Third-Order Nonlinear Optical Properties of Endohedral Fullerene (H2

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C: Plasmonics, Optical Materials, and Hard Matter

Third Order Nonlinear Optical Properties of Endohedral Fullerene (H)@C and (HO)@C Accompanied by the Prospective of Novel (HF)@C 2

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Li Wang, Jin-Ting Ye, Hong-Qiang Wang, Haiming Xie, and Yongqing Qiu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b00623 • Publication Date (Web): 09 Mar 2018 Downloaded from http://pubs.acs.org on March 10, 2018

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The Journal of Physical Chemistry

Third Order Nonlinear Optical Properties of Endohedral Fullerene (H2)2@C70 and (H2O)2@C70 Accompanied by the Prospective of Novel (HF)2@C70 Li Wang,† Jin-Ting Ye,† Hong-Qiang Wang,† Hai-Ming Xie†‡ and Yong-Qing Qiu*†‡ †

Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal University,

Changchun, 130024 Jilin, China. ‡

National & Local United Engineering Laboratory for Power Battery, Faculty of Chemistry,

Northeast Normal University, Changchun 130024, Jilin, China.

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ABSTRACT: In view of experimental observation of (H2)2@C70 and (H2O)2@C70, it has been suggested that HF dimer can completely be localized within the subnano-space inside the fullerene C70 cage. With the aim of quantum chemical prospective of (HF)2@C70, electronic structure calculations of C60 hosting H2, HF and H2O monomers as well as C70 hosting H2, HF and H2O monomers and dimers were performed by using the density functional theory, together with the quantum theory of atoms in molecules, the natural population and interaction energy calculation. The F-H···F bonding energy inside C70 was estimated at -13.25 kcal/mol, which is smaller than that of free dimer in the gas phase (-8.37 kcal/mol). Exploration of various featured properties suggests that (HF)2@C70 may be also regarded as a unique system composed of both inter- and intramolecular interactions like (H2)2@C70 and (H2O)2@C70. In addition, absorption spectroscopy, linear and nonlinear optical coefficients of C60 hosting H2, HF and H2O monomers as well as C70 hosting H2, HF and H2O monomers and dimers have also been forecasted. The results show that there are almost no influence of embedded H2, HF and H2O monomers and dimers on the peak wavelength of absorption spectra for C60 and C70. Endohedral C70 possesses the larger second hyperpolarizabilities with respect to that of endohedral C60, indicating that the effect of cage size is effective in the second hyperpolarizabilities of endohedral fullerenes. The study will benefit the designation and the syntheses of the novel molecular (HF)2@C70, and it will also benefit the understanding of the structures and properties of endohedral fullerenes.

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1. INTRODUCTION Endohedral fullerenes that contains a single molecule, transition metal or ion, rare gas, and so on, have attracted great attention in recent years.1-5 The inner space of the fullerene C60 with a diameter of 7.1 Å is suitable for entrapping the monomer. It is important to control the properties of the outer fullerene cage as well as the inner isolated specie, as an atom or molecule encapsulated in fullerene.6 Endohedral fullerenes encapsulating a wide variety of species, including metal ions,3 rare gases7-8 and nitrogen atoms,9 have been synthesized by means of arc-discharge methods. However, the application of these rigorous conditions for encapsulation of a stable molecule is only limited to [email protected] Another approach is molecular surgical method,11-12 which consists of three steps: (i) unfolding the pristine fullerene cage; (ii) inserting a small molecule; (iii) restoring the cage and reserving encapsulated species. This method has been successfully applied for the synthesis of H2@C60,4,

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HF@C6014 and

[email protected] In all cases, the limited space of 7.1 Å diameter inside C60 is small for the encapsulation of two molecules. However, as is known to all, understanding the hydrogen bonds of water dimer is crucial from fundamental research to applied technology. Hence, it is significant to find an appropriate environment to stable the water dimer. Fortunately, owing to that C70 possesses a larger inner space (7.1 Å×8.0 Å) than C60, C70 can accommodate two chemical species. Until now, (H2)2@C7015 and (H2O)2@C70 with an isolated water dimer inside C7016 have been synthesized successfully by means of

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molecular surgical method. The HF monomer was also isolated in a confined subnano space by a high efficiency of the encapsulation, which was achieved by the synergetic effects of pushing from outside thuough the high-pressure conditions and pulling.17 The successful synthesis of (H2)2@C70 and (H2O)2@C70 provide the first light of morning to synthesize (HF)2@C70. Herein, with the aim to provide a quantum chemical prospective of (HF)2@C70 (Figure 1), the comparative studies of hydrogen bonding, electronic structure, weak interaction, absorption spectrum, linear and nonlinear optical (NLO) coefficients of the H2, H2O and HF monomers encapsulated inside C60 and these dimers inside C70 have been performed. As is well-known, fullerenes are excellent NLO materials. It is due to that fullerene molecules do not exist the carbon-hydrogen and carbon-oxygen bonds that have the interference effect on the NLO properties, hence, compared with other NLO materials, fullerenes possess more superior performance. However, the influence of embedded H2, HF and H2O monomers and dimers on the NLO properties of fullerene C60 and C70 is not clear, so continuing the research of our group before, another purpose of this work is to explore this influence and determine that whether these endohedral fullerenes are good NLO materials.

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Figure 1. Structures of C60 and C70, and endohedral fullerenes H2@C60, H2@C70 and (H2)2@C70; H2O@C60, H2O@C70 and (H2O)2@C70; HF@C60 and HF@C70.

2. COMPUTATIONAL DETAILS The DFT/TDDFT calculations here were all performed by means of the Gaussian 09W program package.18 Geometry optimizations were carried out at the M06-2X/6-31G(d, p) level. Meta-GGA M06-2X functional with a high percentage of HF exchange has been shown to describe noncovalent interactions better than density functionals which are currently in common use.19 UV−Vis absorption spectra of the complexes were performed at the TD-B3LYP-D3/6-31+G*. In order to ensure the reliability of the simulation result, comparisons between the simulation results and the experimental results of C60, C70, H2@C70, H2@C60, HF@C60 and H2O@C60 have been executed. It 5



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indicated that simulated result are in reasonably good agreement with the experimental ones. The binding interaction energies between inner spices and outer fullerene cage were computed by B3LYP-D3/6-311+G(d). The counterpoise (CP) procedure was used to calculate the interaction energy in order to correct the basis set superposition error (BSSE).20 The interaction energy (Eint) can be expressed as flowing equation: Eint ( AB) = E ( AB) AB − [ E ( A) AB + E ( B) AB ]

(1)

Topology analysis of electron density which is a main ingredient of Bader's atoms in molecules (AIM) theory has been performed using Multiwfn software version 3.3.21 Four kinds of critical points (CPs) can be located and real space function values at these points can be easily obtained and topology paths linking CPs and interbasin surfaces can be generated. The value of real space functions at BCP have great significance, for example the value of potential energy density V(r) at BCP are closely related to bonding strength and bonding type respectively in analogous bonding type. The relationship between bond energy Ebond (kJ/mol) and V(r) at corresponding bond critical point (BCP) can be approximately described as22 Ebond = V (rBCP ) / 2 * 2625.5

(2)

Gradient isosurfaces (RDG) were obtained by employing the Multiwfn software version 3.3. Gradient isosurface (RDG) and Sign(λ2)*ρ are a pair of very important functions for revealing weak interaction region RDG (r ) =

∇ρ ( r ) 2(3π ) 1 3 ρ (r ) 4 3 1

(3)

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It can be directly used to reveal the averaged weak interaction regions in the dynamics process and distinguish three different types of noncovalent interactions (i.e., hydrogen–binding, π–π interaction and steric hindrance).23 In a uniform electrostatic field, the dependence of the energy E on an external homogeneous static electric field F as follows:24 E = E 0 − µ i Fi − α ij Fi F j − β ijk Fi F j Fk − γ ijkl Fi F j Fk Fl + ...

(4)

where E0 is the molecular energy; i, j, and k designate the different components along the x, y and z directions, respectively; µi is molecular permanent dipole moment along the i direction; Fi is the applied electric field along the i direction and αij, βijk and γijkl are the polarizability, first, and second hyperpolarizability tensors, respectively. Polarizability tensors αxx, αyy, and αzz have been used for the calculation of the average polarizability:

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α = α ave = (α xx + α yy + α zz )

(5)

The total second hyperpolarizability (γ) has been calculated using the following expression:25

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γ = γ tot = (γ xxxx + γ yyyy + γ zzzz + 2γ xxyy + 2γ xxzz + 2γ yyzz )

(6)

The polarizability and second hyperpolarizability were calculated using the analytic and finite field hybrid method in this work. The Coulomb-attenuated hybrid exchange-correlation (CAM-B3LYP) functional is a hybrid functional with improved long-range properties.26 The BHandHLYP functional is obtained by including a 50% of the exact exchange in BLYP functional.27 Therefore,

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these three functionals CAM-B3LYP, M06-2X and BHandHLYP have been chosen in calculating of polarizability and second hyperpolarizability.

3. RESULTS AND DISCCUSION 3.1 Geometry Structure and Stability. The research field of endohedral fullerene has long been an important branch of fullerene chemistry. Except for (H2)2@C70, these molecular models H2@C60, H2@C70 and (H2)2@C70; H2O@C60, H2O@C70 and (H2O)2@C70; HF@C60 and HF@C70 have been successfully synthesized. Structural models of our work are derived from the crystal structures. Figure 2 shows the hydrogen-bonding energies of the H2O and HF dimers encapsulated inside C70 and free dimers in the gas phase, where E (O-H···O) is the hydrogen-bonding energy of H2O dimer and “inside C70” is representative of in the presence of C70. The comparative result of the H2O dimer encapsulated inside C70 and free dimer in the gas phase

showed that the dimer encapsulated inside C70 have a particular

conformation with shorter O-H···O (1.68 Å) and O···O distances (2.63 Å) than that of a free dimer (O-H···O distance of 1.98 Å and O···O distance of 2.92 Å) about 15% reduction of O-H···O distance and 10% reduction of O···O distance, which are consistent with the results of the reference. It indicated that our molecular models are reasonable and realistic. As is known to all, the O···O distance of ice is 2.75 Å28-29 and the calculated O···O distance of the dimer (2.63 Å) in C70 corresponds to a 4% reduction, suggesting the specific and stable environment of C70. The O-H···O bonding energy inside C70 was

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estimated at -10.50 kcal/mol, which is smaller than that of free dimer in the gas phase (-6.50 kcal/mol), indicating that intermolecular hydrogen bond of the H2O dimer was stronger when encapsulated inside C70. Similar results have been obtained from the comparative result of the HF dimer encapsulated inside C70 and free dimer in the gas phase. The dimer encapsulated inside C70 have a relative vertical conformation with shorter F-H···F (1.69 Å) with respect to that of a free dimer (F-H···F distance of 1.83 Å) about 8% reduction of F-H···F distance. The HF dimer encapsulated inside C70 have a different conformation with a shorter F···F distance (2.60 Å) than that of a free dimer (2.75 Å) about a 5% reduction. The F-H···F bonding energy inside C70 was estimated at -13.25 kcal/mol, which is smaller than that of free dimer in the gas phase (-8.37 kcal/mol), indicating that intermolecular hydrogen bond of the HF dimer was stronger when encapsulated inside C70. As is known to all, HF dimer has a stronger hydrogen bond due to the great electronegativity of F with respect to O and N. When encapsulated inside C70, the HF dimer also has a stronger hydrogen bond. As we all know, hydrogen bond energies were approximately evaluated by equation (3). The problem is that inside the fullerene in the confined space, the value of the potential energy density V(r) at corresponding bond critical point may not correlate the same way with the strength of the bond as in an unconfined situation. Therefore, Wiberg bond order (WBO) analysis has also been used to understand the strength of the hydrogen bond. The O-H···O bond order inside C70 was estimated as 0.06528, which is larger than that of free dimer in

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the gas phase (0.04856). The F-H···F bond order inside C70 was 0.08667, which is larger than that of free dimer in the gas phase (0.05188). It indicates that the results of WBO analysis were exactly consistent with the hydrogen bond energies approximately evaluated by equation (3).

Figure 2. The hydrogen-bonding energies of the H2O and HF dimers encapsulated inside C70 and free dimers in the gas phase.

3.2. Frontier molecular orbital. It is both instructive and useful to accumulate experience on the performance of various methods and basis sets on the evolution of reliable the energy difference (Egap) between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Thus, the numerical outcomes of Egap of C60 computed at B3LYP, M06-2X and BPW91 levels with several basis sets of theory are summarized in Table S1. The experimental Egap value of C60 was 2.86 eV.30 From the Table S1, we demonstrate a good agreement between

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experiment and calculations of the band gap at B3LYP/6-31+G(d), considering the calculation cost, which was the most reliable choice and will be used for subsequent calculations. The frontier molecular orbitals of the complexes (Figure 3) are largely localized on the C60 and C70 cage, meanwhile, the contributions of H2, HF and H2O units are almost negligible. The Egap values in H2@C60, HF@C60 and H2O@C60 are computed to be 2.78, 2.75 and 2.75 eV, respectively. Encapsulation of H2, HF and H2O causes a slight lowering of the energy gaps of C60 by between 0.08 to 0.11 eV. The Egap of C70 was evaluated as 2.73 eV along with -5.93 eV of HOMO and -3.2 eV of LUMO. The Egap in H2@C70, HF@C70 and H2O@C70 are computed to be 2.70, 2.69 and 2.72 eV, respectively, where, the encapsulation of H2, HF and H2O causes a slight lowering of the energy gaps of C70 by between 0.01 to 0.04 eV. Similarly, the encapsulations of H2, HF and H2O dimers also lower the Egap of C70 by between 0.01 to 0.06 eV. The slight perturbations of H2, HF and H2O on the energy gap of encapsulated fullerenes are the results of weak interactions between the inner spices and outer fullerene cage.30 Thus, the decrease of Egap in encapsulated fullerenes can be hailed as a counter mark of the intermolecular weak interaction. It implied that implied that electronic excitations cannot be modeled by excitations in the fullerene unit alone and are lightly influenced by interactions with remaining parts of the molecule.

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Figure 3. Frontline molecular orbital diagrams and energy levels of fullerene C60, C70 and their endohedral molecules.

3.3. The noncovalent interaction. The visualization analysis of the weak noncovalent interactions are performed. The existence of a spike with low electron density (–0.05 < sign(λ2)ρ < 0.05) indicates the presence of weak noncovalent interactions. As shown in Figure 4, two spikes with low electron density marked with pink circles were found. This low density surface provides a good balance between the weakly repulsive and attractive interactions, resulting in the better thermal stability of the complex. For the sake of distinguishing three different types of noncovalent interactions (i.e., strong attraction, van der Waals interaction and steric 12


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hindrance), low-gradient isosurfaces (RDG) (s = 0.5 a.u.) for the complexes were plotted. The noncovalent interaction regions of all complexes are filled as green or light brown, which confirm an overwhelming preponderance of the van der Waals interaction and there is element which can be identified as H-π (probably the most important binding part). Then there is a new interesting discovery that the area of RDG can represent the dispersion range of the interaction energy has positive correlation with the dispersion range to a large extent. Because from Figure 3, we can see that the dispersion range between H2O and C60 is obviously larger than that between H2 (HF) and C60, and the absolute value of interaction energy for H2O@C60 (Eint = -13.32 kcal/mol) is larger with respect to that of H2@C60 (Eint = -6.47 kcal/mol) and HF@C60 (Eint = -8.72 kcal/mol). On the other hand, the dispersion range between H2O and C70 is obviously larger than that between H2 (HF) and C70, at the same time the absolute value of interaction energy for H2O@C70 (Eint = -11.64 kcal/mol) is larger than that of H2@C70 (Eint = -5.57 kcal/mol) and HF@C70 (Eint = -7.20 kcal/mol). Similar results can be also obtained from the comparison among (H2)2@C70 , (HF)2@C70 and (H2O)2@C70.

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Figure 4. Gradient isosurfaces (RDG) of the complexes. The surfaces are colored on a red-green-blue scale according to values of sin(λ2)ρ, ranging from -0.04 to 0.02 a.u., where red signifies strong repulsion, green represents π–π interactions, and blue denotes strong attraction.

3.4. Absorption spectrum. For a comprehensive qualitative as well as quantitative description of transition energies, UV−Vis absorption spectra of the complexes performed at the TD-B3LYP-D3/6-31+G* have been used to study the electron transition property. In order to ensure the reliability of the simulation result, a 14


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comparison between the simulation results in chloroform, cyclohexane and toluene solvents, respectively and the experimental results of C60, C70 and H2@C7015 has been executed (Figure S1). It is found that the UV−Vis spectra are in reasonably good agreement with the experimental ones, not only for the band positions but also the relative peak intensities. On the other hand, a comparison between the simulation results in chloroform, cyclohexane and toluene solvents, respectively and the experimental results of H2@C60,4 HF@C6014 and H2O@C606 has been also executed (Figure 5), which indicated that simulated result are in reasonably good agreement with the experimental ones. However, the results in toluene have overrated absorption peak intensities and the results in chloroform and cyclohexane appear to very close. Therefore, absorption spectra of other complexes were simulated in chloroform.

Figure 5. The experimental and simulative UV−vis absorption spectra of H2@C60, HF@C60 and H2O@C60 in trichloromethane solvent.

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Absorption spectra of H2@C60, H2@C70 (H2)2@C70 and HF@C60, HF@C70, (HF)2@C70

as

well

as

H2O@C60,

H2O@C70,

(H2O)2@C70 simulated

in

trichloromethane were shown in Figure 6, along with the electron density difference maps (EDDM) corresponding to the crucial electronic transitions, for a simple and effective representation of the electronic transition. The results of C60 and C70 have been also shown in Figure S2. The electron density difference can be exactly evaluated as:

∆ρ (r ) = ρ ele (r ) − ρ hole (r )

(7)

where ρ ele (r ) and ρ hole (r ) represent the electron and hole distribution respectively. Purple and cyan parts correspond to the region where electron density is increased and decreased after electron excitation, respectively. The spectroscopic parameters of crucial electronic transitions (low and middle-energy absorption bands) are listed in Table 1. By contrasting the absorption of H2@C60, HF@C60, H2O@C60 and C60, it reveals that with respect to the absorption spectrum of C60, maximum absorption wavelengths of endohedral C60 complexes have little red shifts. Then the comparison between endohedral C70 complexes and C70 have also been performed. The results show that the low-energy spectra of H2@C70, HF@C70, H2O@C70 are red-shifted 5, 5 and 6 nm with respect to that of C70, which indicated that there are little influence of embedded H2, HF and H2O on the absorption spectra of C70. Moreover, there are almost no influence of embedded H2, HF and H2O dimers on the absorption spectra of C70. Perception of EDDMs corresponding to the crucial electronic transitions reveal that the electronic transition of these complexes mainly attributes to intralayer CT within C60 and C70, and embedded H2, HF and H2O monomers and dimers in C70 have 16


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no influence on the electronic transition pattern.

Figure 6. UV−vis absorption spectra of the complexes along with electron density difference maps (EDDM) corresponding to the most intense electronic transitions calculated at the B3LYP/6-31+G* (purple and blue colors indicate accumulation and depletion of electron density, respectively).

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Table 1. Simulated wavelengths (λ, nm), energies (E, eV), oscillator strengths (f) and major contribution for complexes calculated at the B3LYP-D3/6-31+G*. Complex

State

E

λ

f

Excitation (% compositiosn)

C60

S37

3.56

348.52

0.02

C70

S10 (l)

2.41

513.69

0.06

H→L+2 (59%)

S21 (m)

2.76

450.01

0.13

H-5→L (28%), H-4→L+1 (28%)

H-4→L+3 (17%), H-1→L+4 (18%) H→L+4 (10%)

H→L+2 (17%) S46

3.35

369.92

0.44

H-9→L (24%), H-8→L+1 (24%) H-2→L+3 (14%)

H2@C60

S33

3.50

353.86

0.02

Ha→L+5 (22%), H-2→L+3 (10%)

H2@C70

S8 (l)

2.39

518.32

0.07

H→L+2 (57%), H-2→L+1 (12%)

S21 (m)

2.75

450.54

0.13

H-5→L (36%), H-4→L+1 (36%)

S46

3.36

368.53

0.44

H-9→L+1(16%), H-8→L (16%) H-2→L+3 (12%), H-1→L+5 (10%)

S9 (l)

2.40

515.57

0.06

H→L+2 (54%), H-2→L (16%)

S21 (m)

2.77

447.79

0.13

H-4→L (28%), H-5→L+1 (23%)

S46

3.40

364.47

0.45

H-9→L (24%), H-8→L+1 (23%)

HF@C60

S33

3.50

354.37

0.01

H-2→L+5 (12%), H-9→L (10%)

HF@C70

S8 (l)

2.39

518.78

0.06

H-1→L+2 (57%), H-2→L+1 (15%)

S22 (m)

2.74

452.48

0.10

H-4→L+1 (31%), H-5→L (18%)

S46

3.36

368.55

0.44

H-9→L+1 (25%), H-8→L (22%)

S8 (l)

2.39

518.89

0.06

H-1→L+2 (55%), H-2→L+1 (14%)

S24 (m)

2.78

446.38

0.09

H-7→L (45%), H-4→L+1 (11%)

S46

3.36

369.10

0.43

H-9→L+1 (25%), H-8→L (22%)

S35

3.50

353.89

0.02

H-1→L+5 (15%), H-3→L+5 (13%)

(H2)2@C70

(HF)2@C70

H2O@C60

H-2→L+4 (13%), H→L+3 (11%) H2O@C70

S8 (l)

2.39

519.15

0.06

H-1→L+2 (55%), H-2→L (13%)

S23 (m)

2.76

449.10

0.10

H-6→L (27%), H-7→L+1 (23%) H-4→L+1 (13%), H→L+2 (11%)

(H2O)2@C70

S46

3.36

368.93

0.44

H-9→L (20%), H-8→L+1 (19%)

S10 (l)

2.40

516.15

0.05

H-1→L+2 (54%), H-4→L+1 (16%) H-2→L+1 (14%)

S24 (m)

2.78

446.59

0.07

H-7→L+1 (45%), H-4→L+2 (12%)

S46

3.36

369.40

0.42

H-9→L (15%), H-8→L+1 (17%) H-2→L+3 (10%), H-1→L+4 (10%)

a

H=HOMO, L=LUMO. l=low-energy absorption band, m=middle-energy absorption band.

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In order to define the dominant excited state, sum-over-state (SOS) gamma expression has been applied in the SOS investigation performed at the TD-B3LYP-D3 functional level, within the framework of the SOS perturbation theory. Due to that embedded H2, HF and H2O monomers and dimers in C60 and C70 have little influence on the absorption spectra as well as electronic transition pattern, the convergent behaviors of γsos values for complexes H2@C60, H2@C70 and (H2)2@C70 as examples are plotted in Figure 7. As the number of states increased to 50, the γtot values converge to a constant value. Inspection of the figure reveals that the γsos values of complexes display in the order of 4.16×104 a.u. (H2@C60) < 1.03×105 a.u. ((H2)2@C70) < 1.09×105 a.u. (H2@C70). We took a further step into several main excited states that contribute to the γtot values in order to elucidate the dominant contribution of excited states to the γtot values. It reveals that the excited states S33, S34 and S35 have the dominant contributions to the γtot value of H2@C60. For H2@C70 and (H2)2@C70, S46 is the dominant excited state. Therefore, the dominant excited states of HF@C60, HF@C70 and (HF)2@C70 as well as H2O@C60, H2O@C70 and (H2O)2@C70 are similar with that of embedded H2 monomers and dimers in C60 and C70.

19



Figure 7. Convergent behaviors of γsos values for complexes and its dependent on the first 50 states.

3.5. Iinear optical coefficients. There DFT methods were selected to examine the reliability of the calculated polarizabilities and first hyperpolarizabilities (Table 2, S3 and S4). The α values of these complexes obtained by three DFT methods were shown in Figure 8a. It is worth noting that the results of M06-2X provide consistent pictures and smaller values with respect to the CAM-B3LYP and BHandHLYP approaches. Thus the results of BHandHLYP were discussed in detail. The comparison of H2@C60, HF@C60 and H2O@C60 showed that the α values arranged in the increasing order of H2@C60 (528.9 a.u.) < H2O@C60 (529.6 a.u.) < HF@C60 (531.6 a.u.). For endohedral C70, the results were obtained that H2@C70 (650.4 a.u.) < HF@C70 (650.6 a.u.) < H2O@C70 (651.4 a.u.) and (H2)2@C70 (640.9 a.u.) < (HF)2@C70 (651.1 a.u.) < (H2O)2@C70 (652.4 a.u.). Another interesting finding is that the α value of H2@C70 were largest one with respect to H2@C60 and (H2)2@C70. Similar results were obtained from Figure 8b, HF@C70 and H2O@C70 possess larger α

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values as compared with HF@C60 and (HF)2@C70 as well as H2O@C60 and (H2O)2@C70. Moreover, only embedded HF monomer or dimer in C60 and C70 would increase their α values, while the α values of endohedral fullerene decreased when embedded H2 and H2O in C60 and C70. To provide an original understanding of the α values, we focused on the relative electronic spatial extent , which is physical property characterizing the electron density volume around the molecule. The extent increases as the electron cloud becomes more diffused.31 Hence, the more diffuse electron cloud may lead to a larger value. The values and the relationship between and α values were plotted in Figure 7b. It suggested that the values are in good accordance with the increasing order of the α values.

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Page 22 of 34

Table 2. The components of second hyperpolarizabilities γ (a.u.) and total second hyperpolarizabilities (γtot, a.u.) of the complexes computed at various levels of theory. Complex

C60

C70

H2@C60

H2@C70

(H2)2@C70

HF@C60

HF@C70

(HF)2@C70

H2O@C60

H2O@C70

(H2O)2@C70

Method

α

γxxxx

γyyyy

γzzzz

γtot

BHandHLYP

531.0

118343.0

118332.0

118319.0

118335.5

M06-2X

526.6

105529.0

105441.0

105358.0

105461.3

CAM-B3LYP

530.4

117529.0

117519.0

117508.0

117522.6

BHandHLYP

650.4

218916.0

131417.0

131409.0

180826.8

M06-2X

644.2

195275.0

120444.0

120440.0

163810.2

CAM-B3LYP

648.0

207393.0

132169.0

132161.0

177181.5

BHandHLYP

528.9

117026.0

117053.0

116920.0

116961.3

M06-2X

524.5

114057.0

114051.0

113476.0

107090.8

CAM-B3LYP

528.3

116206.0

116205.0

116084.0

116144.2

BHandHLYP

650.4

215832.0

130713.0

130611.0

179712.2

M06-2X

644.5

188659.0

124650.0

124873.0

166353.6

CAM-B3LYP

648.0

200463.0

130957.0

130634.0

174924.1

BHandHLYP

640.9

211261.0

126305.0

126579.0

174660.8

M06-2X

634.9

187325.0

115770.0

116258.0

157902.8

CAM-B3LYP

638.6

200196.0

127493.0

127734.0

171539.8

BHandHLYP

531.6

127689.0

127954.0

128325.0

125137.2

M06-2X

524.7

103377.0

103868.0

104103.0

103787.4

CAM-B3LYP

528.5

116007.0

116139.0

116343.0

116157.4

BHandHLYP

650.6

217343.0

128642.0

129440.0

179365.4

M06-2X

643.3

190122.0

118553.0

119885.0

162161.3

CAM-B3LYP

648.2

205585.0

131606.0

132529.0

176463.5

BHandHLYP

651.1

216968.0

128750.0

129863.0

179180.0

M06-2X

645.0

193136.0

117787.0

118785.0

162153.6

CAM-B3LYP

648.7

205749.0

129785.0

130672.0

175973.1

BHandHLYP

529.6

116738.0

117195.0

116892.0

116977.6

M06-2X

524.7

98835.0

104957.0

98647.0

100013.8

CAM-B3LYP

527.0

107631.0

108754.0

104879.0

107605.2

BHandHLYP

651.4

216354.0

137698.0

130865.0

181360.3

M06-2X

645.2

194289.0

113421.0

112865.0

164499.3

CAM-B3LYP

648.6

205724.0

130989.0

131731.0

176302.9

BHandHLYP

652.4

219351.0

128458.0

128576.0

179279.6

M06-2X

646.3

194134.0

117092.0

117318.0

161343.8

CAM-B3LYP

650.1

207999.0

129494.0

129682.0

175858.8

22


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Figure 8. a) Polarizabilities α (a.u.) of the complexes computed at various levels of theory; b) relationship between the α values at BHandHLYP method and the corresponding values of the complexes; c) total second hyperpolarizabilities γtot (a.u.); d) the relationship between γtot and γsos. (For clarity, in this Figure, 1a, 2a, 3a, 1b, 2b, 3b, 1c, 2c and 3c were on behalf of H2@C60, H2@C70, (H2)2@C70, HF@C60, HF@C70, (HF)2@C70, H2O@C60, H2O@C70 and (H2O)2@C70)

3.6. Third order nonlinear optical coefficient. For these studied fullerenes, the origin of the Cartesian coordinate system is located at the middle of fullerene (Figure 1). In order to understand the role of the different approaches in influencing the second hyperpolarizability, the numerical outcomes of this work computed at CAM-B3LYP, M06-2X and BHandHLYP methods have been summarized in Table 2. At first glance, in the case of γtot values, the M06-2X produces lower results, while BHandHLYP and CAM-B3LYP produces close ones and same trends (Figure 8c). Thus the results of BHandHLYP were discussed in detail. The comparison of H2@C60, 23



HF@C60 and H2O@C60 showed that the γtot values arranged in the increasing order of H2@C60 (116961.3 a.u.) < H2O@C60 (116977.6 a.u.) < HF@C60 (125137.2 a.u.). For endohedral C70, the results were obtained that H2@C70 (179712.2 a.u.) < HF@C70 (179365.4 a.u.) < H2O@C70 (181360.3 a.u.) and (H2)2@C70 (174660.8 a.u.) < (HF)2@C70 (179180.0 a.u.) < (H2O)2@C70 (179279.6 a.u.). Another interesting finding is that the γtot value of H2@C70 were largest one with respect to H2@C60 and (H2)2@C70. Similar results were obtained from Figure 7d, HF@C70 and H2O@C70 possess larger γtot values as compared with HF@C60 and (HF)2@C70 as well as H2O@C60 and (H2O)2@C70. Moreover, though the comparison of γtot values between C60 (or C70) and endohedral fullerene, it revealed that embedded HF monomer or dimer in C60 and C70 would increase their γtot values, while embedded H2 and H2O would decrease the γtot values of C60 and C70, which is in line with the results of α values. Inspection of the Figure 7 reveals that the γsos values of complexes display in the order of 4.16×104 a.u. (H2@C60) < 1.03×105 a.u. ((H2)2@C70) < 1.09×105 a.u. (H2@C70), which is agree with their γtot values shown in Figure 8d. It indicated that convergent values of γsos using the SOS perturbation theory are accurate. Turn our attention to the components of γ values, the γzzzz and γyyyy values are almost equal for these complexes. From Table 2, it shows that the tendency of γxxxx values is in good accordance with that of γtot values, suggesting that the γxxxx value mainly determines the γtot which is due to that the intramolecular charge transfer is mainly along the x axis. Among them, endohedral C70 possesses the larger γxxxx values with respect to that of endohedral C60. The γxxxx amplitude of H2@C70 has been found

24


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to be about 1.8 times larger than that for H2@C60. Similar results can be obtained from the comparison between HF@C60 and HF@C70 as well as between H2O@C60 and H2O@C70. It is found that the effect of cage size is effective in the second hyperpolarizabilities of endohedral fullerenes. The results obtained show that the larger NLO responses depend on the size of the fullerene cage, which might be important for further investigation in such fullerenes and their derivatives.

3.7. Gamma density analysis. Gamma density analysis, which is the spatial contribution of the electrons to the NLO response, have been performed.32, 33 It can explore the nature of the effect of fullerene cage size on the γ values of endohedral ( 3) fullerenes. The γ density, ρ xxx ( r ) , can be calculated by the third-order derivative of

electron density: ( 3) (r ) = ρ xxx

∂ 3 ρ (r , F ) ∂F x ∂F x ∂F x

(9)

F =0

The γ value is given by Equation:

γ xxxx = −

1 x ( 3) r ρ xxx (r )dr 3∫

(10)

(3) Here, rx represents the x-axis component of the electron coordinate and ρ xxx (r ) is

referred to as the static γ density along the x-axis. Integral of all data (ID) can represent the γ values to some extent. ( 3) The plots of –x* ρ xxx ( r ) and ID values for these complexes were shown in Figure

9. Purple and white meshes represent positive and negative contributions to γxxxx values. For endohedral fullerenes, the negative contributions are much smaller with 25



respect to the positive ones and they can be temporarily ignored. The magnitude of the γ densitie contribution is evaluated to be proportional to the density amplitudes multiplied by the distance between the negative and positive contributions. Along with the increase of fullerene size, the density amplitude as well as the distance between the negative and positive contributions gradually increase. Hence, the contribution of γ densities gradually increase, which can well explain the mentioned conclusion above that endohedral C70 possesses larger γxxxx values than that of endohedral C60. However, due to that the γxxxx values of these complexes were in the ( 3) same order of magnitude, the plots of –x* ρ xxx ( r ) can not quantitatively illustrate the

γxxxx value. Hence, ID values come in handy. The results show that the ID values arranged in the increasing order of H2@C60 (1.18×105 a.u.) < (H2)2@C70 (2.28×105 a.u.) < H2@C70 (2.34×105 a.u.); HF@C60 (1.30×105 a.u.) < (H2)2@C70 (2.36×105 a.u.) = H2@C70 (2.36×105 a.u.); H2O@C60 (1.18×105 a.u.) < (H2)2@C70 (2.34×105 a.u.) < H2@C70 (2.39×105 a.u.), which indicated that embedded H2, HF and H2O monomers in C70 were larger ones with respect to embedded monomers in C60 and dimers in C70. on the another hand, it is found that embedded HF monomer or dimer in C60 and C70 have larger ID values when compared with that of embedded H2 and H2O. These regulars obtained from the results of ID values were discovered consistent with that of γxxxx values.

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( 3) Figure 9. The plots of –z* ρ xxx ( r ) and ID values for the complexes, where purple and white

meshes represent positive and negative contributions to γxxxx values with isosurfaces of ±100.00 au, respectively.

4. CONCLUSION The successful synthesis of (H2)2@C70 and (H2O)2@C70 makes possible the existence of (HF)2@C70 in a geometrically well-defined hydrophobic environment. Exploration of various featured properties suggests that (HF)2@C70 may be also regarded as a unique system composed of both inter- and intramolecular interactions like (H2)2@C70 and (H2O)2@C70. The mechanically entrapped HF dimer is not electronically innocent of the presence of the cage; each H atom of HF is weakly F-H···C70 bonded, whereas 27



the F lone-pairs are F···C70 bonded. Comparisons are made between the O-H···O bonding energy and F-H···F bonding energy inside C70, which were estimated smaller than that of free dimer in the gas phase. It indicated that C70 provides secure and reliable environment. The calculation of polarizability α value indicated that the and α values increase linearly as the fullerene size increase. On the other hand, endohedral C70 possesses the larger γxxxx values with respect to that of endohedral C60. It is due to that the magnitude of the contribution to γ values associated γ densities is proportional to the density amplitudes multiplied by the distance, where larger fullerenes possess larger density amplitude and longer distance as compared to smaller fullerenes. The results obtained show that the larger NLO responses depend on the size of the fullerene cage, which might be important for further investigation in such fullerenes and their derivatives.

ASSOCIATED CONTENT The Supporting Information is available free of charge on the ACS Publications website at DOI: Egap of C60 computed at B3LYP, M06-2X and BPW91 levels with several basis sets of theory. Dipole moment µ and atomic charges for isolated and encapsulated H2, HF and H2O. The components of polarizabilities αii and average polarizabilities α of the complexes computed at various levels of theory. The components of second hyperpolarizabilities of the complexes computed at various levels of theory.

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AUTHOR INFORMATION Corresponding Author * E-mail: [email protected] (Y. Q. Qiu)

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT The authors gratefully acknowledge the financial support from the “12th Five-Year” Science and Technology Research Project of the Education Department of Jilin Province ( [2016] 494) and the National Natural Science Foundation of China (No. 21173035).

REFERENCES (1) Saunders, M.; Jiménez-Vázquez, H. A.; Cross, R. J.; Poreda, R. J., Stable Compounds of Helium and Neon: He@C60 and Ne@C60. Science 1993, 259, 1428-1430. (2) Ohtsuki, T.; Masumoto, K.; Ohno, K.; Maruyma, Y.; Kawazoe, Y.; Sueki, K.; Kikuchi, K., Insertion of Be Atoms in C60 Fullerene Cages: Be@C60. Phys. Rev. Lett.

1996, 77, 3522-3524. (3) Aoyagi, S.; Sado, Y.; Nishibori, E.; Sawa, H.; Okada, H.; Tobita, H.; Kasama, Y.; Kitaura, R.; Shinohara, H., Rock-Salt-Type Crystal of Thermally Contracted C60 with Encapsulated Lithium Cation. Angew. Chem. Int. Edit. 2012, 51, 3377-3381.

29



(4) Murata, Y.; Murata, M.; Komatsu, K., 100% Encapsulation of a Hydrogen Molecule into an Open-Cage Fullerene Derivative and Gas-Phase Generation of H2@C60. J. Am. Chem. Soc. 2003, 125, 7152-7153. (5) Sartori, E.; Ruzzi, M.; Turro, N. J.; Decatur, J. D.; Doetschman, D. C.; Lawler, R. G.; Buchachenko, A. L.; Murata, Y.; Komatsu, K., Nuclear Relaxation of H2 and H2@C60 in Organic Solvents. J. Am. Chem. Soc. 2006, 128, 14752-14753. (6) Kurotobi, K.; Murata, Y., A Single Molecule of Water Encapsulated in Fullerene C60. Science 2011, 333, 613-616. (7) Weiske, T.; Wong, T.; Krätschmer, W.; Terlouw, J. K.; Schwarz, H., The Neutralization of He@C60+ in the Gas Phase: Compelling Evidence for the Existence of an Endohedral Structure for He@C60. Angew. Chem. Int. Edit. 1992, 31, 183-185. (8) Sternfeld, T.; Hoffman, R. E.; Saunders, M.; Cross, R. J.; Syamala, M. S.; Rabinovitz, M., Two Helium Atoms inside Fullerenes: Probing the Internal Magnetic Field in C60 and C70. J. Am. Chem. Soc. 2002, 124, 8786-8787. (9) Weidinger, A.; Waiblinger, M.; Pietzak, B.; Almeida Murphy, T., Atomic Nitrogen in C60:N@C60. Appl. Phys. A 1998, 66, 287-292. (10) Ito, S.; Shimotani, H.; Takagi, H.; Dragoe, N., On the Synthesis Conditions of N and N2 Endohedral Fullerenes. Fulle. Nanotube. Car. N. 2008, 16, 206-213. (11) Muratoglu, O. K.; Bragdon, C. R.; O'Connor, D. O.; Jasty, M.; Harris, W. H., A Novel Method of Cross-Linking Ultra-High-Molecular-Weight Polyethylene to Improve Wear, Reduce Oxidation, and Retain Mechanical Properties: Recipient of the 1999 Hap Paul Award. J. Arthroplasty 2001, 16, 149-160.

30


Page 30 of 34

Page 31 of 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(12) Murata, M.; Murata, Y.; Komatsu, K., Surgery of Fullerenes. Chem. Commun.

2008, 6083-6094. (13) Komatsu, K.; Murata, M.; Murata, Y., Encapsulation of Molecular Hydrogen in Fullerene C60 by Organic Synthesis. Science 2005, 307, 238-240. (14) Krachmalnicoff, A., et al., The Dipolar Endofullerene HF@C60. Nat. Chem. 2016, 8, 953-957. (15) Murata, M.; Maeda, S.; Morinaka, Y.; Murata, Y.; Komatsu, K., Synthesis and Reaction of Fullerene C70 Encapsulating Two Molecules of H2. J. Am. Chem. Soc.

2008, 130, 15800-15801. (16) Zhang, R.; Murata, M.; Aharen, T.; Wakamiya, A.; Shimoaka, T.; Hasegawa, T.; Murata, Y., Synthesis of a Distinct Water Dimer inside Fullerene C70. Nat. Chem.

2016, 8, 435-441. (17) Zhang, R.; Murata, M.; Wakamiya, A.; Shimoaka, T.; Hasegawa, T.; Murata, Y., Isolation of the Simplest Hydrated Acid. Sci. Adv. 2017, 3, 1602833 (1-6). (18) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, Revision D.01; Gaussian, Inc.: Wallingford, C., 2009. (19) Zhao, Y.; Truhlar, D. G., The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215-241.

31



(20) da Costa, L. M.; Stoyanov, S. R.; Gusarov, S.; Tan, X.; Gray, M. R.; Stryker, J. M.; Tykwinski, R.; de M. Carneiro, J. W.; Seidl, P. R.; Kovalenko, A., Density Functional Theory Investigation of the Contributions of Π–Π Stacking and Hydrogen-Bonding Interactions to the Aggregation of Model Asphaltene Compounds. Energy Fuels 2012, 26, 2727-2735. (21) Lu, T.; Chen, F., Multiwfn: A Multifunctional Wavefunction Analyzer. J. Comput. Chem. 2012, 33, 580-592. (22) Espinosa, E.; Molins, E.; Lecomte, C., Hydrogen Bond Strengths Revealed by Topological Analyses of Experimentally Observed Electron Densities. Chem. Phys. Lett. 1998, 285, 170-173. (23) Johnson, E. R.; Keinan, S.; Mori-Sánchez, P.; Contreras-García, J.; Cohen, A. J.; Yang, W., Revealing Noncovalent Interactions. J. Am. Chem. Soc. 2010, 132, 6498-6506. (24) Kurtz, H. A.; Stewart, J. J. P.; Dieter, K. M., Calculation of the Nonlinear Optical Properties of Molecules. J. Comput. Chem. 1990, 11, 82-87. (25) Bredas, J. L.; Adant, C.; Tackx, P.; Persoons, A.; Pierce, B. M., Third-Order Nonlinear Optical Response in Organic Materials: Theoretical and Experimental Aspects. Chem. Rev. 1994, 94, 243-278. (26) Yanai, T.; Tew, D. P.; Handy, N. C., A New Hybrid Exchange–Correlation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP). Chem. Phys. Lett.

2004, 393, 51-57. (27) Becke, A. D., A New Mixing of Hartree–Fock and Local Density‐Functional

32


Page 32 of 34

Page 33 of 34 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Theories. J. Chem. Phys. 1993, 98, 1372-1377. (28) Holzapfel, W.; Drickamer, H. G., Effect of Pressure on the Volume of the High‐Pressure (Vii) Phase of H2O and D2O. J. Chem. Phys. 1968, 48, 4798-4800. (29) Isaacs, E. D.; Shukla, A.; Platzman, P. M.; Hamann, D. R.; Barbiellini, B.; Tulk, C. A., Covalency of the Hydrogen Bond in Ice: A Direct X-Ray Measurement. Phys. Rev. Lett. 1999, 82, 600-603. (30) Schwedhelm, R.; Kipp, L.; Dallmeyer, A.; Skibowski, M., Experimental Band Gap and Core-Hole Electron Interaction in Epitaxial C60 Films. Physical Review B

1998, 58, 13176-13180. (31) Shameema, O.; Ramachandran, C. N.; Sathyamurthy, N., Blue Shift in X−H Stretching Frequency of Molecules Due to Confinement. J. Phys. Chem. A 2006, 110, 2-4. (32) Kishi, R.; Ochi, S.; Izumi, S.; Makino, A.; Nagami, T.; Fujiyoshi, J.-y.; Matsushita, N.; Saito, M.; Nakano, M., Diradical Character Tuning for the Third-Order Nonlinear Optical Properties of Quinoidal Oligothiophenes by Introducing Thiophene-S,S-Dioxide Rings. Chem-Eur. J. 2016, 22, 1493-1500. (33) Nakano, M.; Shigemoto, I.; Yamada, S.; Yamaguchi, K., Size‐Consistent Approach and Density Analysis of Hyperpolarizability: Second Hyperpolarizabilities of Polymeric Systems with and without Defects. J. Chem. Phys. 1995, 103, 4175-4191.

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Third-Order Nonlinear Optical Properties of Endohedral Fullerene (H2

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