Linear and Nonlinear Optical Properties of Triphenylamine

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Linear and Nonlinear Optical Properties of Triphenylamine-Indandione Chromophores: Theoretical Study of the Structure-Function Relationship under the Combined Action of Substituent and Symmetry Change Zeyu Liu, Shugui Hua, and Xiufen Yan J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b09186 • Publication Date (Web): 27 Jan 2018 Downloaded from http://pubs.acs.org on January 30, 2018

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The Journal of Physical Chemistry

Linear and Nonlinear Optical Properties of Triphenylamine-Indandione Chromophores: Theoretical Study of the Structure-Function Relationship under the Combined Action of Substituent and Symmetry Change Zeyu Liu†,‡, Shugui Hua§ and Xiufen Yan∗,¶ †

Sericultural Research Institute, Jiangsu University of Science and Technology, Zhenjiang 212018, People’s Republic of China ‡

School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210093, People’s Republic of China §

College of Life Science and Chemistry, Jiangsu Key Laboratory of Biological Functional

Molecules, Jiangsu Second Normal University, Nanjing 210013, People’s Republic of China ¶

School of Environmental and Chemical Engineering, Jiangsu University of Science and Technology, Zhenjiang 212018, People’s Republic of China

Abstract

Linear

and

nonlinear

optical

properties

of

experimental

synthesized

triphenylamine-indandione chromophores were investigated by (time-dependent) density functional theory ((TD-)DFT) calculations. The absorption and emission spectra as well as the static and dynamic first hyperpolarizabilities related to the combined effect of substituent introduction and symmetry breaking were discussed in detail. Theoretical analysis indicated the uniting of indandione acceptor group(s) with precursor (triphenylamine, TriPhA), molecular symmetry is therefore destroyed simultaneously, leads to an obvious change in both the peak

∗

Corresponding author. Tel: +86 511 84401181. E-mail: [email protected]. 1

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position and intensity of the linear spectra. Same process can also substantially magnify the molecular

first

hyperpolarizabilities.

The

triphenylamine-indandione

molecules

exhibit

efficiencies in static first hyperpolarizability relative to that of electron-donating TriPhA part and electron-accepting indandione moiety. The optical nonlinearity would be further expanded under the influence of resonance effect induced by appropriate excitation. Incident light with a wavelength near two times the one-photon absorption is likely to cause greater frequency dispersion response. In particular, the first hyperpolarizabilities of title compounds can be enlarged by about 3.2 times averagely by resonance enhancement at a fundamental wavelength of 1064 nm.

2


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1. Introduction In the recent twenty years, the design and synthesis of organic nonlinear optical (NLO) materials have received a great interest, both experimentally and theoretically.1-12 Scientists have continuously proposed different strategies for achieving high-performance photoelectric functional molecules.2-6,13-15 For purely organic compounds, a well-established method to increase the molecular NLO responses is modification of the molecules with some electron donor (D) and/or acceptor (A) groups.16-18 The introduction of electron donor and/or acceptor unit(s) can increase the polarization abilities and reduce the optical gap of the NLO chromophores. And besides, it is often be neglected that the consequent symmetry breaking of molecule is also one of the critical factors in changing their optical properties. Substituted azobenzene derivatives with electronic “push-pull” character have long been the outstanding representatives of π-conjugated molecules.19,20 Examples are too numerous to mention. Considering the original triphenylamine and indandione derivatives as a novel class of non-azo nonlinear chromophores first began at the end of the last century in the field of material science. The synthesis of indandione derivatives and their potential applications in optical devices have been expatiated in previous works.21-23 Recently, Rutkis et al. have studied the third-order nonlinearities of several triphenylamine and indandione derivatives by using the Z-scan method.23,24 The linear absorption, one- and two-photon luminescence, and second-order NLO properties for a portion of triphenylamine and indandione related chromophores have also been studied by using experiments and Ab initio calculations.24-28 Although all these studies show that the indandione-containing compounds could exhibit high NLO responses, the in-depth analysis for the exact nature of their optical properties is still rare. Molecular orbital calculations can provide 3



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useful information on the inherent relation between their structure and properties of materials on the electronic level. These facts inspired us to theoretically explore the structure-property relationships of indandione-containing chromophores by using the (TD-)DFT method. In this paper, we describe a detailed quantum-chemical analysis for the nature of optical properties of some triphenylamine-indandione chromophores under the combined action of substituent and symmetry change. The results indicated that the introduction of electron-accepting indandione group(s) and damaging symmetry to molecules could affect their optical properties collaboratively. The present work may helpful for experimental design and synthesis of novel functional materials with excellent NLO properties.

2. Computational Details As is well known, electron correlation plays a major role in the description of the structure and the electron transfer properties of a molecule.29 However, since it is extremely time-consuming to calculate the large systems by using the electronic correlation method, DFT calculations are generally adopted as a compromise between the accuracy and computational cost. Many studies have shown that CAM-B3LYP method is more suitable for optimizating the ground-state structures as well as for calculating the NLO properties of the intramolecular charge transfer (ICT)-based chromophores than conventional hybrid functional, such as B3LYP.30-37 Based on this, all of the molecular structures were fully optimized by DFT calculations at the CAM-B3LYP/6-311g(d) levels within the Gaussian 09 package.38 Vibrational frequency calculations were performed to confirm that all structures as the local minima (the number of imaginary frequency is zero) on the potential surfaces. The electronic transitions were then 4


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obtained through TD-DFT studies at the TD-B3LYP/6-311g(d) level of theory.39,40 The simulated spectra obtained by Gaussian-fitting of the vertical excited energies and oscillator strengths within the GaussSum 3.0 program were adopted in spectrum analyses.41 To consider the resonance effects, the static (λ = ∞ nm) and frequency-dependent (λ = 1907, 1460, 1340, and 1064 nm) first hyperpolarizabilities

were

evaluated

by

analytical

third

energy

derivatives

at

the

CAM-B3LYP/aug-cc-pVDZ levels. All calculations were performed in CHCl3 (ε = 4.9) solution, using the self-consistent reaction field (SCRF) approach with the polarizable continuum model within the integral equation formalism (IEFPCM).42 The resulting data referred to the nonlinearity were analyzed by means of code Multiwfn 3.4.1,43,44 in which the average linear polarizability ( α ) is determined by

α = (α x x + α y y + α zz ) 3 the total hyperpolarizability (βtot) and the vectorial part of βtot (βvec)45 are described as

β tot = ( β x 2 + β y 2 + β z 2 )1/2

β vec = ∑ i

µi β i , i = x, y, z µ

where x, y, z

β i = (1 3 ) ∑ ( β ijj +β jji +β jij ), i = x, y , z j

All the first hyperpolarizability values are consistent with convention B in the notation of Willetts et al.46

3. Results and Discussion 3.1 Molecular structures and electronic characteristics 5



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We theoretically investigated the optical properties of five triphenylamine-indandione chromophores in this work. For convenience, the selected molecules adopt the same naming method with those in Ref. 23, as shown in Figure 1. Cartesians coordinates for ground- and excited-state indandione derivatives obtained by (TD-)DFT optimizations are tabulated in Tables S1 and S2, respectively. TriPhA is a precursor and was chosen as a reference structure. DPhABI, PhDiABI, and TriABI were obtained by modificating the TriPhA with one, two, and three indandione acceptor group(s) onto the periphery. Then, DPhABI-tb and PhDiABI-tb could be formed by replacing the terminal hydrogen atom of indandione unit with a tert-butyl group in DPhABI and PhDiABI, respectively. We also attempted to obtain the geometry of TriABI-tb, but it could not be optimized successfully although we tried several times by using various strategies. Among all the above mentioned molecules, TriPhA, DPhABI, DPhABI-tb, PhDiABI, and TriABI have become available and been confirmed to possess third-order NLO responses.23 The PhDiABI-tb molecule, which may be easy to synthesize in experiment, was theoretically designed for the purpose of a contrast analysis. Outwardly, the molecular geometries are changed from higher D3 to lower C1 symmetry before and after being substituted by indandione and tert-butyl group on TriPhA. While from the point of electronic structure, the conjugations of the DPhABI, DPhABI-tb, PhDiABI, and PhDiABI-tb molecules are asymmetrically lengthened by extending the π-orbitals (see below).

6


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Figure 1. Frame structures, electrostatic potential (ESP) charges on molecular domains, and crucial torsion angles involved in the conjugation for title chromophores. The blue, red, and green numbers represent partial charges (in a.u.) in TriPhA, indandione, and tert-butyl groups, respectively. The purple numbers refer to the values of the dihedral angles (in º) between the indandione group and the connecting benzene ring of TriPhA unit (the ground-state data outside parentheses and the excited-state ones in parentheses).

A quantitative analysis shows that the indandione moiety and the connecting benzene ring almost lie in the same plane with the dihedral angles in the range of 0.33º and 3.48º for all the ground-state triphenylamine-indandione chromophores. It is generally known that the conjugacy and planarity of NLO molecules affect the ICT capability, and then their photoelectric properties. A clear determination of the ICT with the substituent could be gained by examining the difference 7



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of the molecular ESP contour in Figure S1. By comparing the ESP contour of TriPhA to those of the substituted molecules (DPhABI, DPhABI-tb, PhDiABI, PhDiABI-tb, and TriABI), one can see the molecular charge populations of the latter have been effectively polarized. The positive charge is clearly located at the TriPhA donor and tert-butyl parts, and the indandione acceptor groups averagely occupy negative charge (mainly on oxygen atoms). As shown in Figure 1, the magnitude of the charge separation is calculated to be about 0.25 a.u. for DPhABI. Nearly doubling or tripling of the charge separation can be seen in PhDiABI and TriABI. Accurately, with the increase in the number of indandione groups, the average degree of charge separation per indandione unit decreases, from 0.25 a.u. through 0.21 a.u. to 0.19 a.u., which might be attributable to the limited electron-donating ability of the TriPhA group and the steric hindrance from the indandione units. Moreover, the introduction of tert-butyl group(s) was found to slightly bring down the positive charge on TriPhA part and evidently increase the negative charge on the indandione group because of their electron-donating ability. 3.2 Linear optical properties: absorption and emission spectra Absorption spectrum Selected data related to transitions for the studied chromophores are listed in Table 1, along with the values available from experiments. The theoretical absorption spectra of molecules in Figure 2 were obtained by fitting the calculated vertical excitation energies and oscillator strengths without any scaling. The positions and relative intensities of the absorption peaks obtained by theoretical calculations are in satisfactory agreement with the experimental observations.23,25,27 The mean absolute deviation is in within 10 nm by comparing calculated data of maximum absorption wavelengh with the experimental values, with a maximum deviation of 25 nm being observed for DPhABI and DPhABI-tb. 8


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Table 1. Calculated absorption and emission wavelengths (λabs and λem), excited states involved (Sn), main transition orbitals (MOs), oscillator strenghs (f0), transition energies (Egm), Stokes shifts (∆EStokes), the difference of the dipole moment (∆µ) between the ground state and the crucial mth excited state, and the values of (f0·∆µ)/Egm3 for title compounds obtained at the TD-B3LYP/6-311g(d) level in CHCl3 solution (with the corresponding experimental values shown in parentheses) λabs/nm 308 308

Sn S2 S3

Absorption MOsc HOMO→LUMO+1 (98%) HOMO→LUMO+2 (98%)

f0 0.31 0.31

DPhABI

475 (499a, 493b) 311

S1 S6

HOMO→LUMO (99%) HOMO-2→LUMO (75%)

DPhABI-tb

475 (499a) 314

S1 S5

PhDiABI

524 (527a) 446 319

PhDiABI-tb

compound TriPhA

TriABI

a

Egm/eV

Emission λem/nm

4.03

353

45

0.03

0.00014

1.11 0.30

2.61

733

258

14.11

0.88

HOMO→LUMO (99%) HOMO-2→LUMO (78%)

1.20 0.30

2.61

722

247

14.48

0.95

S1 S2 S11

HOMO→LUMO (99%) HOMO→LUMO+1 (98%) HOMO-1→LUMO+1 (84%)

1.44 0.30 0.49

2.37

607

83

6.13

0.66

524 446 325

S1 S2 S11

HOMO→LUMO (99%) HOMO→LUMO+1 (98%) HOMO-1→LUMO+1 (87%)

1.57 0.32 0.51

2.37

603

79

6.04

0.71

521 (518a) 521 (518a)

S1 S2

1.07 1.07

340

S13

2.38

588

67

9.41

0.73

340

S14

HOMO→LUMO (99%) HOMO→LUMO+1 (99%) HOMO-2→LUMO+1 (16%) HOMO-1→LUMO (77%) HOMO-2→LUMO (43%) HOMO-1→LUMO+1 (49%)

0.56

∆EStokes/nm ∆µ/Debye

(f0·∆µ)/Egm3

0.56

Experimental results originated from Ref. 23; b Experimental results originated from Ref. 25; c Minor contributions of less than 10% are not shown.

9



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Figure 2. Absorption spectra of the studied chromophores obtained from TD-DFT/PCM calculations at the TD-B3LYP/6-311g(d) level. The numbers on chart refer to the value of approximate absorption wavelengths. A Gaussian function has been employed with a full width at half-maximum of 3000 cm-1.

The electronic excitation from S0 to S1 of TriPhA, corresponding to HOMO→LUMO transition, is forbidden due to the constraint of transition selection rules. For a symmetrical two-dimensional (2D) molecule with D3 symmetry, TriPhA has energetically degenerate unoccupied molecular orbitals, LUMO+1 and LUMO+2, which accordingly give rise to two excited states S2 and S3, originating from HOMO→LUMO+1 and HOMO→LUMO+2, respectively. As a result, two degenerate dipole-allowed transitions, S0→S2 and S0→S3, with oscillator strength for each one of 0.31 are responsible for the only absorption band at 308 nm. Many previous studies on the optical properties of ICT-based chromophores have shown that introduction the electron donor and/or acceptor group(s) to precursor can make the maximum absorption peak red-shift in the system. Similar to this conclusion, after extending the π-orbital by modifying the indandione group(s) onto the terminal of the TriPhA molecule, the absorption of indandione-containing chromophores exhibit a strong electron donor to acceptor (TriPhA part to 10


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indandione moiety) ICT excitations in the visible region of 475-524 nm with a less intense band at about 311-340 nm. The absorptions are observed to be sensitive to the number of the indandione acceptor unit, whereas they are scarcely influenced by subsequent introduction of tert-butyl group. The position of high-energy absorption in DPhABI remains almost unchanged with a negligible red-shifting of 3 nm relative to the original band of the TriPhA, but the oscillator strength is halved to f0 = 0.30 resulting from the symmetry breaking of the electronic structure. This band is mostly composed of transition from HOMO-2 to LUMO. Additionally, the destruction of molecular orbital symmetry leads to the concomitant formation of a new band at lower-energy region of 475 nm. This band can be characterized as a transition mainly from HOMO to LUMO. Introduction of tert-butyl group on indandione to form DPhABI-tb will not cause significant change in the absorption spectrum. The absorption spectrum of PhDiABI chromophore is dominated by a peak at 524 nm following by a band at 319 nm. The maximum absorption feature is basically assigned to the electron excitation from HOMO to LUMO, and the high-energy one comes from the transition involving HOMO-1 and LUMO+1 as starting and arriving orbitals, respectively. The structural rigidity caused by the internal steric hindrance between two indandione groups in PhDiABI leads to the intensity of its two absorption peaks are stronger than the corresponding ones of the DPhABI. The calculated oscillator strengths of the absorption peaks for PhDiABI are large with f0 = 1.44 and 0.49, respectively. Specifically, a marked difference of the absorption band between DPhABI and PhDiABI is that the latter exhibits a shoulder peak appearing at about 446 nm. This relatively weak (f0 = 0.30) absorption band is primarily originated from a HOMO→LUMO+1 excitation. The absorption spectrum of PhDiABI-tb has no distinct difference from that of 11



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PhDiABI molecule, just like the situation of DPhABI vs. DPhABI-tb. Two couples of energetically degenerate frontier molecular orbitals (FMOs), occupied HOMO-1/HOMO-2 and unoccupied LUMO/LUMO+1, are associated with electron transitions involved in optical excitation process of quasi-C3-symmetry TriABI molecule. As a result, two pairs of doubly-degenerate excited states, S1/S2 and S13/S14, contribute most of the one-electron absorption. The maximum absorbance peak at 521 nm of TriABI is derived from the coupling of electron transition from ground state S0 to excited states S1 and S2. This band is mainly associated with the HOMO→LUMO and HOMO→LUMO+1 transitions with an oscillator strength of f0 = 1.07 for each one, and the excitation coupling is obviously doubling the absorption peak intensity. The high-energy absorption band at 340 nm is dominated by the interaction of the ground state S0 with the other two higher-order excited states S13 and S14, basically corresponding to the alternate HOMO-2/HOMO-1→LUMO/LUMO+1 transitions (f0 = 0.56). It is worth mentioning that there exists an inconspicuous shoulder peak at about 460 nm for TriABI in experiments,23,27 whereas the calculation didn't show the transition attributable to this absorption. Possibly this is due to the effect that Kohn-Sham DFT does not account for some symmetry related issues.47 The natural transition orbitals (NTOs) analysis can make the description of the topology of transitions in the electron excitation process more clear. The presentation of crucial excited states by NTOs can greatly simplify the characterization of transition orbits relative to that by molecular orbitals (MOs).48 Displayed in Figure 3 are the NTO pairs involved in the maximum absorption transitions of the chromophores. The NTOs associated with other absorption peaks of the molecules have been presented in Figure S2. In general, different absorptions involve different parts of the molecular skeleton, but the electron transitions in all absorptions are identified from a 12


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bonding to an antibonding π orbital, i.e., assigned as the π→π* type. The NTOs populated in the substituent indandione moiety contribute significantly to the absorption spectrum. By comparison, there is no crucial orbital distribution localized at the tert-butyl group in DPhABI-tb and PhDiABI-tb. That is why there is only slightly distinction in the linear and nonlinear optical properties between each pair of analogues (DPhABI vs. DPhABI-tb and PhDiABI vs. PhDiABI-tb).

Figure 3. The dominant NTO pairs (isovalue = 0.02 a.u.) involved in the maximum absorption obtained at the TD-B3LYP/6-311g(d)/PCM level for the studied indandione derivatives. The starting orbital is on the left, and the arriving one on the right. The numbers on chart refer to the associated eigenvalue for each transition.

13



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Emission spectrum The structural superposition diagrams of ground- and excited-state chromophores are shown in Figure S3. It can be seen that the structures of the ground and excited states of TriPhA molecule are almost the same with an root mean square deviation (RMSD) of 0.055 Å. Whereas, large deviations of the ground- and excited-state structures are observed for DPhABI (1.046 Å) and DPhABI-tb (1.071 Å). By contrast, the ground-excited structural deviations for PhDiABI, PhDiABI-tb, and TriABI decrease significantly with the RMSDs of 0.480, 0.460, and 0.281 Å, respectively, due to the steric crowding of indandione groups. The crucial torsion angles involved in the conjugation (dihedral angle between benzene ring and the plane of indandione moiety) of the excited-state structures are listed in Figure 1. Analysis results show that the conjugacy of the excited state is more remarkable than that of the ground state for PhDiABI and PhDiABI-tb, while the DPhABI and DPhABI-tb are substantially remain unchanged. In other words, from the purely dihedral angle perspective, the change in structure of PhDiABI and PhDiABI-tb are larger than DPhABI and DPhABI-tb after electron excitation. This is different from the general trend of the change in molecular overall RMSD. Therefore, the relaxation of the electronic structure of molecular excited state is thought to be of complex nature. The structural deformations, such as bond lengths, bond angles, and other dihedral angles, will work together to contribute to their RMSD values and hence Storck shifts. The characteristic emission spectra of the studied chromophores are shown in Figure 4. Most results, including peak position and the fluorescence intensity, of theoretical simulated spectra coincided well with the available experimental measurements except the emission wavelength of DPhABI.26 The theoretical fluorescent peak of DPhABI is observed to be about 70 nm deviation from the experimental report. As can be seen from the figure, the precursor TriPhA hardly 14


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exhibits fluorescence emission compared to its indandione-substituted derivatives. Similar to the clear disparity seen in their respective absorption spectra, great changes were observed in the fluorescence excitation with the gradual introduction of the indandione unit in periphery. The emission wavelength of DPhABI is observed at 733 nm with a medium intensity. The calculated fluorescent peak of DPhABI-tb (722 nm) is blue-shifted by 11 nm relative to that of its DPhABI analogues, and the intensity of it hardly changed. The further addition of an indandione acceptor group caused the appearance of a more blue-shifted emission band for PhDiABI at 607 nm. These shifting in maximum emission wavelength resulted in a color change gradually from red to yellow. In conjunction with the color variation, the fluorescence intensity of PhDiABI exhibits a severely increases, indicating considerable fluorescence emission of PhDiABI. The origins of more than 7 times larger fluorescence intensity of PhDiABI compared to that of DPhABI, which is more notable than the ratio of strength in absorption spectra, might be derived from the more promotion of conjugacy in excited state in PhDiABI than in DPhABI (as discussed above). The PhDiABI-tb show a slight increase in fluorescence intensity and the emission peak of it appears at 603 nm with a blue-shift of 4 nm relative to that of PhDiABI. The TriABI molecule shows an intense fluorescence emission at 588 nm in theory calculation.

15



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Figure 4. Emission spectra of the studied chromophores obtained from TD-DFT/PCM calculations at the TD-B3LYP/6-311g(d) level. The inset shows the enlarged drawing of emission spectrum for TriPhA molecule. The numbers on chart refer to the value of approximate emission wavelengths. A Gaussian function has been employed with a full width at half-maximum of 3000 cm-1.

Selected emission features and the relevant Stokes shifts are also listed in Table 1. The Stokes shifts (∆EStokes) of chromophores exhibit a closely related to the geometric changes between the ground and excited states, i.e., the ∆EStokes significantly increase with the increasing RMSD value of the molecules. 3.3 Nonlinear optical properties: static and dynamic molecular (hyper)polarizabilities Static molecular (hyper)polarizability The magnitude of the static dipole moments (µ0), the linear polarizabilities ( α ), the total hyperpolarizability (βtot), and the vectorial part of βtot (βvec) for the chromophores are displayed in Table 2. The TriPhA is a classical octupolar molecule, hence with vanishing dipole moment (µ0 = 0.01 a.u.) and the first hyperpolarizability (βtot = 3 a.u.). Similarly, the TriABI molecule also exhibited a rather small µ0 (0.63 a.u.) and βtot (3644 a.u.) values, although its symmetry is slightly lower than that of the TriPhA. In contrast, theoretical calculations clearly show that the dipole moment and hyperpolarizability are quite large for the 16


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other four chromophores with C1 geometry. The µ0 and βtot values related to the different substituted pattern upon triphenylamine-indandione chromophores are in the order of DPhABI > DPhABI-tb > PhDiABI > PhDiABI-tb, but the trend of the α is just the opposite. The β0 value of more than 20000 a.u. for these asymmetric-substituted indandione derivatives are observed to be above 7000 times larger than that of TriPhA (3 a.u.). The great promotion of molecular hyperpolarizability benefits from the combination of introduction of electron acceptor group(s) and the breaking of the molecular symmetry.

Table 2. Calculated dipole moments (µ0), polarizabilities ( α ), and static first hyperpolarizabilities (βtot(∞) and βvec(∞)) for the investigated chromophores at the CAM-B3LYP/aug-cc-pVDZ level of theory within the static field limit

a

compound

µ0/a.u.

Indandione TriPhA DPhABI DPhABI-tb PhDiABI PhDiABI-tb TriABI

1.52 0.01 1.49 1.03 0.99 0.87 0.63

α /a.u. βtot(∞)/a.u. βvec(∞)/a.u. 134.8 283.0 523.0 589.5 754.4 888.9 972.2

666 3 27630 26875 22440 21611 3644

666 3 26447 24739 17916 12188 -3363

δβa

βvec(∞)/βtot(∞)

1 9210 8958 7480 7204 1215

1.00 1.00 0.96 0.92 0.80 0.56 -0.92

the extent of hyperpolarizability enhancement with respect to the parent molecule TriPhA, δβ =

βtot(∞),compound/βtot(∞),TriPhA.

From the tensor elements of first hyperpolarizabilities listed in Table S3 is not hard to see that large part of components of hyperpolarizability for (quasi-)octupolar molecules (TriPhA and TriABI) are cancelled out due to their symmetry structure. The essential reason of the enlargemen in NLO properties of other chromophores is that the reduction of the symmetry of electronic 17



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structure can cause the differences in hyperpolarizability tensor, which will be no longer counteracts each other. We have also carried out a formulaic calculation based on the poplar equation for two-state model and compared the results from it with those obtained from our theoretical simulations.49,50 By using the relevant values taken from the TD-DFT method, the magnitude of static hyperpolarizability can be estimated by following formula

β tot ∝

f0 ⋅ ∆µ Egm3

where f0, Egm, and ∆µ represent the oscillator strength, the transition energy, and the difference of the dipole moment between the ground state and the crucial mth excited state in turn. The TD-DFT calculated f0, Egm, and ∆µ along with the values calculated from the equation (f0·∆µ)/Egm3 are listed in Table 1. It can be seen that the values for DPhABI, DPhABI-tb, PhDiABI, and PhDiABI-tb derived from the two-state model are close, which is consistent with the TD-DFT analysis. Quantitatively, the results of TriPhA and TriABI calculated from the formula deviate from TD-DFT calculations seriously in proportion, possibly due to some effect that two-state model does not account for the electronic structures of these two (quasi-)octupolar molecules and/or a larger error caused in the process of calculations originated in their small hyperpolarizability cardinality. Moreover, the calculation shows that the f0, Egm, and ∆µ of the triphenylamine-indandione chromophores have no obvious difference before and after being modified by tert-butyl groups, which is the underlying reason that their effect on the alteration of molecular nonlinearity is very small. Besides the total hyperpolarizability (βtot), the projection of it, i.e., the vectorial part of βtot (βvec), along the direction of the dipole moment is a major nonlinear concern as it can usually be 18


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directly compared with the experimental value. For this reason, we also list the βvec values of the title compounds obtained within the static field limit in Table 2. In general, the molecular first hyperpolarizability of conjugated azobenzene derivatives is observed between 10–1000×10-30 esu (1 a.u. = 8.64×10-33 esu).51 The previous theoretical and experimental studies of NLO properties for some indandione derivativatives have also reported the molecular zero frequency hyperpolarizabilities are about 1–100×10-30 esu.25,52 In this work, we have used DFT method to determine a βvec value of 29–230×10-30 esu for asymmetrical triphenylamine-indandione chromophores. They are therefore considered to be promising NLO molecules with large second order NLO properties. It is known that the θ value derived from the formula βvec/β tot = cosθ represents the angle between the vector formed by βvec part and the molecular dipole direction. The ratios of β vec to β tot within the static field limit of the studied chromophores are listed in Table 2. The value of

βvec(∞)/βtot(∞) of the molecules seems to be about unity, except for PhDiABI-tb, indicating the charge transfer process in these molecules should be unidirectional and the β tot values are mainly induced by the response along the direction of the ICT, as described in the work of Misra on tuning of the molecular nonlinearity of aryl-substituted boron-dipyrromethene system.53 Dynamic molecular hyperpolarizability It can be inferred from the two-state model that two specific resonance frequencies, one appears at ω0 and another at ω0/2, are responsible for the second harmonic generation (SHG), where ω0 stands for the frequency of maximum absorption in linear one-photon transitions.49,50 The molecular nonlinearity would undergo a strong enhancement by dispersion effects coming from them. Here, for purposes of comparison, four commonly used wavelengths in experiments (λ = 1907, 1460, 1340, and 1064 nm) were selected 19



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to investigate the dispersion effect on the optical nonlinearity of chromophores. The frequency-dependent hyperpolarizabilities (β(1064), β(1340), β(1460), and β(1907)) of the title compounds, determined by the resonance excitation of the incident light, along with their static ones (β(∞)) are depicted in Figure 5. The same trend exists among the total first-order hyperpolarizability (βtot, cf. Figure 5(a)) of the molecule and its projection in the dipole direction (βvec, cf. Figure 5(b)). The intrinsic hyperpolarizability of the molecule is much less than the dynamic ones no matter how large the frequency of incident light is, and the dynamic value increases with increasing frequency of the incident laser, i.e., β(1064) > β(1340) > β(1460) > β(1907) > β(∞). Most importantly, the dispersion effects on the hyperpolarizability encountered at λ = 1064 nm have improved noticeably and a promotion up to about 3 times in the dynamic hyperpolarizability of the chromophores was observed. Obviously, the larger β(-2ω;ω,ω) does appear when the incident wavelength of dispersion is closer to twice of the wavelength in one photon absorption. This conclusion is consistent with the deduction from the two-level model, as mentioned above.

Figure 5. Calculated static (β(∞)) and dynamic (β(1064), β(1340), β(1460), and β(1907)) first 20


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hyperpolarizabilities of the chromophores at CAM-B3LYP/aug-cc-pVDZ level of theory: (a) the total hyperpolarizability (βtot), and (b) the vectorial part of βtot (βvec).

With the above analysis, one can easily see that the optical properties, both linear spectra and nonlinearities, of the indandione derivatives are all highly dependent on the electronic nature of the indandione unit, while the terminal tert-butyl unit has very little effect on them. Thus, we could be sure that the imaginary TriABI-tb would exhibit the similar optical properties to those of TriABI molecule.

4. Conclusions A series of novel molecules with triphenylamine group as electron donor and indandione nonlinear unit as electron acceptor have been investigated in theory. The optical properties of the triphenylamine-indandione chromophores obtained from DFT calculations are in good agreement with the empirical observations, demonstrating the calculation strategies employed in this work are reliable of describing the electronic characteristics of the compounds. Theoretical calculations show that the introduction of indandione group(s) leads to the splitting of molecular absorption spectra and the red-shifting of the maximum absorption peak. The Stokes shifts of fluorescence of chromophores exhibit a closely related to the geometric changes between the ground and excited states of molecules. The first hyperpolarizability of molecules is jointly determined by the strength of the intramolecular electron acceptors and its overall molecular symmetry, and the latter is seemed to be more influential. Asymmetric modification of indandione acceptor group(s) to chromophores (to form DPhABI and PhDiABI) can greatly increase the molecular first 21



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hyperpolarizability. In contrast, the terminal tert-butyl group(s) (in DPhABI-tb and PhDiABI-tb) has almost no effect on the optical properties of molecules, both linear spectra and nonlinearity. The frequency dispersion response on the molecular nonlinearity is definite existence and the most resonance encountered near the region at an incident wavelength of two times the absorption wavelength. The results would be sure to help us in understanding the relationship between the molecular structures and optical properties of these complexes.

Supporting Information Available: (TD-)DFT optimized Cartesians coordinates for ground- and excited-state indandione derivatives are tabulated in Tables S1 and S2, respectively; Comparison of electrostatic potential (ESP) contours for the studied indandione derivatives are displayed in Figure S1; The dominant NTO pairs involved in the absorption other than the maximum one for the studied indandione derivatives are shown in Figure S2; Molecular structure superposition diagrams of ground- and excited-state chromophores are displayed in Figure S3; Calculated components of first hyperpolarizabilities for the investigated chromophores within the static field limit and the resonance excitation are listed in Table S3. Full citation for Ref. 38 is listed last. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 51402131), Natural Science Foundation of Jiangsu Province (Grant No. BK20140514 and BK20130748), and the Zhenjiang Municipal Science and Technology Support Program (Social Development) Project (Grant No. SH2014011).

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Linear and Nonlinear Optical Properties of Triphenylamine

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