Ab Initio Prediction of Fluorescence Lifetimes Involving Solvent

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Ab Initio Prediction of Fluorescence Lifetimes Involving Solvent Environments by Means of COSMO and Vibrational Broadening Julia Preiß, Daniel Kage, Katrin Hoffmann, Todd J. Martínez, Ute Resch-Genger, and Martin Presselt J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b08886 • Publication Date (Web): 03 Dec 2018 Downloaded from http://pubs.acs.org on December 6, 2018

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The Journal of Physical Chemistry

Ab initio Prediction of Fluorescence Lifetimes Involving Solvent Environments by Means of COSMO and Vibrational Broadening Julia Preiß1,2, Daniel Kage3,4, Katrin Hoffmann3, Todd J. Martínez5,6, Ute Resch-Genger3,*, Martin Presselt1,2,7,8,* 1

Institute of Physical Chemistry, Friedrich Schiller University Jena, Helmholtzweg 4, 07743 Jena,

Germany 2

Leibniz Institute of Photonic Technology (IPHT), Albert-Einstein-Str. 9, 07745 Jena, Germany

3

Bundesanstalt für Materialforschung und –prüfung (BAM), Richard-Willstätter-Straße 11,12489

Berlin, Germany 4

Department of Physics, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany

5

SLAC National Accelerator Laboratory, Menlo Park, California 94309, USA

6

Department of Chemistry and PULSE Institute, Stanford University, Stanford, California 94305, USA

7

Center for Energy and Environmental Chemistry Jena (CEEC Jena), Friedrich Schiller University Jena,

Philosophenweg 7a, 07743 Jena, Germany 8

sciclus GmbH & Co. KG, Moritz-von-Rohr-Str. 1a, 07745 Jena, Germany

*Corresponding authors: Experiment: Ute Resch-Genger, e-mail: [email protected], Tel: +49 30 8104-1134; Theory: Martin Presselt, e-mail: [email protected], Tel: +49 3641 206 418

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ABSTRACT

The fluorescence lifetime is a key property of fluorophores that can be utilized for microenvironment probing, analyte sensing, and multiplexing as well as barcoding applications. For the rational design of lifetime probes and barcodes, theoretical methods have been developed to enable the ab initio prediction of this parameter, which depends strongly on interactions with solvent molecules and other chemical species in the emitter´s immediate environment. In this work, we investigate how a conductor-like screening model (COSMO) can account for variations in fluorescence lifetimes that are caused by such fluorophore-solvent interactions. Therefore, we calculate vibrationally broadened fluorescence spectra using the nuclear ensemble method to obtain distorted molecular geometries to sample the electronic transitions with time-dependent density functional theory (TDDFT). The influence of the solvent on fluorescence lifetimes is accounted for with COSMO. For an example 4-hydroxythiazole fluorophore containing different heteroatoms and acidic and basic moieties in aprotic and protic solvents of varying polarity, this approach was compared to experimentally determined lifetimes in the same solvents. Our results demonstrate a good correlation between theoretically predicted and experimentally measured fluorescence lifetimes except for the polar solvents ethanol and acetonitrile that can specifically interact with the heteroatoms and the carboxylic acid of the thiazole derivative.


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INTRODUCTION

Fluorescence emission spectra, quantum yields, and lifetimes are valuable parameters providing structural information on fluorophores and insight into microenvironment effects or the interaction with certain analytes1. The fluorescence lifetime (directly linked to the fluorescence quantum yield) reflects the dynamics of the excited states of an emitter2. This lifetime can be used to calculate radiative rate constants in dye photophysics3, probe the solute microenvironment4-5, or sense analytes6. Fluorescence is also important for multiplexing6-7 and barcoding applications2 in materials research and the life8 and environmental sciences5,9. Although there is an ever increasing interest in the rational design of fluorescent dyes and stimuli-responsive optical probes10 to minimize synthetic efforts, the prediction of fluorescence quantum yields and lifetimes is still very challenging11-12. Routine simulations of spectroscopic properties are often only employed for the calculation of vertical transition energies and the corresponding transition dipole moments13-17. To account for the full complexity of the emission spectra, computations must go beyond single-geometry calculations at stationary points. Vibrational features can be important contributors to spectral shapes. While vibrational progression can be simulated by predetermined FranckCondon factors18-19, vibrational broadening can be modelled by sampling spectra of an ensemble of nuclear structures distributed around the ground state. This is referred to as nuclear ensemble method11,16,20. Moreover, the consideration of solvent effects is of considerable importance for the reliable modeling of optical spectra21. However, explicit calculation of a solvation shell can be computationally challenging. Therefore, the solvent is often modeled as a polarizable dielectric with the solvent´s dielectric constant εr 22, e.g. with a conductor-like screening model (COSMO)23-25. Polarizable continuum models neglect 3 ACS Paragon Plus Environment


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specific solvent-solute interactions like hydrogen bonds, which can be especially important for molecules that undergo light-induced charge transfer processes that can be affected not only by solvent polarity yet also hydrogen bonding interactions with solvent molecules in the case of protic solvents. The combination of COSMO and the nuclear ensemble method to account for both solvation and vibrational effects has been utilized to model spectral shapes.26-33 Much less studies have used this combination to simulate fluorescence lifetimes. Santoro et al. implicitly draw conclusions about variations of fluorescence lifetimes for uracil originating from solvent effects based on changes in the excited state depopulation pathways by investigating the conical intersections.34 Wong et al.35 calculated fluorescence lifetimes including both solvation and vibrational effects within a Strickler-Berg36 framework, but their study was limited to synbimanes in a single solvent (1,4-dioxane). In the present work, we combine COSMO and the nuclear ensemble method to derive solventdependent and vibrationally broadened fluorescence spectra from which fluorescence lifetimes are calculated and directly compared to experiments. We explore various approaches to calculating the fluorescence lifetimes, which are essentially based on the Strickler-Berg36 analysis. Therefore, different techniques for yielding vibrationally broadened fluorescence spectra are applied. Our computations do not account for competing nonradiative processes, but instead produce the radiative emission rate. Combining this with measured quantum yields allows us to also predict the total excited state lifetime including both radiative and nonradiative processes. We use the fluorophore [2-pyridyl-4-hydroxy-5phenyl-1.3-thiazol-4-yl]oxy acetic acid (PyThPhCOOH)37 containing different heteroatoms, acidic and basic moieties, as a representative dye molecule for this study (see Figure 1) and different aprotic and protic solvents with dielectric constants εr varying between 2.4 and 37.5. 4 ACS Paragon Plus Environment

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METHODS Materials Solvents for spectroscopy were of spectroscopic or absolute grade and have been used without purification as received. The synthesis of [2-pyridyl-4-hydroxy-5-phenyl-1.3-thiazol4-yl]oxy acetic acid is described elsewhere.38 Absorption spectra For measurements of spectral absorbance, a Specord 210 Plus (Analytik Jena AG) dual beam absorption spectrometer was used. The spectral bandpass was set to 1 nm, spectra were acquired with a step width of 1 nm and 1 s integration time. Measurements were carried out with standard 1-cm quartz cuvettes (Hellma GmbH & Co. KG) at room temperature (approx. 22 °C). Steady-state fluorescence and anisotropy measurements Fluorescence spectra have been acquired on an FLS920 (Edinburgh Instruments Ltd.) spectrometer employing magic angle3 polarizer settings and L-geometry for excitation and emission light paths. The emission spectra have been corrected for the wavelengthdependent spectral responsivity of the detection channel. All measurements were performed with standard 1-cm quartz cuvettes (Hellma GmbH & Co. KG) at room temperature (20 °C). The spectral bandpasses for emission and excitation spectra were fixed to 6 and 2 nm, respectively. Spectra were acquired with 1 nm step size and four repetitions with 0.5 s integration time. Absolute uncertainties in emission wavelength are ±2 nm and are determined from an exemplary concentration series.



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Lifetime measurements Time-resolved measurements were accomplished with an FLS920 (Edinburgh Instruments Ltd.) lifetime spectrometer equipped with a Hamamatsu R38090U-50 (Hamamatsu Photonics K.K.) MCP-PMT. Excitation light source was a Fianium Supercontinuum SC400-2-PP (NKT Photonics A/S) laser. The system allows for standard time-correlated single photon counting (TCSPC). The instrument response function has a full width at half maximum of about 250 ps which is mainly determined by the excitation pulse duration. The repetition rate for excitation was set to 10 MHz. To avoid artifacts due to rotational motion, again magic angle polarizer conditions were applied. The uncertainty determined with an exemplary concentration series amounts to ±50 ps. Fluorescence quantum yields Fluorescence quantum yields of dye solutions have been obtained absolutely with a C11347 (Hamamatsu Photonics K.K.) integrating sphere setup using direct excitation. Instrumentspecific long-neck cuvettes were used. A built-in routine was used to correct the data for reabsorption effects39. The obtained quantum yields have an uncertainty of ±0.05. The Strickler-Berg framework The relation between the fluorescence lifetime and spectral properties of a molecular system proposed by Strickler and Berg36, 𝑔 1 ―1 l = 2.880 ⋅ 10 ―9𝑛2〈𝜈𝑓―3〉 ∫𝜖dln𝜈can be used to calculate an estimate of the 𝜏0 𝑔u fluorescence lifetime based on experimentally accessible quantities. 𝑛 is the refractive index of the solvent, 〈𝜈𝑓―3〉 the expectation value of the reciprocal cube of the wavenumber derived from the fluorescence emission spectrum, 𝑔l/u are degeneracy factors and 𝜖 is the molar extinction coefficient. The approximations, however, break down when specific solvent 6 ACS Paragon Plus Environment

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interactions are present. Without such explicit interactions, a very similar approach can be applied to TD-DFT-derived fluorescence spectra, if the obtained single energy-oscillator strength pairs are broadened vibrationally, as detailed below. Time-dependent density functional theory All calculations were done with a development version of TeraChem. We used the functional ωPBE40-42 with ω=0.15. We employed the valence double zeta basis set Ahlrichs-pVDZ with polarization on all atoms as introduced by Ahlrichs and coworkers.43 First, the geometry of the investigated thiazole was optimized using a ground state equilibrium solvation with COSMO23 for each solvent. The absorption spectra were obtained using linear response non-equilibrium solvation. For the simulation of the fluorescence spectra the first excited state was optimized using a linear response equilibrium solvation. Theoretically derived fluorescence lifetimes Because oscillator strengths cannot be derived for the excited and solvated S1-states, the oscillator strengths of the obtained linear response spectra were used (if not stated differently), despite referring to the solvated S0-ground state rather than to a solvated excited S1-state. The vibrational frequencies of the excited state needed for Wigner sampling were calculated numerically, also using the linear response equilibrium solvation. The oscillator strength of the transition between the ground state and the first excited state was calculated with a linear response for the optimized excited state geometries. This value was used as an estimate of the oscillator strength for further calculation of the fluorescence spectra, if not stated otherwise. The obtained linear response spectra were used to estimate



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the oscillator strength of the transitions. The frequencies of the excited state were calculated numerically, also using the linear response equilibrium solvation. For the nuclear ensemble method11,44, 350 geometries were generated employing a harmonic Wigner distribution based on the frequencies of the first excited and solvated state for each solvent studied. The emission energies of all 350 geometries were calculated using statespecific equilibrium solvation. Because no oscillator strength is obtained using state specific COSMO, these were set to the value of the linear response COSMO calculation at the S1 equilibrium geometry, as listed in Table S1. We used the approximation of taking a single oscillator strength for all 350 geometries following the ansatz of Wang et al.35. In Wang et al.’s calculations only the oscillator strength of the S1 minimum geometry is taken into account and the spectral shape that goes into the Strickler-Berg equations used in their paper is accounted for by the use of Franck-Condon factors. Setting the oscillator strength of all 350 geometries to the same value influences the spectral shape only slightly and can therefore be used as an approximation. Subsequently, the emission spectrum is calculated as a superposition of all single emission spectra, which are broadened by a Lorentz function with a width of 0.08 eV. An integration over the emission spectrum yields the radiative lifetime for the specific solvent.11 Emission spectra and lifetimes were calculated using NEWTON-X software.45-47 An in-house code was used to generate the NEWTON-X input, which contains the emission energies of all 350 geometries and the value of one for the oscillator strength. Note that no vibrationally broadened spectrum was calculated for methanol because its stickspectrum shows virtually no difference to the ACN spectrum, see SI. The corresponding


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lifetime in methanol was estimated by multiplying the experimental quantum yield for methanol with the radiative lifetime calculated for ACN.

RESULTS AND DISCUSSION Absorption and fluorescence spectra The experimentally determined and calculated absorption spectra of the thiazole PyThPhCOOH show a broad absorption band between 325 and 425 nm (see inset in Figure 1). The absorption maxima show on average a small hypsochromic shifts with increasing dielectric constant of the solvent as revealed in Table 1. The only exceptions are the spectra in the polar and protic solvents methanol and ethanol, which are slightly bathochromically shifted. The hypsochromic shift observed for the aprotic solvents can be reproduced by the calculated absorption spectra even without consideration of vibrational broadening. However, the bathochromic shift resulting for the protic solvents cannot be predicted (with or without consideration of vibrational broadening) as hydrogen bonding interactions are not wellmodeled with COSMO. The calculated absorption spectra reveal that the vis-absorption bands arise from a single electronic transition corresponding to a HOMO-LUMO transition of ππ* character, which is typical for this type of chromophore38,48-49.



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Figure 1: Normalized experimentally determined (top) and calculated (bottom) absorption spectra of PyThPhCOOH in tetrahydrofuran (green), toluene (red), acetonitrile (purple), ethanol (blue), dichloromethane (black), methanol (light blue), and chloroform (ochre). The calculated spectra (ωPBE/Ahlrichs-pVDZ optimally tuned for the gas phase, spectral energies are not shifted) are broadened by a Gaussian function with a full width at half maximum of 0.5 eV and the vertical lines highlight the calculated transition wavelengths. The inset shows the molecular structure of the investigated [2-pyridyl-4-hydroxy-5-phenyl-1.3-thiazol-4-yl]oxy acetic acid dye.

The experimentally determined fluorescence spectra (Figure 2a) deviate little between the different non-protic solvents. These spectra show a weak vibrational progression and peak at λmax=(445±1) nm (exact values listed in Table 1). In contrast, the spectra of PyThPhCOOH dissolved in the protic alcohols show no vibrational progression and are slightly red shifted. For ab initio reproduction of the experimental fluorescence spectra and their solventdependence the state-specific solvation (here the S1 state) was applied to all molecular geometries distorted during the Wigner sampling. Because the latter techniques yield 10 ACS Paragon Plus Environment

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accurate transition energies but no oscillator strengths, all calculations were repeated in the linear response approach for solvated ground states to yield oscillator strengths of the distorted geometries that depend on the solvent. This combination of state-specific (abbrev. as “ss”) solvation and linear response (abbrev. as “lr”) to yield transition energies (E) and oscillator strengths (f), respectively, is referred to as “E(ss),f(lr)” in the following. Alternatively, following an ansatz similar to the one of Wang et al.35, only the oscillator strength of the S0S1 transition at the S1-minimum geometry of the dissolved dyes was used. This oscillator strength is applied to all structures distorted during the Wigner sampling, what is referred to as “E(ss),fconst(lr)” in the following. As reference, we additionally considered the case of neglecting state-specific solvation and applying the linear response ansatz for calculating energies and oscillator strengths, abbreviated as “E(lr),f(lr)” in the following. This approach is expected to provide less accurate results because in linear response calculations the S0 ground state rather than the S1 excited state is solvated, thus introducing a deviation from the experimental conditions of fluorescence. Naturally, the experimentally observed grouping of spectra for protic and aprotic solvents cannot be reproduced with the COSMO-approach as shown in Figure 2. Instead, the calculated fluorescence spectra basically shift to longer wavelengths with increasing dielectric constant of the solvent. This shift can be regarded as an overestimation of the change in spectral shape observed in the experiments for the aprotic solvents. The bathochromic shift is visible both in the emission spectra obtained with and without vibrational broadening (see SI Figure S1). The emission corresponds to the same transition between HOMO and LUMO as the absorption. The corresponding orbitals, which are of π and π* character, are shown for acetonitrile as insets in Figure 1Error! Reference source not found..



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The comparison between the fluorescence spectra derived ab initio according E(ss),f(lr), E(ss),fconst(lr), and E(lr),f(lr) reveals that the experimentally determined dependence of the transition energies on the solvent dielectric constant is, expectedly, significantly better reproduced by applying state-specific solvation as compared to ground state solvation. Overall, the ab initio derived spectral widths fit the experimental ones quite well, but those derived for E(ss),f(lr), and E(ss),fconst(lr) are smaller than for E(lr),f(lr). The difference in spectral shape between E(ss),f(lr), and E(ss),fconst(lr), appears negligible, but the intensities of the latter are slightly higher than the former, as shown in the SI. Finally, the magnitude of the Stokesshift is overestimated but its dependence on the dielectric constant is in good agreement with the experimental data for aprotic solvents as detailed in Table 1.


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Figure 2: Fluorescence emission spectra of PyThPhCOOH in tetrahydrofuran (green), toluene (red), acetonitrile (purple), ethanol (blue), dichloromethane (black), methanol (light blue), chloroform (ochre). (a) Normalized experimentally determined spectra [excitation at the maximum absorption (cf. Table 1) and calculated spectra with vibrational broadening (b) E(ss), f(lr), (c) E(ss), fconst(lr) and



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(d) E(lr), f(lr), each normalized and redshifted by 0.2 eV to better match the experimental resultsa. All plots share the same x-axis. The inset shows the orbitals involved in the electronic transition of the emission peak. Table 1: Experimentally and theoretically derived absorption and emission maxima of PyThPhCOOH corresponding to Figure 1Error! Reference source not found. and Figure 2 and dielectric constant εr of the solvents. All theoretical values in this table were not shifted. solvent

#

εr

absorption max. / eV (nm)

emission max. / eV (nm)

Stokes shift / eV

exp.

theory

exp.

theory#

exp.

theory#

Toluene

2.38

3.33 (372 ± 1)

3.35 (370)

2.79 (444 ± 2)

3.05 (406)

0.54

0.3

CHCl3

4.81

3.34 (371 ± 1)

3.37 (368)

2.78 (446 ± 2)

3.00 (414)

0.56

0.37

THF

7.58

3.33 (372 ± 1)

3.38 (367)

2.79 (444 ± 2)

2.97 (418)

0.54

0.41

DCM

9.10

3.38 (367 ± 1)

3.38 (367)

2.79 (445 ± 2)

2.97 (417)

0.59

0.41

C2H5OH

24.55

3.29 (377 ± 1)

3.40 (365)

2.74 (452 ± 2)

2.93 (423)

0.55

0.47

CH3OH

32.70

3.32 (374 ± 1)

3.41 (364)

2.74 (452 ± 2)

2.99* (415)

0.58

0.42

ACN

37.50

3.38 (367 ± 1)

3.41 (364)

2.79 (445 ± 2)

2.96 (419)

0.59

0.45

Maxima are taken from the vibrationally broadened spectra

* The emission maximum of methanol was taken from vertical emission spectrum, rather than the vibrationally broadened one, because for methanol no vibrationally broadened spectrum was calculated. This timeconsuming calculation was omitted as the vertical spectra for ACN and methanol are virtually identical as ACN and methanol have very similar correction factors in COSMO.

Fluorescence decay kinetics and quantum yields The experimentally determined fluorescence decay curves, shown in Figure 3, reveal monoexponential decay kinetics for all solvents except acetonitrile. In acetonitrile, we observe

Shifting the calculated fluorescence spectra by -0.2 eV leads to an increase in the resulting fluorescence lifetimes by 13 %. a

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biexponential fluorescence decay, with a 1.15 ns lifetime minor contribution (intensity ratio of the shorter and longer exponential decay components of 2:98). Generally, the fluorescence lifetimes increase with increasing dielectric constants εr of the solvent (see Figure 4a and Table 2). This is in accordance with the literature50-51, where the lifetime is shown to scale inversely with the third power of the transition frequency, which gets slightly smaller upon increasing εr in our simulations, i.e. lifetimes increase upon rising εr. The fluorescence quantum yields are also rising upon growing εr for the aprotic solvents of low and medium polarity, as shown in Table 2, although the changes are only small. An exception may be acetonitrile, where PyThPhCOOH shows the lowest quantum yield (Table 2). The quantum yields in the protic solvents ethanol and methanol are of similar size as the values found in aprotic THF.

Figure 3: Experimentally obtained fluorescence decay curves of PyThPhCOOH in tetrahydrofuran (green), toluene (red), acetonitrile (purple), ethanol (blue), dichloromethane (black), methanol (light blue), and chloroform (ochre).

The radiative lifetimes 𝜏𝐶𝑟, calculated from the vibrationally broadened emission spectra (computed with the nuclear ensemble method) according to equation 36 and 34 in reference 11 published by Crespo-Otero and Barbatti (COB), increase with increasing dielectric constant 15 ACS Paragon Plus Environment


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of the solvent, except for toluene. The radiative lifetime τr and the observed effective lifetimes τ are linked by the quantum yield (Φ) according to τ=Φ∙τr.

(1)

Therefore, we multiplied the calculated radiative lifetimes 𝜏𝐶𝑟 and the experimentally determined quantum yields Φexp to obtain a lifetime 𝜏𝐶, which can be compared to the experimentally observed lifetime 𝜏𝑒𝑥𝑝 (see Table 2). Figure 4a reveals that this necessary correction significantly improves the correlation between experimentally and ab initio determined effective lifetimes. The effective lifetimes obtained via E(ss),f(lr), E(ss),fconst(lr), and E(lr),f(lr) differ just little, as shown in Figure 4a and Table 2. In general, the computed lifetimes 𝜏𝐶 (Figure 4a) are lower than the experimental values, with deviations being in the order of 22 % to 29 % for solvents with εr < 10. For the more polar solvents ethanol and acetonitrile the calculated and experimental lifetime of the thiazole dye differ by 35 % and 45 %. In case of ethanol, this deviation might originate from protic interactions that are not considered in COSMO. For acetonitrile, the deviation might be due to an additional non-radiative decay channel that causes the experimentally observed biexponential fluorescence decay and low fluorescence quantum yield. Those non-radiative decays are not captured by the theoretical approaches employed in this work. The general underestimation of the effective lifetimes by the different applied theoretical approaches applied by us was already adumbrated tentatively by the width of the simulated fluorescence spectra, which is smaller than the width of the experimental spectra. Effects of oscillator strengths, geometric sampling, excited state frequencies, or application of vibronic progression on the fluorescence spectra and predictions instead of


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Gaussian broadening have not been addressed in this work and were beyond the proof-ofconcept scope of this manuscript. Figure 4b highlights the small lifetime differences between E(ss),f(lr), E(ss),fconst(lr), and E(lr),f(lr) an how these effective lifetimes compare to the experimentally determined effective lifetimes. Expectedly, state specific solvation combined with linear response calculations of individual oscillator strengths for the distorted molecules, E(ss),f(lr), yields the best match between ab initio and experimentally determined effective lifetimes. Surprisingly, the E(lr),f(lr)-combination yields effective lifetimes that slightly better match the experimental ones than those obtained from the E(ss),fconst(lr)-combination. Hence, though the E(lr),f(lr)fluorescence spectra deviate significantly from those derived via the optimal E(ss),f(lr)combination, the more accurate treatment of oscillator strengths overcompensates the less accurate description of S1S0 transition energies in case of the E(lr),f(lr)-combination as compared to the E(ss),fconst(lr)-combination.



Figure 4: (a) Lifetime τ as function of the dielectric constant of the solvent. The experimentally determined (𝜏𝑒𝑥𝑝 ), calculated radiative (𝜏𝐶𝑟 ) and calculated effective lifetimes (τC) are given as empty circles, squares and filled circles, respectively. The thin black and red lines are guides to the eye and were obtained as a linear fit of the results for solvents with low dielectric constant (εr < 15). (b) Correlation between the calculated and experimentally determined lifetimes. The thin red and orange lines are guides to the eye and were obtained as a linear fit with a slope of one for the results obtained for the solvents with low dielectric constant (εr < 15). The thick green line represents the perfect match between theory and experiment.

Table 2: Experimental quantum yield Φ and lifetime τexp of PyThPhCOOH in different solvents 𝑒𝑥𝑝 /Φ. (characterized by their dielectric constants εr) and the radiative lifetime as calculated as 𝜏𝑒𝑥𝑝 𝑟 =𝜏

The error of the experimental quantum yield is 0.05 for all solvents. The calculated lifetimes τC were obtained as a product of the experimentally observed quantum yield Φ and the radiative lifetime 𝜏𝐶𝑟 calculated according to Crespo-Otero11 with different combinations of state specific and linear 18 ACS Paragon Plus Environment

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response transition energies and oscillator strength. The radiative lifetimes 𝜏𝑆𝐵 𝑟 were calculated according to Strickler-Berg36 including the factor for the spectral shape based on the vibrationally broadened spectra calculated with E(ss), fconst(lr). Experiment Solvent

εr

Φ

Theory

𝜏𝑒𝑥𝑝 𝑟

E(ss), f(lr)

(𝜏𝑒𝑥𝑝 /Φ)

𝜏𝐶𝑟

𝜏𝐶

𝜏𝐶𝑟

𝜏𝐶

𝜏𝐶𝑟

𝜏𝐶

𝜏𝑆𝐵 𝑟

[ns]

[ns]

[ns]

[ns]

[ns]

[ns]

[ns]

[ns]

[ns]

τexp

E(ss), fconst(lr)

E(lr), f(lr)

Toluene

2.38

0.76

2.88

3.79

3.04

2.31

2.82

2.14

2.92

2.22

2.88

CHCl3

4.81

0.84

3.23

3.85

2.91

2.44

2.74

2.30

2.84

2.39

2.84

THF

7.58

0.89

3.24

3.64

2.92

2.60

2.79

2.48

2.82

2.51

2.95

CH2Cl2

9.10

0.94

3.34

3.55

2.92

2.72

2.80

2.60

2.91

2.71

2.93

C2H5OH

24.55

0.86

3.71

4.31

2.96

2.55

2.84

2.44

2.86

2.46

3.00

CH3OH

32.70

0.88

3.77

4.28

--

2.62

--

2.52

--

2.57

--

CH3CN

37.50

0.65

3.41

5.25

2.98

1.94

2.86

1.86

2.92

1.90

3.06

CONCLUSION Our study revealed that the dependence of the fluorescence lifetimes on the solvent’s dielectric constant can be predicted successfully with the computationally affordable ab initio calculation of vibrationally broadened fluorescence spectra considering solvent-fluorophore interactions via the conductor-like screening model (COSMO). The combination of state specific solvation to reproduce the dependence of the transition energies on the solvent’s dielectric constant and additionally performing linear response calculations with solvated ground states to yield oscillator strengths for all distorted geometries finally gives the best 19 ACS Paragon Plus Environment


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match between ab initio predicted and experimental fluorescence spectra and effective lifetimes. Neglecting variations in the oscillator strengths upon geometric distortion, i.e. using constant oscillator strengths, naturally yields larger deviations from the experimental data. Surprisingly, full linear response calculations, though yielding fluorescence spectra significantly deviating from those obtained with the methods mentioned above, produce effective lifetimes that deviate less from the experimental ones than in case of the state specific solvation combined with constant oscillator strengths. Even if COSMO inherently does not account for explicit solvent-fluorophore interactions, as present between the treated test case of the 4-hydroxythiazole derivative PyThPhCOOH and the protic solvents employed, the experimentally observed trend of increasing lifetimes with increasing dielectric constant of the solvent could be reproduced with the lifetime prediction methods applied. Independent of the prediction method applied, the predicted lifetimes are too short by about 20-30% compared to the experimentally determined values. Our results underline that the nuclear ensemble method together with COSMO is a valuable and computationally efficient method combination capable of predicting fluorescence lifetimes and their dependence on the solvent’s dielectric constant. The presented method combination can most likely be developed into a routine approach for the prediction of fluorescence lifetimes of dissolved fluorophores. In the future, we will investigate how the accuracy of the predictions can be improved if solvent molecules are explicitly considered. This includes the effect of solvent molecules on the sampled distribution of geometries as well as on the calculated transition energies and oscillator strengths. Furthermore, non-radiative decay channels (cf. the work of Santoro et al.34) will be considered in the simulation. Additionally, this work will be extended to other fluorophores with a more pronounced charge transfer (CT) character and a stronger solvatochromism. 20 ACS Paragon Plus Environment

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SUPPORTING INFORMATION DESCRIPTION A further comparison of the calculated fluorescence spectra and lifetimes using different calculation methods for each solvent as well as more details on the calculation formulas used.

ACKNOWLEDGEMENTS The authors thank the Bundesministerium für Bildung und Forschung (BMBF FKZ 03EK3507 and FKZ 13N13357) and the Deutsche Forschungsgemeinschaft (DFG Grant No. PR 1415/2-1) for financial support. J. Preiß acknowledges the Nagelschneider Foundation for her fellowship. This work was partially supported by the AMOS program within the Chemical Sciences, Geosciences, and Biosciences Division of the Office of Basic Energy Sciences in the U.S. Department of Energy. The authors would like to thank Karin Kobow for technical support in the laboratory and Dr. Johannes Fiedler for fruitful discussions on quantum electrodynamics.

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Ab Initio Prediction of Fluorescence Lifetimes Involving Solvent

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