Nonplanar donor-acceptor chiral molecules with large second-order optical nonlinearities: 1,1,4,4-tetracyanobuta-1,3-diene derivatives.

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Non-Planar Donor–Acceptor Chiral Molecules with Large Second-Order Optical Nonlinearities: 1,1,4,4-Tetracyanobuta-1,3-Diene Derivatives Yanling Si, and Guochun Yang J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp4099717 • Publication Date (Web): 27 Jan 2014 Downloaded from http://pubs.acs.org on February 2, 2014

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The Journal of Physical Chemistry

Non-planar Donor–Acceptor Chiral Molecules with Large Second-Order Optical Nonlinearities: 1,1,4,4Tetracyanobuta-1,3-diene Derivatives Yanling Sia and Guochun Yang*,b a College of Resource and Environmental Science, Jilin Agricultural University, Changchun, 130118 Jilin, China b Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal University, Changchun, 130024 Jilin, China. E-mail: [email protected]

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ABSTRACT: We have investigated the chiroptical, linear, and second-order nonlinear optical (NLO) properties of five 1,1,4,4-tetracyanobuta-1,3-diene (TCBD) derivatives and elucidated structureproperty relationships from the micromechanism. The experimental UV-vis absorption and circular dichroism (CD) spectra were well reproduced by our calculations at TDB3LYP/6-31+G* level of theory. The electron transition property and chiroptical origin have been assigned and analyzed. The results show that the studied compounds possess large molecular first hyperpolarizabilities, especially for compound 5 which has a value of 35 × 10−30 esu, which is comparable with the measured value for highly π-delocalized phenyliminomethyl ferrocene complex and about 200 times larger than the average first hyperpolarizability of the organic urea molecule. Despite the nonplanarity of these compounds, efficient intramolecular charge transfer (CT) from electron donor to electron acceptor moieties was observed, which plays the key role in determining the NLO response. The intramolecular charge transfer cooperativity was also probed. In view of the first hyperpolarizability values, intrinsic non-centrosymmetric electronic structure, and high stability, the studied compounds have the possibility to be excellent second-order NLO materials. KEYWORDS: chiral material; nonolinear optics; absolute configuration; charge transfer; TDDFT


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1 INTRODUCTION Designing and synthesizing materials with large nonlinear optical (NLO) responses have become a topic of intensive study because of their potential applications in optical and electro-optical devices.1-5 However, second-order NLO properties derive at the molecular level from the second-order polarizability, which are of the most immediate interest for practical applications. The most prerequisite requirement for second-order NLO materials is non-centrosymmetric electronic structure, which can be satisfied by the following two main strategies. One is the organic molecules that contain electron-donor and electron-acceptor groups linked through an intervening π backbone. Enhancing the electron-donor and electron-acceptor ability or extending π-conjugation length was proved to be an effective method to enhance the NLO properties.6-8 Another way is to use chiral molecules due to their intrinsic non-centrosymmetric structures,9-12 which allows NLO effects to be observed even in highly symmetric media such as chiral isotropic liquids.13-14 Some studies have shown that chiral molecules can be a valuable alternative in the search for new second-order NLO materials.15-21 The role of chirality in second-order NLO has been reviewed.22-23 Allenes due to their axial chirality and synthetic versatility are a unique family of organic molecules and can participate in a diverse range of reactions.24 The chemistry of allenes has experienced a great advancement in the 20th century, as summarized in the monographs by Schuster and Coppola,25 and more recently by Krause and Hashmi.26 Modern synthetic methods allow the construction of allenes with a wide variety of substituents.27 The fascinating structure of allenes caught the attention of chemists interested in molecular materials.28 Now, allenes have been widely used as advanced functional materials such as chiral sensing,29 redoxtriggered chiral switches,30 chiral magnets,31 the induction of chirality in metal complexes,32 amplification of chirality in liquid-crystalline phases,33-34 NLO materials,35-36 and nonplanar push-pull chromophores.37 The development of the non-planar donor–acceptor chromophores has become a very active area of 3 ACS Paragon Plus Environment


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advanced materials research.38-41 It is because that non-planar molecules are more soluble, less aggregating and more readily sublimable, optical transparency, forming amorphous thin films which are good candidates for potential use in opto-electronic devices.42 It was shown recently that 4-N,Ndimethylanilino (DMA) donor-substituted optically active 1,3-diethynylallenes (DEAs) react in a facile [2+2] cycloaddition with tetracyanoethene (TCNE) to form, after retro-electrocyclization, optically active, photostable 1,1,4,4-tetracyanobuta-1,3-diene (TCBD) derivative (1, Figure 1), which has non-planar geometric structure.43 Circular dichroism (CD) spectroscopy revealed a chiral induction from the chiral allene moiety into the sterically crowded TCBD chromophores. DMA usually act as electron donor and TCBD as electron acceptor. Moreover, compounds containing DMA donor and TCBD acceptor moieties have exhibited high third-order optical nonlinearities.44-49 This means that charge transfer from DMA to TCBD moieties may occur in compound 1. It is noted that donorsubstituted TCBD derivatives did not show any significant decomposition at least up to the melting points.50 In view of their intrinsic non-centrosymmetric structures, high thermal and morphological stabilities, and favorable charge-transfer ability, we anticipate that compound 1 might offer some interesting new opportunities

to

second-order NLO materials.

It

is

well

known

that

tetracyanoquinodimethane (TCNQ) and tetrathiafulvalene (TTF) are electron acceptor and electron donor, respectively. Moreover, TCNQ- or TTF-substituted TCBDs and allene derivatives have been reported.42,

51-52

To probe the charge transfer cooperativity and enhance the second-order NLO

response, other four TCBD derivatives with TTF, TCNQ or combinations of TTF and TCNQ were designed (Figure 1). 2 COMPUTATIONAL DETAILS Geometrical optimization of the studied compounds without any symmetry constraint was carried out using the B3LYP53 exchange-correlation functional as implemented in the Gaussian 09 computational chemistry program.54 The B3LYP functional is a combination of Becke’s three-parameter hybrid 4 ACS Paragon Plus Environment

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exchange functional53 and the Lee–Yang–Parr55 correlation functional. Basis sets of 6-31G(d,p) for C, N, O, S, and H atoms were applied. Harmonic vibrational frequency calculations were used to confirm that the optimized structures were minima, as characterized by real vibrational frequencies. Timedependent density functional (TD-DFT) calculations were carried out at the B3LYP/6-31+G* level to determine the electronic transition energy, oscillator strength, and transition character. Rotational strengths were calculated using both length and velocity representations, and only the velocity-gauge representation of the dipole operator is gauge origin independent. In comparison of the calculated UV– vis/CD spectra with experimental ones, Gaussian bandshapes with a bandwidth of 0.20 eV were used to simulate the UV–vis/CD spectra. The static first hyperpolarizability was calculated as performed in the Gaussian 09 program package. In general, electric-field-induced second harmonic generation (EFISHG) and hyper-Rayleigh scattering (HRS) are the two main methods to determine the second-order NLO properties. Here, we focused on the HRS response of the studied compounds. In the case of plane-polarized incident light and observation made perpendicular to the propagation plane without polarization analysis of the scattered beam, the second-order NLO response that can be extracted from HRS data can be described as:56-57 β HRS (0;0,0) = 2 〈 β ZZZ 〉

{〈 β

2 ZZZ

2 〉 + 〈 β XZZ 〉}

(1)

2 and 〈 β XZZ 〉 correspond to the orientational average of the β tensor without assuming Kleinman’s

conditions.58 It is noted that we only concerned the static first hyperpolarizability.



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Figure 1. Chemical structures of the studied compounds 1-5. 3 RESULTS AND DISCUSSION 3.1 MOLECULAR AND ELECTRONIC STRUCTURES In this paper, five chiral TCBD derivatives (1-5) were investigated (Figure 1). Compound 1 was synthesized and characterized by X-ray crystallography. To test the influence of different substituent groups on the photophysical properties, compounds 2-5 were designed, which contain donor groups, acceptor groups, and a combination of donor and acceptor groups. The geometric structures of these compounds were optimized without any symmetry constraint at the B3LYP/6-31G(d,p) level of theory, which were confirmed to be minima by the harmonic frequency calculations. X-ray crystal structure parameters of compound 1 were well reproduced by our calculation (Table S1), which was also agreement with the previous study.59 Since the frontier molecular orbitals (FMOs) play a vital role in determining electron properties, a sketch of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) was shown in Figure 2 and Figure S1. The HOMO of compound 1 is formally localized on DMA moieties, and the LUMO is mainly localized on the TCBD moieties. However, both HOMO and LUMO of compound 2 are mainly localized on TCNQ moieties. For compound 5, the delocalized π orbitals from TTF and TCNQ group mainly contribute to HOMO and LUMO. FMOs of compounds 3 and 4 are similar to those of compounds 1 (Figure S1). This means that different donor or acceptor 6 ACS Paragon Plus Environment

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substitutions greatly influence the distribution of FMOs, which might lead to the different photophysical properties.

Figure 2. HOMO and LUMO of compounds 1, 2, and 5. 3.2 FIRST HYPERPOLARIZABILITY Quantum chemistry calculations can be a useful aid in understanding relationship between molecular structure and NLO property and in prescreening molecules with large NLO response.60-65 In general, the calculated first hyperpolarizability values are sensitive to the selected DFT functionals66-68 and basis sets.69-74 As far as we know, no systemically theoretical investigation has been reported to the first hyperpolarizability of the studied compounds. Recently studies show that the first hyperpolarizabilities predicted by CAM-B3LYP, M05-2X, and BH&HLYP are almost the same and are comparable with those obtained by MP2.75-79 Although the B3LYP has widely been used, the first hyperpolarizability values for most of organic compounds were overestimated. 66 Moreover, the 631+G(d) basis set has been proved to be enough for most organic compounds.75-77 Here, four DFT functionals: B3LYP, CAM-B3LYP, M05-2X, and BH&HLYP, were used to assess the effect of DFT functionals on the first hyperpolarizability. The calculted first hyperpolarizability (βHRS) values of the studied compounds at 6-31+G(d) level were given in Table 1. Compared with the three other DFT



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functionals, the B3LYP overestimates the first hyperpolarizability values, especially for compound 4, which is also in accordance with the previous study.66 The first hyperpolarizability values predicted by CAM-B3LYP, M05-2X, and BH&HLYP are almost the same. In the follwing discussion, the results predicted by the long-range corrected functional CAM-B3LYP was used. For the compounds 1-3, the βHRS value of compound 3 is much larger than of compound 1. However, the βHRS value of compound 2 is smaller than that of compound 1. These results show that the electron donor ability of TTF group is larger than that of DMA group for our studied compounds. And using the electron acceptor groups at R3 and R4 positions is not an effective way to enhance the NLO response, which is due that the TCBD group is also a strong electron acceptor and tert-butyl group is a weak electron donor. Continuing our comparison, compound 4 with four TTF groups at R1, R2, R3, and R4 positions has larger βHRS value. Study show that effective charge transfer between TTF and TCNQ group could occur.80 After observation the structure of compound 4, replacement of the TTF groups in compound 4 with the TCNQ group will get compound 5, which can satisfy the condition of charge transfer between TTF and TCNQ. It is interesting to find that the βHRS value of compound 5 is compareable to that of compounds 4. It indicates that proper combination of the electron donor and acceptor groups at R1, R2, R3, and R4 positions can effectively enhance first hyperpolarizability. It should be noted that the calculated βHRS values of the studied compounds are great larger than those of the typical organic NLO compounds with extensive π-electron conjugation. For example, the calculated βHRS value of compound 5 is comparable with the measured value for highly π-delocalized phenyliminomethyl ferrocene complex81 and about 200 times larger than the average first hyperpolarizability of the organic urea molecule.82 This indicates that the studied compounds have excellent second-order NLO response.


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Table 1. The Calculated Static First Hyperpolarizability (βHRS×10-30 esu) of the Studied Compounds 15 at 6-31+G(d) Level of Theory.

Compound B3LYP CAM-B3LYP

M05-2X

BH&HLYP

1

11

9

9

9

2

1

4

2

1

3

42

12

15

12

4

134

29

35

30

5

34

34

33

34

3.3 UV-VIS AND ECD SPECTRA Time-dependent density functional theory (TDDFT) calculation has emerged as a powerful tool for investigation of chiroptical properties83-91 and electron transition properties92-97 of various compounds. Although the ECD spectra of the studied compound 1 have been assigned at the TDB3LYP/6-31G(d) level of theory, 58 no systematic theoretical investigation has been reported for the studied compounds, especially for electron transition property. Studies have shown that basis sets98-99 and DFT functionals100-107 have to be chosen with due care for the calculation of electronic transition properties, especially in ECD calculation.108-113 Firstly, six Pople’s basis sets: (6-31G(d), 6-311G(d), 6-31+G(d), 6-31+G(d,p), 6-311++G(d), and 6-311++G(d,p)) were selected to evaluate the effect of the basis set extension on the electron transition energies by using B3LYP functional for compound 1. The calculated absorption wavelengths at the different basis sets level were listed in Table S2. It is found that the calculated absorption wavelengths are insensitive to the selected basis sets. Specifically, the difference between the largest basis set and the smallest basis set is within 9 nm. Moreover, the positions of the four experimental observed bands are well reproduced by our calculations. In addition, Jacquemin and Adamo found that diffuse functions are necessary to obtain accurate absorption 9 ACS Paragon Plus Environment


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wavelength and describe electron transition property.98 To achieve good performance with reasonable computational resource, 6-31+G(d) basis set was used in the following calculation. Subsequently, five DFT functionals (CAM-B3LYP,114 M05-2X,115 BH&HLYP,116 PBE0,117 and B3LYP,53) were used to assess the effect of DFT functionals on the absorption wavelength. These functionals have exhibited good performance in predicting the electron transition properties. The calculated absorption wavelengths using these functionals were given in Table S3. It is interesting to find that the computed absorption wavelengths are strongly dependent on the used functionals. For example, the BH&HLYP, CAM-B3LYP, and M05-2X functionals could not give the absorption band at about 520 nm, which might result from the larger energy gaps (Table S4). Although, long-range corrected functionals (LRCFs) were introduced to improve descriptions of charge-transfer excitations by standard DFT functional, the results obtained from the LRCFs sometimes are less accurate than those obtained from the standard DFT functional.118-120 The absorption wavelengths computed with B3LYP and PBE0 functionals are similar to each other, which is due to their similar HF exchange fraction. However, the results of the B3LYP functional are much closer to the experimental ones. Thus, the electronic excitation energies, oscillator strengths, and rotational strengths of the studied compounds were calculated at the TDB3LYP/6-31+G(d) level of theory. A good match between the simulated and measured spectra that covers several well separated excitations can normally be used for a confidential assignment of the absolute configuration (AC).122 Thus, the 150 lowest energy electronic excitations were calculated, which covers the range of experimental measurement (Table S5, available as ESI†). The main concerned electronic transition energies, oscillator strength, and major contributions for the studied compounds, as compared to experimental data, were summarized in Table 2 and Table S6, and their simulated UV-Vis/CD spectra were shown in Figure 3 and Figure 5. For compound 1, the four experimental observation UV-Vis bands were well reproduced by our calculation (Table 2). The simulated UV-Vis/CD spectra are in reasonably good agreement with the experimental spectra, not only for the band positions but also the 10 ACS Paragon Plus Environment

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relative peak intensities. Moreover, the differences between the rotational strengths calculated using the length and velocity-gauge representation of the electric dipole operator are small (Table S5, ESI†). Thus, our adopted method can accurately describe electron transition property and assign the ACs of the charil TCBD derivatives with high confidence. To account for the effect of the CH2Cl2 solvent, the above UV-Vis/CD spectral calculations were repeated under solution phase PCM conditions. The simulated UV-Vis/CD spectra were shown in Figure 3. Comparison of the gas and solution spectra, although the solvent makes the bands at about 400 nm undergo a slightly hypsochromic shift, the whole band shapes are nearly similar to each other. Overall, the inclusion of solvent effects does not improve the agreement between measured and calculated spectra. The molecular orbitals (MO) involved in the main electronic transitions of the studied compounds 15 were shown in Figure 4 and Figure S2, respectively. The analysis of transition orbitals of compound 1 show that charge transfer between DMA and TCBD groups plays a key role in determining the electronic transition properties (Figure 4). The first one appears at about 295 nm with intraligand charge transfer character (Figure S2). The peak at about 447 nm mainly results from the charge transfer between TCNQ and TCBD moieties. For compound 3, there is a strong absorption band at about 298 nm, which corresponds to the charge transfer from TTF to TCBD groups. Compared with compound 3, compound 4 appears another new absorption band at about 445 nm, which mainly results from the central TTF groups to TCBDs group transition. There is common character for compounds 1, 3 and 4, the concerned occupied orbitals are mainly localized on electron donor moieties, the unoccupied orbitals are mainly localized on electron acceptor moieties. For compound 5, the two absorption bands were determined by a mixture transition among TTF, TCNQ and TCBD moieties. It should be noted that the charge transfer between TTF and TCNQ is relative small. Based on above electron transition analysis, it is found that different donor or acceptor substituents not only influence the position of the electron absorption wavelength but also alter the electron transition property. Despite the nonplanarity of our studied compounds, efficient intramolecular charge transfer was 11 ACS Paragon Plus Environment


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observed. Table 2. Calculated Electronic Absorption Energies (λcal, nm), Oscillators Strengths (f), Major Contribution, and Experimental Data in Parenthesis (λexp, nm) of Compound 1 in Gas Phase Band Band 1

λ

f

major contribution

265(260)

0.06

HOMO-1→LUMO+7(54%) HOMO→LUMO +7 (17%)

Band 2

314(305)

0.03

HOMO-5→LUMO+1(70%) HOMO-7→LUMO(12%)

Band 3

394(392)

0.34

HOMO-1→LUMO+3(95%)

Band 4

538(520)

0.01

HOMO→LUMO+1(33%) HOMO-1→LUMO+1(43%)

To clarify the net electron density difference between the ground state and excited state, the electron density difference maps (EDDMs) of these states were calculated using the Gauss-Sum2.2.3 software package123 and were shown in Figure 5 and Figure S3. The purple-colored regions indicate the regions in which electron density decreases upon transition to the excited state, and the bluecolored regions indicate the regions in which electron density increases upon the transition. The net charge transfer among these transitions for compound 1 is from DMA to TCBD groups. For compound 2, the net charge transfer is from allene moiety to TCBD moieties. It is noted that the TCNQ does not participate in the net charge transfer, which can explain why compound 2 has smaller first hyperpolarizability value. The charge transfer character of compound 3 is simillar to that of compound 1. Why does replacement of the tert-butyl groups with TTF moieties for compounds 4 and 5 have a great influence on the first hyperpolarizability? For compouds 1-3, the tert-butyl groups do not participate the charge transfer. TTF moieties in compounds 4 and 5 were involved in the net charge transfer, which will enhance the amount of the charge transfer and lead to the larger first 12 ACS Paragon Plus Environment

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hyperpolarizability (Figure S3).

Figure 3. Calculated UV-Vis (left) and CD (right) spectra in both gas and solution phases for compound 1 at the TDB3LYP/6-31+G(d) level of theory along with experimental UV-Vis and CD (red line). Data to prepare the experimental CD spectra were taken from ref. 59.

5

Figure 4. Molecular orbital isosurfaces involved in the main electronic transitions of compound 1 at the TDB3LYP/6-31+G(d) level of theory.



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265 (nm)

314 (nm)

394 (nm)

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538 (nm)

Figure 5. Electron density difference maps between the ground state and the excited state of interest for compound 1.

5

Figure 6. Calculated UV-Vis (left) and CD (right) spectra in the gas phase for compounds 1-5 at the TDB3LYP/6-31+G(d) level of theory. 14 ACS Paragon Plus Environment

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The studied compounds exhibit different CD spectra (Figure 6), which indicate that CD spectra are sensitive to the substituent groups. To understand the chiral origins of these compounds, molecular orbitals analysis was carried out and shown in Figure S4. Although the appearance of these CD spectra is different, there is common character of their chiral origins, which can be attributed to the exciton 5

coupling between substituent groups (DMA, TCNQ and TTF) and TCBD moieties. 4 CONCLUSION DFT/TDDFT calculations have been used to investigate the electronic circular dichroism (CD), UVVis absorption and second-order NLO properties of the five 1,1,4,4-tetracyanobuta-1,3-diene derivatives. The simulated CD spectra nicely reproduce the experimental one without any shift or scaling, which can be used to assign its absolute configuration (AC) with high confidence. Despite the nonplanarity of the studied compounds, efficient intramolecular charge transfer between electron donor and electron acceptor were observed. The calculated first hyperpolarizability values of the studied compounds range from 4 to 35 × 10-30 esu, which means that NLO response of the studied compounds can be tuned effectively. The studied compounds have a possibility to be excellent secondorder nonlinear optical material from the standpoint of large first hyperpolarizability values, intrinsic non-centrosymmetric electronic structure, and high stability. 5 ACKNOWLEDGEMENTS The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (21273030 and 21203019), Natural Science Foundation of Jilin Province (20140101045JC), the Science and Technology Development Project Foundation of Jilin Province (20090146; 201101116), The Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry. 6 SUPPORTING INFORMATION: The main concerned bond length and Cartesian coordinates; the



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computed absorption energy using different functionals and different basis sets; the calculated excitation energies, oscillator and rotational strengths; molecular orbital isosurfaces involved in the main electronic transitions; electron density difference maps between the ground state and the excited state. This information is available free of charge via the Internet at http://pubs.acs.org. 7 REFERENCE

(1) Wang, C.; Zhang, T.; Lin, W. B. Rational Synthesis of Noncentrosymmetric Metal-Organic Frameworks for Second-Order Nonlinear Optics. Chem. Rev. 2012, 112, 1084-1104. (2) Wu, H. P.; Yu, H. W.; Pan, S. L.; Huang, Z. J.; Yang, Z. H.; Su, X.; Poeppelmeier, K. R. Cs2B4SiO9: A Deep-Ultraviolet Nonlinear Optical Crystal. Angew. Angew. Chem. Int. Ed. 2013, 52, 3406-3410. (3) Coe, B. J.; Fielden, J.; Foxon, S. P.; Brunschwig, B. S.; Asselberghs, I.; Clays, K.; Samoc, A.; Samoc, M. Combining Very Large Quadratic and Cubic Nonlinear Optical Responses in Extended, Tris-Chelate Metallochromophores with Six π-Conjugated Pyridinium Substituents J. Am. Chem. Soc. 2010, 132, 3496-3513. (4) Dalton, L. R.; Sullivan, P. A.; Bale, D. H. Electric Field Poled Organic Electro-optic Materials: State of the Art and Future Prospects. Chem. Rev., 2010, 110, 25-55. (5) Castet, F.; Bogdan, E.; Plaquet, A.; Ducasse, L.; Champagne, B.; Rodriguez, V. Reference Molecules for Nonlinear Optics: A Joint Experimental anTheoretical Investigation. J. Chem. Phys. 2012, 136, 024506. (6) Kanis, D. R.; Ratner, M. A.; Marks, T. J. Design and Construction of Molecular Assemblies with Large Second-order Optical Nonlinearities. Quantum Chemical Aspects. Chem. Rev. 1994, 94, 195242. (7) Kim, S. Y.; Lee, M. Y. Second Molecular Hyperpolarizability of 2,2′-diamino-7,7′-dinitro-9,9′Spirobifluorene: An Experimental Study On Third-Order Nonlinear Optical Properties of a Spiroconjugated Dimer. J. Chem. Phys. 1998, 109, 2593. (8) Plaquet, A.; Champagne, B.; Kulhanek, J.; Bures, F.; Bogdan, E.; Castet, F.; Ducasse, L.; Rodriguez, V. Effects of the Nature and Length of the π-Conjugated Bridge on the Second-Order Nonlinear Optical Responses of Push–Pull Molecules Including 4,5-Dicyanoimidazole and Their Protonated Forms. ChemPhysChem, 2011, 12, 3245-3252. (9) Suresh, S.; Ramanand, A.; Jayaraman, D.; Mani, P. Reviw on Theoretical Aspect of Nonlinear 16 ACS Paragon Plus Environment

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Induction

from

Allenes

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Twisted

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(TCBDs):

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e have investigated the chiroptical, linear, and second-order nonlinear optical properties of five 1,1,4,4tetracyanobuta-1,3-diene derivatives and elucidated structure-property relationships from the micromechanism. 160x96mm (300 x 300 DPI)

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Laser optical separation of chiral molecules.

Electronic Metamaterials with Tunable Second-order Optical Nonlinearities.

Electronic circular dichroism of the chiral rigid tricyclic dilactam with nonplanar tertiary amide groups.

Stability of optical solitons in parity-time-symmetric optical lattices with competing cubic and quintic nonlinearities.

Discriminating interactions between chiral molecules.

Rotating optical microcavities with broken chiral symmetry.

On the determination of the diagonal components of the optical activity tensor in chiral molecules.

Ultrafast control of third-order optical nonlinearities in fishnet metamaterials.

Self-replication and amplification of enantiomeric excess of chiral multifunctionalized large molecules by asymmetric autocatalysis.

Optical nonlinearities and enhanced light transmission in soft-matter systems with tunable polarizabilities.

Enantiomeric guests with the same signs of chiral optical responses.

Chiral Light-Matter Interaction in Optical Resonators.

Demonstration of the stabilization technique for nonplanar optical resonant cavities utilizing polarization.

Computation of Nonlinear Optical Properties of Molecules with Large Amplitude Anharmonic Motions. III. Arbitrary Double-Well Potentials.

Chiral Molecular Science: How were the absolute configurations of chiral molecules determined? "Experimental results and theories".

Functionalized graphene as a gatekeeper for chiral molecules: an alternative concept for chiral separation.

Eigen oscillations of a chiral sphere and their influence on radiation of chiral molecules.

New trans-stilbene derivatives with large two-photon absorption cross-section and non-linear optical susceptibility values--a theoretical investigation.

Continuum model for chiral induced spin selectivity in helical molecules.

Environmental-confinement-induced stability enhancement of chiral molecules.

Local light-induced magnetization using nanodots and chiral molecules.

Enantioselective synthesis of chiral heterocycles containing both chroman and pyrazolone derivatives catalysed by a chiral squaramide.

Small molecules, large molecules, and the new biotechnology.

Demonstration of tunable optical generation of higher-order modulation formats using nonlinearities and coherent frequency comb.