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The structures and properties of (AgCl)n (n = 2–13)
Accepted Manuscript The Structures and Properties of (AgCl)n (n=2
13)
Yue-Hong Yin, Lu Zhang PII: DOI: Reference:
S2210-271X(16)30427-3 http://dx.doi.org/10.1016/j.comptc.2016.10.013 COMPTC 2281
To appear in:
Computational & Theoretical Chemistry
Received Date: Revised Date: Accepted Date:
21 August 2016 17 October 2016 17 October 2016
Please cite this article as: Y-H. Yin, L. Zhang, The Structures and Properties of (AgCl)n (n=2 13), Computational & Theoretical Chemistry (2016), doi: http://dx.doi.org/10.1016/j.comptc.2016.10.013
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The Structures and Properties of (AgCl)n (n=2∼13) Yue-Hong Yin1 , Lu Zhang College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, Peoples Republic of China Key Laboratory of Atomic & Molecular Physics and Functional Materials of Gansu Province, Lanzhou 730070, Peoples Republic of China
Abstract The stable structures of (AgCl)n (n=2∼13) are obtained by using genetic algorithm combined with empirical potential and further optimized by DFT/B3P86 method. The results show that the lowest-energy structures of (AgCl)n (n < 5) are planar single-ring, while for n≥5 are 3D configurations and constructed by several distorted triangles and squares, and for n=11∼13 are cage-like structures. The clusters with the sizes of n=3, 6, 8 and 11 are more stable and the trimer is the most stable one. For the ground state structures, the IR spectra, vertical ionization potentials and electron affinities are also investigated. The electronic structure analysis reveals that the chemical bonds in (AgCl)n are ioniccovalent, and there also exist multi-center covalent bonds composed of the 4d/5s orbitals of Ag and 3p orbitals of Cl, which will further enhance the stability of the cluster. It is also found that (AgCl)n (n=11∼13) are with larger polarizabilities and hyperpolarizabilities. Keywords: (AgCl)n ; Geometrical structure; Stability; Electronic Structure
1. Introduction Silver halide including AgF, AgCl, AgBr and AgI are typical superionic conductors and they can be used as the high temperature conductors because their conductivities increase with the temperature [1, 2, 3]. Among them, AgCl has been paid great attentions due to its applications in photograph, solid electrolytes, and liquid semiconductors[4]. The AgCl crystal under normal conditions is rock-salt structure. Many works have been performed to study the structural, transport and dynamic properties of the solid and molten AgCl[5, 6, 7, 8, 9, 10]. Furthermore, the nano-materials of AgCl such as nanoparticles and nanowires were also prepared and characterized[11, 12, 13, 14]. Clusters are the aggregation including a few to thousands of atoms/molecules, and their structures and properties are different from those of the corresponding bulk materials. The studies on the (AgCl)n clusters were also reported. For experimental works, the photoelectron spectrum and valence shell structure of (AgCl)3 were investigated[15, 16]. T. P. Martin et al have prepared (AgCl)n (n≤3) and examined their infrared adsorption spectra[17]. There were a series of theoretical works on the structures and properties of (AgBr)n and (AgF)n , for example, F. Rabilloud et al have obtained the lowest-energy structures of (AgBr)n (n ≤ 2 and n ≤ 6) by configuration interaction (CI) and DFT calculations, respectively[18, 19]. And also, H. G. Zhang et al studied the geometries of (AgBr)n (n ≤ 9) by DFT computation[20]. In our early study, the structures and properties of (AgBr)n (n ≤ 6) were also explored[21]. F. Rabilloud et al have further investigated the stable isomers and affinities of (AgF)n (n ≤ 6)[22]. Recently, C. S. Song et al have explored the structural evolution of (AgF)n (n= 1∼12) clusters by DFT computations[23]. However, the theoretical exploration on the structures and properties of (AgCl)n is rare. Only F. Rabilloud et al have examined the lowest-energy structures of (AgCl)n (n=1∼6) by using DFT calculations. They found that the most stable structures of small-sized (AgCl)n were nonplanar cycles and the trimmer was particularly stable[24]. In this paper, we have systematically investigated the possible stable isomers of (AgCl)n (n=2∼13) and determined the lowest-energy structures. Moreover, the stabilities, IR spectra, electronic structures, polarizabilities and hyperpolarizabilities of the most stable isomers were also discussed. The paper is organized as follow: In Sec. II we introduce the computational method. In Sec. III we present our results and the discussions. 1 Corresponding
author. Tel 0931-7971503 E-mail address:[email protected]
Preprint submitted to Computational and Theoretical Chemistry
October 18, 2016
2. Computational Methods There are numerous isomers for a cluster with n atoms and the number of isomers increases dramatically with the cluster size. Thus the determination of ground-state structure of a cluster is one of the most complex and challenging problems in cluster physics. The global optimization methods such as simulated annealing, basin-hopping and genetic algorithm (GA) combined with empirical potentials could acquire the possible stable structures of a cluster. Thereinto, GA is an effective global searching technic by simulating the natural selection and evolution process and has been successfully applied in the exploring of cluster structures[25, 26]. However, the results of empirical potentials are debateable because of their lower precision. High precision ab initio methods could provide reliable results, but they are only appropriate to small-sized cluster due to the higher computing costs. A good compromise is to generate the possible stable isomers by global searching techniques combined with empirical potentials, then reoptimize the candidate structures using ab initio methods. In our study, the stable starting structures of (AgCl)n (n=2∼13) are obtained by using the GA combined with empirical potential[27]. These stable structures are further optimized by using DFT/B3P86 method[28, 29]. The number of isomer is increased with the size of cluster. Thus in our calculations, the number of initial structures for DFT optimization is selected according to the size of (AgCl)n . For every sizes of (AgCl)n (n=4∼7), about 8∼14 isomers obtained by GA are further optimized by DFT. While for larger sized cluster, we have selected 16 and 20 trial structures for every sizes of n=8∼10 and n=11∼13, respectively. Therefore, there are total 157 starting motifs are considered at DFT calculations. The basis set for Ag is CEP-31G[30], in which the inner core is represented by pseudo potential and 19 valence electrons are 4s, 4p, 4d and 5s. The double-zeta split valence basis set 6-31G* is employed for Cl. To check the validity of the computational method, we performed the calculations on AgCl molecule. The computed values of the bond length, dipole moment, ionization potential and vibration frequency are 2.31 Å, 5.77 Debye, 10.5 eV and 327 cm−1 , which are in reasonable agreement with the experimental results of 2.28 Å, 5.73 Debye, 10.1 eV and 339 ∼ 345 cm−1 [17]. It indicates that we can get the correct results at this theoretical level. Frequency calculations are achieved for the stable isomers to ensure that they are the true minima on the potential energy surface. For the lowest-energy structures, the electronic structures, polarizabilities and hyperpolarizabilities are also investigated. All the calculations are carried out using Gaussian 09 program[31] and the electronic structure analysis is performed by using the multiwfn program[32]. 3. Results and Discussion 3.1. Geometrical structure The optimized stable isomers of (AgCl)n are shown in Fig 1, Fig 2 and Fig 3. For (AgCl)2 , the lowest-energy structure (2-(a)) is a planar rhombus with Ag-Cl bond length of 2.52 Å, ∠AgClAg of 68.4 ◦ and ∠ClAgCl of 111.6 ◦ . 2-(b) is a linear structure with 0.95 eV in energy higher than that of 2-(a). The most stable structure of (AgCl)3 is a planar triangle (3-(a)). The distances of Ag-Cl are all 2.43 Å, ∠AgClAg and ∠ClAgCl are 75.7 ◦ and 164.3 ◦ , respectively. Isomer 3-(b) is a three-dimension (3D) structure, which can be looked as an AgCl molecule right above a rhombus. 3-(c) is also a linear structure. These two isomers are with lower stabilities and their energies are 1.04 eV and 1.44 eV higher than that of 3-(a), respectively. 4-(a) is a planar square with Ag-Cl bond length of 2.40 Å, ∠AgClAg of 88.8◦ and ∠ClAgCl of 178.8◦ . Both the second and third isomers are 3D structures. 4-(b) is a triangle cone and 4-(c) is a cube-like isomer. Their energies are 0.65 eV and 0.89 eV higher than that of 4-(a), respectively. For (AgCl)n (n=2∼4), the lowest-energy isomers are all planar single-ring, which are also the ground state structures of (AgF)n [22, 23] and (AgBr)n (n=2∼4)[18, 19, 20, 21]. However, for (AgCl)5 , the most stable one is not a planar isomer but a 3D structure. 5-(a) can be described as an upturned pentagon with a dihedral angle of 85.1◦ . Ag-Cl bond lengths are 2.39∼2.40 Å, ∠AgClAg 84.7◦ ∼94.8◦ and ∠ClAgCl 178.2◦ ∼179.3◦ . This isomer is also the ground state structure of (AgBr)5 [18, 19, 20, 21]. The second one 5-(b) is a planar pentagon. C. S. Song et al. have reported the planar pentagon as the ground-state structure of (AgF)5 [23]. Whereas for (AgCl)5 , this isomer is not the lowest-energy one but with energy 0.05 eV above 5-(a). 5-(c) can be looked as a tilted triangle covered on a distorted rhombus and its energy is 0.50 eV higher than 5-(a). The lowest-energy structure of (AgCl)6 (6-(a)) can be viewed as two planar triangles (3-(a)) overlapped up and down. Compared with 3-(a), the Ag-Cl distances in 6-(a) are elongated to 2.47 Å and ∠AgClAg increase to 77.8◦ , 2
while ∠ClAgCl decrease to 160.5◦ . This isomer is also the ground state structure of (AgF)6 [22, 23] and (AgBr)6 [18, 19, 20, 21]. 6-(b) can be described as two tilted triangles superimposed up and down, and its energy is 0.11 eV above 6-(a). 6-(c) is a chair-like structure while 6-(d) a planar hexagon and 6-(e) also a 3D structure with 0.70 eV in energy higher than 6-(a). 7-(a) is composed of a distorted triangle (3-(a)) and square (4-(a)). The Ag-Cl distances in triangle are 2.45∼2.52 Å, while in square are 2.42∼2.28 Å, ∠AgClAg and ∠ClAgCl in triangle and square are 75.6◦ ∼79.0◦ , 89.5◦ ∼90.1◦ , 155.3◦ ∼169.2◦ and 163.1◦ ∼177.3◦ , respectively. 7-(b) is a butterfly-like structure and this isomer is also the most stable one for (AgF)7 [23]. 7-(c) can be looked as a distorted triangle capped on a cube, while 7-(d) can be viewed as a linear isomer of (AgCl)2 vertically located in the center of a distorted pentagon. The energies of these three isomers are 0.56, 0.78 and 0.98 eV higher than that of 7-(a). Isomer 8-(a), 8-(b) and 8-(e) are all composed of two squares. For 8-(a), which is also the lowest-energy one for (AgF)8 [23], can be described as two squares superposed with relatively rotated 90.0◦ . The Ag-Cl bond lengths are 2.43Å and ∠AgClAg and ∠ClAgCl are 89.2◦ ∼98.8◦ and 170.5◦ ∼171.2◦ , respectively. In 8-(b), two up warped squares connect together, while for 8-(e), one square is parallel with the other one. 8-(c) is constituted by a triangle (3-(a)) and the unit of 5-(a). 8-(d) can be viewed as four triangles sharing common edges. 8-(f) is consisted of one square and two tilted rhombuses. Isomer 9-(a), 9-(b) and 9-(c) are all involved in three triangles with different connection modes. In 9-(a), the three triangles overlapped up and down, and the bond lengths of Ag-Cl in triangle are 2.49∼2.62 Å, while ∠AgClAg and ∠ClAgCl are 75.9◦ ∼102.3◦ and 135.9◦ ∼161.8◦ , respectively. It is also the lowest-energy one for (AgF)9 [23]. The energies of 9-(b) and 9-(c) are 0.11 and 0.30 eV higher than that of 9-(a). 9-(d) and 9-(e) are a cage-like and butterfly-like structure, respectively. All the stable isomers of (AgCl)10 are constructed by two seriously distorted triangles and one square. The most stable one 10-(a) can be looked as two distorted triangles vertically located above a tilted square. The bond lengths of Ag-Cl in triangle are 2.44∼2.87 Å, while in square are 2.46∼2.51 Å, ∠AgClAg and ∠ClAgCl in triangle and square are 76.1◦ ∼143.0◦ , 81.5◦ ∼96.2◦ and 100.5◦ ∼176.0◦ , 170.3◦ ∼171.7◦ , respectively. The energies of other isomers are near the most stable one, with only 0.08∼0.35 eV higher than 10-(a). The most stable isomer of (AgCl)11 (11-a) is a quasi-cage structure, which is fused of two distorted triangles and squares with sharing common edges. The bond lengths of Ag-Cl in triangle are 2.45∼2.60 Å, while in square are 2.46∼2.62 Å. The ∠AgClAg and ∠ClAgCl in triangle and square are 75.3◦ ∼92.2◦ , 80.7◦ ∼98.2◦ and 126.4◦ ∼175.6◦ , 143.0◦ ∼176.8◦ , respectively. The second one 11-(b) is a double-layered structure, in which each layer includes one rhombus and two triangles connected by sharing common edges. The other isomers are all constituted by two distorted squares and one triangle with different connection modes. Their energies are closed to the 11-(a), lie 0.02∼0.35 eV higher than that of 11-(a) . For n=12, the isomer 12-(a), which adopts cage-like configuration and comprises of several distorted triangles and squares, is found to be the lowest-energy structure. The bond lengths of Ag-Cl are 2.45∼2.60 Å, while ∠AgClAg and ∠ClAgCl are 74.5◦ ∼101.1◦ and 118.3◦ ∼158.6◦ , respectively. The second one can be looked as two triangles capped up and down on a planar hexagon and lies 0.03 eV in energy higher than 12-(a). The third one is a doublelayered structure, in which each layer includes two rhombus and triangles connected by sharing common edges and this isomer is only above 12-(a) with 0.06 eV. Both 12-(d) and 12-(f) are involved four distorted triangles and 12-(f) is also the lowest-energy isomer of (AgF)12 [23]. However, these two isomers are in energy higher than 12-(a) with 0.09 and 0.12 eV, respectively. Both12-(e) and 12-(g) are composed of three distorted squares and their energies are higher than 12-(a) with 0.11 and 0.16 eV, respectively. 13-(a) is also a quasi-cage structure including nine distorted triangles and two rhombuses connected with sharing common edges. The bond lengths of Ag-Cl are 2.42∼2.67 Å, while ∠AgClAg and ∠ClAgCl are 74.4◦ ∼112.3◦ and 103.8◦ ∼175.6◦ , respectively. 13-(b), 13-(c) and 13-(d) are also cage-like structures with 0.11 eV, 0.43 eV and 0.55 eV higher in energy than 13-(a). While 3-(e), 13-(f) and 13-(g) are all disorder isomers with three distorted triangles and one square. It can be seen from Fig 1∼3 that the energies of some isomers are closed (less than 0.1 eV) to each other by B3P86 calculations. It is also known that the stability order of isomers depends on the methods and the basis sets, thus these quasidegenerate structures are further optimized by using higher precision MP2 method combined with different basis sets such as LANL2DZ/CEP-31G for Ag and 6-31g* for Cl. When the basis set of CEP-31G for Ag and 6-31G* for Cl is applied, the stability orders of the isomers with closed energies by MP2 computations are in full accord with those of 3
B3P86 calculations and the corresponding relative energies are also listed in Fig 1∼3 in parentheses. While the basis set of LANL2DZ for Ag and 6-31g* for Cl is used, the most stable structures are also in good agreement with those of B3P86 calculations, while the stability order of some second and third stable isomers is different. For example, 12-(c) is 0.01eV in energy lower than that of 12-(b). However, the energy differences of these quasidegenerate isomers are small even in MP2 calculations, which implies that these isomers may be coexisted under finite temperature. It is found that the most stable structures of (AgCl)n are planar single-ring for n<5, while from n=5, the 3D isomers are more energy favored and the lowest-energy configurations are all constructed by several distorted triangle and square elements of (AgCl)3 and (AgCl)4 , and for n=11∼13, the most stable motifs are cage-like structures. The 3D lowest-energy structure of (AgBr)n is also first appeared from n=5[18, 19, 20, 21], while for (AgF)n , it is emerged from n=6[22, 23]. It is agreed with the conclusion of Rabilloud et al that the metal fluorides prefer planar rings while metal chlorides adopt nonplanar cycles[24]. The lowest-energy structures of (AgF)n , (AgCl)n and (AgBr)n are similar to each other for n=2∼6. For n>6, there is no report on (AgBr)n . Although both the most stable structures of (AgF)n and (AgCl)n are composed of several fused triangles and squares, they possess high symmetry for (AgF)n [23] while are distorted and with low symmetry for (AgCl)n . This effect may be attributed to the different electrical negative of F− and Cl− and thus the different intensities of ionic-covalent bonds in (AgF)n and (AgCl)n , this will be discussed later. The geometrical characters of (AgCl)n can be summarized as: (1) Ag and Cl atoms form alternative structures due to the ionic interaction between Ag+ and Cl− , just like typical ionic compound such as NaCl; (2) The Cl atoms are always located at the apexes while Ag atoms situated at the center of an edge; (3) Ag atoms are always near, while Cl atoms away from the center of cluster. In other words, the Ag-Ag distances are shorter than those of Cl-Cl; (4) ∠AgClAg mostly are cute angles while ∠ClAgCl near straight angles. These geometrical properties can be explained by their particular ionic-covalent bonds and will be discussed later. 3.2. Infrared Spectra Infrared spectrum (IR) is an important experimental tool to assign the geometrical configuration of a isomer. T. P. Martin et al. have examined the IR spectra of (AgCl)n (n=1∼3); F. Rabilloud et al optimized the stable structures of (AgCl)n (n=2∼6) and computed the IR spectra of the lowest-energy configurations by using B3LYP method[24]. In our calculations, the IR spectra of the ground state structures of (AgCl)n (n=2∼13) are shown in Fig 4 and the vibrational frequencies of IR peaks with higher intensities are also listed in Table 1. It can be seen from Table 1 that our results are agreed well with those of F. Rabilloud et al for the cluster sizes of n=2∼5, but more closed to the experimental results for n=2∼3. For (AgCl)6 , the vibrational frequencies in our calculations (97∼293 cm−1 ) are different from those (70∼309 cm−1 ) of F. Rabilloud et al, despite that the topological structures are similar to each other. However, we also optimized and computed the IR spectrum of the lowest-energy isomer of (AgCl)6 by using other method such as CISD and MP2, the results (95∼295 cm−1 for CISD and 108∼263 cm−1 for MP2) are accord with our results. It can be seen from Fig 4 that the stronger peaks for (AgCl)3 and (AgCl)4 are located at about 100∼300 cm−1 . Because the larger-sized (AgCl)n are constituted by the trimer and tetramer, their IR spectra are also within the scope of 100∼300 cm−1 . Furthermore, the spectra for (AgCl)11 ∼(AgCl)13 exhibit different modes and become more complex due to their cage-like configurations. 3.3. Stability The average binding energy Eav is calculated as:, Eav = (E[(AgCl)n ] − n ∗ E(AgCl))/n
(1)
where the E[(AgCl)n ] and E(AgCl) are the energies of (AgCl)n cluster and AgCl monomer, respectively. Figure 5 plots the Eav of (AgCl)n as a function of cluster size n. The Eav increases rapidly when n=2 to 4, then grows slowly and becomes nearly saturated until n=13. It demonstrates that the overall stability of (AgCl)n is steady increased. To evaluate the relative stability of (AgCl)n , the first (∆1 E) and second energy difference (∆2 E ) are also calculated as follow: ∆1 E = E[(AgCl)n ] − E[(AgCl)n−1 ] 4
(2)
Table 1: The frequencies of the stronger IR vibrational modes of the most stable isomers of (AgCl)n
n 2 3 4 5 6 7 8 9 10 11 12 13
Present work 62, 163, 264 68, 81, 193, 308 61, 95, 235, 317 60, 74, 85, 244, 296, 310, 323, 334 97, 178, 243, 293 85, 100, 272, 282, 292, 301, 317 92, 273, 280, 297, 301 138, 154, 166, 184, 210, 276, 280 96, 124, 238, 256, 265, 280, 286 115, 138, 152, 166, 178, 193, 206, 228, 243, 276, 321 86, 105, 115, 127, 174, 257, 268, 276, 289 125, 136, 146, 176, 194, 233, 243, 279, 294
Ref[24] 62, 153, 245 62, 86, 188, 302 60, 89, 231, 306 61, 74, 85, 240, 294, 301, 309 70, 81, 294, 309 -
Table 2: The NPA charges of Ag/Cl atoms of the most stable structures of (AgCl)n
n 2 3 4 5 6 7 8 9 10 11 12 13
Charge/e 0.65/ − 0.65 0.54/ − 0.54 0.56/ − 0.56 0.54 ∼ 0.59/ − 0.54 ∼ −0.57 0.50/ − 0.50 0.49 ∼ 0.57/ − 0.50 ∼ −0.52 0.52 ∼ 0.54/ − 0.52 ∼ −0.54 0.49 ∼ 0.52/ − 0.49 ∼ −0.54 0.50 ∼ 0.59/ − 0.49 ∼ −0.56 0.48 ∼ 0.55/ − 0.48 ∼ −0.55 0.44 ∼ 0.57/ − 0.50 ∼ −0.55 0.37 ∼ 0.57/ − 0.42 ∼ −0.53
5
Expt[17] 198, 255 96, 199, 322 -
∆2 E = E[(AgCl)n+1 ] + E[(AgCl)n−1 ] − 2E[(AgCl)n ]
(3)
where the E[(AgCl)n+1 ], E[(AgCl)n−1 ] and E[(AgCl)n ] are the energies of (AgCl)n+1 , (AgCl)n−1 and (AgCl)n , respectively. The higher the ∆1 E and ∆2 E are, the more stable the isomer is. The ∆1 E and ∆2 E of (AgCl)n are plotted in Fig 6. It shows that there are relatively larger values of ∆1 E and ∆2 E for n=3, 4, 6, 8 and 11, which means that these isomers are more stable than their neighbors. Moreover, the ∆2 E of the trimer and tetramer are the first and second highest, respectively. It suggests that (AgCl)3 and (AgCl)4 are especially stable. Therefore, all the most stable structures of (AgCl)n (n>6) contain several units of trimer and tetramer. Meanwhile, the hexamer and octamer are constituted by two trimers and tetramers, respectively. Thus these two isomers are also with particular stabilities. While the (AgCl)11 is the first cage-like structure, therefore, it is with higher stability too. The energy gap, the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which indicates the chemical stability of an isomer. The higher energy gap means chemical inertness. The energy gaps of (AgCl)n are shown in Fig 7. There are local maxima at n=3, 4 and 5, which implies that these three ring-like isomers are with higher chemical stabilities. It should be stressed that (AgCl)3 is also with the highest energy gap and thus the chemical stability. That is to say, trimer is the most stable one not only in energy but also in chemical stability. 3.4. Vertical ionization potentials and electron affinities Vertical ionization potential (VIP) and vertical electron affinity (VEA) are the energy difference between the neutral cluster and the corresponding cationic and anionic cluster, which remains the geometrical structure of the neutral cluster. VIP and VEA can measure the capacity of losing and receiving electrons. The VIP and VEA of the most stable structures of (AgCl)n (n=2∼13) are also displayed in Fig 8. It can be seen that the VIP increases firstly from 10.03 eV for n=2 to the maximum of 10.40 eV for n=3, then decreases gradually to 9.34 eV until n=11, while increases again up to n=13. The similar evolution behavior of VIP for (AgF)n (n=2∼12) was also been observed[23]. The VEA of (AgCl)n decreases from 1.63 eV for n=2 to the minimum of 1.33 eV for n=3, then increases slowly to 2.84 eV for n=13. The VIP of (AgCl)n are in the range of 9.35∼10.40 eV, which are larger than those of 8.50∼9.50 eV for (AgF)n (n=2∼12)[23]. While the VEA for (AgCl)n extend from 1.35 to 2.84 eV, which are smaller than those of 3.03∼3.95 eV for (AgF)n (n=2∼6)[22]. The larger VIP means that the (AgCl)n are difficult to lose electrons, while the smaller VEA suggests that they tend to gain electrons easily. 3.5. Chemical bonds Silver halide are known for their ionic-covalent bonds. To explore the electrostatic interaction in (AgCl)n cluster, the Natural Population Analysis (NPA) charges of Ag and Cl atoms are calculated and listed in Table 2. It shows that the charges on Ag atoms are positive (0.37∼0.65 e) while on Cl negative (-0.44∼-0.65 e), which indicates that the charges are transferred from Ag to Cl atoms and there exists stronger ionic interaction between Ag and Cl ions. Thus the (AgCl)n tend to form alternative cycles. For example, all the lowest-energy structures of (AgCl)n (n=2∼5) are alternative rings. Furthermore, because of the strong repulsion, Al anions incline to be far away from each other and thus locate at the apexes of cluster. The electron localization function (ELF) is an effective tool to visually describe the covalent interaction. The concept of ELF was proposed by Becke and Edgecombe and developed by Savin and coworkers[33, 34]. It is defined as follow: 1 ∑ 1 |∇ρ|2 2 i p ∇ψi p − 8 ρ 2 ELF = [1 + ]−1 (4) 3 2 2/3 ρ5/3 10 (3π ) where the ρ,∇ρ and | ψi |2 is the electron density, its gradient and the kinetic energy density, respectively. ELF is within the range of 0∼1. A large ELF value means that electrons are greatly localized, indicating that there will be a covalent bond. Because the trimer and tetramer are the most stable isomers and also the constitution units for large-sized cluster, the ELF of (AgCl)3 and (AgCl)4 are calculated and presented in Fig 9. It shows that the ELF 6
in the areas between Ag and Cl atoms for both the (AgCl)3 and (AgCl)4 are in the range of 0.1∼0.3. These results show that Ag atoms form covalent interaction with Cl atoms. To further study the covalent interaction, the particle density of states (PDOS) of (AgCl)3 and (AgCl)4 are also calculated and presented in Fig 10. It is clear that the PDOS of 4d and 5s components of Ag overlap well with the 3p components of Cl in the energy range of -13∼-8 eV. It implies that the covalent interaction can be described as the 4d and 5s components of Ag hydride and further mix with the 3p components of Cl to form chemical bonds. To deeply understand these covalent bonds, the molecular orbitals of (AgCl)3 and (AgCl)4 are also further studied. It is found that these covalent interactions often lead to multi-center bonds (presented in Fig 11) in (AgCl)n . The multi-center bonds can be divided into three styles, such as Ag-Cl-Ag, Cl-Ag-Cl three-center bonds and multicenter bond composed by Ag atoms. The Ag-Cl-Ag three-center bonds (Fig 11 (a) and (d)) bend the ∠AgClAg into a cute angle while Cl-Ag-Cl three-center bonds (Fig 11 (b) and (e)) make the ∠ClAgCl near a straight angle. Furthermore, the multi-center covalent bonds among Ag atoms (Fig 11 (c) and (f)) incline to drag the Ag atoms closer while the electrostatic repulsions push the Cl atoms away, thus make the Ag-Ag distances are shorter than those of Cl-Cl. Although these multi-center bonds will lead to the geometrical distortions of cluster, they can also greatly promote the stability of cluster. Therefore, the distorted structures are more stable for larger sized (AgCl)n cluster. For example, the stable structures of (AgCl)n (n>6) are composed by distorted triangles and squares. It is also found that the Ag-Ag distance plays an important role to determine the intensity of the multi-center bond. The shorter the Ag-Ag distances are, the stronger the bond is. For example, since the Ag-Ag distances (3.22∼3.63Å) in distorted pentagon (5-(a)) are shorter than those (3.80Å) in planar pentagon (5-(b)), the tilted pentagon is more stable. In addition, although there is a four-center bond composed of Ag atoms in (AgCl)4 (Fig 11 (f)), which is expected to form stronger bond than that of three-center bond in (AgCl)3 (Fig 11 (c)). However, because the Ag-Ag bond lengths in (AgCl)3 (2.98Å) are shorter than those (3.35Å) of in (AgCl)4 , the three-center bond in (AgCl)3 actually is more stable. The chemical bonds in (AgCl)n are ionic-covalent. According to the results of Rabilloud et al that the calculated charges of (AgF)n are larger than those of (AgCl)n for n<7, which implies that the ionic interaction in (AgF)n is stronger than that in (AgCl)n [24]. Our results show that the most stable structures of (AgCl)n are distorted configurations with low symmetry due to the strong covalent interactions. It is different from the results of C. S. Song et al that the fused triangles and squares with high symmetry are more energy favored for (AgF)n . Thus our results indicate that the covalent interactions in (AgCl)n are stronger. 3.6. Dipole moments, polarizabilities and hyperpolarizabilities When a system is in a weak and homogeneous electric field, its energy can be described as: 1 1 E = E 0 − µα Fα − ααβ Fα Fβ − βαβγ Fα Fβ Fγ − · · · 2 6
(5)
where E 0 is the system total energy absence of an electric field and Fα is the electric field component along a direction of α. µα , ααβ and βαβγ denote the dipole moment, the elements of the linear polarizability and the first hyperpolarizabilitiy, respectively. The mean polarizability (α) and hyperpolarizability (β0 ) can be defined as: 1 (α xx + αyy + αzz ) 3
(6)
β0 = (β2x + β2y + β2z )1/2
(7)
α=
in which βi =
3 (βiii + βi j j + βikk ) i, j, k = x, y, z 5
(8)
β0 is also known as the second-order nonlinear optical response coefficient. These physical quantities characters the response of a system in the external electric filed and are closely related to the optical properties. Table 3 lists the dipole moments, polarizabilities and hyperpolarizabilities of (AgCl)n (n=2∼13). The geometrical structures of 7
(AgCl)n (n=2∼6) are with higher symmetries, hence the dipole moment of these isomers are zero. For n=7∼13, the µ increase from 0.18 Debye to 3.29 Debye. The polarizabilities of (AgCl)n are monotonically increased with the cluster sizes. The hyperpolarizabilities of (AgCl)n present even-odd oscillation behavior when n<11, then monotonically increase until n=13. It should be noted that α and β0 of (AgCl)n (n=11∼13) are particularly large (331.74 ∼ 422.77 a. u. for α and 351.79 ∼ 694.85 a. u. for β), which means that (AgCl)n are easily deformed under an external electric filed. On one hand, there is large polarizability in Cl and Ag ions due to their larger ionic radius (181Å for Cl− and 126Å for Ag+ ), on the other hand, (AgCl)n (n=11∼13) are cage-like structures and with lower symmetries, thus their polarizabilities and hyperpolarizabilities are larger. 4. Conclusion The stable structures of (AgCl)n (n<5) are planar single-ring, while from n=5 are 3D configurations and constructed by the distorted triangle and square unties of (AgCl)3 and (AgCl)4 . The cage-like configures are more energy favored for (AgCl)11 ∼(AgCl)13 . The clusters with the sizes of n=3, 6, 8 and 11 are more stable and the trimmer is the most stable one and can be looked as a magic number cluster. The stronger IR peaks of (AgCl)n are located at about 100 ∼300 cm−1 . The VIP of (AgCl)n are in the range of 9.35∼10.40 eV, while the VEA extend from 1.35 to 2.84 eV. The chemical bonds in (AgCl)n are ionic-covalent. The NPA indicates that the charges are transferred from Ag to Cl atoms, which leads to ionic interaction. Moreover, the covalent bonds formed by the 4d and 5s components of Ag and the 3p components of Cl are also observed. It is emphasized that the multi-center bonds such as the Ag-ClAg, Cl-Ag-Cl three-center bonds and the multi-center bonds composed of Ag atoms, will further enhance the stability of (AgCl)n . It is also found that (AgCl)n (n=11∼13)are with larger polarizabilities and hyperpolarizabilities. 5. Acknowledgements We thank financial support from the National Natural Science Foundation of PR China (Grant No. 11164024),the College Research Funding of Gansu Province. We also thank Computational Center of Shenzhen for offering computer facilities. References [1] K. Shahi, J. B. Wagner, Fast ion transport in silver halide solid solutions and multiphase systems. Appl. Phys. Lett. 37 (1980) 757-759. [2] D. E. Day, G. H. Frischat, T. Minami, Preparation, Properties, and Structure of Special GlassesPreparation and properties of superionic conducting glasses based on silver halides. J. Non-Cryst. Solids 56 (1983) 15-26. [3] J. B. Boyce, B. A. Huberman, Superionic conductors: Transitions, structures, dynamics. Phys. Rep. 51 (1979) 189-265. [4] H. Daupor, S. Wongnawa, Flower-like Ag/AgCl microcrystals: Synthesis and photocatalytic activity. Mater. Chem. Phys. 159 (2015) 71-82. [5] C. Tasseven, J. Trull`as, O. Alcaraz, M. Silbert, A. Gir´o, Static structure and ionic transport in molten AgBr and AgCl. J. Chem. Phys. 106 (1997) 7286-7294. [6] C. J. Evans, M. C. L. Gerry, The microwave spectra and structures of Ar-AgX (X=F, Cl, Br). J. Chem. Phys. 112 (2000) 1321-1329. [7] T. Benmessabih, B. Amrani, F. El Haj Hassan, F. Hamdache, M. Zoaeter, Computational study of AgCl and AgBr semiconductors. Phys. B: Cond. Matt. 392 (2007) 309-317. [8] Y. Kawakita, T. Enosaki, S. i. Takeda, K. Maruyama, Structural study of molten Ag halides and molten AgCl-AgI mixture. J. Non-Cryst. Solids 353 (2007) 3035-3039. [9] S. Tahara, H. Fujii, Y. Kawakita, S. Kohara, Y. Yokota,S. i. Takeda, Structure of the molten silver chloride. J. Non-Cryst. Solids 353 (2007) 1994-1998. [10] S. Takeda, Y. Nagata, Y. Kawakita, Slow dynamic properties of molten silver halides. J. Non-Cryst. Solids 353 (2007) 3169-3173. [11] P. Calandra, A. Longo, V. Marcian,V. Turco Liveri, Physicochemical Investigation of Lightfast AgCl and AgBr Nanoparticles Synthesized by a Novel Solid-Solid Reaction. J. Phys. Chem. B. 107 (2003) 6724-6729. [12] T. Sugimoto, K. i. Kimijima, New Approach to the Formation Mechanism of AgCl Nanoparticles in a Reverse Micelle System. J. Phys. Chem. B. 107 (2003) 10753-10759. [13] C. Sun, P. Chen, S. Zhou, AgCl nanoparticle nanowires fabricated by template method. Mater. Lett. 61 (2007) 1645-1648. [14] Y. Sun, Conversion of Ag Nanowires to AgCl Nanowires Decorated with Au Nanoparticles and Their Photocatalytic Activity. J. Phys. Chem. C. 114 (2010) 2127-2133. [15] A. W. Potts, M. L. Lyus, The photoelectron spectrum and valence shell structure of (CuX)3 and (AgCl)3 . J. Elec. Spec. Rela. Phen. 13 (1978) 305-315. [16] J. Schmelzer, U. Lembke ,R. Kranold, Nucleation and growth of AgCl clusters in a sodium borate glass: Numerical analysis and SAXS results. J. Chem. Phys. 113 (2000) 1268-1275. [17] T. P. Martin, H. Schaber, Matrix isolated copper and silver halide clusters. J. Chem. Phys. 73 (1980) 3541-3546.
8
[18] F. Rabilloud, F. Spiegelmann, J. L. Heully, Ab initio calculations of structural and electronic properties of small silver bromide clusters. J. Chem. Phys. 111 (1999) 8925-8933. [19] F. Rabilloud, F. Spiegelman, J. M. LHermite, P. Labastie, Ab initio study of silver bromide Agn Br(+) p clusters (n≤6,p=n,n-1). J. Chem. Phys. 114 (2001) 289-305. [20] H. G. Zhang, Z. A. Schelly, D. S. Marynick, Theoretical Study of the Molecular and Electronic Structures of Neutral Silver Bromide Clusters (AgBr)n , n = 1-9. J. Phys. Chem. A. 104 (2000) 6287-6294. [21] Y. H. Yin, H. S. Chen, Y. Song, The DFT study on the structures and properties of (AgBr)n (n≤¡6). J. Mole. Struc. Theo. 959 (2010) 30-34. [22] F. Rabilloud, O. Bonhomme, J. M. LHermite, P. Labastie, Adiabatic electron affinities of (AgF)n clusters: Experiment and DFT calculations. Chem. Phys. Lett. 454 (2008) 153-157; [23] C. Song, Z. Tian, First principles study on the size evolution and stability of (AgF)n (n= 1-12) clusters. Comp. Theo. Chem. 1074 (2015) 157-162. [24] F. Rabilloud, Structure and stability of coinage metal fluoride and chloride clusters (Mn Fn and Mn Cln , M=Cu, Ag, or Au; n=1-6). J. Comput. Chem. 33 (2012) 2083-2091. [25] D. M. Deaven, K. M. Ho, Molecular Geometry Optimization with a Genetic Algorithm. Phys. Rev. Lett. 75 (1995) 288-291. [26] J. Zhao, R. H. Xie, Genetic Algorithms for the Geometry Optimization of Atomic and Molecular Clusters. J. Comp. Theo. Nano. 1 (2004) 117-131. [27] A. K. Ivanov-Schitz, B. J. Mazniker, E. S. Povolotskaya, A molecular dynamics study of ionic transport in α-AgI-based solid solutions. Solid State Ionics 159 (2003) 63-69. [28] J. P. Perdew, Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Phys. Rev. B. 33 (1986) 88228824. [29] A. D. Becke, Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 98 (1993) 5648. [30] W. J. Stevens, M. Krauss, H. Basch, P. G. Jasien, Relativistic compact effective potentials and efficient, shared-exponent basis sets for the third, fourth, and fifth row atoms. Canadian J. Chem. 70 (1992) 612-630. [31] M. J. Frisch, G. Trucks, H. Schlegel, G. Scuseria, M. Robb, J. Cheeseman, J. Montgomery, T. Vreven, K. Kudin,J. Burant, Gaussian 03, revision C. 02. (2008). [32] T. Lu, F. Chen, Multiwfn: a multifunctional wavefunction analyzer. J. Comp. Chem. 33 (2012) 580-592. [33] B. Silvi, A. Savin, Classification of chemical bonds based on topological analysis of electron localization functions. Nature 371 (1994) 683-686. [34] A. Savin, R. Nesper, S. Wengert, T. F. Fssler, ELF: The electron localization function. Angew. Chem. Int. Ed. 36 (1997) 1808-1832. [35] T. Yanai, D. P. Tew, N. C. Handy, A new hybrid exchangeCcorrelation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem. Phys, Lett. 393 (2004) 51-57.
9
Table 3: The dipole moments (µ), polarizabilities (α) and hyperpolarizabilities (β) (in a. u.) of the most stable structures of of (AgCl)n (n = 2 − 13)
n µ α β
2 0.00 63.49 0.14
3 0.00 99.28 2.75
4 0.00 134.64 0.43
5 0.09 168.75 120.85
6 0.00 195.88 3.53
7 0.97 233.28 307.04
8 0.18 264.05 22.34
9 0.47 291.79 77.10
10 2.86 331.74 51.79
11 1.93 355.69 358.23
12 3.29 396.15 561.03
13 1.27 422.77 694.85
Figure 1: The stable structures of (AgCl)n (n=2∼7), △E is the energy difference (in unit eV) between the isomer and the lowest-energy structure. The values in parentheses are the △E by MP2 calculations. The green and grey balls are Cl and Ag atoms, respectively.
10
Figure 2: The stable structures of (AgCl)n (n=8∼10), △E is the energy difference (in unit eV) between the isomer and the lowest-energy structure. The values in parentheses are the △E by MP2 calculations. The green and grey balls are Cl and Ag atoms, respectively.
Figure 3: The stable structures of (AgCl)n (n=11∼13), △E is the energy difference (in unit eV) between the isomer and the lowest-energy structure. The values in parentheses are the △E by MP2 calculations. The green and grey balls are Cl and Ag atoms, respectively.
11
Figure 4: The IR spectra of (AgCl)n
12
1.7
1.6
1.5
av
E /eV
1.4
1.3
1.2
1.1
1.0
0.9
0.8 2
4
6
8
10
12
14
n Figure 5: The average binding energy Eav of (AgCl)n .
0.8
E 2.4
2.0
0.0
1
E 1.6
-0.8
2
4
6
8
10
n
Figure 6: The △1 E and △2 E of (AgCl)n .
13
12
5.0
Gap/
eV
5.5
4.5
4.0 2
4
6
8
10
12
14
n Figure 7: The energy gap of (AgCl)n .
10.5
3.0
2.7 10.2
9.9 2.1
1.8
9.6
1.5
9.3 1.2 1
2
3
4
5
6
7
8
9
10
11
12
13
n
Figure 8: The VIP and VEA for the lowest-energy isomers of (AgCl)n .
14
14
VEA/eV
VIP/eV
2.4
Figure 9: The ELF of (AgCl)3 (a) and (AgCl)4 (b).
Ag 4d
40
(AgCl)
Cl
3
Ag 4d
3p
40
(AgCl)
Cl
4
3p
Ag 5s
PDOS
PDOS
Ag 5s
20
20
0
0 -12
-10
-8
-6
-12
-4
Energy/eV
-10
-8 Energy/eV
Figure 10: The PDOS of (AgCl)3 and (AgCl)4 .
15
-6
-4
Figure 11: The typical molecular orbitals of (AgCl)3 and (AgCl)4 .
16
Highlights
.The stable structures of (AgCl)n (n=2~13) were obtained.
.The trimer is the most stable one. .The chemical bonds in (AgCl)n are ionic-covalent. . (AgCl)n (n=11~13) are with larger polarizabilities and hyper polarizabilities.
*Graphical Abstract (for review)
13)
Yue-Hong Yin, Lu Zhang PII: DOI: Reference:
S2210-271X(16)30427-3 http://dx.doi.org/10.1016/j.comptc.2016.10.013 COMPTC 2281
To appear in:
Computational & Theoretical Chemistry
Received Date: Revised Date: Accepted Date:
21 August 2016 17 October 2016 17 October 2016
Please cite this article as: Y-H. Yin, L. Zhang, The Structures and Properties of (AgCl)n (n=2 13), Computational & Theoretical Chemistry (2016), doi: http://dx.doi.org/10.1016/j.comptc.2016.10.013
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The Structures and Properties of (AgCl)n (n=2∼13) Yue-Hong Yin1 , Lu Zhang College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, Peoples Republic of China Key Laboratory of Atomic & Molecular Physics and Functional Materials of Gansu Province, Lanzhou 730070, Peoples Republic of China
Abstract The stable structures of (AgCl)n (n=2∼13) are obtained by using genetic algorithm combined with empirical potential and further optimized by DFT/B3P86 method. The results show that the lowest-energy structures of (AgCl)n (n < 5) are planar single-ring, while for n≥5 are 3D configurations and constructed by several distorted triangles and squares, and for n=11∼13 are cage-like structures. The clusters with the sizes of n=3, 6, 8 and 11 are more stable and the trimer is the most stable one. For the ground state structures, the IR spectra, vertical ionization potentials and electron affinities are also investigated. The electronic structure analysis reveals that the chemical bonds in (AgCl)n are ioniccovalent, and there also exist multi-center covalent bonds composed of the 4d/5s orbitals of Ag and 3p orbitals of Cl, which will further enhance the stability of the cluster. It is also found that (AgCl)n (n=11∼13) are with larger polarizabilities and hyperpolarizabilities. Keywords: (AgCl)n ; Geometrical structure; Stability; Electronic Structure
1. Introduction Silver halide including AgF, AgCl, AgBr and AgI are typical superionic conductors and they can be used as the high temperature conductors because their conductivities increase with the temperature [1, 2, 3]. Among them, AgCl has been paid great attentions due to its applications in photograph, solid electrolytes, and liquid semiconductors[4]. The AgCl crystal under normal conditions is rock-salt structure. Many works have been performed to study the structural, transport and dynamic properties of the solid and molten AgCl[5, 6, 7, 8, 9, 10]. Furthermore, the nano-materials of AgCl such as nanoparticles and nanowires were also prepared and characterized[11, 12, 13, 14]. Clusters are the aggregation including a few to thousands of atoms/molecules, and their structures and properties are different from those of the corresponding bulk materials. The studies on the (AgCl)n clusters were also reported. For experimental works, the photoelectron spectrum and valence shell structure of (AgCl)3 were investigated[15, 16]. T. P. Martin et al have prepared (AgCl)n (n≤3) and examined their infrared adsorption spectra[17]. There were a series of theoretical works on the structures and properties of (AgBr)n and (AgF)n , for example, F. Rabilloud et al have obtained the lowest-energy structures of (AgBr)n (n ≤ 2 and n ≤ 6) by configuration interaction (CI) and DFT calculations, respectively[18, 19]. And also, H. G. Zhang et al studied the geometries of (AgBr)n (n ≤ 9) by DFT computation[20]. In our early study, the structures and properties of (AgBr)n (n ≤ 6) were also explored[21]. F. Rabilloud et al have further investigated the stable isomers and affinities of (AgF)n (n ≤ 6)[22]. Recently, C. S. Song et al have explored the structural evolution of (AgF)n (n= 1∼12) clusters by DFT computations[23]. However, the theoretical exploration on the structures and properties of (AgCl)n is rare. Only F. Rabilloud et al have examined the lowest-energy structures of (AgCl)n (n=1∼6) by using DFT calculations. They found that the most stable structures of small-sized (AgCl)n were nonplanar cycles and the trimmer was particularly stable[24]. In this paper, we have systematically investigated the possible stable isomers of (AgCl)n (n=2∼13) and determined the lowest-energy structures. Moreover, the stabilities, IR spectra, electronic structures, polarizabilities and hyperpolarizabilities of the most stable isomers were also discussed. The paper is organized as follow: In Sec. II we introduce the computational method. In Sec. III we present our results and the discussions. 1 Corresponding
author. Tel 0931-7971503 E-mail address:[email protected]
Preprint submitted to Computational and Theoretical Chemistry
October 18, 2016
2. Computational Methods There are numerous isomers for a cluster with n atoms and the number of isomers increases dramatically with the cluster size. Thus the determination of ground-state structure of a cluster is one of the most complex and challenging problems in cluster physics. The global optimization methods such as simulated annealing, basin-hopping and genetic algorithm (GA) combined with empirical potentials could acquire the possible stable structures of a cluster. Thereinto, GA is an effective global searching technic by simulating the natural selection and evolution process and has been successfully applied in the exploring of cluster structures[25, 26]. However, the results of empirical potentials are debateable because of their lower precision. High precision ab initio methods could provide reliable results, but they are only appropriate to small-sized cluster due to the higher computing costs. A good compromise is to generate the possible stable isomers by global searching techniques combined with empirical potentials, then reoptimize the candidate structures using ab initio methods. In our study, the stable starting structures of (AgCl)n (n=2∼13) are obtained by using the GA combined with empirical potential[27]. These stable structures are further optimized by using DFT/B3P86 method[28, 29]. The number of isomer is increased with the size of cluster. Thus in our calculations, the number of initial structures for DFT optimization is selected according to the size of (AgCl)n . For every sizes of (AgCl)n (n=4∼7), about 8∼14 isomers obtained by GA are further optimized by DFT. While for larger sized cluster, we have selected 16 and 20 trial structures for every sizes of n=8∼10 and n=11∼13, respectively. Therefore, there are total 157 starting motifs are considered at DFT calculations. The basis set for Ag is CEP-31G[30], in which the inner core is represented by pseudo potential and 19 valence electrons are 4s, 4p, 4d and 5s. The double-zeta split valence basis set 6-31G* is employed for Cl. To check the validity of the computational method, we performed the calculations on AgCl molecule. The computed values of the bond length, dipole moment, ionization potential and vibration frequency are 2.31 Å, 5.77 Debye, 10.5 eV and 327 cm−1 , which are in reasonable agreement with the experimental results of 2.28 Å, 5.73 Debye, 10.1 eV and 339 ∼ 345 cm−1 [17]. It indicates that we can get the correct results at this theoretical level. Frequency calculations are achieved for the stable isomers to ensure that they are the true minima on the potential energy surface. For the lowest-energy structures, the electronic structures, polarizabilities and hyperpolarizabilities are also investigated. All the calculations are carried out using Gaussian 09 program[31] and the electronic structure analysis is performed by using the multiwfn program[32]. 3. Results and Discussion 3.1. Geometrical structure The optimized stable isomers of (AgCl)n are shown in Fig 1, Fig 2 and Fig 3. For (AgCl)2 , the lowest-energy structure (2-(a)) is a planar rhombus with Ag-Cl bond length of 2.52 Å, ∠AgClAg of 68.4 ◦ and ∠ClAgCl of 111.6 ◦ . 2-(b) is a linear structure with 0.95 eV in energy higher than that of 2-(a). The most stable structure of (AgCl)3 is a planar triangle (3-(a)). The distances of Ag-Cl are all 2.43 Å, ∠AgClAg and ∠ClAgCl are 75.7 ◦ and 164.3 ◦ , respectively. Isomer 3-(b) is a three-dimension (3D) structure, which can be looked as an AgCl molecule right above a rhombus. 3-(c) is also a linear structure. These two isomers are with lower stabilities and their energies are 1.04 eV and 1.44 eV higher than that of 3-(a), respectively. 4-(a) is a planar square with Ag-Cl bond length of 2.40 Å, ∠AgClAg of 88.8◦ and ∠ClAgCl of 178.8◦ . Both the second and third isomers are 3D structures. 4-(b) is a triangle cone and 4-(c) is a cube-like isomer. Their energies are 0.65 eV and 0.89 eV higher than that of 4-(a), respectively. For (AgCl)n (n=2∼4), the lowest-energy isomers are all planar single-ring, which are also the ground state structures of (AgF)n [22, 23] and (AgBr)n (n=2∼4)[18, 19, 20, 21]. However, for (AgCl)5 , the most stable one is not a planar isomer but a 3D structure. 5-(a) can be described as an upturned pentagon with a dihedral angle of 85.1◦ . Ag-Cl bond lengths are 2.39∼2.40 Å, ∠AgClAg 84.7◦ ∼94.8◦ and ∠ClAgCl 178.2◦ ∼179.3◦ . This isomer is also the ground state structure of (AgBr)5 [18, 19, 20, 21]. The second one 5-(b) is a planar pentagon. C. S. Song et al. have reported the planar pentagon as the ground-state structure of (AgF)5 [23]. Whereas for (AgCl)5 , this isomer is not the lowest-energy one but with energy 0.05 eV above 5-(a). 5-(c) can be looked as a tilted triangle covered on a distorted rhombus and its energy is 0.50 eV higher than 5-(a). The lowest-energy structure of (AgCl)6 (6-(a)) can be viewed as two planar triangles (3-(a)) overlapped up and down. Compared with 3-(a), the Ag-Cl distances in 6-(a) are elongated to 2.47 Å and ∠AgClAg increase to 77.8◦ , 2
while ∠ClAgCl decrease to 160.5◦ . This isomer is also the ground state structure of (AgF)6 [22, 23] and (AgBr)6 [18, 19, 20, 21]. 6-(b) can be described as two tilted triangles superimposed up and down, and its energy is 0.11 eV above 6-(a). 6-(c) is a chair-like structure while 6-(d) a planar hexagon and 6-(e) also a 3D structure with 0.70 eV in energy higher than 6-(a). 7-(a) is composed of a distorted triangle (3-(a)) and square (4-(a)). The Ag-Cl distances in triangle are 2.45∼2.52 Å, while in square are 2.42∼2.28 Å, ∠AgClAg and ∠ClAgCl in triangle and square are 75.6◦ ∼79.0◦ , 89.5◦ ∼90.1◦ , 155.3◦ ∼169.2◦ and 163.1◦ ∼177.3◦ , respectively. 7-(b) is a butterfly-like structure and this isomer is also the most stable one for (AgF)7 [23]. 7-(c) can be looked as a distorted triangle capped on a cube, while 7-(d) can be viewed as a linear isomer of (AgCl)2 vertically located in the center of a distorted pentagon. The energies of these three isomers are 0.56, 0.78 and 0.98 eV higher than that of 7-(a). Isomer 8-(a), 8-(b) and 8-(e) are all composed of two squares. For 8-(a), which is also the lowest-energy one for (AgF)8 [23], can be described as two squares superposed with relatively rotated 90.0◦ . The Ag-Cl bond lengths are 2.43Å and ∠AgClAg and ∠ClAgCl are 89.2◦ ∼98.8◦ and 170.5◦ ∼171.2◦ , respectively. In 8-(b), two up warped squares connect together, while for 8-(e), one square is parallel with the other one. 8-(c) is constituted by a triangle (3-(a)) and the unit of 5-(a). 8-(d) can be viewed as four triangles sharing common edges. 8-(f) is consisted of one square and two tilted rhombuses. Isomer 9-(a), 9-(b) and 9-(c) are all involved in three triangles with different connection modes. In 9-(a), the three triangles overlapped up and down, and the bond lengths of Ag-Cl in triangle are 2.49∼2.62 Å, while ∠AgClAg and ∠ClAgCl are 75.9◦ ∼102.3◦ and 135.9◦ ∼161.8◦ , respectively. It is also the lowest-energy one for (AgF)9 [23]. The energies of 9-(b) and 9-(c) are 0.11 and 0.30 eV higher than that of 9-(a). 9-(d) and 9-(e) are a cage-like and butterfly-like structure, respectively. All the stable isomers of (AgCl)10 are constructed by two seriously distorted triangles and one square. The most stable one 10-(a) can be looked as two distorted triangles vertically located above a tilted square. The bond lengths of Ag-Cl in triangle are 2.44∼2.87 Å, while in square are 2.46∼2.51 Å, ∠AgClAg and ∠ClAgCl in triangle and square are 76.1◦ ∼143.0◦ , 81.5◦ ∼96.2◦ and 100.5◦ ∼176.0◦ , 170.3◦ ∼171.7◦ , respectively. The energies of other isomers are near the most stable one, with only 0.08∼0.35 eV higher than 10-(a). The most stable isomer of (AgCl)11 (11-a) is a quasi-cage structure, which is fused of two distorted triangles and squares with sharing common edges. The bond lengths of Ag-Cl in triangle are 2.45∼2.60 Å, while in square are 2.46∼2.62 Å. The ∠AgClAg and ∠ClAgCl in triangle and square are 75.3◦ ∼92.2◦ , 80.7◦ ∼98.2◦ and 126.4◦ ∼175.6◦ , 143.0◦ ∼176.8◦ , respectively. The second one 11-(b) is a double-layered structure, in which each layer includes one rhombus and two triangles connected by sharing common edges. The other isomers are all constituted by two distorted squares and one triangle with different connection modes. Their energies are closed to the 11-(a), lie 0.02∼0.35 eV higher than that of 11-(a) . For n=12, the isomer 12-(a), which adopts cage-like configuration and comprises of several distorted triangles and squares, is found to be the lowest-energy structure. The bond lengths of Ag-Cl are 2.45∼2.60 Å, while ∠AgClAg and ∠ClAgCl are 74.5◦ ∼101.1◦ and 118.3◦ ∼158.6◦ , respectively. The second one can be looked as two triangles capped up and down on a planar hexagon and lies 0.03 eV in energy higher than 12-(a). The third one is a doublelayered structure, in which each layer includes two rhombus and triangles connected by sharing common edges and this isomer is only above 12-(a) with 0.06 eV. Both 12-(d) and 12-(f) are involved four distorted triangles and 12-(f) is also the lowest-energy isomer of (AgF)12 [23]. However, these two isomers are in energy higher than 12-(a) with 0.09 and 0.12 eV, respectively. Both12-(e) and 12-(g) are composed of three distorted squares and their energies are higher than 12-(a) with 0.11 and 0.16 eV, respectively. 13-(a) is also a quasi-cage structure including nine distorted triangles and two rhombuses connected with sharing common edges. The bond lengths of Ag-Cl are 2.42∼2.67 Å, while ∠AgClAg and ∠ClAgCl are 74.4◦ ∼112.3◦ and 103.8◦ ∼175.6◦ , respectively. 13-(b), 13-(c) and 13-(d) are also cage-like structures with 0.11 eV, 0.43 eV and 0.55 eV higher in energy than 13-(a). While 3-(e), 13-(f) and 13-(g) are all disorder isomers with three distorted triangles and one square. It can be seen from Fig 1∼3 that the energies of some isomers are closed (less than 0.1 eV) to each other by B3P86 calculations. It is also known that the stability order of isomers depends on the methods and the basis sets, thus these quasidegenerate structures are further optimized by using higher precision MP2 method combined with different basis sets such as LANL2DZ/CEP-31G for Ag and 6-31g* for Cl. When the basis set of CEP-31G for Ag and 6-31G* for Cl is applied, the stability orders of the isomers with closed energies by MP2 computations are in full accord with those of 3
B3P86 calculations and the corresponding relative energies are also listed in Fig 1∼3 in parentheses. While the basis set of LANL2DZ for Ag and 6-31g* for Cl is used, the most stable structures are also in good agreement with those of B3P86 calculations, while the stability order of some second and third stable isomers is different. For example, 12-(c) is 0.01eV in energy lower than that of 12-(b). However, the energy differences of these quasidegenerate isomers are small even in MP2 calculations, which implies that these isomers may be coexisted under finite temperature. It is found that the most stable structures of (AgCl)n are planar single-ring for n<5, while from n=5, the 3D isomers are more energy favored and the lowest-energy configurations are all constructed by several distorted triangle and square elements of (AgCl)3 and (AgCl)4 , and for n=11∼13, the most stable motifs are cage-like structures. The 3D lowest-energy structure of (AgBr)n is also first appeared from n=5[18, 19, 20, 21], while for (AgF)n , it is emerged from n=6[22, 23]. It is agreed with the conclusion of Rabilloud et al that the metal fluorides prefer planar rings while metal chlorides adopt nonplanar cycles[24]. The lowest-energy structures of (AgF)n , (AgCl)n and (AgBr)n are similar to each other for n=2∼6. For n>6, there is no report on (AgBr)n . Although both the most stable structures of (AgF)n and (AgCl)n are composed of several fused triangles and squares, they possess high symmetry for (AgF)n [23] while are distorted and with low symmetry for (AgCl)n . This effect may be attributed to the different electrical negative of F− and Cl− and thus the different intensities of ionic-covalent bonds in (AgF)n and (AgCl)n , this will be discussed later. The geometrical characters of (AgCl)n can be summarized as: (1) Ag and Cl atoms form alternative structures due to the ionic interaction between Ag+ and Cl− , just like typical ionic compound such as NaCl; (2) The Cl atoms are always located at the apexes while Ag atoms situated at the center of an edge; (3) Ag atoms are always near, while Cl atoms away from the center of cluster. In other words, the Ag-Ag distances are shorter than those of Cl-Cl; (4) ∠AgClAg mostly are cute angles while ∠ClAgCl near straight angles. These geometrical properties can be explained by their particular ionic-covalent bonds and will be discussed later. 3.2. Infrared Spectra Infrared spectrum (IR) is an important experimental tool to assign the geometrical configuration of a isomer. T. P. Martin et al. have examined the IR spectra of (AgCl)n (n=1∼3); F. Rabilloud et al optimized the stable structures of (AgCl)n (n=2∼6) and computed the IR spectra of the lowest-energy configurations by using B3LYP method[24]. In our calculations, the IR spectra of the ground state structures of (AgCl)n (n=2∼13) are shown in Fig 4 and the vibrational frequencies of IR peaks with higher intensities are also listed in Table 1. It can be seen from Table 1 that our results are agreed well with those of F. Rabilloud et al for the cluster sizes of n=2∼5, but more closed to the experimental results for n=2∼3. For (AgCl)6 , the vibrational frequencies in our calculations (97∼293 cm−1 ) are different from those (70∼309 cm−1 ) of F. Rabilloud et al, despite that the topological structures are similar to each other. However, we also optimized and computed the IR spectrum of the lowest-energy isomer of (AgCl)6 by using other method such as CISD and MP2, the results (95∼295 cm−1 for CISD and 108∼263 cm−1 for MP2) are accord with our results. It can be seen from Fig 4 that the stronger peaks for (AgCl)3 and (AgCl)4 are located at about 100∼300 cm−1 . Because the larger-sized (AgCl)n are constituted by the trimer and tetramer, their IR spectra are also within the scope of 100∼300 cm−1 . Furthermore, the spectra for (AgCl)11 ∼(AgCl)13 exhibit different modes and become more complex due to their cage-like configurations. 3.3. Stability The average binding energy Eav is calculated as:, Eav = (E[(AgCl)n ] − n ∗ E(AgCl))/n
(1)
where the E[(AgCl)n ] and E(AgCl) are the energies of (AgCl)n cluster and AgCl monomer, respectively. Figure 5 plots the Eav of (AgCl)n as a function of cluster size n. The Eav increases rapidly when n=2 to 4, then grows slowly and becomes nearly saturated until n=13. It demonstrates that the overall stability of (AgCl)n is steady increased. To evaluate the relative stability of (AgCl)n , the first (∆1 E) and second energy difference (∆2 E ) are also calculated as follow: ∆1 E = E[(AgCl)n ] − E[(AgCl)n−1 ] 4
(2)
Table 1: The frequencies of the stronger IR vibrational modes of the most stable isomers of (AgCl)n
n 2 3 4 5 6 7 8 9 10 11 12 13
Present work 62, 163, 264 68, 81, 193, 308 61, 95, 235, 317 60, 74, 85, 244, 296, 310, 323, 334 97, 178, 243, 293 85, 100, 272, 282, 292, 301, 317 92, 273, 280, 297, 301 138, 154, 166, 184, 210, 276, 280 96, 124, 238, 256, 265, 280, 286 115, 138, 152, 166, 178, 193, 206, 228, 243, 276, 321 86, 105, 115, 127, 174, 257, 268, 276, 289 125, 136, 146, 176, 194, 233, 243, 279, 294
Ref[24] 62, 153, 245 62, 86, 188, 302 60, 89, 231, 306 61, 74, 85, 240, 294, 301, 309 70, 81, 294, 309 -
Table 2: The NPA charges of Ag/Cl atoms of the most stable structures of (AgCl)n
n 2 3 4 5 6 7 8 9 10 11 12 13
Charge/e 0.65/ − 0.65 0.54/ − 0.54 0.56/ − 0.56 0.54 ∼ 0.59/ − 0.54 ∼ −0.57 0.50/ − 0.50 0.49 ∼ 0.57/ − 0.50 ∼ −0.52 0.52 ∼ 0.54/ − 0.52 ∼ −0.54 0.49 ∼ 0.52/ − 0.49 ∼ −0.54 0.50 ∼ 0.59/ − 0.49 ∼ −0.56 0.48 ∼ 0.55/ − 0.48 ∼ −0.55 0.44 ∼ 0.57/ − 0.50 ∼ −0.55 0.37 ∼ 0.57/ − 0.42 ∼ −0.53
5
Expt[17] 198, 255 96, 199, 322 -
∆2 E = E[(AgCl)n+1 ] + E[(AgCl)n−1 ] − 2E[(AgCl)n ]
(3)
where the E[(AgCl)n+1 ], E[(AgCl)n−1 ] and E[(AgCl)n ] are the energies of (AgCl)n+1 , (AgCl)n−1 and (AgCl)n , respectively. The higher the ∆1 E and ∆2 E are, the more stable the isomer is. The ∆1 E and ∆2 E of (AgCl)n are plotted in Fig 6. It shows that there are relatively larger values of ∆1 E and ∆2 E for n=3, 4, 6, 8 and 11, which means that these isomers are more stable than their neighbors. Moreover, the ∆2 E of the trimer and tetramer are the first and second highest, respectively. It suggests that (AgCl)3 and (AgCl)4 are especially stable. Therefore, all the most stable structures of (AgCl)n (n>6) contain several units of trimer and tetramer. Meanwhile, the hexamer and octamer are constituted by two trimers and tetramers, respectively. Thus these two isomers are also with particular stabilities. While the (AgCl)11 is the first cage-like structure, therefore, it is with higher stability too. The energy gap, the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which indicates the chemical stability of an isomer. The higher energy gap means chemical inertness. The energy gaps of (AgCl)n are shown in Fig 7. There are local maxima at n=3, 4 and 5, which implies that these three ring-like isomers are with higher chemical stabilities. It should be stressed that (AgCl)3 is also with the highest energy gap and thus the chemical stability. That is to say, trimer is the most stable one not only in energy but also in chemical stability. 3.4. Vertical ionization potentials and electron affinities Vertical ionization potential (VIP) and vertical electron affinity (VEA) are the energy difference between the neutral cluster and the corresponding cationic and anionic cluster, which remains the geometrical structure of the neutral cluster. VIP and VEA can measure the capacity of losing and receiving electrons. The VIP and VEA of the most stable structures of (AgCl)n (n=2∼13) are also displayed in Fig 8. It can be seen that the VIP increases firstly from 10.03 eV for n=2 to the maximum of 10.40 eV for n=3, then decreases gradually to 9.34 eV until n=11, while increases again up to n=13. The similar evolution behavior of VIP for (AgF)n (n=2∼12) was also been observed[23]. The VEA of (AgCl)n decreases from 1.63 eV for n=2 to the minimum of 1.33 eV for n=3, then increases slowly to 2.84 eV for n=13. The VIP of (AgCl)n are in the range of 9.35∼10.40 eV, which are larger than those of 8.50∼9.50 eV for (AgF)n (n=2∼12)[23]. While the VEA for (AgCl)n extend from 1.35 to 2.84 eV, which are smaller than those of 3.03∼3.95 eV for (AgF)n (n=2∼6)[22]. The larger VIP means that the (AgCl)n are difficult to lose electrons, while the smaller VEA suggests that they tend to gain electrons easily. 3.5. Chemical bonds Silver halide are known for their ionic-covalent bonds. To explore the electrostatic interaction in (AgCl)n cluster, the Natural Population Analysis (NPA) charges of Ag and Cl atoms are calculated and listed in Table 2. It shows that the charges on Ag atoms are positive (0.37∼0.65 e) while on Cl negative (-0.44∼-0.65 e), which indicates that the charges are transferred from Ag to Cl atoms and there exists stronger ionic interaction between Ag and Cl ions. Thus the (AgCl)n tend to form alternative cycles. For example, all the lowest-energy structures of (AgCl)n (n=2∼5) are alternative rings. Furthermore, because of the strong repulsion, Al anions incline to be far away from each other and thus locate at the apexes of cluster. The electron localization function (ELF) is an effective tool to visually describe the covalent interaction. The concept of ELF was proposed by Becke and Edgecombe and developed by Savin and coworkers[33, 34]. It is defined as follow: 1 ∑ 1 |∇ρ|2 2 i p ∇ψi p − 8 ρ 2 ELF = [1 + ]−1 (4) 3 2 2/3 ρ5/3 10 (3π ) where the ρ,∇ρ and | ψi |2 is the electron density, its gradient and the kinetic energy density, respectively. ELF is within the range of 0∼1. A large ELF value means that electrons are greatly localized, indicating that there will be a covalent bond. Because the trimer and tetramer are the most stable isomers and also the constitution units for large-sized cluster, the ELF of (AgCl)3 and (AgCl)4 are calculated and presented in Fig 9. It shows that the ELF 6
in the areas between Ag and Cl atoms for both the (AgCl)3 and (AgCl)4 are in the range of 0.1∼0.3. These results show that Ag atoms form covalent interaction with Cl atoms. To further study the covalent interaction, the particle density of states (PDOS) of (AgCl)3 and (AgCl)4 are also calculated and presented in Fig 10. It is clear that the PDOS of 4d and 5s components of Ag overlap well with the 3p components of Cl in the energy range of -13∼-8 eV. It implies that the covalent interaction can be described as the 4d and 5s components of Ag hydride and further mix with the 3p components of Cl to form chemical bonds. To deeply understand these covalent bonds, the molecular orbitals of (AgCl)3 and (AgCl)4 are also further studied. It is found that these covalent interactions often lead to multi-center bonds (presented in Fig 11) in (AgCl)n . The multi-center bonds can be divided into three styles, such as Ag-Cl-Ag, Cl-Ag-Cl three-center bonds and multicenter bond composed by Ag atoms. The Ag-Cl-Ag three-center bonds (Fig 11 (a) and (d)) bend the ∠AgClAg into a cute angle while Cl-Ag-Cl three-center bonds (Fig 11 (b) and (e)) make the ∠ClAgCl near a straight angle. Furthermore, the multi-center covalent bonds among Ag atoms (Fig 11 (c) and (f)) incline to drag the Ag atoms closer while the electrostatic repulsions push the Cl atoms away, thus make the Ag-Ag distances are shorter than those of Cl-Cl. Although these multi-center bonds will lead to the geometrical distortions of cluster, they can also greatly promote the stability of cluster. Therefore, the distorted structures are more stable for larger sized (AgCl)n cluster. For example, the stable structures of (AgCl)n (n>6) are composed by distorted triangles and squares. It is also found that the Ag-Ag distance plays an important role to determine the intensity of the multi-center bond. The shorter the Ag-Ag distances are, the stronger the bond is. For example, since the Ag-Ag distances (3.22∼3.63Å) in distorted pentagon (5-(a)) are shorter than those (3.80Å) in planar pentagon (5-(b)), the tilted pentagon is more stable. In addition, although there is a four-center bond composed of Ag atoms in (AgCl)4 (Fig 11 (f)), which is expected to form stronger bond than that of three-center bond in (AgCl)3 (Fig 11 (c)). However, because the Ag-Ag bond lengths in (AgCl)3 (2.98Å) are shorter than those (3.35Å) of in (AgCl)4 , the three-center bond in (AgCl)3 actually is more stable. The chemical bonds in (AgCl)n are ionic-covalent. According to the results of Rabilloud et al that the calculated charges of (AgF)n are larger than those of (AgCl)n for n<7, which implies that the ionic interaction in (AgF)n is stronger than that in (AgCl)n [24]. Our results show that the most stable structures of (AgCl)n are distorted configurations with low symmetry due to the strong covalent interactions. It is different from the results of C. S. Song et al that the fused triangles and squares with high symmetry are more energy favored for (AgF)n . Thus our results indicate that the covalent interactions in (AgCl)n are stronger. 3.6. Dipole moments, polarizabilities and hyperpolarizabilities When a system is in a weak and homogeneous electric field, its energy can be described as: 1 1 E = E 0 − µα Fα − ααβ Fα Fβ − βαβγ Fα Fβ Fγ − · · · 2 6
(5)
where E 0 is the system total energy absence of an electric field and Fα is the electric field component along a direction of α. µα , ααβ and βαβγ denote the dipole moment, the elements of the linear polarizability and the first hyperpolarizabilitiy, respectively. The mean polarizability (α) and hyperpolarizability (β0 ) can be defined as: 1 (α xx + αyy + αzz ) 3
(6)
β0 = (β2x + β2y + β2z )1/2
(7)
α=
in which βi =
3 (βiii + βi j j + βikk ) i, j, k = x, y, z 5
(8)
β0 is also known as the second-order nonlinear optical response coefficient. These physical quantities characters the response of a system in the external electric filed and are closely related to the optical properties. Table 3 lists the dipole moments, polarizabilities and hyperpolarizabilities of (AgCl)n (n=2∼13). The geometrical structures of 7
(AgCl)n (n=2∼6) are with higher symmetries, hence the dipole moment of these isomers are zero. For n=7∼13, the µ increase from 0.18 Debye to 3.29 Debye. The polarizabilities of (AgCl)n are monotonically increased with the cluster sizes. The hyperpolarizabilities of (AgCl)n present even-odd oscillation behavior when n<11, then monotonically increase until n=13. It should be noted that α and β0 of (AgCl)n (n=11∼13) are particularly large (331.74 ∼ 422.77 a. u. for α and 351.79 ∼ 694.85 a. u. for β), which means that (AgCl)n are easily deformed under an external electric filed. On one hand, there is large polarizability in Cl and Ag ions due to their larger ionic radius (181Å for Cl− and 126Å for Ag+ ), on the other hand, (AgCl)n (n=11∼13) are cage-like structures and with lower symmetries, thus their polarizabilities and hyperpolarizabilities are larger. 4. Conclusion The stable structures of (AgCl)n (n<5) are planar single-ring, while from n=5 are 3D configurations and constructed by the distorted triangle and square unties of (AgCl)3 and (AgCl)4 . The cage-like configures are more energy favored for (AgCl)11 ∼(AgCl)13 . The clusters with the sizes of n=3, 6, 8 and 11 are more stable and the trimmer is the most stable one and can be looked as a magic number cluster. The stronger IR peaks of (AgCl)n are located at about 100 ∼300 cm−1 . The VIP of (AgCl)n are in the range of 9.35∼10.40 eV, while the VEA extend from 1.35 to 2.84 eV. The chemical bonds in (AgCl)n are ionic-covalent. The NPA indicates that the charges are transferred from Ag to Cl atoms, which leads to ionic interaction. Moreover, the covalent bonds formed by the 4d and 5s components of Ag and the 3p components of Cl are also observed. It is emphasized that the multi-center bonds such as the Ag-ClAg, Cl-Ag-Cl three-center bonds and the multi-center bonds composed of Ag atoms, will further enhance the stability of (AgCl)n . It is also found that (AgCl)n (n=11∼13)are with larger polarizabilities and hyperpolarizabilities. 5. Acknowledgements We thank financial support from the National Natural Science Foundation of PR China (Grant No. 11164024),the College Research Funding of Gansu Province. We also thank Computational Center of Shenzhen for offering computer facilities. References [1] K. Shahi, J. B. Wagner, Fast ion transport in silver halide solid solutions and multiphase systems. Appl. Phys. Lett. 37 (1980) 757-759. [2] D. E. Day, G. H. Frischat, T. Minami, Preparation, Properties, and Structure of Special GlassesPreparation and properties of superionic conducting glasses based on silver halides. J. Non-Cryst. Solids 56 (1983) 15-26. [3] J. B. Boyce, B. A. Huberman, Superionic conductors: Transitions, structures, dynamics. Phys. Rep. 51 (1979) 189-265. [4] H. Daupor, S. Wongnawa, Flower-like Ag/AgCl microcrystals: Synthesis and photocatalytic activity. Mater. Chem. Phys. 159 (2015) 71-82. [5] C. Tasseven, J. Trull`as, O. Alcaraz, M. Silbert, A. Gir´o, Static structure and ionic transport in molten AgBr and AgCl. J. Chem. Phys. 106 (1997) 7286-7294. [6] C. J. Evans, M. C. L. Gerry, The microwave spectra and structures of Ar-AgX (X=F, Cl, Br). J. Chem. Phys. 112 (2000) 1321-1329. [7] T. Benmessabih, B. Amrani, F. El Haj Hassan, F. Hamdache, M. Zoaeter, Computational study of AgCl and AgBr semiconductors. Phys. B: Cond. Matt. 392 (2007) 309-317. [8] Y. Kawakita, T. Enosaki, S. i. Takeda, K. Maruyama, Structural study of molten Ag halides and molten AgCl-AgI mixture. J. Non-Cryst. Solids 353 (2007) 3035-3039. [9] S. Tahara, H. Fujii, Y. Kawakita, S. Kohara, Y. Yokota,S. i. Takeda, Structure of the molten silver chloride. J. Non-Cryst. Solids 353 (2007) 1994-1998. [10] S. Takeda, Y. Nagata, Y. Kawakita, Slow dynamic properties of molten silver halides. J. Non-Cryst. Solids 353 (2007) 3169-3173. [11] P. Calandra, A. Longo, V. Marcian,V. Turco Liveri, Physicochemical Investigation of Lightfast AgCl and AgBr Nanoparticles Synthesized by a Novel Solid-Solid Reaction. J. Phys. Chem. B. 107 (2003) 6724-6729. [12] T. Sugimoto, K. i. Kimijima, New Approach to the Formation Mechanism of AgCl Nanoparticles in a Reverse Micelle System. J. Phys. Chem. B. 107 (2003) 10753-10759. [13] C. Sun, P. Chen, S. Zhou, AgCl nanoparticle nanowires fabricated by template method. Mater. Lett. 61 (2007) 1645-1648. [14] Y. Sun, Conversion of Ag Nanowires to AgCl Nanowires Decorated with Au Nanoparticles and Their Photocatalytic Activity. J. Phys. Chem. C. 114 (2010) 2127-2133. [15] A. W. Potts, M. L. Lyus, The photoelectron spectrum and valence shell structure of (CuX)3 and (AgCl)3 . J. Elec. Spec. Rela. Phen. 13 (1978) 305-315. [16] J. Schmelzer, U. Lembke ,R. Kranold, Nucleation and growth of AgCl clusters in a sodium borate glass: Numerical analysis and SAXS results. J. Chem. Phys. 113 (2000) 1268-1275. [17] T. P. Martin, H. Schaber, Matrix isolated copper and silver halide clusters. J. Chem. Phys. 73 (1980) 3541-3546.
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[18] F. Rabilloud, F. Spiegelmann, J. L. Heully, Ab initio calculations of structural and electronic properties of small silver bromide clusters. J. Chem. Phys. 111 (1999) 8925-8933. [19] F. Rabilloud, F. Spiegelman, J. M. LHermite, P. Labastie, Ab initio study of silver bromide Agn Br(+) p clusters (n≤6,p=n,n-1). J. Chem. Phys. 114 (2001) 289-305. [20] H. G. Zhang, Z. A. Schelly, D. S. Marynick, Theoretical Study of the Molecular and Electronic Structures of Neutral Silver Bromide Clusters (AgBr)n , n = 1-9. J. Phys. Chem. A. 104 (2000) 6287-6294. [21] Y. H. Yin, H. S. Chen, Y. Song, The DFT study on the structures and properties of (AgBr)n (n≤¡6). J. Mole. Struc. Theo. 959 (2010) 30-34. [22] F. Rabilloud, O. Bonhomme, J. M. LHermite, P. Labastie, Adiabatic electron affinities of (AgF)n clusters: Experiment and DFT calculations. Chem. Phys. Lett. 454 (2008) 153-157; [23] C. Song, Z. Tian, First principles study on the size evolution and stability of (AgF)n (n= 1-12) clusters. Comp. Theo. Chem. 1074 (2015) 157-162. [24] F. Rabilloud, Structure and stability of coinage metal fluoride and chloride clusters (Mn Fn and Mn Cln , M=Cu, Ag, or Au; n=1-6). J. Comput. Chem. 33 (2012) 2083-2091. [25] D. M. Deaven, K. M. Ho, Molecular Geometry Optimization with a Genetic Algorithm. Phys. Rev. Lett. 75 (1995) 288-291. [26] J. Zhao, R. H. Xie, Genetic Algorithms for the Geometry Optimization of Atomic and Molecular Clusters. J. Comp. Theo. Nano. 1 (2004) 117-131. [27] A. K. Ivanov-Schitz, B. J. Mazniker, E. S. Povolotskaya, A molecular dynamics study of ionic transport in α-AgI-based solid solutions. Solid State Ionics 159 (2003) 63-69. [28] J. P. Perdew, Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Phys. Rev. B. 33 (1986) 88228824. [29] A. D. Becke, Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 98 (1993) 5648. [30] W. J. Stevens, M. Krauss, H. Basch, P. G. Jasien, Relativistic compact effective potentials and efficient, shared-exponent basis sets for the third, fourth, and fifth row atoms. Canadian J. Chem. 70 (1992) 612-630. [31] M. J. Frisch, G. Trucks, H. Schlegel, G. Scuseria, M. Robb, J. Cheeseman, J. Montgomery, T. Vreven, K. Kudin,J. Burant, Gaussian 03, revision C. 02. (2008). [32] T. Lu, F. Chen, Multiwfn: a multifunctional wavefunction analyzer. J. Comp. Chem. 33 (2012) 580-592. [33] B. Silvi, A. Savin, Classification of chemical bonds based on topological analysis of electron localization functions. Nature 371 (1994) 683-686. [34] A. Savin, R. Nesper, S. Wengert, T. F. Fssler, ELF: The electron localization function. Angew. Chem. Int. Ed. 36 (1997) 1808-1832. [35] T. Yanai, D. P. Tew, N. C. Handy, A new hybrid exchangeCcorrelation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem. Phys, Lett. 393 (2004) 51-57.
9
Table 3: The dipole moments (µ), polarizabilities (α) and hyperpolarizabilities (β) (in a. u.) of the most stable structures of of (AgCl)n (n = 2 − 13)
n µ α β
2 0.00 63.49 0.14
3 0.00 99.28 2.75
4 0.00 134.64 0.43
5 0.09 168.75 120.85
6 0.00 195.88 3.53
7 0.97 233.28 307.04
8 0.18 264.05 22.34
9 0.47 291.79 77.10
10 2.86 331.74 51.79
11 1.93 355.69 358.23
12 3.29 396.15 561.03
13 1.27 422.77 694.85
Figure 1: The stable structures of (AgCl)n (n=2∼7), △E is the energy difference (in unit eV) between the isomer and the lowest-energy structure. The values in parentheses are the △E by MP2 calculations. The green and grey balls are Cl and Ag atoms, respectively.
10
Figure 2: The stable structures of (AgCl)n (n=8∼10), △E is the energy difference (in unit eV) between the isomer and the lowest-energy structure. The values in parentheses are the △E by MP2 calculations. The green and grey balls are Cl and Ag atoms, respectively.
Figure 3: The stable structures of (AgCl)n (n=11∼13), △E is the energy difference (in unit eV) between the isomer and the lowest-energy structure. The values in parentheses are the △E by MP2 calculations. The green and grey balls are Cl and Ag atoms, respectively.
11
Figure 4: The IR spectra of (AgCl)n
12
1.7
1.6
1.5
av
E /eV
1.4
1.3
1.2
1.1
1.0
0.9
0.8 2
4
6
8
10
12
14
n Figure 5: The average binding energy Eav of (AgCl)n .
0.8
E 2.4
2.0
0.0
1
E 1.6
-0.8
2
4
6
8
10
n
Figure 6: The △1 E and △2 E of (AgCl)n .
13
12
5.0
Gap/
eV
5.5
4.5
4.0 2
4
6
8
10
12
14
n Figure 7: The energy gap of (AgCl)n .
10.5
3.0
2.7 10.2
9.9 2.1
1.8
9.6
1.5
9.3 1.2 1
2
3
4
5
6
7
8
9
10
11
12
13
n
Figure 8: The VIP and VEA for the lowest-energy isomers of (AgCl)n .
14
14
VEA/eV
VIP/eV
2.4
Figure 9: The ELF of (AgCl)3 (a) and (AgCl)4 (b).
Ag 4d
40
(AgCl)
Cl
3
Ag 4d
3p
40
(AgCl)
Cl
4
3p
Ag 5s
PDOS
PDOS
Ag 5s
20
20
0
0 -12
-10
-8
-6
-12
-4
Energy/eV
-10
-8 Energy/eV
Figure 10: The PDOS of (AgCl)3 and (AgCl)4 .
15
-6
-4
Figure 11: The typical molecular orbitals of (AgCl)3 and (AgCl)4 .
16
Highlights
.The stable structures of (AgCl)n (n=2~13) were obtained.
.The trimer is the most stable one. .The chemical bonds in (AgCl)n are ionic-covalent. . (AgCl)n (n=11~13) are with larger polarizabilities and hyper polarizabilities.
*Graphical Abstract (for review)