Nonlinear Optical Properties of Fullerene C96 (D3d) and RelatedHeterofullerenesXin Zhou,† Wei-Qi Li,*,‡ Bo Shao,§ and Wei Quan Tian*,†

†State Key Laboratory of Urban Water Resource and Environment; Institute of Theoretical and Simulational Chemistry, Academy ofFundamental and Interdisciplinary Sciences, Harbin Institute of Technology, Harbin 150080, P. R. China‡Department of Physics, Harbin Institute of Technology, Harbin 150001, P. R. China§Sports Institute, Chengdu University of Technology, Chengdu 610059, P. R. China

*S Supporting Information

ABSTRACT: The high stability, tailorability, and the π conjugation offullerene-based nanomaterials render those nanomaterials potentialnonlinear optical (NLO) materials. The sum-over-states model withlinear scaling was employed to model the static and dynamic thirdorder NLO properties of fullerene C96 (D3d) and C96 based boron−nitrogen-doped and metal-doped fullerenes. Doping induces moreelectronic excitations in the heterofullerenes in the visible and infraredregions. The two-photon absorption cross-section of heterofullereneC72B12N12(C3) reaches 1.65 × 105 × 10−50 cm4·s/photon at 892.0 nm.The heterofullerenes have strong NLO responses to external fieldsfrom the ultraviolet−visible to infrared regions. The correlationbetween structure and NLO properties is disclosed for those cages.

■ INTRODUCTION

Since the discovery1 and macroscopic synthesis2 of thefullerene C60, the structure and properties of fullerenes havebeen extensively investigated. However, the increase of thenumber of isomers with the size of fullerenes makes thesynthesis and isolation of bigger fullerenes challenging, and thisslows down the pace of experimental study on higher pristinefullerenes. C96 is so far one of the largest pristine fullerenesstructurally well characterized in experiment3−5 followingstructure and properties studies both theoretically6−8 andexperimentally.9 Ascribed to their curved three-dimensional πconjugation, round shape, nanosize, and good thermal stability,fullerenes are expected to have broad potential applications inelectronics and photonics, e.g., nonlinear optical (NLO)devices. The third order NLO properties of C60 to C96 werefound to increase with fullerene size in general and vary withgeometrical structure or resonance enhancement.9 The thirdorder NLO response of those fullerenes in degenerate fourwave mixing was estimated to be 10−31−10−30 esu (2.1 ± 0.6 ×10−30 esu for C96).

9 However, possible mixing of variousfullerene isomers in sample makes the study of NLO propertyof particular isomers difficult. The isolation of fullereneisomers3−5 makes such detailed studies possible.In the present work, the structure, electronic, and NLO

properties of the isomer of C96 with D3d symmetry (as shown inFigure 1) are studied. It is a clip of (9,0) zigzag carbonnanotube capped with C60 derived ends as identified inexperiment.4 The long wavelength region of its measured UV−vis4 is similar to that observed in the NLO measurement.9

Doping of heteroatom in fullerene changes the structure and

thus the properties of fullerenes10−13 and brings about newpossible applications of those heterofullerenes. Two boron−nitrogen-doped heterofullerenes derived from C96 (D3d) aredesigned to investigate the effect of heteroatom doping on theelectronic and NLO properties of fullerenes. The BN pair (anisoelectronic structure to C2) is used in the doping to mimicthe hybridization of boron nitride nanotube with carbonnanotube. The doping of titanium in heterofullerenes is alsoinvestigated. The advance in materials synthetical technologyensures the synthesis of such molecular materials in the future.

■ MODELS AND COMPUTATIONAL DETAILSThe structures of C96 (D3d), BN-doped fullerenes C72B12N12,and Ti-doped heterofullerene C71B12N12Ti were shown inFigure 1. In the isomer of C72B12N12 with C3v symmetry, BNpairs are separated, while BN pairs in the middle of the cage areconnected in the isomer with C3 symmetry. A carbon atom isreplaced by a Ti atom at the N end of C72B12N12 (C3) resultingin the formation of C71B12N12Ti with Ti bonding to three Natoms. Because of the strong bonding between Ti and N, thisisomer is 91.3 kcal/mol more stable than the isomer dopedwith a Ti atom on the B end. The structures of those cageswere optimized with density functional theory based methodB3LYP14,15 and basis set 6-31G(d).16,17 Vibrational frequencycalculations were carried out to verify the nature of thosestationary points on potential energy surface as minima.

Received: August 26, 2013Revised: September 25, 2013Published: October 4, 2013

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The electronic spectra of those cages were predicted withconfiguration interaction single (CIS) through the ZINDOmethod.18 CIS does not include description for doubly excitedstates, thus in the present work, the prediction on two-photonabsorption (TPA) from CIS has no contribution from doublyexcited states. The performance of ZINDO in predicting theelectronic spectra of fullerenes is well verified.19,20 With thedipole moments and transition dipoles from the CIScalculations, the third order NLO properties of those systemswere predicted with the sum-over-states model.21−23 The goodperformance of ZINDO/SOS on the third order NLOproperties of C60

19,24−26 warrants the present predictions onthe NLO properties of C96 (D3d) and related cages. The overalltrend of NLO property evolution with these fullerenes couldprovide new information for molecular material design. Thereare other methods to simulate NLO properties with responsetheory27,28 and time-dependent density functional theory.Considering the structure−properties interpretation featureand computational efficiency,23 we use ZINDO/SOS tosimulate the third order NLO properties of those cage systems.

■ RESULTS AND DISCUSSION

Structure. In the C96 (D3d) isomer, three hexagons locate atthe three edges of the end hexagon, and around these fourhexagons, six pentagons distribute evenly as that in C60. Thisarrangement of pentagons creates bonding pattern similar tothat in C60, i.e., 6−6 (double bond) and 6−5 (single bond) asobserved in experiment.4 The double bonds connecting thosepentagons have the shortest bond lengths (1.383 Å) (bond B−D in experiment).4 Such an arrangement leads to long bondlength (1.443 Å) for the double bond I−I4 (as labeled in Figure1) in the middle of the cage, thus with enhanced chemicalactivity. C96 (D3d) could be divided into two parts (as indicatedby the blue dashed lines in Figure 1): the hexagon belt with 18hexagons and two C60 cap ends. The middle hexagon belt(atoms I and J4) donates electrons to the two ends.The doping of BN pairs in asymmetric fashion breaks the C2

symmetry of the C96 (D3d) frame. The isolated doping of BNpairs (the C3v isomer as shown in Figure 1, the actual symmetryis Cs due to slight geometry distortion) has slightly higher

stability (18.6 kcal/mol) than that with BN pairs connected(the C3 isomer). C72B12N12 (C3v) has two C60 cap ends, with Nand B close to each end hexagon, respectively. The dipolemoment of the C3v isomer is 8.58 D. However, the doping ofBN pairs at the two ends of the C60 hemispheres leads to alarger dipole moment in the C3 isomer (10.30 D). Chargetransfer from C atoms to N atoms occurs, and this alleviates thecharge transfer from B atoms to N atoms. The replacement of acarbon atom by a Ti atom at the N end of C72B12N12 (C3)polarizes the charge distribution of the system, thus producing alarger dipole moment (as listed in Table 1), and makes the Tiatom an active center in chemical reaction. The energy of thehighest occupied molecular orbital (HOMO) of thoseheterofullerenes is higher than that of C96 (D3d), and theenergy of the lowest unoccupied molecular orbital (LUMO) islower than that of C96 (D3d), resulting in smaller energy gapsbetween the HOMO and LUMO. The narrowing of theHOMO−LUMO energy gaps leads to longer wavelength of thelowest dipole allowed electronic excitation.

Electronic Spectra. The correlation of predicted electronicspectra with the active space chosen in configuration interactionwith ZINDO was displayed in Figure 2. C72B12N12 (C3) servesas the test case with 325(18 × 18), 626(25 × 25), 901(30 ×30), 1297(36 × 36), 1601(40 × 40), and 2026(45 × 45) states,respectively. The electronic spectra of C72B12N12 with 45 × 45CIS active space could be divided into three regions, 0.0−2.0,2.0−7.0, and 7.0 eV to higher energy region. The first region(0.0−2.0 eV) is characterized by a peak around 1.0 eV. Thesecond region has a peak around 3.2 eV and strong absorptionsaround 5.2 eV. The third region has absorption peaks around8.0 eV. The overall shape of the electronic spectra of C72B12N12

with different CIS active space is similar to one another in theregion of 0.0−6.0 eV (206.0 nm) though with varied oscillatorstrengths, and this covers the major absorptions for NLOresponse, i.e., the frontier molecular orbitals are moreresponsive to external field and should have dominantcontribution to such response.19 The electronic spectra andNLO properties predictions in the present work were carriedout with CIS active space of 18 × 18 (325 states).

Figure 1. Structure of C96 (D3d), C72B12N12, and C71B12N12Ti. Atoms in gray are carbon, in blue are nitrogen, and in pink are boron. The white atomin C71B12N12Ti is Ti.

Table 1. Dipole Moments, the Energies of the Highest Occupied Molecular Orbital (HOMO) and the Lowest UnoccupiedMolecular Orbital (LUMO), and the Energy Gaps between the HOMO and LUMO (Egap) Predicted by B3LYP/6-31G(d); theWavelengths of the Lowest Dipole Allowed Electronic Excitation (Ele) Were Predicted by ZINDO

Dip (Debye) EHOMO (eV) ELUMO (eV) Egap (eV) Ele (nm)

C96 0.0 −5.41 −3.32 2.09 531.6C72B12N12 (C3v) 8.58 −5.30 −3.52 1.78 592.2C72B12N12 (C3) 10.29 −4.96 −3.97 0.99 1187.9C71B12N12Ti (C3) 14.30 −4.80 −4.07 0.73 3476.9

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The predicted electronic spectra of those four cages wereplotted in Figure 3. In the (D3d)C96·2Ni(OEP) complex,4 a

strong peak around 520.0 nm and shoulder peaks around 570.0nm were observed. However, no significant absorption above800.0 nm was observed. A relatively weak absorption waspredicted at 2.33 eV (531.6 nm) in the present work for the C96(D3d). Dipole allowed electronic excitations above 400 nmlocate at 3.10 eV (400.0 nm), 2.98 eV (416.4 nm), 2.90 eV(427.8 nm), 2.83 eV (438.5 nm), 2.66 eV (466.6 nm), 2.57 eV(483.3 nm), 2.49 eV (498.6 nm), and 2.33 eV (531.6 nm) withthe strong peaks at 416.0 and 438.0 nm in the ZINDOprediction. Below 400 nm, the strong absorption peaks of C96(D3d) locate at 5.97 eV (207.8 nm), 5.73 eV (216.5 nm), 5.67eV (218.7 nm), 5.59 eV (221.9 nm), and 5.11 eV (242.4 nm).The peak at 2.33 eV involves vertical excitation of electrons inthe MOs of the hexagonal belt at the middle of the cage. The

electronic excitation at 2.98 eV has the similar transition nature.The peak at 2.83 eV has mixture of vertical excitation at the beltand charge transfer based excitation in the C60 cap end.The doping of BN pairs in C72B12N12 (C3v) leads to broad

electronic spectra starting from 2.09 eV (592.2 nm). Below 3.10eV (400.0 nm), there are five noticeable absorption peaks at2.28 eV (544.4 nm), 2.35 eV (528.0 nm), 2.68 eV (462.0 nm),2.83 eV (438.0 nm), and 2.98 eV (415.6 nm). Five strongelectronic excitations occur at 3.61 eV (343.5 nm), 4.27 eV(290.6 nm), 4.78 eV (259.3 nm), 5.46 eV (227.2 nm), 5.63 eV(220.3 nm), and 5.78 eV (216.9 nm).C72B12N12 (C3) has lower dipole allowed electronic excitation

at 1.04 eV (1187.9 nm in near-infrared region) possibly due tothe doping of BN pairs at the C60 cap end. More peaks emergein the visible region with representative excitations at 1.78 eV(696.8 nm), 2.04 eV (607.2 nm), 2.49 eV (498.1 nm), 2.60 eV(477.4 nm), 2.80 eV (443.5 nm), 2.87 eV (431.7 nm), and 3.20eV (388.0 nm) plus two peaks in the near-infrared region at1.36 eV (910.8 nm) and 1.45 eV (852.8 nm). The strongestabsorption peak locates at 4.53 eV (273.8 nm) and anotherstrong absorption occurs at 5.23 eV (236.9 nm).The doping of Ti at the cap lowers the symmetry of the cage

and leads to a split of adsorption peaks as indicated by theelectronic spectra of C71B12N12Ti (as shown in Figure 3). Twonoticeable absorption peaks locate at 0.82 eV (1504.9 nm) and1.48 eV (838.4 nm) in the near-infrared region. Anothernoticeable peak emerges at 1.56 eV (794.7 nm). In the visibleregion, there are three major absorption peaks at 2.32 eV(533.5 nm), 2.60 eV (476.7 nm), and 2.65 eV (468.5 nm). Thelowest (while very weak) excitation essentially involves verticalexcitation (0.36 eV, 3476.9 nm) from the occupied 3d orbital tothe empty 3d and 4p orbital of Ti atom. Beside this weakexcitation, there is another weak peak at 0.62 eV (2012.1 nm).The electronic excitation at 0.82 eV is charge transfer basedtransition essentially from the HOMO (mainly the 3d orbital ofTi and the p orbitals of carbon atoms on the cap) to theLUMO (the p orbitals of atoms at the other cap). Chargetransfer based transition from the hexagon belt to the undopedC60 cap end is responsible for the excitation at 1.48 eV (838.4nm). The strongest absorption peaks locate at 4.82 eV (257.4nm) and 5.20 eV (238.7 nm).

Nonlinear Optical Properties. The third order NLOproperties were predicted with ZINDO and SOS model underexternal fields up to 3.0 eV. The evolution of third harmonicgeneration (THG), electric field induced second harmonicgeneration (EFISH), degenerate four wave mixing (DFWM),and TPA of C96 (D3d) with external fields was presented inFigure 4. The static second hyperpolarizability of C96 (D3d) is37.95 × 10−34 esu. C96 (D3d) reaches maximal responses toexternal field in the process of THG around 2.0 eV. Theelectronic excitations at 5.97 eV (207.8 nm), 5.73 eV (216.5nm), and 5.67 eV (218.7 nm) have significant contributions(about 40.0 × 10−34 esu) to the response of THG around 2.0eV. Those absorption peaks essentially are vertical excitationinvolving MOs of the hexagon belt. EFISH has a strongresponse (177.98 × 10−34 esu) at 2.92 eV with majorcontribution from the excitations at 5.73 eV, 5.59 eV, 5.67eV, and 5.11 eV. The response of DFWM at 2.33 eV (531.6nm) is 70.98 × 10−34 esu, and this is much samller than theexperimental estimation.9 In experiment,9 the structure of C96was not determined yet, and the sample might be a mixture ofC96 isomers. NLO properties have direct correlation with thestructure of a system. In this experiment, the second

Figure 2. Predicted electronic spectra of C72B12N12 (C3) with differentnumber of occupied and virtual molecular orbitals included in CIScalculations. The n and m in n × m are the numbers of active orbitalsincluded in CIS calculations. n is the number of frontier occupiedmolecular orbitals, and m is the number of frontier unoccupiedmolecular orbitals.

Figure 3. Electronic spectra of C96 (D3d) (17 × 19), C72B12N12 (C3v)(18 × 17), C72B12N12 (C3) (18 × 18), and C71B12N12Ti (18 × 18)predicted with CIS.

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hyperpolarizability of C60 at 2.33 eV (531.6 nm) was measuredto be 2.2 ± 0.6 × 10−31 esu. In the present prediction, theresponse of C96 (D3d) in DFWM has a maximum of 676.95 ×10−34 esu at 2.95 eV. This strong response has contributionfrom electronic excitations at 5.11 eV, 5.02 eV (247.2 nm), 3.29eV (377.1 nm), 3.10 eV (400.2 nm), and 2.98 eV(416.4 nm),and those electronic absorptions involve vertical excitations atthe hexagon belt. However, the TPA cross-section has anegative maximum at 2.89 eV (−248958 × 10−50 cm4·s/photon). It is a stimulated emission according to the Kramer−Heisenberg formula,29 and this peak is mainly ascribed to thecontributions of electronic excitations at 5.97, 5.59, 5.11, and5.02 eV.The NLO response of C72B12N12 (C3v) to external fields

occurs at lower fields with weaker magnitude (as shown inFigure 5) in comparison to those of C96 (D3d). The THG ofC72B12N12 (C3v) has similar overall response pattern to that ofC96 (D3d). There is a response minimum (−45.56 × 10−34 esu)at 1.26 eV (984.0 nm) and a plateau from 1.81 to 2.29 eV withmaxima at 2.07 eV (599.0 nm) and 2.17 eV (571.4 nm) (50.83× 10−34 esu). In the EFISH process, the response reaches aminimum of −298.05 × 10−34 esu at 1.80 eV (688.8 nm), and

the electronic excitation at 3.61 eV (343.5 nm, charge transferbased excitation from the B cap end to the N cap end) has thedominant contribution. More responses in the DFWM processoccur. The response minimum locates at 2.51 eV (−248.74 ×10−34 esu, with significant contribution from excitations at 3.61and 4.27 eV) and the response maximum is at 2.68 eV (462.6nm) (274.59 × 10−34 esu, with significant contribution fromexcitations at 3.61, 4.27 (290.4 nm), and 2.83 eV (438.1 nm)).The electronic excitation at 2.83 eV has the mixture of the Nend-cap vertical excitation and charge transfer based transitionfrom the B end hexagon belt edge to the N end-cap. Thosetransitions mainly involve the π MOs of carbon atoms. TheTPA process of C72B12N12 (C3v) has similar response pattern tothat in DFWM. The maximal absorption cross-section locatesat 2.38 eV (520.9 nm) (48322.0 × 10−50 cm4·s/photon) alongwith other two peaks at 2.13 eV (582.1 nm) (14814.0 × 10−50

cm4·s/photon) and 2.86 eV (433.5 nm) (28219.0 × 10−50 cm4·s/photon). A stimulated emission occurs at 2.63 eV (471.4 nm)(−196164.0 × 10−50 cm4·s/photon). The electronic excitationsat 3.61 eV (343.4 nm) and 4.27 eV (290.4 nm) have significantcontributions to those responses. The electronic excitation at4.27 eV involves charge transfer based excitation from the Bend hexagon belt edge (with contribution from B atoms) to theN end hexagon belt edge.The doping of BN pairs at the C60 cap narrows the HOMO−

LUMO gap in C72B12N12 (C3). This in turn leads to the redshift of electronic absorptions and makes electronic excitationenergetically feasible and thus more polarizable in the presenceof external field in comparison with C72B12N12 (C3v). The thirdorder NLO responses (THG, EFISH, and DFWM) ofC72B12N12 (C3) are stronger than those of C72B12N12 (C3v) asshown in Figure 6. A strong response occurs at 0.49 eV (2530.3

nm) with −284.48 × 10−34 esu, and another response occurs at1.39 eV (892.0 nm) with 140.79 × 10−34 esu in the THGprocess. The strong response at 0.49 eV is ascribed to thedominant contribution from the electronic excitation at 1.36 eV(910.8 nm) with electronic transition from the degenerateHOMO (the B end C60 cap) to the degenerate LUMO (the Nend C60 cap). The strongest response (−927.27 × 10−34 esu) toexternal fields in the EFISH process occurs at 0.68 eV (1823nm), and the electronic excitation at 1.36 eV has dominantcontribution to this response (−879.58 × 10−34 esu). Theelectronic excitation of the system at 1.36 eV also has dominant

Figure 4. Evolution of nonlinear optical properties of C96 (D3d) withexternal fields. THG is third harmonic generation. EFISH is electric-field induced second harmonic generation. DFWM is degenerate four-wave mixing. TPA is two-photon absorption. The second hyper-polarizabilities are in units of 10−34 esu. TPA is in units of 10−50 cm4·s/photon.

Figure 5. Evolution of nonlinear optical properties of C72B12N12 (C3v)with external fields. The second hyperpolarizabilities are in units of10−34 esu. TPA is in units of 10−50 cm4·s/photon.

Figure 6. Evolution of nonlinear optical properties of C72B12N12 (C3)with external fields. The second hyperpolarizabilities are in units of10−34 esu. TPA is in units of 10−50 cm4·s/photon.

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contribution to the relatively strong response of EFISH at 1.37eV (223.36 × 10−34 esu). This is the same case for the DFWM.The electronic excitation of the system at 1.36 eV leads to astrong peak at 1.33 eV (2374.59 × 10−34 esu) of DFWM.However, the electronic excitation of the system at 1.36 eV hasabout 23% contribution to the stimulated emission at 1.28 eV(−132075.0 × 10−50 cm4·s/photon) and over 50% contributionto the TPA at 1.39 eV (892.0 nm) (165371.0 × 10−50 cm4·s/photon). The charge transfer (from the B end C60 cap to the Nend C60 cap) based electronic excitation in C72B12N12 (C3v) at1.36 eV is mainly responsible to the strong response of thisheterofullerene in the presence of external fields.The replacement of a carbon atom by a Ti atom at the N end

C60 cap pentagon further lowers the external fields to whichC71B12N12Ti(N) has strong response in the processes of THG,EFISH, DFWM, and TPA, as shown in Figure 7. This is due to

the low energy dipole allowed electronic excitations inC71B12N12Ti(N) (as shown in Figure 3) and enhancement ofdipole moment. The strongest THG response of the systemtakes place at 0.31 eV (3999.5 nm), and this occurs in theinfrared region with dominant contribution (99%) from theelectronic excitation at 0.82 eV (1504.9 nm) with nature ofcharge transfer based excitation from the HOMO (the Ti end)to the LUMO (the B end C60 cap). In the EFISH process, thestrongest response is at 0.41 eV (3024.0 nm) with dominantcontribution from the HOMO−LUMO charge transfer basedexcitation. This HOMO−LUMO excitation also has dominantcontribution (67%) to the strong response at 0.46 eV (2695.3nm) (−386.48 × 10−34 esu) and significant contribution (29%)to the response at 0.78 eV (1589.5 nm) (485.89 × 10−34 esu) inthe DFWM process. In the TPA process, the HOMO−LUMOcharge transfer based excitation has significant contribution(21%) to the TPA peak at 0.88 eV (1408.9 nm) (11748.90 ×10−50 cm4·s/photon). There is a strong stimulated emissionpeak at 2.18 eV (568.7 nm) (−33457.60 × 10−50 cm4·s/photon).In summary, the doping of BN pairs in fullerene leads to

more NLO responses of these heterofullerenes, and theresponsive external field moves to lower energy, i.e., visibleand infrared regions. The introduction of Ti to the C60 cap ofthe heterofullerene makes it feasibly responsive to external fieldin low energy region.

■ CONCLUSIONSAccording to the convergence of electronic spectra with thenumber of states in the configuration interaction in C72B12N12,the dominant contribution to the electronic spectra of fullereneand heterofullerenes comes from the electronic excitationsinvolving frontier molecular orbitals.Doping of BN pairs and Ti polarizes the electronic structure

of those heterofullerenes, narrows their HOMO−LUMOenergy gaps, and leads to more electronic excitations in theUV−vis region (with some in the infrared region). Thoseheterofullerenes have strong NLO response at low externalfields in the UV−vis and infrared regions. The small HOMO−LUMO energy gap and relatively strong charge transfer basedelectronic excitations are responsible for the large NLOresponses. The strong NLO responses of these heterofullerenesin the visible and infrared regions make these heterofullerenespotential NLO materials in low energy field. Charge polar-ization and generation of low lying charge transfer basedelectronic excitation are effective means to enhance the NLOresponse of fullerenes.

■ ASSOCIATED CONTENT*S Supporting InformationThe infrared spectra and Cartesian coordinates of C96 (D3d),C72B12N12 (C3v), C72B12N12 (C3), and C71B12N12Ti (C3). Thismaterial is available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Authors*(W.-Q.L.) E-mail: tccliweiqi@hit.edu.cn.*(W.Q.T.) E-mail: tianwq@hit.edu.cn.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work is supported by Nature Science Foundation of China(21303030, 11104048), the State Key Lab of Urban WaterResource and Environment (HIT) (2012DX02 andQA201116), National Key Laboratory of Materials Behaviors& Evaluation Technology in Space Environments (HIT), andthe Open Project of State Key Laboratory of SupramolecularStructure and Materials (JLU) (SKLSSM201309).

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Figure 7. Evolution of nonlinear optical properties of C71B12N12Ti(N)with external fields. The second hyperpolarizabilities are in units of10−34 esu. TPA is in units of 10−50 cm4·s/photon.

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