Density Functional Study of Nonlinear Optical Properties of Grossly

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A Density Functional Study of the Nonlinear Optical Properties of Grossly Warped Nanographene C H 80

30

Yafei Dai, Zhenyu Li, and Jinlong Yang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp409899n • Publication Date (Web): 23 Jan 2014 Downloaded from http://pubs.acs.org on January 25, 2014

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The Journal of Physical Chemistry

A Density Functional Study of Nonlinear Optical Properties of Grossly Warped Nanographene C80H30 Yafei Dai1,2, Zhenyu Li1,3 and Jinlong Yang1,3* 1

Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China 2

School of Physics Science & Technology and Jiangsu Key Laboratory for NSLSCS , Nanjing Normal University, Nanjing 210023, China 3

Synergetic Innovation Center of Quantum Information & Quantum Physics,

University of Science and Technology of China, Hefei, Anhui 230026, China

Abstract: Recently, a grossly warped nanographene C80H30 has been synthesized experimentally. Its optical properties are studied and compared with bucky ball C60, C70 and a flat nanographene C78H30 in the framework of density functional theory (DFT) with the B3LYP functional. The static polarizability α, first-order hyperpolarizability β and second-order hyperpolarizability γ are calculated using the finite field approach. The average values of and for C80H30 are 151.7 Å3 and 54.5x10-35 esu respectively, much more higher than those of C60 and C70. Both and of planar C78H30 are higher than those of C80H30, which is consistent with the fact that the energy gap of C78H30 is smaller than that of C80H30. However, the diagonal component of α along z axis of C80H30 is 86.2 Å3, much higher than 30.7 Å3 of C78H30. Furthermore, the values of the hyperpolarizability in z direction (γxxzz, γyyzz and γzzzz) of C80H30 are almost one order of magnitude higher than those of C78H30. Relationship between optical properties and electron delocalization in molecules indicated by aromaticity is also discussed. Our results indicate that C80H30 can be used as a promising optical material.

Keywords:

polarizability,

hyperpolarizability,

NICS,

absorption spectra

ACS Paragon Plus Environment

electron

delocalization,


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I.

INTRODUCTION Recently a new form of nanographene has been synthesized successfully by

Kawasumi et al. based on palladium-catalysed bipenylation of polycyclic aromatic hydrocarbons (PAH) through C-H activation followed by cyclodehydrogenation.1,2 Using bowl-shaped PAH corannulene, they obtained chiral, warped C80H30 nanographene as shown in Figure 1.1 Graphene sheets prefer planar, 2-dimensional geometries as a consequence of the sp2 hybridization of carbon atoms comprising a two-dimensional network. The new form of C80H30, however, is wildly distorted from planarity as a consequence of the presence of five 7-membered rings and one 5-membered ring embedded in the hexagonal lattice of carbon atoms.

Figure 1. Optimized structure of C80H30 molecule. The dark and light dark balls represent C and H atoms respectively.

Except the unique double-concave structure caused by odd-membered-ring of this grossly warped C80H30, Scott et al. pointed out the warped naonographene was dramatically more soluble than a planar nanographene of comparable size, which is very desirable for practical applications. Electrochemical measurements revealed that both the planar and the warped nanographenes could be oxidized, but the warped nanographene was more difficult to reduce. By introducing multiple odd-membered ring defects into the graphene lattice, Scott and his collaborators have experimentally demonstrated that the electronic properties of graphene can be modified in a predictable manner through precisely controlled chemical synthesis.3 Warped and


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planar nanographene samples differ significantly in color, indicating very distinguish optical properties. The ability to control the degree of distortion with odd-numbered rings thus opens an avenue of developing new graphene based materials for future optoelectronic devices.3 In this sense, optical properties of this new warped nanographene are very interesting. The nonlinear response of molecules to electromagnetic fields has been studied over the last two decades. It provides a means for amplification, modulation and

changing

the

frequency

of

optical

signals.4

Materials

with

large

hyperpolarizabilities have applications in optoelectronics, such as optical switching for optical computing or high-density optical recording.5 Many experimental6-9 and theoretical9-14 studies have been carried out to identify materials with large hyperpolarizabilities. Organic compounds with extended π electrons are good candidates.5 Due to its unique structure, C80H30 is expected to have interesting optical properties, especially its z component. In order to check its optical properties, we calculate the polarizability α, the first-order hyperpolarizability β, and the second-order hyperpolarizability γ of C80H30 in this study. Comparison to C60, C70, and planar C78H30, is also reported.

II. COMPUTATIONAL DETAILS Density functional theory implemented in the Gaussian 09 package15 was used in this study, with the Becke hybrid exchange-correlation functional of Lee, Yang, and Parr B3LYP16,17 which includes both local and non-local terms. The split-valance 3-ζ basis set 6-31G(d)18 with polarization functions was employed to optimize the structures of the molecules. The Berny algorithm19 based on energy minimization was used for geometry optimization. IR spectra were calculated to ensure that reported conformations are stable. The optimized structure of C80H30 (Figure 1) is the same as that reported by Kawasumi et al. which has a three-dimensional warped shape with a five-membered defect located in the center.1 Sum-over-states (SOS)20 and finite-field (FF)21,22 approach are frequently used to get the static polarizability and second-order hyperpolarizability. The FF method was



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developed based on both an energy expansion and a dipole moment expansion by Kurtz et al..21 This method has been demonstrated to be able to give accurate results for benzene and some other molecules21,23,24. In this paper, the static polarizability α, the first-order hyperpolarizability β, and the second-order hyperpolarizability γ were calculated with the FF approach using the following equations21.

2 2

2 2

2 2

2 2

2 2

(1) (2) (3) (4) (5)

, , , ,

(6)

where µi are the permanent dipole moments, αij, βijk, and γijkl are the tensor elements of the linear polarizabilities and the first and second hyperpolarizbilities, respectively. Fi are the components of the applied field.21 According to the formulas above, the field strengths ±Fi and ±2Fi ( i = x, y, z ) along the molecular axes were added with 12 self-consistent field runs for α components. For γ components, the field strengths (± Fi, ±Fj) along the 45°lines between the molecular axes were used for another 12 self-consistent field runs.24 The choice of field strength is extremely important in the polarizability calculation. The field must be large enough so that the contribution to the dipole moment expansion from the γ term is bigger than the numerical precision. At the same time, the field must be small enough so that the error incurred by the truncation of the expansion is acceptable. 11,24 Based on these considerations, a field strength of 0.005 a.u was used. Once all the components of the static polarizabilities and hyper-polarizabilities have been obtained, the mean polarizability can be calculated from the polarizability components with formulas. 21


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〈〉

(7)

〈〉 2 (8) Aromaticity is characterized by the nucleus-independent chemical shift (NICS) values, 25,26 which is related to electron delocalization in molecules. For this purpose, the NMR shielding tensors are evaluated at the B3LYP/6-31G(d)16-18 level using the gauge-independent atomic orbital (GIAO) method27,28 and ghost atoms are used to designate the positions for the NICS evaluations. 29 Absorption spectrum of warped C80H30 is obtained by calculating the joint electronic density of states (JDOS). 30

III RESULTS DISCUSSION A. Geometric structure and IR spectrum for C80H30 As a benchmark, the C-C and C=C bond length of C60 is calculated to be 1.453 and 1.396 Å, agreeing well with the experimental values of 1.45 and 1.40 Å. 31 Not like C60 and C70, which have high symmetry with a point group of Ih and D5h, respectively, the optimized C80H30 structure does not display any symmetry. The C-C bond lengths of the pentagon located at the center are 1.394, 1.409, 1.404, 1.414 and 1.414 Å, respectively. The vibrational normal mode frequencies of the C60, C70 and the warped C80H30 molecules are calculated with the simulated infrared (IR) spectra shown in Figure 2. IR peaks of both C60 and C70 molecules are predominantly distributed in the region of 420-1700 cm-1, while for the C80H30 molecule, additional IR bands in 3100-3300 cm-1 appear. The near IR region is associated with motions involving C-C bonds stretching and C-H, C-C bonds bending, whereas C-H stretching modes are in the far IR region. There are four strongest peaks for C60 located at 538, 588, 1214 and 1460 cm-1, respectively, which agree well with the experimental data of 525, 576, 1184 and 1432 cm-1 measured at 15 K.32 These peaks for C60 are also found in IR spectrum of C70 except that the 1214 cm-1 peak has been red-shifted to 1167 cm-1. Furthermore, for C70 molecule, three more peaks are found at 468, 575 and 680 cm-1. These frequencies are also in agreement with the peak positions 458, 527, 535, 674, 795, 1134 and 1431



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cm-1 detected in the experiment. 24 The IR peaks for both C60 and C70 molecules are highly degenerated because of their symmetric structures.

Figure 2. Calculated IR vibrational spectra of C60, C70 and C80H30.

Two strongest IR peaks of the warped C80H30 are located at 766 and 790 cm-1, respectively. The first one corresponds to C-C stretching and the second one corresponds to C-C stretching and C-H bending.

B. Polarizability and hyperpolarizability for C80H30 In order to check up the accuracy of our calculations on optical properties, we calculate the average polarizabilities and second-order hyperpolarizabilities of molecules C60 and C70. The calculated results are compared with those from other


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theoretical methods and experiments, as listed in Table 1. Although the calculated for C60 is slightly smaller than results from PBE and VWN10 calculations and slightly larger than that from MNDO/PM-311 calculations, it agrees well with the experimental value of 76.5±8.0 Å3. The value of for C70 calculated here is also larger than the results using MNDO/PM-3.11 In both methods, the value for C70 is about 25% larger than those for C60. For the value of , an obvious discrepancy between experimental values and all calculated values exists for two molecules. Notice that calculated values correspond to at zero frequency, whereas the experimental measurements are made at nonzero frequencies. 11,12 Furthermore, the values from different nonlinear optical process can differ by as much as 40%.24 Therefore, the calculated static second-order hyperpolarizability may not be able to directly compare with experimental data. However, both the theoretical results and the experimental results show that the polarizability of C70 is higher than that of C60. Matsuzawa et al.11 got the similar results with us and pointed out that the "rugby-ball" shape of C70 with more effectively planar segments causing the larger value of .

Table 1. The calculated and experimental average values for the static polarizability (Å3) and the second polarizability (10-35esu) of C60 and C70.

C60

Methods

69.4

1.19

B3LYP/6-31G(d), present

77.6

1.59

PBE10

76.1

1.47

VWN10

63.9

3.59

MNDO/PM-311 Molecular beam deflection6

76.5±8.0 43

Third harmonic generation7

30

Degenerate foure-wave mixing8 Electric-field-induced second

75 C70

86.7

4.83

harmonics9 B3LYP/6-31G(d), present



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79.0

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4.52

MNDO/PM-311

130

THG measurements33

Table 2. The calculated diagonal components and average values of the static polarizability α (Å3),

the first polarizability β (10-31esu) and the second

polarizability γ (10-35esu) for C80H30 and C78H30. αxx

αyy

αzz

αxy

αxz

αyz

C80H30

188.4

180.6

86.2

1.3

-0.6

0.6

151.7

C78H30

233.5

233.5

30.7

0

0

0

165.9

βxxx

βyyy

βzzz

βxyy

βxzz

βyxx

βyzz

βzxx

βzyy

C80H30

45.8

17.8

4.2

4.7

10.4

13.7

5.1

11.4

6.9

C78H30

0

0

0

0

0

0

0

0.3

0.3

γxxxx

γyyyy

γzzzz

γxxyy

γxxzz

γyyzz

C80H30

99.6

85.9

3.7

28.1

6.8

6.7

54.5

C78H30

184.3

183.4

0

56.9

0.0

0.0

96.3

Due to their inversion symmetry, permanent dipole of C60 and C70 molecules is zero and their first hyperpolarizability β is also not need to be considered.34 For C80H30, a permanent dipole (-0.2660, -0.0929, 0.4694) Debye exist, and all components of α, β, and γ tensors are thus considered in this work (Table 2). The average values of α for C80H30 is about twice as much as those of C60 and C70. The second hyperpolarizability of C80H30 are even ten times higher than that of C60 and C70. Comparison of values of C60 , C70 and C80H30 indicates that molecules with more extended planar structure have larger values. At the same time, electron-phonon coupling may have an effect on γ. Notice that IR spectrum of C80H30 shows features in frequency region at 3100-3300 cm-1 which is not found for C60 and C70. To gain more insight into the electronic properties governing the second polarizability γ, we investigated another molecule C78H30 which has a comparable size with C80H30.


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C. A comparison to C78H30 The optimized structure of molecule C78H30 has a high symmetry, the D6h point group, with a planar, defect-free structure composed of 25 hexagons as shown in Figure 3. The C-C bond length of the regular hexagon sitting on the center is 1.423 Å which is very close to the C-C length of graphene (1.421 Å),35 larger than the C-C bond lengths of the pentagon located at the center in C80H30 molecule. The vibrational normal mode frequencies of the C78H30 are also calculated which is shown in Figure 3. IR peaks are also predominantly distributed in two regions as those of C80H30: 420-1700 cm-1 and 3100-3300 cm-1. The two strongest C78H30 IR peaks are found to be located at 761 and 808 cm-1. Both of them correspond to C-H bending without any C-C stretching or bending. There are three other intense IR peaks for C78H30, locating at 3203, 3224 and 3279 cm-1 corresponding to C-H stretching. C-H stretching modes are more degenerated for C78H30 compared to C80H30 due to its higher symmetry.

Figure 3. Optimized structure of C78H30 and its IR spectrum.

The calculated results of the α, β, and γ tensors for C78H30 are listed in Table 2. From the Table 2, it can be seen that the average values of polarizability and the second polarizability of C78H30 are slightly higher than those of C80H30. This is expected since C78H30 has a more extended planar structure. At the same time, our results are consistent with the trend of increasing with the decreasing of the energy gap, as also reported in Ref. [1]. It should be pointed out that, according to our



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calculation, this trend can only be used for comparing of the molecules with similar structures. Taking z axis as the principle axis, the components of α in x direction (αxx) and y direction (αyy) for C78H30 have the same value due to the structural symmetry, and they are larger than that in z direction (αzz). Since the main contribution to the dipole moment for the planar C78H30 is from C atomic orbitals and π electrons in the xy plane, the components of γ in z direction are almost zero as shown in Table 2. In contrast, C80H30 is a three dimensional warped structure with quite low symmetry, therefore the components of α and γ in three directions show a less anisotropic behavior. This is desirable in nonlinear optical applications.

D. Discussions Optical properties are known to be related with electron delocalization. 36,37 In this aspect, a closely related property, aromaticity, is checked for these molecules. Nucleus-independent chemical shifts (NICS)25,26 can be used to characterize aromaticity. NICS for C60, C70, C78H30 and C80H30 molecules are listed in Table 3. The NICS values for the five and six-membered rings in C60 and C70 confirm the expected "antiaromatic-aromatic" nature of the fullerene.36 For C78H30, only five 6-membered rings are needed to be considered due to symmetry. NICS values of all rings in C78H30 are negative indicating a strong aromatic property and the delocalization of the electrons over the 6-membered rings in this molecule. For the warped C80H30, NICS of each cycle in the molecule is calculated. All 5 and 7-membered rings are antiaromatic while all 6-membered rings are highly aromatic. The ratio of aromatic ring number to antiaromatic ring nubmer for these four molecules is C60

Density Functional Study of Nonlinear Optical Properties of Grossly

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