Aggregation-Induced Emission: Materials and Applications Volume 1

Chapter 4

Theoretical Insights into the Mechanism of AIE

Downloaded by CORNELL UNIV on October 2, 2016 | http://pubs.acs.org Publication Date (Web): September 27, 2016 | doi: 10.1021/bk-2016-1226.ch004

Qian Peng*,1 and Zhigang Shuai*,2 1Beijing

National Laboratory for Molecular Science, Institute of Chemistry, Chinese Academy of Sciences, 100190 Beijing, China 2Key Laboratory of Organic Optoelectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, 100084 Beijing, China *E-mails: [email protected] (Q.P.), [email protected] (Z.S.)

AIE has attracted considerable attentions. Better understanding of the mechanism of AIE can help to develop novel AIEgens and exploit novel applications. In this chapter, we have disclosed the microscopic mechanism of AIE by systematically investigating the steric hindrance effect, temperature effect, and aggregation effect on the fluorescence quantum efficiency through theoretical computations. Then we have proposed the plausible ways to probe the mechanism through establishing the relationship between unmeasurable geometrical reorganization energy and experimentally measurable emission and resonance Raman spectroscopy signals.

1. Introduction Traditionally, the investigations of molecular fluorescence are mostly carried out in solution phase. High fluorescence quantum efficiency is closely related to the extent of π-conjugation (1, 2). However, the large planar π-conjugation groups always form over strong intermolecular π-π interactions which would cause fluorescence quenching in concentrated solution or aggregate (1, 2). For a long time, numerous endeavors have been made to recover the solid-state fluorescence by using a variety of complicated physical and chemical methods, which have obtained limited successes (3–5). Since Tang et al. proposed the concept of aggregation-induced emission (AIE) in 2001 (6), a new possibility has been proffered in making highly efficient solid-state luminescent materials. The species of organic luminescent compounds have been unprecedentedly expanded, and both the “bright” and “dark” lumophores can now be chosen as the objects © 2016 American Chemical Society Fujiki et al.; Aggregation-Induced Emission: Materials and Applications Volume 1 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


of study. AIE has become one of the research hot spot in the field of organic luminescence. After considerable efforts in the past decades, hundreds of excellent AIEgens have been synthesized and applied for biological probes, chemical sensor and optoelectronic devices and so on (7). For the further development, it is a desirable but challenging task to reveal the mechanism of AIE at the level of first-principles calculations. Experimentally, considerable attempts have been invested to reveal the mechanism by means of lowering temperature, increasing the viscosity of solution, tuning the molecular stacking through substitution and controlling the aggregation degree and so on. Whereupon, several possible AIE mechanism have been claimed, such as the restriction of intramolecular rotational/vibrational motions (8), J-aggregation formation (9), excimer formation (10), twisting intramolecular charge transfer (11), hydrogen-bonding assistance (12) and so on. Theoretically, intrinsic characteristics have been investigated at various microscopic levels. Motivated by revealing the AIE mechanism, Shuai et al. have developed a vibration correlation function formalism for quantitative evaluations of the radiative and non-radiative decay rates for molecules and aggregate (13). This chapter will largely explore how this method can lead to the computational understanding of AIE at the first-principles level. Li, Hayashi and Lin found the geometrical changes are suppressed due to the molecular packing, which results in small Huang-Rhys factors and low nonradiative decay rate in the solid phase (14). Li and Blancafort adopted a conical intersection model to explain the AIE of diphenyldibenzofulvene (15). The aim of this chapter is to propose the mechanism of AIE through systematically analyzing the effects of steric hindrance, temperature and aggregation on the radiative and nonradiative decay rates at the level of first-principles. And then the mechanism is further confirmed by establishing the relationship between geometrical reorganization energy and experimentally measurable spectral Stokes shift and intensity of resonance Raman spectrum.

2. Theoretical Methodology and Procedure The decay processes for the excited states (Jablonski diagram) are shown in Figure 1. The radiative decay rate constant (fluorescence) from S1 to S0 is denoted as kF, the internal conversion rate constant from S1 to S0 as kIC, intersystem crossing rate constant from S1 to T1 as kISC, the radiative and nonradiative decay rate constants from T1 to S0 as kP and knr, respectively. It should be noted that the higher triplet states and the inverse intersystem crossing from T1 to S1 are not shown in Figure 1 because they are not involved in the AIEgens under investigation here. From Figure 1, the fluorescence quantum efficiency . The intersystem crossing rate is is very slow owing to extremely small spin-orbit coupling and relatively large energy gap between S1 and T1. Hence, kISC can be neglected for the AIEgens involved in the chapter.

36 Fujiki et al.; Aggregation-Induced Emission: Materials and Applications Volume 1 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


Figure 1. Jablonski diagram with straight arrows denoting radiative processes and wavy arrows representing nonradiative ones.

2.1. Spontaneous Radiative Decay Rate In the framework of quantum electrodynamics, the spontaneous photon radiative decay rate per molecule and per unit frequency (so-called the spontaneous emission spectrum) can be expressed as Eq.(1) based on Fermi golden rule and Born-Oppenheimer approximation (16).

Here c is the velocity of light in vacuum.

is the electric

transition dipole moment between the final (f) and initial (i) electronic states and

, which is dependent on the molecular vibrational normal coordinate

Q in principle.

and

is the vibrational wavefucntion of the i

and f electronic states, respectively. is the Boltzmann distribution of the vibration manifolds νi in the initial electronic state. For the strongly dipole-allowed transition, the zero-order term μ0 is dominant and other high-order terms are neglected. represents the adiabatic excitation energy of the two states including the electronic and vibrational states. Applying the Fourier transformation to the delta-functions,


The analytical path integral formalism for emission spectrum can be obtained as

where

is

the

partition


of

the

initial

state

manifold.

is the thermal vibration correlation function and . kB is the Boltzmann

(TVCF) with constant.

function

and

represent the multidimensional harmonic oscillator

Hamiltonian. For the k-th normal mode, they are

and

for the initial and final electronic states, respectively. Here,

and

are the k-th mass-weighted nuclear normal momentum operator

and normal coordinate operator. The eigenvalue of Hk is . By using multidimensional Gaussian integrations in the path integral framework, the TVCF can be easily solved analytically (17). More detailed derivations can be found in Ref. (18). The radiative decay rate is the integration of the spontaneous emission spectrum over the whole range,

The radiative decay rate is mainly determined by two factors, electric transition dipole moment and transition energy. The line-shape of the emission spectrum is determined by the overlap between the vibration states of the two electronic states, so-called Franck-Condon factor. In addition, the absorption coefficient of the absorption spectrum has the similar form with the emission one, see Ref. (18).

2.2. Nonradiative Decay Rate Different from the radiative decay process, the internal conversion is caused by the nuclear kinetic energy perturbation and under the Fermi Golden rule framework, its rate reads (19),

where

. 38 Fujiki et al.; Aggregation-Induced Emission: Materials and Applications Volume 1 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.

Applying the Condon approximation and Fourier transform, Eq. (5) turns into the solvable TCVF form as


with the nonadiabatic electronic coupling

and

the TVCF . The analytical solution and detailed derivations can be seen in Ref. (20). Eq. (6) tells us that the nonradiative internal conversion rate is mainly ruled by three factors. They are non-adiabatic electronic coupling, transition energy and the vibronic relaxation. 2.3. Computational Procedures and Details The detailed computational procedures are given in Figure 2. Firstly, the electronic structure calculations are performed to obtain the optimized geometries, harmonic normal modes, excitation energies and electric transition dipole moments at both the electronic ground and excited states, and non-adiabatic electronic coupling and spin-orbit coupling constants between the two electronic states by using quantum chemistry softwares. For the solution phase, the solvent environment can be described using the polarizable continuum model (PCM). For the aggregate, the environment is mimicked through the electrostatic inter-molecular interaction using the combination of quantum mechanics and molecular mechanics (QM/MM) approach. In view of the nature of localized excitation in the solid-state AIE molecules, it is appropriate to build a computational model by setting the central molecule as the QM part and the surrounding ones as the MM part for an enough large cluster (radius more than 50 Å) cut from the crystal structure. Because the number of heavy atoms in a normal AIEgen is in general more than fifty, the density functional theory (DFT)/time-dependent DFT (TDDFT) is an appropriate choice to balance accuracy and computational cost. There are quantum chemistry software programs such as GAUSSIAN 03 (21), TURBOMOLE 6.5 (22), QCHEM (23), NWCHEM (24), and ORCA (25) all possess the modules for DFT and TDDFT for the QM calculation. Our QM/MM calculations are carried out by using ChemShell 3.4 package (26) interfacing TURBOMOLE for QM and DL-POLY (27) for MM part. General Amber Force Field (GAFF) and the electrostatic embedding scheme are adopted to treat MM part and the QM/MM interactions, respectively. Based on the optimized geometrical Cartesian coordinates and normal modes, the displacement vector Di(f) between the two electronic state potential energy parabolas can be obtained by , where 4x is the displacement in Cartesian coordinates and the Li(f) is the mass-weighted normal modes of the initial (final) state. The correlation and difference between two electronic state potential energy parabolas is expressed as 39 Fujiki et al.; Aggregation-Induced Emission: Materials and Applications Volume 1 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.

for the

k-th normal mode. Here, S is called Duschinsky rotation matrix (DRM) (28), which measures the mixing degree between different normal modes of the initial


and final electronic states and is calculated by . Further combining the electronic transition dipole moment, non-adiabatic coupling or spin-orbit coupling constants, the spectra and different decay rates could be obtained according to the different modules selected in our home-built MOMAP program (29). The MOMAP program has a good interface with the popular quantum chemistry software mentioned above and can be downloaded freely. So far, it has been downloaded more than 1600 times by researchers from all over the world.

Figure 2. Structure of MOMAP: the computational procedures of molecular photophysical properties.

3. The Mechanism of AIE AIEgens always emit weakly in well solute phase while become strongly fluorescent in aggregate phase. This indicates that the radiative or non-radiative decay rate determining the quantum efficiency would be sensitive to different environments. It has been the center of controversy over whether AIE is caused by the enhancement in radiative decay or reduction in non-radiative decay, or the synergetic effect of both of them. Another question is about the role of intramolecular motions with respect to intermolecular interaction. In the following, we systematically study the effects of intramolecular steric hindrance, temperature and aggregation states on the radiative and non-radiative decay rates for the typical AIEgens. Through analyzing the key factors governing radiative and non-radiative decays, it is expected to figure out the mechanism of AIE and establish the structure-property relationships. 40 Fujiki et al.; Aggregation-Induced Emission: Materials and Applications Volume 1 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


3.1. Steric Hindrance Effect Silacyclopentadines (siloles) are the first and typical AIEgens, which exhibit high luminescence quantum efficiency in the solid phase relative to that in solution at room temperature (30). In order to look into the influence of the intramolecular motions on luminescence, a set of silole regioisomers were synthesized by attaching alkyl groups to the periphery rings to tune the molecular steric hindrance and their luminescence quantum efficiencies were measured (31). As found, the bulky alkyl groups dramatically boost the fluorescence efficiency. For instance, the iPr-HPS with isopropyl groups linking to 3,4-position phenyl rings of 1,1,2,3,4,5-hexaphenylsilole show much stronger fluorescence with efficiency of 83% in acetone compared with the parent HPS of 0.3% in cyclohexane. Here, we comparatively investigate the radiative and non-radiative decay rates of the two compounds with and without iPr-substitution (iPr-DMTPS and DMTPS) through quantitatively calculations and clearly reveal luminescence mechanism at the microscopic level (32, 33).

Figure 3. The optimized molecular structures and frontier orbitals of DMTPS and iPr-DMTPS. Both DMTPS and iPr-DMTPS are symmetrical to some extent with equal dihedral angles between the central silacycle and peripheric phenyl rings at 2, 5positons or 3, 4-postions (seen in Figure 3). It also is obvious that iPr-DMTPS is much spaciously crowed and the iPr-substituted phenyl rings twisted to larger angles of 65.5° than the corresponding unsubstituted ones of 58.0° in DMTPS. As a result, more space is released along the direction of C2-C5 in the plane of silole core and the torsional dihedral angles of the phenyl rings at 2,5-positions relative to silacyle decrease from ca. 48.5° to 21.4°. This coplanarity favors the molecular electric dipole transition. Because the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) mainly distribute in the central silacycle and phenyl rings at 2, 5-positions for the silole derivatives seen in Figure 41 Fujiki et al.; Aggregation-Induced Emission: Materials and Applications Volume 1 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


3. And the increase of the conjugation degree along the direction can induce larger transition dipole moment and assist the radiative decay process. As expected, the calculated radiative decay rate of iPr-DMTPS is 7.4×108 s−1, larger than 1.2×108 s−1 of DMTPS.

Figure 4. The reorganization energies versus the normal modes in DMTPS (a) and iPr-DMTPS (b). Contrary to the radiative decay rate, the calculated nonradiative decay rate of iPr-DMTPS is significantly smaller than that of DMTPS under the framework of the linear coupling harmonic model. From the rate theory presented in section 2, it is known that the non-adiabatic electronic coupling and vibrational relaxation are the two key factors to determine the nonradiative decay rate. The latter is more sensitive to the modification of the molecular geometrical structure than the former. Because the vibrational relaxation is characterized via the excited state reorganization energy which is directly determined by the degree of modification in geometrical structure between the excited and for the k-th normal ground states through the formula of mode. Therefore, the reorganization energy represents the ability to accept the excessive excited-state energy of the intramolecular motions and the normal modes with large reorganization energy are regarded as the main nonradiative decay channels. Figure 4 compares the reorganization energy of DMTPS and iPr-DMTPS. The total reorganization energy of DMTPS is 7550 cm-1, much larger than 3821cm-1 of iPr-DMTPS. There are four low-frequency ( 40 cm−1) in the low frequency region when going from solution to aggregate. More importantly, the RRS intensities are gravely reduced in the low frequency region while the ones are almost unchanged in the high frequency region for HPDMCb in aggregate relative to solution. These well characterize the nature of the molecular vibration change in the excited-state decay process in different environment. As expected, the RRS signals perfectly match the reorganization energy for all the normal modes. For instance, in solution the low-frequency modes of 24 cm−1, 51 cm−1 and 78 cm−1 have strong RRS signals and large reorganization energy while only the normal mode of 70 cm−1 in aggregation displays significant RRS signal and 53 Fujiki et al.; Aggregation-Induced Emission: Materials and Applications Volume 1 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


reorganization energy. However, the high-frequency vibrational motions are unaffected by the environment with similar RRS and reorganization energy no matter in solution or aggregate. As assigned, the low-frequency normal modes are related to the out-of-plane rotational/twistable motions of the peripheral phenyl rings, which are always spurred in solution but are clogged owing to the surrounding space restriction and intermolecular interaction in the solid phase. Consequently, the nonradiative decay outweighs the radiative decay for the excited-state AIEgens with active intramolecular motions in solution and the weak even undetectable fluorescence. But in aggregate, the radiative decay process dominates the nonradiative decay one for AIEgens with restricted intramolecular motions leading to strong fluorescence. Thus, we reveal the mechanism of AIE by RRS through theoretical computations.

Figure 16. The resonance Raman spectroscopy (σ(ω)/ω) and the reorganization energy (λ) for HPDMCb in solution and aggregate. Reprinted with permission from Ref. (52). © 2015 by the American Chemical Society.

5. Summary and Outlook In this chapter, we have disclosed the mechanism of AIE at the molecular level through theoretical and computational studies. Firstly, we have presented the general radiative and nonradiative decay rate formalisms by taking into account the difference between the electronic excited-state and ground-state potential energy surfaces at the level of harmonic oscillator, and integrated them into our home-built MOMAP program package. The rate calculations require molecular parameters informations resulted from standard quantum chemistry packages such as the equilibrium structure coordinates, frequencies, normal mode matrixes of the ground and excited states, excitation energy, transition dipole moment, non-adiabatic coupling and spin-orbit coupling etc. In the calculations, the solvent effect is considered by using the polarizable continuum model (PCM) and the aggregation effect is mimicked through the electrostatic molecular interaction by using the combination of quantum mechanics and molecular mechanics (QM/MM) approach. 54 Fujiki et al.; Aggregation-Induced Emission: Materials and Applications Volume 1 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


Then, it is quantitatively investigated about the steric hindrance effect, temperature effect, and the aggregation effect on the radiative and nonradiative decay rates. Through the detailed comparison and analysis, it is found that for the AIEgens under examination, (i) the radiative decay rate is insensitive to internal steric hindrance, and external temperature and molecular packing as long as the extent of molecular conjugation of lumophore group is not changed substantially; (ii) in contrast, the nonradiative decay rate is extremely sensitive to the environment change. Because the geometry relaxation ability controls the nonradiative decay to a large extent and the decisive normal modes relate to the rotatable/twistable intramolecular motions with low frequency. In solution, the molecular rotatable/twistable motions are always spurred at room temperature and make nonradiative decay rate outweigh the radiative decay rate, which leads to the molecule non-emissive. While they are clogged at low temperature or by the steric hindrance and the surrounding space restriction and intermolecular interaction in the solid phase, which slows the nonradiative decay. As a result, the radiative decay starts to dominate and the strong fluorescence is observed. So far, the mechanism of AIE has been unmasked at the molecular level. Finally, through establishing the relationship between the geometrical reorganization energy and the experimentally measured spectroscopy signals, the plausible ways to probe the microscopic mechanism are proposed. According to the Franck-Condon principle, the maximum peak of the optical spectrum always appears at the vertical transition point and the Stokes shift can be regarded as the total reorganization energy in the ground and excited state potential energy surfaces. The decrease of Stokes shift induced by the decreasing reorganization energy causes the aggregation-induced blue-shift emission when going from solution to aggregate, which is a typical spectroscopy character of the AIEgens with RIR mechanism. Furthermore, the ratio of the RRS intensity to the frequency (σ(ω)/ω) is proportional to the reorganization energy of every vibration mode of a molecule. The nature of RRS intensity σ(ω)/ω exactly reflects the change character of the reorganization energy for the AIEgen moving from solution to aggregate. And the mechanism of AIE is confirmed by the RRS signals through theoretical computations, which is expected to be proved by future experiments. Accurately describing excited state structure and decay processes is still a longstanding challenge for both computational chemistry and physics because both the electron-electron correlation and electron-phonon coupling are required to be involved (56). At present, there is no ready-made tool to provide the luminescent properties for all kinds of molecules in the gas phase, let alone, the intermolecular interactions that bring greater complication to depict the excited state decay in the aggregate phase. In the chapter, the QM/MM approach only applies for dealing with molecular crystal. The molecular dynamics should be combined for irregular amorphous aggregates. MM polarization by the electron-density change of the QM molecule in the excited state has not been taken into consideration. Moreover, in the light of only considering one QM molecule in the QM/MM computational model, the effect of the intermolecular charge transfer or exciton interaction on AIE has not been considered. All these are being actively pursued.


Acknowledgments This work is supported by the National 973 Program through Grant Nos. 2013CB834703 and 2015CB655002 and the National Natural Science Foundation of China through Grant Nos. 21290190, 21473214, and 91233105. Contributions from the following collaborators are greatly acknowledged: Shiwei Yin, Qunyan, Wu, Tian Zhang, Yujun Xie.

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