Ab Initio Search for Global Minimum Structures of Pure and Boron

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Ab Initio Search for Global Minimum Structures of Pure and Boron Doped Silver Clusters Yuan-Yuan Jin, Yonghong Tian, Xiaoyu Kuang, Chuan-Zhao Zhang, Cheng Lu, Jingjing Wang, Jian Lv, Liping Ding, and Meng Ju J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 05 Jun 2015 Downloaded from http://pubs.acs.org on June 6, 2015

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The Journal of Physical Chemistry

Ab Initio Search for Global Minimum Structures of Pure and Boron Doped Silver Clusters Yuanyuan Jin,† Yonghong Tian,‡ Xiaoyu Kuang,†,* Chuanzhao Zhang,† Cheng Lu, §,* Jingjing Wang,† Jian Lv, ¶,* Liping Ding,† and Meng Ju† †

Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China.

‡

Department of Physics and Optoelectronic Engineering, Yangtze University, Jingzhou 434023, China.

§

Department of Physics, Nanyang Normal University, Nanyang 473061, China.

¶

Beijing Computational Science Research Center, Beijing 100084, China.

Corresponding Author’ Telephone number: +86-28-85403803 (Xiaoyu Kuang); +86-377-63513721 (Cheng Lu); +86-431-85168276 (Jian Lv)

Abstract： The global minimum structures of pure and boron doped silver clusters up to 16 atoms are determined through ab initio calculations and unbiased structure searching methods. The structural and electronic properties of neutral, anionic and cationic AgnB (n ≤ 15) and AgnB2 (n ≤ 14) clusters are much distinct from the corresponding pure silver. Considering that Ag and B possess one and three valence electrons, respectively, both the single and double boron-atom doped silver clusters with even number of valence electrons are more stable than those with odd number of electrons - a feature also observed in the pure silver clusters. We demonstrate that the

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species with a valence count of 8 and 14 appear to be magic numbers with enhanced stability irrespective of component or the charged state. A new putative global minimum structure of Ag13− cluster, with high symmetry of C2v, is unexpectedly observed as the ground-state, which is lower in energy than the previous suggested bilayer structure.

1. Introduction A large number of experimental and theoretical studies have been performed on silver-based clusters, due to their widely applications in different fields, such as sensing,1,2 catalysis,3-5 and biomedicine.6,7 A silver atom has a filled 4d shell with a single electron in the 5s orbital. A confined nearly free electron gas (NFEG) model, which is developed originally for alkali clusters, is usually used to rationalized the electronic behavior of silver clusters.8-16 The spherical jellium model provides a simplified rule for realization of the shell character of clusters in which the valence electrons fill the spherical orbitals of a cluster according to the pattern of [1S21P61D102S21F142P61G182D10…], where the uppercase letters are used to distinguish from the lowercase symbols labeled in atomic orbitals.17-24 According to the spherical jellium model, clusters with fully filled electronic shells have large energy gaps between the highest occupied (HOMO) and lowest unoccupied molecular orbital (LUMO), and they are generally resistant to reactivity with small molecules.8,23-26 One should note that the spherical jellium model is based on a spherical background. Thus, these magic electron numbers may be changed due to a non-spherical structure. Experimentally, Luo et al.8 investigated the reactivity of silver anions with O2 and suggested the Ag13− cluster exhibits unexpected stability against reactivity with oxygen despite having a valence electron count that is not expected to result in a filled electronic shell within the spherical jellium model. Meanwhile,


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their theoretical studies showed that Agn− clusters with an odd number of valence electrons were more reactive than those with an even number of electrons, indicating that radical active sites play a role in their reactivity. Recently, they25 further studied the gas-phase reactivity of silver clusters with ethanethiol in a fast-flow tube reactor. The results confirmed the enhanced stability of Ag13−. In order to explore the physi- and chemisorption of small silver particles, Schmidt et al.27 examined the reactivity of nitrogen and oxygen to silver cluster cations containing up to 27 atoms. One of the interesting findings was that Ag15+ had the lowest O2 absorption rates among Agn+ for n = 10-25. Based on the density functional theory (DFT) calculations, Reber et al.28 reported that Ag15+, Ag14, and Ag13− clusters with 14 valence electrons that do not correspond to a filled shell in a spherical jellium, all have oblate bilayer atomic structures that lead to a splitting of the superatomic D shell in a manner analogous to crystal field splitting of d-states in transition metals. Liao et al.29 performed a theoretical study of oxygen adsorption on neutral and anionic Agn clusters in a large size range of n = 2-25. The results showed that the neutral silver clusters Agn with an odd number of atoms can adsorb O2, while even-n silver cluster anions Agn− are especially reactive toward O2 adsorption that conform with the experimental results of Luo et al.8 It is known that the range of properties of clusters can be greatly extended by taking mixtures of elements to generate doped clusters or nanoalloys. It would therefore be very helpful if some simple rules could be found for the interactions of different elements in a cluster. A first step towards this direction is the understanding of the role of a single atom impurity. Majer et al.30 measured the photoelectron spectra of low temperature silicon doped silver cluster anions AgnSi with n = 5-82. Using the density functional based tight binding method and time-dependent density functional theory, Mokkath et al.31 systematically investigated the structural and optical properties of neutral, cationic, and anionic Agn and Agn−1Si clusters (n=5-12). The results


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demonstrated that Si bonds covalently to the surface of Ag clusters. Medel et al.32 explored the structural evolution, bonding characteristics, stability, and the spin magnetic moment of neutral and cationic AgnV clusters and demonstrated that the valence of V oscillates between 1 or 2 at small cluster sizes and transitions to 5 as the number of Ag atoms is increased and that this valence transition explains the changes in stability and magnetic moment of AgnV0/+ clusters. Boron is one of the simplest atoms with electron configuration 1s22s22p1. Recently, using a modified stochastic search algorithm, Aztatzi et al.33 explored the potential energy surfaces of a series of gold-boron clusters with formula AunB (n = 1-8) and AumB2 (m = 1-7). Smith et al.34 studied the size-selective reactivity of AlnBm− clusters m = 1, 2 with O2 and found that Al12B− and Al11B2− have large HOMO−LUMO gaps and are highly resistant to reactivity with oxygen, which behaved similarly with Al13−. All of them have filled electronic shells with 40 valence electrons. As we known, silver clusters, as well as gold and aluminum clusters are systems that have unusual properties and the researchers most interested in. So, it is interesting to know how the geometries, stabilities and bonding characteristics of Ag clusters will be affect by doping of boron atoms. In the present work, we undertook systematical first-principle DFT calculations to examine the atomic and electronic structures of neutral, anionic and cationic AgnBm (4 ≤ n + m ≤ 16, 0 ≤ m ≤ 2) clusters up to 16 atoms. As shown below, the ground-state neutral and charged AgnBm clusters do not have the same geometry as pure silver clusters. New putative global minimum structures for pure neutral Ag8-Ag13, anionic Ag6− and Ag13− and cationic Ag6+, Ag10+, Ag11+ and Ag13+ have been proposed. The theoretical studies indicated that neutral and charged AgnBm clusters with an odd number of electrons exhibit lower stability than those with an even number of electrons irrespective of component or the charged state. More importantly, the clusters containing 8 and 14 valence electrons were identified as enhanced stable species.


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According to the observations of boron doping Al, Ag and Au clusters, we conclude that the boron doping has considerable influence on the structural and electronic properties of these metal or transition metal clusters. The current results greatly advanced our understanding on the structural and electronic properties of boron doped silver clusters.

2. Computational method The low-lying structures of neutral and charged Agn, AgnB and AgnB2 clusters were globally searched using particle swarm optimization algorithm, as implemented in the CALYPSO code. The approach involves global minimization of energy surfaces, merging ab initio total energy calculations via CALYPSO cluster prediction.35-37 It has been successful in correctly predicting structures for various systems.37-39 Structure predictions of neutral, anionic and cationic Agn, AgnB and AgnB2 clusters up to 16 atoms are performed in current work. Each generation contains 30 structures, 60% of which are generated by particle swarm optimization algorithm. The others are new and will be generated randomly. We followed 50 generations to achieve the converged structure. The underlying energetic calculation and local structure optimization were performed at the DFT level using the BP86 functional that includes the exchange functional of Becke40 and the correlation one of Perdew41. The basis set labeled GENECP, i.e. the 6-311+G* basis set for B and LanL2DZ basis set for the transition metals, with full consideration of multiple spin states is used for refined structure optimization and vibrational frequency calculation for the isomers with low-lying energy. All the calculations are implemented in the Gaussian 09 package.42

3. Results and discussion


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The optimized global minimum geometries of neutral, anionic and cationic Agn, AgnB and AgnB2 clusters are displayed in Figures 1, 2 and 3, respectively. We summarize their total energies, point symmetries and HOMO−LUMO gaps in Tables S1-S3 in the Supporting Information (SI). All the previously reported structures, experimentally and theoretically, were successfully searched in current work. The geometries and relative stabilities of the low-lying isomers of each cluster are shown in Figure S1-S9 (see SI). To guide future experiments for the neutral and charged Agn, AgnB and AgnB2 systems, the infrared spectra (IR) of their ground-state structures are displayed in Figure S10-S18 (see SI). As depicted in Figure 1, the ground-state geometries of the small pure Agn−/0/+ clusters up to 7 atoms are found to be planar or quasi-planar with rare exceptions, while the large species with n ≥ 8 turn out to be three-dimensional (3D). Based on the spherical jellium model, the transition from planar to 3D structures can be rationalized, i.e., the initial filling of the 1S, 1Px, and 1Py orbitals result in planar structures while the filling of the 1Pz orbitals lead to the 3D compact structures. In good agreement with the earlier results about anions,8 further addition of Ag atoms first makes prolate structures until n = 12, and then results in oblate species for n ≥ 13. It should be noteworthy that the charges have important influence on the structures of silver clusters with exception of Ag4 and Ag16 . Compared to the results of Gamboa et al.,15 there are several different ground-state geometries of silver clusters, including neutral Ag8-13, anionic Ag6,13− and cationic Ag6,10,11,13+, for which we find slightly lower energy structures. These different structures obtained by us and Gamboa et al.15 may be raised by the complexity of the potential energy surfaces of the silver clusters. Our findings point out that the ground-state neutral Ag8 is of a high Td symmetry, 0.05 eV lower in energy than the C2 structure (8b in Figure S1) of Gamboa et al..15 The global minimum Ag9 cluster is found to be of Cs symmetry, 0.02 eV lower than the C2v structure (9b in Figure S1)


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Figure 1. Ground-state structures of pure neutral, anionic and cationic Agn clusters (n ≤ 16) obtained via DFT with BP86 functional.


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obtained by Gamboa et al..15 Gamboa et al.15considered the D4d structure as the ground-state of Ag10 (10b in Figure S1), however, our detailed calculation has found that it is 0.19 eV higher in energy than our D2d symmetry structure. For neutral Ag11, the C2 structure turns out to be the global minimum, 0.04 eV more stable than the C2v structure (11c in Figure S1) of Gamboa et al..15 We observe a C2 symmetry Ag12 cluster that is more stable by 0.22 eV than that (12c in Figure S1) suggested by Gamboa et al..15 For the neutral Ag13 cluster, we find a Cs symmetry structure as ground-state, which is 0.33 eV lower than the C2 structure (13c in Figure S1) of Gamboa et al..15 In the case of anionic Ag6− clusters, although Gamboa et al.15 regarded both C3v and C2v structures (6b in Figure S2) as ground-state, we observe the C3v structure is 0.04 eV lower in energy, in accordance with that of Luo et al..8 It is especially important to note that global minimum Ag13− cluster presents a bilayer oblate structure with C2v symmetry, which is 0.14 eV more stable than the bilayer triangular structure with C2 symmetry (13b in Figure S2) that has been considered as the ground-state geometry of Ag13− by many researchers.8,15,25,28,29 In the case of silver cations, the global minimum Ag6+ cluster is of Cs symmetry, 0.07 eV more stable than the C2v structure (6b in Figure S3) of Gamboa et al..15 We find a D2d structure of Ag10+, 0.10 eV lower in energy than the D4d structure (10b in Figure S3) of Gamboa et al..15 For cationic Ag11+, Gamboa et al.15 suggested a C1 symmetry structure as ground-state (11b in Figure S3), which is 0.07 eV less stable than the C2v structure we observed. A Cs symmetry Ag13+ is found to be ground-state, 0.26 eV more stable than the Cs structure (13c in Figure S3) reported by Gamboa et al..15 The atomic structures of neutral, anionic and cationic AgnB clusters (in Figure 2) are all of 3D structures, except for the neutral Ag3B (D3h) and cationic Ag4B+ (D4h) which have planar geometries. The small neutral AgnB (n < 13) cluster is formed by adding the new Ag atom into


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Figure 2. Ground-state structures of neutral, anionic and cationic AgnB clusters (n ≤ 15) obtained via DFT with BP86 functional.


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the smaller sized Agn−1B clusters. In detail, from n = 3 to 6, any additional Ag atom is just one more vertex to surround the B atom and finally the cluster forms a triangular prism at n = 6. Further addition of Ag atom lead to formation of a third layer until n = 12, and the B atom is still encapsulated in the center of triangular prism. Note that the growth pattern of small anionic AgnB− (n < 13) clusters is the same as the neutrals with rare exceptions, while cationic AgnB+ clusters are quite different from their neutral state. In the case of anionic AgnB− clusters, the anionic Ag3B− and Ag4B− clusters are both of C3v symmetry. The global minimum Ag5B− cluster with Cs symmetry is distorted from its neutral state. Ag6B− is not a triangular prism, but combination of a qusi-planar (formed by five Ag atoms and one B atom) and an Ag atom above it. Further for anionic Agn− with n = 7-12, the B atom is completely encapsulated in the center of triangular prism, just like their neutral state with a little distort. Particularly, the ground-state Ag15B− is formed by addition of a single B atom outside the atomic structure of Ag15− (see Figure 1). In the case of the cationic AgnB+ clusters, Ag6B+ is bipyramid structure with high Oh symmetry. Ag7B+ is formed by adding an Ag atom as a new vertex in the Ag6B+ structure. Ag8B+ is bipyramid structure with a triangular prism as middle layer. It is interesting to see that in the case of the ground-state Ag9B+, seven Ag atoms and one B atom form a plane, and one Ag atom is above the plane and the other is below. Ag10B+ is similar to Ag9B+ that six Ag atoms and one B atom form a plane, and two Ag atoms are above and the rest two are below. Ag11B+ is comprised by two intersected qusi-plane with the B atom semi-encapsulated. Ag12B+ is of C3v symmetry and the B atom is surrounded by two triangles. Note that the atomic geometries of AgnB+/0/− clusters are quite different from the pure silver clusters, namely, one boron doping has considerable influence on not only the valence electron count but also the geometries of silver clusters.


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Figure 3. Ground-state structures of neutral, anionic and cationic AgnB2 clusters (n ≤ 14) obtained via DFT with BP86 functional.


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From Figure 3, except for neutral Ag2B2 and cationic Ag2B2+ with linear structures, and Ag3B2 having planar structure, all AgnB2−/0/+ clusters are of 3D geometries. It is worth noting that the BB bond is much stronger than the Ag-Ag and Ag-B bonds, so the two B atoms do not segregate and prefer to bind to multiple Ag atoms. The small neutral AgnB2 (n ≤ 7) is formed by adding an Ag atom into the smaller Agn-1B2 cluster. Finally, in the case of Ag7B2, seven Ag atoms form two intersected quasi-plane and the two B atoms are caught in the middle. The structures of the neutral Ag12-14B2 appear clear growth pattern, namely, the large clusters are formed by doping one Ag atom into the smaller sized cluster and the double B atoms are not closed by the Ag atoms. The atomic structures of anionic AgnB2− clusters are quite different from their neutral state until n = 12. Ag5-10B2− clusters are all composed by a qusi-plane which contains double B and (n−1) Ag atoms, and one Ag atom above the plane. The structure of Ag11B2− is similar to Ag12-14B2−, while Ag12-14B2− species are same as their neutral state. The ground-state cationic AgnB2+ (n ≤ 12) clusters have distinct geometries, compared to either the neutral or anionic species, while Ag13B2+ and Ag14B2+ possess the similar structures to their neutral state. Note that, for all the species in Figure 3, the two B atoms are not surrounded by the Ag atoms. The charge has great impact on the structures of AgnB2−/0/+ clusters at small size, however, the impact disappears when n ≥ 13. Additionally, the atomic structures of AgnB2−/0/+ clusters are quite different from both the Agn−/0/+ and AgnB−/0/+ species. The inherent stability of the clusters considered can be examined by the average binding energies (Eb), which are defined as follows:

Eb (Agn− /0/ + ) = [(n − 1) E (Ag) + E (Ag− /0/ + ) − E (Agn− /0/ + )] / n

(1)

Eb (Agn B− /0/ + ) = [nE (Ag) + E (B− /0/ + ) − E (Agn B− /0/ + )] / (n + 1)

(2)


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Eb (Agn B2− /0/ += ) [nE (Ag) + E (B) + E (B− /0/ + ) − E (Agn B2− /0/ + )] / (n + 2)

(3)

where E(Ag), E(B), E(Ag−/0/+) and E(B−/0/+) are the total energies of the corresponding neutral or charged Ag and B atoms. E(Agn−/0/+), E(AgnB−/0/+) and E(AgnB2−/0/+) are the total energies of the corresponding neutral, anionic and cationic Agn, AgnB and AgnB2 clusters, respectively. Their plots are depicted in Figure 4, with black symbols for pure silver, red symbols for AgnB−/0/+ and green symbols for AgnB2−/0/+ clusters. The larger Eb value of a cluster indicates the higher

Figure 4. Binding energies of (a) neutral, (b) anionic and (c) cationic AgnBm clusters plotted versus atom number, where the black, red, and green markers refer to the series with m = 0, 1, and 2, respectively.


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stability. It is clearly seen that the Eb values of neutral Agn clusters are the lowest among those of neutral Agn, AgnB and AgnB2, while neutral AgnB2 possess the highest Eb values. The same behavior is also found for both the anionic and cationic species. Namely, at the same charge state, the stability order of considered clusters is AgnB2 > AgnB > Agn. Note that the Eb values of pure Agn−/0/+ clusters tend to be increase with increasing cluster sizes. For neutral AgnB and anionic AgnB− species, the Eb values behave overall stable. While the binding energies of AgnB+ and AgnB2−/0/+ clusters show slightly decrease trend. Ag5B2+ presents the obviously highest binding energy as compared to other species, which indicates its relatively enhanced thermodynamical stability. To further probe the prominent stability of silver boride clusters, we calculate the energy loss by removing an Ag atom from the cluster. The removal energy Ef is given by − /0/ + ) E (Agn −1Bm− /0/ + ) + E (Ag) − E (Agn Bm− /0/ + ) E f (Agn B= m

(4)

In Figure 5 (a), (b) and (c), we display the removal energies of neutral, anoinic and cationic clusters as functions of cluster size, with black symbols for pure silver, red symbols for AgnB−/0/+ and green symbols for AgnB2−/0/+ clusters. The Ef values of the considered species appear evident even/odd oscillations as the increasing cluster size with rare exception. For the neutral species, except for Ag14B, AgnBm clusters with an even number of atoms exhibiting higher Ef values than those with an odd number of atoms with rare exception. However, for the anionic state, the clusters with odd size have higher Ef values except for Ag9B− and Ag2B2−. A similar principle is found in the cationic species, except the contrary Ef vibrations of small cationic AgnB2+ (n < 5) clusters. Note that the cluster with filled electronic shells, i.e. Ag8, Ag7−, Ag9+, Ag5B, Ag4B−, Ag6B+ and Ag2B2 with 8 electrons, and Ag15B, Ag14B−, Ag12B2, Ag11B2− and Ag13B2+ with 18 electrons, as well as Ag14B2 and Ag13B2− with 20 electrons, have significant larger removal


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Figure 5. Calculated remove energies for Ag atom from (a) neutral, (b) anionic and (c) cationic AgnBm clusters, where the black, red, and green markers refer to the series with m = 0, 1, and 2, respectively.

energies than other clusters. Considering the previous report of enhanced stability and remarkable resistance to react with oxygen of 14-electorn silver clusters, we focus on researching the stable behaviors of Ag14, Ag13−, Ag15+, Ag11B, Ag10B−, Ag12B+, Ag8B2, Ag7B2− and Ag9B2+ clusters with 14 electrons and find that these clusters have indeed higher removal energies, along with enhanced stabilities. All the magic clusters have the lowest spin multiplicity. The stability of clusters having 8, 18 or 20 valence electrons is consistent with filling of shells in the spherical


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jellium model. However, the stabilities of these species with a valence electron count of 14 require further scrutiny. From Figure 5, although the single and double B doping affect the atomic geometries greatly, their energetic stabilities are little affected. Furthermore, the species with even electron have higher Ef values irrespective of the component or the charged state. This pattern is due to their fully occupied orbitals. The second-order difference of energy (Δ2E) can reflect a clearer picture of the relative stability for certain cluster sizes, which is defined as

∆2 E (Agn Bm− /0/ + ) = E (Agn −1Bm− /0/ + ) + E (Agn +1Bm− /0/ + ) − 2 E (Agn Bm− /0/ + )

(5)

The Δ2E values of neutral, anionic and cationic considered species are shown in Figure 6 (a), (b) and (c), respectively. The black symbols are for pure silver, while red symbols are for AgnB−/0/+ and green symbols are for AgnB2−/0/+ clusters. One can see strong even/odd vibrations with the increasing cluster size. Note that there are two local maxima for pure neutral Agn clusters containing 8 and 14 Ag atoms, which conform to their enhanced stabilities suggested by previous researchers.15 For neutral AgnB clusters, Ag5B, Ag9B and Ag11B possess the obviously higher Δ2E values than their neighboring sizes, indicating their stronger stability. For AgnB2 species, the local maxima occur at Ag4B2, Ag8B2 and Ag12B2. In the case of anions, the anionic Ag7− and Ag13− clusters have relatively stronger stability due to their higher Δ2E values, which is in good agreement with previous reports.8,15 For anionic AgnB− and AgnB2−, the local maxima occur at Ag4B−, Ag10B−, Ag14B−, Ag7B2− and Ag11B2−, implying that they are more stable than their neighbors. In the case of cations, we find that cationic Ag9+ and Ag15+ really have relatively larger Δ2E values, in agreement with the previous suggestion.15 Furthermore, the Δ2E values of Ag4B+ and Ag12B+ are clearly larger than other AgnB+ species, while the local maxima of AgnB2+ clusters appear at Ag5B2+ and Ag9B2+. These results are internally consistent with the above


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Figure 6. Calculated second-order energy differences of (a) neutral, (b) anionic and (c) cationic AgnBm clusters, where the black, red, and green markers refer to the series with m = 0, 1, and 2, respectively.

discussion that these species constitute the enhanced stability systems among the clusters considered. It is worth noting that for the neutral and anionic species in Figure 6 (a) and (b), the oscillatory behaviors of AgnB2 and AgnB2− clusters are most violent, whereas the most intense oscillation for cationic clusters in Figure 6 (c) occurs at single B doped silver species. Namely, the number of doped B atoms has distinct influence on the stability of clusters with different charges.


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In addition to the discussion above, it is also important to know how the chemical stabilities of silver clusters will be affected by boron doping? As is well known, the chemical stability can be reflected by the HOMO−LUMO energy gap (Egap). In view of this, we have calculated the Egap values for the neutral and charged Agn, AgnB and AgnB2 clusters and plotted them as functions of cluster size in Figure 7 (a), (b) and (c), respectively. A large Egap value is a signature of the chemical stability as the cluster wants to neither donate nor receive electrons. For open-shell

Figure 7. Calculated HOMO−LUMO gaps of (a) neutral, (b) anionic and (c) cationic AgnBm clusters, where the black, red, and green markers refer to the series with m = 0, 1, and 2, respectively.


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AgnBm which has odd number of valence electrons, the HOMO and the LUMO refer to the highest occupied and the lowest unoccupied orbitals irrespective of their spin labels. All the neutral, anionic and cationic Agn, AgnB and AgnB2 clusters reveal well-defined even-odd patterns, and the species with odd number of electrons have smaller Egap values due to the presence of an unpaired electron, while the clusters with even number of electrons have varying Egap values. The maximum Egap value of pure neutral silver clusters occurs at Ag8, which is in agreement with the previous reports.15 For neutral AgnB species, Ag5B, Ag11B and Ag15B have the local larger Egap values. One can notice a stronger variation and an overall decrease in the Egap values of the neutral AgnB2 clusters with even number of electrons as these clusters grow in size. The exceptions are Ag4B2 and Ag8B2. In the case of anions, the local maximum Egap values are observed at Ag7− and Ag13− for pure Agn−, Ag4B−, Ag10B− and Ag14B− for AgnB−, and Ag7B2− and Ag11B2− for AgnB2−. For cationic species, the relative higher Egap values of Ag15+, Ag6B+, Ag12B+, Ag5B2+ and Ag9B2+ illustrate their enhanced chemical stability. The numbers of valence electrons of Ag15B, Ag12B2, Ag13B2+, Ag14B2 and Ag13B2− are 18 and 20, respectively, which are magic numbers according to spherical jellium model. However, our theoretical predictions point out that they do not have an enhanced stability as the cases of Ag14B− and Ag11B2−. Considering the discussions above, the enhanced stability and large HOMO−LUMO gaps observed on Ag5B, Ag4B− and Ag6B+ can be rationalized within the spherical jellium model, which has been successfully used in pure Ag8, Ag7−, and Ag9+ clusters in previous research, since the 8 valence electrons form a filled electronic shell.15 To further confirm it, the molecular orbitals of these magic clusters with 8 valence electrons are analyzed. Due to the higher HOMO−LUMO gaps, the molecular orbitals of pure silver Ag8 clusters, and single B doped


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silver Ag4B− and Ag6B+ clusters are plotted in Figure 8, respectively. The molecular orbitals of other systems with 8 electrons are displayed in Figure S19 (see SI). The solid lines represent filled orbitals while the short dash lines indicate unfilled states. Based on the spherical jellium model, we have examine the nodes of the molecular orbitals of these magic clusters and mark the orbitals according to their effective quantum numbers (1S, 1P, 1D, 2S). Note that due to the different ground-state structure, the molecular orbitals of Ag8 are distinct from the reports of Gamboa et al..15 From Figure 8, there are three nearly dissociative levels near the HOMO for Ag8 cluster, as well as for Ag4B− and Ag6B+, and then several Ag 4d orbitals lying approximately 2.5 eV below the HOMO. For Ag8 cluster, the three orbitals near the HOMO are all 1P characters, while the two orbitals near the LUMOs have 1D feature. So, according to the spherical jellium model, the electronic shell structure of Ag 8 is perfectly described as |1S2|1P6||1D102S2|, in which the | indicates a break of different orbitals while || indicates the break between filled and unfilled orbitals, filling at 8 electrons with a HOMO−LUMO gap of 2.32 eV. It is interesting that the virtual orbitals of the two silver boride clusters are different from that of

Figure 8. Molecular orbital diagrams of Ag8, Ag4B− and Ag6B+.


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pure Ag8 cluster, namely, the 2S orbital is the LUMO of silver borides while for pure Ag8 cluster the 1D orbital is the LUMO. This implies that the shell structures of both Ag4B− and Ag6B+ clusters are of |1S2|1P6||2S21D10|. One should know that the observed number of closed shell electrons of the spherical jellium model is predicted on the basis of a spherical background. Thus, these magic numbers may be changed due to a non-spherical structure. Because of the larger HOMO−LUMO gaps, enhanced stabilities and interesting geometries, we next analyzed the molecular orbitals of Ag13−, Ag10B− and Ag7B2− in Figure 9, which have 14 valence electrons that correspond to unfilled shell within the spherical jellium model. The molecular orbitals of Ag14, Ag15+, Ag11B, Ag12B+, Ag8B2, and Ag9B2+ clusters, which also have 14 valence electrons, is illustrated in Figure S20 (see SI). From Figure 9, the molecular orbitals of anionic Ag13− are much distinct from the results of Gamboa et orbitals, because of the different ground-state geometry of Ag13− we obtained. In this work, the electronic structure of Ag13− is best describe as |1S2|1P6|1D6||1D4|, in which the 1D shell is split

Figure 9. Molecular orbital diagrams of Ag13−, Ag10B− and Ag7B2−.


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into subshells. Note that the electronic shell structure of the Ag10B− cluster in Figure 9 is also of |1S2|1P6|1D6||1D4|, while the electronic structure of Ag7B2− is found to be |1S2|1P6|1D4||1D6|. The splitting of 1D10 into subshells is expected and raised by the unfilled shell with the 14 valence electrons.

4. Conclusions To summarize, we have carried out an in-depth study of the structural and electronic properties of neutral, anionic and cationic Agn, AgnB and AgnB2 clusters up to 16 atoms. New putative global minimum structures of pure neutral Ag8-Ag13, anionic Ag6− and Ag13− and cationic Ag6+, Ag10+, Ag11+ and Ag13+ clusters have been proposed. The present studies show that boron atom doping has considerable influence on not only the valence electron count but also geometries of silvers clusters. The clusters with even electron have enhanced stabilities irrespective of the component or the charged state due to their fully occupied orbitals. One of the important consequences of the structural deformations is the grouping of the electronic states into subshells. According to the jellium model, for clusters with 8 valence electrons, such as Ag7−, Ag8, Ag9+, Ag4B−, Ag5B and Ag6B+, the approximate spherical structures result in a full filled 1S, 1P shell that leads to large HOMO–LUMO gaps. However enhanced stability was also observed for clusters with 14 valence electrons (Ag13−, Ag14, Ag15+, Ag10B−, Ag11B, Ag12B+, Ag7B2−, Ag8B2 and Ag9B2+) due to geometrical distortion of these clusters.

Associated content Supporting Information.


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The total energies, point symmetries and HOMO−LUMO gaps of ground-state structures of Agn−/0/+, AgnB−/0/+ and AgnB2−/0/+ clusters are respectively summarized in Tables S1-S3. The geometries and relative stabilities of the low-lying isomers of each cluster are respectively shown in Figure S1-S9. The infrared spectra (IR) of the ground-state structures are displayed in Figure S10-S18. The molecular orbitals of systems with 8 and 14 electrons are displayed in Figure S19 and S20, respectively. This information is available free of charge via the Internet at http://pubs.acs.org.

Author information Corresponding Authors Electronic mail: [email protected], [email protected], [email protected].

Acknowledgements This work was supported by the National Natural Science Foundation of China (Nos. 11304167 and 11274235), Postdoctoral Science Foundation of China (Nos. 20110491317 and 2014T70280), Program for Science & Technology Innovation Talents in Universities of Henan Province (No. 15HASTIT020), Open Project of State Key Laboratory of Superhard Materials (No. 201405), and Young Core Instructor Foundation of Henan Province (No. 2012GGJS-152). References (1) Henley, S. J.; Carey, J. D.; Silva, S. R. P. Silver-Nanoparticle Decorated Carbon Nanoscaffolds: Application as a Sensing Platform. Appl. Phys. Lett. 2006, 89, 183120.


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TABLE OF CONTENTS - GRAPHIC


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Ab Initio Search for Global Minimum Structures of Pure and Boron

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