Computational Study on Redox-Switchable Second-Order Nonlinear

Article pubs.acs.org/JPCC

Computational Study on Redox-Switchable Second-Order Nonlinear Optical Properties of Totally Inorganic Keggin-Type Polyoxometalate Complexes Chun-Guang Liu*,†,‡,§ and Xiao-Hui Guan† †

College of Chemical Engineering, Northeast Dianli University, Jilin City, 132012, People’s Republic of China Institute of Functional Material Chemistry, Faculty of Chemistry, Northeast Normal University, Changchun 130024, People’s Republic of China § State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China ‡

ABSTRACT: The electronic structure and second-order nonlinear optical (NLO) property of a series of monoruthenium-substituted Keggin-type polyoxometalates (POMs) have been studied by using density functional theory (DFT) and time-dependent (TD)DFT calculations. The DFT calculation supports that these POM complexes possess donor-π-conjugated bridge-acceptor (D-π-A) structure, which the ruthenium atom acts as the role of electron donor and the three vanadium atoms in cap region of Keggin-type POM act as the role of electron acceptor. It is well-known that D-π-A structure, as a simple molecular scheme, has been successfully used in the development of organic NLO materials. However, the totally inorganic molecule having D-π-A structure is very rare. Thereby the second-order NLO properties of these POM complexes have been analyzed in this work. According to the calculations, introduction of the electron acceptor leads to a substantial enhancement on the second-order NLO response. The calculated βHRS(−2ω; ω, ω) value of three-vanadium-atom derivative [{PW9V3O39}RuII(H2O)]8− is 34 times as large as that of [{PW11O39}RuII(H2O)]5− according to CAM-B3LYP/6-31+g* calculations (Lanl2dz basis sets for metal atom) in acetonitrile. Because of the redox-active ruthenium center and large second-order NLO response, the redox switching of second-order NLO responses for the three-vanadium-atom derivative [{PW9V3O39}RuII(H2O)]8− also have been studied. The results show that the RuII→RuIII oxidation leads to the first hyperpolarizability to decrease remarkably.

1. INTRODUCTION The design and synthesis of nonlinear optical (NLO) molecular materials have received tremendous attention owing to their unique applications in optical fibers, data storage, optical limiting, optical computing, optical switching, signal processing, etc.1,2 Much effort has been devoted to develop second-order NLO molecular materials.3 Generally, the reported secondorder NLO materials may be simply classified into two types, inorganic and organic NLO materials. The inorganic NLO materials possess good stability relative to the organic species. For about four decades, many kinds of inorganic NLO materials have been reported, such as inorganic salts, inorganic oxides, quantum dots, semiconductors, cluster compounds, etc.4 Moreover, some inorganic oxide NLO materials (KH2PO4 (KDP), LiNbO3, β-BaB2O4 (BBO), and LiB3O5 (LBO)) have been successfully commercialized.5 However, inorganic NLO materials cannot offer a photoelectric coefficient as large as that of some typical organic NLO molecules. The donor-π-conjugated bridge-acceptor (D-π-A) model, as a simple molecular scheme, has been widely used in the development of second-order organic NLO materials. 6 © XXXX American Chemical Society

However, the application of this scheme was just limited in the organic molecules. By contrast, the totally inorganic molecule with the D-π-A structures is very rare. We have been seeking the totally inorganic compound with D-π-A structure. According to our time-dependent density functional theory (TDDFT) calculations, a transition-metal-trisubstituted polyoxometalate (POM) unit displays the typical D-π-A structure.7 In this D-π-A model, the trimetal centers (red color) act as the role of electron acceptor, and the rest of POM unit displays the electron donor and conjugated bridge character (see Chart 1). The switching of second-order NLO responses is interesting owing to they are potentially useful for the development of electro-optic devices.8 A numbers of meaningful studies have been reported. As a pioneer, Coe and co-worker synthesized a series of ruthenium-based metal complexes.8a,9 The hyperRayleigh scattering (HRS) experiments showed that RuII→RuIII Received: January 7, 2013 Revised: March 25, 2013

A

dx.doi.org/10.1021/jp400185a | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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2. COMPUTATIONAL DETAILS All of the geometries were optimized at B3LYP/6-31g(d) levels,15 as implemented in the GAUSSIAN 09 program.16 Considering the relativistic effects for metal atom, the Lanl2DZ basis set 17 containing effective core potential (ECP) representations of electrons near the nuclei was applied for metal atoms in this work. All of the geometries were characterized as energy minima at the same level. The frequency-dependent hyperpolarizabilities have been calculated using TDDFT method18 with the long-rang corrected CAM-B3LYP functional19 and a wavelength of 1064 nm. Solvent effects have been considered and modeled using the integral equation formulizm polarized continuum model (IEFPCM).20 A dielectric constant of acetonitrile has been employed in this work. The 6-31+g(d) basis sets on main group atoms and Lanl2DZ basis sets on metal atoms were used for all hyperpolarizability calculations in this work. It is known that the conventional DFT-derived result sometimes overestimates the first hyperpolarizabilities of D-π-A systems because of the incorrect long-range charge transfer behaviors between donor and acceptor.21 Although the long-rangcorrected functional has been proposed to specifically overcome this problem,19,22 the improvements of this functional do not hold for all properties. Therefore, the TDHF method,23 as a reference, also has been carried out to calculate the frequencydependent hyperpolarizability in this work. Experimentally, there are two main measurable second-order NLO responses, HRS and electric field-induced second harmonic generation (EFISHG) responses. HRS is the only experimental method to allow measuring the second-order NLO response for the charged POM species in this work. Thus, only the HRS response has been considered in this work. Theoretically, Champagne et al. developed an effective method to estimate the HRS responses.10,24 The second-order NLO response βHRS(−2ω; ω, ω) that can be extracted from HRS data is given by Bersohn’s expression24

Chart 1. Polyhedral Representation of the Donor−Acceptor Substituted Wells-Dawson POM Structurea

a

The gray and red octahedrons signify the electron donor and acceptor in this scheme, respectively.

oxidation of these ruthenium-supported complexes caused the first hyperpolarizability to decrease very substantially.8a However, the reproducible property of this kind of molecular switch can only afford a few cycles because of a series of complicated reasons,9b one of which is the redox instability of organic ligand, which may partially account for this bad reproducibility of the signal. Meanwhile, the quantum chemical calculation also has been performed to probe the switching of the second-order NLO responses. The switching of secondorder NLO response utilizing the photochemical conversion or protonation has been probed by Champagne et al. according to their TD Hartree−Fock (HF), TDDFT, coupled perturbed (CP)HF, and Møller−Plesset (MP2) calculations.10 POMs are early transition metal oxo clusters; this class of inorganic compound is unmatched not only in terms of molecular structural diversity but also due to their rich redox, electronic, and optical properties,11 one of which is their high redox stability which makes POMs excellent candidates as “electron reservoirs”. This may provide a good basis in the development of redox switching of second-order NLO response utilizing totally inorganic POM materials. However, the typical POMs, such as Keggin- and Wells-Dawson-type POMs, are centrosymmetric. A prerequisite to second-order NLO molecule is the molecular noncentrosymmetry. Introduction of the transition metal ion into the POM unit would break the symmetry and achieve the noncentrosymmetrical structure. Thus, the transition-metal-substituted POM would possess potential second-order NLO response. The nature (such as nd configuration, oxidation state, spin state) of transition metal ion is a very important factor in determination of the physical and chemical properties of the transition-metal-substituted POM. Because of the unique redox-active nature of ruthenium, ruthenium-substituted POMs are highly desired.12 A large number of ruthenium-substituted POMs have been investigated experimentally13 and theoretically.14 To date, the search for novel POM structures containing ruthenium is still a hot area of research in POM chemistry. On the basis of our previous report,7 transition-metaltrisubstituted POM complexes possess D-π-A structure and the second-order NLO response of a series of new Keggin-type POM systems will be probed in this work. The aim of this work is (i) further optimizing second-order NLO properties of the totally inorganic POM compound based on the D-π-A model; (ii) redox switching of the second-order NLO properties by introducing the ruthenium center into Keggin-type POM unit.

βHRS( −2ω; ω , ω) =

2 2 {⟨βZZZ ⟩ + ⟨βXZZ ⟩}

(1)

The depolarization ratio (DR), which is associated with the shape of the NLO-phore, given by DR =

2 ⟨βZZZ ⟩ 2 ⟨βXZZ ⟩

(2)

⟨β ZZZ⟩ and are orientational averages of the β-tensor, which were calculated without assuming Kleiman’s conditions.25 In order to obtain a more intuitive description of the trends in the NLO behavior of the studied compounds, TDDFT calculations26 were carried out at the B3LYP/6-31g(d) level (Lanl2DZ basis set for metal atom) in acetonitrile to determine the nature of the excited states. It has been proved that TDDFT is a usefully accurate approach for many applications, especially, low-lying single excitations. TDDFT is the most popular method for calculating excitations currently. 2

⟨β2XZZ⟩

3. RESULTS AND DISCUSSION It is well-known that the nature of frontier molecular orbital (FMO) of the molecule with D-π-A structure is the series of localized molecular orbital in which the highest occupied molecular orbital (HOMO) is mainly localized on the end of the electron donor, and the lowest unoccupied molecular B



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Figure 1. Ball-and-stick representation of the series of monoruthenium-substituted Keggin-type POM complexes.

Figure 2. The frontier molecular orbital of two monoruthenium-substituted Keggin-type POM ([{PW11O39}RuII(H2O)]5− for panel a; [{PW9V3O39}RuII(H2O)]8‑ for panel b.

GAUSSIAN 09 program package, a dielectric constant of acetonitrile have been employed for solvent considerations. The calculated FMO has been shown in Figure 2. We note that all of the monoruthenium-substituted POM complexes studied here possess analogous nature of the FMO. Thus the POM complex [{PW11O39}RuII(H2O)]5− has been employed as an example to analyze the orbital nature. As shown in Figure 2, the HOMO of this POM complex is mainly localized on the ruthenium(II) center. The LUMO is still delocalized over the whole surface of the Keggn-type POM. This result shows that introduction of the ruthenium(II) atom into POM cluster leads to a localized HOMO. But it cannot affect the delocalized nature of the LUMO and adjacent unoccupied orbtials. Inspired by previous works of our group,7 we decided to introduce the vanadium atom into monoruthenium-substituted Keggin-type POM to design a new POM complex [{PW9V3O39}RuII(H2O)]8−, where three vanadium atoms have been assigned to replace the three tungsten atoms in cap region of the Keggin-type POM complex (see Figure 1). We hope that the ruthenium(II) center still displays the nature of electron donor, and the three vanadium atoms in cap region will act as the role of the electron acceptor in this new POM

orbital (LUMO) is mainly localized on the end of the electron acceptor.6 Thus, the orbital transition from HOMO to LUMO will generate a significant charge transfer from donor to acceptor. However, the FMO of the nonsubstituted Keggintype POM complexes are the series of delocalized MO in which the HOMO is formally delocalized over oxo-ligands and LUMO is delocalized over the d-shells of tungstens. Both orbitals are delocalized over the whole molecule.27 In order to obtain the D-π-A structure for these totally inorganic POMs, we introduce the ruthenium atom into the mono lacunary Keggin-type POM to design a series of monoruthenium-substituted Keggin-type POM complexes. Because of the introduction of the ruthenium into the Keggin-type POM unit, the centrosymmetry of the Keggintype POM has been broken. All of the studied systems in this work are noncentrosymmetrical. The ruthenium(II) center is expected to display the role of the electron donor. Meanwhile, the substituted effects of the end ligand (L) also have been considered in this work (see Figure 1, L = H2O, DMSO, Cl−, NH3). It should be stressed that the highly charged anions do not exist in the gas phase. Thus, single point calculations with their optimized geometries in gas phase, IEFPCM in C



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Table 1. The Transition Energy (ΔE, eV), Oscillator Strengths ( fos), and Major Assignment of Optical Transitions for MonoRuthenium-Substituted Keggin-Type POM Complexes Obtained by TDDFT Calculation in Acetonitrile at B3LYP/6-31g(d) Level (Lanl2dz Basis Sets on Metal Atoms) excited state

fos

ΔE (eV)

composition

major assignment

[{PW11O39}Ru (H2O)]

S1 S6a

0.004 0.008

1.49 1.87

[{PW11O39}RuII(Cl)]6−

S1

0.000

1.60

S3a S1 S3a S1 S2a S1 S2a

0.006 0.002 0.011 0.004 0.005 0.001 0.017

1.67 1.90 2.19 1.36 1.56 0.34 0.44

HOMO→LUMO(+91%) HOMO→LUMO+2(+48%) HOMO→LUMO+3(+34%) HOMO-1→LUMO+16(+41%) HOMO-1→LUMO+13(+12%) HOMO-1→LUMO+4(+11%) HOMO→LUMO(+82%) HOMO→LUMO(+71%) HOMO→LUMO+1(+92%) HOMO→LUMO(+91%) HOMO→LUMO+1(+81%) HOMO→LUMO+1(+95%) HOMO→LUMO(+100%)

Ru→W Ru→W Ru→W Ru→W Ru→W Ru→W Ru→W Ru→W Ru→W Ru→W Ru→W Ru→V Cap Ru→V Cap

complexes II

5−

II

[{PW11O39}Ru (DMSO)]

5−

[{PW11O39}RuII(NH3)]5− [{PW9V3O39}RuII(H2O)]8− a

The crucial excited state.

transition energy of the first and crucial excited states of the three-vanadium-atom derivative is lowest among all POM complexes studied here. In the two-level model, the cubic of the transition energy is inversely proportional to the β-value. Thus, the low transition energy is the decisive factor in the large first hyperpolarizability. The relevant low transition energy and large oscillator strength will generate a large increase in the hyperpolarizability. This prediction based on the two-level model will be checked on later. It is important to produce theoretical results that compare more directly to the experiment for the HRS. The frequencydependent hyperpolarizabilities βHRS(−2ω; ω, ω) of all POM complexes have been calculated using TDHF and TDDFT method with CAM-B3LYP functional at 6-31+g(d) levels in acetonitrile (Lanl2dz basis sets for metal atoms). In all the studied systems, the charge transfer axes are chosen as Z-axis. The calculated βHRS(−2ω; ω, ω) values and DR values have been listed in Table 2. It can be found that (i) the βHRS values

complex. The calculated FMO of this POM complex also has been compared in Figure 2. It can be found that the HOMO is still localized on the ruthenium(II) center, and the LUMO and its adjacent unoccupied orbital is mainly localized on the three vanadium atoms in cap region. The tungsten atoms in belt region also have some contributions. Thus, the nature of FMO with the D-π-A structure has been obtained in this POM complex. In order to get the nature of the charge-transfer excitation, we have performed the TDDFT calculation for these POM complexes studied here. The TDDFT calculated transition energies, oscillator strength of first excited state and crucial excited state, together with orbital transition of the most important contributions to these excited states are summarized in Table 1. The crucial excited state is the lowest excited state with relatively large oscillator strength among all excited states calculated by TDDFT calculations. The first excited state of [{PW11O39}RuII(H2O)]5− is generated by the promotion of one electron from HOMO to LUMO. Because of the little overlap between the two orbitals, such electron transitions are forbidden, reflecting the small oscillator strength (fos) (see Figure 2 and Table 1). By contrast, the crucial excited state of the POM complex [{PW11O39}RuII(H2O)]5− arises from HOMO→LUMO+2 and HOMO→LUMO+3 transitions. These molecular orbitals are shown in Figure 2. It can be seen that the two unoccupied orbitals (LUMO+2 and LUMO +3) are localized on the tungsten atoms of the surface of the whole cluster (see Figure 2). These excitations mostly consist of charge transfer from the ruthenium(II) center to the whole molecule. The results also show that the ruthenium(II) center displays the role of the electron donor. As shown in Table 1, the substituted effects of the end ligand cannot largely affect the nature of the orbital transition. All of the monorutheniumsubstituted POM complexes have the same nature of excitations according to our TDDFT calculations. The first and crucial excited states of the three-vanadiumatom derivative arise from the HOMO→LUMO+1 and HOMO→LUMO, respectively (see Table 1). As mentioned above, these molecular orbitals all display the localized character (see Figure 2). Thus, these excitations will generate a more significant charge transfer from the ruthenium(II) center to three vanadium atoms than that of the POM complex [{PW11O39}RuII(H2O)]5−. We also note that the calculated

Table 2. Frequency-Dependent Hyperpolarizabilities βHRS(−2ω; ω, ω) (in Atomic Unitsa, λ = 1064 nm) of Mono-Ruthenium-Substituted Keggin-Type POM Complexes Obtained by the HF and CAM-B3LYP Functional at 6-31+g(d) Levels in Acetonitrile (Lanl2dz Basis Sets for Metal Atoms) complexes [{PW11O39}RuII(H2O)]5− [{PW11O39}RuII(Cl)]6− [{PW11O39}RuII(DMSO)]5− [{PW11O39}RuII(NH3)]5− [{PW9V3O39}RuII(H2O)]8− [PW9V3O40] CH3CN

a

D

6−

method

βHRS

DR

HF CAM-B3LYP HF CAM-B3LYP HF CAM-B3LYP HF CAM-B3LYP HF CAM-B3LYP HF CAM-B3LYP HF CAM-B3LYP

260 957 276 1055 311 552 238 1154 625 11188 571 1088 34 57

2.05 2.34 1.67 7.99 1.49 3.99 1.73 0.43 4.51 7.89 5.22 7.97 3.01 4.37

1 au = 3.62 × 10−42 m4 V−1 = 8.64 × 10−33 esu. dx.doi.org/10.1021/jp400185a | J. Phys. Chem. C XXXX, XXX, XXX−XXX


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Table 3. Comparison of the Redox-Switchable Second-Order NLO Properties, Frequency-Dependent Hyperpolarizabilities βHRS(−2ω; ω, ω) (in Atomic Units, λ = 1064 nm), of Two Mono-Ruthenium-Substituted Keggin-Type POM Complexes [{PW9V3O39}RuII(H2O)]8−‑ and [{PW11O39}RuII(H2O)]5− complexes II

[{PW9V3O39}Ru (H2O)]

8−

[{PW9V3O39}RuIII(H2O)]7− [{PW11O39}RuII(H2O)]5− [{PW11O39}RuIII(H2O)]4−

method

βHRS

DR

fos

ΔE (eV)

HF CAM-B3LYP HF CAM-B3LYP HF CAM-B3LYP HF CAM-B3LYP

625 11188 433 760 260 957 231 327

4.51 7.89 1.36 6.95 2.05 2.34 1.60 2.14

0.017

0.44

0.002

2.15

0.008

1.87

0.001

2.41

6-31+g* calculations (see Table 2). This indicates that this POM complex has excellent second-order NLO properties in totally inorganic compounds. The question we are now concerned with is the redox properties of the monoruthenium-substituted Keggin-type POMs. There is no doubt that the redox property of the molecule is closely associated with the nature of the FMO. As shown in Figure 2 and mentioned above, the HOMOs of both monoruthenium-substituted Keggin-type POMs are localized on the ruthenium(II) center. This indicates that the ruthenium(II) atom will be the one-electron-oxidized center. In order to check the predication from molecular orbital analysis, the spin unrestricted calculation has been performed for the oneelectron-oxidized species of both monoruthenium-substituted Keggin-type POMs in this work. The geometries of both oneelectron-oxidized species have been optimized at UB3LYP/631g(d) levels (Lanl2dz basis sets for metal atoms). And the spin density of both POMs has been calculated at the same level. The result shows that the spin density of both monoruthenium-substituted Keggin-type POMs is mainly localized on the ruthenium center (0.8). This also supports that the ruthenium(II) center is still the one-electron-oxidized center, which is well in agreement with the molecular orbital prediction. On the basis of the large second-order NLO response of the three-vanadium-atom derivative, the frequency-dependent hyperpolarizability βHRS(−2ω; ω, ω) of the one-electronoxidized species of [{PW9V3O39}RuII(H2O)]8− has been calculated in acetonitrile by using HF and CAM-B3LYP functional at 6-31+g* levels (Lanl2dz basis sets on the metal atoms). The calculated values have been compared in Table 3. It can be found that the RuII→RuIII oxidation lead to the first hyperpolarizability and DR value to decrease according to both methods. The HF-derived result shows that the calculated βHRS(−2ω; ω, ω) value of the one-electron-oxidized species (RuIII) is ∼1.5 times as small as that of the divalent species. And the CAM-B3LYP calculation indicates that the calculated βHRS(−2ω; ω, ω) value of the one-electron-oxidized species (RuIII) is ∼15 times as small as that of the divalent species. The TDDFT calculations were carried out to obtain the crucial state of trivalent and divalent species. The transition energy and the oscillator strengths of the crucial excited states for both species are also listed in Table 3. It can be found that the transition energy of the trivalent species is larger than that of the divalent species (2.15 versus 0.44 eV). According to twolevel model, the third power of the transition energy is inversely proportional to the β value; it will generate a ∼116-fold increase in β, regardless of all other factors for both species. Thus, we believe that the HF calculations without the electron-

of all POM complexes are sensitive to the choice of methods. The calculated βHRS(−2ω; ω,ω) value of all POM complexes derived by long-range-corrected functional, CAM-B3LYP, is larger than that of the HF method without electron-correlation effect. (ii) The substituted effect of the end ligand does not significantly affect the βHRS(−2ω; ω, ω) and DR values such as the calculated βHRS values for POM complexes ([{PW11O39}RuII(L)]n−, L = H2O, Cl−, DMSO, NH3) range from 238 to 311 au and the calculated DR values range from 1.5 to 2 according to HF calculations. (iii) A significant enhancement for the calculated βHRS(−2ω; ω, ω) and DR values has been yielded in the three-vanadium-atom derivative according to both HF and DFT calculations. For example, the calculated βHRS(−2ω; ω, ω) value of [{PW9V3O39}RuII(H2O)]8− is ∼34 times as large as that of [{PW11O39}RuII(H2O)]5− according to CAM-B3LYP/6-31+g* calculations. In order to evaluate the ruthenium-substituted effect on the second-order NLO response in our D-π-A model, the frequency-dependent first hyperpolarizability of the three vanadium atoms derivatives [PW9V3O40]6− (there is no ruthenium atom in this reference cluster) also has been calculated at the same levels in this work. The calculated βHRS(−2ω; ω, ω) value has been compared in Table 2. It can be found that an enhancement on the second-order NLO properties caused by introduction of the ruthenium atom into Keggin-type POMs has been achieved. The calculated βHRS(−2ω; ω, ω) value of [{PW9V3O39}RuII(H2O)]8‑ is 10 times as large as that of [PW9V3O40]6− according to CAMB3LYP calculation (1088 versus 11 188 au). We also note that introduction of the ruthenium atom leads to the DR value to decrease according to both of HF and CAM-B3LYP calculations. Besides the ruthenium-substituted effect on the second-order optical nonlinearity, introduction of the ruthenium atom into Keggin-type POMs also provides an activeredox center for switching of second-order NLO responses. For a purpose of comparison, the frequency-dependent hyperpolarizability βHRS(−2ω; ω, ω) of acetonitrile molecule has been calculated at the same theoretical level in this work (see Table 2). The results show that the HF/6-31+g* calculations is well in agreement with the experimental data24b (34 versus 33 ± 3 au). By contrast, the CAMB3LYP/6-31+g* calculation overestimates the experimental results for acetonitrile (57 versus 33 ± 3 au) because of the incorrect electron correction consideration for the first hyperpolarizability calculation, which demonstrates again that the improvements of this functional do not hold for all properties. As shown in Table 2, the calculated βHRS(−2ω; ω, ω) value of [{PW9V3O39}RuII(H2O)]8− is about 18 times as large as that of organic acetonitrile molecule according to HF/ E



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three-vanadium-atom derivative mainly comes from the very low-lying transition energy of the [{PW9V3O39}RuII(H2O)]8−.

correlation effect may underestimate this redox-switchable second-order NLO responses. Such large change of transition energy caused by the one-electron-oxidized process is a decisive factor for this redox-switchable second-order NLO properties. To assess the three-vanadium-atom substituted effects on the redox switching of second-order NLO properties, the βHRS(−2ω; ω, ω) value of the monoruthenium-substituted Keggin-type POM [{PW11O39}RuII(H2O)]5− and its oneelectron-oxidized species also have been calculated in this work. The calculated frequency-dependent hyperpolarizability and DR value also have been listed in Table 3. It can be found that a decrease of βHRS(−2ω; ω, ω) value caused by the RuII→ RuIII oxidation also has been found in this system. The calculated βHRS(−2ω; ω, ω) value of the one-electron-oxidized species (RuIII) is ∼1.1 and 3.0 times as small as that of the divalent species according to both HF and CAM-B3LYP calculations, respectively. This indicates that redox-switchable effect on the second-order NLO properties of this POM complex is not significant when compared with the threevanadium-atom derivative. The calculated transition energy of the crucial excitation for both compounds also listed in Table 3. We found that the difference between them is not substantial (1.87 eV for divalent species versus 2.41 eV for trivalent speices). This result also supports a small difference on the second-order NLO response for both compounds. Thus, threevanadium-atom substituted effects on the redox-switchable second-order NLO properties are significant. As shown in Table 3, the calculated transition energy of the three-vanadium-atom derivative with divalent species [{PW9V3O39}RuII(H2O)]8− is smallest among four monoruthenium-substituted Keggin type POM compounds 0.44 eV. By contrast, the magnitude of the ΔE for the three-vanadiumatom derivative with trivalent species [{PW 9 V 3 O 39 }RuIII(H2O)]7− is on the same order when compared with the [{PW11O39}RuIII(H2O)]4−. Thus, the remarkable redox-switchable second-order NLO effect of the three-vanadium-atom derivative mainly comes from the very low-lying transition energy of the [{PW9V3O39}RuII(H2O)]8−.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 86 0432 64806919. Fax: 86 0432 64806919. Present Address

(C.-G.L.) No. 169, Changchun Road, Jilin City, People’s Republic of China. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author gratefully acknowledges the Scientific Research Foundation for Doctor of Northeast Dianli University (BSJXM201110).

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REFERENCES

(1) (a) Albota, M.; Beljonne, D.; Brédas, J.-L.; Ehrlich, J. E.; Fu, J.-Y.; Heikal, A. A.; Hess, S. E.; Kogej, T.; Levin, M. D.; Marder, S. R.; et al. Design of Organic Molecules with Large Two-Photon Absorption Cross Sections. Science 1998, 281, 1653−1656. (b) Shi, Y.; Zhang, C.; Zhang, H.; Bechtel, J. H.; Dalton, L. R.; Robinson, B. H.; Steier, W. H. Low (Sub-1-V) Halfwave Voltage Polymeric Electro-optic Modulators Achieved by Controlling Chromophore Shape. Science 2000, 288, 119−122. (c) Lee, M.; Katz, H. E.; Erben, C.; Gill, D. M.; Gopalan, P.; Heber, J. D.; McGee, D. J. Broadband Modulation of Light by Using an Electro-Optic Polymer. Science 2002, 298, 1401−1403. (d) Garvey, D. W.; Zimmerman, K.; Young, P.; Tostenrude, J.; Townsend, J. S.; Zhou, Z.; Lobel, M.; Dayton, M.; Wittorf, R.; Kuzyk, M. G. SingleMode Nonlinear-Optical Polymer Fibers. J. Opt. Soc. Am. B 1996, 13, 2017−2023. (e) Elim, H. I.; Ji, W.; Meng, G. C.; Ouyang, J.; Goh, S. H. Nonlinear Optics and Optical Limiting Properties of Multifunctional Fullerenol/Polymer Composite. J. Nonlinear Opt. Phys. Mater. 2003, 12, 175−186. (f) Green, K. A.; Cifuentes, M. P.; Corkery, C.; Smaoc, M.; Humphrey, M. G. Switching the Cubic Nonlinear Optical Properties of an Electro-, Halo-, and Photochromic Ruthenium Alkynyl Complex Across Six States. Angew. Chem., Int. Ed. 2009, 48, 7867−7870. (2) Dalton, L. R.; Sullivan, P. A.; Bale, D. H. Electric Field Poled Organic Electro-optic Materials: State of the Art and Future Prospects. Chem. Rev. 2010, 110, 25−55. (3) (a) Burlan, D. Optical Nonlinearities in Chemistry: Introduction. Chem. Rev. 1994, 94, 1−2. (b) Delarire, J. A.; Nakatani, K. Linear and Nonlinear Optical Properties of Photochromic Molecules and Materials. Chem. Rev. 2000, 100, 1817−1846. (c) de la Torre, G.; Vazquez, P.; Agullo-Lopez, F.; Torres, T. Role of Structural Factors in the Nonlinear Optical Properties of Phthalocyanines and Related Compounds. Chem. Rev. 2004, 104, 3723−3750. (d) Ray, P. C. Size and Shape Dependent Second Order Nonlinear Optical Properties of Nanomaterials and Their Application in Biological and Chemical Sensing. Chem. Rev. 2010, 110, 5332−5365. (e) Wang, C.; Zhang, T.; Lin, W. Rational Synthesis of Noncentrosymmetric Metal−Organic Frameworks for Second-Order Nonlinear Optics. Chem. Rev. 2012, 112, 1084−1104. (4) (a) Wes, R. S.; Gaylord, T. K. Lithium Niobate: Summary of Physical Properties and Crystal Structure. Appl. Phys. A 1985, 37, 191−203. (b) Klein, M. B.; Dunning, G. J.; Valley, G. C.; Lind, R. C.; O’Meara, T. R. Imaging Threshold Detector Using a Phase-Conjugate Resonator in BaTiO3. Opt. Lett. 1986, 11, 575−577. (c) Nie, W. Optical Nonlinearity: Phenomena, Applications, and Materials. Adv. Mater. 1993, 5, 520−545. (d) Hou, H. W.; Wei, Y. L.; Song, Y. L.; Mi, L. W.; Tang, M. S.; Li, L. K.; Fan, Y. T. Metal Ions Play Different Roles in the Third-Order Nonlinear Optical Properties of d10 Metal− Organic Clusters. Angew. Chem., Int. Ed. 2005, 44, 6067−6074.

4. CONCLUSION We have demonstrated that the series of monorutheniumsubstituted Keggin-type POM complexes possess D-π-A structure in which the ruthenium center acts as the role of the electron donor and the three vanadium atoms in the cap region of Keggin-type POM act as the role of electron acceptor according to FMO analysis and TDDFT calculations. The frequency-dependent hyperpolarizability calculations show that introduction of the ruthenium atom into the Keggin-type POM unit only leads to a small enhancement on the βHRS(−2ω; ω, ω) value. And the three-vanadium-atom-substituted effects lead to the first hyperpolarizability to increase significantly. We also note that the end-ligand-substituted effects do not largely affect the second-order NLO properties of the series of monoruthenium-substituted Keggin-type POM complexes. Because of the redox-active ruthenium center, the redox switching of second-order NLO properties of the three-vanadium-atom derivative [{PW9V3O39}RuII(H2O)]8− also have been considered in this work. The present results show that the RuII→RuIII oxidation leads to the first hyperpolarizability to decrease remarkably. The TDDFT calculation on the nature of the excitation shows that the remarkable contrast on the first hyperpolarizability caused by the RuII→RuIII oxidation in the F



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(e) Chen, X. H.; Wu, K. C.; Snijders, J. G.; Lin, C. S. Electronic Structures and Nonlinear Optical Properties of Trinuclear Transition Metal Clusters M−(μ-S)−M′ (M = Mo, W; M′ = Cu, Ag, Au). Inorg. Chem. 2003, 42, 532−540. (f) Sun, C. F.; Xu, X.; Ling, J. B.; Hu, T.; Kong, F.; Long, X. F.; Mao, J. G. BaNbO(IO3)5: A New Polar Material with a Very Large SHG Response. J. Am. Chem. Soc. 2009, 131, 9486− 9487. (g) Kim, H. S.; Yoon, K. B. Increase of Third-Order Nonlinear Optical Activity of PbS Quantum Dots in Zeolite Y by Increasing Cation Size. J. Am. Chem. Soc. 2012, 134, 2539−2542. (5) (a) Smith, W. L. KDP and ADP Transmission in the Vacuum Ultraviolet. Appl. Opt. 1977, 16, 798−798. (b) Boyd, G. D.; Miller, R. C.; Nassau, K.; Bond, W. L.; Savage, A. LiNbO3: An Efficient Phase Matchable Nonlinear Optical Material. Appl. Phys. Lett. 1964, 5, 234− 236. (c) Chen, C.; Wu, B.; Jiang, A.; You, G. Growth and Properties of a Novel UV Nonlinear Optical Crystal β-BaB2O4. Sci. Sin., Ser. B 1984, 14, 598−604. (d) Chen, C.; Wu, Y.; Jiang, A.; Wu, B.; You, G.; Li, R.; Lin, S. New Nonlinear-Optical Crystal: LiB3O5. J. Opt. Soc. Am. 1989, B6, 616−621. (6) Kanis, D. R.; Ratner, M. A.; Marks, T. J. Design and Construction of Molecular Assemblies with Large Second-Order Optical Nonlinearities. Quantum Chemical Aspects. Chem. Rev. 1994, 94, 195− 242. (7) (a) Liu, C. G.; Guan, W.; Song, P.; Wang, E. B.; Yao, C.; Su, Z. M. Second-Order Nonlinear Optical Properties of Trisubstituted Keggin and Wells-Dawson Polyoxometalates: Density Functional Theory Investigation of the Inorganic Donor-Conjugated BridgeAcceptor Structure. Inorg. Chem. 2009, 48, 8115−8119. (b) Liu, C. G.; Guan, W.; Yan, L. K.; Su, Z. M.; Song, P.; Wang, E. B. Second-Order Nonlinear Optical Properties of Transition-Metal-Trisubstituted Polyoxometalate-Diphosphate Complexes: A Donor-Conjugated Bridge-Acceptor Paradigm for Totally Inorganic Nonlinear Optical Materials. J. Phys. Chem. C 2009, 113, 19672−19676. (8) (a) Coe, B. J.; Houbrechts, S.; Asselberghs, I.; Persoons, A. Efficient, Reversible Redox-Switching of Molecular First Hyperpolarizabilities in Ruthenium(II) Complexes Possessing Large Quadratic Optical Nonlinearities. Angew. Chem., Int. Ed. 1999, 38, 366−369. (b) Coe, B. J. Switchable Nonlinear Optical Metallochromophores with Pyridinium Electron Acceptor Groups. Acc. Chem. Res. 2006, 39, 383−393. (c) Sporer, C.; Ratera, I.; Ruiz-Molina, D.; Zhao, Y.; Vidal-Gancedo, J.; Wurst, K.; Jaitner, P.; Clays, K.; Persoons, A.; Rovira, C.; et al. Molecular Multiproperty Switching Array Based on the Redox Behavior of a Ferrocenyl Polychlorotriphenylmethyl Radical. Angew. Chem., Int. Ed. 2004, 43, 5266−5268. (d) Malaun, M.; Reeves, Z. R.; Paul, R. L.; Jeffery, J. C.; McCleverty, J. A.; Ward, M. D.; Asselberghs, I.; Clays, K.; Persoons, A. Reversible Switching of the First Hyperpolarisability of an NLO-Active Donor− Acceptor Molecule Based on Redox Interconversion of the Octamethylferrocene Donor Unit. Chem. Commun. 2001, 49−50. (9) (a) Coe, B. J. Molecular Materials Possessing Switchable Quadratic Nonlinear Optical Properties. Chem.Eur. J. 1999, 5, 2464−2471. (b) Boubekeur-Lecaque, L.; Coe, B. J.; Clays, K.; Foerier, S.; Verbiest, T.; Asselberghs, I. Redox-Switching of Nonlinear Optical Behavior in Langmuir−Blodgett Thin Films Containing a Ruthenium(II) Ammine Complex. J. Am. Chem. Soc. 2008, 130, 3286−3287. (c) Coe, B. J.; Fielden, J.; Foxon, S. P.; Harris, J. A.; Helliwell, M.; Brunschwig, B. S.; Asselberghs, I.; Clays, K.; Garín, J.; Orduna, J. Diquat Derivatives: Highly Active, Two-Dimensional Nonlinear Optical Chromophores with Potential Redox Switchability. J. Am. Chem. Soc. 2010, 132, 10498−10512. (d) Boubekeur-Lecaque, L.; Coe, B. J.; Harris, J. A.; Helliwell, M.; Asselberghs, I.; Clays, K.; Foerier, S.; Verbiest, T. Incorporation of Amphiphilic Ruthenium(II) Ammine Complexes into Langmuir−Blodgett Thin Films with Switchable Quadratic Nonlinear Optical Behavior. Inorg. Chem. 2011, 10, 12886− 12899. (10) (a) Guillaume, M.; Champagne, B.; Markova, N.; Enchev, V.; Castet, F. Ab Initio Investigation on the Second-Order Nonlinear Optical Responses in Keto−Enol Equilibria of Salicylideneanilines. J. Phys. Chem. A 2007, 111, 9914−9923. (b) Mançois, F.; Sanguinet, L.; Pozzo, J.-L.; Guillaume, M.; Champagne, B.; Rodriguez, V.; Adamietz,

F.; Ducasse, L.; Castet, F. Acido-Triggered Nonlinear Optical Switches: Benzazolo-oxazolidines. J. Phys. Chem. B 2007, 111, 9795− 9802. (c) Plaquet, A.; Guillaume, M.; Champagne, B.; Rougier, L.; Mançois, F.; Rodriguez, V.; Pozzo, J.-L.; Ducasse, L.; Castet, F. Investigation on the Second-Order Nonlinear Optical Responses in the Keto−Enol Equilibrium of Anil Derivatives. J. Phys. Chem. C 2008, 112, 5638−5645. (d) Plaquet, A.; Guillaume, M.; Champagne, B.; Castet, F.; Ducasse, L.; Pozzob, J.-L.; Rodriguez, V. In Silico Optimization of Merocyanine-Spiropyran Compounds as SecondOrder Nonlinear Optical Molecular Switches. Phys. Chem. Chem. Phys. 2008, 10, 6223−6232. (e) Mançois, F.; Pozzo, J.-L.; Pan, J.; Adamietz, F.; Rodriguez, V.; Ducasse, L.; Castet, F.; Plaquet, A.; Champagne, B. Two-Way Molecular Switches with Large Nonlinear Optical Contrast. Chem.Eur. J. 2009, 15, 2560−2571. (f) Bogdan, E.; Rougier, L.; Ducasse, L.; Champagne, B.; Castet, F. Nonlinear Optical Properties of Flavylium Salts: A Quantum Chemical Study. J. Phys. Chem. A 2010, 114, 8474−8479. (g) Bogdan, E.; Plaquet, A.; Antonov, L.; Rodriguez, V.; Ducasse, L.; Champagne, B.; Castet, F. Solvent Effects on the Second-Order Nonlinear Optical Responses in the Keto−Enol Equilibrium of a 2-Hydroxy-1-naphthaldehyde Derivative. J. Phys. Chem. C 2010, 114, 12760−12768. (h) Champagne, B.; Plaquet, A.; Pozzo, J.-L.; Rodriguez, V.; Castet, F. Nonlinear Optical Molecular Switches as Selective Cation Sensors. J. Am. Chem. Soc. 2012, 134, 8101−8103. (11) (a) Hill, C. L. Introduction: Polyoxometalates-Multicomponent Molecular Vehicles To Probe Fundamental Issues and Practical Problems. Chem. Rev. 1998, 98, 1−2. (b) Dolbecq, N.; Dumas, E.; Mayer, C. R.; Mialane, P. Hybrid Organic-Inorganic Polyoxometalate Compounds: From Structural Diversity to Applications. Chem. Rev. 2010, 110, 6009−6048. (12) Naota, T.; Takaya, H.; Murahashi, S.-I. Ruthenium-Catalyzed Reactions for Organic Synthesis. Chem. Rev. 1998, 98, 2599−2660. (13) (a) Adam, W.; Alsters, P. L.; Neumann, R.; Saha-Möller, C. R.; Seebach, D.; Beck, A. K.; Zhang, R. Chiral Hydroperoxides as Oxygen Source in the Catalytic Stereoselective Epoxidation of Allylic Alcohols by Sandwich-Type Polyoxometalates: Control of Enantioselectivity through a Metal-Coordinated Template. J. Org. Chem. 2003, 68, 8222−8231. (b) Neumann, R.; Dahan, M. Molecular Oxygen Activation by a Ruthenium-Substituted “Sandwich” Type Polyoxometalate. J. Am. Chem. Soc. 1998, 120, 11969−11976. (c) Neumann, R.; Dahan, M. A Ruthenium-Substituted Polyoxometalate as An Inorganic Dioxygenase for Activation of Molecular Oxygen. Nature 1997, 388, 353−355. (d) Sadakane, M.; Higashijima, M. Synthesis and Electrochemical Behavior of [SiW11O39RuIII(H2O)]5− and Its OxoBridged Dimeric Complex [SiW11O39RuIVORuIIISiW11O39]11−. Dalton Trans. 2003, 659−664. (e) Bonchio, M.; Scorrano, G.; Toniolo, P.; Proust, A.; Artero, V.; Conte, V. Adamantane Selective Hydroxylation by 2,6-Dichloropyridine N-Oxide and Organoruthenium(II) Polyoxometalates as Catalyst Precursors. Adv. Synth. Catal. 2002, 344, 841− 844. (f) Yamaguchi, K.; Mizuno, N. Heterogeneously Catalyzed Liquid-Phase Oxidation of Alkanes and Alcohols with Molecular Oxygen. New J. Chem. 2002, 26, 972−974. (g) Filipek, K. Synthesis, Characterization and Reactivity of Ruthenium Complexes of the Lacunary Keggin Polyoxoanion: [SiW11O39RuL]n−, L = H2O, NO, N2. Inorg. Chim. Acta 1995, 231, 237−239. (h) Rong, C. Y.; Pope, M. T. Lacunary Polyoxometalate Anions Are π-Acceptor Ligands. Characterization of Some Tungstoruthenate(II,III,IV,V) Heteropolyanions and Their Atom-Transfer Reactivity. J. Am. Chem. Soc. 1992, 114, 2932− 2938. (i) Lahootun, V.; Besson, C.; Villanneau, R.; Villain, F.; Chamoreau, L. M.; Boubekeur, K.; Blanchard, S.; Thouvenot, R.; Proust, A. Synthesis and Characterization of the Keggin-Type Ruthenium-Nitrido Derivative [PW11O39{RuN}]4‑ and Evidence of Its Electrophilic Reactivity. J. Am. Chem. Soc. 2007, 129, 7127−7135. (14) (a) Liu, C. G.; Guan, W.; Yan, L. K.; Su, Z. M. Quantum Chemical Characterization of the Generation of High-Valent Oxoruthenium Species of Keggin Type Polyoxometalates: Electronic Structure and Bonding Features. Dalton Trans. 2011, 2967−2974. (b) Liu, C. G.; Su, Z. M.; Guan, W.; Yan, L. K. Quantum Chemical Studies on High-valent Metal Nitrido Derivatives of Keggin-type G



Article

Polyoxometalates ([PW11O39{MVIN}]4‑ (M=Ru, Os, Re)): MVI-N Bonding and Electronic Structures. Inorg. Chem. 2009, 48, 541−548. (c) Romo, S.; Antonova, N. S.; Carbo, J. J.; Poblet, J. M. Influence of Polyoxometalate Ligands on the Nature of High-Valent Transition Metal Nitrido Species. A Theoretical Analysis of Experimentally Known and Unprecedented Compounds. Dalton Trans. 2008, 5166− 5172. (d) Liu, C. G.; Guan, W.; Yan, L. K.; Su, Z. M. Theoretical Studies on Nitrido Ruthenium (VI) Porphyrin and High Valent Ruthenium Nitrido Derivatives of Keggin Typical Polyoxometalate ([PW11O39{RuVIN}]4‑): Electronic Structures and Bonding Features. Dalton Trans. 2009, 6208−6213. (e) Laurencin, D.; Garcí-Fidalgo, E.; Villanneau, R.; Villain, F.; Herson, P.; Pacifico, J.; Stoeckli-Evans, H.; Bénard, M.; Rohmer, M.-M.; Süss-Fink, G.; et al. Framework Fluxionality of Organometallic Oxides: Synthesis, Crystal Structure, EXAFS, and DFT Studies on [{Ru(η6-arene)}4Mo4O16] Complexes. Chem.−Eur. J. 2004, 10, 208−217. (f) Laurencin, D.; Villanneau, R.; Gérard, H.; Proust, A. Experimental and Theoretical Study of the Regiospecific Coordination of RuII and OsII Fragments on the Lacunary Polyoxometalate [α-PW11O39]7‑. J. Phys. Chem. A 2006, 110, 6345−6355. (g) Liu, C. G.; Guan, W.; Yan, L. K.; Su, Z. M. Bonding Interactions between Nitrous Oxide(N2O) and Mono-RutheniumSubstituted Keggin-Type Polyoxometalates: Electronic Structures of Ruthenium/N2O Adducts. Eur. J. Inorg. Chem. 2011, 489−494. (h) Antonova, N. S.; Carbo, J. J.; Poblet, J. M. Theoretical Characterization of a Ru N-heterocyclic Carbene Derivative of a Polyoxometalate. Enhanced π-Interaction in Oxide Supported TMOrganic Linkages. Dalton Trans. 2011, 2975−2982. (15) (a) Becke, A. D. Density Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (b) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785−789. (c) Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Results Obtained with the Correlation Energy Density Functionals of Becke and Lee, Yang and Parr. Chem. Phys. Lett. 1989, 157, 200−206. (16) 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 B.01; Gaussian, Inc.: Wallingford, CT, 2010. (17) (a) Hay, P. J.; Wadt, W. R. Ab Initio Effective Core Potentials for Molecular Calculations. Potentials for the Transition Metal Atoms Sc to Hg. J. Chem. Phys. 1985, 82, 270−284. (b) Wadt, W. R.; Hay, P. J. Ab Initio Effective Core Potentials for Molecular Calculations. Potentials for Main Group Elements Na to Bi. J. Chem. Phys. 1985, 82, 284−299. (c) Hay, P. J.; Wadt, W. R. Ab Initio Effective Core Potentials for Molecular Calculations. Potentials for K to Au Including the Outermost Core Orbitals. J. Chem. Phys. 1985, 82, 299−311. (18) (a) Runge, E.; Gross, E. K. U. Density Functional Theory for Time-Dependent Systems. Phys. Rev. Lett. 1984, 52, 997−1000. (b) Bauernschmitt, R.; Ahlrichs, R. Treatment of Electronic Excitations within the Adiabatic Approximation of Time Dependent Density Functional Theory. Chem. Phys. Lett. 1996, 256, 454−464. (19) Yanai, T.; Tew, D.; Handy, N. A New Hybrid Exchange− Correlation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP). Chem. Phys. Lett. 2004, 393, 51−57. (20) (a) Tomasi, J.; Persico, M. Molecular Interactions in Solution: An Overview of Methods Based on Continuous Distributions of the Solvent. Chem. Rev. 1994, 94, 2027−2094. (b) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 2999−3094. (21) Champagne, B.; Perpéte, E. A.; Jacquemin, D.; van Gisbergen, S. J. A.; Baerends, E.-J.; Soubra-Ghaoui, C.; Robins, K. A.; Kirtman, B. Assessment of Conventional Density Functional Schemes for Computing the Dipole Moment and (Hyper)polarizabilities of Push−Pull π-Conjugated Systems. J. Phys. Chem. A 2000, 104, 4755−4763. (22) Tawada, Y.; Tsuneda, T.; Yanagisawa, S.; Yanai, T.; Hirao, K. A Long-Range-Corrected Time-Dependent Density Functional Theory. J. Chem. Phys. 2004, 120, 8425−8434.

(23) (a) Sekino, H.; Bartlett, R. J. Frequency Dependent Nonlinear Optical Properties of Molecules. J. Chem. Phys. 1986, 85, 976−990. (b) Karna, S. P.; Dupuis, M. Frequency Dependent Nonlinear Optical Properties of Molecules: Formulation and Implementation in the HONDO Program. J. Comput. Chem. 1991, 12, 487−504. (24) (a) Bersohn, R.; Pao, Y. H.; Frisch, H. L. Double-Quantum Light Scattering by Molecules. J. Chem. Phys. 1966, 45, 3184−3199. (b) Castet, F.; Bogdan, E.; Plaquet, A.; Ducasse, L.; Champagne, B.; Rodriguez, V. Reference Molecules for Nonlinear Optics: A Joint Experimental and Theoretical Investigation. J. Chem. Phys. 2012, 136, 024506−024521. (25) (a) Qi, D. NLO Calculator, version 0.2; University of Science and Technology Beijing: Beijing, China, 2012. (b) Zhang, L. J.; Qi, D. D.; Zhao, L. Y.; Chen, C.; Bian, Y. Z.; Li, W. J. Density Functional Theory Study on Subtriazaporphyrin Derivatives: Dipolar/Octupolar Contribution to the Second-Order Nonlinear Optical Activity. J. Phys. Chem. A 2012, 116, 10249−10256. (26) Marques, M. A. L.; Rubio, A. Time-Dependent Densityfunctional theory. Phys. Chem. Chem. Phys. 2009, 11, 4436−4436. (27) (a) Maestre, J. M.; Lopez, X.; Bo, C.; Poblet, J. M.; NasanPastor, N. Electronic and Magnetic Properties of α-Keggin Anions: A DFT Study of [XM12O40]n−, (M = W, Mo; X = AlIII, SiIV, PV, FeIII, CoII, CoIII) and [SiM11VO40]m− (M = Mo and W). J. Am. Chem. Soc. 2001, 123, 3749−3758. (b) Lopez, X.; Maestre, J. M.; Bo, C.; Poblet, J. M. Electronic Properties of Polyoxometalates: A DFT Study of α/β[XM12O40]n− Relative Stability (M = W, Mo and X a Main Group Element). J. Am. Chem. Soc. 2001, 123, 9571−9576. (c) Poblet, J. M.; Lopez, X.; Bo, C. Ab Initio and DFT Modelling of Complex Materials: Towards the Understanding of Electronic and Magnetic Properties of Polyoxometalates. Chem. Soc. Rev. 2003, 32, 297−308.

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