Density Functional Theory Study on the First Hyperpolarizabilities of

To generate strong electronic communication, the synthesis of related compounds in ... It is suggested that the main origin of the NLO properties of o...
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J. Phys. Chem. B 2005, 109, 22332-22336

Density Functional Theory Study on the First Hyperpolarizabilities of Organoimido Derivatives of Hexamolybdates Likai Yan, Guochun Yang, Wei Guan, Zhongmin Su,* and Rongshun Wang Institute of Functional Material Chemistry, Department of Chemistry, Northeast Normal UniVersity, Changchun 130024, People’s Republic of China ReceiVed: July 29, 2005; In Final Form: September 24, 2005

The first hyperpolarizabilities and origin of nonlinear optical (NLO) properties of arylimido molybdate derivatives have been investigated by density functional theory (DFT). The molecular orbital character analysis reveals that organoimido-to-polyanion charge transfer may be responsible for the NLO properties of this kind of molybdate derivatives. The NLO study shows intra-ion charge transfer is helpful to increase the first hyperpolarizability of arylimido molybdate derivatives. The lengthening of organoimido π-conjugation enhances the βvec value. System 4 has the largest βvec value at the static electronic field, 1.238 × 10-27esu. Orbital analysis shows that the degree of charge transfer between polyanion cluster and organic segment was increased when the second organoimido polyanion was introduced. The present investigation provides important insight into NLO origin and properties of polyanion arylimido molybdate derivatives.

1. Introduction Research on photochromic material and nonlinear optical (NLO) material has continued to receive increasing attention in recent years, due to their wide potential applications in optical switching, telecommunications, and optical computing. Investigations have shown that nonlinear optical properties originate from the charge transfer of molecules. It has been reported that electron donor-acceptor complexes are potential highly efficient NLO materials.1 Considerable research efforts have been directed toward understanding the nature of the NLO phenomenon on organic compounds. Organic compounds consisting of push-pull molecules containing a donor and an acceptor connected via a conjugated bridge (D-π-A) have shown good NLO properties.2 Polyoxometalates (POMs) are excellent electron acceptors and can form electron donor-acceptor compounds,3 so they have become new promising NLO materials. Many charge-transfer salts have been synthesized.4,5 These salts are always the combinations of polyoxometalate anions with organic and organometallic cations. However, the quite weak organic and inorganic interactions allowed in the solid state by this kind of charge transfer salts have prevented the occurrence of an effective electron transfer between the two components. To generate strong electronic communication, the synthesis of related compounds in which the donor molecule is covalently linked to the polyanions is being pursued.6 In fact, polyanion clusters offer a large variety of structures and a diversity of electronic properties shaped by the metal-characterized core. They may comprise a promising family of NLO materials, besides their special roles demonstrated in catalytic reactions, biological chemical processes, and magnetic materials. The covalent grafting of electron-accepting POMs into an organic conjugated polymer may result in highly photoconductive materials with photochromic effects. The structure-property * Corresponding author: phone +86-431-5099108; fax +86-4315684009; e-mail [email protected].

relationships with organoimido POMs derivatives will be helpful in designing the new NLO materials. Density functional theory (DFT) has become a significant tool for modeling the properties of molecules and materials. It therefore seems appealing to use DFT for the prediction of NLO properties as well.7 DFT investigations on the POMs have made improvements.8 We have investigated the electronic properties, bonding character, and stability of POMs by DFT.9 Theoretical studies of NLO properties would be helpful in the rationalization of the observed properties of the POM system in itself and in the design of new, interesting POM-based molecular NLO materials. In this paper, we performed DFT calculations on organoimido derivatives of hexamolybdates to predict their NLO properties and illustrate the origin of NLO properties of this kind of POMs. The present study aims to make a first step toward a better understanding of the NLO properties of POMs. 2. Theoretical Details Herein, three organoimido polyanions were chosen and are shown in Figure 1. All calculations reported here have been performed with the ADF2003.01 program.10 Geometries of all systems were optimized, where the initial geometric data were from the crystal data.11 The NLO coefficients of all systems were calculated with the ADF-RESPONSE module12 based on the optimized geometries. We obtained the hyperpolarizabilities through a Taylor series expansion of the induced dipole moment in terms of an external electric field.13 The adiabatic local density approximation (ALDA) was used and the Van LeeuwenBaerends potential14 (LB94) that corrects the LDA potential in the outer region of the molecule was also performed. The basis functions for describing the full electron of the main group elements (C, N, O, and H), and valence electron for molybdenum atom (Mo, 1s-3d) are Slater-type orbitals of TZP quality. The relativistic effects were taken into account by use of the zero-order regular approximation (ZORA).15 We also calculated the static hyperpolarizabilities employing the Hartree-Fock method based on ab initio quantum chemistry with the Gaussian98 program.16 Two kind of basis sets were considered: one

10.1021/jp0542120 CCC: $30.25 © 2005 American Chemical Society Published on Web 10/28/2005

DFT Study on First Hyperpolarizabilities

Figure 1. Calculation models.

is GEN, where molybdenum atoms were used by the LANL2DZ basis set and C, N, O and H atoms were used by 6-31G(d); while in the other one, all the atoms in the calculation were described by the LANL2DZ basis set. For study of hyperpolarizabilities on small molecules, the basis sets need to be extended with diffuse functions. However, for the systems under study, the main effects are related to ordinary bound orbitals. The addition of diffuse functions is therefore not expected to change our results by any significant amount.17

J. Phys. Chem. B, Vol. 109, No. 47, 2005 22333 delocalized π bond coming from the carbon atoms of arylimido and the d-pπ bond from the dxz orbital on the molybdenum atom, which links the nitrogen atom and the px orbital on nitrogen, largely contribute to the highest occupied molecular orbital (HOMO), which implies a strong ground-state interaction between hexamolybdate and organoimido. In systems 1 and 2, the lowest unoccupied molecular orbital (LUMO) has common character in that the LUMO localizes the Mo d orbitals and O p orbitals. However, the LUMO of system 3 has more contributions from the end phenyl ring and the LUMO + 1 mainly concentrates on the polyanion segment. The frontier molecular orbital character reveals that the large intramolecular charge transfer will come into being under the external electronic field. This kind of charge transfer must be responsible for NLO property. It is suggested that the main origin of the NLO properties of organoimido polyanions is organoimido-to-polyanion charge transfer. They form interesting organic donor and inorganic acceptor (D-A) models (Figure 3).

3. Results and Discussion 3.1. Orbital Character. One of the most striking features of these systems is the extensive π-electron delocalization over the organoimido segment and Mo atom with bonding to the N atom. The diagrams for frontier molecular orbitals (FMO) of systems 1-3 are displayed in Figure 2, and the similarity between FMO of systems 1 and 2 is clearly seen. The

Figure 2. Frontier molecular orbitals of systems 1-3.

Figure 3. Sketch map of D-A-type polyoxometalates.

The formation of the Mo-N π bonds leads to increased delocalization of the aromatic π electrons. This strong electronic interaction between polyoxometalate cluster and the orga-

22334 J. Phys. Chem. B, Vol. 109, No. 47, 2005

Yan et al.

TABLE 1: Theoretical First Hyperpolarizabilities at ω ) 0.0 eV (βvecSHG) and ω ) 0.65 eV (βvecSHG, βvecOR) for Systems 1-3 (× 10-30 esu) βvecSHG (DFT)

1 2 3

βvecOR (DFT)

βvecSHG(HF/GEN)

βvecSHG(HF/ LANL2DZ)

ω) 0.0 eV

ω) 0.65 eV

ω) 0.65 eV

ω) 0.0 eV

ω) 0.0 eV

4.732 5.537 206.710

8.330 9.895 355.788

5.669 6.672 243.280

0.867 1.175 125.477

1.056 1.288 143.186

noimido moiety has already been observed and has been noted to be dependent on the conjugated system. 3.2. NLO Properties. In the monosubstituted nitrobenzene, the charge transfer occurs between the nitryl and the benzene. Under the laser frequency of ω ) 1.17 eV, the β value of monosubstituted nitrobenzene is -2.2 × 10-30 esu in experiment18 and 2.268 × 10-30 esu in calculation. The monosubstituted organoimido hexamolybdate has the same geometrical character as the monosubstituted nitrobenzene. How are the NLO coefficients of POMs discussed in this paper? A measurement of the first hyperpolarizability β(-2ω; ω, ω) is related to second-harmonic generation (SHG), For these systems with their dipole moment along the z-axis, βvec is given by

βvec ) βz ) 1/3

∑ (βzii + βizi + βiiz) i)x,y,z

(1)

The first hyperpolarizabilities of all systems considered in this study were calculated under the static electronic field and the laser frequency of ω ) 0.65 eV (λ ) 1907 nm). The results are shown in Table 1. The static HF results are also included. It can be seen that all systems have larger first hyperpolarizability coefficients. In particular, the value of βSHG of system 3 reached 355.788 × 10-30 esu at ω ) 0.65 eV. This further confirmed that a good synergistic effect between polyanion clusters and organic segments was obtained. Lone-pair π-electrons on the linking N atoms are expected to contribute to the extended π-conjugation via N atom. In system 3, the organoimido segment is lengthened via CtC; thus the π-conjugation is extended and the delocalization is improved. In donor-acceptor-substituted NLO molecules, π-conjugation commonly provides a pathway for the redistribution of electrons under the influence of an electric field. In some cases, the nature of π-conjugation can alter the electron-donating and -accepting ability of the substituents.19 From the frontier orbital character of system 3, it can be seen that the organoimido group holds its own chargetransfer character after the bond between the polyanion and the organoimido was formed; that is, the two benzene groups contribute to the charge transfer via conjugated bridge, as the electron transition originates from HOMO to LUMO; at the same time, the charge transfer from organimido to polyanion attributes the electron transition from HOMO to LUMO + 1, just like systems 1 and 2. The NLO properties for system 3 are expected to enhance significantly due to an extent of D-A π-conjugation. The further analysis of orbital excitations shows that the main charge transfer (CT) origins from O f Mo, N f Mo, and C f Mo in system 1. However, the main CT of system 2 comes from organoimido group (R) to Mo atoms. The electron-donating ability of the organoimido group is stronger than that of the O atom, so the βvec value of system 2 is larger than that of system 1. In system 3, more CT comes from organoimido group to Mo atoms, and the large charge transfer is the result of the extended organoimido segment; thus the larger βvec value is generated. From Table 1, it can be seen that

TABLE 2: Individual Components of the First Hyperpolarizabilities for Systems 1-3 (× 10-30 esu) Calculated by DFT βzzz βyyz βxxz βyzy βzyy βxzx βzxx

1

2

3

8.137 -0.983 -0.183 -0.983 -1.054 -0.183 -0.197

-1.448 -7.150 0.235 -7.150 -6.811 0.235 0.247

-295.397 -0.449 -0.795 -0.449 -0.006 -0.795 -0.957

DFT and HF methods give consistent trends on the first hyperpolarizabilities. But the HF results have lower values compared with the DFT, as no correlation consideration in the Hartree-Fock method. This is in accordance with the conclusion of the literature.20 From Table 2, we can see βvec of systems 1 and 3 is mainly determined by βzzz, however, βyyz, βyzy, and βzyy of system 2 jointly determine βvec. In the sum-over-state (SOS) formalism the diagonal βzzz can be expressed as

(µngz)2∆µng2

∑n

βzzz ) 6

(Eng)2

(2)

where ∆µng is the dipole moment difference between the ground and the nth excited state along the z direction, n refers to the excited A1 state, µngz are the matrix elements of the transition moment, and Eng is the difference between the ground and the nth excited state. The energy difference Eng in the denominator of eq 2 is the major factor for determining the value of βzzz. All the compounds investigated here show C2V symmetry. The symmetry axis of systems 1 and 3 is the z-axis; however, the symmetry axis of system 2 is the bisector of the y- and z-axes. The βzzz values of systems 1 and 3 refer to 1A1 f 2A1 excitation according to the symmetry requirement. The transition energy from the 1A1 ground state to the lowest 2A1 excited state has been investigated by employing the time-dependent DFT procedure. The transition energy Eng of 1A1 f 2A1 state is 2.6062 and 2.2809 eV for systems 1 and 3, respectively. Eng of system 3 becomes lower than that of system 1; thus βzzz of system 3 becomes much bigger than that of system 1. For system 2, the main contribution of βvec is in the y and z directions. So βyyz, βyzy, and βzyy of system 2 have larger values than those of the other tensor. This point is accord with the direction of the charge transfer (see Figure 2). 3.3. NLO Properties of System 4. On the basis of the special character of charge transfer and the large βzzz value of system 3, we were inspired to probe into the NLO properties of system 4, which added another organoimido polyanionon (see Figure 4). What are the charge transfer and βzzz values of system 4? As per the discussions above, system 4 should have A-DA-D model character. Does it? The diagrams for FMO of system 4 are shown in Figure 4. Its orbital character becomes more interesting. The main contribution to HOMO and HOMO - 1 comes from different organoimido segments, but HOMO - 2 concentrates on the middle organoimido. LUMO localizes on the side organoimido segments, and LUMO + 1 and LUMO + 2 concentrate on the middle polyanion. The two polyanion segments do not provide contributions simultaneously. It is supposed that the polyanion acting as acceptor also supplies a channel that the electrons transfer from one organoimido to another. The organoimido in system 4 acts as donor that offers electrons to the polyanion; at the same time, it acts as a conjugated bridge to transfer electron. So it is predicted that

DFT Study on First Hyperpolarizabilities

J. Phys. Chem. B, Vol. 109, No. 47, 2005 22335

Figure 5. Frequency-dependent hyperpolarizability βvec of system 1.

4. Summary and Conclusions The present DFT calculations on organoimido derivatives of hexamolybdates provide the first theoretical framework in which the charge transfers and NLO properties may be understood. First, in systems 1 and 2, the charge transfer originated from organoimido to polyanion; however, the charge transfer became more complex when the organoimido was lengthened or another organoimido polyanion was introduced. Second, the organoimido-to-polyanion charge transfer may be responsible for the NLO properties of this kind of compounds. The lengthening of organoimido π-conjugation or increasing organoimido polyanion is helpful to enhance the β value. Third, the HartreeFock method underestimated the hyperpolarizabilities of the systems, and DFT methods used in this paper made significant improvements. At the same time, the present investigation gives insight into the NLO properties of organoimido ployanion and attempts to reveal the origin of the NLO properties of this family of cluster compounds, which are interesting and important in design and synthesis of new promising NLO material. Further studies on NLO properties of organoimido polyanions by the DFT method are in progress. Acknowledgment. We acknowledge the financial support from the National Natural Science Foundation of China (Project 20373009). The Youth Fund of Northeast Normal University (111494017) is gratefully acknowledged. Figure 4. Frontier molecular orbitals of system 4.

a large charge transfer will form in the system under the laser field. To further investigate the NLO of system 4, the DFT resulting βvec value is 1.238 × 10-27 esu under the static electronic field. The static HF results are 0.712 × 10-27 and 0.856 × 10-27 esu, respectively, for GEN and LANL2DZ basis sets. This further proves the organoimido segment acts as acceptor and bridge when another organoimido polyanionon was introduced. The degree of charge transfer and synergistic effect between polyanion cluster and organic segment were obviously enhanced. 3.4. Dispersion Behavior of System 1. The dispersion behavior of SHG and optical rectification (OR) on the secondorder polarizabilities was investigated by the finite field (FF). Figure 5 shows the calculated values βvec of system 1 versus the input energy from 0.0 to 1.1 eV. From this figure we find that the curves below about 0.54 eV appear relatively flat for system 1. These results indicate that system 1 exhibits a small dispersion in a width frequent zone and is more available to be used for frequency conversion optical material.

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