Nonlinear Optical Properties of Fullerene C96 (D3d) and Related

Oct 4, 2013 - Department of Physics, Harbin Institute of Technology, Harbin 150001, P. R. China. § Sports Institute, Chengdu University of Technology...
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Nonlinear Optical Properties of Fullerene C96 (D3d) and Related Heterofullerenes Xin 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 of Fundamental 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 of fullerene-based nanomaterials render those nanomaterials potential nonlinear optical (NLO) materials. The sum-over-states model with linear scaling was employed to model the static and dynamic third order NLO properties of fullerene C96 (D3d) and C96 based boron− nitrogen-doped and metal-doped fullerenes. Doping induces more electronic excitations in the heterofullerenes in the visible and infrared regions. The two-photon absorption cross-section of heterofullerene C72B12N12(C3) reaches 1.65 × 105 × 10−50 cm4·s/photon at 892.0 nm. The heterofullerenes have strong NLO responses to external fields from the ultraviolet−visible to infrared regions. The correlation between structure and NLO properties is disclosed for those cages.

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thus the properties of fullerenes10−13 and brings about new possible applications of those heterofullerenes. Two boron− nitrogen-doped heterofullerenes derived from C96 (D3d) are designed to investigate the effect of heteroatom doping on the electronic and NLO properties of fullerenes. The BN pair (an isoelectronic structure to C2) is used in the doping to mimic the hybridization of boron nitride nanotube with carbon nanotube. The doping of titanium in heterofullerenes is also investigated. The advance in materials synthetical technology ensures the synthesis of such molecular materials in the future.

INTRODUCTION Since the discovery1 and macroscopic synthesis2 of the fullerene C60, the structure and properties of fullerenes have been extensively investigated. However, the increase of the number of isomers with the size of fullerenes makes the synthesis and isolation of bigger fullerenes challenging, and this slows down the pace of experimental study on higher pristine fullerenes. C96 is so far one of the largest pristine fullerenes structurally well characterized in experiment3−5 following structure and properties studies both theoretically6−8 and experimentally.9 Ascribed to their curved three-dimensional π conjugation, round shape, nanosize, and good thermal stability, fullerenes are expected to have broad potential applications in electronics and photonics, e.g., nonlinear optical (NLO) devices. The third order NLO properties of C60 to C96 were found to increase with fullerene size in general and vary with geometrical structure or resonance enhancement.9 The third order NLO response of those fullerenes in degenerate four wave mixing was estimated to be 10−31−10−30 esu (2.1 ± 0.6 × 10−30 esu for C96).9 However, possible mixing of various fullerene isomers in sample makes the study of NLO property of particular isomers difficult. The isolation of fullerene isomers3−5 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 in Figure 1) are studied. It is a clip of (9,0) zigzag carbon nanotube capped with C60 derived ends as identified in experiment.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 © 2013 American Chemical Society

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MODELS AND COMPUTATIONAL DETAILS The structures of C96 (D3d), BN-doped fullerenes C72B12N12, and Ti-doped heterofullerene C71B12N12Ti were shown in Figure 1. In the isomer of C72B12N12 with C3v symmetry, BN pairs are separated, while BN pairs in the middle of the cage are connected in the isomer with C3 symmetry. A carbon atom is replaced by a Ti atom at the N end of C72B12N12 (C3) resulting in the formation of C71B12N12Ti with Ti bonding to three N atoms. Because of the strong bonding between Ti and N, this isomer is 91.3 kcal/mol more stable than the isomer doped with a Ti atom on the B end. The structures of those cages were optimized with density functional theory based method B3LYP14,15 and basis set 6-31G(d).16,17 Vibrational frequency calculations were carried out to verify the nature of those stationary points on potential energy surface as minima. Received: August 26, 2013 Revised: September 25, 2013 Published: October 4, 2013 23172

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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 atom in C71B12N12Ti is Ti.

Table 1. Dipole Moments, the Energies of the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO), and the Energy Gaps between the HOMO and LUMO (Egap) Predicted by B3LYP/6-31G(d); the Wavelengths of the Lowest Dipole Allowed Electronic Excitation (Ele) Were Predicted by ZINDO C96 C72B12N12 (C3v) C72B12N12 (C3) C71B12N12Ti (C3)

Dip (Debye)

EHOMO (eV)

ELUMO (eV)

Egap (eV)

Ele (nm)

0.0 8.58 10.29 14.30

−5.41 −5.30 −4.96 −4.80

−3.32 −3.52 −3.97 −4.07

2.09 1.78 0.99 0.73

531.6 592.2 1187.9 3476.9

stability (18.6 kcal/mol) than that with BN pairs connected (the C3 isomer). C72B12N12 (C3v) has two C60 cap ends, with N and B close to each end hexagon, respectively. The dipole moment of the C3v isomer is 8.58 D. However, the doping of BN pairs at the two ends of the C60 hemispheres leads to a larger dipole moment in the C3 isomer (10.30 D). Charge transfer from C atoms to N atoms occurs, and this alleviates the charge transfer from B atoms to N atoms. The replacement of a carbon atom by a Ti atom at the N end of C72B12N12 (C3) polarizes the charge distribution of the system, thus producing a larger dipole moment (as listed in Table 1), and makes the Ti atom an active center in chemical reaction. The energy of the highest occupied molecular orbital (HOMO) of those heterofullerenes is higher than that of C96 (D3d), and the energy of the lowest unoccupied molecular orbital (LUMO) is lower than that of C96 (D3d), resulting in smaller energy gaps between the HOMO and LUMO. The narrowing of the HOMO−LUMO energy gaps leads to longer wavelength of the lowest dipole allowed electronic excitation. Electronic Spectra. The correlation of predicted electronic spectra with the active space chosen in configuration interaction with ZINDO was displayed in Figure 2. C72B12N12 (C3) serves as 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 × 45 CIS 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. The second region has a peak around 3.2 eV and strong absorptions around 5.2 eV. The third region has absorption peaks around 8.0 eV. The overall shape of the electronic spectra of C72B12N12 with different CIS active space is similar to one another in the region of 0.0−6.0 eV (206.0 nm) though with varied oscillator strengths, and this covers the major absorptions for NLO response, i.e., the frontier molecular orbitals are more responsive to external field and should have dominant contribution to such response.19 The electronic spectra and NLO properties predictions in the present work were carried out with CIS active space of 18 × 18 (325 states).

The electronic spectra of those cages were predicted with configuration interaction single (CIS) through the ZINDO method.18 CIS does not include description for doubly excited states, thus in the present work, the prediction on two-photon absorption (TPA) from CIS has no contribution from doubly excited states. The performance of ZINDO in predicting the electronic spectra of fullerenes is well verified.19,20 With the dipole moments and transition dipoles from the CIS calculations, the third order NLO properties of those systems were predicted with the sum-over-states model.21−23 The good performance of ZINDO/SOS on the third order NLO properties of C6019,24−26 warrants the present predictions on the NLO properties of C96 (D3d) and related cages. The overall trend of NLO property evolution with these fullerenes could provide new information for molecular material design. There are other methods to simulate NLO properties with response theory27,28 and time-dependent density functional theory. Considering the structure−properties interpretation feature and computational efficiency,23 we use ZINDO/SOS to simulate the third order NLO properties of those cage systems.

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RESULTS AND DISCUSSION Structure. In the C96 (D3d) isomer, three hexagons locate at the three edges of the end hexagon, and around these four hexagons, six pentagons distribute evenly as that in C60. This arrangement of pentagons creates bonding pattern similar to that in C60, i.e., 6−6 (double bond) and 6−5 (single bond) as observed in experiment.4 The double bonds connecting those pentagons have the shortest bond lengths (1.383 Å) (bond B− D in experiment).4 Such an arrangement leads to long bond length (1.443 Å) for the double bond I−I4 (as labeled in Figure 1) in the middle of the cage, thus with enhanced chemical activity. C96 (D3d) could be divided into two parts (as indicated by the blue dashed lines in Figure 1): the hexagon belt with 18 hexagons 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 BN pairs (the C3v isomer as shown in Figure 1, the actual symmetry is Cs due to slight geometry distortion) has slightly higher 23173

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electronic excitation at 2.98 eV has the similar transition nature. The peak at 2.83 eV has mixture of vertical excitation at the belt and 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 3.10 eV (400.0 nm), there are five noticeable absorption peaks at 2.28 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 strong electronic 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 to the doping of BN pairs at the C60 cap end. More peaks emerge in 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 3.20 eV (388.0 nm) plus two peaks in the near-infrared region at 1.36 eV (910.8 nm) and 1.45 eV (852.8 nm). The strongest absorption peak locates at 4.53 eV (273.8 nm) and another strong 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 the electronic spectra of C71B12N12Ti (as shown in Figure 3). Two noticeable absorption peaks locate at 0.82 eV (1504.9 nm) and 1.48 eV (838.4 nm) in the near-infrared region. Another noticeable peak emerges at 1.56 eV (794.7 nm). In the visible region, 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). The lowest (while very weak) excitation essentially involves vertical excitation (0.36 eV, 3476.9 nm) from the occupied 3d orbital to the empty 3d and 4p orbital of Ti atom. Beside this weak excitation, there is another weak peak at 0.62 eV (2012.1 nm). The electronic excitation at 0.82 eV is charge transfer based transition essentially from the HOMO (mainly the 3d orbital of Ti and the p orbitals of carbon atoms on the cap) to the LUMO (the p orbitals of atoms at the other cap). Charge transfer based transition from the hexagon belt to the undoped C60 cap end is responsible for the excitation at 1.48 eV (838.4 nm). The strongest absorption peaks locate at 4.82 eV (257.4 nm) and 5.20 eV (238.7 nm). Nonlinear Optical Properties. The third order NLO properties were predicted with ZINDO and SOS model under external fields up to 3.0 eV. The evolution of third harmonic generation (THG), electric field induced second harmonic generation (EFISH), degenerate four wave mixing (DFWM), and TPA of C96 (D3d) with external fields was presented in Figure 4. The static second hyperpolarizability of C96 (D3d) is 37.95 × 10−34 esu. C96 (D3d) reaches maximal responses to external field in the process of THG around 2.0 eV. The electronic excitations at 5.97 eV (207.8 nm), 5.73 eV (216.5 nm), and 5.67 eV (218.7 nm) have significant contributions (about 40.0 × 10−34 esu) to the response of THG around 2.0 eV. Those absorption peaks essentially are vertical excitation involving MOs of the hexagon belt. EFISH has a strong response (177.98 × 10−34 esu) at 2.92 eV with major contribution from the excitations at 5.73 eV, 5.59 eV, 5.67 eV, and 5.11 eV. The response of DFWM at 2.33 eV (531.6 nm) is 70.98 × 10−34 esu, and this is much samller than the experimental estimation.9 In experiment,9 the structure of C96 was not determined yet, and the sample might be a mixture of C96 isomers. NLO properties have direct correlation with the structure of a system. In this experiment, the second

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

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

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

strong peak around 520.0 nm and shoulder peaks around 570.0 nm were observed. However, no significant absorption above 800.0 nm was observed. A relatively weak absorption was predicted at 2.33 eV (531.6 nm) in the present work for the C96 (D3d). Dipole allowed electronic excitations above 400 nm locate 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) with the strong peaks at 416.0 and 438.0 nm in the ZINDO prediction. Below 400 nm, the strong absorption peaks of C96 (D3d) locate at 5.97 eV (207.8 nm), 5.73 eV (216.5 nm), 5.67 eV (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 in the MOs of the hexagonal belt at the middle of the cage. The 23174

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the electronic excitation at 3.61 eV (343.5 nm, charge transfer based excitation from the B cap end to the N cap end) has the dominant contribution. More responses in the DFWM process occur. The response minimum locates at 2.51 eV (−248.74 × 10−34 esu, with significant contribution from excitations at 3.61 and 4.27 eV) and the response maximum is at 2.68 eV (462.6 nm) (274.59 × 10−34 esu, with significant contribution from excitations 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 N end-cap vertical excitation and charge transfer based transition from the B end hexagon belt edge to the N end-cap. Those transitions mainly involve the π MOs of carbon atoms. The TPA process of C72B12N12 (C3v) has similar response pattern to that in DFWM. The maximal absorption cross-section locates at 2.38 eV (520.9 nm) (48322.0 × 10−50 cm4·s/photon) along with 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 excitations at 3.61 eV (343.4 nm) and 4.27 eV (290.4 nm) have significant contributions to those responses. The electronic excitation at 4.27 eV involves charge transfer based excitation from the B end hexagon belt edge (with contribution from B atoms) to the N 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 red shift of electronic absorptions and makes electronic excitation energetically feasible and thus more polarizable in the presence of external field in comparison with C72B12N12 (C3v). The third order NLO responses (THG, EFISH, and DFWM) of C72B12N12 (C3) are stronger than those of C72B12N12 (C3v) as shown in Figure 6. A strong response occurs at 0.49 eV (2530.3

Figure 4. Evolution of nonlinear optical properties of C96 (D3d) with external fields. THG is third harmonic generation. EFISH is electricfield induced second harmonic generation. DFWM is degenerate fourwave mixing. TPA is two-photon absorption. The second hyperpolarizabilities are in units of 10−34 esu. TPA is in units of 10−50 cm4·s/ photon.

hyperpolarizability of C60 at 2.33 eV (531.6 nm) was measured to be 2.2 ± 0.6 × 10−31 esu. In the present prediction, the response of C96 (D3d) in DFWM has a maximum of 676.95 × 10−34 esu at 2.95 eV. This strong response has contribution from electronic excitations at 5.11 eV, 5.02 eV (247.2 nm), 3.29 eV (377.1 nm), 3.10 eV (400.2 nm), and 2.98 eV(416.4 nm), and those electronic absorptions involve vertical excitations at the hexagon belt. However, the TPA cross-section has a negative 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 the contributions of electronic excitations at 5.97, 5.59, 5.11, and 5.02 eV. The NLO response of C72B12N12 (C3v) to external fields occurs at lower fields with weaker magnitude (as shown in Figure 5) in comparison to those of C96 (D3d). The THG of C72B12N12 (C3v) has similar overall response pattern to that of C96 (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 with maxima 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 a minimum of −298.05 × 10−34 esu at 1.80 eV (688.8 nm), and

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

nm) with −284.48 × 10−34 esu, and another response occurs at 1.39 eV (892.0 nm) with 140.79 × 10−34 esu in the THG process. The strong response at 0.49 eV is ascribed to the dominant contribution from the electronic excitation at 1.36 eV (910.8 nm) with electronic transition from the degenerate HOMO (the B end C60 cap) to the degenerate LUMO (the N end C60 cap). The strongest response (−927.27 × 10−34 esu) to external fields in the EFISH process occurs at 0.68 eV (1823 nm), and the electronic excitation at 1.36 eV has dominant contribution to this response (−879.58 × 10−34 esu). The electronic excitation of the system at 1.36 eV also has dominant

Figure 5. Evolution of nonlinear optical properties of C72B12N12 (C3v) with external fields. The second hyperpolarizabilities are in units of 10−34 esu. TPA is in units of 10−50 cm4·s/photon. 23175

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CONCLUSIONS According to the convergence of electronic spectra with the number of states in the configuration interaction in C72B12N12, the dominant contribution to the electronic spectra of fullerene and heterofullerenes comes from the electronic excitations involving frontier molecular orbitals. Doping of BN pairs and Ti polarizes the electronic structure of those heterofullerenes, narrows their HOMO−LUMO energy gaps, and leads to more electronic excitations in the UV−vis region (with some in the infrared region). Those heterofullerenes have strong NLO response at low external fields in the UV−vis and infrared regions. The small HOMO− LUMO energy gap and relatively strong charge transfer based electronic excitations are responsible for the large NLO responses. The strong NLO responses of these heterofullerenes in the visible and infrared regions make these heterofullerenes potential NLO materials in low energy field. Charge polarization and generation of low lying charge transfer based electronic excitation are effective means to enhance the NLO response of fullerenes.

contribution to the relatively strong response of EFISH at 1.37 eV (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 a strong peak at 1.33 eV (2374.59 × 10−34 esu) of DFWM. However, the electronic excitation of the system at 1.36 eV has about 23% contribution to the stimulated emission at 1.28 eV (−132075.0 × 10−50 cm4·s/photon) and over 50% contribution to 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 N end C60 cap) based electronic excitation in C72B12N12 (C3v) at 1.36 eV is mainly responsible to the strong response of this heterofullerene 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 which C71B12N12Ti(N) has strong response in the processes of THG, EFISH, DFWM, and TPA, as shown in Figure 7. This is due to

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ASSOCIATED CONTENT

S Supporting Information *

The infrared spectra and Cartesian coordinates of C96 (D3d), C72B12N12 (C3v), C72B12N12 (C3), and C71B12N12Ti (C3). This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*(W.-Q.L.) E-mail: [email protected]. *(W.Q.T.) E-mail: [email protected].

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

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by Nature Science Foundation of China (21303030, 11104048), the State Key Lab of Urban Water Resource and Environment (HIT) (2012DX02 and QA201116), National Key Laboratory of Materials Behaviors & Evaluation Technology in Space Environments (HIT), and the Open Project of State Key Laboratory of Supramolecular Structure and Materials (JLU) (SKLSSM201309).

the low energy dipole allowed electronic excitations in C71B12N12Ti(N) (as shown in Figure 3) and enhancement of dipole moment. The strongest THG response of the system takes place at 0.31 eV (3999.5 nm), and this occurs in the infrared region with dominant contribution (99%) from the electronic excitation at 0.82 eV (1504.9 nm) with nature of charge transfer based excitation from the HOMO (the Ti end) to the LUMO (the B end C60 cap). In the EFISH process, the strongest response is at 0.41 eV (3024.0 nm) with dominant contribution from the HOMO−LUMO charge transfer based excitation. This HOMO−LUMO excitation also has dominant contribution (67%) to the strong response at 0.46 eV (2695.3 nm) (−386.48 × 10−34 esu) and significant contribution (29%) to the response at 0.78 eV (1589.5 nm) (485.89 × 10−34 esu) in the DFWM process. In the TPA process, the HOMO−LUMO charge 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 emission peak 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 the responsive external field moves to lower energy, i.e., visible and infrared regions. The introduction of Ti to the C60 cap of the heterofullerene makes it feasibly responsive to external field in low energy region.

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REFERENCES

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The Journal of Physical Chemistry C

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