Spiral Graphene Nanoribbons with Azulene Defects as Potential

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Spiral Graphene Nanoribbons with Azulene Defects as Potential Nonlinear Optical Materials Yuan-Yuan He, Jiu Chen, Xue-Lian Zheng, Xiaodong Xu, Weiqi Li, Ling Yang, and Wei Quan Tian ACS Appl. Nano Mater., Just Accepted Manuscript • DOI: 10.1021/acsanm.9b00089 • Publication Date (Web): 27 Feb 2019 Downloaded from http://pubs.acs.org on February 28, 2019

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ACS Applied Nano Materials

Spiral Graphene Nanoribbons with Azulene Defects as Potential Nonlinear Optical Materials Yuan-Yuan He1§, Jiu Chen1§, Xue-Lian Zheng1, Xiaodong Xu2, Wei-Qi Li2*, Ling Yang3*, Wei Quan Tian1* 1Chongqing

Key Laboratory of Theoretical and Computational Chemistry, College of

Chemistry and Chemical Engineering, Chongqing University, Huxi Campus, Chongqing, 401331, P. R. China 2Department 3MIIT

of Physics, Harbin Institute of Technology, Harbin, 150001, P. R. China

Key Laboratory of Critical Materials Technology for New Energy Conversion and

Storage, Institute of Theoretical and Simulational Chemistry, School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin, 150080, P. R. China *Corresponding author: [email protected], [email protected], [email protected] §: the first two authors contribute equally to this work ABSTRACT Inducing new nonlinear optical (NLO) properties while keeping the thermal stability of carbon based nanomaterials paves a new path for the application of carbon nanomaterials in opto-electronics. In the present work, azulene units are introduced to spiral carbon nanoribbons to enhance the polarity of the charge distribution in spiral carbon nanoribbons, significantly enhancing the first hyperpolarizabilities of those nanoribbons and making the nanoribbons potential nonlinear optical materials. For example, the static first hyperpolarizability of azulene-defected spiral graphene nanoribbon with eight units (ADSGN8) is 2499.01030 esu, whereas that of azulene spiral graphene nanoribbon (SGN8) is only 12.01030 esu. The two-dimensional second-order NLO spectra predicted by the sum-over-states model reveal the strong second-order NLO responses of the nanomaterials under external fields, particularly within the visible region of approximately 600.0 nm. The origin of the first hyperpolarizability of azulene-defected spiral carbon nanoribbons is scrutinized, and further improvement on the NLO responses of those systems is proposed. KEYWORDS nonlinear optics, hyperpolarizability, spiral graphene nanoribbon, azulene defect, sum-over-states model, two-dimensional second-order nonlinear optical spectrum

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INTRODUCTION Searching for or designing new materials with good nonlinear optical (NLO) properties has been the ultimate goal for both experimental and theoretical endeavors since the discovery of second harmonic generation.1 Because of their synthetic feasibility and flexible tailorability, organic NLO materials have been extensively investigated with regard to applications to generate higher harmonic frequencies, electro-optic modulation, frequency mixing, optical storage, optical rectification, telecommunication.2-5 However, the thermal stabilities of organic materials hinder such applications. Though inorganic NLO materials have high thermal stabilities and have been extensively utilized for such applications as laser guidance, laser frequency conversion technology and laser systems for harmonic generation and optoelectrical switching,6-9 the relatively weak NLO response limits those applications. It is highly desirable to search for materials with a high stability and strong NLO responses. The flexible bonding of carbon, the susceptibility of  electrons and the high stability of carbon based materials make carbon materials potential NLO materials.10-12 For NLO responses with even-order (e.g. second-order NLO susceptibility), the NLO materials are required to be polar and noncentrosymmetric, but most carbon based materials (fullerenes, nanotubes, graphite and graphenes) are nonpolar. Therefore, such carbon materials need further molecular engineering to generate even-order NLO responses. Azulene with fused pentagon and heptagon is aromatic according to the Hückel's rule, and it is also polar.13 The introduction of azulene in carbon materials14 could induce charge distribution polarity in such materials, thereby generating nonvanishing even-order NLO responses. The NLO susceptibility of materials also depends on the packing of materials. Helicenes,15 with spiral arrangements of fused benzene rings and inherent chiral structures, have significant second NLO responses,16,17 and their aggregates are noncentrosymmetric. The interlayer charge transport in helicenes18 may enhance the systems’ charge polarization, and the introduction of azulene into helicenes could make the chiral structures more polar to form well-aligned aggregates thus enhancing the systems’ even order NLO responses. The spiral frame of spiral graphene nanoribbons (SGN) gives the materials good elasticity along the spiral axis. Under stress, the spring-like frame gets compressed or stretched with varying interlayer interaction, which, in turn, could affect the electronic structure and the optical response of the SGNs. In the present work, the structure, electronic spectra, and the first hyperpolarizabilities of azulene-based helicenes in relaxed state and under stress are studied with density functional theory (DFT)19-20 based method, the semi-empirical method (ZINDO)21 and the sum-over-states (SOS)


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model22,23 to search for the strongest NLO response of the materials under external fields for NLO applications, e.g., electro-optical Pockels effect, optical rectification and harmonic generation. MODELS AND COMPUTATIONAL DETAILS The structures of pristine and azulene-defected spiral graphene nanoribbons are shown in Figure 1. In the pristine spiral grapehene nanoribbon, a naphthalene unit and a phenanthrene unit are added at the edge of the core spiral frame (Figure 1a). If the naphthalene and phenanthrene in the SGN are modified to include azulene, an azulene-defected spiral graphene nanoribbon (ADSGN) forms (Figure 1b). The structures of those two SGNs were optimized through the DFT method PBEPBE24 with 6-31G(d, p) basis sets25,26 in periodic boundary condition (PBC) as implemented in Gaussian0927. The structure of the ADSGN was also relaxed with a fixed spiral length (varied in 0.05 Å under compression and 0.1 Å under tension) to simulate the system under compression or tension through constrained optimization. Since only the electronic spectra of a cluster model can be predicted with ZINDO at the present stage, SGN segments were constructed from the PBC relaxed geometry of the SGNs and the two ends of the segments are passivated with hydrogen. The electronic spectra of the ADSGN segments with up to eight units are predicted. Based on the predicted electron transition energy, transition moments and dipole moments from ZINDO, the first hyperpolarizabilities, including two-dimension second-order NLO spectra28,29 of those ADSGNs are predicted with the sum-over-state model22,23,30 using the code LinSOSProNLO.31 The two-dimension second-order NLO spectra include all possible second-order NLO responses of a system.28,29 Since the NLO properties from the SOS model are predicted and interpreted based on single electron excitations,22 the electronic spectra of all systems are predicted and discussed in detail in the following section. For consistency with the following discussion of electronic spectra and nonlinear optical properties, the electronic density of states (DOS) and the frontier molecular orbitals are plotted based on the ZINDO predictions, and those based on the DFT predictions are provided in the supporting information. The energy gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) predicted from ZINDO are larger than those predicted from DFT methods.


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a

b

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c

Figure 1. Structure of spiral graphene nanoribbons. a: pristine spiral graphene nanoribbon unit structure. b: spiral graphene nanoribbon unit structure with azulene defects. r in part c is the length of one unit of spiral graphene nanoribbon along the spiral (the z-axis) [r = 3.76 for SGN and r = 3.77 Å for ADSGN predicted with PBEPBE/6-31G(d, p)]. RESULTS AND DISCUSSION Structure of ADSGNs When the phenanthrene unit at the edge of SGN transforms to azulene, the length of the unit cell of the spiral frame lengthens slightly from 3.76 Å (SGN) to 3.77 Å (ADSGN). The one-dimensional graphene-like spiral frame behaves similar to a spring under compression or tension, and the  electron conjugation and interlayer coupling (thus the electronic and magnetic properties) change with external strain.18,32 Under compression, the energy of the system increases more rapidly than under tension (Figure 2 and Table S1) with the same variation length; thus, the structure and properties of the ADSGN with unit cell lengths ranging from r=r0-m0.05 to r=r0+m0.1 (m=1-5) are investigated in the present work. The electronic properties of ADSGNs with lengths ranging from two units to eight units were predicted, and only those of the ADSGN (ADSGN8) with eight units are discussed in detail (the electronic properties of other ADSGNs are provided in the supporting information). With the introduction of azulene into SGN, the charge distribution (wavefunction) is polarized by the polarity of azulene. In the SGN, frontier molecular orbitals (FMOs) essentially distribute evenly in the spiral frame (Figure 3). On the other hand, the FMOs obviously localize (thus being polarized) at specific regions in the spiral frame of the ADSGNs. In the ADSGNs, the distribution of frontier molecular orbital (HOMO and LUMO) becomes polarized as the length of the spiral increases. The occupied frontier molecular orbitals essentially localize on the pentagon end and the unoccupied frontier molecular orbitals mainly localize on the heptagon end (Figure 3 and Figure S1); i.e., charge


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transfer occurs from the heptagon end to the pentagon end. The frontier MO distribution in ADSGNs clearly reveals the polarizing force on the molecular orbital distribution that is generated by the introduction of azulenes. The polarizing effect is also indicated by the large dipole (Table S2) and polarized charge distribution of the ADSGNs. The pentagon end could be functionalized with a strong electron acceptor and the heptagon end could bond with a strong electron donor to further enhance the polarity of the ADSGN. The introduction of azulene into the SGNs destabilizes the system with energetically elevated molecular orbitals and with a smaller HOMO-LUMO energy gap in the ADSGNs. This is clearly indicated by the electronic DOS of SGN8 (SGN with eight units) and ADSGN8 (Figure 3).

Figure 2. Relative energies per unit of azulene-defected spiral graphene nanoribbons with eight units under strain predicted with PBEPBE/6-31G(d, p). r is the deviation of the unit length from the unit length of the relaxed structure (3.77 Å). The interlayer  electron overlap opens a new charge transport channel in spiral conjugated systems.18 The interlayer  electron overlap changes with interlayer distance under external strain. The interlayer  electron overlap strengths under compression and it weakens under tension as revealed by the HOMO and LUMO of ADSG8 under external strain (Figure 4). As ADSGN8 is compressed, the  electrons become delocalized (Figure 4a), and then become localized as the interlayer distance increases. The  electron localization along the spiral axis stabilizes the HOMO and destabilizes the LUMO of ADSGN8, thus generating a large HOMO-LUMO energy gap. The polarization and localization of  electron conjugation along the spiral axis leads to a net positive charge distribution at the heptagon end; i.e., polarization from the heptagon to the pentagon in azulene makes the carbon spiral nanoribbon polar. The impact of external strain on the electronic structure of ADSGN is also reflected by the electronic DOS. In the compressed ADSGN8, the


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energies of molecular orbitals show an upward shift, and the frontier occupied MOs have large densities in the electronic DOS of the stretched ADSGN8.

LUMO+2

(-1.40 eV)

(-1.67 eV)

LUMO+1

(-1.43 eV)

(-1.72 eV)

LUMO

(-1.45 eV)

(-1.80 eV)

HOMO

(-6.14 eV)

(-5.65 eV)

HOMO-1

(-6.12 eV)

(-5.70 eV)

HOMO-2

(-6.23 eV)

(-5.75 eV)

SGN

ADSGN

Figure 3. Electronic DOS (plotted with the full width at half maximum of 0.1 eV and in arbitrary units) and frontier molecular orbitals of relaxed ADSGN8 and SGN8 as predicted from ZINDO. The P denotes the pentagon end of ADSGN8.


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L -1.85 eV

-1.80 eV

-1.79 eV

-5.42 eV

-5.65 eV

-5.69 eV

3.57 eV

3.84 eV

3.90 eV

H

E(H-L)

a

b

c

Figure 4. The HOMO (H), LUMO (L) and electronic DOS (in arbitrary units) of ADSGN8 [plotted from the ZINDO wavefunctions with an isosurface value of 0.006 (e/bohr3)1/2]. a. compressed (3.52 Å); b. relaxed (3.77 Å); c. stretched (4.27 Å). E(H-L) is the energy gap between HOMO and LUMO. The P denotes the pentagon end of ADSGN8. The vertical, dashed line is at the edge of HOMO in the DOS plot. The HOMOs and LUMOs predicted with PBEPBE are shown in Figure S2. Electronic spectra of ADSGNs The electronic spectra of the ADSGNs with lengths of two to eight units in relaxed state were predicted with ZINDO. Up to 40 occupied and unoccupied frontier molecular orbitals, respectively, were included in the active space for configuration interaction single (CI/S) calculations for all ADSGNs. The major absorption peaks in the electronic spectra of the ADSGNs show a redshift as the spiral length increases (Figure 5a). There is an absorption peak approximately at 10.0 eV in the ADSGNs with two and three units, however, this absorption peak disappears in the ADSGNs with more than three units. On the other hand, the long wavelength absorption near 2.0 eV remains in all those ADSGNs. With the increase in spiral length, major absorption peaks locate between 4.0 eV and 6.0 eV. Compared to the SGN of the same length (Figure 5b), the electronic spectra of ADSGN8 show an overall redshift. The major absorptions in both SGNs and ADSGNs occur in the range from


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4.0 eV to 6.0 eV. There is a strong absorption peak at 6.0 eV in SGN8, whereas the strong absorption peaks in ADSGN8 are below 6.0 eV (Figure 5b). The electronic spectra of graphene have a strong absorption peak at 267 nm (4.64 eV) and a very weak peak at 550 nm (2.25 eV).33 The absorption peaks of SGNs and ADSGNS from 4.0 eV to 6.0 eV possibly have a similar transition nature to that in graphene.33 From the compressed to the stretched structures, the electronic spectra of ADSGN8 show a redshift in this order, as revealed in Figure 5b, and the absorption bands get sharper, which might be due to the weakening of the interlayer  orbital overlap that leads to the decrease in the mixture of vertical and charge transfer excitations (the nature of the electronic transition of major absorptions in ADSGN8 is listed in Table S3). There are two conspicuous peaks at 4.9 eV and 5.4 eV in the electronic spectra of the ADSGN stretched to 4.27 Å/unit.

a b Figure 5. Electronic spectra of ADSGNs and the oscillator strengths (dimensionless) are scaled with respect to the strongest absorption of the system. [a. with different spiral lengths (n) in relaxed state;

b. SGN8 and ADSGN8 under compression (3.52 Å), relaxed (3.77 Å), and stretched (4.27 Å)]. Second-order nonlinear optical properties of ADSGNs The electronic second-order nonlinear optical properties of graphene nanoribbons were predicted with the perturbative SOS model, whose performance was well verified,34-37 and the combination of configuration interaction singles with SOS is suitable for the NLO simulations of nanosystems.30 The tensor of the first hyperpolarizability ijk is calculated through the rewritten SOS formula,23,30 ijk(;1,2)m,n= h2 P  ijk 

m,n ( g )

k

i rgm r mn rngj

(mg   -i m )(ng  1 -i n )

(1)


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where ħ is the Dirac constant, and =(1+2). rigm is the transition moment rigm= in the i direction, andrkmn =m|k|ng|k|gmn is the dipole moment fluctuation in the k direction. m(m=0.008m/2) is the inverse radiative lifetime of the excited state m (or damping coefficients) with m as the mth excitation energy and 2 as the second (also the lowest) excitation energy. Pijk sums all terms through permutations of pairs of transition moment (or dipole moment fluctuation) and external field (rigm, ), (rmn, 1), and (ring,2). ħmg is the excitation energy from the ground state to the excited state m. If dipole moment is taken as a vector, then the transition moment rigm= should also be a vector (=) and this gives the tensor nature of the first hyperpolarizability components ijk(;1,2). For comparison, the predictions of second-order NLO properties of those graphene nanoribbons with transition moment rigm= treated as scalar (=) are reported in the supporting information (Figures S3-S6). The two predictions (vector and scalar) are quantitatively similar, but with different signs for some tensor components. The orientation averaged hyperpolarizabilities are predicted through i=iii+(ijj+jij+jji+ikk+kik+kki)/3 [i,j,k(x,y,z)] and =(xrx+yry+zrz)/(rx2+ry2+rz2)1/2.

Figure 6. Variation of the static first hyperpolarizability (0 in 1030 esu) of azulene-defected spiral graphene nanoribbon of eight units in relaxed state (r=3.77 Å) with electron excitations. The oscillator strengths (dimensionless) are scaled with respect to the strongest absorption of the system. The P denotes the

pentagon end of ADSGN8.


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The spiral arrangement of azulene units in the ADSGNs polarizes the nanoribbons and leads to charge transfer based electron excitations in the long wavelength region of visible light. The nature of the peaks approximately at 2.0 eV is essential vertical excitation mixed with minor charge transfer excitation (for example in ADSGN8 as shown in Figure 6), and those excitations have large contributions (approximately1.010-27 esu in ADSGN8) to the static first hyperpolarizability of the ADSGN. In the relaxed ADSGN8, there are two major absorption peaks at 1.88 eV and 2.05 eV with essential vertical excitation in the low energy region. Those two excitations contribute 228.71030 esu (1.88eV) and 247.61030 esu (2.05 eV) to the static first hyperpolarizability of ADSGN8 respectively (Figure 6). The other electron excitations with excitation energies larger than 2.05 eV (up to 7.2 eV) contribute approximately 1.41027 esu to the static first hyperpolarizability (0) of ADSGN8. The 0 of a typical electron push–pull chromophores (D/A) with polymethine (C155O3N4F3H150) was studied with the same methods.29 The of C155O3N4F3H150 is 2049.41030 esu (12.41030 esu/heavy-atom), and the of ADSGN8 (2498.91030 esu, 8.21030 esu/heavy-atom). Although the per heavy-atom of C155O3N4F3H150 is larger than that of ADSGN8, with the thermal stability of those compounds for applications in strong external fields taken into account, ADSGN8 would be the candidate for NLO applications in strong external fields.

Figure 7. Variation in the static first hyperpolarizability (in 1030 esu) and dipole moments (r in Debye, predicted by ZINDO) of spiral graphene nanoribbons with lengths (n units) under different strains (r=3.77 Å is the relaxed state). The z-axis is oriented parallel to the direction of elongation of the spiral nanoribbon.


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The total static first hyperpolarizability (0) of ADSGN increase as the nanoribbon length increases (Figure 7), and the static first hyperpolarizability per unit of ADSGN starting from ADSGN with four units [in 1030 esu, 198.7 (four units), 225.9 (five units), 236.4 (six units), 265.7 (seven units), 312.4 (eight units)] also increases with nanoribbon length. [The large deviation of the dipole moment direction away from the z axis (the elongation direction of nanoribbon) makes comparison of the static first hyperpolarizability tensors in short ADSGNs difficult.] Although the total dipole moment of ADSGN increases roughly linearly with nanoribbon length, the dipole moment per unit of ADSGN decreases with nanoribbon length. With the increase in nanoribbon length, the 0z (along the spiral axis) increases more significantly than 0x and 0y, which is a similar case to the variation of dipole moment with nanoribbon length. According to the evaluation of the orientation averaged first hyperpolarizability, the larger increase in 0z explains the increase in the static first hyperpolarizability per unit of ADSGN with nanoribbon length. From a compressed to stretched state under external strain, the variation in the static first hyperpolarizability has a different order compared to that of dipole moment, as shown in Figure 7.

Figure 8. Variation in the static first hyperpolarizability ( in 1030 esu) and dipole moments (r in Debye) of azulene-defected spiral graphene nanoribbons with a length of six units under different strains predicted with ZINDO/SOS. The z-axis is oriented parallel to the direction of elongation of the spiral nanoribbon. r is the deviation of unit length from that of the relaxed structure (3.77 Å). The variation in static first hyperpolarizability with external strain was investigated on the ADSGN with six units (Figure 8) while the compromise between system size and computational cost was considered. From the compressed to the stretched structures, the static first hyperpolarizability has small changes and slightly decrease as the nanoribbon is stretched. According to the variation in


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dipole moment with the compressional/tensile strain, the change in static first hyperpolarizability mainly occurs along the nanoribbon spiral. The strong second-order NLO responses of ADSGN8 under external fields, particularly at 2.05 eV, form a basin in the regions with external fields weaker than 2.05 eV [surrounded by 1(2) = 2.05 eV, 1 + 2 = 2.05 eV, and 1  2 = 2.05 eV] in the two-dimensional second-order nonlinear optical spectra (Figure 9.). 1(2) = 2.05 eV is one-photon resonance. 1 + () 2 = 2.05 eV is sum (difference) frequency generation with two photon process. The response at (0.0, 2.05 eV) is the strong electro-optical Pockels effect, and that at (2.05 eV, 2.05 eV) is optical rectification. Beyond the basin, ADSNG8 has strong responses to external fields, although they are weaker than those at 2.05 eV. Under external strain, the second-order NLO responses of ADSGN8 are similar to those in the relaxed structure while with resonance under different externals fields (Figure S7).

Figure 9. The two-dimensional second-order nonlinear optical spectra (in 1025 esu) of ADSGN8 in relaxed state (r=3.77 Å).

CONCLUSIONS AND PERSPECTIVES The structure, linear and nonlinear optical properties of azulene-defected spiral graphene nanoribbons were studied using the density functional method and semi-empirical methods combined with the sum-over-states model in relaxed and constrained states.


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The interlayer  orbital overlap is enhanced in compressed ADSGNs and is weakened in the stretched ADSGNs. From the compressed ADSNGs to the stretched ADSGNs, the electronic spectra show redshift. The introduction of azulene in spiral graphene nanoribbons leads to a polar charge distribution in the pentagon end and thus makes the azulene-defected spiral graphene nanoribbons polar materials. The SOS predictions reveal noticeable second-order NLO properties of the ADSGNs. The static first hyperpolarizability increases exponentially with nanoribbon length, which is similar to the stacked Bucky bolws.38 The ADSGNs show strong second-order NLO responses in the presence of external fields, as revealed by the two-dimensional seconder-order NLO spectra. However, the second-order NLO properties of ADSNG show only slight changes under external strain. In the present work, the second-order NLO properties of carbon based materials were realized through the introduction of polar azulene (which could be further polarized by adding a strong electron donor at the heptagon end and an electron acceptor at the pentagon end). The ADSGNs are good second-order NLO materials at external field approximately at 600.0 nm. This work hopes to pave a path for tuning NLO properties of carbon based materials for practical NLO applications and to inspire experimental exploration. ACKNOWLEDGMENTS

This work is supported by the National Natural Science Foundation of China (11574062, 21203042, 21673025), the Open Project of Key Laboratory of Polyoxometalate Science of Ministry of Education (NENU) and State Key Laboratory of Supramolecular Structure and Materials (JLU) (SKLSSM201818). ASSOCIATED CONTENT

Supporting Information is available free of charge on the ACS Publications website http://pubs.acs.org/.

Energies, dipole moments, nature of major electron excitations, frontier molecular orbitals, electronic density of states, variation of the static first hyperpolarizability of ADSGNs with spiral length and external stress, two-dimensional second-order nonlinear optical spectra of ADSGNs


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TOC GRAPHICS


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Spiral Graphene Nanoribbons with Azulene Defects as Potential

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