Second-Order Nonlinear Optical Response of Electron Donor

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Second Order Nonlinear Optical Response of Electron DonorAcceptor Hybrids Formed Between Corannulene and Metallofullerenes Li Wang, Wen-Yong Wang, Yongqing Qiu, and Hui-Zhe Lu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b06870 • Publication Date (Web): 14 Oct 2015 Downloaded from http://pubs.acs.org on October 15, 2015

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The Journal of Physical Chemistry

Second Order Nonlinear Optical Response of Electron Donor-Acceptor Hybrids Formed between Corannulene and Metallofullerenes Li Wang,† Wen-Yong Wang,† Yong-Qing Qiu,*† and Hui-Zhe Lu*‡ †

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

Changchun 130024, People’s Republic of China ‡

Department of Applied Chemistry, China Agricultural University, Beijing 100193, China

1

ACS Paragon Plus Environment


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ABSTRACT: A charge transfer (CT) complex was formed between C20H10 and Li+@C60 in the ground state by the concave-convex π-π CT interaction. Herein, the structures, binding interactions, electronic absorption spectra and first hyperpolarizabilities of a series of Li+ and Li atom in contact with C60 have been explored at the density functional theory methods. It is found that independent of the doping position, doping Li atom can significantly narrow the wide gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) (Egap = 2.82 eV) of the pure C20H10/C60 in the range of 0.86-0.99 eV. Among them, the Li-doped outer isomer C20H10/LiC60 can exhibit the intriguing ntype characteristic, where a high energy level containing the excess electron is introduced as the new HOMO orbital in the original gap of C20H10/C60. Further, the diffuse excess electron also brings C20H10/C60 the considerable first hyperpolarizability, which are 3.53 × 10-29 esu. When Li+ and Li were encapsulated into the C60 cage, inner complexes C20H10/Li+@C60 and C20H10/Li@C60 of enhanced static first hyperpolarizabilities (5.39 and 2.13 × 10-29 esu, respectively) are also delivered due to that encapsulated Li+@C60 and Li@C60 show enhanced electron acceptability as compared to pristine C60, leading to more obvious intermolecular CT transitions. From a certain point of view, such systems can be considered as high-performance NLO materials that combine the basic characteristics of a classical donor-acceptor superstructure and systems with cations and easily polarizable excess electrons.

2


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1. INTRODUCTION The design of novel materials with excellent nonlinear optical (NLO) properties has aroused great interests in experimental and theoretical fields, 1-6 in view of the potential application in optical and electro-optical devices in the past several decades. Advances in the field of NLO materials depend on the characterization and synthesis of novel chromophores with large static first (or higher) hyperpolarizabilities.7 Considerable interest has been shown in the organic molecules with donor-acceptor (D-A) framework as potential building blocks exhibiting considerably large hyperpolarizabilities,8-10 which is mainly attributed to the fact that the large charge transfer (CT) can cause a large difference between the ground-state and excited-state dipole moments and low energy CT transitions.11,12 The simplest noncovalent D-A systems are derived from CT interactions between D and A molecules.13,14 The spatial proximity between the electron D and A via noncovalent interactions enable unidirectional and efficient CT interactions.15-19 CT interactions are known to be enhanced by concave-convex π-π interactions between π-electron donors with curved π-surfaces and fullerenes.20-22 Fullerenes have been generally used as efficient π-electron accepters due to the small reorganization energy, which results from the highly delocalized π-electrons over the three-dimensional π-sphere.23-25 Owing to that fullerenes have spacious inner cavities, some metals can be

encapsulated

inside

of

the

fullerene

cages

to

form

endohedral

metallofullerenes.26-28 Such endohedral fullerenes, being spherical molecules like C60, have recently gained increasing attention with regard to the potential applicability due 3



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to the specific reactivities. For instance, lithium ion-encapsulated C60 (Li+@C60) shows enhanced electron acceptability as compared to pristine C60.29-33 Corannulene (C20H10), a fragment of fullerenes, naturally offer good geometric compatibility with nonequivalent concave and convex curved π-surfaces, providing enhanced intermolecular electrostatic interactions for concave-convex interactions.34-36 As a result of better synthetic availability of bowl-shaped polyarenes,37-43 experimental studies of C20H10 as a suitable fullerene host derived from the curved π-surface have been initiated. Cocrystal of C20H10 and C60 in solid state and interaction between C20H10 and C60 in the gas phase have been reported to exhibit the availability of C20H10 to catch C60.44 A CT complex was formed between C20H10 and Li+@C60 in the ground state by the concave-convex π-π CT interaction. It revealed that the use of Li+@C60, a much stronger electron acceptor than C60, has made it possible to observe the significant CT interaction with C20H10.45 CT-type complexes are usually aligned in the solid state so that dipole moments (and longitudinal component of beta tensor) of neighboring complexes cancel each other. The obtained optimized structures are possible flexible at room temperature. Therefore, these CT-type C60-based complexes require extra synthetic efforts. In real application, introducing a large steric hindrance group to isolate monomer is the most popular and easy way to attenuate the dipole-dipole interactions.46 Further, it could control the shape and reduce flexibility of the structure.47 As for the systems with positive charge, introducing a negative counter-ion would be an effective way. Although so far several experiments on C20H10/Li+@C60 were done in solution 4


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phase, these complexes are promising to be utilized for second-order NLO device in the solid state. In light of the aforementioned, concave-convex D-A complexes C20H10/C60 (1), inner complexes C20H10/Li+@C60 (2+) and C20H10/Li@C60 (2) together with outer cases C20H10/Li+C60 (3+) and C20H10/LiC60 (3) (Figure 1) are the focus of our work. We performed density functional theory (DFT) to calculate the structures, binding interactions, electronic absorption spectra and first hyperpolarizabilities of the complexes. Specifically, we will mainly address the following issues: (1) Can the Li atom effectively bind with the C60 moiety with considerable binding energies? Whilst, predicting the stability of inner and outer isomers theoretically, (2) If yes, can doping Li+ and Li atom effectively narrow the HOMO-LUMO gap of C20H10/C60? (3) If the diffuse excess electron is produced, can it cause large first hyperpolarizability for the doped complex? (4) Are the first hyperpolarizability values of the doped complexes dependent on the doping position? After resolving them, this work may evoke one’s attention to design novel and highly efficient multifunctional D-A devices exhibiting excellent electronic property as well as considerable second-order NLO response with building blocks of the endohedral metallofullerenes.

2. COMPUTATIONAL DETAILS Geometry optimizations were carried out using the B3LYP-D3 functional. The B3LYP-D3 functional incorporating the long-range dispersion energy proposed by Grimme et al. has been demonstrated for a wide variety of non-covalent complexes 5



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including large van der Waals interaction systems and molecules with atoms beyond the second-row.48 This method of dispersion correction as an add-on to standard Kohn-Sham density functional theory has been refined regarding higher accuracy, broader range of applicability, and less empiricism.49 The binding interaction energies of the complexes were computed by using the same method as for the optimization of the structures. To correct the basis set superposition error (BSSE), the counterpoise (CP) procedure was used to calculate the interaction energy.50 The interaction energy (Eint) can be expressed as flowing equation: Eint ( AB) = E ( AB) AB − [ E ( A) AB + E ( B) AB ]

(1)

NLO properties are induced by nonlinear charge displacements that are generated under a strong electric field of light. The energy of the perturbed system is described by the expansion:51, 52

1 1 1 E = E 0 − µi Fi − ( )α ij Fi F j − ( ) β ijk Fi Fj Fk − ( )γ ijkl Fi F j Fk Fl + ... 2! 3! 4!

(2)

where E0 is the molecular energy in the absence of the applied electric field; µi is the molecular permanent dipole moment along the i direction; Fi is the Cartesian component of the applied electric field along the i direction; αij, βijk and γijkl are the polarizability, first, and second hyperpolarizability tensors, respectively; and i, j, and k designate the different components along the x, y and z directions, respectively. The orientationally averaged first hyperpolarizability (β) 53 has been calculated by using the following expression:

β tot = ( β x2 + β y2 + β z2 )1 / 2

(3) 6


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where β i is defined as:

β i = (1 / 3 ) ∑ ( β ijj + β

jji

+ β jij )

i , j = { x , y , z}

(4)

j

The projection of β on dipole moment vector can be obtained by,

β vec = ∑ i

µi βi i = x, y , z µ

(5)

where µi is dipole moment along the direction of i. Choosing a proper method for the evolution of the first hyperpolarizability is not an easy task. It was recognized early on that the theoretical determination of the first hyperpolarizability was very challenging for ab initio and semiempirical methods.54 Because high scaling order of ab initio methods leads to tremendously large computational requirements with increasing system size. Furthermore, the conventional DFT methods have also been reported to provoke an overestimation of the first hyperpolarizability. It is commonly believed that this overestimation of the first hyperpolarizabilities associated with CT excitations is the result of their wrong asymptotic exchange potential.55 Luckily, these deficiencies can be alleviated using DFT functionals with long-range corrections such as the Coulomb-attenuated hybrid exchange-correlation (CAM-B3LYP) functional that is a hybrid functional with improved long-range properties.56 Morover, in order to guarantee the accuracy of calculation, BhandHLYP and M06-2X have also been chosen. The BHandHLYP functional is obtained by including a 50% of the exact exchange in rgw BLYP functional, and thus, it is slightly different from the original half and half funtional proposed by Becke.57,58 Meta-GGA M06-2X functional with a high percentage of HF exchange developed by Zhao and Truhlar have been shown to describe noncovalent 7



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interactions better than density functionals which are currently in common use.59 Time-dependent DFT (TD-DFT) has nowadays become general tools to the understanding and predicting the behavior of the electron transition property.60,61 To obtain more insight on the description of the trend of second-order NLO responses, the vertical electronic transition energies between the ground and excited states were calculated using TD- B3LYP-D3. All of the calculations were carried out by using the Gaussian 09W program package.62 Localized orbital locator (LOL) and Gradient isosurfaces (RDG) were obtained by employing the Multiwfn software version 3.3.63 and RDG were plotted using VMD 1.9.1.64

3. RESULTS AND DISCCUSION 3.1.1 Geometrical structure. The optimized structures are shown in Figure 1. Normal coordinates and harmonic frequencies (cm-1) of all the complexes obtained by B3LYP-D3 functional (Table S1-S3) have been shown in supporting information. The results show that there are no imaginary frequency for the complexes except for the very small imaginary frequency value of complex 2, which indicates that the structure is possibly existent structure with slight flexibility, which is due to that the concave-convex π-π interaction stabilize the CT complex. The C20H10 moiety has the concave-convex π-π interaction with the C60 moiety by using their curved π-surfaces. The concave-convex π-π CT interaction was previously reported more stabilize the CT complex than the convex-convex π-π interaction because of the large electrostatic 8


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interaction which plays a pivotal role in determining the energetically accessible stacking motifs.65 A comparative analysis of geometrical parameters shows that the distance of 1 between C20H10 and C60 (3.3 Å) is nearly equal to that in experimental study of 1 on Cu(110) (3.3 ± 0.1 Å).66 A further comparison of 2+ that d1 is close to the calculated value (3.8 Å) at the B3LYP/6-31(d) level obtained by Yamada. ect.45 The slight difference between two values is the result of dispersion correction. Li+ and Li can be encapsulated inside the fullerene cages to form inner forms (2+ and 2), which increased the d1 and d2 by the range of 0.1~0.3 Å. It is due to that encapsulated Li+ and Li have slight effects on the size of C60 cage. For outer cases 3+ and 3, the distances between C60 and C20H10 are about 4.0 Å. The distances are further increased because of two-layer weak interactions, including relatively strong interactions formed between C60 and Li+/Li along with strong interactions between C20H10 and Li+/Li. On the other hand, when Li+/Li were encapsulated inside between C60 and C20H10, the steric hindrance also contributed to the increasing distances. It is also found that the total stabilization energies give a similar sequence for inner and outer cases of these complexes. Inspection of Figure 1 reveals that the outer structures 3+ and 3 show the lower relative energies with respect to the inner forms 2+ and 2, supporting the chemical stabilities of the outer isomers. This predication has been further supported by their corresponding interaction energies (Eint). Interaction energy of 2 is similar to that of 1 which is due to that the doped Li atom is neutral. So it can not affect the electrostatic interaction between C60 cage and C20 fragment. However, the negatively larger value for 2+ is attributed to that encapsulated Li+@C60 9



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show enhanced electron acceptability as compared to pristine C60. As for outer cases 3+ and 3, the significant increases of the binding interaction energies were the results of larger orbital interactions according to the energy decomposition analysis. (See the related discussion in 3.2 section).

Figure 1. The structures of complexes and the relative energies of complexes 2+- 3+ (where Erel (2) = E(2) - E(2+), Erel (3+) = E(3+) - E(2+), and Erel (3) = E(3) - E(2+)).

Table 1. Two different typed of distances (Å) of the complexes, their corresponding interaction energies (Eint, kcal/mol) and HOMO-LUMO energy gap (Egap, eV). Complex

d1

d2

Eint

Egap

1

3.3 10.3 -16.1 2.82

2+

3.6 10.5 -20.1 1.80

2

3.4 10.4 -16.0 0.86

3+

4.0 11.1 -42.8 2.67

3

4.0 11.0 -34.1 0.99

10


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Charge of natural population analysis (NPA) has been performed to interpret the amount and direction of charge transfer in the ground state. For all complex, the positive value of the C20H10 (Table S4) indicates a charge flow from C20H10 fragment. With

regard

to

the

inner

complexes

2+

and

2,

Li+/Li

and

C60 being an indispensable integrity aggregates a small amount of electrons, which results from a charge flow from C20H10 molecule to Li+@C60 and Li@C60, respectively. However, when it comes to the outer complexes 3+, the positive value of charge distribution upon C20H10 and C60 indicates a charge flow from C20H10 and C60 to Li+. For the outer complex 3, the negative charge distributed on C60, suggesting that there was CT from C20H10 and Li to C60 in the complex formation, and C60 as electron acceptor during the transformation.

3.1.2 Electronic structure. From the point of molecular orbital theory, for C20H10/C60, there is no orbital overlap between the C20H10 and C60. It reveals that weak interaction between C60 cage and C20H10 are formed by concave-convex π-π interactions between curved C20H10 and fullerenes. Likewise, inner complexes 2+ and 2 are similar. For outer complexes, for example 3, a small overlap between π orbitals of C60 and s orbital of Li+ is observed in distribution of HOMO. It reveals that weak σ-π interaction between

C60

(or

C20H10)

and

Li is

formed.

There

have

no

direct

weak interaction between C60 and C20H10 in outer complexes. However, strong orbital interaction provides the crucial factor for the stability. 11



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The frontier molecular orbitals are often used to reveal the relationship between the electronic and geometric structures. Correspondingly, highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are shown in Figure 4. In the case of complex 1, it can be noted the specific localization of HOMO on the whole molecule. When Li+ was encapsulated inside of the fullerene cages to form the inner somer C20H10/Li+@C60 (2+), the HOMO was found on the on C20H10 fragment. However, HOMO of outer case 3+ distribute on C60 cage, suggesting that location of Li+ has a great influence on highest occupied molecular orbital distribution. For Li-doped complexes, the HOMOs of 2 and 3 were both located on C60 cage. LUMOs have rather similar shapes except for that of complex 3. The localization of the LUMO for 3 was on Li atom and C20H10 fragment, whereas, LUMOs of other complexes distribute on C60. The tremendous different distribution between HOMO and LUMO of complex 2+ results in large difference between excited and ground state dipole moments coupled with a long-range intermolecular charge transfer transition from C20H10 fragment to C60 cage. The distinction between HOMO and LUMO of complex 3 was also enormous due to the polarization of the excess electron that is usually produced by an inward pull the 2s valence electron of the Li atom, which can be supported by its molecular electrostatic potential (MEP, Figure S1). It has been analyzed that newly designed models with excess electron have large NLO responses and the excess electron has played a crucial role to enhance the first hyperpolarizability.67,68

Therefore,

complex

3

may

exhibit

large

first

hyperpolarizability. In addition, doping the Li+ can significantly narrow the wide gap 12


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between the HOMO and LUMO (Egap = 2.82 eV) of complex 1 in the range of 1.8~2.67 eV (Figure S2). On the other hand, the doped C60 cages with Li atom can also effectively narrow the wide HOMO-LUMO gap (from 2.82 eV to 0.86~0.99 eV) and conspicuously improve the energy level. This is due to that there is unpaired electron. It endows the doping structure 3 with the intriguing ntype characteristic, where a high energy level containing the excess electron is introduced as the new HOMO orbital in the original gap of pure C20H10/C60.

Figure 2. The frontier molecular orbital diagram the studied complexes.

3.2 Binding interaction. Localized orbital locator (LOL, Figure S3) is often used to interpret the structure and chemical bond in a clear and intuitive manner.69 The fasted electron regions (0.0 < LOL < 0.5, plotted in lighter blue, blue, and deep blue) represent regions in space that are increasingly avoided by electrons, such as the space far away from nuclei and the space between the shells of the atoms. It is revealed that no covalent bond has been formed. To distinguish three different types of noncovalent 13



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interactions (i.e., hydrogen-binding, van der Waals interaction and steric hindrance), low-gradient isosurfaces (s = 0.5 a.u.) for the complexes (Figure S4) were plotted.70 The interaction region of complexes marked by large green circle can be identified as van der Waals interaction region because the filled-color is green or light brown, meaning that the density electron in this region is low. In order to understand which part of the complex contributes to the stabilization of structures, we considered isomerization energy decomposition analysis (IEDA) proposed by Contreras.71 Contributions to the isomerization energy are defined as (Figure 3): inner ∆Eint = ECinnerH

+

outer ∆Eint = ECouterH

+

20

20

10 /Li

10 /Li

@C 60

C60

− [ ECinner + ELiinner ] + @C 20 H10

− [ ECouter + E Liouter ] + C 20 H10

(7)

60

outer inner ∆∆Eint = ∆Eint − ∆Eint

(8)

∆Edist_ C20H10 = ECouter − ECinner 20 H10 20 H10

∆Edist_Li +and C = E Liouter − ELiinner + + C @C 60

(6)

60

60

(9) (10) 60

∆∆Edist = ∆Edist_C 20 H10 + ∆Edist_Li + and C

(11) 60

∆Eiso = ∆∆Eint + ∆∆Edist

(12)

These equations (7-13) decompose the isomerization energy ( ∆Eiso ) into two terms, the distortion energy ( ∆∆Edis ) and binding interaction energy difference ( ∆∆Eint ). The ∆∆Edist value is directly related to the fragment’s capacity to transform one isomer into the other, while the ∆∆Eint value reflects the binding capability of each isomer. It is apparent that the absolute values of ∆∆Eint are larger with respect to the ∆∆Edist values for all complexes, indicating that the binding capability of each isomer mainly 14


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contributes to the stabilization of structure (Table 2). In addition, the ∆∆Edist values remain near zero suggesting that mobility model for which the current position of Li+ or Li does not cause deviations of the chemical stabilities.

Figure 3. Energetic reaction cycle involving the isomerization of 2+ and 3+ with different positions of Li+.

Table 2. Results of the IEDA at the B3LYP-D3/6-31+G(d) level for 2+-3 with C20H10 and Li+ or Li and C60 as fragments (energy values are in kcal/mol). Li+-doped complex

∆Eiso

outer ∆Eint

inner ∆Eint

∆∆Eint

∆E dist_C 20 H10

∆Edist_Li + and C

2+ and 3+

-62.9

-42.8

-20.1

-62.9

0.006

-0.007

∆ Eiso

outer ∆Eint

inner ∆Eint

∆∆ Eint

∆E dist_C 20 H10

-50.1

-34.1

-16.0

-50.1

0.003

Li-doped complex 2 and 3

∆Edist_Li

60

and C 60

0.006

∆∆Edist

-0.001 ∆∆Edist

0.010

In order to quantify the different contributions to the binding energy, energy 15



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decomposition analysis (EDA) was performed by using the energy decomposition scheme of the Amsterdam density functional (ADF) 2012.01 program72,73 at the B3LYP-D3/TZ2P level of theory. We used ADF code for its ease of use and relatively exact treatment of decomposition energy that offers the total binding energy with respect to the defined fragments. In EDA, the binding interaction energy Ebind between the interacting fragments is divided into four parts:74,75 Ebind = Eelstat + Epauli + Eorb + Edisp

(13)

where, Eelstat is the electrostatic interaction, EPauli is termed Pauli repulsion, the term Eorb is orbital interaction and the final Edisp is dispersion energy.

Results in Table 3 show that the trend of binding interaction energies is in satisfactory agreement with the corresponding interaction energies in Gaussian. These slightly different values of the interaction energies may be due to the different basis set. As for the binding energy, the Pauli repulsion energy term is a very important energy term for understanding chemical binding. A binding model that considers only Pauli repulsion as the crucial factor for determining molecular geometries is the valence shell electron pair repulsion scheme. In contrast, the orbital and electrostatic interaction term provide the crucial factors for stabilizing binding energy. In general, the orbital interaction suggests covalent bond character, while the electrostatic interaction usually implies ionic bond character. The dispersion energy can be more related to the weak non-covalent interaction. It is clear that the dominant contribution between the C20H10 and C60 fragments is non-covalent intermolecular interaction in nature. However, a significant increase of the binding interaction energy and roughly 16


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the same increase of total stabilization energy were found in outer cases 3+ and 3. In both cases, the orbital contributions are much larger than that in the previous three complexes and responsible for the total stabilization energy increase.

Table 3. Decomposition energies of the complexs obtained by ADF program (energies in kcal/mol)). Complex

Epauli

Eelstst

Eorb

Edisp

Ebind

1 2+ 2 3+ 3

28.4 34.6 29.9 19.7 24.5

-12.4 -14.9 -13.1 -4.4 -8.2

-5.8 -11.6 -6.5 -35.3 -27.1

-26.4 -28.4 -26.5 -19.1 -20.0

-16.2 -20.2 -16.2 -39.0 -30.8

3.3 Absorption spectrum. For a comprehensive qualitative as well as quantitative description of transition energies, time-dependent density functional theory (TD-DFT) calculations have also been performed at the B3LYP-D3/6-31+G* (6-311+G* basis set for Li ion) to get the transition energies of crucial excited states of the studied systems. UV-vis absorption spectra of the complexs along with electron density difference maps (EDDM) corresponding to the crucial electronic transitions were shown in Figure 4, for a simple and effective representation. The TD-DFT principal electronic transitions parameters and dipole moment variations of excited state with respect to ground state in y and the total variations calculated for the singlet excited states are summed in Table 4. The variations of dipole moment in x and z have been listed in Table S5. The origin of the Cartesian coordinate system is located at bottom of C60 cage and y-axis points to the central of C20H10 as shown in Figure 1. The 17



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positive ∆µ y values of crucial excited transition states of complexes 1, 2+ revealed that during a polarization process electronic charge from C20H10 is expected to migrate to the C60 and Li+@C60. The results can be confirmed by electron density difference maps (EDDM). The sign ∆µ y of complex 3 is also positive, suggesting the electronic charge from the Li atom and bottom of C60 cage to the upper part in combination with the shape of EDDM. However, for complexes 2 and 3+ with different excited states, the exact opposite electronic transition patterns cancel each other.

Figure 4. Absorption spectra of the complexes along with electron density difference maps (EDDM) corresponding to the most intense electronic transitions calculated at the B3LYP-D3/6-31+G* (6-311+G* basis set for Li ion) (purple and blue colors indicate accumulation and depletion of electron density, respectively). 18


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Table 4. Simulated wavelengths (λ, nm), energies ( ∆E ge , au), oscillator strengths (fos), differences of dipole moment between the ground and crucial excited state (au) and major contribution for complexes calculated at the B3LYP-D3/6-31+G* (6-311+G* basis set for Li ion) level. Complex

State

1

S15 S27 S12 S39 S4 S31 S11 S20 S36 S5 S6 S31

2+ 2 3+

3

a

∆µ y

∆µ ge

λ

0.92 10.19 11.21 9.40 -2.14 2.18 -1.42 -10.65 3.12 3.53 1.94 -2.04

0.92 10.19 11.26 9.44 2.16 2.19 1.42 10.66 3.15 3.53 1.94 2.05

546.1 469.1 678.7 419.3 963.6 568.3 573.0 405.6 388.4 939.8 836.4 565.7

∆E ge

0.083 0.097 0.067 0.109 0.047 0.080 0.079 0.112 0.117 0.049 0.054 0.080

Excitation (% composition)

fos

0.0019 0.0463 0.0481 0.0557 0.0281 0.0048 0.0012 0.0037 0.0054 0.0341 0.0186 0.0072

a

H-3→L+2 (46%), H-4→L+2 (29%) H-7→L+2 (94%) H-3→L+2 (87%), H-3→L+1 (11%) H-3→L+5 (97%) αH→αL+3 (90%) αH→αL+8(45%), αH-2→αL+1(15%) H→L+1 (60%), H-3→L (29%) H-1→L+4 (45%), H→L+4 (42%) H-6→L+1 (33%), H→L+7 (10%) αH→αL+4 (97%) αH→αL+5 (92%) αH→αL+8 (55%)

assignment: H = HOMO, L = LUMO, H-1= HOMO-1, L+1 = LUMO+1, etc.

Absorption spectrum of complex 1 contains only one strong absorption peak at 469.1 nm that was assigned to HOMO-7→LUMO+2 (Figure S5), where the HOMO-7 is delocalized on full C20H10 fragment with slight electron density distribution located on the C60 cage, whilst the LUMO+2 is located on C60 cage, reflecting obvious donor-acceptor interaction and intermolecular CT from C20H10 fragment to C60 cage. Another low-energy transition at 546.1 nm is largely described by the HOMO-3→LUMO+2 and HOMO-4→LUMO+2 excitations. This excited state has small oscillator strength because it is dominated by one-electron transitions with small transition dipole moment. According to the EDDM (Figure 4), the low-energy 19



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transition can also be assigned as intramolecular CT within C60 cage. Absorption spectrum of complex 2+ contains one high-energy electronic transition absorbing at 419.3 nm along with a low-energy electronic transition at 678.7

nm,

which

are

described

by

the

HOMO-3→LUMO+5

and

HOMO-3→LUMO+2, HOMO-3→LUMO+1 excitations, respectively. The HOMO-3 is delocalized through C20H10 fragment, while the LUMOs are located on C60 cage (Figure S6), suggesting very obvious donor-acceptor interaction between C20H10 fragment and C60 cage. Consistent results can also be found in EDDM (Figure 4). It indicates that the low-energy and high-energy electronic transitions can be both viewed as intermolecular CT transition from C20H10 to C60 cage. Note that similar orbital localization has been observed in past computational studies.45 This is due to the fact that Li+@C60 (2+) shows enhanced electron acceptability as compared to pristine C60. Coming to complex 2, the simulated absorption spectrum exhibits one intense low-energy electronic transition absorbing at 963.6 nm along with a high-energy electronic transition of lower intensity absorbing at 568.3 nm. It is worth noting that C60 cage undertakes both accumulation and depletion of electron density (EDDM, Figure 4). Taking into account of the shape of HOMOs and LUMOs, the αHOMOs are delocalized through full fullerene cage with very slight electron density distribution located on the C20H10. On the other hand, the αLUMOs are also located on full fullerene cage (Figure S7). It indicates that the low-energy and high-energy electronic transitions can be both assigned to the intramolecular CT excited transition 20


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within C60 cage. The CT transition is not very strong, suggesting the possibility of a relative weaker second-order NLO optical response as compared to complex 2+. With regard to complex 3+, the absorption spectrum exhibits one intense high-energy absorption peak at 388.4 nm along with an electronic transition of lower intensity absorbing at 405.6 nm and a low-energy absorption peak at 573.0 nm. EDDM of complex 3+ shows that the intense electronic transition at 388.4 nm was assigned to the intermolecular CT from C20H10 to C60 cage along with a little intramolecular CT excited transition within C60 cage. For electronic transition at 405.6 nm, it is viewed as the intermolecular CT from C60 cage to C20H10. The exact opposite electronic transition patterns will significantly reduce the second-order NLO optical responses. The same results have been found considering the shape of HOMOs and LUMOs (Figure S8). The low-energy absorption peak at 573.0 nm with small oscillator

strength

was

mainly

described

by

HOMO→LUMO+1

and

HOMO-3→LUMO, which are all delocalized through full fullerene cage. Considering the relevant EDDM involved in these transitions, we could assign them as the intramolecular CT excited one within C60 cage. For complex 3, the simulated absorption spectrum is qualitative quite similar to that of complex 2, i.e., one intense low-energy absorbing peak, which has been associated to doubly degenerate excited states labeled as S5 and S6, along with a high-energy absorbing at 565.7 nm. The S5 state of low-energy electronic transition is mainly described by the αHOMO → αLUMO+4, while the S6 state is dominated by the αHOMO → αLUMO+5. The αHOMO, αLUMO+4 and αLUMO+5 are all located 21



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on Li atom and full fullerene cage (Figure S9), reflecting the intramolecular CT excited transition within C60 cage. The high-energy electronic transition was assigned to αHOMO → αLUMO+8, and αLUMO+8 is mainly located on C20H10 fragment, Li atom and the bottom of C60 cage, account for the slight intermolecular CT excited transition. Inspection of EDDM reveals that the electronic transitions of complex 3 can be mostly viewed as obvious intramolecular CT transition from the Li atom and bottom of C60 cage to the upper part. The contribution of Li atom to the orbitals of the doping structure 3 is due to that the excess electron produced by an inward pull the 2s valence electron is introduced as the new HOMO orbital in the original one of pure C60 cage. From the above, the charge transfer patterns of the five complexes are generally intra- and intermolecular CT excited transitions, in which the C60 cage plays an important role. Owing to the fact that Li+@C60 shows enhanced electron acceptability as compared to pristine C60, the electronic transition of complex 2+ can be viewed as more obvious intermolecular CT transition from C20H10 to C60 cage. Additionally, the excess electron will play a crucial role to enhance the first hyperpolarizability of complex 3. It suggests the possibility of a strong second-order NLO optical response for such complexes.

3.4 First Hyperpolarizability. As the aforementioned, obvious intermolecular charge transfers from C20H10 to C60 cage and the excess electron produced by the 2s valence electron are associated with remarkably large first hyperpolarizabilities. The facts 22


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inspired us to further investigate the second-order NLO properties of the complexes. It is both instructive and useful to accumulate experience on the performance of various methods on the evolution of the reliable hyperpolarizability.76,77 Therefore, several density functionals were selected to examine the reliability of the calculated dipole moments and first hyperpolarizabilities (Table 5). It's worth noting that the BHandHLYP results provide consistent first hyperpolarizability pictures with respect to the CAM-B3LYP method verified also by the M06-2X approach (Figure 5). Different functionals have almost no significant influence on the dipole moments. However, the β values of M06-2X are slightly smaller than values of CAM-B3LYP and BHandHLYP. This means that β value is sensitive to functionals. It is because dipole moment µ is a first rank tensor, while β is a third rank tensor. To discuss these results in more detail, we use the data of the BHandHLYP functional to evaluate the trend of dipole moments and first hyperpolarizabilities.

23



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Table 5. Dipole moments (au), components of first hyperpolarizabilities β (10-30 esu, using Convention T), total first hyperpolarizabilities (10-30 esu), and projection of β on dipole moment (10-30 esu) of the complexes computed at various levels of theory. Complex Functionals BHandHLYP 1 M06-2X CAM-B3LYP BHandHLYP 2+ M06-2X CAM-B3LYP BHandHLYP 2 M06-2X CAM-B3LYP BHandHLYP 3+ M06-2X CAM-B3LYP BHandHLYP 3 M06-2X CAM-B3LYP

µy -0.24 -0.26 -0.24 -2.92 -2.91 -2.94 -0.45 -0.50 -0.43 3.38 3.36 3.39 4.53 4.54 4.53

µtot 0.24 0.26 0.24 2.95 2.94 2.97 0.46 0.52 0.44 3.40 3.38 3.40 4.54 4.54 4.54

βx βy βz 1.8 15.1 0.0 1.0 14.1 0.0 1.0 13.9 0.0 -0.3 53.9 1.1 -0.3 50.9 1.1 -0.3 49.1 1.0 2.6 -19.4 -8.4 2.3 -11.6 -9.3 2.9 -26.2 -11.3 0.1 -3.1 0.0 0.0 -3.2 0.0 0.0 -3.2 0.0 1.8 35.3 0.0 0.0 17.8 0.0 1.4 35.5 0.0

βtot 15.1 14.2 13.9 53.9 51.0 49.1 21.3 15.1 28.6 3.1 0.5 3.2 35.3 17.8 35.5

βvec -14.9 -14.0 -13.8 -53.4 -50.5 -48.6 21.0 13.5 28.1 -3.0 -0.4 -3.2 35.3 17.8 35.5

Figure 5. Relationship between the βtot values of the complexes computed at various levels of theory.

In all cases, the dipole moments are strong apart from that of complex 1, which is due to that ground-state C60 is not a sufficiently strong electron acceptor unless very 24


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strong electron donors are employed. The principal component of dipole moment is

µ y . The signs of µ y of 3+ and 3 are opposite to those of complexes 1, 2+ and 2 which is supported by the opposite charge distribution implied by the total molecular electronic potential (MEP) as shown in Figure S1. As described by the magnitude of the respective dipole moment, dipole moments increase as µtot1 < µtot2 < µtot2+ < µtot3+ < µtot3. The βyyy tensorial component with some contributions of βxyy and βyzz tensorial

components is the dominant one that describes the βtot responses with respect to the rest tensorial components (Table S6), leads inevitably to the largest βy total component (Table 3). In all species, βtot is dictated by only one of its three independent tensorial components and thus the charge transfer is unidirectional and parallel to the molecular dipole moment, the βvec values are found very identical to the corresponding βtot ones. Except for inner complex 2, the βz values of other complexes are given as close to 0 esu. Complex 2 has considerable βz values. It is due to that Li was encapsulated inside of the fullerene cages but not the center of C60 cage. As a result, the symmetry along z-direction was broken significantly in the complex. Inspection of electron density difference maps (EDDM) corresponding to the most intense electronic transition of complex 2 clearly revealed that the distinct intramolecular charge transfer within C60 cage was along z direction and the amount of charge transfer along the z+ and z- direction are not equal. In order to investigate the effect of Li+ and Li atom on the first hyperpolarizability of the parent 1 and more importantly to solve an interesting issue that if the first hyperpolarizability values of the doped complexes dependent on the doping position, 25



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comparative analysis of βtot values in systems 1, 2+, 3+ and 1, 2, 3 were carried out. By incorporating the Li+ into C60 cage, the inner somer C20H10/Li+@C60 (2+) can exhibit considerable βtot values of 5.39×10-29 esu, almost 4 times larger as compared to that of the undoped C20H10/C60 (only 1.51×10-29 esu). Unexpectedly, Li+ doped outer one C20H10/Li+C60 (3+) shows a small βtot value of 3.1×10-30 esu with a decrease of 1.2 ×10-29 esu from its undoped case. It is the result from that opposite electronic transition patterns that are intra- and intermolecular CT transitions in one intense electronic transition, which has been associated to doubly degenerate excited states labeled as S20 and S36. After doping Li atom, the inner isomer C20H10/Li@C60 (2) can present the βtot value as 2.31×10-29 esu, significantly greater than complex 1. Amazingly, the βtot value of outer case C20H10/LiC60 (3) is 3.53 ×10-29 esu, larger with respect to that of inner one 2, in which the s valence electron of the alkali Li atom is pulled to produce the diffuse excess electron owing to the electron-withdrawing characteristic of C60 cage. It is found that encapsulated Li+@C60 and Li@C60 show enhanced electron acceptability as compared to pristine C60. Further, the diffuse excess electron of Li atom in outer isomer C20H10/LiC60 brings the considerable first hyperpolarizabilities because it can exhibit the intriguing ntype characteristic. The measured βtot value of P-nitroaniline (pNA), as the typical organic D-A molecule, in the experiment of was 9.2×10-30 esu.78 In order to make a reasonable comparison between the systems we studied and pNA, the βtot values of pNA have been calculated using three functionals (BHandHLYP, M06-2X and CAM-B3LYP). The results are 5.1×10-30 esu, 4.6×10-30 esu and 5.3×10-30 esu, respectively. The 26


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calculated values were a little less than experiment value, which is due to that the test condition is at 1064 nm laser so that there will be a resonance effect. On the other hand, the influence of the DFT functional on the β values is also a problem. At a given methodology BHandHLYP, the results show that the βtot values of complex 3 are about 7 times larger with respect to that of pNA. But for system 3+, the βtot value decreased to a certain degree which attributed to the exact opposite electronic transition patterns. However, it is noteworthy that the largest βtot value of complex 2+ was 53.9×10-30 esu (BHandHLYP), which was about 11 times larger as compared to that of pNA. The molecular first hyperpolarizability which evaluates the second-order NLO efficiency, can be predicted from two-level model79-81 that links the β value and the low-lying CT character. The two-level SOS expression for β in the T-convention is probably expressed by Willettset al.82, 83

βT = 9

f os ∆µ ge 3 ∆E ge

(14)

where ∆µ ge = µ ee − µ gg is the difference of dipole moment between the ground and crucial excited state, µee and µgg are the ground and excited state dipole moments, fos is the oscillator strength, ∆E ge is the transition energy. Hence, the ∆E ge values might be considered as the decisive factors in effecting the β values, whilst fos and ∆µ ge are also important ones. The contributions of all excited states we listed in Table 4 to the two-level model expression were taken into account. The sum of βT values of all excited states has been calculated for five complexes, respectively. The results have been listed in Table 27



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S7 (shown in supporting information). It is found that the sum of βT values show an increasing trend, that is, βT3+ < βT1

Second-Order Nonlinear Optical Response of Electron Donor

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