Second-Order Nonlinear Optical Properties of Transition-Metal

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J. Phys. Chem. C 2009, 113, 19672–19676

Second-Order Nonlinear Optical Properties of Transition-Metal-Trisubstituted Polyoxometalate-Diphosphate Complexes: A Donor-Conjugated Bridge-Acceptor Paradigm for Totally Inorganic Nonlinear Optical Materials Chun-Guang Liu,†,‡ Wei Guan,†,‡ Li-Kai Yan, Zhong-Min Su,*,†,‡ Ping Song,†,‡ and En-Bo Wang*,‡ Institute of Functional Material Chemistry, Key Laboratory of Polyoxometalate Science of Ministry of Education, Faculty of Chemistry, Northeast Normal UniVersity, Changchun 130024, P. R. China ReceiVed: July 22, 2009; ReVised Manuscript ReceiVed: September 14, 2009

To date, the most widely used second-order nonlinear optical (NLO) materials are the totally inorganic crystals. However, the small photoelectric coefficients of inorganic NLO materials are the bottleneck in practical applications. The donor-conjugated bridge-acceptor (D-A) model, which is successfully used in the development of organic second-order NLO materials, is still prohibitive in totally inorganic molecules. In the present paper, time-dependent density functional (TDDFT) has been employed to investigate the secondorder NLO properties of a series of transition-metal-trisubstituted polyoxometalates (POMs)-diphosphate clusters. We find that these totally inorganic POM clusters possess D-A structure, and the large static first hyperpolarizability can be effectively designed based on this D-A model. The results show that the substituted transition metal centers can be viewed as electron acceptor, and the POM cluster serves as both electron donor and conjugated bridge. The three vanadium atoms derivative of 30-molybdobipyrophosphate POM cluster displays large static first hyperpolarizability by ∼700 × 10-30 esu, and it is ∼70 times as large as that of typical organic NLO molecule p-nitroaniline (PNA) according to LB94/TZP calculations. Thus, this POM cluster seems to be promising totally inorganic materials for application in nonlinear optics. 1. Introduction Second-order nonlinear optical (NLO) materials have attracted considerable attention owing to their application in photonic technologies.1 The totally inorganic compounds have high thermal stability relative to the organic molecules, and hence they are natural candidates for NLO materials and have been commercialized successfully.2 To date, the most widely used such materials are the inorganic crystals, but the relatively small photoelectric coefficients of these inorganic NLO materials are the bottleneck in practical applications. The donor-conjugated bridge-acceptor (D-A) model is a successful motif for the design of organic, organometallic, and metal complex NLO molecular materials.3 However, totally inorganic molecules are hard to be modified to obtain the D-A structures for optimization of their second-order NLO responses (apart from the organic-inorganic hybrids). Polyoxometalates (POMs) are compounds of early transition metals (M ) V, Nb, Ta, Mo, W) in their highest oxidation states bounded to oxygen atoms form discrete oxygen cluster anions.4 Their unique chemical, electronic, medical, and optical properties have prompted studies of possible application in virtually every scientific discipline. POMs reveal a huge variety of shapes, sizes, and compositions and provide a good basis for molecular design.5 In POM chemistry as well as other areas, increasing the size and complexity of structures is expected to generate multifunctionalityofinterestinmaterialsscience.6 POM-diphosphate complexes display very interesting structural features through the interaction of pyrophosphate (P2O74-) with molybdate. * Corresponding authors. E-mail: [email protected] (Z.-M.S.); [email protected] (E.-B.W.). † Institute of Functional Material Chemistry. ‡ Key Laboratory of Polyoxometalate Science of Ministry of Education.

CHART 1: Structural Diagram of 30-Molybdobipyrophosphate POM Clustera

a For the purpose of comparison, a carbon nanotube structure also has been listed here.

Although molybdate complexes of pyrophosphate were first reported over 100 years ago,7 the crystal structures of these complexes have been characterized recently. Pope and Kortz reported8 the structure of an 18-molybdophosphate anion [(P2O7)Mo18O54]4-; this POM cluster can be hypothetically viewed as a fused dimer of B-type PMo9 units, which is different from the Wells-Dawson (W-D) structure. The larger sized 30-molybdobipyrophosphate [{(P2O7)Mo15O45}2]8- is the dimer of a lacunary ion deriving from 18-molybdophosphate missing one cap of Mo3O6, and this POM-diphosphate complex has been structurally characterized by Kortz.9 This nanosized POM cluster possesses considerably long cage-shape structure and displays analogous structure of carbon nanotube (see Chart 1). In the past two decades, the locations of added electrons in transition metal trisubstituted Keggin and W-D POM clusters have been determined by using 183W and 31P nuclear magnetic

10.1021/jp906979z CCC: $40.75  2009 American Chemical Society Published on Web 10/14/2009

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Figure 1. Polyhedral representation of the donor-acceptor derivatives of Wells-Dawson (a), 18-molybdophosphate (b), and 30-molybdophosphate (c). The gray and red octahedrons can be viewed as the electron donor and acceptor in this scheme, respectively.

resonance (NMR), X-band electron spin resonance (ESR) spectroscopic measurements, and density functional calculations (DFT).10 These observations suggested that the transition-metaltrisubstituted effect in these POMs leads to the charge separation; the substituted transition metal atoms can be viewed as the electron acceptor. Recent theoretical reports of these POM clusters by our group have shown that these POM clusters possessed the D-A structure,11 where the oxygen atoms in the cap region and three metal (vanadium and molybdenum) atoms in the opposite cap region in these POM clusters can be viewed as the electron donor and acceptor, respectively (see Figure 1). In terms of molecular design, we will show that totally inorganic POM clusters with larger static first hyperpolarizabilities relative to our previous reported compounds can be designed based on this D-A structure. We examine β values of these transition-metal-trisubstituted POM clusters, considering two specific structural aspects: (i) the influence of electron acceptor strength and (ii) the influence of conjugated bridge length. This is not unusual when compared with the perspective of the traditional push-pull “D-A” organic NLO paradigm. However, it should be stressed that all of these designs are based on the totally inorganic compounds; the well-known electron donor dimethylamino, acceptor nitryl moiety, and conjugated bridge alkene or benzene moiety, etc., do not exist. In this work, the static second-order NLO responses of transition-metaltrisubstituted 18- and 30-molybdobipyrophosphate POM nanoclusters, [(P2O7)Mo15M3O54]7- and [{(P2O7)2Mo27M3O90}]11- (M ) VV, NbV, TaV), have been calculated by using the timedependent (TD) DFT method. The geometrical optimizations of these clusters are under C3V symmetry, and the shorthand notation without oxygen atoms and charge has been used in this paper. We shall be mainly interesting in the static first hyperpolarizability along the molecular dipole moment direction

βvec ) ∑µiβi /|µ| i

i ) x, y, z

(1)

where βi ) (1/3)∑j(βijj + βjij + βjji) and µi is the dipole moment in the ith direction. Due to the C3V symmetry and molecular coordinates, the βzzz and βzxx components are larger than the other nonzero individual β tensor components in this work. 2. Computational Details All of the POM clusters studied here have been optimized with BP8612 generalized gradient approximations and VWN13

local density functional, triple-ζ basis plus polarization Slatertype orbital basis sets (TZP), and the integration parameter 6.0, as implemented in the ADF 2008 program system.14 The 1s shell of O, 1s to 2p shells for P and V, 1s to 3d shells for Nb and Mo, and 1s to 4d shells for Ta have been treated by the frozen core approximation. The relativistic effects were taken into account by using the zeroth-order regular approximation (ZORA).15 The linear response equation of TDDFT16 is adopted to compute linear polarizability, R, the (2n + 1) theorem17 is used for obtaining the first hyperpolarizability β in ADF program. TDDFT method has been broadly applied to investigate the NLO responses of organic and inorganic compounds and nanosized species.18 The Van Leeuwen-Baerends (LB94) potential,19 the BP86 functional, and hybrid functional, PBE0,20 have been adopted to calculate the hyperpolarizabilities of all clusters in this work. In order to obtain a more intuitive description the trends in the NLO behavior of the studied clusters, TDDFT methods were used to describe the electronic spectrum. 3. Results and Discussion 3.1. Donor-Acceptor Structure. The push-pull paradigm is a successful guiding principle for organic dipolar molecular NLO chromophore design. However, our tests on these transition-metal-trisubstituted POM clusters suggest that POM clusters can serve as both conjugated bridge and donor, which is different from the typical paradigm. The highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) and their adjacent orbitals of P2Mo15V3 and P4Mo27V3 are shown in Figure 2. An electron donor is usually associated with a spatially localized HOMO, whereas an electron acceptor is associated with a spatially localized LUMO. For P2Mo15V3, it can be found that the HOMO and HOMO-1 are mainly localized at the oxygen atoms in cap end (donor), whereas the LUMO and LUMO+1 are mainly localized at the vanadium atoms in opposite cap end (acceptor) and adjacent molybdenum atoms (conjugated bridge) in this POM cluster. It is clearly seen that an excitation corresponding these occupied and unoccupied orbitals would generate charge transfer from the donor to acceptor across the conjugated bridge. The nonsubstituted 18-molybdophosphate anion, P2Mo18, also has been optimized at the same theoretical levels in this work, and the relevant molecular orbitals are listed in Figure 2. It can be found that the occupied orbitals (HOMO and HOMO-1) are delocalized over the oxygen atoms of POM

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Liu et al. TABLE 1: Experimental and BP86/TZP Optimized Average Bond Lengths, Bond-Length Alternation (∆r) Values [Å], and HOMO-LUMO (H-L) Gap [eV] for Nonsubstituted and Transition-Metal-Trisubstituted 30-Molybdophosphate Cluster

Figure 2. Frontier molecular orbitals of nonsubstituted and D-A substituted 18-molybdophosphate and 30-molybdophosphate.

cage surface, and the unoccupied orbitals (LUMO and LUMO+1) are delocalized over the molybdenum atoms of the POM belt position (see Figures 1 and 2). The difference in the frontier molecular orbitals of the two POM clusters (P2Mo15V3, P2Mo18) indicates that the transition-metal-trisubstituted effect on cap end leads to electronic asymmetry and generates the electron donor and acceptor simultaneously. As shown in Figure 1, the conjugated bridge length of P4Mo27V3 is 2 times as long as that of P2Mo15V3. It is wellknown that the length and electronic structure of conjugated bridge can affect the electronic communication between D and A, and the effective D-A electronic interaction mediated by the conjugated bridge can enhance second-order NLO response. However, if the D-A bridge-mediated mixing is too large, the D and A states will lose their electronic asymmetry and thus cannot give effective charge transfer. There is no charge transfer transition in the extreme limit, so the second-order NLO responses will be diminished. This always appears in organic NLO molecules as elongation of the conjugated bridge. For the totally inorganic POM systems, as shown in Figure 2, the HOMO and HOMO-1 of P4Mo27V3 are mainly localized at the oxygen atoms in cap end; LUMO and LUMO+1 are still localized on the terminal vanadium atoms and adjacent molybdenum atoms. Thus, the frontier molecular orbitals of this POM cluster with long conjugated bridge have significant electron D and A character, which provides the good orbital basis for the charge transfer transition. The bond length alternation (BLA) value (∆r) is defined as the average difference between the bond lengths of two consecutive bonds. The BLA pattern can reflect the nature of conjugated bridge in D-A substituted organic polyene. It has been demonstrated that the BLA value of conjugated bridge decreases when D and A is connected via the conjugated bridges.21 Thus, the BLA value in the middle of the conjugated

complex

A

B

C

D

E

F

P4Mo30(calc) P4Mo30(exp) P4Mo27V3(calc) P4Mo27Nb3(calc) P4Mo27Ta3(calc)

2.065 2.065 2.040 2.025 2.023

1.827 1.779 1.876 1.877 1.878

2.221 2.157 2.064 2.054 2.053

1.780 1.767 1.849 1.852 1.852

2.267 2.183 2.110 2.100 2.100

1.779 1.775 1.841 1.843 1.843

∆r H-L gap 0.389

1.532

0.216 0.202 0.200

3.312 3.316 3.309

chain is an important parameter that defines the NLO response for organic D-A molecules. We will show that this pattern is also suitable for our totally inorganic D-A POM clusters. In POM chemistry, the alternating bond length of Mo-O bond has attracted considerably attention because it is an important factor for designing chiral POM structures.22 The recent paper reported by Poblet et al. showed a comprehensive statistical analysis of alternating bond lengths in POMs and provided an explanation on the basis of DFT calculations.23 They showed that these distortions are more pronounced when the HOMO-LUMO gap in the POM is decreased. Thus, the effect of bond alternation is more remarkable in larger POMs, such as Lindqvist < Keggin < W-D structure. As mentioned above, the 30-molybdophosphate cluster has larger size than W-D structure; thus, the significant Mo-O bond alternations are expected. For the purpose of comparison, the nonsubstituted 30molybdophosphate anion, P4Mo30, has been optimized in this work; the optimized structures are reported in Table 1. The results first show that the Mo-O bond in the middle of conjugated bridge displays alternating feature, the long Mo-O bond length (A, C, E) appears at ∼2.1 Å, and the short Mo-O bond length appears at ∼1.8 Å for nonsubstituted cluster P4Mo30, which is in well agreement with the experimental structure determined by X-ray crystallography (see Table 1).9 The optimized calculations show that the series transition-metaltrisubstituted effects act to reduce the long Mo-O bond (A, C, E) and to increase the short Mo-O bond (B, D, F). As a consequence, the BLA values decrease from 0.4 to 0.2 Å when the transition metal trisubstituted at the end of these POM clusters. As expect, this result is in agreement with the D-A model. The HOMO-LUMO gaps of all 30-molybdophosphate clusters studied here calculated by BP86/TZP calculations are listed in Table 1. It can be found that the transition-metaltrisubstituted effects effectively increase the HOMO-LUMO gap; all of the trisubstituted clusters possess analogous HOMO-LUMO gap of ∼3.3 eV. This value is about 2 times as large as that of nonsubstituted 30-molybdophosphate cluster. The relevant large HOMO-LUMO gaps of transition-metaltrisubstituted clusters suggest that, at least theoretically, these species are stable entities. 3.2. Static First Hyperpolarizability. From the molecular design perspective, it is useful to discuss the second-order NLO

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TABLE 2: Static First Hyperpolarizabilities (×10-30 esu) of All Clusters and p-Nitroaniline (PNA) Molecule Obtained by the LB94/BP86/PBE0/TZP Calculations clusters P2Mo15V3 P2Mo15Nb3 P2Mo15Ta3 P4Mo27V3 P4Mo27Nb3 P4Mo27Ta3 PNA

functionals LB94 PBE0 BP86 LB94 PBE0 BP86 LB94 PBE0 BP86 LB94 PBE0 BP86 LB94 PBE0 BP86 LB94 PBE0 BP86 LB94 BP86 PBE0

βzzz -50.5 -42.0 -42.2 -46.2 -21.6 -21.3 -36.9 -31.9 -31.9 -1129.8 -776.2 -776.3 -989.7 -750.2 -737.7 -979.2 -722.9 -713.1 -17.7 -16.4 -16.3

βzxx -3.9 -2.6 -2.7 -2.9 -1.5 -1.5 -1.8 -1.2 -1.2 -23.4 -16.0 -16.0 -20.8 -16.2 -15.8 -20.1 -13.8 -13.7 1.4 1.3 1.4

TABLE 3: LB94/TZP Calculated Excited Energy (∆Ege, eV), Oscillator Strengths (fos), and Major Assignment of the Crucial Excited States for All Clusters

βvec -35.0 -28.3 -28.5 -31.2 -14.8 -14.6 -24.2 -20.5 -20.6 -705.9 -484.9 -478.9 -618.8 -469.5 -461.6 -611.6 -450.2 -444.2 9.5 8.7 8.7

responses with respect to diverse donor/acceptor strength and conjugated bridge for optimization of the first hyperpolarizability. We have demonstrated that three vanadium atoms in cap end in Keggin and W-D structures were strong electron acceptor,11 and the interplay between vanadium atoms (acceptor) and molybdenum atom (conjugated bridge) enhanced the static first hyperpolarizability. In this work, we will test the acceptor strength by replacement of the transition metal M (M ) V, Nb, Ta) and conjugated bridge nature by change of the geometrical structure of these POM clusters (see Figure 1). We find that three vanadium atoms in cap end are still strong electron acceptor, and the optimal β values appear at vanadomolybdate in these POM structures. The static first hyperpolarizability values of at least ∼500 × 10-30 esu are predicted to be assessable using these totally inorganic POM clusters with optimal substitution. The optimal β value is ∼70 times as large as that of typical organic NLO molecule p-nitroaniline (PNA) according to LB94/TZP calculations (see Table 2). The static first hyperpolarizabilities, βvec, of all POM clusters calculated by different functionals in ADF program are shown in Table 2. It can be found that the βvec values of all clusters are functional-dependent, the LB94 potential corrected by asymptotic behavior seems to overestimate the hyperpolarizabilities when compared with the BP86 and PBE0 results, and the two functionals (BP86 and PBE0) give analogous βvec values for all POM clusters. All the functionals predict that three vanadium atoms derivatives in two structures display large second-order NLO responses. This indicates that three vanadium atoms in cap end is a strong electron acceptor compared with niobium and tantalum atoms in the two structures. For the 18molybdophosphate derivatives, the calculated β value is slightly smaller than that of W-D structure, such as the β value of vanadomolybdate with W-D structure (-44.3 × 10-30 esu)11 is 1.26 times as large as that of 18-molybdophosphate derivative (see Table 2). By contrast, the elongation of conjugated bridge effectively enhances the second-order NLO responses; the β value of the three vanadium atoms derivative of 30-molybdophosphate, P4Mo27V3, is ∼16 and 20 times as large as that of W-D POM11 and 18-molybdophosphate structures, P2Mo15V3, according to LB94/TZP calculations, respectively (see Table 2). Obviously, the size effect is the key factor in

clusters P2Mo15V3 P2Mo15Nb3 P2Mo15Ta3 P4Mo27V3 P4Mo27Nb3 P4Mo27Ta3

excited state (symmetry) ∆Ege S1 (A1) S1 (A1) S1 (A1) S2 (A1) S2 (A1) S2 (A1)

1.492 1.644 1.664 0.870 0.888 0.883

fos

major assignment

0.004 0.003 0.002 0.032 0.044 0.045

HOMO f LUMO (98%) HOMO f LUMO+1 (95%) HOMO f LUMO+1 (95%) HOMO-5 f LUMO (96%) HOMO-5 f LUMO (91%) HOMO-5 f LUMO (88%)

determination of the second-order NLO responses. Thus, the transition-metal-trisubstituted carbon-nanotube-like POM cluster holds much promise in terms of its NLO characteristics. On the basis of the complex sum-over-states expression, Oudar and Chemla established a simple link between molecular hyperpolarizability and a low-lying energy charge transfer transition through the two-level model24

β ∝ (µee - µgg)

fos ∆Ege3

(2)

where µgg and µee are the ground and excited state dipole moments, fos is the oscillator strength, and ∆Ege is the transition energy. These factors (µee - µgg, ∆Ege, and fos) are all intimately related and are controlled by the electron properties of the donor/ acceptor and the nature of conjugated bridge. In order to gain more insight into second-order NLO response of all clusters, the electronic spectra of all clusters have been calculated by using TDDFT methods. The calculated excited energies and oscillator strengths of the crucial excited states are listed in Table 3. The crucial excited state is defined as the lowest optically allowed excited state with substantial oscillator strength. We employed vanadomolybdate in the two structures as an example to analyze the charge transfer transitions based on the TDDFT calculations. It can be found that the crucial excited state of 18-vanadomolybdate (P2Mo15V3) is mainly composed of the HOMO f LUMO transition. As mentioned above, this excitation would generate the charge transfer from the oxo donor to the metal acceptor (see Figure 2). The crucial excited state of 30-vanadomolybdatecluster (P4Mo27V3) is composed of the HOMO-5 f LUMO transition. The HOMO-5 in this cluster is mainly localized on the oxygen atoms in the cap end; combining with the localized LUMO (see Figure 2), this excitation also gives the clearly charge transfer from donor to acceptor. The TDDFT calculated excited energies of crucial excited states for 30-molybdophosphate derivatives are significantly lower than that of 18-molybdophosphate derivatives, such as the crucial excited energy of 18-vanadomolybdate is ∼1.7 times as large as that of 30-vanadomolybdate (P2Mo15V3 vs P4Mo27V3). Obviously, this decrease of excited energy is mainly due to the elongation of the conjugated bridge. For the same structure, the different transition metal substitution effects, that is, the acceptor strength, also affect the excited energy. As expected, the vanadomolybdate in each structure gives the lowest excited energy because of the strong electron acceptor. The relevant low excited energy will generate an increase in the static hyperpolarizability, which is well in agreement with the TDDFT calculations for the first hyperpolarizabilities (see Table 2). 4. Conclusion In the present paper, electronic structure analysis predicts that these transition-metal-trisubstituted POM nanoclusters possess

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D-A structure, and the large static first hyperpolarizability can be achieved by using this D-A structure. We found that the POM cluster acts as both conjugated bridge and electron donor, and the three transition metal atoms can be viewed as electron acceptor in our D-A model. The three vanadium atoms derivative is a strong electron acceptor in the two POM structures. Our calculations indicate that the large static first hyperpolarizabilities appear at carbon-nanotube-like vanadomolybdate POM cluster P4Mo27V3. The calculated β values of ∼700 × 10-30 esu is ∼70 times as large as that of typical organic NLO molecule PNA according to LB94/TZP calculations. Thus, the three vanadium atoms derivative of 30molybdobipyrophosphate POM cluster seems to be promising totally inorganic materials for application in nonlinear optics. Acknowledgment. The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (Project No. 20971020), Program for Changjiang Scholars and Innovative Research Team in University (IRT0714), Department of Science and Technology of Jilin Province (20082103), the Training Fund of NENU’s Scientific Innovation Project (STC07017), and Science Foundation for Young Teachers of Northeast Normal University (20090401). We also thank Yuhe Kan for computational support. References and Notes (1) Chen, C.; Liu, G. Annu. ReV. Mater. Sci. 1986, 16, 203. (2) (a) Smith, W. L. O. Appl. Opt. 1977, 16, 798. (b) Boyd, G. D.; Miller, R. C.; Nassau, K.; Bond, W. L.; Savage, A. Appl. Phys. Lett. 1964, 16, 1856. (c) Chen, C.; Wu, B.; Jiang, A.; You, G. Sci. Sin., Ser. B 1985, 235. (d) Chen, C.; Wu, Y.; Jiang, A.; Wu, B.; You, G.; Li, R.; Lin, S. J. Opt. Soc. Am. 1989, B6, 616. (3) (a) Kanis, D. R.; Ratner, M. A.; Marks, T. J. Chem. ReV. 1994, 94, 195. (b) de la Torre, G.; Vzquez, P.; Agull-Lpez, F.; Torres, T. Chem. ReV. 2004, 104, 3723. (c) Di Bella, S. Chem. Soc. ReV. 2001, 30, 355. (d) Lacroix, R. G. Eur. J. Inorg. Chem. 2001, 339. (4) Pope, M. T. Heteropoly and Isopoly Oxometalates; Springer-Verlag: Berlin, 1983. (5) Hill, C. L. Chem. ReV. 1998, 98, 1. (6) Proust, A.; Thouvenot, R.; Gouzerh, P. Chem. Commun. 2008, 1837.

Liu et al. (7) (a) Gibbs, O. W. Am. Chem. J. 1885/1886, 7398; Proc. Am. Acad. Arts Sci. 1886, 21, 107. (b) Rosenheim, A.; Schapiro, M. Z. Anorg. Chem. 1923, 129, 196. (8) Kortz, U.; Pope, M. T. Inorg. Chem. 1994, 33, 5643. (9) Kortz, U. Inorg. Chem. 2000, 39, 623. (10) (a) Kozik, M.; Hammer, C. F.; Bader, L. C. W. J. Am. Chem. Soc. 1986, 108, 2748. (b) Kozik, M.; Hammer, C. F.; Bader, L. C. J. Am. Chem. Soc. 1986, 108, 7627. (c) Harmalder, S. P.; Pope, M. T. J. Am. Chem. Soc. 1981, 103, 7381. (d) Lopez, X.; Bo, C.; Poblet, J. M. J. Am. Chem. Soc. 2002, 124, 12574. (11) Liu, C. G.; Guan, W.; Song, P.; Su, Z. M.; Yan, L. K.; Wang, E. B. Inorg. Chem. 2009, 48, 8115. (12) (a) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (b) Perdew, J. P. Phys. ReV. B 1986, 33, 8822. (13) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. (14) (a) Te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. J. Comput. Chem. 2001, 22, 931. (b) Fonseca Guerra, C.; Snijders, J. G.; Te Velde, G.; Baerends, E. J. Theor. Chem. Acc. 1998, 99, 391. (c) ADF 2008 01, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands, http://www.scm.com. (15) (a) Chang, C.; Pelissier, M.; Durand, M. Phys. Scr. 1986, 34, 394. (b) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1993, 99, 4597. (c) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1994, 101, 9783. (16) Gross, E. K. U. ; Kobson, J. F.; Petersilka, M. In Density Functional Theory; Nalewajski, R. F., Ed.; Topics in Current Chemistry; Springer: Heidelberg, Germany, 1996. (17) van Gisbergen, S. J. A.; Snijders, J. G.; Baerends, E. J. J. Chem. Phys. 1998, 109, 10644. erratum 1999, 111, 6652. (18) (a) van Gisbergen, S. J. A.; Snijder, J. G.; Baerends, E. J. Phys. ReV. Lett. 1997, 78, 3097. (b) van Gisbergen, S. J. A.; Snijder, J. G.; Baerends, E. J. J. Chem. Phys. 1998, 109, 10657. (c) Hieringer, W.; Evert, J. B. J. Phys. Chem. A 2006, 110, 1014. (d) Powell, C. E.; Cifuenties, M. P.; Morrall, J. P.; Stranger, R.; Humphrey, M.; G.; Samoc, M.; Luther-Davies, B.; Heath, G. A. J. Am. Chem. Soc. 2003, 125, 602. (19) van Leeuwen, R.; Baerends, E. J. Phys. ReV. A 1994, 49, 2421. (20) (a) Grimme, S. J. Comput. Chem. 2004, 25, 1463. (b) Ernzerhof, M.; Scuseria, G. J. Chem. Phys. 1999, 110, 5029. (21) (a) Meyers, F.; Marder, S. R.; Pierce, B. M.; Bre´das, J. L. J. Am. Chem. Soc. 1994, 116, 10703. (b) Liu, C. G; Qiu, Y. Q.; Sun, S. L.; Li, N.; Yang, G. C.; Su, Z. M. Chem. Phys. Lett. 2007, 443, 163. (22) Hasenknopf, B.; Micoine, K.; Lacote, E.; Thorimbert, S.; Malacria, M.; Thouvenot, R. Eur. J. Inorg. Chem. 2008, 5001. (23) Yan, L. K.; Lopez, X.; Carbo, J. J.; Sniatynsky, R.; Duncan, D. C.; Poblet, J. M. J. Am. Chem. Soc. 2008, 130, 8223. (24) (a) Oudar, J. L.; Chemla, D. S. J. Chem. Phys. 1977, 66, 2664. (b) Oudar, J. L. J. Chem. Phys. 1977, 67, 446.

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