Theoretical Investigations on the Photophysical Properties for a Series

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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Theoretical Investigations on the Photophysical Properties for a Series of Symmetrical and Asymmetrical Carbazole -Based Cationic Two-Photon Fluorescent Probes: The Magic of Methyl Groups Xue-Li Hao, Jing-Fu Guo, Lu-Yi Zou, and Ai-Min Ren J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01483 • Publication Date (Web): 13 Mar 2019 Downloaded from http://pubs.acs.org on March 14, 2019

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The Journal of Physical Chemistry

Theoretical Investigations on the Photophysical Properties for a Series of Symmetrical and Asymmetrical Carbazole -based Cationic Two-Photon Fluorescent Probes: The Magic of Methyl Groups Xue-Li Hao,† Jing-Fu Guo,‡ Lu-Yi Zou,† Ai-Min Ren*† † Laboratory

of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University,

Liutiao Road 2#, Changchun 130061 ‡School

of Physics, Northeast Normal University, 130024, P.R.China

ABSTRACT: The biological fluorescence imagining for nucleic acid has attracted attention due to the essential role of nucleic acid in living system. Two-photon (TP) fluorescent probes are important molecular tools for biological imaging due to their high resolution and low photo-damage to tissues. However, the practically applicable TP fluorescent probes are still limited, because of indistinct fluorescent mechanism and ambiguous relationship between molecular structures and two-photon excited fluorescent properties. In this contribution, we researched the photophysical properties for a series of symmetrical and asymmetrical carbazole-based cationic TP fluorescent probes for nucleic acid, and explained the fluorescent mechanism of the nucleic acid probes from the aspect of excited-state dynamics. It is firstly proposed that the fluorescence quenching for the cationic probes with terminal methyl chains is derived from methyl rotating motion in low-frequency regime rather than vinyl rotating motion in water solvent. We illuminated the origin of better TPA properties for cationic compounds compared with corresponding neutral compounds. The TPA 1

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efficiency is much higher for symmetrical compound than that for asymmetrical compound, and the symmetrical compound is more stable due to restricted molecular bending vibrations. Besides, the electron-donating/withdrawing ability of substituent groups and the position of methyl at acceptor also have important influence on TPA properties of cationic compounds. 1. INTRODUCTION The biological fluorescence imagining has emerged as one of the most novel and powerful techniques for monitoring and tracking targets in living system, which is invaluable for chemical biological research and medical diagnosis.1-3 Fluorescent probes are important molecular tools for biological imaging due to their high sensitivity and easy modulation.4 Traditional one-photon (OP) fluorescent probes have the absorption and emission wavelengths mainly in the ultraviolet or visible region, which hinders them to be employed for labeling and imaging in vivo, because of the interference of auto-fluorescence and the limited tissue penetration.5 However, two-photon (TP) fluorescent probes based on the simultaneous absorption of two photons with low energy can alleviate these deficiencies, which possess high resolution, deep tissue penetration, less photo-damage and photo-bleaching to tissues.6-9 But the practical application of TP fluorescent probes is far from that of OP fluorescent probes, which is related to the much less efficiency of two-photon absorption (TPA) at low laser power levels. However, the high-powered laser beams are harmful for sample, so it is very needed to investigate and obtain the organic materials with high TPA efficiency (large TPA cross section value) for practical 2


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application of TP fluorescence imaging.10 As we all known, enlarging the extent of intramolecular charge transfer (ICT) is a useful way to increase the TPA cross section of a molecule, but the enhanced ICT may give rise to reduction in the fluorescence, which is detrimental to TP fluorescent brightness.10 Thus, it is essential to explore the relationship between molecular structures and TP fluorescent properties, and obtain the optimal measures for both large TPA cross section and high fluorescent efficiency. What’s more, it’s also quite urgent to further illuminate the fluorescent mechanism11,12, the deficiency of which is also a huge hindrance for the development of TP fluorescent probe. Nucleic acid (DNA), the carrier of genetic information, is closely related to the process of gene transcription, replication and recombination, thus the damage to DNA can cause some diseases such as cancer, mutagenesis and neurodegenerative disorders.13-16 Therefore, it’s very useful and important to visualize DNA at subcellular level by TP fluorescence imagining. In 2003, Chang et al. have researched a carbazole derivative BMVC for labeling and stabilizing the G-quadruplex structure.17 Then, they further explored the effect of different substituent groups at 9-position of BMVC on molecular properties, and they suggested the solvent viscosity plays an important role in determining fluorescence quantum yield.18 In the last years, there are a lot of researches on molecular substituent modification based on carbazole and triphenylamine scaffold in order to obtain highly efficient TP fluorescent probes with good stability and selectivity.19-27 The cationic groups at 3 and 6-positions of carbazole scaffold play major roles in the enhancing their binding potency on DNA. 3



In general, DNA binding modes are intercalation and groove binding mainly.28,

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29

There is one viewpoint that carbazole-vinyl derivatives being non-fluorescent in the free state is derived from the torsional motion of the vinyl group in bridging the donor and acceptor.18, 20, 30 But many compounds with similar molecular structures are used in TP fluorescent detection for organelles and they possess high fluorescent intensity in non-viscous solvent.31-37 Then whether the fluorescent off-on mechanism of such fluorescent probes is original from vinyl group or not still remains unknown to date. But this is very important for further designing fluorescent probes with extended conjugated systems, especially for two-photon fluorescent probes. Our previous researches showed that the length of terminal alkyl chain has an essential influence on both specific recognition and fluorescent efficiency.38,39 Thus, we speculated that fluorescent mechanism for classical nucleic acid probes molecule BMVC and its derivatives may be connection with the motion of terminal alkyl. Therefore, it’s very interesting and important to explore the excited states photophysical process and illuminate fluorescent mechanism for cationic TP fluorescent probes in detail. What’s more, the studies of molecular scaffolds also have attracted attention recently, which is not only connection with the molecular selectivity, but also related to two-photon excited fluorescent properties.39-45 Usually, the two dimensional compounds have better two-photon absorption properties, but the natural difference between symmetrical and asymmetrical compounds has not been expounded. In this work, we theoretically explained the fluorescent quenching and binding mechanism for cationic carbazole-based nucleic acid probes for the first time and 4


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thoroughly explored the radiative and non-radiative processes of excited states. We analyzed the absorption and emission properties for cationic compounds compared with neutral compounds in order to illuminate the effect of cationic groups on molecular optical properties. Besides, we further researched the natural difference of photophysical properties between symmetrical and asymmetrical TP fluorescent probes. What’s more, we also took into account the influence of different substituent groups at 3, 6 and 9-position of carbazole scaffold on TPA cross section, which is hoped to provide useful guidelines for designing and synthesizing high efficient two-photon fluorescent probes. 2. THEORETICAL METHODS 2.1 Two-Photon Absorption Two-photon absorption cross section (σTPA) is a vital index for two photon fluorescence probe, determining the two-photon absorption intensity, which is connection with two-photon transition probability (δa.u.) and can be obtained by:46, 47



TPA

4 2 a 50 2   a.u 15c

(1)

Here, α, a0 and c are the fine structure constant, Bohr radius and speed of light, respectively. Besides, ω represents the photon energy in atomic units and Г is the broadening factor describing the spectral broadening of an excitation, which is assumed to 0.1 eV commonly.48 The TPA cross section σTPA is in the unit of GM and δa.u.in atomic unit can be calculated from the TPA transition tensor S as:49, 50

 a.u 

1  ( FSaa S bb  GSab S ab  HSab S ba ) 30 ab

(2)

5



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Where, a, b  {x, y, z} , the value of F, H and G are 2, 2 and 2 for linearly polarized light, and those are -2, 3 and 2 for the circular case, respectively. Under the electric dipole approximation, the TPA transition tensor Sif between the initial state i and the final state f is defined as:47 if S ab (1 , 2 )   { n i

i a n n  b f

ni  1



i b n n  a f

ni  2

}

(3)

Here, i a n denotes the a-th component of the transition dipole moment, which is between the initial electric state i and intermediate state n, and ωin is the associated excitation energy. In addition, ω1 and ω2 are the energies of the two photons. When it’s simulated by two-state model (n=f), the equation above can be reduced to:

S ab0 f (1 , 2 ) 

a0 f b b0 f a  0 f  1 0 f  2

(4)

△μ is the dipole moment difference between the ground state S0 and final state Sf. Besides, these physical parameters such as the TPA transition tensor (Sif), TPA transition probability (δa.u.) and TPA cross section (σTPA) also can be calculated with the help of quadratic response theory by DALTON program51. 2.2 The Fluorescence Quantum Yield The fluorescence quantum yield is determined by radiative decay rate (kr) and non-radiative decay rate (knr), and can be expressed as:



kr kr  knr

(5)

The spontaneous emission rate kr can be calculated by using Einstein transition probabilities:52

6


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kr 

2 fE 2 c3

(6)

Here, c is the speed of light, f is the oscillator strength and E is the transition energy. When vibronic coupling and harmonic oscillator approximation are taken into account, the kr can be obtained according to the formula:53

kr (i 0 fa )

S aj i  S j 64 4 2 3  4 3   (if   a j j )  e hc a j j aj !

(7)

Where, μ is the electric transition dipole moment; h is the Plank constant; c is the speed of light and Sj is the Huang-Rhys factor for the j-th mode. The frequency of spontaneous transition from the initial state to final state vi0→fa can be expressed as

i 0 fa  if   a j j . j

As for non-radiative decay, it’s usually determined by internal conversion (kic) from S1 to S0 and intersystem crossing (kisc) from a singlet to a triplet state. The internal conversion (kic) can be defined as:54

kic 

2 ' 2 H fi  ( E fi  E f  f  E ii ) h

(8)

Here, the non-Born-Oppenheimer coupling is described as:55

H 'fi  h2   f  fv f l

 i ii Q fl Q fl

(9)

Under the Condon approximation, the eq (9) can be expressed as:56

¶   P ¶  H 'fi    f P fl i fv f fl ivi

(10)

l

Then, the eq (10) is inserted into eq (8) and the delta function is Fourier transformed, we can get that:57

7



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

k

ic , kl 

1 i t Rkl  e if Z i 1 ic ,kl (t , T )dt 2 h 

µ fk   P µ fl  Rkl   f P i i f

(11) (12)

Here, Ziv-1 and ρic,kl (t,T) are the partition function and thermal vibration correlation, which are shown in the references in detail. In addition, these physical parameters above can be obtained using MOMAP program58. In this paper, the ground-state and the first excited-state geometric structures of investigated molecules are optimized at the B3LYP/6-31G (d, p) level of theory by Gaussian 09 program package59. Based on the optimized geometries, we carried out the frequency calculation, and no imaginary frequency was founded. After that, we analyzed the electronic structure and evaluated one-photon absorption (OPA) and two-photon absorption (TPA) properties by using the range separated CAM-B3LYP functional60-62, which can be used for describing charge-transfer character of the investigated compounds well. The TPA physical parameters were calculated with the help of quadratic response theory by DALTON program51. The solvent effects were also taken into account by using polarizable continuum model (PCM)63. Besides, the photophysical processes of the excited state for all investigated compounds were evaluated with the help of MOMAP program58 developed by Shuai et al, and the normal modes displacements and Duschinsky rotation matrix were simulated through DUSHIN program64, 65. 3. RESULTS AND DISCUSSION 3.1 Molecular Design and Geometry Optimization

8


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In order to explore the natural difference of photophysical properties for symmetrical and asymmetrical carbazole-based cationic two photon probes, we researched

the

classical

cationic

compounds

9M-3MP-6PVC as shown in Figure 1.39,

41, 42

9M-MVC,

9M-BMVC

and

Besides, the corresponding neutral

compounds 9M-VC and 9M-BVC were designed as a reference so that it can be explicit to analyze the influence of cationic groups on optical properties. The geometrical configurations of these investigated compounds were optimized in water solvent and shown in the Figure S1 in the Supporting Information. It is clearly that all molecules have good planarity in both the ground state and the first excited state. However, the first excited state structure of neutral compound in gas still possesses good planar rigid, but that for cationic compound has a degree of distortion (see Figure S2). As for solvent effect, we have designed the cationic compounds (HVC, BHVC and 3HP-6PVC) without terminal alkyl, and optimized their geometrical structures in different solvents as shown in the Figure S3. It can be seen that the geometric distortion of the excited-state is more severe with the decline of solvent polarity. What’s more, we also researched the effect of substituent groups on TPA properties. Thus, we designed several compounds with different electron-donating/ withdrawing substituent groups at 3, 6 or 9-positon of carbazole scaffold as shown in the Figure S4. 3.2 One-photon absorption (OPA) and fluorescent emission properties It’s a useful way to explore the optical properties of compounds through one-photon absorption (OPA) and fluorescent emission (FE) spectra. The calculated 9



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results of OPA and FE properties are listed in the Table 1 and Table 2, and the spectra of all studied molecules are shown in the Figure 2. The calculated maximum OPA peaks for 9M-MVC and 9M-BMVC are 416.21 nm and 424.40 nm, and FE peaks are respective 531.99 nm and 555.42 nm, which are in good agreement with the experimental values39,41,42. The essential nature of the maximum OPA peak is relative to the electron transition from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) for all studied compounds. The electron of HOMO is delocalized, and mainly distribute in carbazole core and vinyl double bond, while the LUMO is mainly contributed by the orbitals from vinyl double bond and methyl-pyridine, thus these compounds possess satisfied charge transfer (CT) character (see Figure 3) and their Stocks shifts are all larger than 115 nm. Besides, there is another OPA peak in short wavelength spectral region for bilateral chain compound (316 nm, 371 nm and 319 nm for 9M-BVC, 9M-BMVC and 9M-3MP-6PVC),

which

is

connection

with

the

transition

configurations

HOMO→LUMO+1 and HOMO-1→LUMO, and the molecular orbitals LUMO and LUMO+1 are near-degenerate for symmetrical bilateral chain compounds 9M-BVC and 9M-BMVC (see Figure 4). What’s more, both the maximum OPA and FE wavelengths of compounds with positive charge are longer than that of corresponding neutral compounds, because the strong electron-withdrawing group (cationic methyl-pyridine) pulls down the energy of LUMO and decrease the energy gap △EH-L as shown in Figure 4. The OPA spectra are slightly red-shift and the oscillator strengths (f) are obviously enhanced for symmetrical bilateral chain compound 10


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9M-BVC (9M-BMVC) compared with asymmetrical unilateral chain compound 9M-VC (9M-MVC). The smaller energy gap △EH-L and excitation energy ω are conductive to the red-shifted spectra. The oscillator strength (f) indicates the transition probability, which is not only connection with excitation energy ω but also related to transition dipole moment μ. As shown in the Table 1, the OPA transition dipole moment is up to 4.55 D for symmetrical bilateral chain compound 9M-BVC (5.29 D for 9M-BMVC), while the value for asymmetrical unilateral chain compound 9M-VC (9M-MVC) is only 3.77 D (4.58 D), leading to the electron transition probability from S0 to S1 for symmetrical compound is much larger than that for asymmetrical compound. For asymmetrical bilateral chain compound 9M-3MP-6PVC, the transition dipole moment (4.88 D) is less than that of symmetrical bilateral chain compound 9M-BMVC (5.29 D), because the electron-withdrawing ability of cationic methyl-vinyl-pyridine is much stronger than the neutral vinyl-pyridine. Besides, the larger value of μ for cationic compound indicates that cationic methyl compound is more sensitive for electrical polarization than corresponding neutral compound, which is contribute to improving nonlinear optical response for cationic compound. As for fluorescent spectra, the oscillator strength (f) of FE for asymmetrical bilateral chain compound 9M-3MP-6PVC is apparently small due to the smallest transition dipole moment μ (9.01 D) and excitation energy Evt (1.98eV) in all compounds (see Table 3), while the excitation energy (2.94 eV) of 9M-3MP-6PVC is similar to that of 9M-BMVC (2.92 eV) in OPA process, which means the excited state relaxation energy is quite large for compound 9M-3MP-6PVC and is detrimental to fluorescence 11



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efficiency. 3.3 Fluorescence quantum yield, radiative and non-radiative decay In order to explore the fluorescence mechanism, we researched the excited-state dynamics and the fluorescence quantum yield (Φ) that is an important index for fluorescence efficiency. Radiative and non-radiative decay are two important photophysical processes from the first single excited state (S1) to the ground state (S0). The fluorescence quantum yield (Φ) is determined by the radiative decay rate (Kr) and non-radiative decay rate (Knr) that mainly depends on internal conversion for these investigated compounds due to the intersystem crossing rate is too small (~106 s-1)38. As shown in the Table 3, the studied cationic compounds (9M-MVC, 9M-BMVC and 9M-3MP-6PVC) with methyl groups at terminal are fluorescence quenching20,

30, 42,

while the corresponding neutral compounds (9M-VC and

9M-BVC) possess high fluorescence quantum yield, which is due to the extremely large Knr (~1011 s-1) for the former in water solvent. What’s the reason of fluorescence quenching for the cationic methyl compounds above? Is it really derived from vinyl group rotation?18,

20, 30

To solve this problem, we deeply researched

geometric relaxation of the excited state, which can be evaluated by reorganization energies or Huang-Rhys (HR) factors at crucial vibrational modes. Reorganization energy is an important index for electron-vibration coupling between two different electronic states, indicating the extent of geometry relaxation.53 As shown in Figure 5, it can be seen that (1) the total reorganization energy of the first excited electronic state for neutral compound (1554.83 cm-1 for 9M-VC and 1194.07 cm-1 for 12


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9M-BVC ) is much larger than that for its corresponding cationic compound

(687.57

cm-1 for 9M-MVC and 579.33 cm-1 for 9M-BMVC ) generally, while the contribution of the low frequency (< 500 cm-1) modes to the total reorganization energy is more than 25% for cationic compound (39.86% for 9M-MVC and 26.03% for 9M-BMVC) but only about 5% for its neutral compound (5.50% for 9M-VC and 4.30% for 9M-BVC). It is clearly that the molecular skeleton stretching modes at 1672.44 cm-1 and 1619.50 cm-1 respectively possess large reorganization energies 449.46 cm-1 and 305.63 cm-1 for neutral compounds 9M-VC and 9M-BVC in high frequency regime (> 1000 cm-1). The skeleton stretching modes in high frequency regime are suppressed for cationic compounds; (2) in low-frequency regime, the reorganization energies in general for symmetric bilateral chain molecules (eg. 9M-BMVC with maximum value of 33.40 cm-1) are much smaller than those for unilateral chain molecules (eg. 9M-MVC with maximum value of 68.13 cm-1); (3) comparing with neutral compound 9M-VC, the 9-methyl rotating motion at 76.59 cm-1 possesses obviously large reorganization energy 68.13 cm-1 for cationic compound 9M-MVC. Similarly, there is a 3, 6-methyl-rotating mode at 47.52 cm-1 with the largest reorganization energy 33.40 cm-1 in low-frequency regime for cationic compound 9M-BMVC, which is not existent for corresponding neutral compound 9M-BVC. Besides, there are slightly weak the molecular torsional vibration at 169.25 cm-1 and 178.89 cm-1 for compound 9M-MVC and 9M-BMVC, respectively. Therefore, we speculate that the fluorescence quenching for the cationic compounds above may be connection with the methyl rotating motion rather than vinyl rotation. 13



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For further exploration, we designed cationic compounds without methyl HVC and BHVC, besides we also adopt the corresponding neutral compounds VC and BVC as referenced molecules (see Figure S3 in Supporting Information). Amazingly, the fluorescence quantum yields are extremely large for all designed compounds (see Table 3), which indicates the fluorescence quenching mechanism is not related to molecular cationic property. To thoroughly explain the quenching mechanism of experimental molecules, HR factors are calculated according the formula HR j  ( j D 2j ) 2h , and are depicted in the Figure 6 for all studied compounds. HR

factors characterize the change of vibrational quanta from one electronic state to another, which are important for determining the Knr.53 As shown in the Figure 6, methyl rotating mode is a very important and unique channel of geometric relaxation from S1 to S0 for cationic compound with methyl compared with other compounds (see Figure 6a~d). Interestingly, 9-methyl rotating modes at 76.59 cm-1 and 105.14 cm-1 possess notably large HR factors 0.89 and 1.73 for asymmetrical compounds 9M-MVC and 9M-3MP-6PVC, while there are quite distinct 3, 6-methyl rotating motions at 47.52 and 78.30 cm-1 for symmetrical compound 9M-BMVC. In addition, molecular scissor bending vibrations in low-frequency regime also possess large HR factors for all studied compounds. Comparing with neutral compound VC (BVC), the smaller Φ and larger Knr for cationic compound HVC (BHVC) is related to more remarkable molecular bending vibration and smaller adiabatic energies difference. The geometrical structures of cationic compounds at the first excited state have a degree of torsion in gas (see Figure S2 and Figure S3). To research the solvent effect 14


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on cationic structures, we theoretically simulate the stable first-excited geometrical configuration in different solvent as shown in Figure S3, and calculated fluorescence properties as listed in Table S4 in the Supporting Information. It can be seen that whether in water solvent or in gas, neutral compounds (VC and BVC) own quite high fluorescence efficiency. For cationic compounds, the IC rates are declined and values of Φ become large with the increase of solvent polarity. It’s worthwhile to mention that cationic compounds possess pretty rigid plane in high polar solvent (aqueous), but vinyl rotation in excited state structures is obvious in low polar solvent as shown in the Figure S3, and asymmetrical unilateral chain and bilateral chain compounds are more sensitive for solvent polarity, while symmetrical bilateral chain compound is relatively stable. Therefore, we can conclude that the fluorescence quenching for the cationic compounds (9M-MVC, 9M-BMVC and 9M-3MP-6PVC) is derived from methyl rotating motion in low-frequency regime rather than vinyl rotating motion in water solvent. For these probes after interaction with nucleic acid, those low-frequency motions of methyl rotating are hindered, thus their contribution to IC decay are suppressed, leading to fluorescent emission. Molecular vinyl rotation is associated with solvent polarity. The symmetrical compounds are more stable due to restricted molecular scissor bending vibrations in low-frequency regime comparing with asymmetrical compounds. For cationic compounds, the skeleton stretching modes in high-frequency regime are hindered compared with corresponding neutral compounds, though the formers possess smaller excitation energies and adiabatic 15



Page 16 of 37

energies difference between S1 and S0. 3.4 Two-photon absorption (TPA) properties As mentioned above, it’s one of the main aims of this study to research the relationship between TPA properties and molecular structures. As a two-photon fluorescent probes, the molecules only to be with the large TPA cross-section can utilize near-infrared photons at low laser power.10 To evaluate two-photon response for the investigated compounds, we theoretically calculated and analyzed their electronic transition nature and TPA important parameters (the maximum TPA cross section σTmax and corresponding λTmax in the NIR spectral region), which are in good agreement with the experimental values41 as shown in the Table 4 and Figure 7. It can be seen that the TPA peaks are red-shifted for cationic compounds compared with corresponding neutral compounds due to the lower energies of LUMO and smaller energy gaps △EH-L for the former. The TPA cross sections are much larger for corresponding cationic compounds than neutral ones. For example, the cationic compound 9M-BMVC possesses a quite large σTmax (1310 GM at 738 nm), which is more than 2.5 times as large as that of neutral compound 9M-BVC (452 GM at 631 nm), because of the larger intramolecular charge transfer (ICT) for cationic compound, which is attributed to the stronger electron-withdrawing ability of cationic methyl-pyridine. As for symmetrical bilateral chain compounds, the maximum TPA can be described as a mixture of configurations HOMO→LUMO+1 and HOMO-1→LUMO, which is connection with the near-degenerate orbitals LUMO and LUMO+1. Besides, there are two more TPA peaks at 841 nm (209 GM) and 647 nm 16


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(745 GM) in NIR spectral region for symmetrical compound 9M-BMVC. The phenomenon of multiple TPA peaks is connection with the effect of inter-chain coupling. The maximum TPA peak (670 GM/ 636 nm) for asymmetrical bilateral chain compound 9M-3MP-6PVC is connection with the charge transfer from carbazole to one side-chain methyl-vinyl-pyridine (see Figure S5), which is mainly attributed to the electronic excitation HOMO→LUMO+1, and the secondary TPA peak (454 GM/ 835 nm) is derived from the electronic excitation configuration HOMO→LUMO. Both of them have significantly large ICT, but nothing to do with the inter-chain coupling, and the orbitals LUMO and LUMO+1 are not degenerate any more for asymmetrical bilateral chain compound. However, there is only one main TPA peak in NIR spectral region for single chain compound. The unilateral chain compound 9M-MVC (9M-VC) possesses the maximum TPA cross section 443 GM at 827 nm (202 GM at 668 nm), which is related to electron transfer from carbazole to side-chain vinyl pyridine (see Table 4 and Figure 3). In order to explain the relationship of extremely large TPA cross sections and molecular structures for cationic compounds and explore the difference of TPA properties between symmetrical and asymmetrical compounds, we further analyzed the TPA tensor elements (Sab) and transition dipole moments (μa) for these investigated compounds. Under the two-photon excitation by a linearly polarized single beam of light, the two-photon transition probability δa.u. ( in atomic units) can be evaluated by the expression66, 67

 a.u .  6( S xx2  S yy2  S zz2 )  8( S xy2  S xz2  S yz2 )  4( S xx S yy  S yy S zz  S xx S zz ) 17



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As shown in Table 5, TPA tensor elements Sxx component plays a leading role in the maximum TPA process for all investigated compounds. Besides, the Sxy and Syy components also have some moderate contributions in this process, but the rest of other TPA tensor elements (Szz, Sxz and Syz) barely have an effect on the δa.u values. However, the TPA tensor element Sxy has a major contribute to TPA process of the first-excited state as final state for symmetrical compounds (9M-BVC and 9M-BMVC), while the Sxx component doesn’t have any effect on TPA cross section according to direct product operation principle of group theory (see Two-photon absorption properties in Supporting Information). Combining with the Figure 3 and Figure S5, we can get that the electron transfer from carbazole to side-chain control the TPA process for asymmetrical single and bilateral chain compound (9M-VC, 9M-MVC and 9M-3MP-6PVC), while the TPA process for symmetrical bilateral chain compound (9M-BVC, 9M-BMVC) may be related to inter-chain coupling. To further gain insight about the origin of the TPA process, it is helpful to analyze the key TPA tensor elements (Sxx, Sxy and Syy) through a few-state model.47, 68 As shown in Table 5 and Table S8, the rules of Sab simulated by two-state model are in good agreement with that calculated by response theory in the excited process S0→S1 for all investigated compounds. However, the Sab is needed to be described by a three-state model at least in the excited process S0→S2 and S0→S3, which is confirmed that there is the other important optical (the S1 as an intermediate state as shown in Table S9~S11) contributed predominately to these TPA processes. The corresponding transition dipole moment elements (μab) and the difference between the 18


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final excited and ground state dipole moments elements (△μa) for dominative TPA tensor elements (Sxx, Sxy and Syy) are listed in Table 6. It is clearly that the difference of excited energies (△En) is much smaller for cationic compound compared with corresponding neutral compound, which is contribute to increasing TPA tensor element S and TPA cross section σT. Compared with neutral compounds, the enlarged transition dipole moment element μx has an important influence on TPA process S0→S1, resulting in the rather larger S and σT for cationic compounds. For bilateral chain compounds, the first excited state S1 plays an important role in the TPA process (S0→S2 or S0→S3) as the paramount intermediate state, which closely couple with the final excited state. The cationic compound 9M-BMVC possess rather larger 𝜇12 𝑥 (-4.05 a.u.) and Sxx (812 a.u.) than that for compound 9M-BVC (2.90 and -413.2 a.u.), which leads to the σTmax for 9M-BMVC (1310 GM) is nearly three times larger than that for 9M-BVC (452 GM). It’s noteworthy that the value 𝜇12 𝑥 is obviously small for asymmetrical compound, giving rise to their Sxx and σT of the second exited state are not as large as those for symmetrical compound. It’s explained that the maximum TPA cross section for symmetrical compound is derived from inter-chain coupling, which is connection with the molecular symmetry. As for compound 9M-3MP-6PVC, the maximum TPA cross section is closely related to the transition dipole 𝜇01 𝑥 and 𝜇13 𝑥 , and the difference between the final excited and ground state dipole moment (△μx) also has an crucial contribution to the TPA process S0→S3 due to the prominent intramolecular charge transfer. More importantly, the transition dipole 𝜇13 for 𝑥 cationic compound is distinctly large than that for corresponding neutral compound, 19



Page 20 of 37

resulting in the remarkable nonlinear optical response of the third excited state for the former. Based on the analysis above, we can get that it’s useful way to obtain large TPA cross sections though enlarging electronic transition dipole moments. The electron-donating/-withdrawing ability of substituent groups is also a key factor for modulating charge transfer capacity and TPA efficiency. Therefore, we also researched the effect of substituent groups on TPA properties for cationic compounds. Based on the analysis in Supporting Information, we can get that (1) the electron-donating group at 9-position of carbazole is beneficial to increasing TPA cross section and corresponding wavelength, which is more distinct for asymmetrical compounds than symmetrical compounds; (2) the strong electron-withdrawing groups at 3, 6 position of carbazole can give rise to the enlargement of intramolecular electron transfer extent, contributing to enhancement of TPA cross section; (3) the position of methyl also plays an essential role in TPA properties, and TPA cross section is much larger for the compound with methyl at terminal than that for the compound with methyl at side of acceptor. It is hoped that the summing-up can provide guidance for design and synthesis of TPA materials. 4. CONCLUSIONS In this work, the geometrical structures, electronic configurations, TPA properties

and

fluorescence

efficiency

for

symmetrical

and

asymmetrical

carbazole-based cationic compounds have been explored in detail. Based on the research above, we theoretically proved the luminous mechanism of nucleic acid 20


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two-photon probes for the first time. The fluorescence quenching for the cationic probes (9M-MVC, 9M-BMVC and 9M-3MP-6PVC) is derived from methyl rotating motion in low-frequency regime rather than vinyl rotating motion in water solvent. For these probes after interaction with nucleic acid, those low-frequency motions of methyl rotating are hindered, thus their contribution to IC decay are suppressed, leading to fluorescent emission. Compared with neutral compounds, the absorption and emission spectra are obviously red-shifted and TPA cross sections are much larger for corresponding cationic compounds, which is derived from the cationic groups can decrease the energy gaps △EH-L and increase transition dipole moments μ. Besides, the geometric relaxations for cationic compound are more drastic at low-frequency regime. Geometric structures at the first excited state for cationic compounds are environmentally sensitive, and the rotating motion of the vinyl group in bridging the donor and acceptor is connection with solvent polarity, which can be happened in the solvent with low polar leaving out solvent viscosity. As for symmetrical and asymmetrical compounds, the TPA cross sections are much larger for symmetrical compounds (eg. 1310 GM/738 nm for compound 9M-BMVC) than that for asymmetrical compounds (eg. 443 GM/827 nm for compound 9M-MVC and 670 GM/636 nm for 9M-3MP-6PVC) due to extremely large transition dipolar moments, and the molecular orbitals LUMO and LUMO+1 are near-degenerate for symmetrical bilateral chain compounds, which is related to inter-chain coupling. Besides, the symmetrical compounds are more stable due to restricted molecular scissor bending vibrations in low-frequency regime comparing with asymmetrical 21



Page 22 of 37

compounds. What’s more, the effect of substituent groups on TPA properties for cationic compounds was also researched. Both the electron-donating groups at 9-position and the electron-withdrawing groups at 3, 6 position of carbazole are beneficial to increasing TPA cross section and corresponding wavelength, which is more distinct for asymmetrical compounds than symmetrical compounds. In addition, the position of methyl also plays an essential role in TPA properties. TPA cross section is much larger for the compound with methyl at terminal than that for the compound with methyl at side of acceptor. In a word, we sincerely expect that these researches can provide guidance for designing and synthesizing high efficient and stabilized cationic two-photon fluorescent probes for nucleic acid. APPENDICES Supporting information Figure, table and corresponding analysis of considered compounds, and methods of theoretical calculation AUTHOR INFORMATION ORCID Ai-Min Ren: 0000-0002-9192-1483

Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest.

22


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ACKNOWLEDGMENTS This work is supported by the Natural Science Foundation of China (No. 21473071, 21173099, 20973078 and 20673045), the Natural Science Foundation of Jilin Province of China (Grant No.20190201228JC) and the Major State Basis Research Development Program (2013CB 834801).

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Page 28 of 37

Figure 1. Structures and corresponding names of the investigated molecules

Figure 2. One-photon absorption and fluorescence spectra of the studied molecules in water

28


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Figure 3. Contour surfaces of the frontier molecular orbitals for all studied compounds in ground state

Figure 4. Calculated the frontier molecular orbital levels for the studied compounds in ground state

29



Page 30 of 37

Figure 5. Reorganization energies and crucial displacement vectors for the normal modes with large reorganization energies for molecules

30


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Figure 6. Huang-Rhys (HR) and crucial displacement vectors for the normal modes with large HR in low-frequency regime (< 500 cm-1) for molecules 31



Page 32 of 37

Figure 7. Two-photon absorption spectra for symmetrical and asymmetrical molecules

Table 1. Calculated OPA properties including maximum absorption peak (λmax), vertical excitation energy (ω0f), oscillator strength (f), transition moment (μ0f) and corresponding transition nature of the all molecules by CAM-B3LYP/6-311+G(d) in water solvent. The absorption wavelengths (λexp) are experimental results39. Molecule 9M-VC 9M-MVC 9M-BVC

9M-BMVC

9M-3MP-6P VC

λexp/nm 418

440

λmax/nm

ω0f /eV

f

μ0f /D

334.59 416.21 351.18 316.33

3.71 2.98 3.53 3.92

1.32 1.53 1.79 0.67

3.77 4.58 4.55

424.40 371.25

2.92 3.34

2.01 0.83

421.18

2.94

1.72

318.82

3.89

0.6932

5.29

4.88

Transition nature S0→S1 S0→S1 S0→S1 S0→S2

S0→S1 S0→S2 S0→S1 S0→S3

H→L H→L H→L H→L+1 H→L+2 H-1→L H→L H→L+1 H-1→L H→L

(88.98%)

H→L+1 H→L+2

(48.92%)

(90.71%) (78.61%) (50.39%) (23.23%) (12.56%) (78.47%) (59.37%) (32.33%) (75.01%)

(18.18%) 32


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Table 2. Fluorescence properties including fluorescent emission peak (λems), oscillator strength (f), fluorescent lifetime (τ) and transition nature of all studied compounds are calculated by B3LYP/6-31G (d, p) in water. Molecules 9M-VC 9M-MVC

9M-BVC 9M-BMVC

λexp/nm 564 580 568 551 555 568

9M-3MP-6PVC

λems/nm

f

τ/ns-1

445.30 531.99

1.58 1.26

1.88 3.37

S1→S0 S1→S0

H→L H→L

(99.62%) (99.60%)

465.44 555.42

1.78 1.75

1.82 2.64

S1→S0 S1→S0

H→L H→L

(98.37%) (98.34%)

626.74

0.61

9.66

S1→S0

H→L

(99.17%)

Transition nature

*The experimental fluorescent emission peaks for 9M-MVC (9M-BMVC) are 564nm (551nm) in water39, 580 nm (555 nm) in Tris-Hcl buffer42 and 568 nm (568 nm) in methanol41, respectively.

Table 3. Fluorescence properties including the vertical excitation energy (Evt), the adiabatic energy difference between S1 and S0 (Ead), the electric transition dipole moment (U), the radiative rate (Kr), non-radiative rate (Knr) and corresponding fluorescence quantum yield (Φ) are calculated by B3LYP/6-31G (d, p) method in water solvent. Molecules

Evt/eV

Ead/eV

U/Debye

Kr/ s-1

Knr/ s-1

Φ

9M-VC 9M-MVC 9M-BVC 9M-BMVC 9M-3MP-6PVC HVC VC BHVC BVC 3HP-6PVC

2.78 2.33 2.66 2.23 1.98 2.40 2.82 2.29 2.71 2.00

2.97 2.40 2.81 2.29 2.17 2.46 3.02 2.35 2.87 2.19

12.23 11.92 13.28 14.39 9.01 11.73 12.16 14.11 13.30 8.34

5.30×108 3.00×108 5.50×108 3.80×108 1.00×108 3.14×108 5.46×108 3.90×108 5.80×108 9.10×107

7.52×106 1.90×1011 4.36×105 1.43×1011 1.20×1011 1.99×107 7.85×104 2.14×107 2.89×105 1.24×107

0.99 0 1.00 0 0 0.94 1.00 0.95 1.00 0.88

33



Page 34 of 37

Table 4. TPA properties of the molecules calculated using quadratic response theory Molecules

λTmax /nma

σTmax/GMa

9M-VC

9M-MVC

880

470

9M-BVC

9M-BMVC

800

1737

9M-3MP-6PVC

a b

λTmax /nmb

σTmax /GMb

668.38 610.76

202 4.97

S0→S1 S0→S2

537.90

9.58

S0→S3

826.57

443

S0→S1

639.10

19.9

S0→S2

578.02

204

S0→S3

700.48

92.5

S0→S1

630.97

452

S0→S2

623.04

24.7

S0→S3

840.58

209

S0→S1

738.01

1310

S0→S2

647.44

745

S0→S3

834.92

454

S0→S1

661.25

13.7

S0→S2

635.82

670

S0→S3

Transition natureb H→L H→L+1 H-1→L H-1→L+1 H-1→L H→L

(88.98%) (76.68%) (10.87%) (70.78%) (12.38%) (90.71%)

H-1→L H→L+1 H→L+1 H-1→L H→L H-1→L+1 H→L+1 H→L+2 H-1→L H→L+2 H-1→L H→L H-1→L+1 H→L+1 H-1→L H-1→L H-2→L H→L+1 H→L+2 H→L H-1→L H-1→L H→L+1 H→L+1 H→L+2

(67.78%) (17.23%) (51.13%) (29.83%) (78.61%) (13.82%) (50.39%) (23.23%) (12.56%) (50.36%) (31.13%) (78.47%) (13.20%) (59.37%) (32.33%) (42.48%) (12.18%) (18.31%) (15.93%) (75.01%) (14.86%) (60.39%) (9.90%) (48.92%) (18.18%)

Experimental data from reference41 The results were computed at CAM-B3LYP/6-31+G(d) level of theory using DALTON programs in water solvent

34


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Table 5. TPA tensor elements (Sab) of all investigated compounds are calculated at CAM-B3LYP/6-31+G (d) using DALTON program in water Systems 9M-VC

9M-MVC

9M-BVC

9M-BMVC

9M-3MP-6PVC

Ex.States 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

TPA tensor elements (in a.u.) Sxx

Syy

Szz

Sxy

Sxz

Syz

-317.7 23.9 -48.1 -580.3 -68.7 -275.3 0.0 -413.2 56.4 -0.1 812.0 595.5 467.2 28.6 529.2

9.5 -5.3 0.4 10.3 -5.5 1.4 0.0 -80.2 69.7 -0.1 178.8 -23.8 92.0 -83.1 39.3

0.0 0.3 -0.9 0.0 -0.2 -0.7 0.0 -0.5 0.0 0.0 0.3 0.7 0.2 0.1 0.6

-26.7 33.9 23.6 -44.3 54.7 -10.1 194.6 0.0 0.0 -351.2 0.0 0.1 268.3 19.7 -61.3

-0.4 0.3 -0.4 -1.2 -0.1 -0.9 0.9 0.0 0.0 -1.2 1.4 0.6 3.1 0.7 0.8

0.3 0.1 0.1 0.0 0.1 0.0 0.0 0.4 0.2 -0.5 0.1 -0.1 1.1 -0.8 0.5

35



Page 36 of 37

Table 6. The transition dipole moment (μ in a.u.), the difference (△μ) between the final excited and ground state dipole moments (in a.u.), and the difference of excited energies △En =ωn-ωf /2 (eV) for the studied molecules in water are calculated at CAM-B3LYP/ 6-31+G (d) using Gaussian 09 program. Systems

f

n

△En

𝜇0𝑓 𝑥

𝜇0𝑓 𝑦

△μx

△μy

9M-VC

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

1.86 2.03 2.31 1.50 1.94 2.15 1.77 1.97 1.99 1.48 1.68 1.92 1.49 1.88 1.95

Systems

f

n

△En

-3.82 0.28 1.82 4.56 -0.03 -0.43 4.56 0.00 0.00 5.27 0.00 0.00 4.62 0.86 -1.54 𝜇0𝑛 𝑥

-0.19 -0.59 -0.09 0.17 0.00 -0.89 0.00 -2.83 0.60 0.00 -3.17 0.12 1.52 -1.81 2.02 𝜇0𝑛 𝑦

3.91 -0.59 0.84 -4.00 -6.43 -1.98 0.00 0.00 0.00 0.00 0.00 0.00 4.60 1.20 3.64 𝜇𝑛𝑓 𝑥

0.34 0.47 0.42 0.59 0.06 -0.43 2.11 1.79 -0.09 2.95 2.67 2.67 2.54 2.19 1.89 𝜇𝑛𝑓 𝑦

9M-VC

2 3 2 3 2 3 2 3 2 3

1 1 1 1 1 1 1 1 1 1

1.68 1.41 1.06 0.86 1.58 1.55 1.27 1.04 1.10 1.02

-3.82 -3.82 4.56 4.56 4.56 4.56 5.27 5.27 4.62 4.62

-0.19 -0.19 0.17 0.17 0.00 0.00 0.00 0.00 1.52 1.52

0.56 -0.40 0.26 1.12 2.90 -0.85 -4.05 2.46 -0.43 -1.79

0.19 0.07 -0.15 0.13 0.00 0.00 0.00 0.00 -0.02 0.12

9M-MVC

9M-BVC

9M-BMVC

9M-3MP-6PVC

9M-MVC 9M-BVC 9M-BMVC 9M-3MP-6PVC

36


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TOC Graphic

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Theoretical Investigations on the Photophysical Properties for a Series

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