Data analysis - From Chromophores to Materials: Structure-Property Relationships in Multichromo

A review summarizing the data analysis tools used in our group has been published recently.¹¹In addition to conventional global lifetime analysis, model free analysis was applied in paper IV and is discussed in detail in the supporting information presented in section 8.4.

References 41

References

1. Lang, B.Rev. Sci. Instrum.2018,89, 093112.

2. Buchvarov, I.; Trifonov, A.; Fiebig, T.Opt. Lett., OL2007,32, 1539–1541.

3. Johnson, P. J. M.; Prokhorenko, V. I.; Miller, R. J. D.Opt. Express, OE2009, 17, 21488–21496.

4. Herrmann, D.; Niesar, S.; Scharsich, C.; K¨ohler, A.; Stutzmann, M.; Riedle, E.

J. Am. Chem. Soc.2011,133, 18220–18233.

5. Bradler, M.; Baum, P.; Riedle, E.Appl. Phys. B 2009,97, 561.

6. Schmidhammer, U.; Jeunesse, P.; Stresing, G.; Mostafavi, M.Appl. Spectrosc.

2014,68, 1137–1147.

7. Young, R. M.; Dyar, S. M.; Barnes, J. C.; Jur´ıˇcek, M.; Stoddart, J. F.;

Co, D. T.; Wasielewski, M. R.J. Phys. Chem. A2013, 117, 12438–12448.

8. Dobryakov, A. L.; Kovalenko, S. A.; Weigel, A.; P´erez-Lustres, J. L.; Lange, J.;

M¨uller, A.; Ernsting, N. P.Rev. Sci. Instrum.2010,81, 113106.

9. Lang, B.; Mosquera-V´azquez, S.; Lovy, D.; Sherin, P.; Markovic, V.; Vau-they, E.Rev. Sci. Instrum.2013,84, 073107.

10. Tokunaga, E.; Terasaki, A.; Kobayashi, T. J. Opt. Soc. Am. B 1966, 13, 496–513.

11. Beckwith, J. S.; Rumble, C. A.; Vauthey, E.Int. Rev. Phys. Chem.2020,39, 135–216.

CHAPTER 3 Paper I -Lifetime broadening and impulsive generation of vibrational coherence triggered by ultrafast electron transfer

Stationary Absorption Time / ps

T₁> T₁> T₁ ≈T₂*

Ion Pair

Aster A.; Bornhof A.-B.; Sakai N, Matile S.; and Vauthey E. Life-time broadening and impulsive generation of vibrational coherence triggered by ultrafast electron transfer. - Reprinted with permission fromJ. Phys. Chem. Lett. 2021,12, 3, 1052–1057. Copyright 2021 American Chemical Society.

Lifetime Broadening and Impulsive Generation of Vibrational Coherence Triggered by Ultrafast Electron Transfer

Alexander Aster, Anna-Bea Bornhof, Naomi Sakai, Stefan Matile, and Eric Vauthey*

Cite This:J. Phys. Chem. Lett.2021, 12, 1052−1057 Read Online

ACCESS Metrics & More Article Recommendations *^sı Supporting Information ABSTRACT:The absorption band shape of chromophores in liquid solution

at room temperature is usually dominated by pure electronic dephasing dynamics, which occurs on the sub-100 fs time scale. Herein, we report on a series of dyads consisting of a naphthalenediimide (NDI) electron acceptor with one or two phenyl-based donors for which photoinduced intramolecular electron transfer is fast enough to be competitive with pure electronic dephasing. As a consequence, the absorption band of theπ−π*transition of these dyads is broader than that of the NDI alone to an extent that scales with the electron transfer rate. Additionally, this reaction is so fast that it leads to the impulsive excitation of a low-frequency vibrational mode of the

charge-separated product. Quantum-chemical calculations suggest that this vibration involves the C−N donor−acceptor bond, which shortens considerably upon electron transfer.

E

lectronic absorption bands in the condensed phase at room temperature are usually very broad as a con-sequence of ultrafast electronic dephasing.¹⁻³In principle, this process is due to changes in both amplitude and phase of the electronic wave functions of the states involved in the transition.^4,5In the phenomenological Bloch model,⁶these changes are described by two exponential functions with time constants 2T₁andT₂*, respectively, withT₁being the excited-state lifetime andT2*the pure dephasing time. Although the pure electronic dephasing can usually not be described by a simple exponential function, it typically occurs on a sub-100 fs time scale,⁷⁻¹⁰that is, much faster than the decay of theﬁrst singlet excited state, which takes place on the longer picoseconds−nanoseconds time scale. As a consequence, the impact of the excited-state lifetime on the S₁←S₀band shape is usually negligible, and lifetime broadening of the ﬁrst electronic absorption band is not common for organic molecules in liquids.

Herein, we investigate the lifetime broadening of the lowest-energy electronic absorption band of electron donor−acceptor (DA) dyads with an A−Dn(n= 1, 2) motif in solution. This broadening is a consequence of a photoinduced intramolecular charge separation (CS) process that occurs on a similar time scale as that of pure dephasing. We show that electron transfer (ET) is so fast that it leads to the impulsive excitation of low-frequency vibrational modes in the ensuing charge-separated state (CSS). Comparison of the frequencies of these vibrational wavepackets with those obtained from quantum-chemical calculations allows identifying one of the intra-molecular modes associated with the CS coordinate.

These dyads consist of a naphthalenediimide (NDI) with phenyl-based electron-donating groups linked to one or both

imide N atoms (Figure 1A). Small structural modiﬁcations of the phenyl donors allow for a systematic increase of the CS driving force,−ΔGCS, by at least 0.5 eV upon going fromIto IV(section S3,Supporting Information), which is expected to accelerate ET and to shorten the lifetime of the locally excited state (LES). Furthermore, symmetric (s) or asymmetric (a) addition of one or two donors, respectively, gives another leverage to inﬂuence the ET dynamics. The spectral character-istics ofI−IVare compared to the reference compoundpNDI, with two innocent ethylhexyl (EH) groups on the imide nitrogen atoms.

As illustrated in Figure 1B, the position and vibronic structure of the lowest-energy absorption band ofI−IVare nearly identical with those ofpNDIin acetonitrile, reflecting theπ−π*character of this transition localized on the NDI center. It is indeed known that, in contrast to core substitution, axial functionalization of NDIs does not significantly affect the frontier molecular orbitals.¹¹⁻¹³However, the width of the absorption band increases with the CS driving force as well as the number of electron donors (#D).

This eﬀect cannot be accounted for by the presence of a broad and featureless charge-transfer (CT) band underlying the π−π* band. Although such a CT band should gain intensity with the number of donors, as found here, it should

Received: December 10, 2020 Accepted: January 5, 2021 Published:January 20, 2021

Letter pubs.acs.org/JPCL

1052 https://dx.doi.org/10.1021/acs.jpclett.0c03641

J. Phys. Chem. Lett.2021, 12, 1052−1057 Downloaded via UNIV OF GENEVA on February 16, 2021 at 16:23:25 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

shift to lower energy with increasing ET driving force,^14,15 contrary to the observation. Moreover, the increase of intensity with the electron-donor strength is not consistent with a CT band. The dipole moment associated with a CT transition is directly related to the electronic coupling,¹⁶which is rather expected to decrease as the CT character of the transition increases. This is conﬁrmed by quantum-chemical calculations that predict a negligible oscillator strength for the CT transition inIVa(Figure S12).

The absorption bands ofII−IVcan be well reproduced by the convolution of the absorption band of pNDI with a Lorentzian line-broadening function (Figure S2). In the case of IVaandIVs, the bestﬁt is obtained by using a Lorentzian broadening function with a full width at half-maximum (fwhm),Δ ̃νL, of 194 and 88 cm⁻¹, respectively. If we assume a pure lifetime broadening eﬀect when going frompNDIto the dyads, i.e.,Δ ̃ =ν_L (2πcT₁)⁻¹, these widths imply an excited-state lifetime of 60 fs forIVaand 27 fs forIVs(section S4, Supporting Information). Narrower broadening functions and,

thus, longerT1are obtained for the other dyads (Figure S2and Table S2).

To determine whether theseT1values are consistent with the lifetime of the photopopulated state, we turned to transient absorption (TA) spectroscopy upon excitation of the 0−0 transition at 26500 cm⁻¹. For all dyads, the population of the LES can be identiﬁed by an excited-state absorption (ESA) band at 16750 cm⁻¹and a stimulated emission (SE) band at 24900 cm⁻¹(Figure 2A), both of which can also be observed with pNDI.¹⁷These spectral signatures of the LES disappear on the subpicoseconds time scale, and new bands, which can be assigned to the NDI radical anion,¹⁸appear at 21200 and 16600 cm⁻¹, indicating the population of the charge-separated state (CSS).

The lifetime of the LES was estimated by analyzing the time dependence of the TA within a small spectral window around the ESA band of the LES at 16750 cm⁻¹ by using the convolution of a Gaussian instrument response function (IRF) with a biexponential function and by taking the amplitude-averaged lifetimes,⟨τ⟩. Such non-single-exponential population dynamics are expected for a process occurring on similar time Figure 1.(A) Structures of the dyadsI−IV: the naphthalenediimide (NDI) core is symmetrically (s) or asymmetrically (a) linked to electron donors (D), which systematically varies the driving force for charge separation,−ΔGCS. Innocent ethylhexyl (EH) groups are linked on both axial positions forpNDIand on one side for the asymmetric compounds. (B) Increasing the CS driving force and the number of donors (#D) leads to an increase of the absorption bandwidth in acetonitrile. (C, top) The bandwidth is identical with that of pNDI if the excited-state lifetime exceeds a certain threshold. (C, bottom) Two dyads with the same excited-state lifetime show the same bandwidth. (D) The amplitude averaged lifetimes (⟨τ⟩, circles) obtained from a biexponential analysis of theπ−π*excited-state dynamics are compared to the excited-state lifetimes (T1, triangle) obtained from the width of the Lorentzian band broadening function.

Figure 2.(A) Contour plot of the transient absorption measured withIVsin ACN upon excitation at 26500 cm⁻¹. Charge separation is visible as a decay of the excited-state absorption (ESALES) and stimulated emission of the locally excited state (SELES) and a concurrent rise of the charge-separated (CSS) bands. (B) The residual contour plot is obtained by subtracting the contributions of the population and solvation dynamics obtained from a global lifetime analysis from the TA data. Because the nodes match the band maxima of the two CSS bands, the wavepacket is attributed to a vibrational coherence of the CS product. (C, top) The maximum of the CSS band (ν̃max) shifts at early times due to solvent relaxation and then oscillates around a constant value. (C, bottom) Subtraction of the band-shift dynamics gives the residual (res), which illustrates the dephasing of the vibrational coherence.

The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letter

https://dx.doi.org/10.1021/acs.jpclett.0c03641 J. Phys. Chem. Lett.2021, 12, 1052−1057 1053

Paper I 45

scales as those of solvent and vibrational relaxation.¹⁹⁻²¹This approach was preferred to a global lifetime analysis because of the wavelength dependence of the IRF as well as the early shift of the intense CSS band at 21200 cm⁻¹caused by solvent relaxation. The width of the IRF, determined from the Kerr eﬀect, was ﬁxed to 85 fs for all dyads to ensure proper comparison (Figure S3).

As illustrated inFigure 1D andTable S2, the resulting values of⟨τ⟩decrease from 206 to 31 fs by going fromIatoIVs.

Moreover,⟨τ⟩systematically shortens by a factor∼2 upon increasing the number of donors from one (a) to two (s). Such behavior is expected if the two CS pathways in the symmetric dyads are unrelated and independent (incoherent limit). In this case, the overall CS rate constant,k_CS, is proportional to V12 +V22, whereViis the electronic coupling for the CS between the NDI core and the donori. In the coherent limit, the two donors act as a single reacting unit andkCS∝(V1+ V₂)². As a consequence, CS in the symmetric systems should be 4 times as fast as in the asymmetric ones.²²

However, such a distinction between coherent and incoherent ET is only feasible ifV1∼V2. This might not be the case here because of the thermal ﬂuctuations of the dihedral angle between the NDI and the donor planes that should aﬀectV_i. As a consequence, coherent ET cannot be excluded here on the basis of this shortening by a factor of 2.

In addition to the number of donors,⟨τ⟩also correlates with the CS driving force. The similarity betweenIIandIIIis most likely due to the higher torsionalﬂexibility ofII, which allows for larger electronic coupling,²³and compensates for the lower ΔG_CS.

Comparison of Figures 1B and 1D reveals that the absorption band broadening and ⟨τ⟩ exhibit the same dependence onΔGCSand the number of donors. Moreover, IIIsandIVa, which have the same bandwidth, have also a nearly identical ⟨τ⟩. Finally, Figure 1D compares the experimental⟨τ⟩values with those of T₁ estimated above from the analysis of the band broadening. Considering the very simple approach used here, the agreement between these two sets of values is very good.

These results are thus unambiguous evidence that the band broadening of II−IV compared to pNDI is a direct consequence of an ultrafast ET in the excited state. Lifetime broadening due to ultrafast heterogeneous electron injection was invoked previously to account for the absorption band of a perylene derivative attached to semiconductors.^24,25However, a subsequent study concluded that other factors than the injection dynamics were responsible for the bandwidth.²⁶The fact that the absorption band shape ofIais identical with that of pNDI indicates that lifetime broadening is not longer operative with⟨τ⟩= 200 fs. This points to a pure electronic dephasing time scale not exceeding a few tens of femtoseconds.

In addition, the TA spectra also reveal that the position of both CSS bands oscillates with an ∼250 fs period. In acetonitrile, the most intense band also exhibits an∼120 fs initial red-shift, which is not observed in the nonpolar methylcyclohexane and can thus be attributed to the solvent relaxation around the CSS via inertial motion.²⁷ The pure wavepacket oscillations were isolated by subtracting the solvent shift from the time dependence of the CSS band maximum, ν̃CSS (Figure 2C), and the oscillation frequencies were determined from subsequent Fourier transformation (Figure 3A). The pure wavepacket dynamics over the entire spectral window was also extracted by subtracting the bestﬁt of a

global multiexponential analysis from the whole TA data matrix (Figure 2B). The resulting contour plots of the residual matrix show clearly that the wavepacket oscillation nodes coincide with both CSS bands maxima, conﬁrming that the vibrational coherence is associated with the CS product.²⁸ Such vibrational wavepacket oscillation is only observed when

⟨τ⟩< 100 fs, that is, withIIs,IIIs, andIVa,s. For theﬁrst three of them, the Fourier transform spectrum points to the presence of a single frequency between 140 and 170 cm⁻¹, whereas for IVs, where CS is the fastest, an additional component at 206 cm⁻¹is visible (Figure 3A). These frequencies are independent of the solvent but depend on the nature and number of attached donors (Figures S5−S9).

In principle, the coherent wavepacket motion observed in the CSS could have been initially launched in the LES upon coherent optical excitation of Franck−Condon-active modes.²⁹⁻³¹However, ET in these molecules is too fast to detect the presence of a vibrational coherence in the LES.

Close examination of the TA data measured with pNDI and dyads undergoing slower CS (⟨τ⟩> 100 fs) do not reveal any oscillation of the LES band at 16750 cm⁻¹or the SE band around 24900 cm⁻¹. This suggests that the oscillation of the CSS band is not due to a spectator mode initially excited in the LES. Therefore, it most probably arises from impulsive excitation during the ultrafast CS process itself. Only those intramolecular modes, whose equilibrium value change signiﬁcantly upon ET, can be excited. If the reaction time is signiﬁcantly shorter than a vibrational period of these CS-active modes, the latter oscillate coherently in the same way as Franck−Condon-active modes upon ultrafast optical excita-tion. Consequently, the mode(s) associated with the observed coherence should be involved in the CS coordinate.³² In principle, modes that are not directly linked to CS but are anharmonically coupled to a CS-active mode could also be excited.

Given the∼250 fs period of the oscillation, the impulsive excitation of this mode requires⟨τ⟩< 100 fs. This explains why Figure 3.(A) Fourier transformation of the TA oscillations measured withIVspoints to the presence of two frequency components irrespective of the solvent polarity. On the basis of quantum-chemical calculations, they can be assigned to the symmetric and asymmetric in-plane ring deformation of the NDI core that modulates the donor−

acceptor distance. (B) Ground- and excited-state optimization suggests a change of the equilibrium geometry along this coordinate when going from the local excited state (LES) to the charge-separated state (CSS). A coherent superposition of vibrational states is populated by the ultrafast electron transfer, whose time constant is shorter then a vibrational period,T.

The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letter

https://dx.doi.org/10.1021/acs.jpclett.0c03641 J. Phys. Chem. Lett.2021, 12, 1052−1057 1054

no vibrational wavepacket motion is observed withI,IIa, and IIIawhich undergo slower CS. The impulsive generation of coherent vibrational wavepackets upon an ultrafast ET was predicted theoretically³³and was reported for heterogeneous photoinduced ET at a chromophore−semiconductor inter-face,^34,35 for photoinduced ET in an electron-donating solvent,³²for photoisomerization in liquid,³⁶and for singlet ﬁssion in a crystal.³⁷However, to the best of our knowledge, it has not been observed so far for an intramolecular CS process in a liquid.

Quantum-chemical calculations at the density functional theory (DFT) level were performed to identify the possible normal modes associated with this oscillation (section S8, Supporting Information). The assignment was based not only on the absolute frequency but also on its dependence on the nature and number of donors. As the latter is not expected to change signiﬁcantly in the LES and CSS, calculations were performed at the electronic ground state to reduce the computational cost.

Among the few vibrations predicted between 100 and 200 cm⁻¹, only one follows the observed dependence on the electron donor. The frequency of this mode varies from 137 to 176 cm⁻¹by going fromIVs toIIs, whereas the observed frequency changes from 142 to 168 cm⁻¹ (Table S3). This mode involves a symmetric ring deformation of the NDI core as well as a modulation of the distance between the NDI and the donor(s) (Figure S10). Time-dependent (TD) DFT calculations and geometry optimization ofIVaconfirm that the frequency of this mode,ν̅^DA, in the LES and CSS does not differ significantly (Table S4).

ForIVs, which undergoes the fastest CS, a weaker oscillation is also present at 206 cm⁻¹. This frequency matches that of the antisymmetric combination of the above-mentioned mode (Table S3). As these two modes modulate the donor−acceptor distance, they can be expected to be CS active.

TD-DFT calculations performed with IVa (section S9, Supporting Information) predict a dark excited state with large charge transfer character, which can be associated with the CSS, about 0.3 eV below the LES (Figures S12 and S13). The N−C donor-acceptor bond length remains unaﬀected upon excitation to the LES, in agreement with the absence of vibrational wavepacket in the LES band. On the other hand, the N−C donor-acceptor bond is predicted to decrease from 1.45 to 1.42 Å in the CSS (Figure S14).

The two conditions for the impulsive generation of vibrational coherence by ultrafast ET are therefore fulﬁlled:

(i) the equilibrium geometry along this intramolecular coordinate changes signiﬁcantly upon CS, and (ii) the reaction occurs on a time scale that is considerably shorter than a vibrational period of this mode.

To sum up, we presented electron donor−acceptor dyads where CS is so fast that it results in a coherent excitation of vibrations in the product state. This phenomenon can be exploited for a better understanding of the nature of the reaction coordinate. In the present case, the CS dynamics is the same in polar and apolar solvents, revealing that the reaction coordinate involves only intramolecular modes. This result goes along with previous observations of ultrafast ET processes occurring on a faster time scale than that of solvent relaxation and/or exhibiting no signiﬁcant dependence on the solvent polarity.^32,38−45 In agreement with the two-dimen-sional Sumi−Marcus model,⁴⁶ ET can proceed entirely via intramolecular coordinates if the barrier along these

coordinates is low enough to be overcome on a shorter time scale than that of solvent motion.

A second consequence of the ultrafast CS in these dyads is that it leads to a lifetime broadening of the LES←S0transition.

Although this lifetime broadening is known in the gas phase,⁴⁷⁻⁴⁹ or at very low temperatures,⁵⁰⁻⁵² such clear correlation between the excited-state lifetime and the absorption bandwidth was, to the best of our knowledge, never reported so far for organic systems in room-temperature solution. In fact, this eﬀect might not be so uncommon and could, for example, underlie the spectral changes often

Dans le document From Chromophores to Materials: Structure-Property Relationships in Multichromophoric Systems (Page 57-103)