Theoretical studies on tricarbonyl metal derivatives of Lindqvist-type polyoxometalate complexes: electronic structures and nonlinear optical properties

Abstract

The density functional theory (DFT) method and natural bond orbital (NBO) analysis have been employed to investigate the electronic structures and second-order nonlinear optical (NLO) properties for tricarbonyl metal derivatives of a Lindqvist-type polyoxometalate, [Nb₂W₄O₁₉M(CO)₃]^3−/2− (M = Mn^I, Tc^I, Re^I, Fe^II, Ru^II and Os^II). The position of the tricarbonyl metal ligand and the substitution of different metal atoms M have an influence on the electronic absorption spectra and NLO responses of all complexes. Among the three isomers of [Nb₂W₄O₁₉Mn(CO)₃]³⁻, the β₀ value of isomer 1^a is the largest, which is 1.4 times and 2.3 times larger than those of isomers 1^b and 1^c, respectively. The β₀ value also depends on the tricarbonyl metal M, the β₀ value decreases in the order M = Ru > Re > Fe > Os > Mn > Tc. In addition, the analysis of the main transition orbitals shows that the tricarbonyl metal ligand acts as an electron donor in [Nb₂W₄O₁₉M(CO)₃]^3−/2− (M = Mn^I, Tc^I, Re^I, Ru^II and Os^II), while the [Fe(CO)₃]²⁺ ligand acts as an electron acceptor in [Nb₂W₄O₁₉Fe(CO)₃]²⁻.

---

Introduction

Polyoxometalate (POM)-supported metal carbonyl derivatives as a peculiar class of organometallic oxides have attracted increasing attention owing to their unique structures, potential catalytic properties, photochemical properties and potential applications in solar energy production.^1–10 This kind of complex can be regarded as a subcategory of functionalized POMs, which can be prepared by step-wise and controlled methods. Most of these complexes contain Lindqvist-type,^1–4 lacunary Keggin-type⁹ and lacunary Dawson-type POMs.¹⁰ All these POM-supported metal carbonyl complexes contain a fac-{M(CO)₃}⁺, d⁶ low-spin metal (Mn^I, Re^I) carbonyl fragment.^1–10

In 1980, Besecker and co-workers synthesized [Nb₂W₄O₁₉M(CO)₃]³⁻ (M = Mn, Re) complexes in which [Nb₂W₄O₁₉]⁴⁻ is coordinated to a tricarbonyl Mn/Re unit by a triangle of three adjacent bridging oxygens (O_b).^1,2 Interestingly, ¹⁷O NMR spectroscopy provides conclusive evidence for the presence of all three [Nb₂W₄O₁₉M(CO)₃]³⁻ isomers. The studies of POM-supported metal carbonyl derivatives have been in progress all the time.^3–10 Recently, Hill and co-workers have synthesized [P₄W₃₅O₁₂₄{Re(CO)₃}]¹⁶⁻ and [X₂W₂₀O₇₀{M(CO)₃}₂]¹²⁻ (X = Sb, Bi; M = Mn, Re) complexes, and density functional theory (DFT) calculations show that these complexes exhibit an intense Re-to-POM charge-transfer (CT) transition, an example of a potentially general transition, called metal-to-POM (MP)CT.^9,10 The chromophoric and catalytic properties, and photoactivities of these CT complexes are under investigation.

Nonlinear optical (NLO) materials have received tremendous attention owing to their unique applications in optical fibers, data storage, optical limiting, computing and switching. Among these NLO materials, the donor–acceptor (D–A) model has been widely used. POM complexes with the electron storage ability can be designed as a good electron-acceptor group.^11–13 So the POM-based complexes with good thermal and photochemical stability as well as redox switching ability are potential NLO materials. Theoretical studies would be helpful in rationalization of the observed properties and design of novel POM-based hybrid materials with excellent properties. Previous studies on related POMs show that DFT calculations give a satisfactory description of the geometrical structures, bonding character, redox properties, charge-transfer and NLO properties.^14–17

Obviously, POM-supported metal carbonyl derivatives are potential NLO materials, while studies on second-order NLO properties and electronic structures of tricarbonyl metal polyanions are rare. In the present work, DFT calculations were performed to investigate the electronic structures and nonlinear optical properties of tricarbonyl metal derivatives of the Lindqvist-type POM. The calculation models of complexes are shown in Fig. 1. In cis-[Nb₂W₄O₁₉]⁴⁻, there are three different types of bridging oxygen atoms, which bond to two niobiums (O_b1), one niobium and one tungsten (O_b2), or two tungstens (O_b3). The experimental spectra² provide conclusive evidence for the presence of all three isomers. In isomer a, the M(CO)₃ binding site is formed by one ONb₂ oxygen and two ONbW oxygens. In isomer b, two ONbW oxygens and one OW₂ oxygen are involved, and in isomer c, three OW₂ oxygens form the binding site. The complex [Nb₂W₄O₁₉Mn(CO)₃]³⁻ was taken as an example to investigate the difference in geometrical and electronic structures among the three isomers. In order to investigate the effect of the tricarbonyl center metal M on NLO properties of [Nb₂W₄O₁₉M(CO)₃]^3−/2−, Mn or Re was substituted by other d⁶ metals (Tc^I, Fe^II, Ru^II, and Os^II).

Fig. 1 Structures of [Nb₂W₄O₁₉Mn(CO)₃]³⁻ (1^a, 1^b, 1^c) and other systems [Nb₂W₄O₁₉M(CO)₃]³⁻ M = Tc (2), Re (3), Fe (4), Ru (5) and Os (6); light blue is Nb, dark blue is W, purple is M, grey atom is C and red atom is O.

Computational details

The quantum chemical calculations were carried out using the GAUSSIAN 09W program package.¹⁸ The ground states of all the studied complexes were closed-shell singlet states and the geometries were optimized at the BP86/6-31G(d) level. This functional has given good insight into the structure. Considering the relativistic effects for transition-metal atoms, the LANL2DZ basis set was applied for metal atoms in this work. The static first hyperpolarizabilities (β₀) were calculated by using analytical third energy derivatives, which are more efficient and less expensive than numerical derivatives¹⁹ and with the pure functional MPWPW91*²⁰ and the long-range corrected CAM-B3LYP functional²¹ to examine the reliability of the calculated results. The static first hyperpolarizability is termed as the zero-frequency hyperpolarizability and is an estimate of the intrinsic molecular hyperpolarizability in the absence of any resonance effects. Thus, β₀ is defined as

β₀ = (β_x² + β_y² + β_z²)^1/2

where

In order to obtain a more intuitive description of the second-order NLO behavior of the studied complexes, time-dependent DFT (TDDFT) methods were used to simulate the molecular electronic spectra at the PBE1PBE/6-31+G(d) level (LANL2DZ basis set for metal atoms). PBE1PBE, also known as PBE0, is obtained by casting the function and correlation of Perdew, Burke and Erzenrhof in the hybrid HF/DFT scheme with a fixed 1/4 ratio.²² This functional has been shown to improve the accuracy of excitation energies and CT bands in metal complexes for solvation calculations.

All the calculations were performed in acetonitrile solvent. The solvent effect was considered using the polarizable continuum model (PCM)²³ using the integral equation formalism variant. The Wiberg bond index (WBI) was computed by natural bond orbital (NBO) calculations at the same level with the geometrical optimization.

Results and discussion

Ground-state structures

In this study, all complexes have similar structures which contain one identical cis-[Nb₂W₄O₁₉]⁴⁻ unit joined by one fac-{M(CO)₃}^+/2+ moiety, M = Mn (1), Tc (2), Re (3), Fe (4), Ru (5), and Os (6). It exhibits slight differences in bond distances of MO₃C₃ coordinated octahedra with different M centres. In all complexes, a tricarbonyl metal unit bonds to a triangle bridging oxygen on the surface of a [Nb₂W₄O₁₉]⁴⁻ anion. We take 1 as an example to discuss the difference in structural parameters of the three isomers (1^a, 1^b, 1^c) in detail. 1^a and 1^c contain a mirror plane, and possess C_s symmetry, while 1^b has no symmetry. The calculations indicate that 1^a is the most stable isomer with energies of 0.8 and 0.9 kcal mol⁻¹, which are lower than 1^b and 1^c, respectively. The small energy differences are compatible with the existence of the three isomers in solution (Table 1).

Table 1 Selected average optimized bond lengths (Å) of systems 1^a–1^c and 2–6

	Bond length
	C–O	M–C	M–Ob
1^a	1.173	1.780	2.087
1^b	1.173	1.781	2.079
1^c	1.174	1.781	2.071
Exp	1.144	1.843	2.001
2	1.175	1.909	2.213
3	1.180	1.908	2.200
4	1.156	1.800	1.987
5	1.158	1.923	2.121
6	1.163	1.913	2.122

---

Among 1^a, 1^b and 1^c, the calculated average bond length of C–O is 1.17 Å, which is in good agreement with the experimental results 1.14 Å. It suggests that the functional and basis sets that we adopted are reliable for the studied complexes. In 1^a, 1^b and 1^c, the difference in Mn–C and C–O bond lengths is about 0.001 Å, illustrating that the structure of the tricarbonyl metal ligand in the three isomers is basically consistent. The Mn–O_b bond length is 2.087 Å for 1^a, 2.079 Å for 1^b, and 2.071 Å for 1^c, showing that the position of the tricarbonyl metal ligand slightly affects the Mn–O_b bond length.

The experimental results confirmed that isomer b predominates in solution. For 2–6, the isomer b was investigated. The M–O_b bond length increases in the order 1^b (2.079) < 2 (2.213) ≈ 3 (2.200); 4 (1.987) < 5 (2.121) ≈ 6 (2.122), which is consistent with the radii of the metal atom. The M–O_b bond length decreases in the order: 4 < 1^b, 5 < 2, 6<3, indicating that the interactions between the metal M (M = Fe, Ru and Os) and O_b are stronger than those of Mn, Tc and Re.

NBO analysis

The experimental X-ray diffraction study confirms that Mn(CO)₃⁺ bonds to three adjacent bridging oxygen atoms (O_b) of [Nb₂W₄O₁₉]⁴⁻. However, the interaction between metal M and bridge-oxygen O_b has never been reported. In order to investigate the bonding interaction between metal M and bridge-oxygen O_b in the [Nb₂W₄O₁₉M(CO)₃]³⁻ anion, WBI was computed using NBO theory and the results are listed in Table 2.

Table 2 Selected NBO-calculated WBI of all systems

Bond	1^a (M = Mn)	1^b (M = Mn)	1^c (M = Mn)	2 (M = Fe)
M–C1	1.169	1.182	1.180	1.290
M–Ob1	0.386	0.384	0.389	0.379
M–Ob2	0.386	0.399	0.389	0.390
M–Ob3	0.399	0.393	0.404	0.383

---

Bond	3 (M = Re)	4 (M = Fe)	5 (M = Ru)	6 (M = Os)
M–C1	1.365	0.962	1.059	1.195
M–Ob1	0.398	0.483	0.466	0.490
M–Ob2	0.410	0.498	0.482	0.505
M–Ob3	0.401	0.494	0.473	0.494

---

The Mn–C bonds in three isomers (1^a–1^c) are very similar with obvious single-bond nature as indicated by the calculated WBI of 1.169–1.182. However, with different metals, M = Mn (1), Tc (2), Re (3), Fe (4), Ru (5), Os (6), the interaction between M and C is slightly different, 3 (1.365) > 6 (1.195); 2 (1.290) > 5 (1.059); 1^b (1.182) > 4 (0.962), which is consistent with the M–C bond length, 3 (1.908) < 6 (1.913); 2 (1.909) < 5 (1.923); 1^b (1.781) < 4 (1.800). It indicates that the interactions between M and C in [Nb₂W₄O₁₉M(CO)₃]³⁻ (M = Mn, Tc and Re) are stronger than those of [Nb₂W₄O₁₉M(CO)₃]²⁻ (M = Fe, Ru and Os). The WBI of Mn–O_b for the three isomers (0.384–0.404) shows weak interactions between Mn and bridging oxygen O_b. Compared with 1 and 3, the M–O_b1 bond orders of 4, 5 and 6 are larger, 6 (0.490) > 4 (0.483) > 5 (0.466) > 3 (0.398) > 1^b (0.384) > 2 (0.379), which are consistent with the M–O_b bond lengths.

Electronic spectrum

Based on the BP86 optimized structures of tricarbonyl metal Lindqvist-type polyoxometalate complexes [Nb₂W₄O₁₉M(CO)₃]^3−/2− (M = Mn^I, Tc^I, Re^I, Fe^II, Ru^II and Os^II), TDDFT was used to calculate the excited-state properties of complexes. The calculated absorption wavelengths, oscillator strength (f₀) and major transition states for the studied complexes are summarized in Table 3. The absorption UV-Vis spectra of all complexes are illustrated in Fig. 2. As shown in Fig. 2(a), the UV-vis absorption spectra of 1^a–1^c display one intense absorption (λ_max) in the range of 260–270 nm, which follows the order: 1^a (270 nm) > 1^b (264 nm) > 1^c (260 nm). It also can be seen that the absorption bands of 1^a–1^c undergo a slight shift from 270 nm to 260 nm. The frontier molecular orbitals involved in the dominant electronic transitions in 1^a–1^c are shown in Fig. 3. The charge transition characteristics of 1^a, 1^b and 1^c are similar and the transition molecular orbitals of 1^b are taken as representatives, so the charge transition characteristic 1^b is analyzed. In 1^b, the H−2 → L+6 and H−1 → L+5 transitions can be assigned to the CT from the p orbitals of O_b atoms in POM and the tricarbonyl metal ligand to Nb/W atoms. The H−6 → L+1 and H−11 → L transitions occur between Nb/W atoms and O atoms in POM. The [Nb₂W₄] acts as an electron acceptor and the tricarbonyl metal ligand acts as an electron donor. The charge transition characteristics of 1^a, 1^b and 1^c show that the position of the tricarbonyl metal ligand has a slight influence on the orbital transition.

Fig. 2 (a) The absorption UV-Vis spectra of three isomers 1^a–1^c; (b) the absorption UV-Vis spectra of systems 1^b–6.

Fig. 3 The molecular orbitals of systems 1^a–1^c involved in the dominant electronic transitions.

Table 3 The calculated absorption wavelengths (nm), excitation energy (ΔE, eV), oscillator strengths (f₀) and the corresponding dominant moment transition of all systems (H = HOMO, L = LUMO, L+1 = LUMO+1, etc.)

	λ	ΔE	f 0	Major contribution
1^a	276.3	4.49	0.0400	H−3 → L (19%)
	275.1	4.51	0.0342	H−4 → L (40%)
				H−2 → L+3 (20%)
	268.8	4.61	0.0954	H−5 → L+1 (33%)
				H−6 → L+1 (17%)
1^b	265.0	4.68	0.0392	H−2 → L+6 (17%)
				H−6 → L+1 (13%)
	264.7	4.69	0.0194	H−2 → L+6 (16%)
				H−11 → L (12%)
	262.7	4.72	0.0199	H−1 → L+5 (17%)
				H−2 → L+6 (14%)
1^c	263.0	4.71	0.0212	H−2 → L+5 (42%)
	260.7	4.76	0.0760	H−5 → L+1 (34%)
				H−7 → L+1 (22%)
	254.3	4.88	0.0151	H−6 → L+2 (58%)
2	267.0	4.64	0.0152	H−5 → L+1 (33%)
	264.6	4.69	0.0195	H−6 → L+1 (11%)
	263.9	4.70	0.0661	H−5 → L+1 (17%)
3	263.7	4.70	0.0283	H−6 → L+2 (11%)
	262.6	4.72	0.0426	H−8 → L (14%)
	261.0	4.76	0.0215	H−2 → L+9 (16%)
4	268.8	4.61	0.0525	H−6 → L+1 (39%)
	253.3	4.89	0.0158	H−8 → L+2 (7%)
				H → L+4 (6%)
	251.9	4.92	0.0140	H → L+4 (14%)
5	261.4	4.74	0.0264	H−9 → L (8%)
	261.0	4.75	0.0429	H−4 → L+2 (19%)
				H−7 → L+1 (18%)
	253.8	4.88	0.0199	H−5 → L+2 (16%)
6	262.9	4.71	0.0130	H−4 → L+2 (16%)
	257.0	4.82	0.0222	H−7 → L+1 (21%)
	252.3	4.91	0.0156	H−9 → L (16%)

---

As shown in Fig. 2(b), 1^b, 2 and 3 show an intense absorption at around 265 nm, 4–6 show a broad band at 240–260 nm. The spectra of 2 and 3 have similar transition features to 1^b. The blue shifts of the absorption are observed in 4–6 compared with 1^b, 2 and 3. It indicates that the more positive charge of [M(CO)₃] (Fe^II, Ru^II and Os^II) units causes the blue shifted absorption peak. In order to concisely describe the transition character, the electron density differences between the ground state and the dominant excited state were also plotted using GaussSum2.2 (Fig. 4). For 2, 3, 5 and 6, the decreasing electron density mainly localizes on the tricarbonyl segment and oxygen atoms of POM, while the increasing electron density mainly localizes on the Nb/W atoms. The tricarbonyl ligand acts as an electron acceptor and the POM acts as an electron donor, which is consistent with MPCT. It can be seen that the increasing electron density in 4 mainly localizes on the tricarbonyl segment and oxygen atoms of POM, while the decreasing electron density mainly localizes on the Nb/W atoms. We infer that the large electronegativity of Fe^II (4) has an important influence, which leads to the tricarbonyl ligand acting as an electron acceptor.

Fig. 4 The electron density difference maps (EDDM) of systems 2–6 between the ground state and the dominant electronic transitions with an isodensity surface of 0.001 au.

Static second-order polarizability

The β₀ values computed by MPWMPW91* and CAM-B3LYP functionals are listed in Table 4. The functional CAM-B3LYP results are larger than that of the MPWMPW91* functional. For 1^a–1^c, 2, 4 and 6, two functionals yield the same order of β₀ values: 4 > 6 > 1^a > 1^b > 1^c > 2. The β₀ values of 3 and 5 are calculated to be 11.325 and 11.221 × 10⁻³⁰ esu by the CAM-B3LYP functional, the little difference may be in the range of calculation errors. Therefore, the MPWMPW91* functional was used to compute the second-order polarizabilities. The β₀ value of 1^a is about 1.5 times as large as that of 1^b, which is about 1.6 times as large as that of 1^c. It indicates that the orientation of the tricarbonyl metal ligand affects the β₀ values of 1^a–1^c. For all complexes, the tricarbonyl ligand locates the y-axis direction. The larger β_y component indicates that the CT between the tricarbonyl ligand and POM is decisive for 1^a and 1^b.

Table 4 Computed transition moment (Debye) and static second-order NLO polarizabilities (×10⁻³⁰ esu) of all clusters obtained by the MPWPW91* and CAM-B3LYP functionals

	Δμ	Function	β x	β y	β z	β 0
1^a	3.27	MPWPW91*	3.28	8.22	−0.16	8.85
		CAM-B3LYP	3.80	8.25	−0.16	9.08
1^b	7.05	MPWPW91*	−0.19	2.97	5.54	6.29
		CAM-B3LYP	−0.19	2.41	6.33	6.77
1^c	9.12	MPWPW91*	−3.52	−1.73	−0.00	3.92
		CAM-B3LYP	−3.98	−2.81	0.00	4.87
2	7.23	MPWPW91*	−0.41	−0.46	5.42	5.46
		CAM-B3LYP	−0.38	−0.91	6.24	6.32
3	6.43	MPWPW91*	−0.41	−9.60	5.39	11.02
		CAM-B3LYP	−0.38	−9.45	6.23	11.33
4	15.92	MPWPW91*	−0.76	9.74	4.62	10.81
		CAM-B3LYP	−0.80	8.95	5.39	10.48
5	17.06	MPWPW91*	−0.36	11.285	5.26	12.46
		CAM-B3LYP	−0.38	9.46	6.03	11.22
6	14.22	MPWPW91*	−0.49	4.88	4.92	6.95
		CAM-B3LYP	−0.52	3.43	5.76	6.72

---

When M is Mn, Tc and Re, the β₀ values present the order: β₀ (3) > β₀ (1^b) > β₀ (2); when M is Fe, Ru and Os, the β₀ values present the order: β₀ (5) > β₀ (4) > β₀ (6). Among all complexes, 5 shows the largest β₀ value, 12.456 × 10⁻³⁰ esu according to the MPWPW91* calculations. Compared with those of 1^b and 2 (6.287 and 5.455 × 10⁻³⁰ esu), 4 and 5 have larger β₀ values, 10.807 and 12.456 × 10⁻³⁰ esu, respectively. Furthermore, for all complexes except for 2β_y tensor components are small; the large β_y tensor components of complexes indicate that the charge transfer in the y direction plays an important role.

In order to elucidate the origin of second-order nonlinear responses of all complexes, we took a further step to analyse the main excited states that contribute to the β value. From the two-level model

where f₀, ΔE, (μ_ee − μ_gg) and μ_ge are the oscillator strength, transition energy, the change of the dipole moment between the ground and excited states and the transition moment, respectively. All complexes possess the general skeleton, and therefore there is not much difference in the Δμ_ge value. In this way, a well-performing NLO chromophore should possess a low-energy CT excited state with a large oscillator strength and transition moment. Among the three isomers, 1^a with the smallest transition energy and the largest oscillator strength presents the largest β₀ value. The oscillator strength of 3 is 0.0426, which is larger than 1^b (0.0392). Therefore, system 3 shows a larger β₀ value than 1^b. The two-level model is not suitable for the system which contains the radioactive element Tc. The transition moment is a decisive factor for the β₀ values of 4–6. The transition moment of 5 is 17.06 Debye, which is larger than 4 (15.92 Debye) and 6 (14.22 Debye).

Conclusions

We report a theoretical study on the first hyperpolarizabilities, electronic transitions, and charge transfer involved in the second-order nonlinear optical response of tricarbonyl metal derivatives of a Lindqvist-type polyoxometalate [Nb₂W₄O₁₉M(CO)₃]^3−/2− (M = Mn^I, Tc^I, Re^I, Fe^II, Ru^II and Os^II). The relative energy analysis suggests that the isomer 1^a is the most stable among the three isomers, 1^a, 1^b, 1^c. The calculations show that the nonlinear optical response coefficient of the isomer 1^a is the largest among the three isomers. Interestingly, among metal-substituted complexes, [Nb₂W₄O₁₉Ru(CO)₃]²⁻ has the largest β₀ value. The analysis of the molecular orbital indicates that [Nb₂W₄O₁₉]⁴⁻ acts as an electron acceptor and the tricarbonyl metal ligand acts as an electron donor in all complexes except for [Nb₂W₄O₁₉Fe(CO)₃]²⁻. In [Nb₂W₄O₁₉Fe(CO)₃]²⁻, the tricarbonyl metal ligand [Fe(CO)₃]²⁺ displays the electron acceptor character.

Acknowledgements

The authors gratefully acknowledge financial support by NSFC (21131001), the Program for New Century Excellent Talents in University (NCET-10-318), the Doctoral Fund of Ministry of Education of China (20100043120007), and the Science and Technology Development Planning of Jilin Province (20100104, 20100320).

Notes and references

1. C. J. Besecker and W. G. Klemperer, J. Am. Chem. Soc., 1980, 102, 7598.
2. C. J. Besecker, V. W. Day and W. G. Klemperer, Inorg. Chem., 1985, 24, 44.
3. W. G. Klemperer and D. J. Main, Inorg. Chem., 1990, 29, 2355.
4. W. G. Klemperer and B. X. Zhong, Inorg. Chem., 1993, 32, 5821.
5. T. Nagata, M. Pohl, H. Weiner and R. G. Finke, Inorg. Chem., 1997, 36, 1366.
6. A. V. Besserguenev, M. H. Dickman and M. T. Pope, Inorg. Chem., 2001, 40, 2582.
7. C. C. Zhao, Z. Huang, C. W. Rodríguez, C. S. Kambara, K. P. O'Halloran, K. I. Hardcastle, D. G. Musaev, T. Lian and C. L. Hill, J. Am. Chem. Soc., 2011, 133, 20134.
8. J. Y. Niu, L. P. Yang, J. W. Zhao, P. T. Ma and J. P. Wang, Dalton Trans., 2011, 40, 8298.
9. H. Wang, S. Hamanaka and Y. Nishimoto, J. Am. Chem. Soc., 2012, 134, 4918.
10. C. C. Zhao, C. S. Kambara, Y. Yang, A. L. Kaledin, D. G. Musaev, T. Lian and C. L. Hill, Inorg. Chem., 2013, 52, 671.
11. D. L. Long, E. Burkholder and L. Cronin, Chem. Soc. Rev., 2007, 36, 105.
12. D. L. Long, R. Tsunashima and L. Cronin, Angew. Chem., Int. Ed., 2010, 49, 1736.
13. H. Wang, S. Hamanaka, Y. Nishimoto, S. Irle, T. Yokoyama, H. Yoshikawa and K. Awaga, J. Am. Chem. Soc., 2012, 134, 4918.
14. T. Zhang, L. K. Yan, S. Cong, W. Guan and Z. M. Su, Inorg. Chem. Front., 2014, 1, 65.
15. T. Zhang, N. N. Ma, L. K. Yan, T. Y. Ma and Z. M. Su, Dyes Pigm., 2014, 106, 105.
16. C. G. Liu, Z. M. Su, W. Guan and L. K. Yan, Inorg. Chem., 2009, 48, 541.
17. C. G. Liu, W. Guan, L. K. Yan, Z. M. Su, P. Song and E. B. Wang, J. Phys. Chem. C, 2009, 113, 19672.
18. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski and D. J. Fox, GAUSSIAN 09 (Revision A.2), Gaussian, Inc., Wallingford, CT, 2009.
19. P. Chopra, L. Carlacci, H. F. King and P. N. Prasad, J. Phys. Chem., 1989, 93, 7120.
20. (a) J. Lin, K. C. Wu and M. K. Zhang, J. Comput. Chem., 2009, 30, 2056; (b) According to the parameter in ref. 20a, we worked out the iops keywords: Iop(3/76 = 1000004000), Iop(3/77 = 0600006000), Iop(3/78 = 1000010000).
21. T. Yanai, D. P. Tew and N. C. Handy, Chem. Phys. Lett., 2004, 393, 51.
22. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1997, 78, 1396.
23. J. Tomasi, B. Mennucci and R. Cammi, Chem. Rev., 2005, 105, 2999.

---