fast as 1 × 1014 s−1, which negates the possibility of any Sn reactivity on a longer time scale.115 For azulene, the classical example emitting from the S2 state, the energy gap is large (up to 15000 cm−1), so the internal conversion S2 → S1 should be less probable than the S2 → S0 emission. In typical organic molecules, the Sn−Sn−1 gap is much smaller (