Article pubs.acs.org/JPCA
Reverse Intersystem Crossing in Rhodamines by Near-Infrared Laser Excitation Christel M. Marian,*,† Mihajlo Etinski,‡ and Vidisha Rai-Constapel† †
Institute of Theoretical and Computational Chemistry, Heinrich Heine University Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany ‡ Faculty of Physical Chemistry, University of Belgrade, Studentski Trg 12-16, 11000 Belgrade, Serbia S Supporting Information *
ABSTRACT: The population of the long-lived first excited triplet state (T1) of a fluorescence dye represents a major limitation in single-molecule spectroscopy. Reverse intersystem crossing (ReISC) is one of the processes that may prevent considerable loss of luminescence. In the present quantum chemical study we have analyzed rhodamine A in aqueous environment. The T2 ⇝ S1 and T3 ⇝ S2 ReISC channels are predicted to be viable. The rate constant computed for the former channel is ≈2 × 106 s−1. Hence, an excitation with suitable wavelength to one of the triplets should help repopulate the optically bright singlet state S1.
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INTRODUCTION Outstanding photophysical and photochemical properties turn rhodamines into ideal tools for a wide range of applications. Rhodamines are used, for example, as amplifying medium in lasers,1 stains in confocal and super-resolution microscopy,2−5 or molecular labels in fluorescence-based confocal singlemolecule detection and related techniques.6−8 Their typical fluorescence quantum yields close to unity result from the high oscillator strengths of the S1−S0 absorption and emission combined with a relatively low probability for singlet−triplet intersystem crossing (ISC). Experimentally determined rates of the latter process range from kISC ≈ 105 s−1 to ≈106 s−1 in polar protic environments.7,9−14 Hence, ISC can hardly compete with fluorescence that occurs on a time scale of nanoseconds. Although triplet quantum yields of rhodamines are typically well below 1%,1,4,11 the population of the long-lived first excited triplet state (T1) represents a major limitation in singlemolecule spectroscopy where high repetition rates of excitation and fluorescence (≥105 counts per molecule) are required. The nonradiative transition to the long-lived T1 state from which the molecule relaxes to the electronic ground state after some time causes photoblinking.15 The long lifetime of the T1 state can be used favorably in photoswitching spectroscopy to increase the resolution in fluorescence imaging.3,4 In general, however, it is an unwanted property of fluorescence dyes. Various strategies have been pursued to increase the photostability of rhodamine dyes. Common procedures aim at reducing the lifetime of the nonfluorescent state by adding triplet quenchers, thus deminishing the probability of photochemical degradation.16−18 Alternatively, reverse ISC (ReISC) was proposed as a mechanism for decreasing the population of the T1 state.14 To this end, the triplet molecule is excited by a second laser of appropriate wavelength to enable a transition back to the singlet manifold. So far, these attempts were not crowned with resounding success: Enhancements of a few © 2014 American Chemical Society
percent at most were achieved. Triplet relaxation (T-Rex) microscopy avoids illumination of the sample in the triplet state by using bunched pulsed excitation,19 thus preventing photodissociation of the dye that is known to proceed via the triplet intermediate.20 Theoretical studies that could give insight into the mechanistic details of the rhodamine photophysics are scarce. Earlier work performed in this laboratory focused on the energetics of the S1 and T1 states of rhodamine A (RhA) and the spectral shifts brought about in ethanol solution.18 In that study, combined density functional theory (DFT) and multireference configuration interaction (MRCI) methods were employed. Solvent effects on the S1- and T1-state energies were also a major topic of a very recent time-dependent density functional theory (TDDFT) study of various rhodamine dyes.21 Ågren and co-workers concentrated on two-photon absorption cross sections of rhodamine B and other fluorophores.22 Furthermore, investigations on the electronic structures and optical properties of rhodamine 6G23 and rhodamine B dimers24 were published. Very recently, we investigated singlet−triplet ISC of isolated RhA.25 Our quantum chemical calculations yielded a rate constant of kISC ≈ 104 s−1 for the S1 ⇝ T1 channel and of kISC ≈ 107 s−1 for the ISC from the S1 state to the near-degenerate T2 state. Major conclusions drawn in that work with regard to ISC of RhA in the gas phase were that vibronic effects substantially enhance the ISC rate and that the S1 ⇝ T2 nonradiative transition is the predominant source of triplet formation. Our present work aims at an understanding of ISC and possibly ReISC mechanisms in rhodamine molecules in aqueous solution. To this end, absorption and emission spectra, Received: July 10, 2014 Revised: August 4, 2014 Published: August 7, 2014 6985
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COSMO,31 (III) a combination of models (I) and (II). It turned out that the electrostatic continuum had only very minor influence on the vertical excitation spectra (Table S1 in the Supporting Information). Henceforth, the pure microhydration model (I) was employed in all further calculations. The SNF32 program was employed for the numerical determination of vibrational wave functions and frequencies in harmonic approximation. In addition to electronic SOMEs, these entities are required for computing ISC rates in the Fermi golden rule approximation.33 As it turned out, all low-lying electronic states of rhodamines exhibit ππ* character. Their direct spin−orbit coupling is very small and a Condon-type approximation may not be sufficient. El-Sayed forbidden transitions may gain substantial probability, however, by linear vibronic spin−orbit interactions, as demonstrated in our laboratory in several cases (see, e.g., ref 25 and references therein). Derivatives of the SOMEs with respect to massweighted normal coordinates were determined by a three-point finite difference scheme. Due to the large number of vibrational degrees of freedom, the recent implementation of a timedependent approach in the VIBES program was employed for computing ISC rates.25,34 With this method, rates for direct (Condon-type) and vibronic (Herzberg−Teller-type) ISC can be determined according to Fermi’s golden rule. Moreover, different temperatures can be simulated by assuming a Boltzmann distribution in the initial electronic state.25,35 Potential energy profiles along a linearly interpolated path (LIP) between the S1 and T2 minima of the water cluster were calculated using the DFT/MRCI method. For a better overview, the LIP was extrapolated on both sides.
excited-state absorption, and ISC rates for RhA, i.e., cationic 2(3,6-diaminoxanthen-9-yl)benzoic acid ethyl ester (Figure 1),
Figure 1. Chemical structure of rhodamine A (RhA).
are determined. RhA is the ethyl ester of rhodamine 110 (Rh110). We have chosen the ester form in our study to avoid complications due to acid−base equilibria or internal transformation into the lactonic form.1,26 RhA differs from rhodamine 123 (Rh123) only in the ester group where a methyl ester is found in Rh123. Because the photophysical properties are mainly determined by the xanthenyl and phenyl moieties, the differences are believed to be minor, however. Our theoretical findings will therefore be compared with experimental results for RhA, Rh110, and Rh123 where available.
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COMPUTATIONAL DETAILS Technical parameters and methods for computing geometries, energies, and wave functions of the spin-free Hamiltonian are the same as in previous work.18,25 To investigate excited-state absorption (ESA) in the first excited singlet and triplet states, a total of 30 singlet and 30 triplet states were computed by means of the DFT/MRCI approach.27 For the computation of the spin−orbit matrix elements (SOMEs) between the correlated DFT/MRCI wave functions we used the spin−orbit coupling kit (SPOCK) developed in our laboratory.28,29 For reasons of efficiency, a one-center mean-field approximation to the full Breit−Pauli spin−orbit coupling Hamiltonian was used.30 We tested three different models for simulating the water solution: (I) a solvent shell of six explicit water molecules, two each on the two amino groups and another two close to the central oxygen atom of the xanthenyl moiety (Figure 2), (II) a pure continuum model of the electrostatic interactions using
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RESULTS AND DISCUSSION Absorption Spectrum. The experimental Rh123 absorption spectrum in neutral aqueous solution consists of an intensive band having a maximum around 500 nm, a shoulder at 475 nm and less pronounced bands with maxima at 330 and 240 nm.36 An overview over the calculated vertical absorption spectrum is given in Figure 3. Full details such as excitation energies, electronic structures, oscillator strengths, as well as orientations of the electric transition dipole moments are provided in the Supporting Information and compared with experimental data where those are available. In short, we obtain a theoretical value for the S1 ← S0 absorption wavelength of 493 nm (2.52 eV) which compares favorably with the maximum of the first absorption band in RhA and Rh110 in aqueous solution.36−39 The transition is associated with the πH → πL* excitation and exhibits an oscillator strength f(r) close to unity. The orbital densities of both MOs involved in the transition are predominantly localized on the xanthenyl moiety (Figure 4). Accordingly, this electronic excitation may be characterized as a xanthenyl transition. Also, the S2 ← S0 absorption, dominated by the πH−1 → π*L excitation, corresponds to a pure xanthenyl transition. It is not formally forbidden but has a very small transition dipole moment. S3 is located 3.78 eV above S0 in aqueous solution and originates from the πH → π*L+1 excitation with intramolecular charge transfer (ICT) from the xanthenyl to the carboxyphenyl moiety. Although this ICT state (as well as the related triplet state T4) is not visible in the spectrum, it is mentioned here because it might play an important role in the redox reactions of the dye. The only triplet state lying below the S1 state of RhA in the Franck−Condon (FC) region is the T1 state. Like S1, it stems
Figure 2. Cluster model of rhodamine A in aqueous solution. 6986
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at 524 nm.37,38 The rate constant of the pure electronic transition is calculated as kF ≈ 2.3 × 108 s−1, in perfect accord with the experimental value of kF ≈ 2.1 × 108 s−1 for the fluorescence of Rh123 in water.37 Despite the relatively short lifetime of the S1 state, excitedstate absorption processes may occur. An overview over the most important excitations and their oscillator strengths is found in Figure 3; further details are provided in Table S4 of the Supporting Information. Of particular interest is the absorption probability at the wavelength of the primary laser excitation. Our calculations place the medium strong S14 ← S1 ESA in this wavelength region. In the MO picture, it is associated with an excitation of the outer valence electron from πL* to πL+4 * , both MOs being classified as xanthenyl orbitals (Figure S2, Supporting Information). Further, we find a very strong transition from S1 to S26 at about 400 nm. With respect to the electronic ground state, the dominant configuration of that state is a double excitation π2H → π*L 2, which makes it a πH → πL* single excitation with respect to S1. It is thus no wonder that the oscillator strength of the S26 ← S1 excited-state absorption is of the same order of magnitude as the S1 ← S0 absorption. This should be kept in mind in multiple-color laser experiments. Triplet Formation from the S1 State. For the efficiency of ISCs several factors are decisive: the electronic SOME, the adiabatic energy difference, the coordinate displacement of the singlet and triplet potential energy surfaces, and further factors such as the Duschinsky rotation of the respective normal modes. The relaxed T1 geometry is nearly identical to the nuclear arrangement at the S1 minimum. Hence, the nonradiative transition from S1 ⇝ T1 comes close to the weak coupling case in the sense of Englman and Jortner where the energy gap law applies.40 For isolated RhA we computed a rate constant of kISC ≈ 1 × 102 s−1 at 0 K for direct S1 ⇝ T1 ISC, which increases to kISC ≈ 1 × 104 s−1 when vibronic spin−orbit interaction is invoked.25 The probability for ISC was found to be only slightly temperature dependent, increasing the calculated rate constant to kISC ≈ 3 × 104 s−1 at ambient temperatures. To our knowledge, no experimental gas-phase value is available for comparison. The overlap of the vibrational wave functions of the initial and final states increases substantially when going from isolated RhA to the water cluster. In addition, nonvanishing matrix elements for all three Cartesian components of the electronic spin−orbit Hamiltonian are obtained (Table S5 of the Supporting Information) due to symmetry breaking. This means that all T1 fine-structure levels are populated upon ISC from S1 already in Condon approximation. Despite the slightly larger adiabatic energy difference of the S1 and T1 states (ΔE = 4830 cm−1 in water solution as compared to ΔE = 4436 cm−1 in vacuum), we obtain a rate constant of kISC ≈ 3 × 104 s−1 for direct S1 ⇝ T1 ISC at 0 K. Vibronic spin−orbit coupling leads to a further increase of the ISC rate constants, yielding a total rate (direct+vibronic) of kISC ≈ 1 × 105 s−1. Temperature enhances this process, in agreement with experimental observations. At room temperature, we compute a rate constant of kISC ≈ 2 × 105 s−1 (direct) and kISC ≈ 9 × 106 s−1 (direct +vibronic) for S1 → T1 ISC of RhA in water solution. Experimentally determined singlet−triplet ISC rates for rhodamines range from kISC ≈ 105 s−1 in frozen hydroxylic glasses at 77 K to kISC ≈ 106 s−1 in polar protic solutions at room temperature.7,9−14
Figure 3. Vertical excitation energies and dipole oscillator strengths of rhodamine A in aqueous solution at the S0 ground-state and the S1 and T1 excited-state minimum geometries.
Figure 4. Frontier MOs of RhA in aqueous solution.
from the πH → πL* excitation. The energy separation between the S1 and the T2 (πH−1 → πL*) states is larger than in the gas phase. The latter state might nevertheless play an important role in the ISC and ReISC processes in RhA. Higher-lying triplet states that might be interesting for triplet−triplet excitedstate absorption will be addressed below. Emission and Excited-State Absorption in S1. Relaxation of the nuclear frame in the S1 state leads to an energy release of 0.09 eV relative to the FC point. With the ground state only slightly destabilized (by 0.05 eV) with respect to its equilibrium geometry, the Stokes shift is quite small. We obtain a vertical emission energy of 2.39 eV corresponding to a wavelength of 520 nm, in excellent agreement with the intensity maximum of the fluorescence of Rh123 in water, which occurs 6987
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either the π*L+4 or the π*L+5 orbital. The medium strong transition in the blue spectral region (458 nm) exhibits partial charge transfer character from the phenyl ring of rhodamine to the perpendicular xanthenyl tricycle. Between 452 and 400 nm we find only transitions with very low oscillator strength. This agrees nicely with the intensity minimum in the experimental T−T absorption spectrum of Rh123 in water. The band observed in the violet region stems from two excitations involving an electron located at the ester carbonyl oxygen that is used to fill the hole in the πH occupation of the T1 state. Because of its closed-shell character, a state comparable to S26 is not present in the triplet manifold. Strong πH → πL* type transitions do thus not occur in the T−T absorption spectrum. Reverse Intersystem Crossing. Ringemann et al. investigated the effect of ReISC on the photokinetics of Rh110 in various solvents.14 To this end, these authors irradiated the sample with a second laser line of 568 or 671 nm wavelength, red-shifted with respect to the fluorescence excitation wavelength at 488 nm. They report stimulated emission and, most importantly, an increase in photobleaching concomitant with ReISC. They conclude that the success of their experimental approach depends on the ratio of the efficiency of ReISC and photobleaching from Sn and Tn and that this ratio is highly sensitive to the wavelength chosen for inducing ReISC, on the environmental conditions, and on the properties of the dye selected as fluorescence marker. To avoid photobleaching, we propose here to use laser lines in the near-infrared for the purpose of invoking ReISC. ESA from the T1 state to either the T2 or T3 states should be highly feasible because both transitions have significant oscillator strengths. As will be detailed below, there is a certain probability for T2 ⇝ S1 and T3 ⇝ S2 ISC to occur at substantial rates. Moreover, T2 and T3 are located energetically well below the first ICT states (S3 and T4/5, also Figure 3) which keeps the probability of ion pair formation low. As suggested previously,43,44 excitation into such high electronic levels could open up additional bleaching pathways. When possible triplet formation processes were analyzed (see above), it became apparent that the T2 potential energy surface is flatter than those of S1 and T1. A linearly interpolated path between the S1 and T2 minimum geometries (Figure 5)
Our calculations placed the T2 state adiabatically very close to the S1 state in isolated RhA (ΔE = −154 cm−1).25 Due to the flatter potential energy surface of the T2 state, its vibrational ground state was found to lie about 2250 cm−1 below the one of the S1 state in the gas phase, making the S1 ⇝ T2 decay possible even at low temperatures. Actually, the rate constant for this process determined in our calculations (kISC ≈ 4 × 107 s−1 at 10 K; kISC ≈ 5 × 107 s−1 at 298 K) is larger than for the S1 ⇝ T1 channel. This situation changes in aqueous solution where the S1 ⇝ T2 transition becomes an activated process. The solvent shift experienced by the T2 state is much smaller than those of S1 and T1 (compare Table S1 of the Supporting Information). Thus, in aqueous solution, the lowest vibrational level of the T2 state is found to lie about 2320 cm−1 above the corresponding S1 vibronic state. Our calculations yield a rate constant of kISC ≈ 101 s−1 for the S1 ⇝ T2 ISC at room temperature. Hence, this process plays only a subordinate role in the triplet formation of rhodamine A in water solution. On the basis of a comparison of estimated solvent shifts (Table S1 of the Supporting Information), similar results are expected for RhA in ethanolic solution. Triplet−Triplet Absorption Spectrum. Our calculated triplet−triplet (T−T) absorption spectrum is in excellent agreement with experiment. Ferguson et al. used the acridine triplet to sensitize the triplet formation in Rh123.41 The transient absorption spectrum recorded 40 μs after the primary irradiation of acridine in the wavelength range between 470 and 340 nm was attributed to the Rh123 triplet state. Correction of this spectrum for the loss of absorption due to the rhodamine ground state gave the absolute triplet absorption spectrum. Similar measurements by the same authors using xanthone as triplet sensitizer covered a broader wavelength range from 355 to 660 nm. In aqueous solution, Ferguson et al. find a broad and intense peak with its maximum at the red edge of their observation window and a shoulder near 430 nm. This band is clearly separated from a second peak with its maximum lying approximately at 390 nm and exhibiting a shoulder at about 370 nm. Theory (Table S6 of the Supporting Information and Figure 3) predicts strong triplet absorption to occur already in the near-infrared region outside the experimental observation window. These transitions are associated with electronic excitations from lower-lying xanthenyl orbitals filling the πH hole in the T1 occupation. Vertical excitation with a wavelength of λ ≈ 1280 nm will populate the T2 state. The T3 ← T1 transition at λ ≈ 990 nm possesses the largest oscillator strength in our computed triplet ESA spectrum. Near-infrared lasers, typically employed in multiphoton excitation microscopy of rhodamines,42 might be used for these triplet excitations as well. The medium intense transition in the yellow region of the visible spectrum (still outside the observation window in the acridine-sensitized spectrum) results from an excitation of the singly occupied πL* orbital localized in the xanthenyl moiety to * orbital. (For MO density plots see Figures the delocalized πL+3 S1 and S2 of the Supporting Information.) The band might be present in the experimental transient absorption spectrum after xanthone senzitation but is obscured by the maximum of the xanthone triplet absorption at 580 nm. Theory predicts strong triplet absorption in the green spectral region (515−506 nm) where the ground-state absorption and fluorescence emission exhibit their maximum intensities. The transitions to the T8 and T10 states originate from single excitations of the πL* electron to
Figure 5. Energy profiles of low-lying excited states along a linearly interpolated path connecting the minima of the S1 (geometry difference = 0) and T2 (geometry difference = 1) states and extended on both sides. Solid lines denote singlet states; dashed lines, triplet states. Stars: S1 and T1. Rectangles: S2 and T2. Triangles: T3. 6988
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× 106 s−1. Lasers with excitation wavelengths in the near IR region may, hence, lead to notable reduction in the singlet population loss via triplet formation.
reveals an intersection of the S1 and T2 potential energy surfaces close to the T2 minimum geometry. Here, electronic SOMEs are of the order of 0.1i cm−1 (Table S7 of the Supporting Information). Using these coupling elements and the vibrational overlaps of the two states, we obtain a rate constant of kISC ≈ 2 × 106 s−1 for the T2 ⇝ S1 ReISC. Although this process is most certainly slower than the spin-allowed internal conversion (IC) back to the T1 state, repeated excitation with laser light at this wavelength could lead to a substantial back transfer of triplet RhA molecules to the singlet manifold. Figure 5 also shows that the excited T3 state is nearly degenerate with S2. The Cartesian components of their electronic SOME are of the order of 0.1i cm−1; i.e., they have about the same size as the SOMEs coupling T2 and S1. Hence, reverse ISC should also be possible via the T3 ⇝ S2 channel.
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ASSOCIATED CONTENT
* Supporting Information S
Full details of calculated spectroscopic properties, molecular orbital pictures, vertical excitation energies, and spin−orbit matrix elements. This material is available free of charge via the Internet at http://pubs.acs.org/.
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AUTHOR INFORMATION
Corresponding Author
*C. M. Marian. E-mail: [email protected]. Notes
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The authors declare no competing financial interest.
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CONCLUSIONS AND OUTLOOK The photophysics of isolated RhA has been the topic of discussion in a former work.25 It was seen that in this case the vibronic coupling bolsters the nonradiative relaxation channel, making the S1 ⇝ T2 (kISC ≈ 107 s−1) channel the most feasible for singlet population loss. The topic of investigation in the present work is RhA in aqueous environment. The vertical absorption spectrum was seen to be nearly independent of the influence from the electrostatic continuum. However, the effect of specific bonding with explicit water molecules was not negligent. On the basis of these two facts we carried out the study of aqueous RhA with six explicit water molecules, without an electrostatic continuum shell. In the FC region, the S1 (πH → πL*) state was the bright state absorbing at 493 nm. Most of the other higher-lying singlet excited states were mostly dark in character. A few, however, do possess considerable oscillator strength ranging up to 0.3. The excellent agreement of computed vertical excitation energies with experimentally observed absorption maxima lends confidence to the reliability of the applied theoretical methods. Only the first triplet excited state with πH → πL* character lies below the bright S1 state in the vertical absorption spectrum. The photoexcited S1 state may relax radiatively with a computed rate constant of kf ≈ 2.3 × 108 to the ground state. Though El-Sayed forbidden, triplet formation may also provide a photorelaxation channel via vibronic coupling. The S1 ⇝ T1 ISC has been computed to proceed with a rate of ≈105 s−1 at 0 K and ≈9 × 106 s−1 at room temperature. The S1 ⇝ T2 channel is no longer as feasible as in a vacuum and is found to have a rate constant of ≈101 s−1 at room temperature. The purpose of this study is to propose suitable laser wavelengths for invoking ReISC, a channel that could help evade photobleaching of RhA in aqueous solution. Hence, a detailed analysis of the triplet−triplet excitation spectrum has been carried out. Even in that case the agreement with experimetally known data is very good. Our analysis reveals two additional transitions to triplet states, T2 and T3, in the near IR region, which possess large oscillator strengths with respect to vertical excitation from the lowest-lying triplet state. The potential wells of these states cross with those of the S1 and S2 states, respectively. Also, the magnitude of the electronic SOMEs for T2−S1 and T3−S2 coupling is of the order of 0.1i cm−1. These facts, together with the vibronic coupling lead us to conclude that ReISC should be facilitated for T2 ⇝ S1 and T3 ⇝ S2 channels, promoting the back-population of the singlet manifold. In fact, the rate of ReISC for T2 ⇝ S1 totals up to ≈2
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(16) Heupel, M.; Gregor, I.; Becker, S.; Thiel, E. Photophysical and Photochemical Properties of Electronically Excited Fluorescent Dyes: A New Type of Time-Resolved Laser-Scanning Spectroscopy. Int. J. Photoenergy 1999, 1, 1−7. (17) Widengren, J.; Chmyrov, A.; Eggeling, C.; Löfdahl, P.-Å.; Seidel, C. A. M. Strategies to Improve Photostabilities in Ultrasensitive Fluorescence Spectroscopy. J. Phys. Chem. A 2007, 111, 429−440. (18) Pfiffi, D.; Bier, B. A.; Marian, C. M.; Schaper, K.; Seidel, C. A. M. Diphenylhexatrienes as Photoprotective Agents for Ultrasensitive Fluorescence Detection. J. Phys. Chem. A 2010, 114, 4099−4108. (19) Donnert, G.; Eggeling, C.; Hell, S. W. Triplet-Relaxation Microscopy with Bunched Pulsed Excitation. Photochem. Photobiol. Sci. 2009, 8, 481−485. (20) Sassin, N. A.; Everhart, S. C.; Dangi, B. B.; Ervin, K. M.; Cline, J. I. Fluorescence and Photodissociation of Rhodamine 575 Cations in a Quadrupole Ion Trap. J. Am. Soc. Mass Spectrom. 2009, 20, 96−104. (21) Greisch, J.-F.; Harding, M. E.; Kordel, M.; Klopper, W.; Kappes, M. M.; Schooss, D. Intrinsic Fluorescence Properties of Rhodamine Cations in Gas-Phase: Triplet Lifetimes and Dispersed Fluorescence Spectra. Phys. Chem. Chem. Phys. 2013, 15, 8162−8170. (22) Chandra Jha, P.; Wang, Y.; Ågren, H. Two-Photon Absorption Cross-Sections of Reference Dyes: A Critical Examination. ChemPhysChem 2008, 111−116. (23) Gavrilenko, V. I.; Noginov, M. A. Ab Initio Study of Optical Properties of Rhodamine 6G Molecular Dimers. J. Chem. Phys. 2006, 124, 044301−1−044301−6. (24) Setiawan, D.; Kazaryan, A.; Martoprawiro, M. A.; Filatov, M. A First Principles Study of Fluorescence Quenching in Rhodamine B Dimers: How Can Quenching Occur in Dimeric Species? Phys. Chem. Chem. Phys. 2010, 12, 11238−11244. (25) Etinski, M.; Rai-Constapel, V.; Marian, C. M. Time-Dependent Approach to Spin-Vibronic Coupling: Implementation and Assessment. J. Chem. Phys. 2014, 140, 114104−1−114104−14. (26) Weininger, H.; Schmidt, J.; Penzkofer, A. Absorption Spectroscopic Investigation of Rhodamine Dye Vapors. Chem. Phys. 1989, 130, 379−387. (27) Grimme, S.; Waletzke, M. A Combination of Kohn-Sham Density Functional Theory and Multi-Reference Configuration Interaction Methods. J. Chem. Phys. 1999, 111, 5645−5655. (28) Kleinschmidt, M.; Tatchen, J.; Marian, C. M. Spin−Orbit Coupling of DFT/MRCI Wavefunctions: Method, Test Calculations, and Application to Thiophene. J. Comput. Chem. 2002, 23, 824−833. (29) Kleinschmidt, M.; Marian, C. M. Efficient Generation of Matrix Elements of One-Electron Spin−Orbit Operators. Chem. Phys. 2005, 311, 71−79. (30) Heß, B. A.; Marian, C. M.; Wahlgren, U.; Gropen, O. A MeanField Spin−Orbit Method Applicable to Correlated Wavefunctions. Chem. Phys. Lett. 1996, 251, 365−371. (31) Klamt, A.; Schüürmann, G. COSMO: A New Approach to Dielectric Screening in Solvents with Explicit Expressions for the Screening Energy and its Gradient. J. Chem. Soc., Perkin Trans. 1993, 2, 799−805. (32) Neugebauer, J.; Reiher, M.; Kind, C.; Hess, B. A. Quantum Chemical Calculation of Vibrational Spectra of Large Molecules Raman and IR Spectra for Buckminsterfullerene. J. Comput. Chem. 2002, 23, 895−910. (33) Marian, C. M. Spin−Orbit Coupling and Intersystem Crossing in Molecules. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2012, 2, 187− 203. (34) Etinski, M.; Tatchen, J.; Marian, C. M. Time-Dependent Approaches for the Calculation of Intersystem Crossing Rates. J. Chem. Phys. 2011, 134, 154105−1−154105−9. (35) Etinski, M.; Tatchen, J.; Marian, C. M. Thermal and Solvent Effects on the Triplet Formation in Cinnoline. Phys. Chem. Chem. Phys. 2014, 16, 4740−4751. (36) Pakalnis, S.; Sitas, V.; Schneckenburger, H.; Rotomskis, R. Photostability of Fluorescent Dyes for Single-Molecule Spectroscopy: Mechanisms and Experimental Methods for Estimating Photobleaching in Aqueous Solution. The Third Internet Photochemistry 6990
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Reverse Intersystem Crossing in Rhodamines by Near-Infrared Laser Excitation Christel M. Marian,*,† Mihajlo Etinski,‡ and Vidisha Rai-Constapel† †
Institute of Theoretical and Computational Chemistry, Heinrich Heine University Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany ‡ Faculty of Physical Chemistry, University of Belgrade, Studentski Trg 12-16, 11000 Belgrade, Serbia S Supporting Information *
ABSTRACT: The population of the long-lived first excited triplet state (T1) of a fluorescence dye represents a major limitation in single-molecule spectroscopy. Reverse intersystem crossing (ReISC) is one of the processes that may prevent considerable loss of luminescence. In the present quantum chemical study we have analyzed rhodamine A in aqueous environment. The T2 ⇝ S1 and T3 ⇝ S2 ReISC channels are predicted to be viable. The rate constant computed for the former channel is ≈2 × 106 s−1. Hence, an excitation with suitable wavelength to one of the triplets should help repopulate the optically bright singlet state S1.
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INTRODUCTION Outstanding photophysical and photochemical properties turn rhodamines into ideal tools for a wide range of applications. Rhodamines are used, for example, as amplifying medium in lasers,1 stains in confocal and super-resolution microscopy,2−5 or molecular labels in fluorescence-based confocal singlemolecule detection and related techniques.6−8 Their typical fluorescence quantum yields close to unity result from the high oscillator strengths of the S1−S0 absorption and emission combined with a relatively low probability for singlet−triplet intersystem crossing (ISC). Experimentally determined rates of the latter process range from kISC ≈ 105 s−1 to ≈106 s−1 in polar protic environments.7,9−14 Hence, ISC can hardly compete with fluorescence that occurs on a time scale of nanoseconds. Although triplet quantum yields of rhodamines are typically well below 1%,1,4,11 the population of the long-lived first excited triplet state (T1) represents a major limitation in singlemolecule spectroscopy where high repetition rates of excitation and fluorescence (≥105 counts per molecule) are required. The nonradiative transition to the long-lived T1 state from which the molecule relaxes to the electronic ground state after some time causes photoblinking.15 The long lifetime of the T1 state can be used favorably in photoswitching spectroscopy to increase the resolution in fluorescence imaging.3,4 In general, however, it is an unwanted property of fluorescence dyes. Various strategies have been pursued to increase the photostability of rhodamine dyes. Common procedures aim at reducing the lifetime of the nonfluorescent state by adding triplet quenchers, thus deminishing the probability of photochemical degradation.16−18 Alternatively, reverse ISC (ReISC) was proposed as a mechanism for decreasing the population of the T1 state.14 To this end, the triplet molecule is excited by a second laser of appropriate wavelength to enable a transition back to the singlet manifold. So far, these attempts were not crowned with resounding success: Enhancements of a few © 2014 American Chemical Society
percent at most were achieved. Triplet relaxation (T-Rex) microscopy avoids illumination of the sample in the triplet state by using bunched pulsed excitation,19 thus preventing photodissociation of the dye that is known to proceed via the triplet intermediate.20 Theoretical studies that could give insight into the mechanistic details of the rhodamine photophysics are scarce. Earlier work performed in this laboratory focused on the energetics of the S1 and T1 states of rhodamine A (RhA) and the spectral shifts brought about in ethanol solution.18 In that study, combined density functional theory (DFT) and multireference configuration interaction (MRCI) methods were employed. Solvent effects on the S1- and T1-state energies were also a major topic of a very recent time-dependent density functional theory (TDDFT) study of various rhodamine dyes.21 Ågren and co-workers concentrated on two-photon absorption cross sections of rhodamine B and other fluorophores.22 Furthermore, investigations on the electronic structures and optical properties of rhodamine 6G23 and rhodamine B dimers24 were published. Very recently, we investigated singlet−triplet ISC of isolated RhA.25 Our quantum chemical calculations yielded a rate constant of kISC ≈ 104 s−1 for the S1 ⇝ T1 channel and of kISC ≈ 107 s−1 for the ISC from the S1 state to the near-degenerate T2 state. Major conclusions drawn in that work with regard to ISC of RhA in the gas phase were that vibronic effects substantially enhance the ISC rate and that the S1 ⇝ T2 nonradiative transition is the predominant source of triplet formation. Our present work aims at an understanding of ISC and possibly ReISC mechanisms in rhodamine molecules in aqueous solution. To this end, absorption and emission spectra, Received: July 10, 2014 Revised: August 4, 2014 Published: August 7, 2014 6985
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COSMO,31 (III) a combination of models (I) and (II). It turned out that the electrostatic continuum had only very minor influence on the vertical excitation spectra (Table S1 in the Supporting Information). Henceforth, the pure microhydration model (I) was employed in all further calculations. The SNF32 program was employed for the numerical determination of vibrational wave functions and frequencies in harmonic approximation. In addition to electronic SOMEs, these entities are required for computing ISC rates in the Fermi golden rule approximation.33 As it turned out, all low-lying electronic states of rhodamines exhibit ππ* character. Their direct spin−orbit coupling is very small and a Condon-type approximation may not be sufficient. El-Sayed forbidden transitions may gain substantial probability, however, by linear vibronic spin−orbit interactions, as demonstrated in our laboratory in several cases (see, e.g., ref 25 and references therein). Derivatives of the SOMEs with respect to massweighted normal coordinates were determined by a three-point finite difference scheme. Due to the large number of vibrational degrees of freedom, the recent implementation of a timedependent approach in the VIBES program was employed for computing ISC rates.25,34 With this method, rates for direct (Condon-type) and vibronic (Herzberg−Teller-type) ISC can be determined according to Fermi’s golden rule. Moreover, different temperatures can be simulated by assuming a Boltzmann distribution in the initial electronic state.25,35 Potential energy profiles along a linearly interpolated path (LIP) between the S1 and T2 minima of the water cluster were calculated using the DFT/MRCI method. For a better overview, the LIP was extrapolated on both sides.
excited-state absorption, and ISC rates for RhA, i.e., cationic 2(3,6-diaminoxanthen-9-yl)benzoic acid ethyl ester (Figure 1),
Figure 1. Chemical structure of rhodamine A (RhA).
are determined. RhA is the ethyl ester of rhodamine 110 (Rh110). We have chosen the ester form in our study to avoid complications due to acid−base equilibria or internal transformation into the lactonic form.1,26 RhA differs from rhodamine 123 (Rh123) only in the ester group where a methyl ester is found in Rh123. Because the photophysical properties are mainly determined by the xanthenyl and phenyl moieties, the differences are believed to be minor, however. Our theoretical findings will therefore be compared with experimental results for RhA, Rh110, and Rh123 where available.
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COMPUTATIONAL DETAILS Technical parameters and methods for computing geometries, energies, and wave functions of the spin-free Hamiltonian are the same as in previous work.18,25 To investigate excited-state absorption (ESA) in the first excited singlet and triplet states, a total of 30 singlet and 30 triplet states were computed by means of the DFT/MRCI approach.27 For the computation of the spin−orbit matrix elements (SOMEs) between the correlated DFT/MRCI wave functions we used the spin−orbit coupling kit (SPOCK) developed in our laboratory.28,29 For reasons of efficiency, a one-center mean-field approximation to the full Breit−Pauli spin−orbit coupling Hamiltonian was used.30 We tested three different models for simulating the water solution: (I) a solvent shell of six explicit water molecules, two each on the two amino groups and another two close to the central oxygen atom of the xanthenyl moiety (Figure 2), (II) a pure continuum model of the electrostatic interactions using
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RESULTS AND DISCUSSION Absorption Spectrum. The experimental Rh123 absorption spectrum in neutral aqueous solution consists of an intensive band having a maximum around 500 nm, a shoulder at 475 nm and less pronounced bands with maxima at 330 and 240 nm.36 An overview over the calculated vertical absorption spectrum is given in Figure 3. Full details such as excitation energies, electronic structures, oscillator strengths, as well as orientations of the electric transition dipole moments are provided in the Supporting Information and compared with experimental data where those are available. In short, we obtain a theoretical value for the S1 ← S0 absorption wavelength of 493 nm (2.52 eV) which compares favorably with the maximum of the first absorption band in RhA and Rh110 in aqueous solution.36−39 The transition is associated with the πH → πL* excitation and exhibits an oscillator strength f(r) close to unity. The orbital densities of both MOs involved in the transition are predominantly localized on the xanthenyl moiety (Figure 4). Accordingly, this electronic excitation may be characterized as a xanthenyl transition. Also, the S2 ← S0 absorption, dominated by the πH−1 → π*L excitation, corresponds to a pure xanthenyl transition. It is not formally forbidden but has a very small transition dipole moment. S3 is located 3.78 eV above S0 in aqueous solution and originates from the πH → π*L+1 excitation with intramolecular charge transfer (ICT) from the xanthenyl to the carboxyphenyl moiety. Although this ICT state (as well as the related triplet state T4) is not visible in the spectrum, it is mentioned here because it might play an important role in the redox reactions of the dye. The only triplet state lying below the S1 state of RhA in the Franck−Condon (FC) region is the T1 state. Like S1, it stems
Figure 2. Cluster model of rhodamine A in aqueous solution. 6986
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at 524 nm.37,38 The rate constant of the pure electronic transition is calculated as kF ≈ 2.3 × 108 s−1, in perfect accord with the experimental value of kF ≈ 2.1 × 108 s−1 for the fluorescence of Rh123 in water.37 Despite the relatively short lifetime of the S1 state, excitedstate absorption processes may occur. An overview over the most important excitations and their oscillator strengths is found in Figure 3; further details are provided in Table S4 of the Supporting Information. Of particular interest is the absorption probability at the wavelength of the primary laser excitation. Our calculations place the medium strong S14 ← S1 ESA in this wavelength region. In the MO picture, it is associated with an excitation of the outer valence electron from πL* to πL+4 * , both MOs being classified as xanthenyl orbitals (Figure S2, Supporting Information). Further, we find a very strong transition from S1 to S26 at about 400 nm. With respect to the electronic ground state, the dominant configuration of that state is a double excitation π2H → π*L 2, which makes it a πH → πL* single excitation with respect to S1. It is thus no wonder that the oscillator strength of the S26 ← S1 excited-state absorption is of the same order of magnitude as the S1 ← S0 absorption. This should be kept in mind in multiple-color laser experiments. Triplet Formation from the S1 State. For the efficiency of ISCs several factors are decisive: the electronic SOME, the adiabatic energy difference, the coordinate displacement of the singlet and triplet potential energy surfaces, and further factors such as the Duschinsky rotation of the respective normal modes. The relaxed T1 geometry is nearly identical to the nuclear arrangement at the S1 minimum. Hence, the nonradiative transition from S1 ⇝ T1 comes close to the weak coupling case in the sense of Englman and Jortner where the energy gap law applies.40 For isolated RhA we computed a rate constant of kISC ≈ 1 × 102 s−1 at 0 K for direct S1 ⇝ T1 ISC, which increases to kISC ≈ 1 × 104 s−1 when vibronic spin−orbit interaction is invoked.25 The probability for ISC was found to be only slightly temperature dependent, increasing the calculated rate constant to kISC ≈ 3 × 104 s−1 at ambient temperatures. To our knowledge, no experimental gas-phase value is available for comparison. The overlap of the vibrational wave functions of the initial and final states increases substantially when going from isolated RhA to the water cluster. In addition, nonvanishing matrix elements for all three Cartesian components of the electronic spin−orbit Hamiltonian are obtained (Table S5 of the Supporting Information) due to symmetry breaking. This means that all T1 fine-structure levels are populated upon ISC from S1 already in Condon approximation. Despite the slightly larger adiabatic energy difference of the S1 and T1 states (ΔE = 4830 cm−1 in water solution as compared to ΔE = 4436 cm−1 in vacuum), we obtain a rate constant of kISC ≈ 3 × 104 s−1 for direct S1 ⇝ T1 ISC at 0 K. Vibronic spin−orbit coupling leads to a further increase of the ISC rate constants, yielding a total rate (direct+vibronic) of kISC ≈ 1 × 105 s−1. Temperature enhances this process, in agreement with experimental observations. At room temperature, we compute a rate constant of kISC ≈ 2 × 105 s−1 (direct) and kISC ≈ 9 × 106 s−1 (direct +vibronic) for S1 → T1 ISC of RhA in water solution. Experimentally determined singlet−triplet ISC rates for rhodamines range from kISC ≈ 105 s−1 in frozen hydroxylic glasses at 77 K to kISC ≈ 106 s−1 in polar protic solutions at room temperature.7,9−14
Figure 3. Vertical excitation energies and dipole oscillator strengths of rhodamine A in aqueous solution at the S0 ground-state and the S1 and T1 excited-state minimum geometries.
Figure 4. Frontier MOs of RhA in aqueous solution.
from the πH → πL* excitation. The energy separation between the S1 and the T2 (πH−1 → πL*) states is larger than in the gas phase. The latter state might nevertheless play an important role in the ISC and ReISC processes in RhA. Higher-lying triplet states that might be interesting for triplet−triplet excitedstate absorption will be addressed below. Emission and Excited-State Absorption in S1. Relaxation of the nuclear frame in the S1 state leads to an energy release of 0.09 eV relative to the FC point. With the ground state only slightly destabilized (by 0.05 eV) with respect to its equilibrium geometry, the Stokes shift is quite small. We obtain a vertical emission energy of 2.39 eV corresponding to a wavelength of 520 nm, in excellent agreement with the intensity maximum of the fluorescence of Rh123 in water, which occurs 6987
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either the π*L+4 or the π*L+5 orbital. The medium strong transition in the blue spectral region (458 nm) exhibits partial charge transfer character from the phenyl ring of rhodamine to the perpendicular xanthenyl tricycle. Between 452 and 400 nm we find only transitions with very low oscillator strength. This agrees nicely with the intensity minimum in the experimental T−T absorption spectrum of Rh123 in water. The band observed in the violet region stems from two excitations involving an electron located at the ester carbonyl oxygen that is used to fill the hole in the πH occupation of the T1 state. Because of its closed-shell character, a state comparable to S26 is not present in the triplet manifold. Strong πH → πL* type transitions do thus not occur in the T−T absorption spectrum. Reverse Intersystem Crossing. Ringemann et al. investigated the effect of ReISC on the photokinetics of Rh110 in various solvents.14 To this end, these authors irradiated the sample with a second laser line of 568 or 671 nm wavelength, red-shifted with respect to the fluorescence excitation wavelength at 488 nm. They report stimulated emission and, most importantly, an increase in photobleaching concomitant with ReISC. They conclude that the success of their experimental approach depends on the ratio of the efficiency of ReISC and photobleaching from Sn and Tn and that this ratio is highly sensitive to the wavelength chosen for inducing ReISC, on the environmental conditions, and on the properties of the dye selected as fluorescence marker. To avoid photobleaching, we propose here to use laser lines in the near-infrared for the purpose of invoking ReISC. ESA from the T1 state to either the T2 or T3 states should be highly feasible because both transitions have significant oscillator strengths. As will be detailed below, there is a certain probability for T2 ⇝ S1 and T3 ⇝ S2 ISC to occur at substantial rates. Moreover, T2 and T3 are located energetically well below the first ICT states (S3 and T4/5, also Figure 3) which keeps the probability of ion pair formation low. As suggested previously,43,44 excitation into such high electronic levels could open up additional bleaching pathways. When possible triplet formation processes were analyzed (see above), it became apparent that the T2 potential energy surface is flatter than those of S1 and T1. A linearly interpolated path between the S1 and T2 minimum geometries (Figure 5)
Our calculations placed the T2 state adiabatically very close to the S1 state in isolated RhA (ΔE = −154 cm−1).25 Due to the flatter potential energy surface of the T2 state, its vibrational ground state was found to lie about 2250 cm−1 below the one of the S1 state in the gas phase, making the S1 ⇝ T2 decay possible even at low temperatures. Actually, the rate constant for this process determined in our calculations (kISC ≈ 4 × 107 s−1 at 10 K; kISC ≈ 5 × 107 s−1 at 298 K) is larger than for the S1 ⇝ T1 channel. This situation changes in aqueous solution where the S1 ⇝ T2 transition becomes an activated process. The solvent shift experienced by the T2 state is much smaller than those of S1 and T1 (compare Table S1 of the Supporting Information). Thus, in aqueous solution, the lowest vibrational level of the T2 state is found to lie about 2320 cm−1 above the corresponding S1 vibronic state. Our calculations yield a rate constant of kISC ≈ 101 s−1 for the S1 ⇝ T2 ISC at room temperature. Hence, this process plays only a subordinate role in the triplet formation of rhodamine A in water solution. On the basis of a comparison of estimated solvent shifts (Table S1 of the Supporting Information), similar results are expected for RhA in ethanolic solution. Triplet−Triplet Absorption Spectrum. Our calculated triplet−triplet (T−T) absorption spectrum is in excellent agreement with experiment. Ferguson et al. used the acridine triplet to sensitize the triplet formation in Rh123.41 The transient absorption spectrum recorded 40 μs after the primary irradiation of acridine in the wavelength range between 470 and 340 nm was attributed to the Rh123 triplet state. Correction of this spectrum for the loss of absorption due to the rhodamine ground state gave the absolute triplet absorption spectrum. Similar measurements by the same authors using xanthone as triplet sensitizer covered a broader wavelength range from 355 to 660 nm. In aqueous solution, Ferguson et al. find a broad and intense peak with its maximum at the red edge of their observation window and a shoulder near 430 nm. This band is clearly separated from a second peak with its maximum lying approximately at 390 nm and exhibiting a shoulder at about 370 nm. Theory (Table S6 of the Supporting Information and Figure 3) predicts strong triplet absorption to occur already in the near-infrared region outside the experimental observation window. These transitions are associated with electronic excitations from lower-lying xanthenyl orbitals filling the πH hole in the T1 occupation. Vertical excitation with a wavelength of λ ≈ 1280 nm will populate the T2 state. The T3 ← T1 transition at λ ≈ 990 nm possesses the largest oscillator strength in our computed triplet ESA spectrum. Near-infrared lasers, typically employed in multiphoton excitation microscopy of rhodamines,42 might be used for these triplet excitations as well. The medium intense transition in the yellow region of the visible spectrum (still outside the observation window in the acridine-sensitized spectrum) results from an excitation of the singly occupied πL* orbital localized in the xanthenyl moiety to * orbital. (For MO density plots see Figures the delocalized πL+3 S1 and S2 of the Supporting Information.) The band might be present in the experimental transient absorption spectrum after xanthone senzitation but is obscured by the maximum of the xanthone triplet absorption at 580 nm. Theory predicts strong triplet absorption in the green spectral region (515−506 nm) where the ground-state absorption and fluorescence emission exhibit their maximum intensities. The transitions to the T8 and T10 states originate from single excitations of the πL* electron to
Figure 5. Energy profiles of low-lying excited states along a linearly interpolated path connecting the minima of the S1 (geometry difference = 0) and T2 (geometry difference = 1) states and extended on both sides. Solid lines denote singlet states; dashed lines, triplet states. Stars: S1 and T1. Rectangles: S2 and T2. Triangles: T3. 6988
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× 106 s−1. Lasers with excitation wavelengths in the near IR region may, hence, lead to notable reduction in the singlet population loss via triplet formation.
reveals an intersection of the S1 and T2 potential energy surfaces close to the T2 minimum geometry. Here, electronic SOMEs are of the order of 0.1i cm−1 (Table S7 of the Supporting Information). Using these coupling elements and the vibrational overlaps of the two states, we obtain a rate constant of kISC ≈ 2 × 106 s−1 for the T2 ⇝ S1 ReISC. Although this process is most certainly slower than the spin-allowed internal conversion (IC) back to the T1 state, repeated excitation with laser light at this wavelength could lead to a substantial back transfer of triplet RhA molecules to the singlet manifold. Figure 5 also shows that the excited T3 state is nearly degenerate with S2. The Cartesian components of their electronic SOME are of the order of 0.1i cm−1; i.e., they have about the same size as the SOMEs coupling T2 and S1. Hence, reverse ISC should also be possible via the T3 ⇝ S2 channel.
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ASSOCIATED CONTENT
* Supporting Information S
Full details of calculated spectroscopic properties, molecular orbital pictures, vertical excitation energies, and spin−orbit matrix elements. This material is available free of charge via the Internet at http://pubs.acs.org/.
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AUTHOR INFORMATION
Corresponding Author
*C. M. Marian. E-mail: [email protected]. Notes
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The authors declare no competing financial interest.
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CONCLUSIONS AND OUTLOOK The photophysics of isolated RhA has been the topic of discussion in a former work.25 It was seen that in this case the vibronic coupling bolsters the nonradiative relaxation channel, making the S1 ⇝ T2 (kISC ≈ 107 s−1) channel the most feasible for singlet population loss. The topic of investigation in the present work is RhA in aqueous environment. The vertical absorption spectrum was seen to be nearly independent of the influence from the electrostatic continuum. However, the effect of specific bonding with explicit water molecules was not negligent. On the basis of these two facts we carried out the study of aqueous RhA with six explicit water molecules, without an electrostatic continuum shell. In the FC region, the S1 (πH → πL*) state was the bright state absorbing at 493 nm. Most of the other higher-lying singlet excited states were mostly dark in character. A few, however, do possess considerable oscillator strength ranging up to 0.3. The excellent agreement of computed vertical excitation energies with experimentally observed absorption maxima lends confidence to the reliability of the applied theoretical methods. Only the first triplet excited state with πH → πL* character lies below the bright S1 state in the vertical absorption spectrum. The photoexcited S1 state may relax radiatively with a computed rate constant of kf ≈ 2.3 × 108 to the ground state. Though El-Sayed forbidden, triplet formation may also provide a photorelaxation channel via vibronic coupling. The S1 ⇝ T1 ISC has been computed to proceed with a rate of ≈105 s−1 at 0 K and ≈9 × 106 s−1 at room temperature. The S1 ⇝ T2 channel is no longer as feasible as in a vacuum and is found to have a rate constant of ≈101 s−1 at room temperature. The purpose of this study is to propose suitable laser wavelengths for invoking ReISC, a channel that could help evade photobleaching of RhA in aqueous solution. Hence, a detailed analysis of the triplet−triplet excitation spectrum has been carried out. Even in that case the agreement with experimetally known data is very good. Our analysis reveals two additional transitions to triplet states, T2 and T3, in the near IR region, which possess large oscillator strengths with respect to vertical excitation from the lowest-lying triplet state. The potential wells of these states cross with those of the S1 and S2 states, respectively. Also, the magnitude of the electronic SOMEs for T2−S1 and T3−S2 coupling is of the order of 0.1i cm−1. These facts, together with the vibronic coupling lead us to conclude that ReISC should be facilitated for T2 ⇝ S1 and T3 ⇝ S2 channels, promoting the back-population of the singlet manifold. In fact, the rate of ReISC for T2 ⇝ S1 totals up to ≈2
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