Elucidating the Mechanism of Zn2+ Sensing by a Bipyridine Probe

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Elucidating the Mechanism of Zn Sensing by Bipyridine Probe Based on Two-Photon Absorption Joanna Bednarska, Robert Zalesny, Arul Murugan Natarajan, Wojciech Bartkowiak, Hans Ågren, and Michael Odelius J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b04949 • Publication Date (Web): 05 Aug 2016 Downloaded from http://pubs.acs.org on August 6, 2016

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The Journal of Physical Chemistry

Elucidating the Mechanism of Zn2+ Sensing by Bipyridine Probe Based on Two-Photon Absorption Joanna Bednarska,∗,† Robert Zaleśny,† N. Arul Murugan,‡ Wojciech Bartkowiak,† Hans Ågren,‡ and Michael Odelius∗,¶ Department of Physical and Quantum Chemistry, Faculty of Chemistry, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, PL–50370 Wrocław, Poland, Division of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, SE–10691 Stockholm, Sweden, and Division of Chemical Physics, Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden E-mail: [email protected],Tel.+48(71)3204577; [email protected],Tel.+46-8-55378713

∗

To whom correspondence should be addressed Department of Physical and Quantum Chemistry, Faculty of Chemistry, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, PL–50370 Wrocław, Poland ‡ Division of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, SE–10691 Stockholm, Sweden ¶ Division of Chemical Physics, Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden †

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Abstract In this work we examine, by means of computational methods, the mechanism of Zn2+ sensing by a bipyridine centered, D-π-A-π-D type, ratiometric molecular probe. According to recently published experimental data [Chem. Sci., 2014, 5, 3469–3474], after coordination to zinc ions the probe exhibits a large enhancement of the two-photon absorption cross section. The goal of our investigation was to elucidate the mechanism behind this phenomenon. For this purpose, linear and nonlinear optical properties of the unbound (cation-free) and bound probe were calculated including the influence of solute-solvent interactions, implicitly using a polarizable continuum model and explicitely employing the QM/MM approach. Since the results of the calculations indicate that many conformers of the probe are energetically accessible at room temperature in solution and hence contribute to the signal, structure-property relationships were also taken into account. Results of our simulations demonstrate that the one-photon absorption bands for both the unbound and bound form correspond to the bright π → π ∗ transition to the first excited state which, on the other hand, exhibits a negligible twophoton activity. Based on the results of the quadratic response calculations, we put forward a notion that it is the second excited state which gives the strong signal in the experimental nonlinear spectrum. In order to explain the differences in the two-photon absorption activity for the two lowest-lying excited states and nonlinear response enhancement upon binding, we employed the generalized few-state model including the ground, first and second excited states. The analysis of the optical channel suggests that the large two-photon response is due to the coordination-induced increase of the transition moment from the first to the second excited state.

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INTRODUCTION Two-photon microscopy (TPM) serves as one of the most popular contemporary bioimaging techniques. 1,2 Contrary to one-photon microscopy, TPM allows deep specimen penetration, high spatial resolution, limited autofluorescence and photodamage of the sample. 3–5 The increasing interest in this field has contributed to the development of fluorescent probe molecules specific to two-photon absorption and used to label various sample targets. Fluorescent molecular probes are usually organic compounds built of a fluorophore (two-photon reporter) that determines the photochemical behaviour, a receptor that binds selectively to the target and a spacer linking moiety. After incorporation to the specimen, the receptor binds to the analyte by covalent or non-covalent interactions, triggering a change in the spectroscopic properties of the fluorophore, such as changes in intensity or energy of emission or absorption. 6,7 The response of the probe and its selectivity towards a particular target may be modeled using well-established design strategies. 8–12 Accordingly, the compound should ideally possess a number of characteristics, like a high two-photon action cross section, appropriate fluorescence intensity and absorption/emission wavelength, good solubility in water, cell permeability, photostability and sufficient binding affinity to the target. Various criteria can be employed for the classification of two-photon probes. Depending upon the signalling mode, probes may be categorized into two groups: turn on/turn off and ratiometric. 13 The first type undergoes a change in fluorescence intensity (intensity-responsive probes). In the case of the second one the shift of fluorescence band, as a result of binding to analyte, is recorded. Ratiometric probes allow to evaluate quantitatively the concentration of the analyte by the proportional change of the ratio of emission band intensities. 14 Alternatively, the mechanism of detection can be divided into reaction-based, where the chemical conversion takes place, and coordination-based, where the receptor containing free electron pairs is coordinated by the metal ion. 13 The response of metal ion probes can be based on different molecular mechanisms, 15–17 such as: photoinduced electron transfer, Förster resonance energy transfer, 18 intramolecular charge transfer, formation of excimer/exciplex and 3



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excited-state intramolecular proton transfer. 19 In the first case, the photoinduced electron transfer between ionophore (metal ion receptor) and fluorophore is blocked after reaction, causing a rapid increase of fluorescence intensity. 20–22 In the second case, the resonance energy transfer, occuring between donor and acceptor moieties of fluorophore, can be facilitated or attenuated upon reaction with metal ions by altering either the overlap of their absorption and emission spectra or distance. 6,23,24 Moreover, many two-photon probes exploit the intramolecular charge transfer that is triggered by the change of electron-donating and/or electron-withdrawing abilities of moieties. 16,25 As a result, a shift is observed in the spectra which is usually accompanied by a concomitant change of nonlinear optical properties of the probe. The response of the probe can be based on the phenomenon of excimer/exciplex formation due to π − π stacking of adjacent fluorophores yielding a red-shifted emission band. 25–27 For more information on metal-responsive molecular probes readers are referred to excellent reviews, see Refs. 7,8,16,28–32. One of the most desirable type of probes are those for sensing of biologically relevant ions, such as Na+ , Ca2+ , Mg2+ or Zn2+ . 8 Zinc ions occur in the living systems either bound to proteins and enzymes or they are present in a labile form. 33–35 Accessible Zn2+ ions play an important role in various cellular processes. 36–38 The concentration of Zn2+ ions is controlled by few different types of proteins and the disturbance of its balance is associated with neurological disorders, such as Alzheimer disease. 13,39–41 Thus, monitoring the distribution and dynamics of zinc ions in cells and tissues is of pivotal importance. Recently, many ratiometric bipyridine-centered probes undergoing a coordination-based mechanism of Zn2+ sensing have been proposed. 42–49 One of them, the 5,5’-Bis((E)-2-(9-(2-(2-(2methoxyethoxy)ethoxy)ethyl)-9H-carbazol-3-yl)vinyl)-2,2’-bipyridine investigated by Divya and coworkers (hereafter referred to as GBC, see original work 42 ) exhibits 13-fold enhancement in the two-photon absorption cross section and a 9-fold enhancement in the two-photon action cross section, in the presence of Zn2+ ions. The latter quantity is the product of twophoton absorption cross section and fluorescence quantum yield. The probe fulfills many

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criteria needed to be successfully used in bioimaging. The molecule is built of a fluorophore of D-π-A-π-D architecture, connected by a spacer with bipirydine moiety being a chelator. It exhibits a response to the presence of zinc ions with 27 nm red-shift in absorption spectra and 80 nm red-shift in the fluorescence spectra. These results were attributed to the increase of electron-withdrawing ability of bipyridine moiety, facilitating the intramolecular charge transfer. 50 Since the authors did not make an attempt to investigate the mechanism of Zn2+ sensing using quantum-chemical methods, the goal of this work is to fill this gap and gain insight into structure and property changes for the system upon sensing. For this purpose, we employ recently developed computational approaches to simulate one- and two-photon absorption spectra of molecules in solution. This article is organized as follows. We start with the analysis of the structural aspects of zinc ion binding. Later, we discuss the changes in electronic structure and nonlinear absorption spectra of the probe itself and its complex with the zinc ion. Details of the computational protocol and its assessment are given in the Supporting Information.

RESULTS AND DISCUSSION Conformational Analysis The primary goal of this work is to investigate the linear and nonlinear optical properties of the cation-free GBC probe and its zinc complex in order to elucidate the molecular mechanism of a 13-fold enhancement of two-photon absorption cross section upon binding to Zn2+ cation. As the geometry of GBC rearranges during coordination, we consider three species, namely: trans-GBC, cis-GBC, cis-GBC*Zn2+ , including their stable conformers (see Figure 1). One should note that model structures do not posses full-length 2-(2-(2methoxyethoxy)ethoxy)ethyl substituents as studied in the reference work; 42 instead they are replaced with 2-methoxyethyl groups. Moreover, we have chosen a simplified geometry where the coordination center is not surrounded by chloride ions. The validity of this model 5



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is presented in Supporting Information. As shown therein, different structural models of ligands lead to similar optical properties of the probe. Due to the presence of four single bonds, connecting a spacer with the carbazole group and the bipyridine moiety, each of the analyzed GBC species can adopt ten potentially stable conformations, labeled herein as: TTTT, CTTT, CTTC, TCTT, CCTT, CTCT, TCCT, CCTC, CCCT, CCCC (optimized structres are depicted in Figure S1 and Figure S2 in Supporting Information). Their relevance for the experiment was estabilished by conformational analysis with solvent effects taken implicitly into account. The estimated population of conformers, which is presented in Table 1, suggests that solution with the probe contains a mixture of structures at room temperature. Note that zero-point vibrational energy is included and entropic effects are assumed to be equal for all considered conformers. According to the Boltzmann distribution, the ratio between population of the most and the least stable conformers of trans-GBC, TTTT and CCCC differing in energy by 1.4 kcal/mol, is equal to 10:1. Analogous trend was observed for the cis-GBC and cis-GBC*Zn2+ (for more detailed information regarding conformer energies the reader is reffered to the Supporting Information, see Table S1 and Table S2). In order to investigate the energetics of the rearrangement process of trans-GBC to cis-GBC, the potential energy scan with respect to the N1-C1-C2-C3 dihedral angle was performed (see Figure 2). As seen, the rotational barrier between trans-GBC and cis-GBC is approximately equal to 4 kcal/mol. The estimated population ratio between cis-GBC and trans-GBC is equal to 1:862 at room temperature. However, the result may depend on the conformer’s geometry (see Table S3 in Supporting Information). One can note that for the cis conformer there is a double well potential with two equivalent local minima around 150 and 210 degrees and a small (0.4 - 0.7 kcal/mol) barrier inbetween them. It should be noted that the solvation in aqueous solution decreases the rotational barrier significantly. Moreover, the results of calculations with relaxation of the moieties taken into account do not differ significantly from the scan performed at twisted frozen geometries.

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One-Photon Absorption Spectra Static Approach In this paragraph we focus on the one-photon properties of the investigated probe, starting from the analysis of experimental data. Figure 3a) presents the UV-Vis spectra of the cation-free and bound probe measured in 1:1 acetonitrile–water solution. 42 Positions of absorption band maxima are presented in Table 2. As can be seen, the maximum of absorption for the unbound form is located at 403 nm (3.07 eV) and is red shifted by 27 nm (0.19 eV) after the cation coordination. Both bands are characterized by the same value of the FWHM equal to 0.61 eV and both exhibit similar structureless shape. The ratio of bands absorbances is equal to 0.8 as reported by Divya et al. 42 In order to elucidate the character of the transition and excited state involved, we calculated vertical excitation energies to the five lowest lying singlet excited states for all species and conformers of the probe. 51–53 The results revealed that the absorption band of the highest intensity corresponds to the π → π ∗ transition to the first excited state and involves the HOMO and LUMO orbitals. On the other hand, the values of oscillator strength corresponding to transition to second excited state and higher states are much smaller and do not exceed 0.3. This observation holds true for the whole set of conformers. It should not be overlooked that calculated values of vertical excitation energies are consistent with experimental data (see Tables 2 and 3). Insignificant discrepancies may emerge from the solvent representation, i.e. we considered water solution instead of 1:1 water/acetonitrile mixture. It is worth mentioning that the obtained values of oscillator strengths vary slightly in the set of conformers; from 3.02 (CTTC) to 3.29 (TCTT) for cis-GBC, 2.61 (CTTC) - 2.86 (CCCC) for cis-GBC*Zn2+ and 3.05 (CTTC) - 3.31 (TCCT) for trans-GBC. The excitation energies to S1 state and corresponding oscillator strengths weighted by conformer population are depicted in Figure 4. It can be clearly seen that there is no significant difference in the transition energy values in the data sets. The difference between maximal and minimal ver-

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tical excitation energy for the trans-GBC is equal to 0.08 eV and 0.14 eV for cis-GBC*Zn2+ . Hence, we can assume that despite of large number of conformers present in a solution, their specific distribution does not influence significantly the effective band shape and its width.

Dynamic Approach Besides the static calculations using the continuum solvation model, we also simulated optical band shapes using the discrete polarizable embedding linear response approach. 54,55 As reported in several studies, 56–60 the methodology used in this study is capable of accurately reproducing the band width via evaluation of vertical excitation energies of sampled solute configurations extracted from molecular dynamics trajectory where a chromophore can be represented either as a the rigid (RBMD) or flexible body (FBMD). In this study, the computations were carried out for two GBC species, trans-GBC and cis-GBC*Zn2+ in their most stable TTTT arrangement, employing both flexible and rigid schemes. 61,62 In what follows we will briefly describe results of performed computations (for the computational details of the simulations see Supporting Information). Insets b)-e) in Figure 3 present the histograms representing a population of the chromphore conformations with respect to its transition energy to the S1 and S2 state (within intervals of 0.025 eV). Comparing to RBMD, in which case the estimated broadening parameter (standard deviation, σ) for the cation-free and bound probe are 0.08 eV and 0.07 eV, the simulated FBMD bands have larger widths. Hence, they are characterized by the larger value of σ parameter: 0.16 eV for trans-GBC and 0.13 eV for cis-GBC*Zn2+ . Deviations between two aforementioned models are not surprising, since simulations using a frozen chromophore structure take into account only broadening due to solute-solvent interactions. In turn, the differences in numbers for the free and bound form can be explained by the limited conformational freedom of the bipyridine moiety imposed by the constraints of coordinating Zn2+ ion. Both schemes, the RBMD and FBMD, however, do not reproduce experimental

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FWHM of the bands (Γf (FWHM) = 2

√

2 ln 2σ = 0.61 eV). In these comparisons we as-

sume gaussian broadening in each case. It is worthwhile to mention that underestimation of spectral widths was recently explained in several studies, 63,64 and emerges from neglecting quantum effects on the high-frequency modes. On the other hand, a satisfactory evaluation of simulated band positions via RBMD scheme should be highlighted. While the experimetal band maxima lie at 3.07 eV (403 nm) for GBC and 2.88 eV (430 nm) for GBC*Zn2+ , the simulated ones have peaks at 3.11 eV (399 nm) and 3.01 eV (412 nm), respectively.

Analysis of Nonlinear Spectrum To elucidate the molecular mechanism of the two-photon response enhancement of the probe upon coordination to the zinc cation, we conducted the quadratic response (QR) calculations, 65–68 considering a sub-set of the energetically most stable conformers so as to gain an in-depth view into the structure-property relationships. In the calculations of two-photon absorption cross section, σ (2) , the experimental value of the Γf parameter was employed (it is half of experimental one-photon band width and it is equal to 0.3 eV). An assessment of the computational methods, we employ, is presented in the SI. Outcomes of performed computations are included in Table 3 and are depicted in Figure 5. Based on the obtained results one may draw a few significant conclusions. The two-photon probability depends on the probe bound state and structure. As seen, the complex exhibits approximately three times higher nonlinear response than cation-free form. The trans-GBC has larger two-photon response than cis-GBC. Furthermore, the σ (2) varies among the set of investigated conformers. For each of the species the dominant TTTT conformer exhibits the highest nonlinear response, while the least stable struture (CCCC) exhibits the lowest σ (2) value. The differences are equal to 676 GM, 505 GM and 937 GM 4

cm s ). We note for trans-GBC, cis-GBC and cis-GBC*Zn2+ , respectively (1 GM = 10−50 photon

that in each case the TCCT conformer exhibits the largest energy gap between ground and first as well as ground and second excited state, whereas the CTTC has the lowest excitation 9



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energies. The difference in the position of absorption band maxima corresponding to the first and second excited state for the most stable TTTT conformer of trans-GBC, cis-GBC and cis-GBC*Zn2+ is equal to 60 nm, 51 nm and 71 nm, respectively. The probability of the two-photon transition to the first excited state is negligible for all considered conformers, contrary to the probability of the one-photon transition that has already been presented in the previous paragraph. Experimental and theoretical two-photon absorption cross sections are presented in Tables 2 and 3. The agreement between the measured and calculated two-photon absorption cross section is satisfactory, considering the accuracy of electronic structure methods in predicting this property. 69 Moreover, it should be noted that the results presented in Table 3 are in line with other studies for similar structures containing bipyridine moiety. 70 It is important to highlight that spectral dependencies presented by Divya et al. were measured using a narrow wavelength range (760 - 840 nm i.e. 1.63 - 1.47 eV) corresponding to the main one-photon feature of the unbound GBC. Considering that quantum-chemical calculations predict that for both forms of GBC, i.e. bound and cation-free, there is a negligible two-photon absorption cross section corresponding to S1 ←S0 transition, one may put forward a notion that it is the second excited state which gives the strong signal in the experimental nonlinear spectrum. This is schematically presented in Figure 6 which includes comparison between experimental measurements and the results of computer simulations. Experimental 13-fold enhancement of two-photon absorption cross section upon zinc ion binding can, presumably, have two sources: i/ 3-fold increase of two-photon absorption cross section for second excited state, ii/ red shift of absorption band corresponding to S2 ←S0 transition. To explain the differences between the one-photon and two-photon band intensities for the first and second excited state as well as the changes in σ (2) upon coordination to the zinc cation, we made an attempt to gain insight into the role of particular excited states involved in the absorption process. In so doing, we employed the generalised few-state-model (GFSM) proposed by Alam and coworkers. 71 The GFSM is derived from the sum-over-states

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approach 72 and re-evaluates the overall expression of the TP activity as a sum of three terms dependent on the magnitudes and orientation of transition moments and the excitation energies to a given intermediate state: 0→f = δ ii + δ jj + 2δ ij , δ3SM 2 8 |µ0i | · |µif | ii 2 if δ = · 2cos θ + 1 , ω 0i 30 ωi − 2f 16 |µ0i ||µ0f ||µif ||µf f | ij · δ = ω 30 ωf (ωi − 2f ) ff if if 0f ff ff )cos(θ0i ) , ) + cos(θ0f )cos(θ0i ) + cos(θ0i )cos(θif · cos(θ0f

(1) (2) (3)

where the 0 and f stand for the ground and final state; i, j are intermediate states and ~ω is the excitation energy to a given state. In our treatment, we included three states: the ground, first and second excited state. Corresponding transition moment vectors were extracted from the residues of quadratic response functions in the time-dependent density functional theory (TDDFT) framework. Note that the results from GFSM analysis are consistent with the exact quadratic response calulations as one can see from Table 4. This confirms the validity of the adopted three-state model. It is also evident that the term corresponding to channel interference, δ ij , has a negligible contribution to the δ3SM , even though several reports can be found in the literature on its either constructive or destructive influence on two-photon activity, depending on the orientation of transition vectors. 73–76 Since the performed optical channel analysis did not provide an explanation of different two-photon response for investigated GBC species, we studied the contributions to δ 11 , δ 22 and δ 12 in detail. Results are shown in the Table 5. The terms: µ00 , µ11 and µ22 describe the dipole moment in the ground, first and second excited state. Not surprisingly, the trans-GBC exhibits zero dipole moment, since the TTTT geometry has a center of inversion symmetry. The dipole moment appearing upon binding to Zn2+ results both from loosing inversion symmetry and from intramolecular charge transfer. Moreover, as seen from Table 5, vanishing TPA cross section for trans-GBC corresponding to the transition to the first 11



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excited state can be directly linked with µ02 = 0 and µ11 = 0. It is also evident that twophoton response enhancement upon binding to Zn2+ is triggered mainly by the increase of |µ12 | from 4.87 to 7.82 a.u. with a concomitant decrease of energy gaps, ~ω1 and ~ω2 , from 0.119 to 0.103 a.u. between ground and first excited state and from 0.136 to 0.123 a.u. between ground and second excited state. We conclude this section with a schematic representation of optical channel analysis depicted in Figure 7.

CONCLUSIONS In this work we have presented the results of theoretical investigations of the mechanism of Zn2+ sensing of the ratiometric molecular probe, studied experimentally by Divya and coworkers. 42 Our efforts were aimed at understanding a strong enhancement of its nonlinear properties upon binding to zinc ions. Due to the fact that GBC structure rearranges during cation coordination, three molecular species, namely: trans-GBC, cis-GBC, cis-GBC*Zn2+ , and their ten stable conformers, were examined. The performed linear response calculations revealed that one-photon features are completely dominated by the absorption to the first excited state, via π → π ∗ transition, yielding the peaks at 396 nm and 441 nm, for cation-free and bound probe correspondingly, that is in line with the experimental data. Considering that quantum-chemical calculations predict that for both forms of GBC, i.e. bound and cation-free, there is a negligible two-photon absorption cross section corresponding to S1 ←S0 transition, one may put forward a notion that it is the second excited state which gives the strong signal in the experimental nonlinear spectrum. Experimental 13-fold enhancement of two-photon absorption cross section upon zinc ion binding can, presumably, have two sources: i/ 3-fold increase of two-photon absorption cross section for second excited state, ii/ red shift of absorption band corresponding to S2 ←S0 transition. In order to explain the variations of two-photon intensity, we have employed the threestate model. Results indicate the pivotal role of the first excited state which makes an

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important contribution to TPA activity for S2 ← S0 transition through sum-over-states expression. Moreover, this study demonstrate that the increase of the magnitude of transition moment (µ12 , from the first to the second excited state) is the source of a three-fold increase of two-photon activity, which stems from the intramolecular charge-trasfer upon binding to zinc ion. Finally, let us conclude that this work indicates that computational techniques, i.e. nonlinear response functions combined with density functional theory, can successfully be applied to analyze important metal ion probes used for biomolecular detection using nonlinear spectroscopy.

Supporting Information Details of the computational protocol and its assessment are given in the Supporting Information. Figure S1 and S2 depict geometries of trans-GBC, cis-GBC and cis-GBC*Zn2+ conformers. Histograms determined based on the results of polarizable embedding linear response calculations are presented in Figure S3 and S4. Geometries of models of bound probe are shown in Figure S5. Table S1 includes relative energies of trans-GBC, cis-GBC and cis-GBC*Zn2+ conformers. Table S2 presents relative energies of trans-GBC conformations with different arrangement of 2-methoxyethyl groups. The values of energy difference for cis-GBC and trans-GBC for various conformers are listed in Table S3. Table S4 contains wavalengths and oscillator strengths corresponding to the vertical S1 ←S0 transition for the conformers of trans-GBC. Table S5 presents a summary of average excitation energies and standard deviation values obtained from gaussian fitting and from statistical population analysis for trans-GBC and cis-GBC*Zn2+ . Table S6 demonstrates a comparison of exchange-correlation functionals in the calculations of two-photon absorption cross section. Table S7 contains two-photon absorption cross section values for considered coordination models. Summary of two-photon cross section calculations performed based on three state model is given in Table S8, S9 and S10. This material is available free of charge via the Internet at http://pubs.acs.org.

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Acknowledgement J.B. thanks the Polish Ministry of Science and Higher Education for financial support (Grant 0237/DIA/2014/43). R.Z. acknowledges financial support from the Polish National Science Centre (Grant No. DEC-2013/10/A/ST4/00114). M.O. acknowledges financial support from the Swedish Research Council (VR) and the Carl Trygger Foundation. The calculations were performed in part at the Wroclaw Center for Networking and Supercomputing. This work was also supported by the Swedish Infrastructure Committee (SNIC) for the project ”Multiphysics Modeling of Molecular Materials” (SNIC2015-16-10).

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Page 24 of 36

Table 1: Boltzmann population [%] of the GBC conformers in water calculated at the B3LYP/6-31+G(d) level of theory. Zero-point vibrational energy is included and entropic effects are assumed to be equal for all conformers. Conformer

trans-GBC

cis-GBC

cis-GBC*Zn2+

TTTT CTTT CTTC TCTT CCTT CTCT TCCT CCTC CCCT CCCC

26 19 14 9 7 7 6 5 4 3

27 17 12 11 8 8 4 7 3 3

28 21 15 7 7 6 5 5 4 2

24


Page 25 of 36

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 2: Summary of the experimental measurements of the one- and twophoton absorption spectra for the species in 1:1 acetonitrile-water solution. 42

trans-GBC cis-GBC*Zn2+

OPA

TPA

λmax [nm]

λmax [nm] σ (2) [GM]

403 430

25

800 815


107 1433


Table 3: Two-photon absorption cross section corresponding to transition to the first (S1 ) and the second excited state (S2 ) of trans-GBC, cis-GBC and cisGBC*Zn2+ calculated at the CAM-B3LYP/TZVP level of theory. E denotes the energy difference between the excited state and the ground state.

cis-GBC

trans-GBC

Conformer

cis-GBC*Zn2+

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 36

E [eV]

TTTT CTTT CTTC TCTT CCTT CTCT TCCT CCTC CCCT CCCC

3.13 3.11 3.10 3.16 3.14 3.14 3.19 3.13 3.17 3.15

TTTT CTTT CTTC CCTT CTCT TCCT CCTC CCCT CCCC TTTT CTTT CTTC TCTT CCTT CTCT TCCT CCTC CCCT CCCC

λ[nm] σ (2) [GM] S1 ←S0

E [eV]

396 399 399 392 395 395 388 396 391 394

0 1 0 6 2 2 0 0 1 0

3.69 3.65 3.61 3.72 3.67 3.67 3.73 3.63 3.68 3.64

3.23 3.21 3.19 3.24 3.23 3.29 3.22 3.28 3.26

384 386 389 383 384 377 385 378 380

1 0 1 0 7 14 2 7 2

2.81 2.81 2.80 2.88 2.87 2.87 2.93 2.86 2.92 2.91

441 441 442 430 432 432 423 433 424 426

2 0 5 10 2 23 43 11 23 10

26

λ[nm] σ (2) [GM] S2 ←S0 336 340 343 333 338 338 332 341 336 341

1396 1107 933 1240 993 1027 1131 844 867 720

3.72 3.67 3.63 3.68 3.69 3.75 3.65 3.71 3.66

333 338 342 337 336 330 340 334 339

1016 824 678 716 725 764 604 609 511

3.35 3.34 3.32 3.42 3.39 3.40 3.46 3.38 3.44 3.42

370 371 373 362 366 365 358 366 360 363

3517 3271 3022 3341 3014 2966 2843 2750 2712 2580


Page 27 of 36

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 4: Two-photon cross section (given in [GM]) values calculated at the CAM-B3LYP/TZVP level of theory employing the three-level model.

trans-GBC cis-GBC cis-GBC*Zn2+

σ 11

σ 22

σ 12

0→2 σ3SM

0→2 σexact

1279 1003 3161

0 1 9

0 -10 56

1279 984 3282

1396 1016 3517

27



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Page 28 of 36

Table 5: Terms contributing to δ 11 . All values are given in a.u. |µ00 |


|µ01 |

|µ11 |

|µ12 |

|µ02 |

|µ22 |

ω1

ω2

0 6.510 0 4.878 0 0 0.115 0.136 1.845 6.345 2.018 4.587 0.755 2.177 0.119 0.136 7.602 6.303 7.346 7.825 0.544 7.107 0.103 0.123

28


12 |cos θ01 |

0.999 0.999 0.999

22 |cos θ02 |

0.555 0.834 0.968

Page 29 of 36


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2: Potential energy profile for the TTTT conformer of cation-free GBC in water and in vacuo. Calculations were performed at the B3LYP/6-31G(d) level of theory employing either frozen or relaxed geometries.

30


Page 30 of 36

Page 31 of 36

OPA exper. GBC OPA sim. trans-GBC 2+ OPA exper. GBC*Zn 2+ OPA sim. cis-GBC*Zn

a) Normalized inten.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


b)

2.6 2.8 GBC flex.

c)

GBC rigid

S1 S2

d) GBC*Zn2+ flex.

S1 S2

e) GBC*Zn2+ rigid

S1 S2

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2 S1 S2

3.0

3.2 3.4 3.6 EOPA [eV]

3.8

4.0

4.2

Figure 3: a) Experimental and simulated one-photon absorption spectra. All absorption band maxima are normalized to allow comparison of spectral features. b)-e) Normalized histograms determined based on the results of polarizable embedding linear response calculations for uncorrelated GBC configurations sampled from either RBMD or FBMD simulations. Each histogram is fitted by the normalized gaussian function. Shown is the number of configurations per energy interval equal to 0.025 eV. 31



2+

Norm. inten.*pop[%]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 36

trans-GBC fit trans-GBC conformers

cis-GBC*Zn fit 2+ cis-GBC*Zn conformers 1

2.6

2.7

2.8

2.9

3.0

EOPA [eV]

3.1

3.2

3.3

3.4

Figure 4: Simulated absorption bands corresponding to the transition to the first excited state of the most stable conformers of trans-GBC and cis-GBC*Zn2+ . The intensities of component bands were weighted by conformer population and normalized. Dark red and dark green lines correspond to the convoluted spectra, assuming constant Gaussian broadening for each transitions (σ=0.08 eV).

32


Page 33 of 36

4000


3500

(2)

[GM]

3000 2500 2000

σ 1500 1000

CCCC

CCCT

CCTC

TCCT

CTCT

CCTT

TCTT

CTTC

CTTT

500 TTTT

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Conformers Figure 5: Calculated two-photon absorption cross section values corresponding to the second excited state of trans-GBC, cis-GBC and cis-GBC*Zn2+ .

33



TPA exper. GBC TPA sim. trans-GBC 2+ TPA exper. GBC*Zn 2+ TPA sim. cis-GBC*Zn

3000

σ(2) [GM]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 36

2000

1000

1.2

1.4

1.6

1.8

2.0

2.2

E [eV] Figure 6: Comparison of experimental and simulated two-photon absorption spectra of the cation-free and bound GBC. Simulated bands correspond to S2 ←S0 transition.

34


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

TOC Graphic

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Elucidating the Mechanism of Zn2+ Sensing by a Bipyridine Probe

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