Reverse Intersystem Crossing in Rhodamines by Near-Infrared LaserExcitationChristel M. Marian,*,† Mihajlo Etinski,‡ and Vidisha Rai-Constapel†

†Institute of Theoretical and Computational Chemistry, Heinrich Heine University Dusseldorf, Universitatsstrasse 1, D-40225Dusseldorf, 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 fluorescencedye 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 thepresent quantum chemical study we have analyzed rhodamine A in aqueous environment. TheT2 ⇝ S1 and T3 ⇝ S2 ReISC channels are predicted to be viable. The rate constant computedfor the former channel is ≈2 × 106 s−1. Hence, an excitation with suitable wavelength to one ofthe triplets should help repopulate the optically bright singlet state S1.

■ INTRODUCTION

Outstanding photophysical and photochemical properties turnrhodamines into ideal tools for a wide range of applications.Rhodamines are used, for example, as amplifying medium inlasers,1 stains in confocal and super-resolution microscopy,2−5

or molecular labels in fluorescence-based confocal single-molecule detection and related techniques.6−8 Their typicalfluorescence quantum yields close to unity result from the highoscillator strengths of the S1−S0 absorption and emissioncombined with a relatively low probability for singlet−tripletintersystem crossing (ISC). Experimentally determined rates ofthe latter process range from kISC ≈ 105 s−1 to ≈106 s−1 in polarprotic environments.7,9−14 Hence, ISC can hardly compete withfluorescence that occurs on a time scale of nanoseconds.Although triplet quantum yields of rhodamines are typicallywell below 1%,1,4,11 the population of the long-lived first excitedtriplet state (T1) represents a major limitation in single-molecule spectroscopy where high repetition rates of excitationand fluorescence (≥105 counts per molecule) are required. Thenonradiative transition to the long-lived T1 state from whichthe molecule relaxes to the electronic ground state after sometime causes photoblinking.15 The long lifetime of the T1 statecan be used favorably in photoswitching spectroscopy toincrease 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 aimat reducing the lifetime of the nonfluorescent state by addingtriplet quenchers, thus deminishing the probability of photo-chemical degradation.16−18 Alternatively, reverse ISC (ReISC)was proposed as a mechanism for decreasing the population ofthe T1 state.

14 To this end, the triplet molecule is excited by asecond laser of appropriate wavelength to enable a transitionback to the singlet manifold. So far, these attempts were notcrowned with resounding success: Enhancements of a few

percent at most were achieved. Triplet relaxation (T-Rex)microscopy avoids illumination of the sample in the triplet stateby using bunched pulsed excitation,19 thus preventing photo-dissociation of the dye that is known to proceed via the tripletintermediate.20

Theoretical studies that could give insight into themechanistic details of the rhodamine photophysics are scarce.Earlier work performed in this laboratory focused on theenergetics of the S1 and T1 states of rhodamine A (RhA) andthe spectral shifts brought about in ethanol solution.18 In thatstudy, combined density functional theory (DFT) andmultireference configuration interaction (MRCI) methodswere employed. Solvent effects on the S1- and T1-state energieswere also a major topic of a very recent time-dependent densityfunctional theory (TDDFT) study of various rhodamine dyes.21

Ågren and co-workers concentrated on two-photon absorptioncross sections of rhodamine B and other fluorophores.22

Furthermore, investigations on the electronic structures andoptical properties of rhodamine 6G23 and rhodamine Bdimers24 were published.Very recently, we investigated singlet−triplet ISC of isolated

RhA.25 Our quantum chemical calculations yielded a rateconstant 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 T2state. Major conclusions drawn in that work with regard to ISCof RhA in the gas phase were that vibronic effects substantiallyenhance the ISC rate and that the S1 ⇝ T2 nonradiativetransition is the predominant source of triplet formation.Our present work aims at an understanding of ISC and

possibly ReISC mechanisms in rhodamine molecules inaqueous solution. To this end, absorption and emission spectra,

Received: July 10, 2014Revised: August 4, 2014Published: August 7, 2014

Article

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excited-state absorption, and ISC rates for RhA, i.e., cationic 2-(3,6-diaminoxanthen-9-yl)benzoic acid ethyl ester (Figure 1),

are determined. RhA is the ethyl ester of rhodamine 110(Rh110). We have chosen the ester form in our study to avoidcomplications due to acid−base equilibria or internal trans-formation into the lactonic form.1,26 RhA differs fromrhodamine 123 (Rh123) only in the ester group where amethyl ester is found in Rh123. Because the photophysicalproperties are mainly determined by the xanthenyl and phenylmoieties, the differences are believed to be minor, however.Our theoretical findings will therefore be compared withexperimental results for RhA, Rh110, and Rh123 whereavailable.

■ COMPUTATIONAL DETAILSTechnical parameters and methods for computing geometries,energies, and wave functions of the spin-free Hamiltonian arethe same as in previous work.18,25 To investigate excited-stateabsorption (ESA) in the first excited singlet and triplet states, atotal of 30 singlet and 30 triplet states were computed by meansof the DFT/MRCI approach.27 For the computation of thespin−orbit matrix elements (SOMEs) between the correlatedDFT/MRCI wave functions we used the spin−orbit couplingkit (SPOCK) developed in our laboratory.28,29 For reasons ofefficiency, a one-center mean-field approximation to the fullBreit−Pauli spin−orbit coupling Hamiltonian was used.30

We tested three different models for simulating the watersolution: (I) a solvent shell of six explicit water molecules, twoeach on the two amino groups and another two close to thecentral oxygen atom of the xanthenyl moiety (Figure 2), (II) apure continuum model of the electrostatic interactions using

COSMO,31 (III) a combination of models (I) and (II). Itturned out that the electrostatic continuum had only veryminor influence on the vertical excitation spectra (Table S1 inthe Supporting Information). Henceforth, the pure micro-hydration model (I) was employed in all further calculations.The SNF32 program was employed for the numerical

determination of vibrational wave functions and frequenciesin harmonic approximation. In addition to electronic SOMEs,these entities are required for computing ISC rates in the Fermigolden rule approximation.33 As it turned out, all low-lyingelectronic states of rhodamines exhibit ππ* character. Theirdirect spin−orbit coupling is very small and a Condon-typeapproximation may not be sufficient. El-Sayed forbiddentransitions may gain substantial probability, however, by linearvibronic spin−orbit interactions, as demonstrated in ourlaboratory in several cases (see, e.g., ref 25 and referencestherein). Derivatives of the SOMEs with respect to mass-weighted normal coordinates were determined by a three-pointfinite difference scheme. Due to the large number of vibrationaldegrees of freedom, the recent implementation of a time-dependent approach in the VIBES program was employed forcomputing ISC rates.25,34 With this method, rates for direct(Condon-type) and vibronic (Herzberg−Teller-type) ISC canbe determined according to Fermi’s golden rule. Moreover,different temperatures can be simulated by assuming aBoltzmann 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 werecalculated using the DFT/MRCI method. For a betteroverview, the LIP was extrapolated on both sides.

■ RESULTS AND DISCUSSIONAbsorption Spectrum. The experimental Rh123 absorp-

tion spectrum in neutral aqueous solution consists of anintensive band having a maximum around 500 nm, a shoulderat 475 nm and less pronounced bands with maxima at 330 and240 nm.36 An overview over the calculated vertical absorptionspectrum is given in Figure 3. Full details such as excitationenergies, electronic structures, oscillator strengths, as well asorientations of the electric transition dipole moments areprovided in the Supporting Information and compared withexperimental 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 comparesfavorably with the maximum of the first absorption band inRhA and Rh110 in aqueous solution.36−39 The transition isassociated with the πH → πL* excitation and exhibits anoscillator strength f(r) close to unity. The orbital densities ofboth MOs involved in the transition are predominantlylocalized on the xanthenyl moiety (Figure 4). Accordingly,this electronic excitation may be characterized as a xanthenyltransition. Also, the S2 ← S0 absorption, dominated by the πH−1→ πL* excitation, corresponds to a pure xanthenyl transition. Itis not formally forbidden but has a very small transition dipolemoment. S3 is located 3.78 eV above S0 in aqueous solution andoriginates from the πH → πL+1* excitation with intramolecularcharge transfer (ICT) from the xanthenyl to the carboxyphenylmoiety. Although this ICT state (as well as the related tripletstate T4) is not visible in the spectrum, it is mentioned herebecause it might play an important role in the redox reactionsof 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 1. Chemical structure of rhodamine A (RhA).

Figure 2. Cluster model of rhodamine A in aqueous solution.

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from the πH → πL* excitation. The energy separation betweenthe S1 and the T2 (πH−1 → πL*) states is larger than in the gasphase. The latter state might nevertheless play an importantrole in the ISC and ReISC processes in RhA. Higher-lyingtriplet states that might be interesting for triplet−triplet excited-state absorption will be addressed below.Emission and Excited-State Absorption in S1. Relaxa-

tion of the nuclear frame in the S1 state leads to an energyrelease of 0.09 eV relative to the FC point. With the groundstate only slightly destabilized (by 0.05 eV) with respect to itsequilibrium geometry, the Stokes shift is quite small. We obtaina vertical emission energy of 2.39 eV corresponding to awavelength of 520 nm, in excellent agreement with the intensitymaximum of the fluorescence of Rh123 in water, which occurs

at 524 nm.37,38 The rate constant of the pure electronictransition is calculated as kF ≈ 2.3 × 108 s−1, in perfect accordwith the experimental value of kF ≈ 2.1 × 108 s−1 for thefluorescence of Rh123 in water.37

Despite the relatively short lifetime of the S1 state, excited-state absorption processes may occur. An overview over themost important excitations and their oscillator strengths isfound in Figure 3; further details are provided in Table S4 ofthe Supporting Information. Of particular interest is theabsorption probability at the wavelength of the primary laserexcitation. Our calculations place the medium strong S14 ← S1ESA in this wavelength region. In the MO picture, it isassociated with an excitation of the outer valence electron fromπL* to πL+4* , both MOs being classified as xanthenyl orbitals(Figure S2, Supporting Information). Further, we find a verystrong transition from S1 to S26 at about 400 nm. With respectto the electronic ground state, the dominant configuration ofthat state is a double excitation πH

2 → πL*2, which makes it a πH

→ πL* single excitation with respect to S1. It is thus no wonderthat the oscillator strength of the S26 ← S1 excited-stateabsorption is of the same order of magnitude as the S1 ← S0absorption. This should be kept in mind in multiple-color laserexperiments.

Triplet Formation from the S1 State. For the efficiency ofISCs several factors are decisive: the electronic SOME, theadiabatic energy difference, the coordinate displacement of thesinglet and triplet potential energy surfaces, and further factorssuch as the Duschinsky rotation of the respective normalmodes. The relaxed T1 geometry is nearly identical to thenuclear arrangement at the S1 minimum. Hence, the non-radiative transition from S1 ⇝ T1 comes close to the weakcoupling case in the sense of Englman and Jortner where theenergy gap law applies.40 For isolated RhA we computed a rateconstant 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−orbitinteraction is invoked.25 The probability for ISC was found tobe only slightly temperature dependent, increasing thecalculated rate constant to kISC ≈ 3 × 104 s−1 at ambienttemperatures. To our knowledge, no experimental gas-phasevalue is available for comparison.The overlap of the vibrational wave functions of the initial

and final states increases substantially when going from isolatedRhA to the water cluster. In addition, nonvanishing matrixelements for all three Cartesian components of the electronicspin−orbit Hamiltonian are obtained (Table S5 of theSupporting Information) due to symmetry breaking. Thismeans that all T1 fine-structure levels are populated upon ISCfrom S1 already in Condon approximation. Despite the slightlylarger 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 fordirect S1 ⇝ T1 ISC at 0 K. Vibronic spin−orbit coupling leadsto a further increase of the ISC rate constants, yielding a totalrate (direct+vibronic) of kISC ≈ 1 × 105 s−1. Temperatureenhances this process, in agreement with experimentalobservations. At room temperature, we compute a rate constantof 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 rhod-amines range from kISC ≈ 105 s−1 in frozen hydroxylic glasses at77 K to kISC ≈ 106 s−1 in polar protic solutions at roomtemperature.7,9−14

Figure 3. Vertical excitation energies and dipole oscillator strengths ofrhodamine A in aqueous solution at the S0 ground-state and the S1 andT1 excited-state minimum geometries.

Figure 4. Frontier MOs of RhA in aqueous solution.

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Our calculations placed the T2 state adiabatically very closeto the S1 state in isolated RhA (ΔE = −154 cm−1).25 Due to theflatter potential energy surface of the T2 state, its vibrationalground state was found to lie about 2250 cm−1 below the oneof the S1 state in the gas phase, making the S1 ⇝ T2 decaypossible even at low temperatures. Actually, the rate constantfor 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 shiftexperienced by the T2 state is much smaller than those of S1and T1 (compare Table S1 of the Supporting Information).Thus, in aqueous solution, the lowest vibrational level of the T2state is found to lie about 2320 cm−1 above the correspondingS1 vibronic state. Our calculations yield a rate constant of kISC ≈101 s−1 for the S1 ⇝ T2 ISC at room temperature. Hence, thisprocess plays only a subordinate role in the triplet formation ofrhodamine A in water solution. On the basis of a comparison ofestimated solvent shifts (Table S1 of the SupportingInformation), similar results are expected for RhA in ethanolicsolution.Triplet−Triplet Absorption Spectrum. Our calculated

triplet−triplet (T−T) absorption spectrum is in excellentagreement with experiment. Ferguson et al. used the acridinetriplet to sensitize the triplet formation in Rh123.41 Thetransient absorption spectrum recorded 40 μs after the primaryirradiation of acridine in the wavelength range between 470 and340 nm was attributed to the Rh123 triplet state. Correction ofthis spectrum for the loss of absorption due to the rhodamineground state gave the absolute triplet absorption spectrum.Similar measurements by the same authors using xanthone astriplet sensitizer covered a broader wavelength range from 355to 660 nm. In aqueous solution, Ferguson et al. find a broadand intense peak with its maximum at the red edge of theirobservation window and a shoulder near 430 nm. This band isclearly separated from a second peak with its maximum lyingapproximately at 390 nm and exhibiting a shoulder at about 370nm.Theory (Table S6 of the Supporting Information and Figure

3) predicts strong triplet absorption to occur already in thenear-infrared region outside the experimental observationwindow. These transitions are associated with electronicexcitations from lower-lying xanthenyl orbitals filling the πHhole in the T1 occupation. Vertical excitation with a wavelengthof λ ≈ 1280 nm will populate the T2 state. The T3 ← T1transition at λ ≈ 990 nm possesses the largest oscillatorstrength in our computed triplet ESA spectrum. Near-infraredlasers, typically employed in multiphoton excitation microscopyof rhodamines,42 might be used for these triplet excitations aswell. The medium intense transition in the yellow region of thevisible spectrum (still outside the observation window in theacridine-sensitized spectrum) results from an excitation of thesingly occupied πL* orbital localized in the xanthenyl moiety tothe delocalized πL+3* orbital. (For MO density plots see FiguresS1 and S2 of the Supporting Information.) The band might bepresent in the experimental transient absorption spectrum afterxanthone senzitation but is obscured by the maximum of thexanthone triplet absorption at 580 nm. Theory predicts strongtriplet absorption in the green spectral region (515−506 nm)where the ground-state absorption and fluorescence emissionexhibit their maximum intensities. The transitions to the T8 andT10 states originate from single excitations of the πL* electron to

either the πL+4* or the πL+5* orbital. The medium strongtransition in the blue spectral region (458 nm) exhibits partialcharge transfer character from the phenyl ring of rhodamine tothe perpendicular xanthenyl tricycle. Between 452 and 400 nmwe find only transitions with very low oscillator strength. Thisagrees nicely with the intensity minimum in the experimentalT−T absorption spectrum of Rh123 in water. The bandobserved in the violet region stems from two excitationsinvolving an electron located at the ester carbonyl oxygen thatis used to fill the hole in the πH occupation of the T1 state.Because of its closed-shell character, a state comparable to S26 isnot present in the triplet manifold. Strong πH → πL* typetransitions do thus not occur in the T−T absorption spectrum.

Reverse Intersystem Crossing. Ringemann et al.investigated the effect of ReISC on the photokinetics ofRh110 in various solvents.14 To this end, these authorsirradiated the sample with a second laser line of 568 or 671 nmwavelength, red-shifted with respect to the fluorescenceexcitation wavelength at 488 nm. They report stimulatedemission and, most importantly, an increase in photobleachingconcomitant with ReISC. They conclude that the success oftheir experimental approach depends on the ratio of theefficiency of ReISC and photobleaching from Sn and Tn andthat this ratio is highly sensitive to the wavelength chosen forinducing ReISC, on the environmental conditions, and on theproperties 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. ESAfrom the T1 state to either the T2 or T3 states should be highlyfeasible because both transitions have significant oscillatorstrengths. As will be detailed below, there is a certainprobability for T2 ⇝ S1 and T3 ⇝ S2 ISC to occur atsubstantial rates. Moreover, T2 and T3 are located energeticallywell below the first ICT states (S3 and T4/5, also Figure 3)which keeps the probability of ion pair formation low. Assuggested previously,43,44 excitation into such high electroniclevels could open up additional bleaching pathways.When possible triplet formation processes were analyzed

(see above), it became apparent that the T2 potential energysurface is flatter than those of S1 and T1. A linearly interpolatedpath between the S1 and T2 minimum geometries (Figure 5)

Figure 5. Energy profiles of low-lying excited states along a linearlyinterpolated path connecting the minima of the S1 (geometrydifference = 0) and T2 (geometry difference = 1) states and extendedon both sides. Solid lines denote singlet states; dashed lines, tripletstates. Stars: S1 and T1. Rectangles: S2 and T2. Triangles: T3.

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reveals an intersection of the S1 and T2 potential energysurfaces close to the T2 minimum geometry. Here, electronicSOMEs are of the order of 0.1i cm−1 (Table S7 of theSupporting Information). Using these coupling elements andthe vibrational overlaps of the two states, we obtain a rateconstant of kISC ≈ 2 × 106 s−1 for the T2 ⇝ S1 ReISC. Althoughthis process is most certainly slower than the spin-allowedinternal conversion (IC) back to the T1 state, repeatedexcitation with laser light at this wavelength could lead to asubstantial back transfer of triplet RhA molecules to the singletmanifold.Figure 5 also shows that the excited T3 state is nearly

degenerate with S2. The Cartesian components of theirelectronic SOME are of the order of 0.1i cm−1; i.e., they haveabout the same size as the SOMEs coupling T2 and S1. Hence,reverse ISC should also be possible via the T3 ⇝ S2 channel.

■ CONCLUSIONS AND OUTLOOKThe photophysics of isolated RhA has been the topic ofdiscussion in a former work.25 It was seen that in this case thevibronic coupling bolsters the nonradiative relaxation channel,making the S1 ⇝ T2 (kISC ≈ 107 s−1) channel the most feasiblefor singlet population loss. The topic of investigation in thepresent work is RhA in aqueous environment. The verticalabsorption spectrum was seen to be nearly independent of theinfluence from the electrostatic continuum. However, the effectof specific bonding with explicit water molecules was notnegligent. On the basis of these two facts we carried out thestudy of aqueous RhA with six explicit water molecules, withoutan electrostatic continuum shell. In the FC region, the S1 (πH→ πL*) state was the bright state absorbing at 493 nm. Most ofthe other higher-lying singlet excited states were mostly dark incharacter. A few, however, do possess considerable oscillatorstrength ranging up to 0.3. The excellent agreement ofcomputed vertical excitation energies with experimentallyobserved absorption maxima lends confidence to the reliabilityof 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 acomputed rate constant of kf ≈ 2.3 × 108 to the groundstate. Though El-Sayed forbidden, triplet formation may alsoprovide a photorelaxation channel via vibronic coupling. The S1⇝ T1 ISC has been computed to proceed with a rate of ≈105s−1 at 0 K and ≈9 × 106 s−1 at room temperature. The S1 ⇝ T2channel is no longer as feasible as in a vacuum and is found tohave 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 helpevade photobleaching of RhA in aqueous solution. Hence, adetailed analysis of the triplet−triplet excitation spectrum hasbeen carried out. Even in that case the agreement withexperimetally known data is very good. Our analysis reveals twoadditional transitions to triplet states, T2 and T3, in the near IRregion, which possess large oscillator strengths with respect tovertical excitation from the lowest-lying triplet state. Thepotential wells of these states cross with those of the S1 and S2states, respectively. Also, the magnitude of the electronicSOMEs for T2−S1 and T3−S2 coupling is of the order of 0.1icm−1. These facts, together with the vibronic coupling lead usto conclude that ReISC should be facilitated for T2 ⇝ S1 andT3 ⇝ S2 channels, promoting the back-population of the singletmanifold. In fact, the rate of ReISC for T2 ⇝ S1 totals up to ≈2

× 106 s−1. Lasers with excitation wavelengths in the near IRregion may, hence, lead to notable reduction in the singletpopulation loss via triplet formation.

■ ASSOCIATED CONTENT*S Supporting InformationFull details of calculated spectroscopic properties, molecularorbital pictures, vertical excitation energies, and spin−orbitmatrix elements. This material is available free of charge via theInternet at http://pubs.acs.org/.

■ AUTHOR INFORMATIONCorresponding Author*C. M. Marian. E-mail: Christel.Marian@hhu.de.NotesThe authors declare no competing financial interest.

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The Journal of Physical Chemistry A Article

dx.doi.org/10.1021/jp506904v | J. Phys. Chem. A 2014, 118, 6985−69906990