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Optical Nature and Binding Energetics of Fluorescent Fluoride Sensor Bis(bora)calix[4]arene and Design Strategies of Its Homologues Jaehyeok Jin,† Ji Young Park,‡ and Yoon Sup Lee* Department of Chemistry, Korea Advanced Institute of Science and Technology (KAIST), Yuseong-gu, Daejeon 34141, Korea S Supporting Information *

ABSTRACT: We report a theoretical assessment on F− sensing with bis(bora)calix[4]arene, a known fluorescent sensor. Geometries of bis(bora)calix[4]arene and its fluoride-binding complex are optimized at the ONIOM(B3LYP/631+G(d):B3LYP/3-21G) level of theory in both the gas phase and the CH2Cl2 solution by using the Polarizable Continuum Model (PCM). Decreases in UV absorption and fluorescence of bis(bora)calix[4]arene upon F− binding are explained by Time-Dependent Density Functional Theory (TD-DFT) calculation. The theoretical calculations indicate that the fluorescence quenching behavior when F− binds with bis(bora)calix[4]arene is the result of cooperative endo- and exo-bindings, which contradicts the previously reported experiment that suggested only the endo-binding. Furthermore, the observed fluorescence can be understood as an emission from the second and higher excited states via prompt fluorescence. This sensor-anion binding is predicted only with fluoride, but not with chloride or bromide anions. The substitution of boron atoms with group 13 and 15 atoms is also explored for the design of effective fluoride sensors. To predict the binding affinity, we calculate the binding energy of chemosensors with F−. Some of the substituted homologues studied here are expected to be potential fluoride sensors. In this regard, degrees of pyramidality and parallelity act as useful indicators to predict the binding affinity as well as the structure of both homonuclear and heteronuclear motifs.

1. INTRODUCTION The sensing and recognition of fluoride anions, the most electronegative anion, are areas of intensive attention because of their key roles in human health.1−6 It is well-known that adequate ingestion of the fluoride is highly related to dental care and the cure of osteoporosis.7−9 However, an overdose of fluoride can cause skeletal fluorosis and even destroy the immune system, leading to cancer.10 In this regard, the detection of fluoride anions has recently received intensive attention. Especially, fluorescent sensors appear to be an attractive detection method due to low cost, high sensitivity, and selectivity.11,12 A sensing of fluorescent sensors accompanies quantitative changes in colorimetric visualization upon complexation with anion. Up to now, several research groups have developed efficient fluoride sensors based on hydrogen-bonding interaction, chemodosimetric reaction, π-conjugation framework, and electrostatic interaction.6,13,14 Corresponding selectivity and binding affinity are highly affected by the topology of the sensor molecule.15 Calixarene, a methylene bridged cyclic oligomer of phenols, has received significant attention as a framework for selective anion sensing due to its conformational flexibility.16−18 There are a wide variety of calixarene derivatives that have been designed for binding with distinct ions and even molecules, including calix[4]crown, thiacalix[4]crown, calix[4]pyrrole, calix[4]imidazolium, and tetrahomodioxacalix[4]arene.19−24 © XXXX American Chemical Society

Among the derivatives of calix[4]arene, bis(bora)calix[4]arene is of particular interest because the oxygen atom between the main ring and organoboron can provide the space adequate only for F−. Arimori and co-workers synthesized and characterized a selective and fluorescent fluoride sensor, bis(bora)calix[4]arene (denoted as 1 hereafter).25 Experimentally, 1 acts as an efficient fluoride sensor by fluorescence quenching upon binding with fluoride. However, a detailed discussion of the binding and corresponding colorimetric changes has not been reported.25 It is also important to note that 1 is the first calixarene derivative containing boron atoms in the lower rim. Therefore, some structural homologues of 1 are worth investigating for their capacity as heteronuclear or homonuclear sensor molecules.6 It has been suggested that some heteronuclear motifs including P, B, Sn, Sb, and Hg act as Lewis acidic fluoride sensors and consequently accompany the spectroscopic changes.6,26−30 Also, the newly reported route to synthesize 1 using perfluoroaryl substituents indicates an experimental possibility to construct the homologues of 1.31 Herein, we report a theoretical study of 1 for the first time. The detailed investigation is based on the Density Functional Theory (DFT) and Time-Dependent DFT (TD-DFT) Received: July 5, 2016 Revised: September 13, 2016

A

DOI: 10.1021/acs.jpcc.6b06729 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C calculations and is composed of three parts:32−34 structural and electronic property of 1 and binding complex with F− (denoted as 1-F), theoretical insights on the optical nature originated from higher excited states, and design of a new and effective fluoride sensor as homologues of bis(bora)calix[4]arene. First, the calculated structural properties demonstrate the suitability of using DFT approaches through comparison with the experiment by Arimori et al.25 Simulated spectra from the ground and higher excited states provide the nature of changes in fluorescence. Furthermore, novel fluoride sensors are searched by substituting boron atoms in 1 with other atoms (Al, N, and P) and predicting their binding affinity with F− using a simple structural indicator.

The main reasons for defining the two layers are based on two factors: most of the host−guest interactions are expected in layer A, and the t-butylbenzene groups in layer B present high steric hindrance. Unlike a single B3LYP calculation with two types of basis sets, the ONIOM method utilizes the link atom connection between the layers. The validity of this two-layer ONIOM(QM:QM) model is supported by comparisons of the structural parameters listed in Table 1a as well as from agreement between computed absorption behavior and experimental data, which will be discussed later. The minimum-energy structure of the binding complex 1-F is also optimized at the same level of theory while freezing the lower layer. In this contribution, solvent effects are considered by the Polarizable Continuum Model (PCM),40,41 in which the chloroform solvent is regarded as the continuum with permittivity ε = 4.7113. In terms of computing the binding energy, single point energies corresponding to optimized structures are calculated using the B3LYP functional with two different basis sets, 6-311G and 6-311G(d). The Basis Set Superposition Error (BSSE) is corrected using the counterpoise (CP) correction to obtain a better estimate of binding energy.42 To validate the optimized geometry, we calculate the 1H NMR chemical shifts and compare the simulated spectra with the experimental NMR spectra.25 NMR shielding tensors and corresponding chemical shifts are computed by the Gauge Independent Atomic Orbital (GIAO) method.43 To consider long-range interactions in the calix[4]arene framework,44,45 Barone and Adamo’s Becke-style one-parameter functional using modified Perdew−Wang exchange and Perdew−Wang 91 correlation method, MPW91PW91,46,47 with 6-31G(d,p) basis set is used to calculate the 1H chemical shift of preoptimized geometries for both 1 and its fluoride-binding complexes. Furthermore, TD-DFT calculation is used to optimize the structure and calculate vertical excitation energies of excited states.34 Among the tested methods, the PBE1W,48 a generalized gradient approximation (GGA) functional, with 6311G(d) level of theory is the most reasonable and effective method to reproduce the experimental data and structural behavior of calix[4]arene in the solution phase. The calculated TD-DFT spectra are analyzed using the Chemissian program.49

2. COMPUTATIONAL DETAILS In this work, all calculations are performed via the Gaussian 09 program package with several density functionals.35 After the consideration of previously conducted studies,36 we choose the B3LYP37,38 functional to perform geometry optimization. The overall geometry is optimized by the two-layer Our-own-Nlayered Integrated molecular Orbital and molecular Mechanics (ONIOM) method to impose accuracy on the binding site while maintaining calculation efficiency; see Scheme 1.39 For the ONIOM(QM:QM) calculations, we define layer A (lower rim) as high layer with B3LYP/6-31+G(d) and layer B (upper rim) as a lower layer with B3LYP/3-21G level of theory. Scheme 1. Structure Optimization by Using the Two-Layer ONIOM(QM:QM) Model

3. RESULTS AND DISCUSSION 3.1. Optimized Geometry of Bis(bora)calix[4]arene. The optimized structure of 1 with labeled atoms is shown in Figure 1, and some important geometry parameters, experimental data from X-ray scattering, and charge population analyses are summarized in Table 1.25 The vibrational Table 1. Geometrical Properties and Population Analyses Using ONIOM(B3LYP/6-31+G(d):B3LYP/3-21G) (a) Structural Parameters bond length (Å) experimenta calculation δ (difference)

a

B50−O45

B50−O47

O47−C24

O45−C14

1.3698 1.3781 0.0083

1.3844 1.3763 −0.0081

1.390 1.382 1.4004 1.399 0.0104 0.017 (b) Mulliken Charge Analysis

C12−C9

C6−C1

1.5235 1.3883 1.5284 1.4005 0.0049 0.0122 (c) NBO Charge Analysis

B49−C62 1.536 1.547 0.011

state

boron (l)

boron (r)

state

boron (l)

boron (r)

gas acetonitrile chloroform

1.030 0.958 0.960

1.030 0.958 0.960

gas acetonitrile chloroform

1.123 1.133 1.133

1.123 1.133 1.133

From ref 25. B


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The Journal of Physical Chemistry C

0.958 (Mulliken) and 1.133 (NBO), and in the chloroform solution as 0.960 (Mulliken) and 1.133 (NBO). Moreover, the positive charge at boron is the key to understanding the ability of 1 to bind to F− in this Lewis acid−base reaction. The result that the assigned charges at each side of boron atom are identical can be understood by the symmetry of chemical environments at each boron atom. 3.2. Validation of the Calculation Methods and Computed Structure. To validate the optimized structure, we compare the structural parameters and 1H chemical shift with previous experimental results. Table 1a compares several selected bond lengths of 1. The difference (δ) between experiment and calculation is negligible with the maximum difference smaller than 0.02 Å. The 1H NMR chemical shift is calculated and compared to the experimental NMR spectra data to complement the structural validation of the compound. The calculation is held in the acetonitrile solution using the PCM (ε = 35.688) to describe solvent environment in the experiments. The GIAO calculations are performed using the MPW91PW91, which has been proven to be accurate for calixarene derivatives.44,45 Virtually reproduced chemical shifts of 1, provided in Table S1, agreeably match with the experimental values.25 3.3. Optimized Geometry of 1-F. On the basis of the calculations of 1, we optimized its fluoride-binding structure (denoted as 1-F). Arimori et al. suggested from experiment that 1 works as 1:1 complex with F−, proposing the binding in the endo-mode rather than in the exo-mode because of the steric hindrance by stacked benzene walls.25 However, in the present study, both the endo- and the exo-modes are proposed as binding complexes. The calculated molecular orbitals (MO), especially the lowest unoccupied molecular orbital (LUMO) of 1 and the highest occupied molecular orbitals (HOMO)−1 and HOMO−4 of both endo-1-F and exo-1-F, are depicted in Figure 2. Notably, localized electron density near the boron atoms indicates that bonding with F− would occur only at both the endo- and the exo-modes. The top-view and side-view of the LUMO (Figure 2a) show that the interaction should take place in the middle of upper plane and each side of the boron atoms. An interesting property of calix[4]arene is that calix[4]arene forms a square-like ring because of t-butylbenzene; thus the four edges of 1 are available to bind to F− via the exo-manner. However, computational results indicate that the exo-binding is likely to happen only with left (B50 in Figure 1) or right (B49 in Figure 1) boron. The LUMO depicted in Figure 2a shows the presence of high density in the localized region between the two boron atoms. Also, the HOMO−1 and HOMO−4 of both endo-1-F (Figure 2b) and exo-1-F (Figure 2c) show the interaction picture between the F− and 1. Optimization of each complex is carried out by the same method employed for the neutral receptor molecule. For the

Figure 1. Optimized structure with labels for selected atoms of bis(bora)calix[4]arene using ONIOM(B3LYP/6-31+G(d):B3LYP/321G).

frequency calculation is conducted at the same level as the geometry optimization and shows that the optimized structure is a local minimum on the ground-state energy surface. Detailed results are described in the Supporting Information section S2. The distance between the two boron atoms is 3.621 Å, and the angle between the two benzene rings is 95°. A slight deviation from the parallel conformation of two benzenes is due to the short distance between two boron atoms.50 The benzene walls move slightly outside to reduce the repulsion. The spacing between boron atoms enables F− to interact with boron atoms via the endo-mode, which implies that the F− can occupy the space between the two boron atoms with a van der Waals diameter of 1.19 Å. Bonding angles from coordination to each boron atom are 118.9°, 119.2° (∠C−B−Os), and 121.9° (∠O−B−O), which indicate the locally planar structure at each boron atom. Differing from other boron-based chemosensors, this planar framework of 1 provides an additional binding site for F−.51 Especially, the outer space of 1 enables F− to bind to the boron atom (the exo-mode). We note that the upper rim of 1 (below the 16-membered ring) represents high steric hindrances; thus the binding can only happen in the lower rim of 1 (above the 16-membered ring). As can be seen from Table 1b and c, both Mulliken52 and Natural Bond Orbital (NBO)53,54 charges show that the two boron atoms are positively charged in the gas phase as 1.030 (Mulliken) and 1.123 (NBO), in the acetonitrile solution as

Figure 2. MO diagrams of 1 and fluoride binding complexes using B3LYP/6-311G(d). The green arrows point to the F−: (a) the top and side-view of the LUMO of 1; (b) the side-view of the HOMO−1 and HOMO−4 of endo-1-F; and (c) the side-view of the HOMO−1 and HOMO−4 of exo1-F (MOs with isovalue = 0.04). C


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Figure 3. Optimized structures of 1-F using ONIOM(B3LYP/6-31+G(d):B3LYP/3-21G) and electron density using B3LYP/6-311G(d): (a) optimized structure of endo-1-F; (b) optimized structure of exo-1-F; (c) electron contour map of endo-1-F; and (d) electron contour map of exo-1-F (isovalue = 0.004).

initial structure of the endo-binding complex, F− is placed at the midpoint that is equidistant to the two boron atoms. Although only the endo-binding is hypothesized in the experimental report, the exo-binding is also obtained in the calculations. In particular, exo-1-F gains stability by forcing the benzene walls to be parallel in a slightly staggered form. ∠B−F−B is 117.6° in endo-1-F, which indicates that F− is located between the two boron atoms and thus can interact with both atoms, but preferentially with one boron atom (see Figure 3c). Also, endo1-F is more stable than exo-1-F by 5.35 kcal/mol in the gas phase with 6-311G(d) basis sets. This additional stability can be understood by the interaction between boron and F−. In exo-1F (Figure 3d), F− can only interact with one boron laterally, and therefore the total interactions are much smaller than those in endo-1-F. Differences in the binding characteristics are provided by the Wiberg Bond Indices55 and electron density map in Figure 3d. The Wiberg Bond Indices of the B−F bonds in endo-1-F are 0.4626 (at left B−F bond in Figure 3a) and 0.0189 (at right B−F bond in Figure 3a), indicating preferential bonding with the left boron as shown by the electron contour map in Figure 3c. For exo-1-F, the Wiberg bond indices of the B−F bonds are obtained as 0.5290 (at left B−F bond in Figure 3b) and 0.0009 (at right B−F bond in Figure 3b), which correspond to the localized electron density between fluoride and boron in Figure 3d. 3.4. Binding Energy Analysis. The high selectivity of 1 can be understood by the binding energies of F− with 1. We calculate the BSSE-corrected binding energies of both the endoand the exo-bindings in the gas phase and chloroform solution (an experimental condition). In Table 2, binding energies in the chloroform solution are much smaller than those in the gas phase. For all cases, binding energies of the endo-binding are larger than those of the exo-binding, and this can be understood as the interaction characteristics between 1 and F− from previous sections. However, in the chloroform solution, both Cl− and Br− display positive binding energies. Especially, Cl− weakly binds with 1 in the gas phase, but the magnitude of binding energy is about 3−5% of fluoride binding. In the chloroform solution, further reduction for Cl− results in positive binding energy for the endo-binding, which means that the larger size of Cl− than F− prevents binding in the solution phase. This size effect is even larger for Br−. Because of the short distance between the two boron atoms, larger anions such as Cl− and Br− are less likely to access the region between two benzene walls, and therefore only the exo-binding is favorable. However, the large size of Cl− and Br− makes this

Table 2. Binding Energies for Halogen Atoms at Different Phases Using B3LYP/6-311G and 6-311G(d) Levels of Theory (kcal/mol) (a) Gas endo-

exo-

halogen anion

6-311G

6-311G(d)

F− Cl− Br−

−50.818 4.567 11.913

halogen anion

6-311G

6-311G(d)

F− Cl− Br−

−33.085 20.380 25.886

−40.149 13.381 20.354

−59.236 −3.750 5.352 (b) Chloroform

6-311G

6-311G(d)

−50.238 −2.738 8.367

−57.153 −2.469 4.243

endo-

exo6-311G

6-311G(d)

−28.914 −33.997 minimum not founda 3.969 3.672

“Minimum not found” implies that the optimization does not locate a minimum for the complex. a

interaction weaker than F−, which leads to positive binding energies (Figure S2). Especially, the nature of anion and sensor molecule in this system may enable us to understand the differences in binding affinities of F− with Cl−/Br− due to the size effect. First, because the halides do not have a directionality to the receptor due to the spherical structure, the selectivity is controlled by the size of the cavity of the receptor molecule.56 Also, the cavity size of 1 is determined by the distance between boron atoms of 1 and has a value of 3.621 Å. This cavity size is substantially larger than the reported ionic diameter of fluoride (2.48 Å) but smaller than that of chloride (3.62 Å) and bromide (3.92 Å).57 The tendency of the binding energy to correlate with the size of the halide ions is in line with the experimental data that report a selectivity of 1 only for fluoride by titration.25 3.5. 1H NMR Calculation of 1 and 1-F. The effect of an increased local electron density by F− can be observed from the 11 B chemical shift. For endo-1-F, the upfield shifts by Δδ = −17.19 and −0.01 ppm are observed for both boron atoms. However, for exo-1-F, the upfield shift by Δδ = −16.70 ppm is only observed at one boron binding site with F−, while the other boron shows a downfield shift by Δδ = 0.096 ppm. The 1H chemical shifts of 1-F complexes are also calculated to analyze electronic density differences and obtain structural information on the interaction of 1 with fluoride ion as shown in Figure 4. As compared to the simulated spectra of 1, some major shifts of proton peaks are observed. As shown in Figure D


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Figure 4. 1H NMR chemical shift calculation using MPW91PW91/6-31G(d,p): (a) Labeling scheme of hydrogen atoms in the main ring of 1. (b) Changes of the 1H chemical shift while binding with F−.

4a, the 1H chemical shift change takes place in the main 16membered ring of the calixarene. The first 1H chemical shift is the downfield shift of 11−33H by Δδ = 0.5 ppm. This downshift is ascribed to the changes in the charge population of atoms. The changes in Mulliken charge52 are 0.014 (11H) and 0.017 (33H) for the endobinding, 0.010 (11H) and 0.0093 (33H) for the exo-binding, which leads to the downfield shift. Similarly, a slightly upfield shift by Δδ = −0.6 ppm is assigned for 21−43H. This shift can be understood as the change in electron density from rearranging the two benzene rings in the lower rim. A shielding pattern is observed for 32− 21H and 28−7H by Δδ = −0.6 ppm, respectively. The calculated NMR spectra may serve as a guideline to identify complexes in experiment in the future. 3.6. TD-DFT Calculation and Fluorescent Behavior. In the discussion above, the complexation of 1 with F− is considered as both the endo- and the exo-bindings. However, previous experiment was only able to observe a colorimetric change rather than distinguish the binding mode from the two modes.25 The nature of an excited state is simulated by TDDFT calculations using PBE1W/6-311G(d). To demonstrate the behavior of the fluorescent sensor, we consider the following two points: • The absorbance near 320 nm is highly affected by binding with F−. • The measured fluorescence shows F− dependence for the peak near the 400 nm region. Thus, the absorbance of both the ground and the excited states at the 400 nm region is highly affected by binding with F−. First, to provide the detailed examinations on the characteristics of transition in the ground state, frontier MO composition58 by Mulliken population analysis is conducted. Table 3 lists frontier MOs that are highly correlated with electronic properties of 1. Detailed composition of 1 is carried out on the basis of significant fragments, including the two boron atoms as the reaction site, the main ring (a 16-membered ring) as the fragment displaying the major proton chemical shifts upon F− binding, the wall benzenes, and oxygen atoms that connect the boron atoms with the main ring. Interestingly, some MOs present similar electronic density compositions regardless of their energies. In the LUMO and LUMO+1, more than onehalf of the MOs are localized on the wall benzenes, and the rest of the MOs are observed at the boron atoms. A high contribution of the two boron atoms in unoccupied MOs is consistent with the binding between the boron and the

Table 3. Frontier Molecular Orbital Composition Using PBE1W/6-311G(d): Mulliken Percent Contributionsa composition (%) MO

wall benzenes

borons

oxygens

main ring

energy (eV)

LUMO+2 LUMO+1 LUMO HOMO HOMO−1 HOMO−2

0 66 60 0 0 7

0 21 23 1 1 2

0 5 6 20 20 10

100 8 11 79 79 80

−1.539 −1.818 −2.191 −5.141 −5.223 −5.563

a Detailed visualizations of fragments are represented in the Supporting Information.

fluoride. The wall benzenes are considered as electron reservoir due to their π orbitals. However, the HOMO and HOMO−1 have nearly identical composition, as 79% of the MOs is concentrated on the main ring. These nearly degenerate MOs with the same composition have most of the electrons populated in the hydrocarbon moiety of the main ring. However, dramatic differences are observed between the LUMO and LUMO+2. From the experiment, it is known that the majority of fluorescence changes near 370 nm.25 The calculated absorption spectra of 1, endo-1-F, and exo-1-F near the 370 nm region are shown in Figure 5. The obtained vertical transitions corresponding to Figure 5 at each absorption peak from the lowest energy are listed in Table 4. As shown in Table 4, the main transitions occur among the HOMO−1, HOMO, LUMO, and LUMO+1 with negligible contributions from the LUMO+2 and HOMO−2, reflecting clear differences in composition

Figure 5. Calculated UV−vis spectrum of 1, endo-1-F, and exo-1-F in the ground state using PBE1W/6-311G(d). The shape of the spectrum is obtained by employing Gaussian with half-width of 0.330 eV. E


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The Journal of Physical Chemistry C Table 4. Vertical Excitations of 1, endo-1-F, and exo-1-F with Corresponding Energies, Oscillator Strengths, and Its Contribution Using PBE1W/6-311G(d)

Table 5. Vertical Excitations of 1, endo-1-F, and exo-1-F near 320 nm with Corresponding Energies and Oscillator Strength Using PBE1W/6-311G(d)

(a) Bis(bora)calix[4]arene Λcalc (nm) band I band II band III

band I band II band III

(a) Bis(bora)calix[4]arene Λcalc (nm)

fcalc

416.25 HOMO → LUMO (71%) 0.0001 404.58 HOMO−1 → LUMO (70%) 0.0316 369.94 HOMO → LUMO+1 (70%) 0.0312 (b) Bis(bora)calix[4]arene with Fluoride (endo-Binding) Λcalc (nm)

band I band II band III

assignment

assignment

band A band B

Λcalc (nm)

assignment

fcalc

548.08 449.19 432.75

HOMO → LUMO (71%) HOMO−1 → LUMO (71%) HOMO → LUMO+1 (70%)

0.0000 0.0017 0.0057

fcalc

HOMO−1 → LUMO+3 0.0070 HOMO−4 → LUMO 0.2005 HOMO−2 → LUMO+1 (b) Bis(bora)calix[4]arene with Fluoride (endo-Binding) 313.87 325.40

Λcalc (nm)

fcalc

504.70 HOMO → LUMO (71%) 0.0000 443.22 HOMO−1 → LUMO (71%) 0.0002 430.90 HOMO → LUMO+1 (70%) 0.0069 (c) Bis(bora)calix[4]arene with Fluoride (exo-Binding)

assignment

band A band B band B′

band A band B band B′

assignment

fcalc

346.04 HOMO−1 → LUMO+3 0.0063 332.76 HOMO−4 → LUMO 0.0096 320.89 HOMO−2 → LUMO+1 0.0274 (c) Bis(bora)calix[4]arene with Fluoride (exo-Binding) Λcalc (nm)

assignment

fcalc

335.29 359.01 324.02

HOMO−1 → LUMO+3 HOMO−4 → LUMO HOMO−2 → LUMO+1

0.0003 0.0023 0.0006

illustrated in section S6. It appears that the HOMO to the LUMO excited state is the lowest excited state with vanishing oscillator strength, suggesting the dark-state nature of this state. For the excited-state properties of 1, we first calculate the S1 state optimized structures of 1 and endo-1-F. Optimized structures are discussed in section S5. Corresponding absorption spectra are obtained by TD-DFT calculation with the same level of theory as with the ground-state structures. Tables 4, 5, and S3 show that the vertical excitations of 1 and endo-1-F have all near-zero oscillator strengths, supporting the dark-state nature of the compound. Thus, we suggest that 1-F might have a long-lived dark-state that gives the near-zero oscillator strength and no emission for the transition to the ground state. The structures of the next excited S2 state are also computed using the same method. In Figure 6, a single point calculation from the S2 geometry of 1 shows two peaks at 320 and 420 nm. The peak near 320 nm quenches completely for 1F, which results in a peak with reduced oscillator strength near 380 nm, consistent with the experiment.25 Becuse of the nearzero oscillator strength from the S0 to the S1 transition by the TD-DFT calculation and the quenching pattern at the S2 geometry, the fluorescence pattern of 1 strongly implies emission from the higher excited states. This pattern violates Kasha’s rule, but may be plausible considering other known compounds that violate Kasha’s rule: azulene, cycl[3.3.3]azine, and ovalene.61 It is believed that the fluorescence emission from the higher excited states occurs through three different mechanisms: thermal population from the S1 state, reverse internal conversion from the S1 state via vibronic couplings, and prompt fluorescence from the S2 and the higher states without any involvement of the emission component.62 For the first case, the ratio of fluorescence quantum yield, ΦF(S2) , is

between the LUMO+2 and LUMO or the LUMO+1 and HOMO−2 or the HOMO and HOMO−1. The lowest energy transition band corresponding to the transition from the HOMO to the LUMO has vanishing oscillator strength. The second lowest energy transition band with a non-negligible oscillator strength, which corresponds to the transition from the HOMO−1 to the LUMO, is dramatically quenched for the endo-binding, but this transition is not fully quenched in the case of the side-binding. Also, the next lowest energy transition band (from the HOMO to the LUMO+1) is red-shifted with decreased oscillator strength upon fluoride binding. The experimental fluorescent spectra of 1 and 1-F indicated that the intensity was rapidly decreased around 400−450 nm region while adding F− with an emission maximum at 395 nm.25 The quenching pattern while binding with F− expected from the calculated absorption spectra is in line with the experimental quenching of intensity in fluorescence spectrum, in which the intensity was decreased by 20−45 times near 395 and 450 nm. We also conduct a similar calculation for endo-1-Cl, but no changes are observed in the oscillator strength, which implies that the quenching behavior is presumably related to the absorptivity of molecule. The above analysis based upon excitations from the ground state is valid when that the lowest excited state is not involved in the fluorescence and the structure is same for the emitting state and the ground state. Because there is no direct evidence on this, absorption and emission of the complex are examined in more detail. Also, as described in Figure 5 and Table 5, the region near 320 nm, the excitation wavelength used in the fluorescence spectroscopy, is the region of quenched oscillator strengths for the binding complexes, endo-1-F and exo-1-F.25 In Table 4a, the oscillator strength of the transition from the HOMO to the LUMO is calculated to be 0.0001 for the neutral 1 molecule and even smaller for the two 1-F complexes. This transition pattern is similar for all other DFT functionals considered when the TD-DFT calculation is performed at the ground-state structure optimized using respective functionals. As an example, when the CAM-B3LYP is chosen to correctly consider the effect of long-range corrections on the excitation energy in systems involving charge-transfer,59,60 the transition from the HOMO to the LUMO appears at 251.89 nm with the oscillator strength of 0.0004. Detailed calculations are

ΦF(S1)

kF ΦF(S2 ) = 2 × e−ΔE(S1− S2)/ kBT k F1 ΦF(S1)

where kFi is the intrinsic radiative constants of the Si state. The calculation of the energy difference of the S1 and S2 states accompanied by the thermal population from the S1 to the S2 states, Δ(S1−S2), is conducted by the scheme described in F


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Figure 6. Calculated UV−vis spectrum of 1 and endo-1-F using PBE1W/6-311G(d) from optimized structure in the S2 state: (a) 1; (b) endo-1-F (Gaussian half-width as 0.330 eV and NStates = 20; see the Supporting Information for the MO assignment).

section S7.63 The Δ(S1−S2) value for 1 is about 3910 cm−1, which gives the Boltzmann factor of approximately 6.2 × 10−9 at T = 298 K. When the ratio of the intrinsic radiative constants k F2 k F1

is 200, the ratio of quantum yield

ΦF(S2) ΦF(S1)

neighboring atoms (two oxygens and one carbon) and can interact with F− through the endo- and exo-bindings. However, the effective distance of 1, which is determined by the difference between the van der Waals diameter of the boron atom and the distance between the two boron atoms, restricts further interactions with Cl− and Br− because of the large size of nonfluoride anions. The pyramidality at the center can thus affect the effective distance of the sensor. We use the degree of pyramidality, defined as 360° − (x + y + z)°, as a direct indicator of the structure of the sensor to bind to F−.70 Although the effective space is estimated by the pyramidality of the center atom, the two benzene rings in the lower rim are important regions for controlling anion affinity. To implement these structural characteristics, we define the degree of parallelity as 180° − (a + b)° to quantify how parallel the two benzene rings are to each other; see Figure 7a and b.

is about 1.2 × 10−6.

The S1−S2 energy gap of 1 is higher than that of other chemical systems showing the S2 fluorescence through thermal population from the S1 state. For example, the reported systems are generally known as having Δ(S1−S2) smaller than 2000 cm−1, such as diphenyl, picene vapor, and hexane.62,64 Hence, it is unlikely that the suggested S2 fluorescence originates from the thermal activation of the S1 state. Also, the second mechanism can be ruled out due to the large S1 and S2 energy separation, Δ(S1−S2), of 1 at 3910 cm−1 and the fact that reverse internal conversion is not favorable in the condensed phase.64 Thus, it is conceivable that the fluorescence in 1 might originate from the third mechanism: the higher excited states contribute to the fluorescence by prompt fluorescence. This type of fluorescence does not involve thermal population or reverse internal conversion because of the increased Δ(S1−S2) value. The prompt fluorescence was reported for conjugated systems including azulene with Δ(S1−S2) = 14 000 cm−1, 1,3,5-heptatrienylbenzene with 4000 cm−1, and hexadecaheptaene with 5500 cm−1,62,65,66 and may be applicable to the present system containing six benzene rings. The computed oscillator strengths of fluoride-binding complexes indicate the existence of the dark-state feature and are consistent with experimental studies that some of the calix[4]arene molecule systems, including calix[4]arene-linked perylene bismide dimers and pure calix[4]arene molecule, have a long-lived dark-state even in solution.67,68 This dark-state is related to the strong vibronic coupling in the calix[4]arene system,61,69 which is also observed by laser spectroscopy of vibronic bands,67 and suggests that the quenching patterns of endo-1-F and exo-1-F could also originate from the internal conversion to the dark-state. Therefore, the observed fluorescence of 1 can be understood as an emission from the higher states by prompt fluorescence, and the quenched fluorescence of endo-1-F and exo-1-F might be a result of the dark singlet state by the vibronic coupling. 3.7. Examination of Other Potential Fluoride Sensors. In general, anion sensors that follow the Lewis acid−base formalism are dictated by structural characteristics of the center atom, which acts as a Lewis acid. We further apply the bindingselectivity and fluorescent probes of 1 by changing the structure of potential sensors slightly. In the case of 1, two boron atoms are located nearly in the plane formed by their three

Figure 7. Defining structural parameters: (a) The degree of parallelity. (b) The degree of pyramidality.

After defining the two structural parameters, we substitute boron atoms with other atoms. To retain the local structure of a bridging atom, we replace the boron atoms with elements in groups 13 and 15. This approach can be categorized by two motifs: homonuclear and heteronuclear motifs for the sensor molecule.6,71 An asymmetric structure of heteronuclear sensors allows them to have different binding affinities to anions. For homonuclear sensors, we substitute a boron center with aluminum, nitrogen, and phosphorus. Similar investigations are conducted for heteronuclear sensors, BP-1, BAl-1, and NP1. Geometry optimizations are performed at the same level of theory as 1, optimizing with ONIOM(B3LYP/6-31+G(d):B3LYP/3-21G) and calculating the single point energy with B3LYP/6-311G and 6-311G(d) by correcting the BSSE for each sensor motif. The optimized structures are depicted in Figure 8. Because UV−vis peaks of 1 originate from the interaction between F− and boron atom, interactions between F− and other elements in group 13 are expected to retain similar Lewis acid− base interactions. Although the interactions of F− with nitrogen and phosphorus in group 15 are not considered as simple Lewis G


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Figure 8. Optimized structures of homologues of 1 using ONIOM(B3LYP/6-31+G(d):B3LYP/3-21G): Homonuclear and heteronuclear sensors.

Table 6. Structure Properties of Potential Sensors Using ONIOM(B3LYP/6-31+G(d):B3LYP:3-21G) bridging angle (deg) x (a) Homonuclear Sensors BB 118.9 NN 108.13 PP 98.37 AlAl 120.71 (b) Heteronuclear Sensors BAl 122.6 BAl 115.8 NP 100.1 NP 111.8 BP 97.97 BP 119.0 a

distance (Å)

y

z

121.9 105.23 104.23 117.18

119.2 109.09 105.18 120.69

114.5 128.1 97.6 106.0 98.12 118.7

122.1 116.0 98.0 109.5 99.71 122.2

benzene angle

a

degree

pure

eff.

95.91 83.67 68.32 102.17

3.62 4.74 5.59 4.05

129.6 63.8 61.3 91.9 56.32 110.7

b

pyramid

parallel

−0.22 1.64 1.99 0.37

0.04 37.6 52.22 1.42

−11.82 12.65 43.35 −24.36

3.42

−0.34

−13.4

5.09

1.74

4.56

0.84

0.8 0.1 64.3 32.7 64.2 0.03

26.8 13.04

The two angles are almost identical for homonuclear cases. bThe effective distance is calculated from the pure distance value.50

acid−base interactions, TD-DFT calculations in the gas phase using PBE1W/6-311G(d) show the quenching behavior upon binding with F− (see section S8), suggesting effectiveness as fluoride sensors. In the treatment of 1, we regard the distance between two boron atoms as an effective space for allowing anion to interact with bridging atoms. The distance is calculated by the difference between the van der Waals diameter of bridging atom and the distance between bridging atoms. We also extend this structural property to homologues of 1 with different bridging atoms and listed all of the structural properties of potential sensors in Table 6. The homonuclear analogues of 1 show interesting structures. The Al-center sensor (AlAl-1) shows a structure quite similar to that of 1. Increased radius of aluminum enlarges both the open-angles between two benzenes (the degree of parallelity changes to 24.3 from 11.8) and the allocated space for binding while retaining its locally planar geometry (the degree of pyramidality slightly changes to 1.42 from 0.04). The overall structures rapidly change in the group 15 cases, as can be seen in Figure 8. Because of lone pair electrons, the degree of pyramidality is dramatically increased in both NN-1 and PP-1. For the group 15 cases, the upper rim is distorted from a square-like ring to a rectangular-like ring. These two possible conformations of the annulus are also explained by the isomerization of free calix[4]arene. Rozhenko et al. also reported that the square-like annulus corresponds to the crown conformation and the rectangularlike (squeezed) conformation corresponds to the boat conformation of the calix[4]arene. Relative stability of the

crown conformation is 4−5 kcal/mol lower than that of the boat conformation.72 We expect that the structural distortion is highly dependent on the structure of the upper rim, which can be conveniently estimated by the degree of pyramidality and parallelity. The effective distance is increased by the distortion of the upper rim, so the two benzene walls form an angle slightly smaller than 90° with the positive degree of parallelity. The major differences between NN-1 and PP-1 are caused by the extra orbitals in the phosphorus atom. As can be seen in Figure 8, heteronuclear homologues of 1 show mixed structures with two distinct centers in the molecule. This mixed nature is also apparent in the structural parameters. Interestingly, the degree of pyramidality of the one atom is not strongly affected by the other center atom. The degree of pyramidality of boron is less than 0.1 as compared to aluminum’s pyramidality of 1.42. For group 15 atoms, the pyramidality of nitrogen is between 50 and 60, but the value of phosphorus is near 30. In this regard, the degree of parallelity in the homologues with group 13 atoms is negative while that with group 15 is positive. The value of NP-1 is nearly between those of NN-1 and PP-1 (same analogy applies to the case of BP-1 and BAl-1). The most interesting point of heteronuclear homologues is the locally distorted geometry of center. The overall geometry is asymmetrical, and the benzene walls bend toward the aluminum atom in the case of BAl-1. Because of the larger van der Waals radius of the aluminum atom than the boron atom, the z-coordinates of the aluminum atoms are higher from the 16-membered ring than the boron atom, leading to the shift of both benzenes to retain the planar H


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fluoride via both the endo- and the exo-manners. In contrast to previous sensors such as NN-1 and PP-1, the binding energy in the exo-binding is higher than that in the endo-binding. The endo-binding of NP-1 is attributed to the extra space for F− by the distorted geometry of heteronuclear centers. However, the exo-binding is related to the presence of the phosphorus atom, and F− freely interacts with phosphorus via the exo-manner, leading to a higher binding energy than through the endomanner. In conclusion, our study in the homologues of 1 as potential sensors to detect F− suggests that AlAl-1 would perform as a better sensor than boron-based sensors because of positive charges. PP-1 sensor would be only sensitive to the exobinding. Heteronuclear motifs are expected to show the average binding performance between two homonuclear sensors composed of each center atom. While the homologues studied appear to have F−-sensing potential, their selectivity to F− over Cl− or Br− remains to be established.

geometry. The asymmetric structure also implies that the exobinding of fluoride with BAl-1 can only happen with boron. As compared to the geometry of BAl-1, the structure of NP-1 has distorted benzene walls toward nitrogen, probably due to the rigidity of the phosphorus atom. The distortion of BP-1 is a mixed result of both BAl-1 and NP-1. In this molecule, the phosphorus atom is located at a higher position from the main ring and phosphorus with high pyramidality (64.3), and boron with zero-like pyramidality (0.03) distorts the benzene walls as described in Figure S4. Also, the positive degree of parallelity for NP indicates closed benzene walls. Therefore, we expect that the NP-1 would prefer the exo-binding rather than the endo-binding. 3.8. Binding Energy Comparison. To consider the host− guest interaction in these potential sensors, we calculated the binding affinity in the gas phase to observe the intrinsic nature of complexation process.73 The binding energetics using B3LYP/6-311G and 6-311G(d) with BSSE corrections are summarized in Table 7. (Optimized structures are available in Figure S3.)

4. CONCLUDING REMARKS We report the quantum chemical characterization of the binding behavior of 1 with F−. By employing DFT calculations, we optimize the structure of 1 and the binding complexes with F−. It is shown that DFT using the ONIOM(QM:QM) model can provide optimized geometries in reasonable agreement with experimental chemical shifts and crystallographic data. In contrast to the previous hypothesis, we propose that the selective binding affinity of 1 with F− results from cooperative interactions between the endo- and exo-bindings, which are not observed with Cl− and Br−. Near 400−450 nm, known as the emission wavelength, vertical transitions calculated with TDDFT using the PBE1W functional are in close agreement with fluorescence and UV−vis properties. Changes in the absorbance estimated from the corresponding oscillator strength in this region are partially responsible for the fluorescent changes. In addition, the energy difference between the S1 and S2 geometries of 1 and the nature of vibronic coupling indicate that the fluorescence of 1 originates from a prompt fluorescence from the higher excited states, while no fluorescence is observed in the fluoride-binding complexes, suggesting the lack of prompt fluorescence. Vertical transitions from the HOMO or HOMO−1 to the LUMO or LUMO+1 are quite similar for 1 and 1-F despite the added F− for 1-F complexes. Changes in the 11B/1H chemical shift and MO analysis while binding with the fluoride are considered to understand the binding process. Homologues of 1 with Al, N, or P in the position of B are investigated for their effectiveness as fluoride sensors. The degrees of pyramidality and parallelity are useful to represent the structural properties and also correlate very well with roughly estimated binding affinities. We hope that this examination can provide an understanding of fluorescent fluoride sensors at the atomistic level and can suggest a blueprint for constructing potential sensors.

Table 7. BSSE Corrected Binding Energy Analyses Using B3LYP/6-311G and 6-311G(d) Levels of Theory (kcal/mol) (a) Homonuclear Sensor endo6-311G BB AlAl NN PP

−50.818 −133.50 7.2780 26.726

exo6-311G(d)

6-311G

−59.236 −50.238 −57.153 −135.79 −99.982 −103.47 1.1778 minimum not found 17.286 −32.164 −43.885 (b) Heteronuclear Sensor endo-

BAl BP NP

6-311G(d)

exo-

6-311G

6-311G(d)

6-311G

6-311G(d)

−86.636 −48.190 −19.211

−91.881 −56.231 −21.528

−64.754 −41.412 −29.352

−70.758 −47.635 −40.714

Similar to the binding profile of 1, binding energy analyses of AlAl-1 with the fluoride demonstrate preference to the endobinding rather than the exo-binding. Binding energies of AlAl-1 are −133.50 (6-311G) and −135.79 (6-311G(d)) kcal/mol for the endo-binding and are −99.982 (6-311G) and −103.47 (6311G(d)) for the exo-binding. The energy gap between 1 and AlAl-1 is 76 kcal/mol for the endo-binding and 46 kcal/mol for the exo-binding, and this energy difference indicates that the aluminum homologues are expected to bind to fluoride via the endo-mode rather than the exo-mode. This difference is due to more positive charge assigned at the aluminum atom. The endo-binding is observed in neither NN-1 nor PP-1 (positive binding energies) in the group 15 elements. The exobinding is only observed in PP-1, which corresponds to the fact that the phosphorus atom has expanded valence shell in comparison to nitrogen. In this regard, PP-1 could be an effective fluoride sensor, which accommodates only the exobinding with F−. For heteronuclear homologues, BAl-1 is predicted to bind to F−, with the binding energy between those of 1 and AlAl-1. As mentioned earlier, the exo-binding in BAl-1 is observed only with boron because of its distorted geometry. For BP-1, both the endo- and the exo-binding are observed with similar magnitudes in binding energies. NP-1 is predicted to bind to

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b06729. 1 H chemical shifts and vibrational analyses of 1 and 1-F, detailed fragments of frontier MO composition, and additional TD-DFT calculations in the excited state (PDF) I


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AUTHOR INFORMATION

Corresponding Author

*Tel.: +82-42-350-2821. Fax: +82-42-350-2810. E-mail: yslee@ kaist.edu. Present Addresses †

Department of Chemistry, The University of Chicago, 5735 South Ellis Avenue, Chicago, Illinois 60637, United States. ‡ Center for Catalytic Hydrocarbon Functionalizations, Institute for Basic Science (IBS), Daejeon 34141, Korea. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by the EDISON (EDucationresearch Integration through Simulation On the Net) project and NRF grants (2007-0056095, 2013K1A3A1A09076131). Y.S.L. thanks Prof. A. Rahmouni for discussion.

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