Third-Order Nonlinear Optical Properties and Electroabsorption

Article pubs.acs.org/JPCC

Third-Order Nonlinear Optical Properties and Electroabsorption Spectra of an Organic Biradical, [Naphtho[2,1‑d:6,5‑d′]bis([1,2,3]dithiazole)] Keigo Takauji,† Rie Suizu,†,§ Kunio Awaga,*,† Hideo Kishida,*,‡ and Arao Nakamura‡,⊥ †

Department of Chemistry and Research Center for Materials Science, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8602, Japan ‡ Department of Applied Physics, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan S Supporting Information *

ABSTRACT: Thin films of a thiazyl biradical, naphtho[2,1-d:6,5-d′]bis([1,2,3]dithiazole), abbreviated as NT, exhibit nonlinear optical properties with a large third-order nonlinear susceptibility of 2.1 × 10−11 esu. The electroabsorption and low-temperature-absorption measurements reveal a series of degenerate electronic states, which is probably caused by the biradical character of NT. It is concluded that this degeneracy should enhance the third-order nonlinear optical properties.

to closed-shell compounds7 such as polydiacetylene,8 polythiophene,9 and donor−acceptor polymers.10−12 In such compounds, the electronic excited states related to the NLO properties are essentially described by the one-dimensional exciton models.13 The lowest excited state is the one-photon transition-allowed state and has a large binding energy. On the other hand, the second excited state is a one-photon transitionforbidden state and is not degenerate with the lowest state. The second excited state is located at much higher energy. These states are called essential states14 and govern the NLO properties irrespective of the difference of the NLO processes. Thus, the determination of the essential state is meaningful to the study of the exploration of NLO materials. The NLO properties of open-shell organic molecules, such as singlet biradicals, are attracting much attention because these systems are expected to have completely different electronic excited states. Their electronic structures can be written as a resonance between a closed-shell and a biradical form15−20 as shown in Figure 1a for the present compound, naphtho[2,1-d:6,5d′]bis([1,2,3]dithiazole), abbreviated as NT. Nakano and coworkers proposed the enhancement of the third-order nonlinear susceptibility of an organic singlet biradical.21−24 Because such singlet biradicals have an attractive feature for NLO materials such as an optical gap above 1 eV, this proposal expanded the NLO studies toward air-stable open-shell

1. INTRODUCTION Recent developments in the production of semiconductor lasers and optical fibers have resulted in enormous progress in optoelectronics and optoelectronic materials,1,2 and extensive efforts have been devoted to establishing optical circuits.3 If the intensity and phase of light could be freely regulated by light irradiation, the operation speeds would be much faster than those in conventional electronic circuits. Among optical functions, the nonlinear optical (NLO) property is the key to realizing this goal, and so organic materials are now attracting much attention because of their large polarizability, which promises NLO responses, in addition to their various advantages,4,5 such as fast optical responses, architectural flexibility, and ease of fabrication. The NLO properties are induced by nonlinear charge displacements that are generated under a strong electric field of light. The molecular dipole moment μ and the macroscopic polarization P can be generally represented by μ = μ0 + αE + βEE + γEEE + ···

and P = P0 + χ (1) E + χ (2) EE + χ (3) EEE + ···

where E is the electric field; μ0 is the permanent dipole moment of the molecule; α is the linear polarizability; β and γ are the molecular first and second hyperpolarizabilities, respectively; P0 is the permanent polarization in the medium; and χ(1), χ(2), and χ(3) are the optical susceptibilities.6 Until recently, the development of new NLO materials had been limited mostly © 2014 American Chemical Society

Received: September 18, 2013 Revised: January 8, 2014 Published: February 17, 2014 4303

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Thin films of NT (100 nm) were prepared by vacuum deposition at 170 °C onto the synthesized quartz substrates for THG measurements or onto the interdigitated array electrodes for EA measurements. Figure S2 of the Supporting Information shows the X-ray diffraction (XRD) pattern of a thin film of NT on quartz. The diffraction peaks are very sharp with a half-width of 0.36° and indicate high crystallinity of the thin films. The absorption spectra for the solution and thin-film samples of NT on SiO2 are compared in Figure 2. Although the solution

Figure 2. The absorption spectra of NT. The solution state is indicated by the black line (right axis), and the film state is indicated by the red line (left axis). In the solution state, only an absorption peak is observed at 2.0 eV, while in the thin film state, the two absorption peaks split by the Davydov splitting are observed at 1.5 and 2.3 eV. Figure 1. (a) The molecular structure of NT. (b, c) The crystal structure of NT. There are two kinds of molecules which are inclined at different angles in the unit cell. NT forms multidimension networks because it has electrostatic Sδ+...Nδ− interactions and π−π interactions between molecules. Monoclinic, P21/n, a = 3.8860(3) Å, b = 17.3150(13) Å, c = 7.7830(7) Å, β = 102.586(3)°, V = 511.10(7) Å3..

spectrum exhibits a strong single absorption at ca. 2.0 eV, which is ascribable to the highest occupied molecular orbital−lowest unoccupied molecular orbital (HOMO−LUMO) π−π* transition, the absorption in thin film exhibits a significant splitting into two structures, which are located at 1.5 and 2.3 eV. This is probably caused by the Davydov splitting due to the presence of the two molecules in the unit cell with a herringbone-type molecular alignment (see Figure 1b). Because the π−π* transition originates the polarization along the long axis of the NT molecule, two types of combinations of polarizations give energy splitting. In the present case, the low (1.5 eV) and high energy bands (2.3 eV) can be assigned to the transitions along the b and a axes, respectively.

materials such as biradical molecule systems, and two-photon absorption spectra of the singlet biradical compounds were examined.25−27 In the present work, we studied the thirdharmonic generation (THG) and electroabsorption (EA) spectra of NT. THG is one of the reliable measurement methods to determine the magnitude of the third-order nonlinear susceptibility χ(3) because optical harmonic generation process is free from the thermally induced change of optical constants. On the other hand, the EA method is used to determine the electronic-state structure. It has an advantage that the applied electric field breaks inversion symmetry, so that optically forbidden states from the ground state are observed. Our analysis based on the experimental results of THG and EA revealed a characteristic feature of the electronic structure of NT as a singlet biradical, which brings about large χ(3) values.

3. THIRD-ORDER NONLINEAR OPTICAL PROPERTIES The third-order optical nonlinearity was examined on the NT thin films by the THG, and the spectrum of the third-order nonlinear susceptibility, |χ(3)(−3ω;ω,ω,ω)| (hereafter, abbreviated as |χ(3)|), was obtained. Excitation laser light in the range of 0.44−0.99 eV was generated by a system consisting of Spitfire Pro (Spectra-Physics) and TOPAS (Light Conversion) with a pulse width of 100 fs and a repetition rate of 1 kHz. The |χ(3)| measurements were performed by the standard Maker fringe method29 with a quartz reference sample. To avoid the THG effects of ambient air, the measurements were done in a vacuum. Figure 3 shows a comparison between the THG (circles) and absorption (solid curve) spectra. Though the |χ(3)| values are negligibly small at excitation photon energies below 0.45 eV, they show an increase above this value. After making a broad maximum at 0.52 eV in the excitation photon energy, the |χ(3)| values show a gradual decrease. By triplicating the excitation photon energy, we find that the spectral shape of |χ(3)| approximately coincides with that of the absorption spectrum.

2. THIN-FILM FABRICATION AND ABSORPTION SPECTRA The crystal structure of NT has been reported elsewhere.28 Figure 1 shows the molecular and crystal structures of NT. The unit cell involves two molecules; the normal axes of these planar molecules make angles of ±52° with respect to the a axis. These molecules form separate π stacking columns along the a axis. In addition to π stacking, the two molecules in the unit cell are connected by a short electrostatic contact between the N−N−S moieties, which makes a zigzag chain of NT along the b axis. 4304

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Figure 3. The third-order nonlinear susceptibility |χ(3)(−3ω;ω,ω,ω)| obtained by THG measurements (black dots) and absorption spectrum α (red line) of NT.

Therefore, this structure is assigned to the three-photon resonance of the lower band of Davydov splitting (1.5 eV). On the other hand, |χ(3)| does not form a maximum at the energy of the second peak of the Davydov splitting (2.3 eV). The |χ(3)| values at the two absorption peaks are 1.76 × 10−11 and 1.41 × 10−11 esu at 1.62 and 2.25 eV in THG photon energy, respectively, and at the former, the figure of merit is |χ(3)|/α = 1.19 × 10−16 cm esu, where α is the absorption coefficient at THG photon energy. Considering that |χ(3)| values of typical conjugated polymers, polythiophene, evaluated with the same method are 2.72 × 10−11 and 9.08 × 10−12 esu for regioregular and regiorandom ones, respectively,9 we can remark that the |χ(3)| values of NT are relatively large among the organic thinfilm materials. According to the three-energy-state model, which consists of the ground state (|g⟩), a one-photon allowed state (|i⟩), and a one-photon forbidden state (|j⟩), the optical parameters, α, |χ(3)|, and |χ(3)|/α, can be written with the transition matrix elements between the states as follows: α ∝⟨g|x|i⟩2, |χ(3)| ∝ ⟨g|x| i⟩2⟨i|x|j⟩2, and |χ(3)|/α ∝ ⟨i|x|j⟩2. Here, x is the coordinate parallel to the electric field. Therefore, when the magnitude of ⟨i|x|j⟩ is independent of the relevant one-photon allowed state | i⟩, χ(3) is expected to be proportional to the absorption coefficient α, but this is not the case for NT. This was presumably because the transition matrix elements (⟨i|x|j⟩) related to the energy state located at 1.62 eV made a larger contribution than those in the other energy ranges. As a result, the |χ(3)| values around 1.62 eV were enhanced. Therefore, the other structures which have relatively smaller |χ(3)| values are masked in the |χ(3)| spectrum.

Figure 4. EA spectra under the application of different electric fields (20−100 kV/cm). The results in panel a are for an electric field applied in parallel with the thin film surface and in parallel with the polarizing direction (E//F), while those in b are for an electric field applied in parallel with the thin film surface and perpendicular with the polarizing direction (E⊥F).

The thin-film absorption spectra of NT were measured at 4 and 100 K in the range of 1.2−3.0 eV. The results in the range of 1.4−2.0 eV are shown in Figure 5. At 4 K, several structures,

4. ELECTROABSORPTION SPECTROSCOPY To understand the electronic structure of NT, especially with respect to the broad structure at around 1.7 eV in THG, the electroabsorption spectra of the NT thin films were examined at room temperature. We applied an electric field (F) in the range of F = 0−100 kV/cm to an NT thin film (100 nm) through interdigitated electrodes with a gap width of 2 μm and then recorded the field-induced change (ΔT) of transmission (T) spectra. Figure 4a and b shows the EA spectra under the condition that the polarization of light E is parallel (E//F) and perpendicular (E⊥F) to the applied electric field F, respectively. In −ΔT/T spectra shown in Figure 4, the positive signal is the decrease of the transmittance, indicating the increase of absorption. EA spectra exhibit three positive and three negative structures in the range of 1.3−2.0 eV, suggesting that the absorption band at 1.7 eV would be a complex of several excited states.

Figure 5. Absorption spectra measured at 4, 150, and 300 K. The fine structure can be observed at low temperature.

which are located between 1.65 and 1.70 eV and between 1.45 and 1.50 eV, are observed in the broad absorption structure centered at 1.9 eV. Figure 6a shows the second differential of the absorption at 4 K. It is found that this derivative spectrum is nearly coincident with the E⊥F EA spectrum (Figure 4b) in the whole range of 1.3−3.0 eV. The temperature dependence of the absorption spectrum does not give such a second differential spectrum. In such cases, the agreement between the two spectra is known to be caused by a degeneracy between one-phonon allowed and forbidden states.30 This means that each allowed excited state in the range of 1.3−3.0 eV should be associated with a forbidden degenerate state. 4305

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Figure 6. (a) Second differential of the absorption spectrum at 4 K. (b) EA spectra (E⊥F) at 80 kV/cm. The shapes of the two graphs are highly similar. (c) Calculated and experimental EA spectra (80 kV/cm, E⊥F). The calculated spectrum under the assumption of the degeneracy of the two excited states essentially reproduces the experimental one.

The excitation energies of these degenerate excited states are estimated from the minimums of the second differential of the absorption spectrum at 4 K as 1.47, 1.52, 1.64, and 1.85 eV. To confirm the above interpretation, we carried out quantitative analysis for the EA spectra, adopting an oscillator model in which the system is regarded as an assembly of various oscillators with individual eigenfrequencies. The absorption spectra are analyzed by the following calculation. The complex dielectric constant (ε̃) can be written as

ε ′̃ = ε ̃ + 3ε0χ (3) E2

Figure 6c shows a comparison between the EA spectrum (80 kV/cm, E⊥F) and the theoretical one calculated by the above process in which degeneracy of the excited states is assumed. The used parameters are shown in Table S1 of the Supporting Information. The agreement between the experimental and theoretical curves strongly supports that each of the four allowed states obtained from absorption measurements has a degenerate forbidden state. We can make a similar argument for the other Davydov splitting energy level located at 2.3 eV. In fact, the spectral similarity between the experimental and calculated ones guarantees the discussions. The degenerated excited-state structure found in NT is evidently different from that of π-conjugated polymers. In conjugated polymers, the energy separation between the onephoton allowed and forbidden states contributing to the nonlinear optical responses is generally 0.5−0.6 eV.31

ε̃ = (n + iκ )2 ε0 =1+

+

Ne 2 ε0ℏ

⎧ ⎪

1 ω − ω − iγj ⎩ j

∑ ⟨g |x|j⟩⟨j|x|g ⟩⎨ ⎪

j

⎫ ⎪ 1 ⎬ ⎪ ωj + ω + iωγj ⎭

5. DISCUSSION In this section, we have analyzed the electronic structure of NT. As is concluded in the last section, the EA and absorption spectra of the NT thin films indicated the degeneracy between the allowed and forbidden states at each energy level of 1.47, 1.52, 1.64, and 1.85 eV. Because the energy separations among these states are about 10−2 or 10−1 eV, the three higher-energy states would be vibronic states associated with the lowestexcited electronic state at 1.47 eV. Moreover, considering that the lowest-excited state of 1.47 eV is degenerate, and assuming that the forbidden state also has vibronic states, the degeneracy at each level can be automatically explained. In fact, the energy interval among 1.47, 1.64, and 1.8 eV corresponds to the Raman band at 1357.6 cm−1 (Figure S5 of the Supporting Information), which is assignable to a carbon−carbon double bond stretching. The states of 1.64 and 1.85 eV can be explained as one- and two-phonon side bands, respectively. The ground state of the biradical NT can be expressed as 1,3 Φ = [·NT·], where the superscripts indicate a singlet and a triplet state, respectively (Figure 7). As described in Section 2, the excitation should produce large transition matrix elements along the molecular long axis of NT, namely, [·NT·] → [+NT−]. Therefore, the excited states can be written as 1Φs = [+NT−] + [−NT+] and 1Φa = [+NT−] − [−NT+]. Because the ground state is symmetric, the 1Φ0 → 1Φs excitation is forbidden, while 1Φ0 → 1Φa is allowed. The singlet spin state

where ε0 is the vacuum permittivity, n is the refractive index, κ is the extinction coefficient, N is the number of the relevant electrons per unit volume, e is the electron charge, ωj is the eigen angular frequency, and γj is the dumping energy. The κ value can be evaluated by the equation, α = 2ωκ/c, where c is the velocity of light. By using these formulas, we fitted the absorption spectra and obtained the parameters of the onephoton allowed states. Then, we analyzed the EA spectra using the following quantum mechanical model.6 The main terms in the third-order nonlinear susceptibility χ(3)(−ω;0,0,ω), which determines the EA spectra, can be written as follows: χ (3) ( −ω;0,0,ω) =

Ne 4 3! ε0ℏ3

∑ ⟨g |x|a⟩⟨a|x|b⟩⟨b|x|c⟩⟨c|x|g ⟩ abc

⎡ ⎤ 1 ⎥ × 2⎢ ⎢⎣ (ωa − iγa − ω)(ωb − iγb − ω)(ωc − iγc − ω) ⎥⎦

Here, |g⟩ is the ground state, and |a⟩, |b⟩, and |c⟩ are the excited states. The integral, ⟨i|x|j⟩ (i,j= a, b, c), is the transition matrix elements between the states, |i⟩ and |j⟩, ωi is the resonant frequency between |g⟩ and |i⟩, and γi is the damping parameter for the i state. The change in α caused by the electric field, which is the nonlinear absorption αNL, is related to the ∼ ∼ nonlinear complex dielectric constant ε′. ε′ can be written as follows: 4306

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χ (3) ( −3ω;ω ,ω ,ω) =

Ne 4 3! ε0ℏ3

∑ ⟨g |x|a⟩⟨a|x|b⟩⟨b|x|c⟩⟨c| abc

x |g ⟩ ⎡ ⎤· 1 ⎥ ×⎢ ⎢⎣ (ωa − iγa − 3ω)(ωb − iγb − 2ω)(ωc − iγc − ω) ⎥⎦

In a simple case when |a⟩ and |c⟩ are the same state and when | a⟩ and |b⟩ are degenerated, we can observe a three-photon resonance, a two-photon resonance, and a three-photon resonance in order from lower to higher energy. In such a simplified picture, χ(3) for the two-photon resonance and that for the three-photon resonance have opposite signs in the complex χ(3) plain. Therefore, if the two-photon resonance and the three-photon resonance occur at a similar photon energy, they can cancel each other and blur the resonant structure in the |χ(3)| spectrum. This mechanism is a possible cause that makes a resonant peak not clearly observed between 0.7 and 0.8 eV.

Figure 7. A schematic of the mechanism of degeneracy at 1.47 eV. The effective wave functions Φs and Φa are derived from ϕ1 and ϕ2 expressing one of the radicals transits to the other side. The energies of Φs and Φa are nearly the same.

Φ0 is stabilized compared to the triplet state 3Φ0 because this singlet spin state interacts with 1Φs. Actually, the electron paramagnetic resonance (EPR) measurements indicate a thermally accessible triplet excited state with an activation energy of 0.05 eV (Figure 8). This value is much smaller than the photoexcitation energy of 1.47 eV. Namely, the pseudodegeneracy of the allowed and forbidden excited states in NT can be explained as an intrinsic feature of the singlet biradicals. As shown before, the intensity of χ(3) is proportional to ⟨g|x|i⟩2⟨i|x|j⟩2 in which |i⟩ and |j⟩ correspond to Ψa and Ψs for NT, respectively. It is highly possible that the degenerate |i⟩ and |j⟩ would produce a large transition matrix element ⟨i|x|j⟩ because these two states occupy nearly the same space. The degenerate electronic structure might explain the spectral shape of |χ(3)| observed in the THG measurements. We observed a clear three-photon resonance at 0.50 eV in the excitation photon energy, which corresponds to the lower band of the Davydov splitting; this is not observed between 0.7 and 0.8 eV, which corresponds to the upper band. Between 0.7 and 0.8 eV, we can expect the two-photon resonance to the lower branch because the (one-photon) allowed and the (onephoton) forbidden states are degenerate and because the twophoton resonance to the forbidden state located at 1.5 eV is possible. The main term of χ(3) for THG can be represented as6 1

6. CONCLUSION We have demonstrated that the singlet biradical compound NT shows a large third-order nonlinear susceptibility. The EA spectroscopy and the low-temperature absorption measurements revealed a series of degenerate excited states, where one is allowed and the other is forbidden. This feature can be interpreted as an intrinsic property of biradicals, and the large transition matrix elements between the allowed and forbidden states can produce a large nonlinear susceptibility. We believe that this discussion would be applicable to any type of biradical compounds and should be a guide for the design of third-order nonlinear optical materials.

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ASSOCIATED CONTENT

S Supporting Information *

SEM image, XRD measurement, electronic structure, synthesis, Raman spectrum, and parameters of the three-level model used for the calculation of EA spectra. This information is available free of charge via the Internet at http://pubs.acs.org.

Figure 8. (a) EPR spectra at several temperatures. The observed peaks are derived from the triplet radical state. (b) Arrhenius plot. 4307

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Present Addresses §

Department of Nanomaterials Science, Graduate School of Advanced Integration Science, Chiba University, Chiba 2638522, Japan. ⊥ Toyota Physical and Chemical Research Institute, Nagakute, Aichi 480−1192, Japan. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Grants-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) and the Japan Society for the Promotion of Science (JSPS).

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REFERENCES

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dx.doi.org/10.1021/jp4093332 | J. Phys. Chem. C 2014, 118, 4303−4308