DFT studies on nonlinear optical properties of neutral nest-shaped heterothiometallic [MOS3Py5Cu3X] (M = Mo, W; X = F, Cl, Br, I) clusters

Spectrochimica Acta Part A 74 (2009) 228–232

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DFT studies on nonlinear optical properties of neutral nest-shaped heterothiometallic [MOS3 Py5 Cu3 X] (M = Mo, W; X = F, Cl, Br, I) clusters Guo-dong Tang a , Zheng-jing Jiang a , Rong-qing Li a , Jin-fang Zhang b , Yu Zhang a,∗ , Chi Zhang b,∗∗ a b

Jiangsu Province Key Laboratory for Chemistry of Low-dimensional Materials, Department of Chemistry, Huaiyin Teachers College, Huai’an 223001, Jiangsu Province, PR China Research Center for Advanced Molecular Materials, School of Chemistry and Chemical Engineering, Jiangsu University, Zhenjiang 212013, PR China

a r t i c l e

i n f o

Article history: Received 22 October 2008 Received in revised form 12 May 2009 Accepted 7 June 2009 Keywords: Density functional theory Hyperpolarizabilities Nonlinear optics Neutral nest-shaped heterothiometallic clusters

a b s t r a c t Theoretical calculations were carried out on some neutral nest-shaped heterothiometallic cluster compounds [MOS3 Py5 Cu3 X] (M = Mo, W; X = F, Cl, Br, I) with the high first static hyperpolarizabilities ˇ values. The geometries of these cluster compounds were optimized by the restricted DFT method at B3LYP level with LanL2DZ base set without any constrains. In order to understand the relationship between the first static hyperpolarizabilities and the compositions of these clusters, the frontier orbital compositions and energy gaps between the HOMO and LUMO orbitals were calculated and analysed. In these clusters the HOMO orbitals are mainly composed of halogen atoms and the first static hyperpolarizability increases from F to I atom. The LUMO orbitals of clusters [MoOS3 Py5 Cu3 X] are comprised of Mo, O and S atoms while the LUMO orbitals of clusters [WOS3 Py5 Cu3 X] composed of W atom and pyridine ring. The energy gaps between the HOMO and LUMO orbitals of the clusters [MoOS3 Py5 Cu3 X] are smaller than those of the clusters [WOS3 Py5 Cu3 X]. As a result the first static hyperpolarizability values of the clusters [MoOS3 Py5 Cu3 X] are higher than those of the clusters [WOS3 Py5 Cu3 X]. © 2009 Elsevier B.V. All rights reserved.

1. Introduction With the development of laser technique, optical communication, optical signal processing, transmission and optical limiting effects utilized in the protection of optical sensors, unremitting efforts have been made to the design, synthesis and microstructure studies of new nonlinear optical (NLO) materials. Among these materials, transition-metal cluster NLO materials have attracted increasing interest due to their potential device applications in IR spectroscopic region [1–6]. In 1994, Shi et al. first found that the cubane-like clusters (n-Bu4 N)3 [WM3 Br4 S4 ] (M = Cu, Ag) have a good optical limiting effect [7]. Over 400 heterothiometallic cluster compounds Mo(W)/S/Cu(Ag) containing [MX S3 ]2− (X = O, S; M = V, Mo, W, Re) moiety have been synthesized and studied over the past two decades [8]. It has been found that many of the heterothiometallic cluster compounds Mo(W)/S/Cu(Ag) possess promising NLO properties since these kinds of Mo(W)/S/Cu(Ag) clusters were found to combine the advantages of both inorganic compounds with the involvement of heavy atoms and organic molecules with the facility of structural alteration.

∗ Corresponding author. Tel.: +86 517 83525318; fax: +86 517 83525320. ∗∗ Corresponding author. E-mail addresses: [email protected] (Y. Zhang), [email protected] (C. Zhang). 1386-1425/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.saa.2009.06.035

The second-order molecular NLO studies about organic molecular systems have been extensively studied experimentally and theoretically [9–12]. However, theoretical studies on the heterothiometallic cluster compounds Mo(W)/S/Cu(Ag) containing the [M X S3 ]2− (X = O, S; M = V, Mo, W, Re) moiety have received much less attention due to the difficulty in calculating the first static hyperpolarizability (ˇ) in the presence of transition-metal atoms, since these cluster compounds contain many heavy atoms and the calculations of NLO characteristics of these clusters need heavy computational cost. According to our knowledge, Wu and co-workers have calculated a series of polynuclear (3–12 nuclear) metal cluster compounds of Mo(W)/Cu(Ag, Au) sulfur system, using first principle quantum chemical methods, to elucidate the influence of geometric configuration and element substitution on the static polarizabilties and hyperpolarizabilities [13–15]. In this work, we have made an attempt to utilize the accurate DFT method to study NLO characteristics of some clusters. Of them one cluster with NLO activity has been synthesized [16]. In order to understand the relationship between the first static hyperpolarizability (ˇ) and composition of these clusters, very accurate DFT method at B3LYP level with LanL2DZ basis set was used to optimize the structures of these Mo(W)/S/Cu/X (X = F, Cl, Br, I) clusters without any constrains in bond lengths, bond angles and dihedral angles and calculate the first static hyperpolarizability (ˇ) of the clusters. The results would be helpful in the simulation, screening and design of new metal cluster NLO materials.

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229

Fig. 1. The optimized geometries of WOS3 Py5 Cu3 I cluster.

2. Computational procedures Due to the high accuracy, DFT has been proved to be more useful in calculating molecular properties of the organometallic compounds than the traditional ab initio electronic structure methods [17,18]. Some reports indicated that the metal clusters are a new and promising system to discover novel NLO crystals [19–21]. However, the use of DFT theories for the calculation of the first static hyperpolarizability (ˇ) of organometallic complexes with heavy transition-metal ions has been limited due to the enormous computational cost. In this paper the DFT method was used to optimize

and calculate the first static hyperpolarizability (ˇ) of some neutral nest-shaped clusters. The geometries of these neutral nest-shaped clusters were optimized using the Becke’s three-parameter hybrid functional density functional theory with LYP correlation functional (B3LYP) and the Los Alamos ECP plus double-zeta (LANL2DZ) basis set (B3LYP/LANL2DZ). The first static hyperpolarizability (ˇ) of these clusters was calculated with the same method. Geometry optimization is one of the most important steps in the theoretical calculations. This procedure proceeds in two steps. Firstly the geometry was constructed by MM+ molecular dynamics in Hyper-

Table 1 Select bond lengths for [MOS3 Py5 Cu3 X] (M = Mo, W; X = F, Cl, Br, I) clusters.

W(20)–S(14) W(20)–S(15) W(20)–S(27) W(20)–O(26) Cu(18)–S(14) Cu(18)–S(27) Cu(18)–N(25) Cu(11)–N(5) Cu(19)–N(29) Cu(11)–N(13) Cu(19)–S(27) Cu(11)–S(15) Cu(19)–S(15) Cu(11)–S(14) Cu(19)–N(28) I(30)–Cu(18)

WOS3 Py5 I

WOS3 Py5 Br

WOS3 Py5 Cl

WOS3 Py5 F

MoOS3 Py5 I

MoOS3 Py5 Br

MoOS3 Py5 Cl

MoOS3 Py5 F

2.3131/2.247 2.363/2.265 2.3132/2.252 1.7319/1.710 2.5524/2.315 2.5443/2.312 2.1344/2.063 2.0996/2.090 2.0326/2.082 2.0298/2.036 2.4682/2.294 2.4907/2.283 2.4905/2.276 2.475/2.282 2.0964/2.100 2.6243/2.615

2.3127 2.362 2.3107 1.733 2.5626 2.5533 2.1388 2.1051 2.0373 2.0305 2.4644 2.5007 2.4973 2.466 2.0993 2.4745

2.3124 2.3617 2.3122 1.7334 2.5525 2.5508 2.157 2.1014 2.0399 2.0383 2.463 2.4966 2.4948 2.4633 2.1022 2.3297

2.3175 2.3597 2.3214 1.7347 2.509 2.5078 2.2228 2.1065 2.0373 2.0414 2.4676 2.4919 2.4986 2.465 2.1047 1.9359

2.3124 2.3785 2.3188 1.726 2.5257 2.5238 2.1481 2.1157 2.0304 2.0491 2.4533 2.4591 2.4711 2.4493 2.1117 2.6258

2.3134 2.3762 2.3188 1.7266 2.5177 2.5223 2.1544 2.1127 2.0345 2.0468 2.4515 2.4601 2.4738 2.4485 2.1075 2.4706

2.315 2.3758 2.3203 1.7267 2.5092 2.5129 2.1735 2.1133 2.0354 2.0496 2.4499 2.4611 2.4707 2.4468 2.1044 2.3247

2.3225 2.3728 2.3301 1.7278 2.4648 2.4788 2.2441 2.1138 2.0322 2.0502 2.4538 2.4596 2.4758 2.449 2.1062 1.9248

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Table 2 All ˇ (a.u.) components and ˇtot × 10−30 (esu) value calculated using B3LYP level of theory for all cluster molecules. Mole.

ˇxxx

ˇxxy

ˇxyy

ˇyyy

ˇxxz

ˇyyz

ˇxzz

ˇyzz

ˇzzz

ˇtot

WOS3 Py5 Cu3 F WOS3 Py5 Cu3 Cl WOS3 Py5 Cu3 Br WOS3 Py5 Cu3 I MoOS3 Py5 Cu3 F MoOS3 Py5 Cu3 Cl MoOS3 Py5 Cu3 Br MoOS3 Py5 Cu3 I

−24.73 −3.67 115.82 1895.58 119.04 142.45 127.20 −321.59

−273.69 −347.03 357.21 887.10 −394.25 −475.18 525.11 772.82

−10.65 3.09 94.78 896.14 −74.62 −68.13 −101.44 −797.73

271.72 −73.67 1331.97 1543.62 130.77 −445.06 2011.04 4154.19

−691.85 −629.95 623.99 1300.34 −675.47 −619.83 603.39 655.53

−1294.92 −1729.60 1934.82 1166.88 −1414.42 −1986.71 2295.01 2220.25

−5.21 4.72 59.68 −224.60 −31.17 −36.69 −56.58 −82.78

99.44 −31.39 −199.32 −315.44 82.36 −196.16 25.37 −193.26

−77.60 −630.85 1059.37 1949.12 −167.95 −879.87 1301.10 1813.99

17.86 26.13 33.89 44.13 19.57 31.63 42.50 58.50

Chem 7.0 package [22], and then optimized by the DFT method at B3LYP level with LanL2DZ basis set [23,24] using Gaussian 03W program package. The maximum values of the converged criterion are default. All geometries converged perfectly. The NLO response calculation was performed on the optimized geometry using the same level of theory. The first static hyperpolarizability (ˇ) is a third rank tensor that can be described by a 3 × 3 × 3 matrix. The 27 components of the 3D matrix can be reduced to 10 components due to the Kleinman symmetry [25] (ˇxyy = ˇyxy = ˇyyx , ˇyyz = ˇyzy = ˇzyy . . ., likewise other permutations also take same

value). It can be given in the lower tetrahedral format. The output from Gaussian 03W provides 10 components of this matrix as ˇxxx , ˇxxy , ˇxyy , ˇyyy , ˇxxz , ˇxyz , ˇyyz , ˇxzz , ˇyzz , ˇzzz , respectively. Many types of hyperpolarizabilities have been discussed in the literature [26]. When reporting a single value of ˇ, one of the common formats is to simply treat the three independent values for ˇ as a quasi-Pythagorean problem and solve for the average ˇ by Eq. (1): ˇtot = (ˇx2 + ˇy2 + ˇz2 )

1/2

Fig. 2. The HOMO and LUMO orbitals composition of clusters [MOS3 Py5 Cu3 X] (M = W, Mo; X = F, Cl, Br, I).

(1)

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The complete equation for calculating the magnitude of the total first static hyperpolarizability from Gaussian 03W output is given as Eq. (2): 2

2

2 1/2

ˇtot = [(ˇxxx + ˇxyy + ˇxzz ) + (ˇyyy + ˇyzz + ˇyxx ) + (ˇzzz + ˇzxx + ˇzyy ) ]

Table 3 HOMO–LUMO analysis of the molecular orbital composition (%). HOMO

(2)

Since these ˇ values of the first static hyperpolarizability(ˇ) tensors of the output file of Gaussian 03W are reported in atomic units (a.u.), the calculated values were converted into electrostatic units (1 a.u. = 8.6393 × 10−33 esu). 3. Results and discussion The fully optimized geometries of [MOS3 Py5 Cu3 X] (M = Mo, W; Py = pyridine, X = F, Cl, Br, I) clusters are shown in Fig. 1. The selected bond lengths are given in Table 1, along with the available experimental data [16]. The best geometric parameters, which are close to the experimental values, were obtained with B3LYP/LanL2DZ theory. These clusters are isomorphous, of which, only the structure of cluster [WOS3 Py5 Cu3 I] is described in detail due to its similarity to those of other clusters. The structure of [WOS3 Py5 Cu3 I] is of C2/c symmetry. The skeleton is composed of one W, three Cu, one I and three S atoms, forming a nest-shaped structure. The W atom is tetrahedrally coordinated by three S atoms and one terminal O atom. The W O bond length of 1.7319 A´˚ is typical for a W O double bond. The other calculated bond lengths of the cluster are longer than the experimental values, with the differences being −0.006 to 0.23 A´˚ for [WOS3 Py5 I]. This is probably because that the calculated bond lengths are in the gas phase while the experiment values were obtained from crystals. There are three Cu (Cu11, Cu18 and Cu19) atoms in the cluster (Fig. 1). All of the three Cu atoms adopt distorted tetrahedral geometry. The average N–Cu–S, S–Cu–S, N–Cu–I, and S–Cu–I angles in the cluster are 107.9(3)◦ , 105.3(1)◦ , 109.6(5)◦ and 116.3(3)◦ , respectively. But there are two different coordination environments about Cu atoms: Cu18 atom binds to one I atom, two ␮3 -S atoms and one N atom of a pyridine ring while the other two Cu atoms (Cu11 and Cu19) bind to two ␮3 -S atoms and two N atoms of two pyridine rings. Although there is a small difference in bond lengths between the optimized geometry and the crystal structure, in general the optimized geometry can simulate the crystal geometry. So the minimum energy conformations of all clusters were used to calculate the first static hyperpolarizability tensors. The components of ˇ and the final ˇtot values were calculated for these clusters and are shown in Table 2. From Table 2, we can see that all the clusters have large first static hyperpolarizability (ˇ). The second-order NLO response can be dictated by charge transfer (CT) excitations involving the HOMO and LUMO frontier orbitals. The HOMO and LUMO frontier orbitals are shown in Fig. 2 and the analysis of the orbital compositions of those clusters given in Table 3. From Fig. 2 and Table 3, we can see that in clusters [WOS3 Py5 Cu3 X], the HOMO orbital is obtained from the linear combination of the orbitals of X and Cu18 atoms while the LUMO orbital is produced from the linear combination of the orbitals of W, and the pyridine ring (involving N13 atom). In the HOMO orbitals, the contribution of the Cu18 orbitals decreases (57.28–14.55%) with X atoms changing from F to I while the contribution of the X orbitals increases (16.02–72.16%) from F to I. In the LUMO orbitals, the main contribution is from the pyridine ring (61.99–84.91%). In the case of clusters [MoOS3 Py5 Cu3 X], composition of the HOMO orbital is the same as that of clusters [WOS3 Py5 Cu3 X], but the LUMO orbital is produced from the linear combination of the orbitals of Mo, S and O atoms. In these LUMO orbitals, the main

231

WOS3 Py5 Cu3 F WOS3 Py5 Cu3 Cl WOS3 Py5 Cu3 Br WOS3 Py5 Cu3 I MoOS3 Py5 Cu3 F MoOS3 Py5 Cu3 Cl MoOS3 Py5 Cu3 Br MoOS3 Py5 Cu3 I

LUMO

Cu18

X30

M20 (M = W, Mo)

Py cycle (N13)

57.28 35.25 21.67 14.55 53.53 31.20 22.42 12.61

16.02 38.16 60.29 72.16 15.79 41.44 57.90 72.21

3.72 3.45 6.17 1.81 51.22 51.23 51.28 51.19

82.49 61.99 75.2 84.91

OS

27.54 27.61 27.66 27.41

Table 4 Changes in the energy levels of HOMO–LUMO orbital of clusters. Mole.

HOMO

LUMO

Difference (a.u.)

ˇtot

WOS3 Py5 Cu3 F WOS3 Py5 Cu3 Cl WOS3 Py5 Cu3 Br WOS3 Py5 Cu3 I MoOS3 Py5 Cu3 F MoOS3 Py5 Cu3 Cl MoOS3 Py5 Cu3 Br MoOS3 Py5 Cu3 I

−0.1651 −0.16929 −0.16308 −0.15474 −0.16921 −0.17034 −0.16437 −0.15732

−0.06332 −0.06624 −0.06802 −0.06976 −0.07372 −0.07772 −0.07818 −0.07826

0.10178 0.10305 0.09506 0.08498 0.09549 0.09262 0.08619 0.07906

17.86 26.13 33.89 44.13 19.57 31.63 42.50 58.50

contribution is from Mo atom orbital (51.19–51.28%) and the O, S atoms orbital (27.41–27.66%). In the clusters [MOS3 Py5 Cu3 X] (M = Mo, W), the first static hyperpolarizability increases with X atom changing from F to I. According to the frontier orbital theory, the X atom acts as a donor. From F to I atom, electronegativity of X decreases, so the control of electrons is reduced, and the charge transfer becomes easier. The first static hyperpolarizability of [MoOS3 Py5 Cu3 X] is larger than that of [WOS3 Py5 Cu3 X]. The only difference in chemical composition between clusters [WOS3 Py5 Cu3 X] and [MoOS3 Py5 Cu3 X] is the metal atom (Mo and W). However, as described above, the components of LUMO orbitals in the Mo and W clusters are different although the composition of HOMO orbitals is same. The difference in the composition of LUMO orbitals between the Mo and W clusters should have influence on their first static hyperpolarizability. Our calculation showed that the LUMO orbital of clusters [MoOS3 Py5 Cu3 X] is composed of Mo atom orbital (51.19–51.28%), O and S atom orbitals (27.41–27.66%) while the main component of the LUMO orbitals in clusters [WOS3 Py5 Cu3 X] is the pyridine ring (61.99–84.91%). The Mo(VI) ion is a better electron acceptor than the pyridine ring and O has bigger electronegativity, thus electrons move easier from HOMO to LUMO orbitals in clusters [MoOS3 Py5 Cu3 X]. As a result, the first static hyperpolarizability in the clusters with Mo atom is larger than the clusters with W atom. To understand the relationship between the first static hyperpolarizability (ˇ) and the HOMO–LUMO energy gap, namely, the lower the HOMO–LUMO energy gap the larger the ˇ value, we examined the molecular HOMOs and LUMOs generated via Gaussion 03W. The results for all the clusters are shown in Table 4. Table 4 shows that in clusters [MOS3 Py5 Cu3 X] the HOMO–LUMO energy gaps decrease with X atom changing from F to I. Correspondingly, the values of static hyperpolarizability of the clusters increase from F to I. Similarly, since the HOMO–LUMO energy gaps of clusters [WOS3 Py5 Cu3 X] are larger that those of clusters [MoOS3 Py5 Cu3 X], smaller values of the static hyperpolarizability of [WOS3 Py5 Cu3 X] were obtained. 4. Conclusion The optimization of the geometries of some neutral nest-shaped clusters [MOS3 Py5 Cu3 X] (M = Mo, W; X = F, Cl, Br, I) and the calcu-

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lation of their ˇ values of first static hyperpolarizability have been performed using DFT method at B3LYP level with LanL2DZ base set. It is evident that the B3LYP/LANL2DZ method can simulate the crystal geometries of these clusters and calculate their first static hyperpolarizability. In order to understand the relationship between the ˇ values and the compositions of the clusters, the frontier orbital compositions have been analysed and the energy gaps between the HOMO and LUMO orbitals calculated. The HOMO orbital of clusters [MOS3 Py5 Cu3 X] (M = Mo, W) is composed of X and Cu(18) atom orbitals. With the halogen atom changing from F to I, the value of the first static hyperpolarizability increases. However, the components of LUMO orbitals in the Mo and W clusters are different. The LUMO orbital of clusters [MoOS3 Py5 Cu3 X] is composed of Mo atom orbital (51.19–51.28%), O and S atom orbitals (27.41–27.66%) while the main component of the LUMO orbitals in clusters [WOS3 Py5 Cu3 X] is the pyridine ring (61.99–84.91%). The energy gaps between the HOMO and LUMO orbitals of clusters [MoOS3 Py5 Cu3 X] are smaller than those of clusters [WOS3 Py5 Cu3 X]. These differences in the composition of LUMO orbitals and the energy gaps between the HOMO and LUMO orbitals between the Mo and W clusters have influence on their first static hyperpolarizability made clusters [MoOS3 Py5 Cu3 X] have higher first static hyperpolarizabilities than clusters [WOS3 Py5 Cu3 X]. The present study demonstrated that these clusters may have potential applications in the development of NLO materials. Acknowledgements This work was supported by the Jiangsu Key Laboratory for the Chemistry of Low-Dimensional Materials (grant No. JSKC08053) and the Development Program of Huai’an (No. HAG07014). References [1] C. Zhang, Y.L. Song, F.E. Kühn, Y.X. Wang, H. Fun, X.Q. Xin, W.A. Herrmann, New J. Chem. 26 (2002) 58–65.

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