Structural Stability and Evolution of Scandium-Doped Silicon Clusters

Oct 1, 2018 - Synopsis. Theoretical electron affinities of Sc-doped silicon clusters (ScSin) are compared with the experimental values...
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Structural Stability and Evolution of Scandium-Doped Silicon Clusters: Evolution of Linked to Encapsulated Structures and Its Influence on the Prediction of Electron Affinities for ScSin (n = 4−16) Clusters Yuming Liu,† Jucai Yang,†,‡ and Lin Cheng*,†

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†

School of Chemical Engineering, Inner Mongolia University of Technology, and Inner Mongolia Key Laboratory of Theoretical and Computational Chemistry Simulation, Hohhot 010051, People’s Republic of China ‡ School of Energy and Power Engineering, Inner Mongolia University of Technology, Hohhot 010051, People’s Republic of China S Supporting Information *

ABSTRACT: Sc-doped semiconductor clusters are the simplest transition metal- and rare-earth metal-doped semiconductor clusters. In this work, the structural evolution behavior and electronic properties of Sc-doped neutral and anionic Sin (n = 4−16) clusters were studied using the ABCluster global search technique coupled with a hybrid density functional method. The results revealed that although neutral and anionic configurations are different for ScSin (n = 6−14) clusters, the evolution pattern of the ground-state structures is consistent (evolution of linked to encapsulated structures starting from n = 14). The good agreement between the theoretical and experimental photoelectron spectra demonstrated that the obtained anionic global minimum structures are reasonable. The excellent agreement between the adiabatic electron affinities corrected by considering the structural correction factor and the experimental data indicated that the structural correction factor is important for reproducing the experimental data and that the obtained ground-state structures for the neutral ScSin clusters reported herein are reliable. The relative stability and chemical bonding analysis showed that the fully encapsulated ScSi16− cluster is a magic cluster with good thermodynamic and chemical stability.

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INTRODUCTION Rare-earth metal-doped silicon clusters have been applied extensively in microelectronics, the chemical industry, aerospace, optical fiber communication, energy fields, and so on because of their remarkable magnetic, electronic, and optical properties as well as their gas sensitivity and catalytic performance. Meanwhile, they can be used not only as building blocks for assembling materials but also as new functional materials themselves by manipulation of their composition, shape, and size.1−4 Scandium is a 3d transition metal and also a rare-earth metal. Since the photoelectron spectra and electron affinities of ScSin− (n = 2−20) clusters were reported experimentally,5−9 theoretical studies were carried out to find the ground-state structures on one hand and a method for accurately predicting their electron affinities on the other hand.10−21 Recently, small-sized ScSin (n = 2−6) clusters were calculated using the CCSD(T), CASSCF/CASPT2, ccCA-TM, and/or G4 methods.10−13 Although these methods predict reliable structures and accurate properties, they are not suitable for larger clusters because of the limitations of current computer capability. Therefore, for medium-sized Sc-doped Si clusters, density functional theory (DFT) was selected to study the geometric structures and electronic properties. For instance, starting from n = 14, the encapsulated structures were predicted © XXXX American Chemical Society

to be the ground-state structures for ScSin and their anions when the PBE, B3LYP, BLYP, and B3PW91 functionals were used.17−21 However, it is known that different DFT methods may give different ground-state structures. For example, the ground-state structure of the anion ScSi14− was predicted by PBE to be a distorted hexagonal prism (DHP) structure with Si2 decorating the lateral prism faces,17,18 but it was predicted by B3PW91 to have a three hexagon, six quadrangle (THSQ) structure.21 For neutral ScSi14, the ground-state structure is predicted by BLYP to be a six pentagon, three quadrangle (SPTQ) structure19 and by B3LYP to be a DHP structure.20 The situations of ScSi15 and ScSi16 are analogous to ScSi14.15−19,21 Although previous studies have reported the ground-state structures of ScSin−/0 (n ≤ 18), problems still exist. First, it is known that the ground-state structure of the cluster is the prerequisite for predicting accurate electronic and spectral properties.22−25 However, as mentioned earlier for ScSin (n = 14−16), different density functionals predicted different ground-state structures. In addition, a comparison of different theoretical methods was also conducted in a previous study.26 Received: July 31, 2018

A

DOI: 10.1021/acs.inorgchem.8b02159 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 1. Ground-state structures of ScSin− (n = 4−16) and their symmetries.

Figure 2. Ground-state structures of ScSin (n = 4−16) and their symmetries. Si atoms. Frequency analysis was performed at the same level to ensure that the isomers were true local minima on the potential energy surface. After completion of the initial geometry optimization by PBE, we selected the low-lying structural candidates and reoptimized them using mPW2PLYP34 (a double hybrid functional) with the cc-pVTZ basis set.32,33 Frequency analysis was not performed at the mPW2PLYP level. To further refine the energies, single-point energy calculations were performed by the mPW2PLYP/aug-cc-pVTZ method.32,33 Based on Koopmans’ theorem,35,36 the theoretical PES spectra of the anionic clusters were simulated by the mPW2PLYP/ aug-cc-pVTZ method using the Multiwfn program37 and compared with the experimental data. Chemical bonding analysis based on the adaptive natural density partitioning (AdNDP) method38 was carried out to gain chemical insight. After the single-point energy was available, natural population analysis (NPA) was also conducted to further understand the interaction between the Sc atom and Si cluster. To test the reliability of our calculations, single-point energy calculations were also carried out using the ROCCSD(T) method with the aug-cc-pVTZ-DK basis set32,33 and the Douglas−Kroll−Hess scalar relativistic correction39−41 for small neutral and anionic clusters ScSin0/− (n = 4−9) and compared with several DFT methods (PBE, B3LYP, TPSSh, wB97X, and mPW2PLYP). The calculated results are listed in Tables S1 and S2 in Supporting Information. As can be seen from Tables S1 and S2, only the ground-state structures and vertical detachment energies (VDEs) predicted by the mPW2PLYP method are in excellent agreement with the results obtained using the ROCCSD(T) method. Therefore, we think that the results calculated with mPW2PLYP should be reliable, and the discussion below is based on the mPW2PLYP results.

Furthermore, an experimental method for directly determining the ground-state structures of the clusters is still lacking. Therefore, reliable theoretical predictions can be obtained only by comparing the calculated results with the experimental data such as photoelectron spectroscopy (PES), infrared, and Raman spectra. This combined strategy can be used to predict the structures and properties. Second, since the prediction of the ground-state structure is difficult, it is possible to lose the ground-state structures during the geometry search, especially in the optimization process without a global search technique. Third, there is still little knowledge of the structural evolution patterns of Sc-doped silicon clusters, which is of crucial importance for understanding the bonding characters and properties of Sc-doped Si clusters. Motivated by the above problems, in this study extensive geometry searches using the ABCluster global search technique were carried out for neutral and anionic Sc-doped Sin (n = 4−16) clusters. The purpose of this study was to elucidate the structural evolution pattern of their ground states, understand the effect of structural characteristics on the calculated electron affinities, and provide valuable information for further theoretical and experimental studies of semiconductor clusters doped with scandium or other transition or rare-earth metals.

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THEORETICAL METHODS

The initial configuration searches for ScSin (n = 4−16) clusters and their anions were based on three techniques. First, with the ABCluster global search technique27 combined with the Gaussian 09 package,28 more than 300 isomers for each ScSin0/− (n = 4−16) cluster were optimized using the PBE functional29 with the ECP10MDF basis set30,31 for Sc atoms and the 6-31G basis set for Si atoms. Second, the “substitutional structure” method was used, in which a Sc atom was substituted for a Si atom in the ground-state structure of Sin+1. Third, configurations already reported in the previous literature15−21 were used. The obtained low-lying isomers were reoptimized using PBE in conjunction with the all-electron cc-pVTZ basis set32,33 for Sc and

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RESULTS AND DISCUSSION Equilibrium Configurations. The ground-state structures of ScSin0/− (n = 4−16) clusters are shown in Figures 1 and 2. The structures of the corresponding low-lying isomers, together with their energies and symmetries, are shown in Figures S1 and S2. The electronic states, binding energies, highest occupied molecular orbital (HOMO)−lowest unoccupied molecular B

DOI: 10.1021/acs.inorgchem.8b02159 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Table 1. Electronic States, Average Bonding Energies (Eb, in eV), HOMO−LUMO Energy Gaps (Egap, in eV), and Charges on the Sc Atom (QSc, in a.u.) of the Ground-State Structures of ScSin0/− (n = 4−16) Clusters ScSin− n 4 5 6 7 8 9 10 11 12 13 14 15 16

state 1

A1 1 A′ 1 A1 1 A′ 1 A 1 A1 1 A′ 1 A′ 1 A′ 1 A′ 1 Ag 1 A1 1 A1

ScSin

Eb

Egap

QSc

3.02 3.24 3.35 3.38 3.48 3.56 3.56 3.59 3.63 3.61 3.66 3.70 3.75

2.87 3.07 3.86 3.71 3.66 3.24 3.85 4.60 4.26 4.39 3.28 3.18 5.25

0.08 0.13 0.17 0.15 −0.09 0.18 −0.29 −0.45 −1.14 −0.74 −3.88 −4.86 −5.87

state

Eb

Egap

QSc

A′ 2 A′ 2 A1 doublet doublet 2 A′ doublet doublet doublet doublet 2 A1 2 A′ 2 A′

2.81 3.10 3.16 3.23 3.30 3.38 3.40 3.42 3.47 3.47 3.50 3.55 3.60

3.99 4.20 3.81 4.18 4.14 3.24 3.78 3.67 4.28 3.70 2.89 3.43 4.54

0.46 0.38 0.43 0.22 −0.04 0.25 0.13 −0.14 −0.85 0.00 −3.43 −4.85 −5.52

2

For n = 7, the lowest-energy isomer is derived by capping the pentagonal-bipyramidal ground-state structure of ScSi6− with a Si atom. For n = 8, the most stable geometry can be viewed as the ScSi7 structure capped by a Si atom adjacent to the Sc atom. For n = 11−13, the lowest-energy structures are linked configurations. The ground-state structures of ScSi11 and ScSi12 are distorted compared with those of the corresponding anions. The Sc atom in ScSi13 links rhombic Si4 and capped tetragonal-antiprismic Si9 subclusters, which differs from its anion. Starting from n = 14, the most stable structures have the Sc atom encapsulated in a Si cage. The THSQ structure is predicted to be the ground-state structure for n = 14, which also differs from its anion. For n = 15, the most stable structure is the TPTQ structure, analogous to its anion. The ground state of ScSi16 is a distorted Frank−Kasper polyhedron. Our results for ScSi14 are different from those reported previously.19,20 For ScSi16, our result is different from that in ref 15 but analogous to the one in ref 16. PES of Anionic Clusters. The reliability of the obtained ground-state structures had to be tested further. It is known that PES is sensitive to structural changes, so the reliability of the lowest-energy structures can be assessed by comparing their theoretical and experimental PES spectra. There are two ways to compare theoretical and experimental PES spectra. One is to compare the first vertical detachment energy (VDE), and the other is to compare the number of distinct peaks and their relative positions in the low-binding-energy portion of the PES spectrum. The simulated PES spectra for the most stable structures and the experimental PES spectra are shown in Figure 3. The first theoretical and experimental VDEs of the ground-state structures are listed in Table 2. Moreover, the first VDEs of low-lying isomers of ScSin0/− (n = 4−16) are summarized in Table S3 along with experimental data. As can be seen from Table S3, the VDEs of the ground-state structures are much closer to the experimental values than those of the low-lying isomers. It can be seen from the simulated PES spectra of ScSi4− that there are three major peaks centered at 2.65, 3.27, and 4.14 eV, which match the three peaks of 2.57, 3.00, and 3.74 eV observed in the experimental study,8 especially the first peak of 2.65 eV. For ScSi5−, four distinct peaks located at 2.17, 2.91, 3.32, and 3.96 eV are obtained, and the first three peaks agree with the experimental data of 2.35, 3.07, and 3.25 eV.8

orbital (LUMO) energy gaps, and NPA charges on the Sc atom of the ground-state structures are listed in Table 1. The examined spin states for the anionic and neutral clusters are singlets and doublets, respectively. For the anionic clusters (Figure 1), the ground-state structures are a trigonal bipyramid for n = 4, a face-capped trigonal bipyramid for n = 5, and a pentagonal bipyramid for n = 6, which can be viewed as swapping a Si atom of the ground-state structure of Sin+142−45 with a Sc atom. This is the “substitutional structure”. For n = 7−13, the most stable structures are linked configurations, with the exception of ScSi9−, which is a bicapped tetragonal antiprism (one of the capped atoms is Sc). For ScSi7−, the Sc atom links the Si3 and tetrahedral Si4 subclusters. The Sc atom in ScSi8− links two tetrahedral Si4 subclusters. The Sc atom in ScSi10− links two trigonal-bipyramidal Si5 subclusters. The Sc atom in ScSi11− links a trigonalbipyramidal Si5 subcluster and a capped trigonal-bipyramidal Si6 subcluster. The Sc atom in ScSi13− links a trigonal-bipyramidal Si5 subcluster and a bicapped tetrahedral-bipyramidal Si8 subcluster. For ScSi12−, the Sc atom links Si2 and two trigonalbipyramidal Si5 subclusters, which can also be viewed as attaching a Si2 cluster to the ScSi10− cluster. For n = 14−16, the lowestenergy structures are encapsulated configurations, with the Sc atom located at the center of silicon cage. The most stable structure for ScSi14− is the distorted hexagonal prism with two additional Si atoms decorated on the lateral prism faces and with C2h symmetry (named DHP-C2h). The cage consisting of two pentagonal faces and ten quadrangles (TPTQ) is calculated to be the ground-state structure for ScSi15−. For ScSi16−, the lowest-energy structure is a Frank−Kasper polyhedron. It is noted that the ground-state structures for n = 7, 8, 10, 12, and 14 presented in this work are different from the previously reported structures.17,18,21 The ground-state structures for n = 15 and 16 are different from those reported in ref 21 but analogous to those in refs 17 and 18. For the neutral clusters (Figure 2), the most stable geometries of ScSi4 and ScSi5 are similar to those of their anions. For n = 6−10, the ground-state structures are different from those of the corresponding anions. The lowest-energy structure for ScSi6 is a substitutional structure. The ground states of ScSi9 and ScSi10 are also substitutional structures, which can be regarded as the ground-state structures of Si10 and Si11,42,43 respectively, with a Si atom replaced by a Sc atom. C

DOI: 10.1021/acs.inorgchem.8b02159 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 3. Simulated PES spectra of the most stable ScSin− (n = 4−16) clusters. The insets show the experimental PES spectra.7,8

for further experimental studies on these important Sc-doped silicon anionic clusters. Adiabatic Electron Affinity. The adiabatic electron affinity (AEA) is defined as follows:

Table 2. Theoretical and Experimental Vertical Detachment Energies (VDEs) and Adiabatic Electron Affinities (AEAs) for ScSin− (n = 4−16) VDE n 4 5 6 7 8 9 10 11 12 13 14 15 16

AEA

theor

exptl

2.65 2.17 3.33 3.07 3.11 3.34 3.47 3.83 3.63 4.25 4.13 4.07 4.04

± ± ± ± ± ± ± ± ± ± ± ± ±

2.57 2.35 3.28 3.20 3.40 3.36 4.19 4.17 3.58 4.38 4.21 4.25 4.25

a

0.08 0.08a 0.08a 0.1b 0.1b 0.1b 0.1b 0.1b 0.1b 0.1b 0.1b 0.1b 0.1b

theor

exptl

2.34 2.08 2.56 2.50 2.85 3.06 3.05 3.25 3.13 2.92 3.22 3.21 3.46

± ± ± ± ± ± ± ± ± ± ± ± ±

2.19 2.15 2.60 2.40 2.70 2.60 3.40 3.30 3.00 2.90 3.20 3.30 3.40

AEA = Eneutral − Eanion + ΔEsc

(1)

where Eneutral and Eanion are the ground-state energies of the neutral and anionic clusters, respectively, and ΔEsc is the structural correction factor related to the charge of the Sc atom in the anionic cluster. Generally, the charge of a metal atom in a cluster tends to be positive or slightly negative, but as the number of silicon atom increases, the metal atom will be negatively charged when the cluster becomes a cage structure. According to the change in the charges, we divided these structures into three types, namely, no-cage, half-cage, and cage. The NPA charges on the Sc atom in the ground-state structures of ScSin0/− (n = 4−16) are shown in Figure 4 and

a

0.08 0.08a 0.004b 0.004b 0.004b 0.004b 0.004b 0.004b 0.004b 0.004b 0.004b 0.004b 0.10b

a

From ref 8. bFrom ref 7.

Three peaks for ScSi6− are situated at 3.33, 4.47, and 5.53 eV, in excellent agreement with the experimental values of 3.28, 4.47, and 5.50 eV.7,8 For the ScSin− (n = 7−16) clusters, the first peak ranges from 3.07 to 4.25 eV, consistent with the experimental data except for n = 10. The theoretical PES spectra of ScSi15− and ScSi16− are slightly shifted to lower energy compared with the experimental ones.7 The simulated and experimental PES spectra of ScSi10− have large differences. On the other hand, for ScSi8− and ScSi11−, the second peak is much closer to the first peak in the experimental PES spectrum compared with the simulated one. For the theoretical PES spectrum of ScSi8−, besides the first peak at 3.11 eV, the other four peaks are located at 3.45, 4.02, 4.78, and 5.22 eV, which reproduce well the experimental data of 3.4, 4.0, 4.7, and 5.3 eV.7 It seems experimentally that the first peak is not observed. The deviation of the theoretical and experimental PES spectra may be attributed to the lower energy of the detachment laser in the experimental measurement. Quantitative analysis showed that the average absolute deviation of the theoretical first VDEs of ScSin− (n = 4−7, 9, 12−16) from the experimental values is only 0.11 eV. We believe that our reliable theoretical predictions will provide strong motivation

Figure 4. Natural population analysis charges of the Sc atom for the most stable structures of ScSin0/− (n = 4−16) clusters.

Table 1. As can be seen from Figure 4, there are two declining points at n = 12 and 14. The clusters before the first declining point (n ≤ 11) are no-cage structures, and the clusters between the first and second declining points (n = 12, 13) are half-cage structures, while the clusters after the second declining point D

DOI: 10.1021/acs.inorgchem.8b02159 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry (n = 14−16) are cage structures. As an empirical correction, the values of ΔEsc are assigned to be 0.00, −0.20, and −0.40 eV for no-cage, half-cage, and cage structures, respectively. The calculated AEAs and experimental data are listed in Table 2. It can be concluded that the theoretical AEAs of ScSin (n = 4−8, 11−16) are in excellent agreement with the experimental results. The mean absolute deviation is only 0.08 eV. It is noted that the AEA of ScSi9− predicted by ROCCSD(T) is 3.06 eV, which is larger than the experimental value (2.60 ± 0.004 eV).7 As we know, the anionic PES spectrum is a powerful tool for determining AEA. However, if the anionic PES spectrum shows a long, round tail with no obvious features, it is difficult to determine the exact experimental AEA value. The anionic PES spectrum of ScSi9− is such a case.7 Therefore, on the basis of the ROCCSD(T) results and the experimental PES spectrum of the ScSi9− cluster, we suggest that the experimentally measured AEA of the ScSi9 −cluster should be checked further. The excellent agreement between the theoretical and experimental AEAs indicated that the ground-state structures for neutral ScSin reported herein are reliable. Stability. The relative stabilities of the determined globalminimum structures of the ScSin0/− (n = 4−16) clusters were examined in terms of both dissociation energy per atom (DEPA) and disproportionation reaction energy (DRE). The DEPA is the energy required for the following reactions: ScSi n → nSi + Sc

(2)

ScSi n− → (n − 1)Si + Si− + Sc

(3)

The DRE is the energy required for the following reactions: 2ScSi n → ScSi n + 1 + ScSi n − 1

(4)

2ScSi n− → ScSi n + 1− + ScSi n − 1−

(5)

The calculated DEPA and DRE values are shown in Figure 5. As can be seen in Figure 5a, the DEPA curves for the anionic and neutral clusters are nearly parallel, and the DEPA values for the anionic clusters are larger than those for the neutral cluster. This is the case because the ScSin clusters possess open-shell electronic configurations. When they gain an electron, the electron configurations change to closed-shell ones, and the electronic repulsions are minimized based on the Pauli exclusion principle. As shown in Figure 5b, the DRE is a sensitive measure of relative stability. For n = 9 and 12, both neutral and anionic clusters are more thermodynamically stable than their neighboring clusters. In addition to ScSi90/− and ScSi120/−, ScSi14− is more stable than its neighboring clusters. The HOMO−LUMO energy gap is known to be related to the chemical reactivity: the smaller the HOMO−LUMO energy gap, the stronger the chemical reactivity. The HOMO− LUMO energy gaps for ScSin0/− (n = 4−16) and Sin0/− (n = 4−16) clusters46 are plotted Figure 5c as functions of the number of Si atoms, and the corresponding data are summarized in Tables S4 and S5. As can be seen from Figure 5c, there is no odd−even oscillation behavior for the clusters. Sc-doped Sin clusters narrow the HOMO−LUMO gap for n = 4−15 and widen the gap for n = 16. This may be attributed to the lowest energy of the HOMO for ScSi16 among all of the Sc-doped silicon clusters. Sc-doped anionic silicon clusters for n = 11 and 16 obviously broaden the HOMO−LUMO gap. The local minima occur at n = 6, 9, 11, and 14 for neutral ScSin and n = 5, 9, 12, and 15 for anion ScSin −, suggesting that their chemical reactivities are stronger than those of their neighbors.

Figure 5. Size dependences of (a) the dissociation energy per atom (DEPA), (b) the disproportionation reaction energy (DRE), and (c) the HOMO−LUMO energy gap for the ground-state ScSin0/− (n = 4−16) clusters.

For n = 6, 9, and 12, the HOMO−LUMO energy gaps of ScSin are nearly the same as those of the corresponding anions, indicating that the extra electron does not change their chemical reactivities. On the basis of the DEPA and DRE energy values, ScSi16− is a magic cluster. Chemical Bonding Analysis. As mentioned above, the anionic ScSi16− cluster has good thermodynamic and chemical stability. To gain a deeper understanding, the character of the bonding between the Sc atom and Si16 shell was examined by the AdNDP method, which is a generalized natural bond orbital (NBO) method to analyze localized and delocalized multicenter bonds (encoded as nc−2e, where n can range from 1 (lone pair) to the number of atoms in the cluster) proposed E

DOI: 10.1021/acs.inorgchem.8b02159 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry by Zubarev and Boldyrev.38 As shown in Figure 6, the chemical bonding of 68 valence electrons can be categorized into three

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study was supported by the National Natural Science Foundation of China (Grant 21863007), the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region (Grant NMGIRT-A1603), and the Inner Mongolia Natural Science Foundation (Grant 2015MS0216).

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Figure 6. AdNDP analysis of the ScSi16− cluster. ON stands for the occupation number.

(1) Hang, T. D.; Hung, H. M.; Nguyen, M. T. Structural assignment, and electronic and magnetic properties of lanthanide metal doped silicon heptamers Si7M0/− with M = Pr, Gd and Ho. Phys. Chem. Chem. Phys. 2016, 18, 31054−31063. (2) Zhao, R. N.; Han, J. G. Geometrical stabilities and electronic properties of Sin (n = 12−20) clusters with rare earth holmium impurity: a density functional investigation. RSC Adv. 2014, 4, 64410−64418. (3) Yang, J.; Wang, J.; Hao, Y. Europium-doped silicon clusters EuSin (n = 3−11) and their anions: structures, thermochemistry, electron affinities, and magnetic moments. Theor. Chem. Acc. 2015, 134, 81. (4) Yang, J.; Feng, Y.; Xie, X.; Wu, H.; Liu, Y. Gadolinium-doped silicon clusters GdSin (n = 2−9) and their anions: structures, thermochemistry, electron affinities, and magnetic moments. Theor. Chem. Acc. 2016, 135, 204. (5) Koyasu, K.; Akutsu, M.; Mitsui, M.; Nakajima, A. Selective Formation of MSi16 (M = Sc, Ti, and V). J. Am. Chem. Soc. 2005, 127, 4998−4999. (6) Koyasu, K.; Atobe, J.; Akutsu, M.; Mitsui, M.; Nakajima, A. Electronic and Geometric Stabilities of Clusters with Transition Metal Encapsulated by Silicon. J. Phys. Chem. A 2007, 111, 42−49. (7) Koyasu, K.; Atobe, J.; Furuse, S.; Nakajima, A. Anion photoelectron spectroscopy of transition metal− and lanthanide metal−silicon clusters: MSin− (n = 6−20). J. Chem. Phys. 2008, 129, 214301−214307. (8) Xu, H. G.; Wu, M. M.; Zhang, Z. G.; Sun, Q.; Zheng, W. J. Structural and bonding properties of ScSin− (n = 2−6) clusters: photoelectron spectroscopy and density functional calculations. Chin. Phys. B 2011, 20, 043102−043109. (9) Xu, H. G.; Zhang, Z. G.; Feng, Y.; Zheng, W. J. Photoelectron spectroscopy and density-functional study of Sc2Sin− (n = 2−6) clusters. Chem. Phys. Lett. 2010, 498, 22−26. (10) Pham, L. N.; Nguyen, M. T. Electronic Structure of Neutral and Anionic Scandium Disilicon ScSi2−/0 Clusters and the Related Anion Photoelectron Spectrum. J. Phys. Chem. A 2016, 120, 9401− 9410. (11) Tran, Q. T.; Tran, V. T. Quantum chemical study of the geometrical and electronic structures of ScSi3−/0 clusters and assignment of the anion photoelectron spectra. J. Chem. Phys. 2016, 144, 214305−214313. (12) Nguyen, M. T.; Tran, Q. T.; Tran, V. T. A CASSCF/CASPT2 investigation on electron detachments from ScSin− (n = 4−6) clusters. J. Mol. Model. 2017, 23, 282. (13) Lu, J.; Yang, J. C.; Kang, Y. L.; Ning, H. M. Probing the electronic structures and properties of neutral and anionic ScSin(0,−1) (n = 1−6) clusters using ccCA-TM and G4 theory. J. Mol. Model. 2014, 20, 2114. (14) Xiao, C. Y.; Abraham, A.; Quinn, R.; Hagelberg, F.; Lester, W. A. Comparative Study on the Interaction of Scandium and Copper Atoms with Small Silicon Clusters. J. Phys. Chem. A 2002, 106, 11380−11393. (15) Wang, J.; Ma, Q. M.; Xu, R. P.; Liu, Y.; Li, Y. C. 3d transition metals: Which is the ideal guest for Sin (n = 15, 16) cages? Phys. Lett. A 2009, 373, 2869−2875.

classes: lone-pair, 2c−2e, and 4c−2e. The Si atom on each of the four triad axes has a lone pair (ScSi16− has Td symmetry). The remaining Si12 cage (excluding the four Si atoms on the triad axes) is characterized by 18 2c−2e localized Si−Si σ bonds with 1.81−1.85 electrons in each bond. The last class includes 12 delocalized 4c−2e σ bonds (each triad axis connects three 4c−2e bonds symmetrically), which are responsible for the connection between the central Sc atom and the outer Frank−Kasper Si16 shell and stabilize the completely encapsulated ScSi16− cluster.

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CONCLUSIONS The structural evolution behavior and electronic properties of Sc-doped Sin (n = 4−16) clusters have been studied using the ABCluster global search technique coupled with a hybrid DFT method. The results revealed that although the neutral and anionic configurations are different from each other for n = 6−14, the evolution patterns of the ground-state structures are consistent (evolution of linked to encapsulated structures starting from n = 14). The theoretical adiabatic electron affinities obtained by considering the structural correction factor are in excellent agreement with the experimental data. The analyses of relative stability and chemical bonding show that the completely encapsulated ScSi16− cluster is a magic cluster with good thermodynamic and chemical stability. We hope that our study will provide useful motivation for further experimental and theoretical investigations to probe the structural and electronic properties of rare-earth metal-doped silicon clusters.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the Web site. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.inorgchem.8b02159. Figures showing the structures, symmetries, and relative energies of low-lying isomers of ScSin0/− (n = 4−9) clusters and tables showing relative energies of ScSin0/− (n = 4−9) clusters, theoretical and experimental VDEs for ScSin− (n = 4−9) clusters, and HOMO and LUMO energies and HOMO−LUMO gaps of ScSin0/− and Sin0/− (n = 4−16) clusters (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Lin Cheng: 0000-0002-4264-5523 F

DOI: 10.1021/acs.inorgchem.8b02159 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry (16) Ulises Reveles, J.; Khanna, S. N. Electronic counting rules for the stability of metal-silicon clusters. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 74, 035435. (17) Torres, M. B.; Fernández, E. M.; Balbás, L. C. Theoretical study of isoelectronic SinM clusters (M = Sc−, Ti, V+; n = 14−18). Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 75, 205425. (18) Torres, M. B.; Balbás, L. C. Relative stability of Sin and SinSc− clusters in the range n = 14−18. Eur. Phys. J. D 2007, 43, 217−220. (19) Guo, L. J.; Zhao, G. F.; Gu, Y. Z.; Liu, X.; Zeng, Z. Densityfunctional investigation of metal-silicon cage clusters MSin (M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn; n = 8−16). Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 195417. (20) He, J. G.; Wu, K. C.; Liu, C. P.; Sa, R. J. Stabilities of 3d transition-metal doped Si14 clusters. Chem. Phys. Lett. 2009, 483, 30− 34. (21) Borshch, N.; Kurganskii, S. Geometric structure, electronenergy spectrum, and growth of anionic scandium-silicon clusters ScSin− (n = 6−20). J. Appl. Phys. 2014, 116, 124302−124309. (22) Sun, W. G.; Wang, J. J.; Lu, C.; Xia, X. X.; Kuang, X. Y.; Hermann, A. Evolution of the Structural and Electronic Properties of Medium-Sized Sodium Clusters: A Honeycomb-like Na20 Cluster. Inorg. Chem. 2017, 56, 1241−1248. (23) Chen, B. L.; Sun, W. G.; Kuang, X. Y.; Lu, C.; Xia, X. X.; Shi, H. X.; Maroulis, G. Structural Stability and Evolution of Medium-Sized Tantalum-Doped Boron Clusters: A Half-Sandwich-Structured TaB12− Cluster. Inorg. Chem. 2018, 57, 343−350. (24) Xia, X. X.; Hermann, A.; Kuang, X. Y.; Jin, Y. Y.; Lu, C.; Xing, X. D. Study of the Structural and Electronic Properties of Neutral and Charged Niobium-Doped Silicon Clusters: Niobium Encapsulated in Silicon Cages. J. Phys. Chem. C 2016, 120, 677−684. (25) Jin, Y. Y.; Tian, Y. H.; Kuang, X. Y.; Zhang, C. Z.; Lu, C.; Wang, J. J.; Lv, J.; Ding, L. P.; Ju, M. Ab Initio Search for Global Minimum Structures of Pure and Boron Doped Silver Clusters. J. Phys. Chem. A 2015, 119, 6738−6745. (26) Maroulis, G. Quantifying the Performance of Conventional DFT Methods on a Class of Difficult Problems: The Interaction (Hyper)Polarizability of Two Water Molecules as a Test Case. Int. J. Quantum Chem. 2012, 112, 2231−2241. (27) Zhang, J.; Dolg, M. ABCluster: the artificial bee colony algorithm for cluster global optimization. Phys. Chem. Chem. Phys. 2015, 17, 24173−24181. (28) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö .; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, revision C.01; Gaussian, Inc.: Wallingford, CT, 2009. (29) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (30) Dolg, M.; Wedig, U.; Stoll, H.; Preuss, H. Energy-adjusted ab initio pseudopotentials for the first row transition elements. J. Chem. Phys. 1987, 86, 866−872. (31) Martin, J. M. L.; Sundermann, A. Correlation consistent valence basis sets for use with the Stuttgart−Dresden−Bonn relativistic effective core potentials: The atoms Ga−Kr and In−Xe. J. Chem. Phys. 2001, 114, 3408−3420. (32) Woon, D. E., Jr.; Dunning, T. H., Jr. Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon. J. Chem. Phys. 1993, 98, 1358−1371.

(33) Balabanov, N. B.; Peterson, K. A. Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc-Zn. J. Chem. Phys. 2005, 123, 064107−064121. (34) Schwabe, T.; Grimme, S. Towards chemical accuracy for the thermodynamics of large molecules: new hybrid density functionals including non-local correlation effects. Phys. Chem. Chem. Phys. 2006, 8, 4398−4401. (35) Tozer, D. J.; Handy, N. C. Improving virtual Kohn−Sham orbitals and eigenvalues: Application to excitation energies and static polarizabilities. J. Chem. Phys. 1998, 109, 10180−10189. (36) Akola, J.; Manninen, M.; Häkkinen, H.; Landman, U.; Li, X.; Wang, L. S. Photoelectron spectra of aluminum cluster anions: Temperature effects and ab initio simulations. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 60, R11297−R11300. (37) Lu, T.; Chen, F. Multiwfn: A Multifunctional Wavefunction Analyzer. J. Comput. Chem. 2012, 33, 580−592. (38) Zubarev, D. Y.; Boldyrev, A. I. Developing paradigms of chemical bonding: adaptive natural density partitioning. Phys. Chem. Chem. Phys. 2008, 10, 5207−5217. (39) Hess, B. A. Applicability of the no-pair equation with freeparticle projection operators to atomic and molecular structure calculations. Phys. Rev. A: At., Mol., Opt. Phys. 1985, 32, 756−763. (40) Hess, B. A. Relativistic electronic-structure calculations employing a two-component no-pair formalism with external-field projection operators. Phys. Rev. A: At., Mol., Opt. Phys. 1986, 33, 3742−3748. (41) Jansen, G.; Hess, B. A. Revision of the Douglas−Kroll transformation. Phys. Rev. A: At., Mol., Opt. Phys. 1989, 39, 6016− 6017. (42) Yang, J. C.; Xu, W. G.; Xiao, W. S. The small silicon clusters Sin (n = 2−10) and their anions: structures, themochemistry, and electron affinities. J. Mol. Struct.: THEOCHEM 2005, 719, 89−102. (43) Shvartsburg, A. A.; Liu, B.; Jarrold, M. F.; Ho, K. M. Modeling ionic mobilities by scattering on electronic density isosurfaces: Application to silicon cluster anions. J. Chem. Phys. 2000, 112, 4517−4526. (44) Yoo, S.; Zeng, X. C. Structures and stability of medium-sized silicon clusters. III. Reexamination of motif transition in growth pattern from Si15 to Si20. J. Chem. Phys. 2005, 123, 164303−164308. (45) Li, B. X.; Xu, Q. Lowest energy structures of anionic Sin (n = 11−25) clusters. Phys. Status Solidi B 2004, 241, 990−997. (46) The HOMO−LUMO energy gaps for the neutral and anionic silicon clusters were calculated at the mPW2PLYP/aug-cc-pVTZ// mPW2PLYP/cc-pVTZ level. The most stable structures of the Sin clusters were taken from ref 43 for n = 4−15 and ref 44 for n = 16. The lowest-energy geometries of Sin− clusters were taken from ref 43 for n = 4−14 and 16 and ref 45 for n = 15.

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DOI: 10.1021/acs.inorgchem.8b02159 Inorg. Chem. XXXX, XXX, XXX−XXX