Structure-dependent luminescence of tetra-(4-pyridylphenyl)ethylene: a first-principles study

Abstract

Luminescent materials with tunable wavelengths have been attracting much attention due to their many promising applications. In the present work, the recently reported supramolecular coordination complexes of tetra-(4-pyridylphenyl)ethylene (TPPE) that produce variable-wavelength light emissions were investigated by time-dependent density functional theory (TDDFT) calculations. We discovered that variations in the luminescent wavelength of TPPE mainly depend on the structural deviations from molecular planarity, which affect the molecular orbital wavefunction distribution. An interesting trigonometric-functional relationship between the emission wavelength (the emission energy) and the dihedral angle defining deviations from molecular planarity was uncovered. The solvent effect was also considered to reveal the mechanism of the solvent-dependent fluorescence color. These findings may be helpful to rational molecular design for high-performance luminescent materials with tunable color.

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Fluorescent materials are widely used in many fields, such as fluorescent probes and sensors, bioimaging, light emitting diodes (LED) and so on.^1–4 Materials exhibiting wavelength tunability attract much attention⁵ because of the greater design versatility enabled by their more flexible fluorescence properties. As a consequence of Kasha's rule⁶—that fluorescence emission always occurs only from the lowest excited state to the ground state—the emission wavelength is independent of the excitation wavelength.⁷ This constraint greatly increases the difficulty of designing color-tunable luminescent materials. Shifting the fluorescence emission peak has been realized mainly by modifying the structure of chromophores,^8–10 requiring the independent synthesis of many molecules, each with a different emission wavelength. Recently, systems of solvatochromic luminogens exhibiting aggregation-induced emission (AIE) have been reported; by changing the solvents, the emission peak of these systems is tunable over a wide range.^11,12

Tetraphenylethylene (TPE) and its derivatives are well-known AIE fluorogens. These molecules are non-fluorescent in solution because the fast rotation of the phenyl rings and the twisting of the ethylenic C=C bond always quench the fluorescence.¹³ In contrast, they are strongly emissive upon aggregation due to restricted intramolecular rotation.^14–16 It has also been found that TPE can emit light when used as a ligand in metal–organic frameworks,^17,18 and some of its derivatives exhibit both solvatochromism and AIE properties.^11,19 Yan et al. found that a TPE-based ligand—tetra-(4-pyridylphenyl)ethylene (TPPE) used in coordination metallacages—exhibits solvent-dependent tunable emissions.¹⁹ They attributed these results to two factors: first, the solvent induces the formation of aggregates and further restricts the conformational flexibility of the fluorophores.²⁰ Second, the solvent polarity affects metal-to-ligand charge transfer (MLCT) and consequently shifts the emission color.²¹ However, detailed information on the solvent-induced aggregation and MLCT is still lacking, and so no mechanism has been established regarding how to predictively tune the emission wavelength of TPPE. Therefore, we started this theoretical research from the simplest molecular structure and identified an approach for tuning the luminescent wavelength characteristics.

In this work, we computed the structure, absorption and emission properties of TPPE, with its molecular planarity varied by changing the dihedral angles at two locations. The emission wavelength of TPPE shifted over a wide range with the variation of molecular planarity. The relationships between emission wavelength (the emission energy) and molecular planarity were explained by a trigonometric function. It was found that the molecular orbital wavefunction distributions affect the emission energy directly. Simulations of TPPE in different solvents showed that solvents could directly change the molecular structure in a small range, but this is expected to constrain the molecular configurations in the excited state by affecting the molecular aggregation behavior. Combining the relationships that we have found and reasonable assumptions about molecular configuration, we can successfully estimate the fluorescence wavelength range of TPPE in experiments.

All calculations were carried out with the Gaussian09 program.²² The ground state (S₀) equilibrium structures were optimized by density function theory (DFT)²³ at the B3LYP/6-31G(d) level.^24–26 Solvent effects were approximated using the polarizable continuum model (PCM),²⁷ and CH₂Cl₂ is the solvent unless mentioned otherwise. Time-dependent density functional theory (TDDFT) calculations at the same level of theory were carried out to simulate the electronic excited states.^28,29 The absorption spectra were generated by Doppler broadening based on the electronic structure. The emission wavelength (or the vertical emission energy of S₁) was calculated on the basis of the optimized structure of the lowest excited state (S₁). To ensure the adequacy of B3LYP, we also carried out parallel calculations using the PBE0³⁰ functional (Fig. S7, ESI†). The partitions of the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) of different organic groups were carried out according to the Mulliken population analysis scheme,^31,32 where the off-diagonal terms between the two atomic basis functions were equally divided.

Adjustments in molecular planarity were realized by changing the magnitude of the dihedral angle at two locations (α and β, Fig. 2), corresponding to rotation about the central C–C bonds and the ethylenic C=C bond, respectively. Optimization of geometry by adjusting each specified dihedral angle was computed using the keyword “Opt=ModRedundant”. During optimization, the dihedral angles between the phenyl rings and the ethylenic C=C bond were frozen, while the other degrees of freedom were allowed to relax.

The optimized geometry of TPPE at the ground state (S₀) is very well consistent with experiments (Table S1, ESI†). The simulated absorption spectrum is shown in Fig. 1b. There are three absorption peaks located at 395 nm, 339 nm and 292 nm. The peak at 395 nm corresponds to the lowest excited state (S₁), with an excited energy of 3.14 eV. The equilibrium geometry of the S₁ energy surface was obtained by TDDFT optimization. With TPPE in this geometry, the energy difference between S₁ and S₀ is 1.54 eV, which corresponds to a fluorescence wavelength of 803 nm. Energy this low means that the fluorescence of TPPE is likely to be very weak due to strong nonradiative relaxation. Moreover, the equilibrium geometry of S₁ is quite different from that of the ground state, such that in S₁ the phenyl rings have rotated 26° (corresponding to the α in Fig. 2a), and the ethylenic C=C bond has twisted about 45° with respect to S₀ (corresponding to the β in Fig. 2a). The active intramolecular rotations of these bonds consume the energy of the excited state through nonradiative decay and result in fluorescence quenching, as confirmed by experiments.^14,19

Fig. 1 The molecular structure of TPPE (a) and its simulated absorption spectrum in CH₂Cl₂ (b), and the transition orbital energies with wavefunctions of the lowest excited state S₁ based on the equilibrium geometries of the ground state S₀ (c) and S₁ (d), respectively. Here HOMO (LUMO) represents the highest occupied molecular orbital (lowest unoccupied molecular orbital).

Fig. 2 Two dihedral angles: α and β (a), defined by the four atoms in the center colored blue (red arrow indicates the rotation of the corresponding bond). Emission ability (reflected by transition oscillator strength) versus wavelength for TPPE with α (b) and β (c) varying from 0° to 80° respectively (the detailed data are shown in Table S2, ESI†). Plots of emission energy from the lowest excited state (S₁) of TPPE versus α (d) and β (e) varying from 0° to 120°.

The planarity of TPPE was abrogated by adjusting either of two dihedral angles: α or β (Fig. 2a). The angle α represents any of the four dihedral angles which reflect rotation of a given phenyl ring; these dihedral angles are almost equal due to the nearly perfect molecular symmetry. The angle β reflects the rotation of the ethylenic C=C bond. In the optimized structure of S₀, α is 50.0° and β is 12.8°. As we varied α from 0° to 80° with β at its optimized value in S₀, then optimized the geometries at S₁ with fixed α and β, the α-dependent fluorescent properties were investigated, and the β-dependent fluorescent properties were obtained in an analogous way. As shown in Fig. 2b and c, the emission wavelength blue-shifts from 730 nm to 350 nm with increasing α, while it red-shifts from 450 nm to 1250 nm with increasing β. Thus the deviations from planarity of TPPE determine its peak fluorescence wavelength as we predicted. Importantly, the range in emission wavelength is wide, exceeding the whole range of visible light. Thus there is great potential to exploit further the fluorescence properties of this molecule.

To further determine the relationship between emission properties and deviations from molecular planarity, we carried out calculations for a greater range of angles. According to the above discussions, the emission energy from S₁ increases as α increases from 0° to 80°. However, when α increases beyond 90°, the energy begins to decrease (see Fig. 2d). So the emission energy from S₁ was fitted to sin² α, achieving an R-square as high as 0.992 (see Fig. S2, ESI†). The function obtained is

E_S1,β=12.8° = a₁ sin² α + b₁ (1)

where the parameters a₁ = 1.862 eV and b₁ = 1.618 eV. Here, E_S1,β=12.8° denotes that the energies were obtained with β fixed at its optimized value of 12.8°. Similarly, β was fitted with a reciprocal tangent function. Fig. 2e shows the emission energy from S₁ plotted against the values of β from 0° to 120° (except 90° which is unsuitable for modeling). In the case of α fixed at its optimized value of 50.0°, the energy of the lowest excited state S₁ is governed bywhere the parameters a₂ = 0.1158 eV⁻¹ and b₂ = 0.3379 eV⁻¹. Here the R-square value is 0.989, suggesting good convergence. Replacing the emission energy with its reciprocal improves R-square (see Fig. S3a and b, ESI†).

Combining eqn (1) with eqn (2), the emission energy from S₁ can be written as

where parameter c = −1.109 eV. Eqn (3) describes the relationship between the emission energy from S₁ and the two dihedral angles more concretely. Based on it, the emission wavelength of TPPE at other angles can be predicted easily. A comparison of emission energies calculated by eqn (3) and TDDFT was performed, and the mean error is as small as 0.06 eV, with the largest individual one being 0.28 eV (Table S3, ESI†). This is definitely within the error bar of excitation energies calculated at the TDDFT level. Therefore, eqn (3) is qualified to predict the emission energy (or wavelength) of TPPE and avoid the complicated TDDFT calculations. Vice versa, it can help us to predict the possible configuration of TPPE according to its fluorescence wavelength, which is hard to do with TDDFT calculations.

The property of TPPE that intramolecular rotations change fluorescence performances is similar to the twisted intramolecular charge transfer (TICT) phenomenon.^33–35 In the case of β, the emission wavelength red-shifts and the intensity (reflected by transition oscillator strength) is weakened with the twisting of the C=C bond (the increasing β) (Fig. 2c), which looks like the TICT phenomenon. However, TPPE does not exhibit an appreciable intramolecular charge transfer property in both S₀ and S₁, even in an extremely twisted configuration (Fig. S5, ESI†), indicating that its mechanism is completely different from TICT. Moreover, the phenomenon of α is inconsistent with TICT. Therefore, the TICT mechanism may not be applicable to TPPE, and we will clarify the mechanism through the electron wavefunction distribution. The molecule TPPE can be divided into two regions: a central group—including the ethylenic C=C double bond—and a circumjacent group—including the four pyridylphenyls. The HOMO electronic wavefunction distribution shifts in opposite directions depending on whether α (Fig. 3a) or β (Fig. 4a) is varied. The wavefunction shifts outward from the central to the circumjacent region with increasing α (Fig. 3c) but becomes more centralized as β is increased (Fig. 4c). Shifts in the LUMO distribution behave similarly (Fig. 3c and 4c). These trends are in line with the excitation energy of S₁. It can be concluded that a more-centralized wavefunction lowers the excitation energy (in nm), as a result both of the increase in HOMO energy and the decrease in LUMO energy associated with the more centralized charge at smaller α (Fig. S6, ESI†). This phenomenon can be attributed to the interaction between groups. As α increases, the adjacent two phenyls approach a “face to face” configuration, which strengthens the π–π interactions between them. Conversely, molecular orbitals delocalized on the circumjacent groups become merged into the central group as β increases, weakening the π–π interactions between circumjacent groups.

Fig. 3 The percentage contributions to the HOMO (a) and LUMO (b) of TPPE made by the central ethylenic C=C group (red) and the other circumjacent groups (blue) as a function of α, and the spatial distribution of the HOMO and LUMO wavefunctions when α takes the values of 0°, 30°, 60° and 80° (c).

Fig. 4 The percentage contributions to the HOMO (a) and LUMO (b) of TPPE made by the central ethylenic C=C group (red) and the other circumjacent region groups (blue) as a function of β, and the spatial distribution of the HOMO and LUMO wavefunctions when β takes the values of 0°, 30°, 60° and 80° (c).

To reveal the solvent effects, we simulated the absorption spectra of TPPE in various solvents. As shown in Fig. 5a, the absorption of TPPE in different solvents occur at similar wavelengths (change from 393.7 nm to 396.9 nm), as well as the molecular structures at S₀ (Table S4, ESI†). As shown in Fig. 5b, the absorption of TPPE in different solvents occurs at similar wavelengths (change from 393.7 nm to 396.9 nm), as well as the molecular structures at S₀ (Table S4, ESI†). As shown in Fig. 5b, the size of β at S₁ increases with increasing solvent dielectric constant, and α is changed very little (less than 0.5°, Table S5, ESI†). More importantly, emission wavelength varies with dielectric constant in nearly the same way as β (Fig. 5b). Therefore, a polar environment tends to reduce molecular planarity and red-shifts the emission wavelength for monomer TPPE. Nevertheless, the molecular planarity and emission wavelength of TPPE are affected by solvents to a small degree (α changes from 24.0° to 23.6°, β changes from 55.0° to 57.8°, emission wavelength change from 763.5 nm to 802.7 nm). This indicates that the influence of solvent on a TPPE monomer is not prominent. However, it should be noted that the configurational change is significant from S₀ to S₁ for monomer TPPE (Tables S4 and S5, ESI†). In the case of CH₂Cl₂, α changes from 49.9° to 23.6° and β changes from 12.8° to 57.5°. An external physical confinement (such as aggregation) will restrict the intramolecular rotations, thus the configuration change from S₀ to S₁ will not be comparable with that in the monomer. Owing to these restrained factors on structures, the emission wavelength of TPPE is estimated to range from 450 nm to 800 nm (450 nm is calculated by eqn (3) substituting the values of α and β in the S₀ configuration; 800 nm is the emission wavelength of monomer TPPE as shown in Fig. 1d), and this range can be further narrowed to 450–640 nm considering that β is difficult to change in the aggregated state (640 nm is calculated by eqn (3) assuming that α is 23.6° and β keeps the S₀ value of 12.8°). The estimated emission wavelength range covers all of the experimental values (∼530 nm when TPPE is coordinated with Hg²⁺ and HSO₄⁻,¹⁴ 450–560 nm when it is incorporated into Pt(II) metallacages,¹⁹ and ∼465 nm when it is in a poor solvent³⁶) and validates our assumption. Similarly, one can predict the fluorescence wavelength range of TPPE in experiments more accurately if there is more specific structural information. In general, the stronger physical confinement results in the excited configuration being closer to the S₀ configuration and shorter emission wavelength. Consequently, the wide range of emission wavelength of TPPE in different solvents¹⁹ is fundamentally due to the deviations from molecular planarity in the excited state, as a consequence of solvent-induced specific aggregation behaviors which lead to different physical confinements. However, how the solvent affects the molecular aggregation behavior is still unknown and it is difficult to describe by quantum chemical calculations because it is computationally enormous. We will make efforts in this direction in future research.

Fig. 5 (a) Computed absorption spectra of TPPE in various solvents. (b) Plots of β and the emission wavelength versus dielectric constant of the solvent (the detailed data and α are shown in Table S5, ESI†).

In summary, we have revealed the primary cause of the variable-wavelength emission of TPPE—the deviations from molecular planarity which affects group interactions and leads to molecular orbital wavefunction redistribution, with a more-centralized wavefunction resulting in a lower emission energy. Mathematical expressions were presented to describe the relationship between emission wavelength (the emission energy) and molecular configuration, which can be applied to other TPE derivatives, providing a simple and convenient way to predict the emission wavelength. In addition, we expect that solvent-induced aggregation can affect the physical confinement on molecular planarity in the excited state and cause different emission colors, which will be the direction in our future research.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This work was financially supported by the National Basic Research Program of China (973 Program, No. 2014CB848900), the National Natural Science Foundation of China (No. 21633006, 21473166), and the CAS Strategic Priority Research Program B (No. XDB01020000).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp06643k

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