PnicogenâHydride Interaction between FH2X - American Chemical

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Pnicogen−Hydride Interaction between FH2X (X = P and As) and HM (M = ZnH, BeH, MgH, Li, and Na) Qing-Zhong Li,* Ran Li, Xiao-Feng Liu, Wen-Zuo Li, and Jian-Bo Cheng The Laboratory of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Yantai University, Yantai 264005, People’s Republic of China ABSTRACT: A pnicogen−hydride interaction has been predicted and characterized in FH2P− HM and FH2As−HM (M = ZnH, BeH, MgH, Li, and Na) complexes at the MP2/aug-cc-pVTZ level. For the complexes analyzed here, P(As) and HM are treated as a Lewis acid and a Lewis base, respectively. This interaction is moderate or strong since, for the strongest interaction of the FH2As−HNa complex, the interaction energy amounts to −24.79 kcal/mol, and the binding distance is equal to about 1.7 Å, much less than the sum of the corresponding van der Waals radii. By comparison with some related systems, it is concluded that the pnicogen−hydride interactions are stronger than dihydrogen bonds and lithium−hydride interactions. This interaction has been analyzed with natural bond orbitals, atoms in molecules, electron localization function, and symmetry adapted perturbation theory methods.

1. INTRODUCTION Hydrogen bonding plays an important role in chemistry, physics, and biology.1 It is responsible for the functions and properties of many materials, such as the binding of a substrate to its enzyme, the base pairing in nucleic acids, and the selectivity of a catalyst.2 It is usually designated as A−H···B, where A and B are F, O, and N elements. In this type of hydrogen bond, the lone pair electrons in B transfer into the antibonding orbital of the A−H bond. With progress of the study on hydrogen bonding, it was found that other molecules can also act as the electron donors in hydrogen bonding if they have base sites.3−8 The subject of dihydrogen bonding has received a great deal of attention due to its applications in chemical reactions.9,10 It is an attractive interaction between a protonic H atom and a hydridic H atom. Custelcean and Jackson11 have presented an extensive review for the structure, binding, and properties of dihydrogen bonds. Recently, much attention has been paid to hydrogen bondlike interactions, such as lithium bonding12−14 and halogen bonding.15−17 The existence of lithium bonding was first suggested as a possibility by Shigorin18 in 1959 due to the fact that lithium is a congener of hydrogen, but the study for it is not very much. Even so, it has been demonstrated that, like hydrogen bonding, it can also be formed between the Li atom and different bases.19−25 Lithium−hydride interaction was predicted and characterized in HMgH−LiX (X = H, OH, F, CCH, CN, and NC) complexes.25 Halogen bonding is an electrostatically driven noncovalent interaction between a region of positive electrostatic potential on the outside of the halogen X in a molecule R−X and a negative site. Its origin has now been well understood by electrostatic potentials,26 and it was shown that a region of positive electrostatic potential is present on the outermost portions of covalently bonded halogen atoms.27 Halogen−hydride interaction is a type of halogen bonding like dihydrogen bonding, which was first proposed in 2006.28 Because of its weak strength,29−32 this interaction was found only four cases in the Cambridge © 2012 American Chemical Society

Structural Database. Recently, it has been demonstrated that this weak interaction can become stronger with help of other types of intermolecular interactions.33,34 Similarly, the region of positive electrostatic potential on halogen atoms was also observed on some covalently bonded group IV−VI atoms.35−42 This depletion is labeled as a σ-hole, which can similarly interact electrostatically with negative sites. These interactions are all called σ-hole bonds. For the group VI atoms, this interaction is also called a chalcogen bond,43 while the pnicogen bond is named for this interaction of the group V atoms.44 Pnicogen bonding was noticed first when HSN interacts with PH3 or other phosphines.45 Scheiner and coauthors46−50 have presented a series of investigations on the structures, energies, properties, and nature of pnicogen bonds. In these investigations, the electron donors are from lone pair electrons in O, N, and S atoms. However, the study of pnicogen bonding with metal hydrides as the electron donors is less. In this article, we thus studied FH2P−HM and FH2As−HM (M = ZnH, BeH, MgH, Li, and Na) complexes with quantum chemical calculations. HLi, HNa, HBeH, HMgH, and HZnH are often taken as the electron donors in dihydrogen bonds.51−54 The F presence in FH2P makes the P atom form a stronger pnicogen bond than PH3.47 FH2As is selected for comparison with FH2P. Our aim is to predict the pnicogen− hydride interaction in these complexes. Its formation mechanism, properties, and nature have also been analyzed with natural bond orbital (NBO), atoms in molecules (AIM), and symmetry adapted perturbation theories. Received: November 28, 2011 Revised: February 20, 2012 Published: February 21, 2012 2547

dx.doi.org/10.1021/jp211435b | J. Phys. Chem. A 2012, 116, 2547−2553

The Journal of Physical Chemistry A

Article

2. THEORETICAL METHODS FH2X−HM (X = P and As; M = ZnH, BeH, MgH, Li, and Na) complex and its respective monomers have been optimized at the MP2/aug-cc-pVTZ level. The frozen core (FC) approximation was applied in all calculations. Frequency calculations were carried out at the same level to affirm that the obtained structures are energetic minima with no imaginary frequency. All calculations were performed with the aid of the Gaussian09 program.55 The interaction energy is calculated as a difference by subtracting the energy sum of the monomers from the energy of the complex. For a further check on the computational method, the interaction energy was also obtained at the CCSD(T)/aug-cc-pVTZ level with a single-point energy calculation on the MP2/aug-cc-pVTZ geometries. The basis set superposition error (BSSE) was used to correct the interaction energy with the counterpoise method of Boys and Bernardi.56 Natural bond orbital (NBO) analysis57 was carried out via the procedures contained within Gaussian09 at the HF/aug-ccpVTZ level with the MP2/aug-cc-pVTZ wave functions. The atoms in molecules (AIM) theory of Bader58 was applied to analyze the critical points in terms of electron densities and their Laplacians as well as electronic energy densities. The AIM calculations were performed with the use of the AIM2000 program.59 The Multiwfn 2.01 suite of programs60 has been used to analyze the areas of charge concentration in terms of the electron localization function (ELF). The core−valence bifurcation (CVB) index obtained in ELF analyses can also be used to estimate the strength of hydrogen bonds61,62 because this index has a linear relationship with the electron density at the intermolecular bond critical point. The electrostatic potentials at the 0.001 electrons Bohr−3 isodensity surfaces of FH2P were calculated with the WFA Surface analysis suite63 at the MP2/aug-cc-pVTZ level. To have a deeper insight for the nature of the investigated interactions, the interaction energy decomposition was performed with the symmetry adapted perturbation theory (SAPT) method using the SAPT2002 program.64

Figure 1. Optimized structures of FH2P−HM and FH2As−HM (M = ZnH, BeH, MgH, Li, and Na) complexes.

can see from Figure 1 that the HM monomer suffers a deformation in the complexes. This is affirmed by the change of H−M−H angle. It deviates from 180° in the HBeH and HMgH complexes. This is also different from dihydrogen bonded complexes with HM as the electron donors.51−54 Such deformation provides a hint that the interaction between the two molecules may be stronger. The P···H distance is about 1.6−2.4 Å, while the As···H distance is also about 1.6−2.4 Å. Both values are much smaller than the sum of van der Waals Radii of the respective atoms (3.0 Å for the P and H atoms, 3.3 Å for the As and H atoms). This shorter distance indicates an attractive force is present between the two molecules. This interaction is named the pnicogen−hydride interaction according to the terminology for the name of noncovalent interaction suggested by Glaser and Murphy.65 Given that FH2X (X = P and As) is constant, the binding distance becomes shorter in the order of HZnH > HBeH > HMgH > HLi > Na. Thus, the corresponding pnicogen bond becomes stronger. In the complexes, the H−M bond is elongated. This is consistent with that in dihydrogen bonded complexes.51−54 However, the H−M bond elongation in the pnicogen bonded complexes is much larger than that in dihydrogen bonded complexes. For example, the H−Zn bond is lengthened by 0.013 Å in the FH2P−HZnH complex, while it is elongated by only 0.001 Å in the FKrCCH−HZnH complex.51 This is in agreement with the shorter binding distance in the pnicogen bonded complexes. Like in the FH2P−NH3 complex,47 the distant of F−P also has a prominent lengthening in pnicogen− hydride bonded complexes. A further analysis shows that the

3. RESULTS AND DISCUSSION 3.1. Structures and Interaction Energies. Figure 1 shows the optimized structures of FH2P−HM and FH2As−HM (M = ZnH, BeH, MgH, Li, and Na) complexes. The geometrical parameters are summarized in Table 1. Equilibrium structures have Cs symmetry, and the M subunit of HM and two H atoms of FH2P or FH2As are located at the same side with respect to the P···H or As···H axis. The H atom in HM approaches the P or As atom in these complexes. This can be understood with help of the maps of molecular electrostatic potentials of FH2P as shown in Figure 2. The center of the maximum positive electrostatic potentials of FH2P deviates from the F−P axis and is located in the triangle composed of two H atoms and one P atom. Thus, it is easy to understand that the F, P(As), and H atoms are not in a line and that the F−P(As)···H angle is in the range of 159−170°. It is different from dihydrogen bonded complexes with HM as the electron donors,51−54 in which the hydrogen bond angle is close to 180°. This nonlinear phenomenon in FH2P−HM and FH2As−HM (M = ZnH, BeH, MgH, Li, and Na) complexes can be proved with another angle of P(As)···H−M, which varies form 85.2° in the FH2As− HBeH complex to 122.2° in the FH2P−HZnH complex. One 2548



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Table 1. Binding Distance (R, Å), Changes of Bond Lengths (Δr, Å), Stretching Frequency Shift (Δv, cm−1), and Bond Angles (θ) in the FH2P−HM and FH2As−-HM (M = ZnH, BeH, MgH, Li, and Na) Complexes FH2P−HZnH FH2P−HBeH FH2P−HMgH FH2P−HLi FH2P−HNa FH2As−HZnH FH2As−HBeH FH2As−HMgH FH2As−HLi FH2As−HNa

R

ΔrP−F

ΔrH−M

ΔvH−M

θF−P(As)···H

θP(As)···H‑M

θH−M−H

2.342 1.943 1.822 1.643 1.609 2.321 2.090 1.963 1.768 1.726

0.126 0.141 0.172 0.253 0.170 0.146 0.156 0.189 0.267 0.174

0.013 0.059 0.080 0.114 0.169 0.019 0.055 0.080 0.123 0.184

−109 −182 −220

169.9 163.4 169.7 164.3 166.6 167.7 159.1 165.5 160.5 162.6

122.2 85.5 101.3 91.7 89.1 114.4 85.2 99.0 90.6 97.2

177.9 156.5 165.3

−80 −175 −193

HM in the complex relative to the isolated monomer, the interaction energy was corrected for the deformation energy (DE) of HM, besides BSSE. The DE contribution is negligible in the HZnH complex, smaller in the HLi complex, but prominent in the HBeH, HMgH, and HNa complexes. The DE value is related with the H−M−H angle in the complex. The BSSE contribution amounts to about 5−27% of the crude interaction energy and increases in the order HNa < HLi < HMgH < HBeH < HZnH. The results show that it is necessary to consider the effect of BSSE and DE in studying the interaction energy of the pnicogen−hydride interaction. As expected, the MP2 method overestimates the interaction energy relative to the CCSD(T) method. Even so, the method including correlation leaves the interaction energy essentially unchanged and has no effect upon the trends. The interaction energy of the pnicogen−hydride interaction becomes more negative in the order HZnH < HBeH < HMgH < HLi < HNa. This is related with the activity of metal hydrides, which is like that in dihydrogen bonds.51−54 Furthermore, the strength of the pnicogen−hydride interaction has a greater dependence on the activity of metal hydrides. Its interaction energy varies from −3.10 kcal/mol in FH2P−HZnH complex to −24.79 kcal/mol in the FH2As−HNa one. Thus, it is reasonable to think that the K and Ca counterparts form a stronger pnicogen−hydride interaction although their results are not calculated. However, the pnicogen−hydride interaction is much stronger than dihydrogen bonds. For example, the interaction energy is −20.29 kcal/mol in the FH2P−HLi complex and −7.50 kcal/mol in the FH−HLi complex.66 The pnicogen−hydride interaction is stronger in the As complex than in the P analogue. This is due to the fact that the most positive electrostatic potential on the surface of the As atom is larger than the P counterpart.41 The result indicates that the electrostatic interaction is important in the formation of pnicogen−hydride bonded complexes. It is also found that the pnicogen−hydride interaction is sometimes stronger than the pnicogen bond with lone pair electrons as the electron donors.47 It is even stronger than lithium−hydride lithium bonds.25 It has been known that the properties and applications of intermolecular interactions are mainly dependent on their strength. Hence, we think that pnicogen−hydride's interaction may have its contribution to chemical reactions and crystal engineering like hydrogen and halogen bonds. Figure 3 shows the relationship of the interaction energy and the binding distance in the FH2P−HM and FH2As-H−M (M = ZnH, BeH, MgH, Li, and Na) complexes. A trend for an exponential decay is observed for them like that in hydrogen bonds.67

Figure 2. Electrostatic potentials on the molecular surfaces of FH2P monomer at the MP2/aug-cc-pVTZ level. Color ranges: blue, more negative; green, less negative; yellow, less positive; red, more positive.

F−P bond suffers a prominent elongation in the latter than in the former. The elongation of F−X and H−M bonds follows the same order of the binding distance. However, the F−X suffers a smaller elongation in the HNa complex than in the HLi analogue. Accompanied with the H−M bond elongation, the H−M stretch vibration shows a red shift. This red shift is larger in the FH2P complex than in the FH2As counterpart and becomes larger in the order of HZnH < HBeH < HMgH. Table 2 presents the interaction energies in the complexes. The interaction energy was calculated with two methods: MP2 and CCSD(T). Considering there is prominent deformation of Table 2. Interaction Energies (ΔEcorr, kcal/mol) Corrected for BSSE (kcal/mol) and Deformation Energy (DE, kcal/ mol) of HM in the FH2P−HM and FH2As−HM (M = ZnH, BeH, MgH, Li, and Na) Complexes at the MP2 and CCSD(T) Levels FH2P− HZnH FH2P− HBeH FH2P− HMgH FH2P−HLi FH2P−HNa FH2As− HZnH FH2As− HBeH FH2As− HMgH FH2As−HLi FH2As−HNa

BSSE(MP2)

DE(MP2)

ΔEcorr(MP2)

ΔEcorr(CCSD(T))

0.64

0.01

−3.10

−2.77

1.27

3.19

−4.86

−4.39

1.09

1.22

−7.40

−6.18

1.25 1.22 1.46

0.85 1.32 0.06

−20.29 −22.40 −3.96

−18.25 −19.45 −3.57

2.89

3.22

−5.83

−5.52

2.37

1.41

−9.24

−8.33

2.85 2.87

0.99 1.54

−22.37 −24.79

−20.76 −22.32

179.0 156.9 167.3

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interaction energy due to this orbital interaction is 9.72 and 15.73 kcal/mol in FH2P−HZnH and FH2As−HZnH complexes, respectively. This value is smaller than 18.18 kcal/mol in the FH2P−NH3 complex.47 This is not consistent with the interaction energy in both types of complexes. Additionally, the ratio of stabilization energy is about 1.6 and that of interaction energy is about 1.3 in both HZnH complexes. The results indicate that the orbital interaction is of minor importance in the formation of the pnicogen−hydride bonded complex. Analysis of the electron density indicates the presence of a bond critical point (BCP) and a corresponding bond path (Figure 5), which links the phosphorus and hydrogen atoms in each complex. This provides a further evidence for the existence of the pnicogen−hydride interaction in the complexes. Table 3

Figure 3. Relationship of the interaction energy and the binding distance in the FH2P−HM (■) and FH2As−HM (▲) (M = ZnH, BeH, MgH, Li, and Na) complexes.

3.2. NBO, AIM, and ELF Analyses. The ELF isosurfaces depicted in Figure 4 indicate that the 1H atom of HBeH

Table 3. Electron Density (ρ, au) and its Laplacian (∇2ρ, au) As Well As Energy Densities (au) at the Intermolecular Bond Critical Point in the FH2P−HM and FH2As−HM (M = ZnH, BeH, MgH, Li, and Na) Complexes FH2P−HZnH FH2P−HBeH FH2P−HMgH FH2P−HLi FH2P−HNa FH2As−HZnH FH2As−HBeH FH2As−HMgH FH2As−HLi FH2As−HNa

Figure 4. ELF isosurfaces for FH2P−HBeH complex.

deviates from the P−F axis due to the repulsion between its negative charge and the lone pair electrons on P atom. In addition, it also allows for an attractive interaction between the Be of HBeH and the H atoms of FH2P. In A−H···H−M dihydrogen bond, there is an interaction of the occupied σ orbital of the H−M acceptor with the unoccupied σ* orbital of the A−H donor.68 We think that the like orbital interaction is also present in the pnicogen− hydride interaction. However, this interaction was found only in the HZnH complex. The second-order stabilization

ρ

∇2ρ

G

V

H

0.0217 0.0556 0.0684 0.1019 0.1092 0.0253 0.0457 0.0561 0.0861 0.0937

0.0437 0.0565 −0.0036 −0.1217 −0.1502 0.0475 0.0821 0.0483 0.0300 −0.0157

0.0125 0.0301 0.0286 0.0477 0.0508 0.0142 0.0321 0.0277 0.0462 0.0516

−0.0141 −0.0397 −0.0452 −0.0880 −0.1391 −0.0166 −0.0501 −0.0563 −0.1229 −0.0993

−0.0016 −0.0096 −0.0166 −0.0403 −0.0883 −0.0024 −0.0180 −0.0286 −0.0767 −0.0477

presented the values of the electron density at the BCP and the Laplacian in these complexes. It was pointed out that the electron density at the bond critical point correlates well with the H-bond energy.69 Figure 6 presents the correlation between the interaction energy and the electron density at the P···H and As···H bond critical points in the complexes analyzed here. The correlation coefficient is equal to 0.997 in the FH2P complex and 0.994 in the FH2As complex.

Figure 5. Molecular graphs of FH2P−HM and FH2As−HM (M = ZnH, BeH, MgH, Li, and Na) complexes at the MP2/aug-cc-pVTZ level. Small red balls indicate the bond critical points. 2550



Article HF Eind, and Edisp terms are stabilizing, and the δEint,r term is stabilizing in the HZnH complex but destabilizing in other complexes. The destabilizing contribution of Eexch is largest to the total energy in most complexes except for the FH2As−HLi and FH2As−HNa ones. The Eexch arises mainly from the antisymmetry requirement of the wave function, thus the big Eexch is consistent with the shorter binding distance. It is found that the Eexch term becomes larger with the decrease of the distance between the monomers. For all stabilizing terms, the Eelst is the largest contribution to the total energy in most complexes. The exception is the HLi system and FH2As−HNa complex in which the Eind term is most negative. The Eelst term is more negative in the As system than in the P counterpart, and it becomes more negative in the order of HZnH < HBeH < HMgH < HLi < HNa. The electrostatic effect can be interpreted mainly as the dipole− dipole and dipole−quadrupole interactions. The dipole moment is 1.637 D for FH2P and 2.197 D for FH2As. The dipole moment of HLi and HNa is larger, while it is very small for the other three metal hydrides. This is also seen from the NPA charge on the H atom. It is −0.456e (HBeH) and −0.627e (HMgH). The Eind reflects the electric polarization caused by both the charge of electron cloud and the nuclei charges. Consequently, the effect would be the larger for the more polar H−M bond. In the HLi and HNa complexes, this contribution to the total interaction energy is far larger than that for the HZnH complex. In the HLi and HNa complexes, it is even much greater than the electrostatic effect. This is probably due to the larger polarizability of HLi and HNa. Such effect is also reflected in the deformation of HM in the complex and can be weighed by the charge transfer in the complexes. The larger induction energy corresponds to the larger charger transfer. The other attraction effect comes from dispersion energy, and this term is greater than the induction energy in the FH2P− HZnH complex. Both terms are close to each other in the FH2As−HZnH complex. In other complexes, this term is much (HF) amounts to the third- and smaller than Eelst and Eind. δEint‑resp higher-order Hartree−Fock induction and exchange induction contributions. This term is very large in the HLi and HNa complexes due to the small intermolecular separation.

Figure 6. Relationship of the interaction energy and the electron density at the P···H (■) and As···H (▲) bond critical points in the FH2P−HM and FH2As−HM (M = ZnH, BeH, MgH, Li, and Na) complexes.

The Laplacian is positive in most complexes except for the FH2P−HMgH, FH2P−HLi, FH2Ps−HNa, and FH2As−HNa complexes. In both systems, there is an initial increase before a more pronounced decrease for the Laplacian with decreasing distances. This behavior has been predicted for hydrogen bonds,70 leading to more shared-shell interaction types. The electron density is in a range of 0.02−0.11 au, and most of them are out of the proposed range (0.002−0.04 au) for closed-shell interactions as H-bonds proposed by Koch and Popelier.71 One sees that the positive Laplacian is within the proposed range (0.02−0.15 au) for closed-shell interactions.71 It has been demonstrated that very strong H-bonds are often partly covalent interactions and that for such systems as for the other shared-shell interactions the values of Laplacians of the electron density at BCPs are negative. Hence, the results indicate a stronger interaction in these complexes. The electronic energy density (H) at the BCP allows a deeper insight into the nature of interactions, and it is the sum of kinetic energy density (G) and potential energy density (V). One sees from Table 3 that the G is positive and the V is negative. Furthermore, the absolute value of V is greater than G, and |V| is less than 2G in most complexes except for the FH2P− HNa, FH2As−HMgH, and FH2As−HLi complexes. Thus, the H is less than zero, indicating that the pnicogen−hydride interaction has some degree of covalent character.72 3.3. SAPT Analysis. The energy decomposition is very useful for unveiling the nature of noncovalent interactions, thus we performed a SAPT analysis for the pnicogen−hydride SAPT2 are interaction in these complexes. The components of Eint collected in Table 4. The Eexch term is destabilizing, the Eelst,

4. CONCLUSIONS By means of quantum chemical calculations, we predicted and characterized a pnicogen−hydride interaction in FH2P−HM and FH2As−HM (M = ZnH, BeH, MgH, Li, and Na) complexes. It may be designated as P(As)···Hδ−M, where

Table 4. SAPT Components (in kcal/mol) of the Interaction Energy and Charge Transfer (CT, e) in the FH2P−HM and FH2As−HM (M = ZnH, BeH, MgH, Li, and Na) Complexes FH2P−HZnH FH2P−HBeH FH2P−HMgH FH2P−HLi FH2P−HNa FH2As−HZnH FH2As−HBeH FH2As−HMgH FH2As−HLi FH2As−HNa

Eelst

Eexch

Eind

Edisp

HF δEint,r

SAPT2 Eint

CT

−9.48 −51.27 −60.10 −113.17 −111.42 −14.67 −46.85 −60.37 −119.23 −121.71

19.18 98.97 106.01 176.57 177.70 27.33 84.63 95.51 165.12 170.72

−3.18 −41.58 −51.02 −143.52 −150.95 −6.68 −40.71 −59.09 −187.50 −207.86

−5.01 −13.97 −14.56 −21.39 −22.94 −6.18 −12.16 −12.53 −18.00 −19.58

−2.55 1.38 9.59 61.32 63.60 −1.65 7.29 23.32 115.51 130.02

−1.04 −6.47 −10.09 −40.20 −44.02 −1.86 −7.80 −13.16 −44.09 −48.40

0.025 0.040 0.179 0.413 0.494 0.035 0.074 0.138 0.364 0.458

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P(As) is the Lewis acid and H−M is the Lewis base. The binding distance is much smaller than the sum of the corresponding van der Waals radii. The interaction energy varies from −3.10 kcal/mol in the FH2P−HZnH complex to −24.79 kcal/mol in the FH2As−HNa one. This interaction is stronger than dihydrogen bonds and pnicogen−bonds with lone pair electrons as the electron donors. The pnicogen− hydride interaction exhibits some similar properties with dihydrogen bonds although their strengths are different. The AIM analysis shows that this interaction has some degree of covalent character. The energy decomposition indicates that the electrostatic and induction interactions are important in the formation of pnicogen−hydride bonded complexes, and even the latter is more prominent in the HLi and HNa complexes. As a new type of interaction, it is not found much in the Cambridge Structural Database. Considering its stronger strength, we think that this interaction will be receiving increased attention in new crystal materials in the future.

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AUTHOR INFORMATION

Corresponding Author

*Tel: (+086) 535 6902063. Fax: (+086) 535 6902063. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (20973149), the Outstanding Youth Natural Science Foundation of Shandong Province (JQ201006), and the Program for New Century Excellent Talents in University.

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