S1

Supporting Information for

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

*Corresponding author: Ai-Min Ren

Tel.: +86 431 88498961; Fax: +86 431 88945942;

E-mail addresses: aimin_ren@yahoo.com

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Table of ContentsElectronic structures, one-photon absorption (OPA) and fluorescent emission (FE) properties1. Figure S1. Structures and corresponding names of the investigated molecules in

water

2. Figure S2. Structures and corresponding names of the investigated molecules in

gas

3. Figure S3. The first excited state geometrical structures and corresponding names

of the designed molecules

4. Figure S4. Structures and corresponding names of the investigated molecules in

the ground state

5. Figure S5. Contour surfaces of hole-electron distribution

6. Figure S6. Contour surfaces of the frontier unoccupied molecular orbitals for all

studied compounds in ground states

7. Table S1. Calculated vertical excitation energy (Evt), maximum absorption peak

(λmax), and corresponding oscillator strength (f) at the ground state geometries of

experimental molecules (9M-MVC and 9M-BMVC) by TD-DFT methods using

different functionals

8. Table S2. Calculated vertical excitation energies (Evt), maximum emission peaks

(λems), and corresponding oscillator strengths (f) at the exited-state geometries of

experimental molecules (9M-MVC and 9M-BMVC) by TD-DFT methods, using

different functionals

9. Table S3. Calculated the maximum two-photon absorption cross section (σmax)

and corresponding TPA wavelength (λmax) at the ground state geometries of

experimental molecules (9M-MVC and 9M-BMVC) by TD-DFT methods using

different functionals

10. Table S4. The Fluorescence properties including the vertical excitation energy,

the adiabatic energy difference between S1 and S0, the electric transition dipole

moment, the raditive rate, non-radiative rate and corresponding fluorescence quantum

yield are calculated by B3LYP/6-31G (d, p) method in water solvent

S3

Two-photon absorption properties

11. Figure S7. Structures and corresponding names of the model molecules

12. Figure S8. Contour surfaces of the frontier unoccupied molecular orbitals for the

model compounds in ground state

13. Table S5. TPA properties of the model molecules

14. Table S6. TPA tensor elements (Sab) of the model compounds are calculated by

using DALTON in water.

15. Table S7. The transition dipole moment, the difference between the final excited

and ground state dipole moments, and the difference of excited energies for the

model molecules in water are calculated using Gaussian 09 program.

16. Table S8. TPA tensor elements (Sab) of all investigated compounds are calculated

at CAM-B3LYP/6-31+G (d) using few-state models in water.

17. Table S9. TPA tensor elements (Sab) of all investigated compounds are calculated

at CAM-B3LYP/6-31+G(d) using few-state models in gas

18. Table S10. The special TPA tensor elements (Sab) between the ground state (S0)

and the second excited state (S2) for all investigated compounds using few-state

models in gas

19. Table S11. The special TPA tensor elements (Sab) between the ground state (S0)

and the third excited state (S3) for all investigated using few-state models in gas

20. Table S12. TPA properties of the designed molecules calculated using quadratic

response theory

21. Table S13. TPA tensor elements (Sab) of the investigated molecules are

calculated in water solvent

22. Table S14. The transition dipole moment, the difference between the final excited

and ground state dipole moments, and the difference of excited for the studied

molecules

23. Figure S9. Calculated the frontier molecular orbital levels

24. Figure S10. Contour surfaces of the frontier molecular orbitals

25. Figure S11. Contour surfaces of hole-electron distribution

26. Figure S12. Two-photon absorption spectra for the investigated molecules

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Electronic structures, one-photon absorption (OPA) and fluorescent emission (FE) properties

Figure S1. Structures and corresponding names of the investigated molecules in water

S5

Figure S2. Structures and corresponding names of the investigated molecules in gas

S6

Figure S3. The first excited state geometrical structures and corresponding names of the

designed molecules in different solvents and gas

S7

Figure S4. Structures of compounds with different electron-donating/withdrawing substituent

groups at 3, 6 or 9-positon of carbazole scaffold in the ground state

S8

Figure S5. Contour surfaces of hole-electron distribution

S9

Figure S6. Contour surfaces of the frontier unoccupied molecular orbitals for all studied compounds in ground state

S10

Table S1. Calculated vertical excitation energy (Evt), maximum absorption peak (λmax), and

corresponding oscillator strength (f) at the ground state geometries of experimental molecules

(9M-MVC and 9M-BMVC) by TD-DFT methods using different functionals

Molecule functional B3LYP BHandHLYP CAM-B3LYP

Experimental data1

HF% 20 50 19, 659M-MVC Evt/eV 2.60 3.02 2.98

λmax/nm 477 411 416 418f 1.20 1.56 1.53

9M-BMVC Evt/eV 2.42 2.95 2.92λmax/nm 513 420 424 440f 1.38 2.02 2.01

Table S2. Calculated vertical excitation energy (Evt), maximum emission peak (λems), and

corresponding oscillator strength (f) at the exited state geometries of experimental molecules

(9M-MVC and 9M-BMVC) by TD-DFT methods using different functionals

Molecule functional B3LYP

BHandHLYP

CAM-B3LYP

wB97XD Experimental data

HF% 20 50 19, 65 22.2, 1009M-MVC Evt/eV 2.33 2.55 2.63 2.55

λmax/nm 532 471 487 486 5641，5803，5682

f 1.26 1.84 1.88 1.85

9M-BMVC Evt/eV 2.23 2.64 2.56 2.57λmax/nm 555 470 484 483 5511，5553，5682

f 1.75 2.21 2.12 2.09

Table S3. Calculated the maximum two-photon absorption cross section (σmax) and corresponding

TPA wavelength (λmax) at the ground-state geometries of experimental molecules (9M-MVC and

9M-BMVC) by TD-DFT methods using different functionals

Molecule functional B3LYP BHandHLYP CAM-B3LYP

Experimental data2

HF% 20 50 19, 659M-MVC λmax/nm 946 816 827 880nm, 470GM

σmax/GM 442 417 443

9M-BMVC λmax/nm 902 731 738 800nm, 1737GMσmax/GM 2100 1240 1310

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Table S4. The Fluorescence properties including the vertical excitation energy (Evt), the adiabatic

energy difference between S1 and S0 (Ead), the electric transition dipole moment (U), the raditive

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 Solvent Evt/eV Ead/eV U/ Debye Kr/ s-1 Knr/ s-1 ΦVC water 2.82 3.02 12.16 5.46×108 7.85×104 1.00

gas 3.3172 3.4642 9.23 4.5×108 4.7×105 1.00BVC water 2.71 2.87 13.30 5.80×108 2.89×105 1.00

gas 3.0301 3.1700 10.20 3.8×108 1.2×105 1.00HVC water 2.4015 2.4590 11.73 3.1×108 1.9×107 0.94

DMSO 2.3976 2.4563 11.56 2.2×108 2.4×107 0.90 MeOH 2.3904 2.4563 11.36 2.1×108 3.5×108 0.38 CHCL3 1.9574 2.3096 5.55 7.5×105 3.8×1010 0toluene 1.2902 1.9410 0.04 2.1×10-2 3.2×1010 0

3HP-6PVC water 1.9964 2.1895 8.3381 9.10×107 1.24×107 0.88DMSO 1.9852 2.1785 8.2680 7.85×107 3.38×107 0.70MeOH 1.9699 2.1665 8.1212 7.38×107 3.51×108 0.17CHCL3 1.7150 1.9370 6.7621 3.08×107 1.90×109 0.02toluene 1.3516 1.6927 5.6328 2.88×105 3.26×1010 0

BHVC water 2.2879 2.3453 14.1099 3.9×108 2.14×107 0.95DMSO 2.289 2.3452 14.0763 3.3×108 4.39×107 0.89MeOH 2.29 2.3450 14.0403 3.4×108 4.38×107 0.89CHCL3 2.3081 2.3463 13.3364 2.7×108 3.63×108 0.43toluene 2.3265 2.3392 9.37336 1.2×108 2.25×108 0.36

S12

Two-photon absorption properties

If the excitation process is contributed mainly by two different states viz., the

ground state and the final state, according to the formula

1 21 2

( , ) { }b aa bifab

n i ni ni

i n n f i n n fS

TPA tensor elements (Sab) is expressed as

0 02 2( )f f

SM a b b aabS

There, the ω is the excitation energy. The μa0f is the a th component of transition

dipole moment from the ground to the f excited state, and △μa is the a th component

of difference between the excited and the ground state dipole moments.

C2v E C2 σ (y z) σ' (x y)

A1 1 1 1 1 y x2, y2, z2

A2 1 1 -1 -1 Ry xz

B1 1 -1 1 -1 z, Rx yz

B2 1 -1 -1 1 x, Rz xy

Cs E σh

A’ 1 1 x, y, Rz x2, y2, z2, xy

A’’ 1 -1 z, Rx, Ry yz, xz

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Figure S7. Structures and corresponding names of the model molecules

Figure S8. Contour surfaces of the frontier unoccupied molecular orbitals for the model compounds in ground state

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Table S5. TPA properties of the model molecules calculated at CAM-B3LYP/6-31+G (d) level

using quadratic response theory in water solvent.

Molecules λTmax /nm σT

max/GM Transition natureBVC 690.72 73.8 S0→S1 H→L (77.29%)

H-1→L+1 (15.18%)623.04 363 S0→S2 H→L+1 (50.40%)

H-1→L (41.76%)612.27 50.5 S0→S3 H→L+2 (71.30%)

H-2→L (8.96%)BHVC 829.33 158 S0→S1 H→L (77.49%)

H-1→L+1 (14.28%)729.32 997 S0→S2 H→L+1 (55.24%)

H-1→L (36.81%)642.41 740 S0→S3 H-1→L (41.41%)

H→L+1 (22.61%)H-2→L (14.33%)H→L+2 (11.72%)

3HP-6PVC 823.82 363 S0→S1 H→L (69.69%)H-1→L (20.06%)

663.02 20.1 S0→S2 H-1→L (60.98%)H→L (10.38%)

627.77 670 S0→S3 H→L+1 (55.15%)H→L+2 (10.40%)H-1→L+1 (10.13%)H-2→L (9.87%)

Table S6. TPA tensor elements (Sab) of the model compounds are calculated at

CAM-B3LYP/6-31+G (d) using DALTON program4 in water.

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Systems Ex.States TPA tensor elements (in a.u.)Sxx Syy Szz Sxy Sxz Syz

BVC 1 0.0 0.0 0.0 171.1 0.0 0.02 355.6 91.9 0.8 0.0 0.0 0.03 150.3 -22.8 1.7 0.0 0.0 0.0

BHVC 1 0.0 0.0 0.0 301.2 0.0 0.02 -705.4 -149.6 -0.2 0.0 0.0 0.03 588.0 -20.6 1.4 0.0 0.0 0.0

3HP-6PVC 1 392.0 104.4 0.1 248.0 0.0 0.02 95.2 -70.6 0.4 13.1 0.0 0.03 526.4 36.7 1.5 -33.6 0.0 0.0

Table S7. The transition dipole moment (μ in a.u.), the difference (△μ) between the final excited

and ground state dipole moments, and the difference of excited energies △En =ωn-ωf /2 for the

model molecules in water are calculated at CAM-B3LYP/ 6-31+G (d) using Gaussian 09

program5.

Systems f n △En 𝜇0𝑓𝑥 𝜇0𝑓

𝑦 △μx △μy

BVC 1 1 1.80 4.59 0.00 0.00 1.892 2 1.99 0.00 2.65 0.00 1.783 3 2.03 0.00 0.69 0.00 -0.38

BHVC 1 1 1.50 -5.17 0.00 0.00 2.662 2 1.70 0.00 -2.90 0.00 2.463 3 1.93 0.00 -0.15 0.00 2.79

3HP-6PVC 1 1 1.51 -4.43 -1.67 4.18 2.562 2 1.87 -0.90 1.54 2.56 2.283 3 1.98 -1.89 1.88 3.29 2.31

Systems f n △En 𝜇0𝑛𝑥 𝜇0𝑛

𝑦 𝜇𝑛𝑓𝑥 𝜇𝑛𝑓

𝑦

BVC 2 1 1.60 4.59 0.00 -2.75 0.003 1 1.57 4.59 0.00 -0.60 0.00

BHVC 2 1 1.29 -5.17 0.00 3.65 0.003 1 1.06 -5.17 0.00 -2.51 0.00

3HP-6PVC 2 1 1.14 -4.43 -1.67 0.73 0.003 1 1.04 -4.43 -1.67 -1.81 -0.03

The symmetrical compounds BVC and BHVC belong to C2v point group, and asymmetrical

3HP-6PVC only has Cs symmetry. According to direct product operation principle of group

theory, the two-photon excited transition S0→S1 along the x and y directions for BVC and BHVC

S16

are forbidden, so the TPA tensor elements Sxx and Syy don’t have any effect on the σ values of

symmetrical compounds, while asymmetrical compound 3HP-6PVC has good TPA properties at

S1 (see Table S6). However, the maximal TPA cross sections for symmetrical compounds are

derived from the transition S0→S2, which is connection with the inter-chain coupling (see Table

S5 and Figure S8), and the transition dipole moment plays an important role in the TPA 𝜇12𝑥

process (see Table S7). The value of for the symmetrical BHVC (3.65 a.u.) is much larger 𝜇12𝑥

than that for asymmetrical 3HP-6PVC (0.73 a.u.), thus the TPA tensor element Sxx at S2 of BHVC

is more than 7 times as large as that of 3HP-6PVC. As for the transition S0→S3, the quite large

and small △En of cationic compounds lead to that the TPA tensor elements and TPA cross 𝜇13𝑥

sections for BHVC and 3HP-6PVC are much large than that of the neutral compound BVC.

Table S8. TPA tensor elements (Sab) of all investigated compounds are calculated at

CAM-B3LYP/6-31+G (d) using few-state models in water.

Systems Ex.States TPA tensor elements (in a.u.)Sxx Syy Szz Sxy Sxz Syz

9M-VC 1 -437.70 -1.86 0.00 -29.66 -0.72 -0.052 -73.32 -8.51 0.00 -7.05 -0.16 -0.183 95.19 -1.33 0.00 4.74 0.54 0.01

9M-MVC 1 -662.59 3.54 0.00 36.81 -1.29 0.102 65.38 -1.26 0.00 -16.11 -0.01 -0.043 347.60 11.04 0.00 48.84 1.05 0.18

9M-BVC 1 0.00 0.01 0.00 148.02 0.61 0.002 456.25 -139.92 0.00 0.01 0.00 -0.243 -135.52 -1.51 0.00 0.00 0.00 0.09

9M-BMVC 1 0.00 0.05 0.00 286.65 0.91 0.542 -913.16 -273.36 0.00 -0.01 -1.59 -0.503 681.17 9.00 0.00 0.05 0.94 0.24

9M-3MP-6PVC 1 780.15 141.94 0.02 343.90 4.29 1.812 -70.01 -116.16 -0.02 -22.77 -0.74 -1.363 -597.88 115.83 0.01 3.43 -0.27 1.35

Table S9. TPA tensor elements (Sab) of all investigated compounds are calculated at

CAM-B3LYP/6-31+G (d) using few-state models in gas.

Systems Ex.States TPA tensor elements (in a.u.)Sxx Syy Szz Sxy Sxz Syz

9M-VC 1 -232.16 -1.14 -0.0 -16.42 -0.38 -0.029M-MVC 1 -599.20 -0.95 -0.0 -24.12 -1.41 -0.06

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9M-BVC 1 -0.0 0.0 0.0 78.80 0.34 0.02 78.97 -8.33 0.0 0.0 0.0 0.033 307.11 82.30 -0.0 -0.0 -0.0 0.15

9M-BMVC 1 -0.02 0.0 -0.0 -200.34 -0.67 -0.372 934.29 -169.37 0.0 0.02 1.68 -0.333 741.39 -2.56 0.0 -0.0 1.11 0.13

9M-3MP-6PVC 1 -586.64 -41.67 -0.01 157.69 -2.48 0.652 -174.38 -86.76 0.01 8.06 0.38 -0.043 683.84 61.93 0.0 -147.68 1.57 -0.44

Table S10. The special TPA tensor elements (Sab) between the ground state (S0) and the second

excited state (S2) for all investigated compounds at CAM-B3LYP/6-31+G (d) using few-state

models in gas.

Molecules n 𝑆02𝑥𝑥 𝑆02

𝑦𝑦 𝑆02𝑧𝑧 𝑆02

𝑥𝑦 𝑆02𝑥𝑧 𝑆02

𝑦𝑧

9M-VC 2 -34.24 16.41 0.0 -0.06 -0.04 0.201, 2 56.83 17.48 0.0 10.23 0.18 0.231, 2,3 50.69 16.84 0.0 13.70 0.12 0.241, 2, 3, 4 50.59 16.85 0.04 13.70 -2.81 0.801, 2, 3, 4, 5 47.68 14.97 0.04 16.06 -2.82 0.80

9M-MVC 2 -61.48 3.43 0.0 -30.26 0.0 -0.041, 2 50.90 3.15 0.0 -30.69 0.28 -0.0361, 2,3 63.92 4.19 0.0 -26.97 0.31 -0.021, 2, 3, 4 64.02 4.14 0.0 -26.49 0.32 -0.021, 2, 3, 4, 5 59.51 3.00 0.0 -18.08 0.30 -0.01

9M-BVC 2 0 -8.33 0.0 0.0 0.0 0.031, 2 78.97 -8.33 0.0 0.0 0.0 0.031, 2,3 78.97 -0.14 0.0 0.0 0.0 0.281, 2, 3, 4 113.94 -0.14 0.0 0.0 0.0 0.281, 2, 3, 4, 5 113.94 -4.37 0.0 0.0 0.0 0.39

9M-BMVC 2 0.0 -169.37 -0.0 0.01 0.0 -0.331, 2 934.29 -169.37 0.0 0.0 1.68 -0.331, 2,3 934.29 -169.33 0.0 0.02 1.68 -0.331, 2, 3, 4 941.90 -169.33 0.0 0.03 1.72 -0.331, 2, 3, 4, 5 941.90 -158.90 0.0 0.03 1.72 -0.29

9M-3MP-6PVC 2 501.13 -79.89 0.01 -105.83 2.75 -0.321, 2 -174.38 -86.76 0.0 8.06 0.38 -0.041, 2,3 -194.80 -100.30 0.01 24.87 0.34 0.01

S18

1, 2, 3, 4 -200.93 -89.78 0.0 23.00 0.40 -0.041, 2, 3, 4, 5 -200.84 -92.33 0.0 24.24 0.38 -0.03

Table S11. The special TPA tensor elements (Sab) between the ground state (S0) and the third

excited state (S3) for all investigated compounds at CAM-B3LYP/6-31+G (d) using few-state

models in gas.

Molecules n 𝑆03𝑥𝑥 𝑆03

𝑦𝑦 𝑆03𝑧𝑧 𝑆03

𝑥𝑦 𝑆03𝑥𝑧 𝑆03

𝑦𝑧

9M-VC 3 40.06 -1.41 0.0 5.09 0.20 -0.01, 3 24.39 -1.11 -0.0 6.35 0.0 -0.011, 2,3 21.07 -3.47 0.0 9.21 -0.01 -0.011, 2, 3, 4 21.19 -3.47 0.02 9.22 3.20 0.021, 2, 3, 4, 5 21.51 -2.44 0.02 8.51 3.21 0.01

9M-MVC 3 -171.12 4.04 -0.0 -12.09 -0.43 0.01, 3 493.91 -0.53 0.0 -46.16 0.84 -0.091, 2,3 499.65 1.45 0.0 -42.22 0.85 -0.081, 2, 3, 4 499.54 1.83 0.0 -45.76 0.87 -0.101, 2, 3, 4, 5 505.75 5.19 0.0 -57.57 0.89 -0.10

9M-BVC 3 0 82.30 -0.0 0.0 0.0 0.151, 3 307.11 82.30 -0.0 -0.0 -0.0 0.151, 2,3 307.11 85.82 0.0 -0.0 0.0 0.271, 2, 3, 4 317.82 85.82 0.0 -0.0 -0.0 0.271, 2, 3, 4, 5 317.82 89.30 0.0 -0.0 -0.0 0.24

9M-BMVC 3 0 -2.56 0.0 -0.0 0.0 0.131, 3 741.39 -2.56 0.0 -0.01 1.11 0.131, 2,3 741.39 2.03 0.0 -0.01 1.11 0.211, 2, 3, 4 533.32 2.03 0.0 -0.01 0.51 0.211, 2, 3, 4, 5 533.33 19.09 0.0 -0.01 0.51 0.23

9M-3MP-6PVC 3 -214.41 16.75 -0.0 63.10 -1.45 0.181, 3 683.84 61.93 0.0 -147.68 1.57 -0.441, 2,3 761.33 110.54 -0.0 -210.03 1.60 -0.52

S19

1, 2, 3, 4 796.06 119.82 -0.0 -178.55 1.38 -0.441, 2, 3, 4, 5 795.46 114.02 -0.0 -187.31 1.51 -0.44

Figure S4. Structures of compounds with different electron-donating/withdrawing substituent groups at 3, 6 or 9-positon of carbazole scaffold in the ground state

Table S12. TPA properties of the designed molecules calculated using quadratic response theory

Molecules/nm𝜆𝑇𝑎

𝑚𝑎𝑥 /GM𝜎𝑇𝑎𝑚𝑎𝑥 /nm𝜆𝑇𝑏

𝑚𝑎𝑥 /GM𝜎𝑇𝑏𝑚𝑎𝑥

Transition natureb

9M-MVC 880 470 826.57 443 S0→S1 H→L (90.71%)

S20

9P-MVC 821.09 481 S0→S1 H→L (89.64%)9SA-MVC 843.44 728 S0→S1 H→L (74.02%)

H-1→L (16.90%)9M-BMVC 800 1737 840.58 209 S0→S1 H→L (78.47%)

738.01 1310 S0→S2 H→L+1 (59.37%)H-1→L (32.33%)

647.44 745 S0→S3 H-1→L (42.48%)H-2→L (12.18%)H→L+1 (18.31%)H→L+2 (15.93%)

9P-BMVC 832.11 241 S0→S1 H→L (77.20%)H-1→L+1 (14.25%)

738.01 1190 S0→S2 H→L+1 (58.16%)H-1→L (33.10%)

9SA-BMVC 846.31 365 S0→S1 H→L (69.30%)H-1→L+1 (12.08%)H-2→L (10.79%)

760.64 1400 S0→S2 H→L+1 (60.06%)H-1→L (21.47%)

9M-BMQVC 911.65 223 S0→S1 H→L (74.49%)H-1→L+1 (15.90%)H-2→L+1 (3.57%)

805.10 1590 S0→S2 H→L+1 (59.03%)H-1→L (30.83%)

670.19 1910 S0→S3 H-1→L (51.28%)H→L+1 (22.80%)H-2→L (8.47%)

9M-BMAVC 976.26 223 S0→S1 H→L (67.51%)H-1→L+1 (19.74%)

898.44 933 S0→S2 H→L+1 (56.34%)H-1→L (28.10%)

744.65 2260 S0→S4 H-3→L+1 (38.59%)H-2→L (24.40%)H→L+1 (16.90%)H-4→L (12.27%)

9M-BMPVC 767.71 152 S0→S1 H→L (70.58%)H-1→L+1 (13.48%)

704.46 563 S0→S2 H→L+1 (60.68%)H-1→L (27.02%)

9M-BMIVC 885.61 75.3 S0→S1 H→L (79.23%)H-1→L+1 (14.87%)

760.64 343 S0→S2 H→L+1 (47.90%)H-1→L (45.22%)

S21

670.19 1070 S0→S3 H-1→L (32.33%)H-2→L (26.30%)H→L+1 (25.89%)

a Experimental data2 b The results were computed at CAM-B3LYP/6-311+G(d) level of theory using DALTON

programs4 in water solvent

Table S13. TPA tensor elements (Sab) of all the studied molecules are calculated in water solvent.

Systems Ex.States TPA tensor elements (in a.u.)Sxx Syy Szz Sxy Sxz Syz

9M-BMVC 1 -0.1 -0.1 0.0 -351.2 -1.2 -0.52 812.0 178.8 0.3 0.0 1.4 0.13 595.5 -23.8 0.7 0.1 0.6 -0.1

9M-BMQVC 1 0.0 -0.1 0.0 392.3 1.2 -4.32 1007.0 160.4 -0.6 0.1 -19.5 0.13 -979.9 10.5 -0.9 -0.1 19.5 0.0

9M-BMAVC 1 -0.1 -0.1 0.0 403.1 -116.7 0.02 835.5 171.0 9.5 0.1 0.0 -62.63 0.3 0.0 0.0 358.7 -94.9 0.04 1101.4 182.8 3.6 0.0 0.0 -65.3

9M-BMPVC 1 -0.5 -0.2 0.0 273.1 0.9 0.12 -480.7 -163.5 0.3 -0.1 0.0 0.0

9M-BMIVC 1 0.0 0.0 0.0 221.8 0.6 0.02 444.1 64.4 0.5 0.0 0.0 0.93 737.8 -24.3 0.8 0.0 0.0 0.0

S22

Table S14. 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 program5.

Systems f n △En 𝜇0𝑓𝑥 𝜇0𝑓

𝑦 △μx △μy

9M-BMVC 1 1 1.48 5.27 0.00 0.00 2.952 2 1.68 0.00 -3.17 0.00 2.673 3 1.92 0.00 0.12 0.00 2.67

9M-BMQVC 1 1 1.36 -5.59 0.00 0.00 2.872 2 1.54 0.00 -2.95 0.01 2.483 3 1.85 0.00 0.17 0.02 3.42

9M-BMAVC 1 1 1.27 -4.61 0.00 0.00 3.132 2 1.38 0.00 -2.58 0.00 2.604 4 1.67 0.00 0.06 0.00 0.81

9M-BMPVC 1 1 1.62 4.40 0.00 -0.01 3.082 2 1.76 0.00 -2.56 0.01 3.263 3 1.98 0.04 -0.06 0.03 3.36

9M-BMIVC 1 1 1.40 -5.17 0.00 0.00 1.732 2 1.63 -0.01 3.37 0.00 0.943 3 1.85 0.00 -0.32 0.00 2.56

Systems f n △En 𝜇0𝑛𝑥 𝜇0𝑛

𝑦 𝜇𝑛𝑓𝑥 𝜇𝑛𝑓

𝑦

9M-BMVC 2 1 1.27 5.27 0.00 -4.05 0.003 1 1.04 5.27 0.00 2.46 0.00

9M-BMQVC 2 1 1.18 -5.59 0.00 -4.40 0.003 1 0.87 -5.59 0.00 3.22 0.00

9M-BMAVC 2 1 1.16 -4.61 0.00 -4.35 0.004 1 0.88 -4.61 0.00 -4.20 0.004 2 1.10 0.00 -2.58 0.00 1.69

9M-BMPVC 2 1 1.47 4.40 0.00 4.25 0.00

S23

3 1 1.26 4.40 0.00 -0.73 -0.019M-BMIVC 2 1 1.17 -5.17 0.00 -1.84 0.00

3 1 0.95 -5.17 0.00 2.57 0.00

Figure S9. Calculated the frontier molecular orbital levels for the studied compounds in ground

state

S24

Figure S10. Contour surfaces of the frontier molecular orbitals for the investigated compounds in ground state

S25

Figure S11. Contour surfaces of hole-electron distribution for the investigated compounds

Figure S12. Two-photon absorption spectra for the investigated molecules

S26

As shown in Figure S12, it is clearly that the electron-donating group at

9-position is beneficial to increasing TPA cross section and corresponding

wavelength, which is more distinct for asymmetrical compounds than symmetrical

compounds. For example, the σTmax for single chain compound 9SA-MVC (728 GM)

with methoxy-vinylbenzene is more than 1.5 times as large as that for 9M-MVC (443

GM), while the σTmax for bilateral chain compound 9SA-BMVC (1400 GM) is just

slightly larger than that for 9M-BMVC (1310 GM). As for the electron-withdrawing

group at 3, 6-position, the strong electron-withdrawing groups can give rise to the

enlargement of intramolecular electron transfer extent (see Figure S11), contributing

to enhancement of TPA cross section. The compound 9M-BMAVC possesses a

dramatically large σTmax (2260 GM) at 745 nm due to exceptional charge transfer

capacity. The excited state S1 and S2 play important roles in the TPA process (S0→S4)

as the paramount intermediate states, which closely couple with the final excited state

S4, thus the transition dipole moments between them are very large leading to pretty

good TPA properties.(see Table S14) Besides, the position of methyl also plays an

essential role in TPA properties. The TPA cross section for compound 9M-BMPVC

(563 GM) with methyl at pyridine side is not as large as that for compound

9M-BMVC (1310 GM) with terminal methyl, due to the smaller TPA tensor elements

Sxx (-480.7 a.u. for 9M-BMPVC, 812 a.u. for 9M-BMVC) and transition dipole

moment (4.40 a.u. for 9M-BMPVC, 5.27 a.u. for 9M-BMVC) (see Table S12, 𝜇01𝑥

Table S13 and Table S14).

S27

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