The absorption, emission spectra as well as ground and excited states calculations of some dimethine cyanine dyes

Journal of Molecular Structure: THEOCHEM 906 (2009) 50–55

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Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem

The absorption, emission spectra as well as ground and excited states calculations of some dimethine cyanine dyes Xiang-Han Zhang a, Lan-Ying Wang a,*, Gao-Hong Zhai a, Zhen-Yi Wen b, Zu-Xun Zhang a a

Key Laboratory of Synthetic and Natural Functional Molecule Chemistry, Ministry of Education, College of Chemistry and Materials Science, Northwest University, Tai Bai Bei Lu 229, Xian 710069, PR China b Institute of Modern Physics, Northwest University, Xian 710069, PR China

a r t i c l e

i n f o

Article history: Received 16 February 2009 Received in revised form 30 March 2009 Accepted 30 March 2009 Available online 10 April 2009 Keywords: Dimethine cyanine dye Ground and excited state calculation Electronic absorption spectrum Electronic emission spectrum Solvent effect

a b s t r a c t The absorption and emission properties as well as electronic structure in the ground (S0) and excited states (S1) of seven dimethine cyanine dyes were investigated by time dependent density functional theory (TD-DFT) and configuration interaction singles (CIS) levels. The effect of water on the absorption and emission spectra of the dyes was taken into account using the polarizable continuum model (PCM). TDDFT calculations provided a correct description of the electronic absorption spectra and showed that the dominant transitions of seven dye molecules presented a p–p* character. Scaling factor 0.72 was used on the absorption and emission wavelengths obtained by CIS method, and the scaled emission wavelengths were in good agreement with the experimental values. Compared with experimental counterparts, the average relative deviations of the absorption and emission maxima were about 2.4% and 1.7%, respectively. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Methine cyanine dyes present typical optical properties and act as the most important organic functional dyes in many processes of technological interest like sensitizers in photography [1] and solar cell [2], optical recording materials in laser disks [3], etc. A very attractive additional feature of dimethine cyanine dyes is their excellent fluorescent properties and the affinity for biological structures, especially for DNA [4–6]. They have been utilized in many fields, such as gel staining [7,8], DNA sequencing [9], and flow cytometry [10]. Besides, these dyes are the practical tool for cell imaging research [11,12]. Designing dyes and tuning their optical properties are of particular interest in their application area. The tool of theoretical chemistry can be valuable, which can help to rationalize the design of dyes and to refine their structure in order to optimize their electronic spectral property, solubility, and/or solid-state structure. Among a variety of quantum chemistry techniques, time dependent density functional theory (TD-DFT) based on optimization ground-state (S0) geometries at DFT [13,14] has become the accessible method for treating the electronic absorption properties of large organic molecules [15,16]. The configuration interaction with single excitation (CIS) [17] method based on optimization the first excited state (S1) structures [18,19] is important for the investiga* Corresponding author. Tel.: +86 29 88303403; fax: +86 29 88303798. E-mail address: [email protected] (L.-Y. Wang). 0166-1280/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2009.03.031

tion of electronic emission properties. In this paper, the absorption and emission spectra of seven dimethine cyanine dyes a–g (Fig. 1) are investigated by TD-DFT and CIS levels based on S0/S1 optimized structures. In order to obtain deeper insight into electronic spectral properties of the dimethine dyes, the effect of aqueous solvent on the absorption and emission spectra is taken into account with the polarizable continuum model (PCM) [20,21]. Detailed results and discussion are elaborated in the following sections. 2. Calculation details In this work, DFT calculations were carried out using hybrid exchange–correlation functional PBE1PBE [22], which referred to hybrid functional of Perdew, Burke, and Ernzerh including 25% of Hartree–Fock (HF) exchange and 75% correlation weighting. S0 geometries were fully optimized at the DFT level using 6-31G basis set. However, charge transfer excited states were not well described by DFT level within the adiabatic approximation and with the usual exchange–correlation functional [23–25]. S1 of seven dye molecules were optimized by CIS/6-31G level. Both TDPBE1PBE/6-31G levels and CIS/6-31G were used to predict the absorption spectra on S0 optimized structures and emission spectra on S1 optimized structures, respectively. We also took into account the solvent polarity effect and adopted the PCM model at PBE1PBE/6-31G and CIS/6-31G level, respectively. In this model, the dye molecules were embedded in a cavity surrounded by an infinite dielectric with the value of the

X.-H. Zhang et al. / Journal of Molecular Structure: THEOCHEM 906 (2009) 50–55

18 1.4 2 1 1 .4 1.404 2 1.386 1.432 1.407 0 1.363 1 .3

3 4 12 2

13 R 11 10 I

5

N1 6 CH3

8

NH

7

14

N 1.466

1.381 1.394

9

1.509 1.499

CH3 a

17 1.4.420 1 1.405 9 9 1.386 1.434 1 .336 8 1.362 1. 1.4 NH N1.466 1.404 1.3951 5 1.380 1.464 1.420 1.393

CH3


18 1.4.42 3 1 1.405 0 0 1.385 1.430 1.4371 1. NH 1.363 1. 4 N 1.467 1.404 1.39719 1.378 1.465 1.418 1.393

Cl

1.745 1.722

CH3


c

b 16 1.4422 1 . 1.407 8 1.386 1.430 1 .3971 1.363 1.3

Br1.893 1.873

1. NH 1.34 18 96


Cs

H3C

1.404 1.464 1.419

51

N 1.378 1.467 1.405 1.393 1.465 1.418

1 NH 1.3 .41 7 97

CH3


1.508

17 1.4 419 1. 1.404 01 1.388 1.434 1.4 68 3 1.364 1.4 NH 1. N 1.466 1.404 1.39517 1.380 1.464 1.420 1.394

CH3

H3C 1.500


e

d 16 1. 4 21 1 .4 1.405 0 1.387 1.430 1.4 0 71 1.365 1. NH 1.3 N 1.467 1.404 1.394718 1.378 1.464 1.418 1.393

CH3 1.742 1.721
Br

1.896 1.872

16 1 .4 .421 1 1.406 00 1.386 1.430 1.4 71 1.365 1 .3 1 1. 41 NH .3 8 N 1.405 97 1.379 1.467 1.418 1.393 1.464

CH3


g

f

Fig. 1. Some selected bond lengths (Å) and torsion angles (°) of S0 and S1 for dyes a–g (bold for S1 and light italics for S0).

desired solvent (e = 78.39 for water). In our calculation, the anion was neglected as the experiment proved that the anion would not affect the spectra of the cationic dyes in the solvent. Analytic frequency calculations were done to confirm the optimized structures to be an energy minimum. All calculations reported in this work were carried out with the Gaussian 03 program [26]. The first 20 singlet–singlet electronic transitions in aqueous solution were also calculated by TD-PBE1PBE/PCM level, the theoretically simulated absorption spectra of the seven dyes were calculated using the SWizard program, Revision 2.0 [27]. Absorption profiles were calculated using Gaussian model (1) with the halfbandwidth D1/2,I = 5000 cm1. 3. Results and discussion 3.1. Geometries and charges of S0 and S1 for seven dye molecules S0 and S1 geometries of seven dyes a–g are optimized by PBE1PBE/6-31G and CIS/6-31G levels, respectively. The key geometric parameters of the optimized structures are presented in Fig. 1. It can be found that the carbon–carbon bond lengths on seven dye molecular skeletons are intermediate between typical C–C single (1.54 Å) and C@C double (1.34 Å) bonds, and carbon–nitrogen bond lengths are also intermediate between typical C–N single (1.47 Å) and C@N double (1.27 Å) bonds for both S0 and S1. All C–C– C, C–N–C, and C–C–N bond angles are close to 120°. It indicates that the p electrons in seven dye molecules are delocalized for both S0 and S1. The torsion angles of R(13)–C(12)–C(11)–C(10) and

R(13)–C(11)–C(10)–C(2) are in the range from 179.3° to 179.8°, which show that the substituted groups are not significantly distorted both from planarity and from coplanarity with the quinoline rings. In addition, the dye molecules have trans-configuration as indicated by torsion angle C(4)–C(5)–C(6)–C(7) (175°–178°). The net charge population of seven dyes is also investigated. The mulliken charges in S1 and S0 are given in Table 1. For S0, the positive charges mostly are concentrated on quinoline groups with the values of 0.6668–0.6941, the indole groups have a slightly positive charges of 0.3147–0.3375. The negative charges are localized on vinyl fragments with the values from 0.0042 to 0.0088. For S1, the positive charges are concentrated mostly on quinoline groups with the values of 0.6457–0.6691, the indole groups and vinyl fragments have slightly positive charges of 0.2273–0.2899 and 0.0523–0.0645. Meanwhile, it could be found that CH3 is a electron-donation substituent with negative charges for b and e, Cl is a electron-withdrawing substituent for c and f, and Br is a weak electrondonation substituent for d and g. Compared with the charge population of a, the positive charges decrease for S1 and the negative charges increase for S0 on vinyl fragments, the positive charges increase on quinoline groups and decrease on indole groups both for S0 and S1 of b and e, but the variation of net charge population over subunits of c, d, f, and g shows a contrary tendency. 3.2. Methodology To obtain a theoretical support for the electronic properties of seven dyes, the electronic absorption and emission spectra are pre-

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X.-H. Zhang et al. / Journal of Molecular Structure: THEOCHEM 906 (2009) 50–55

Table 1 Net charge population over subunits of seven dyes on S1 and S0. Dyes

C/Cl/Br13

Vinyl fragment

Quinoline group

Indole group

Sum of Mulliken charges

a b c d e f g

– 0.5135/0.6055 0.0661/0.0916 0.0448/0.0213 0.5226/0.6085 0.0744/0.0957 0.0349/0.0154

0.0603/0.0057 0.0580/0.0082 0.0644/0.0042 0.0643/0.0044 0.0576/0.0088 0.0645/0.0043 0.0644/0.0044

0.6594/0.6794 0.6672/0.6929 0.6457/0.6668 0.6461/0.6683 0.6691/0.6941 0.6469/0.6668 0.6476/0.6687

0.2802/0.3264 0.2748/0.3153 0.2899/0.3373 0.2896/0.3361 0.2732/0.3147 0.2886/0.3375 0.2880/0.3357

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

Bold for S1 and light italics for S0.

dicted with both TD-DFT/PCM and CIS/PCM methods at the S0 or S1 geometries. The scaling factor 0.72, which proposed by Broo and Holmen [28], is used on the absorption and emission wavelengths obtained by CIS method, which has already been proved to remove these systematic errors. 3.2.1. Absorption spectra Previously, we have investigated the electronic absorption and emission spectra of seven dimethine dyes in aqueous solution experimentally [29]. In this paper, theoretical kmax of seven dimethine cyanine dyes are calculated by TD-PBE1PBE and CIS levels. The values are shown in Table 2 and the experimental and simulated absorption spectra of seven dyes are depicted in Fig. 2. It can be seen that the kmax obtained by pure CIS method deviates significantly from the experimental data. When divided by the scaling factor 0.72, the kmax obtained by CIS level reduces the absolute deviation to 12.1–21.0 nm for dyes a–g (Route 1). TD-PBE1PBE overestimates kmax 12.5–19.2 nm for dyes a–g relative to experimental data. The introduction of a solvent reaction field and the combination of PCM and TD-PBE1PBE method makes the kmax much closer with the experimental values, which overestimates the kmax 6.0 nm for dye a, about 9 nm for e, f, and c, 14.4 nm for b, and about 15 nm for d and g, and the average relative deviation is 2.4% in aqueous solution. Comparison of absolute deviation for each dye reveals that TD-PBE1PBE method is more suitable for studying the absorption spectra of the dimethine cyanine dyes. It indicates that the accuracy is increased when the solvent effect is taken into account. From Fig. 2, it also can be found that dyes a–g in the region 453–470 nm show intense and broad absorption with log eexp of 4.04–4.34 in aqueous solution. The shape of simulated absorption spectra is in a principal agreement the experimental spectra. The molar extinction coefficients can be calculated using Gaussian model (1) by SWizard program [27]:

eðxÞ ¼ c1

X

f1

1

D1=2;I

exp 2:773

ðx  x1 Þ2

! ð1Þ

D21=2;I

where f is oscillator strength, x is the electronic transitions with energies in cm1, and D1/2,I corresponds to the half-bandwidth in cm1. The half-bandwidth D1/2,I is taken equal to 5000 cm1 according to empirical values so that all the bands for all the dyes are supposed the have the same width. Table 4 lists the calculated and experimental molar extinction coefficients. According to the Eq. (1), the dyes have log ecal of 4.61–4.63 in aqueous solution. The calculated molar extinction coefficients are in the same order of magnitude as experimental values. TD-PBE1PBE correctly predicts the intensity of the absorption band of seven dyes. 3.2.2. Fluorescent emission spectra The experimental and theoretical kem of seven dyes are summarized in Table 3. The emission maxima of the dyes calculated by TD-PBE1PBE and CIS on S1 optimized structures are predicted at 477.3–487.5 nm and 372.0–376.8 nm, respectively. The kem is underestimated 18.1–35.0 nm with the scaling factor 0.72 to divide the kem calculated by CIS level (Route 2). When the solvent effect is taken into account, the absolute deviations are 0.2 nm for dye b, 5.8 nm for a, 7.3 nm for e, 10.3 nm for d, 11.4 for g, 13.2 for f, and 16.8 for c, and the average relative deviation is 1.7%. The kem obtained by Route 2 in aqueous solution is in good agreement with the experimental values. Overall, the outcomes are quite satisfactory and the scaling factor 0.72 used for scaling CIS method is reasonable. 3.3. Assignment of the calculated transition and molar extinction coefficients Table 4 lists the main orbital compositions of the computed lower-lying singlet excited state and transition feature of the dyes

Table 2 The absorption maximum (kmax) of dyes obtained by CIS and TD-PBE1PBE levels (in nm). Dyes

a b c d e f g % A.R.D.d

TD-PBE1PBE

Route 1a

CIS c

c

Gas

Aqueous

Gas

Aqueous

474.6(16.6) 474.1(21.1) 483.5(13.5) 484.2(19.2) 472.7(14.7) 482.5(12.5) 483.6(18.6) 3.6

464.0(6.0) 467.4(14.4) 479.1(9.1) 480.1(15.1) 466.7(8.7) 478.9(8.9) 480.5(15.5) 2.4

341.2(143.8) 340.0(113.0) 346.3(123.7) 346.4(118.6) 342.4(115.6) 347.1(122.9) 347.8(117.2) 26.4

343.6(114.4) 342.0(111.0) 349.4(120.6) 349.6(115.4) 340.2(117.8) 350.4(119.6) 351.1(113.9) 21.8

Data in parentheses are absolute deviations between experimental and calculated kmax. a kmax obtained by CIS level, then scaled by 0.72. b The experimental values are obtained in aqueous solution, Ref. [29]. c PCM model is used for calculation in aqueous solution. d Average relative deviation.

Exp.b c

Gas

Aqueous

473.9(15.9) 472.2(19.2) 481.0(21.0) 481.1(16.1) 475.6(17.6) 482.1(12.1) 483.1(18.1) 3.1

477.2(19.2) 475.0(22.0) 485.3(15.3) 485.6(20.6) 472.5(14.5) 486.7(16.7) 487.6(22.6) 4.1

458.0 453.0 470.0 465.0 458.0 470.0 465.0 –

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X.-H. Zhang et al. / Journal of Molecular Structure: THEOCHEM 906 (2009) 50–55

0.04

Experimental spectra Simulated spectra

a

0.04 0.03

Absorbance

0.03

Absorbance

Experimental spectra Simulated spectra

b

0.02

0.01

0.02 0.01 0.00

0.00 -0.01 -0.01 350

450

400

550

500

600

350

c

500

550

600

Wavelength (nm) 0.05

0.04

450

400

Wavelength (nm)

Experimental spectra Simulated spectra

d

Experimental spectra Simulated spectra

0.04

0.03

Absorbance

Absorbance

0.03 0.02 0.01

0.02 0.01

0.00

0.00

-0.01

-0.01

350

450

400

550

500

350

600

0.04

500

550

600

Wavelength (nm) 0.05

Experimental spectra Simulated spectra

e

450

400

Wavelength (nm)

0.04

Experimental spectra Simulated spectra

f

0.03

Absorbance

Absorbance

0.03 0.02 0.01 0.00

0.02 0.01 0.00

-0.01 -0.01 -0.02 350

400

450

550

500

600

350

400

450

500

550

600

Wavelength (nm)

Wavelength (nm) 0.05

Experimental spectra Simulated spectra

g 0.04

Absorbance

0.03 0.02 0.01 0.00 -0.01 350

400

450

500

550

600

Wavelength (nm) Fig. 2. Experimental and simulated absorption spectra of dyes a–g in aqueous solution.

molecules obtained at the TD-PBE1PBE(PCM)/6-31G level. From Table 4, it can be seen that the lowest energy absorption in the seven dyes is due to the first dipole-allowed p ? p* transition from HOMO to LUMO with the largest oscillator strength. From our calculation, it can also be found that the frontier orbitals of seven

dyes are very similar. For instance, the molecular orbitals of dye b are depicted in Fig. 3. It can be seen that the HOMO of dye b is mainly localized on the indole group, and the LUMO of dye b is mainly distributed at quinoline nucleus and vinyl fragment. The HOMO ? LUMO transition of dye b goes from the indole group

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X.-H. Zhang et al. / Journal of Molecular Structure: THEOCHEM 906 (2009) 50–55

Table 3 The emission spectra of dyes obtained by CIS and TD-PBE1PBE levels (in nm). Dyes

TD-PBE1PBE

a b c d e f g % A.R.D.d

Route 2a

CIS c

c

Gas

Aqueous

Gas

Aqueous

477.4(63.2) 478.0(58.4) 486.8(69.4) 488.3(61.5) 477.3(66.9) 485.9(67.9) 487.5(64.9) 11.8

485.2(55.4) 484.3(52.1) 493.5(62.7) 493.7(56.1) 486.0(58.2) 493.5(60.3) 493.5(58.9) 10.4

372.0(168.6) 373.2(163.2) 375.3(180.9) 375.8(174.0) 373.7(170.5) 376.1(177.7) 376.8(175.6) 31.6

385.1(155.5) 386.0(150.4) 388.4(167.8) 388.5(161.3) 386.5(157.7) 389.2(164.6) 389.5(162.9) 29.2

Exp.b c

Gas

Aqueous

516.6(24.0) 518.3(18.1) 521.2(35.0) 521.9(27.9) 519.1(25.1) 522.3(31.5) 523.3(29.1) 4.1

534.8(5.8) 536.2(0.2) 539.4(16.8) 539.5(10.3) 536.9(7.3) 540.6(13.2) 541.0(11.4) 1.7

540.6 536.4 556.2 549.8 544.2 553.8 552.4 –

Data in parentheses are absolute deviations between experimental and calculated kem. a kem obtained by CIS level, then scaled by 0.72. b The experimental values are obtained in aqueous solution, Ref. [29]. c PCM model is used for calculation in aqueous solution. d Average relative deviation.

Table 4 Main calculated orbital transitions by PBE1PBE/PCM for the dyes. Dyes

States

a b c d e f g

Transition feature *

p?p p ? p* p ? p* p ? p* p ? p* p ? p* p ? p*

1A 1 A 1 A 1 A 1 A 1 A 1 A a b c

DE (eV)

Transition charactera

f

2.67 2.65 2.59 2.58 2.66 2.59 2.58

HOMO ? LUMO HOMO ? LUMO HOMO ? LUMO HOMO ? LUMO HOMO ? LUMO HOMO ? LUMO HOMO ? LUMO

0.9742 0.9375 0.9627 0.9855 0.9451 0.9596 0.9758

(82.9%) (82.5%) (81.7%) (81.8%) (82.5%) (72.2%) (81.8%)

b

log ecal

log eexp

4.63 4.61 4.62 4.63 4.61 4.62 4.63

4.34 4.11 4.04 4.20 4.11 4.23 4.20

c

The proportion of the main transition are given in parenthesis. Oscillator. The experimental values were obtained in aqueous solution, Ref. [29].

to the quinoline moiety. It involves an intramolecular charge transfer, whereas indole and quinoline moiety act as an electron donor and an electron acceptor, respectively. Thus, only valence p/p* molecular orbitals are involved in the electronic transition.

the major systematic errors of the CIS computational scheme, the values of the fluorescent emission spectra are in good agreement with the experimental values. Compared with experimental counterparts, the average relative deviations of the absorption and emission maxima are about 2.4% and 1.7%, respectively.

4. Conclusions Acknowledgements PBE1PBE and CIS methods give reliable descriptions of the S1 and S0 geometries of the dimethine cyanine dyes. TD-PBE1PBE/PCM level not only successfully reproduces the experimental absorption maxima, but also presents that the first vertical excited singlet state is the only allowed state with the strongest oscillator strength, which corresponds to p–p* excitation of solely HOMO ? LUMO for the seven dyes. After applying the scaling factor 0.72 to correct

We appreciate the financial support for this research by a grant from the Natural Science Foundation of Shaanxi Province (No. SJ08B04), the Special Science Research Foundation of Education Committee (No. 08JK458), NWU Excellent Doctoral Dissertation Foundation (No. 08YYB04) and the Science Research Startup Foundation of Northwest University. References

0 -1 -2

E/eV

-3

LUMO+3 83rd LUMO+2 82nd LUMO+1 81st LUMO 80th

-4 -5 -6

HOMO 79th

-7

HOMO-1 78th HOMO-2 77th HOMO-3 76th

-8

Fig. 3. Molecular orbitals of dye b.

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