SEMICONDUCTOR PHYSICS

First principles study of structural, electronic and magnetic properties of SnGen(0, ±1) (n = 1–17) clusters

Soumaia Djaadi1, , Kamal Eddine Aiadi1 and Sofiane Mahtout2

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 Corresponding author: Soumaia Djaadi, djaadi58@gmail.com

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Abstract: The structures, relative stability and magnetic properties of pure Gen+1, neutral cationic and anionic SnGen (n = 1–17) clusters have been investigated by using the first principles density functional theory implemented in SIESTA packages. We find that with the increasing of cluster size, the Gen+1 and SnGen(0, ±1) clusters tend to adopt compact structures. It has been also found that the Sn atom occupied a peripheral position for SnGen clusters when n < 12 and occupied a core position for n > 12. The structural and electronic properties such as optimized geometries, fragmentation energy, binding energy per atom, HOMO–LUMO gaps and second-order differences in energy of the pure Ge n+1 and SnGen clusters in their ground state are calculated and analyzed. All isomers of neutral SnGen clusters are generally nonmagnetic except for n = 1 and 4, where the total spin magnetic moments is 2μb. The total (DOS) and partial density of states of these clusters have been calculated to understand the origin of peculiar magnetic properties. The cluster size dependence of vertical ionization potentials, vertical electronic affinities, chemical hardness, adiabatic electron affinities and adiabatic ionization potentials have been calculated and discussed.

Key words: DFT calculationsSn–Ge clustersstructural propertieselectronic propertiesmagnetic properties



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Fig. 3.  (Color online) Ground state structures of cationic and anionic SnGen(±1) (n = 1–17) clusters.

Fig. 2.  (Color online) Ground state structures and their corresponding isomers for SnGen (n = 1–17) clusters.

Fig. 1.  (Color online) Ground state structures and their isomers for Gen+1 (n = 1–17) clusters.

Fig. 4.  (Color online) Size dependence of the binding energies of Gen+1 and SnGen(0, ±1) (n = 1–17) clusters.

Fig. 5.  (Color online) Size dependence of the fragmentation energy of Gen+1 and SnGen(0, ± 1) (n = 1–17) clusters.

Fig. 6.  (Color online) Second energy differences for Gen+1 and SnGen(0, ± 1) (n = 1–17) clusters.

Fig. 7.  (Color online) Size dependence of the HOMO-LUMO gaps of Gen+1 and SnGen(0, ± 1) (n = 1–17) clusters.

Fig. 8.  (Color online) (a) Vartical (VIP) and adiabatic (AIP) ionization potential; (b) Vartical (VEA) and adiabatic (AEA) electron affinity, (c) chemical hardness for SnGen (n = 1 – 17) clusters.

Fig. 9.  (Color online) The total density of states (DOS) for SnGe monomer and the projected density of states (PDOS) for Sn and Ge atoms in SnGe.

Table 1.   Average bond length a (Å), binding energy Eb (eV), adiabatic electronic affinity (AEA) (eV) and adiabatic ionisation potential (AIP) (eV) for Ge2 and Ge3 clusters.

Cluster Our works Theoretical values Experimental values
a Eb AEA AIP a Eb AEA AIP a Eb AEA AIP
Ge2 2.625 1.28 2.060 7.753 2.548d 1.3e 2.10i 7.9j / 1.32g 2.035g 7.58–7.76j
2.54b 1.31f 1.41m 2.074h
2.413c 1.32j
2.41a 1.230l
2.61k 1.812k
Ge3 2.476 1.86 1.907 8.126 2.428i 1.92e 2.09i 7.92j / 2.24n 2.23g 7.97–8.09j
2.400l 1.98d 2.15m 2.23h
2.378d 2a
2.296i 2.04c
a Ref. [34]. b Ref. [35]. c Ref. [19]. d Ref. [36]. e Ref. [37]. f Ref. [38]. g Ref. [4]. h Ref.[5]. I Ref.[11]. j Ref.[39]. k Ref. [2]. l Ref. [12]. m Ref. [40]. n Ref. [41].
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Table 2.   Symmetry group, binding energy per atom Eb, HOMO-LUMO gap ΔE and average bond length for pure Gen+1 (n = 1–17) clusters.

Size (n+1) Symmetry group Eb (eV/atm) ΔE (eV) a (Å)
1 (a) D∞h 1.28 0.367 2.625
2 (a) C2v 1.86 1.368 2.476
3 (a) D2h 2.25 1.152 2.714
4 (a) D3h 2.44 1.815 2.668
5 (a) C2v 2.55 1.650 2.823
(b) Cs 2.49 1.321 2.811
6 (a) D5h 2.66 1.557 2.900
(b) C2v 2.59 2.111 2.722
7 (a) Cs 2.64 1.179 2.796
(b) C2 2.61 1.143 2.837
(c) C2h 2.61 1.153 2.836
8 (a) C2v 2.70 1.588 3.000
(b) C1 2.64 1.306 2.854
9 (a) C3v 2.80 1.609 2.857
(b) Cs 2.73 1.415 2.854
(c) C2v 2.60 0.817 2.849
10 (a) Cs 2.76 1.148 2.857
(b) C1 2.76 1.140 2.857
(c) C2 2.73 1.143 2.944
11 (a) C2v 2.76 1.536 2.884
(b) C1 2.75 1.113 2.940
(c) Cs 2.71 1.299 2.855
12 (a) C1 2.77 0.982 2.943
(b) C2 2.75 1.235 2.836
(c) Cs 2.75 1.096 2.788
13 (a) Cs 2.83 1.372 2.867
(b) C1 2.80 1.335 2.888
(c) C2 2.76 1.014 2.871
14 (a) C2v 2.82 0.864 2.925
(b) C1 2.78 1.116 2.768
(c) Cs 2.77 1.163 2.862
15 (a) C2h 2.83 1.164 2.893
(b) C1 2.78 0.978 2.852
(c) C1 2.77 1.172 2.825
(d) C1 2.77 1.138 2.875
16 (a) Cs 2.82 0.884 2.893
(b) C1 2.82 0.908 2.861
(c) C1 2.82 1.116 2.836
17 (a) C1 2.81 1.322 2.822
(b) C1 2.79 0.626 2.845
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Table 3.   Symmetry group, binding energy per atom Eb, HOMO-LUMO gap ΔE, vertical electronic affinity (VEA), vertical ionisation potential (VIP), chemical hardness η and total spin magnetic moments μ for SnGen (n = 1–17) clusters.

Size (n) Symmetry group Eb (eV/atom) ΔE (eV) VEA (eV) VIP (eV) η (eV) μ (μb)
1 (a) C∞v 1.19 0.344 1.199 7.383 6.184 2.000
2 (a) Cs 1.81 1.311 1.441 7.982 6.541 0.000
(b) C∞v 1.71 1.643 1.264 8.719 7.455 0.000
(c) C2v 1.80 0.984 1.702 7.936 6.234 0.000
3 (a) C2v 2.20 0.227 1.715 8.039 6.324 0.000
(b) C2v 1.79 1.132 2.386 7.072 4.686 0.000
4 (a) C2v 2.40 1.739 1.649 8.912 7.263 0.000
(b) C3v 2.35 1.556 1.255 8.447 7.192 0.000
(c) Cs 2.19 0.499 2.687 7.367 4.680 2.000
(d) C2v 2.14 0.889 2.959 6.840 3.881 2.000
5 (a) Cs 2.53 1.663 1.845 8.022 6.177 0.000
(b) Cs 2.48 1.450 2.056 7.798 8.742 0.000
(c) Cs 2.44 1.228 1.873 7.786 5.913 0.000
6 (a) C1 2.63 1.853 2.064 8.241 6.177 0.000
(b) C1 2.61 1.512 2.357 8.153 5.796 0.000
(c) C2v 2.53 1.451 1.590 7.856 6.266 0.000
7 (a) C1 2.62 1.197 2.059 7.538 5.479 0.000
(b) C1 2.59 1.149 2.076 7.416 5.340 0.000
(c) Cs 2.58 0.947 2.047 7.179 5.132 0.000
8 (a) C1 2.68 1.486 1.749 7.745 5.996 0.000
(b) C1 2.68 1.515 1.978 7.425 5.447 0.000
9 (a) Cs 2.77 1.551 2.306 7.714 5.408 0.000
(b) C1 2.69 1.434 2.197 7.497 5.300 0.000
10 (a) Cs 2.73 1.202 2.291 7.204 4.913 0.000
(b) C1 2.72 1.031 2.378 7.133 4.755 0.000
(c) C1 2.71 1.121 2.511 7.324 4.813 0.000
11 (a) C1 2.74 1.529 2.225 7.321 5.096 0.000
(b) C5v 2.70 1.155 2.583 7.388 4.805 0.000
(c) Cs 2.67 1.104 2.667 7.359 4.692 0.000
(d) C1 2.64 1.027 3.628 6.242 2.614 0.000
12 (a) C1 2.73 0.992 2.230 7.207 4.977 0.000
(b) C2v 2.70 1.014 2.822 7.421 4.599 0.000
(c) D3d 2.62 1.046 2.754 6.804 4.050 0.000
13 (a) C1 2.81 1.353 2.556 7.310 4.754 0.000
(b) C1 2.78 1.310 2.585 7.329 4.744 0.000
(c) C1 2.60 0.554 2.913 6.951 4.038 0.000
(d) C6v 2.72 0.517 3.115 7.122 4.007 0.000
14 (a) Cs 2.79 0.950 2.889 6.396 3.507 0.000
(b) C1 2.75 1.078 2.721 7.125 4.404 0.000
(c) D6h 2.58 0.010 2.916 6.358 3.442 0.002
(d) C1 2.73 1.097 2.690 7.070 4.380 0.000
15 (a) C2 2.80 1.031 3.022 7.357 4.335 0.000
(b) C1 2.77 0.997 2.758 7.026 4.268 0.000
(c) Cs 2.69 0.591 2.975 6.816 3.841 0.000
(d) C2v 2.64 0.520 2.758 6.424 3.666 0.000
16 (a) C1 2.81 0.899 2.780 6.939 4.159 0.000
(b) C1 2.80 0.994 2.953 7.069 4.116 0.000
(c) C2h 2.74 0.537 2.571 6.348 3.777 0.000
17 (a) C1 2.80 1.332 2.664 7.136 4.472 0.000
(b) Cs 2.71 1.018 2.747 6.863 4.116 0.000
(c) C2v 2.69 1.015 2.219 6.826 4.607 0.000
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Table 4.   Average bond length aGe-Ge and aSn-Ge for neutral, cationic and anionic SnGen(0 ± 1) (n = 1–17) clusters.

Cluster size (n) SnGen SnGen+ SnGen
aGe-Ge aSn-Ge aGe-Ge aSn-Ge aGe-Ge aSn-Ge
1 / 2.805 / 2.910 / 2.495
2 2.472 2.658 2.626 2.833 2.551 2.900
3 2.741 2.857 2.656 2.884 2.689 2.844
4 2.665 2.852 2.691 3.026 2.683 2.861
5 2.850 2.911 2.867 2.974 2.856 3.034
6 2.714 2.927 2.912 3.010 2.452 3.047
7 2.581 3.130 2.892 3.154 2.862 3.042
8 2.939 3.062 2.978 3.107 2.908 2.999
9 2.851 3.059 2.498 3.008 3.022 2.976
10 2.846 3.088 3.033 3.071 2.848 3.002
11 2.866 3.052 2.873 3.086 2.641 2.996
12 2.904 3.059 2.931 3.078 2.901 3.029
13 2.860 3.083 2.787 3.049 2.850 3.057
14 2.980 3.038 2.855 3.054 2.917 2.969
15 2.906 2.907 2.925 2.929 2.882 2.931
16 2.895 3.037 3.081 3.029 2.897 3.021
17 2.865 2.996 2.837 2.986 2.854 3.002
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Table 5.   (A) Symmetry group, binding energy per atom Eb (eV/atom), HOMO-LUMO gap ΔE (eV), total spin magnetic moments μ(μB), adiabatic ionisation potential (AIP) (eV) for cationic SnGen+ (n = 1−17) clusters. (B) Symmetry group, binding energy per atom Eb, HOMO-LUMO gap ΔE, total spin magnetic moments μ, adiabatic electron affinity (AEA) for anionic SnGen (n = 1−17) clusters.

(A) SnGen+ (B) SnGen-
Cluster
size (n)
Symmetry
group
Eb (eV/atm) ΔE (eV) μ(μb) AIP (eV) Symmetry
group
Eb (eV/atm) ΔE (eV) μ (μb) AEA (eV)
1 C∞v 1.285 1.476 3.000 7.360 C∞v 1.819 0.247 1.000 1.451
2 Cs 1.761 0.410 1.000 7.706 Cs 2.365 0.601 1.000 1.850
3 C2v 2.156 0.674 1.000 7.729 C2v 2.640 0.990 1.000 1.948
4 C2v 2.316 0.405 1.000 7.971 C2v 2.833 0.930 1.000 2.357
5 C2v 2.515 1.027 1.000 7.624 C2v 2.878 0.892 1.000 2.300
6 C2v 2.597 0.530 1.000 7.796 C2v 2.956 1.284 0.996 2.460
7 C1 2.655 0.894 0.999 7.252 C1 2.909 0.827 1.000 2.525
8 C1 2.711 0.420 0.998 7.277 C1 2.975 0.430 0.998 2.844
9 Cs 2.760 0.372 0.997 7.597 Cs 3.007 0.669 0.999 2.611
10 C1 2.775 0.944 0.997 7.012 Cs 2.945 0.376 0.999 2.596
11 C1 2.772 0.430 0.992 7.158 C1 2.934 0.376 0.994 2.521
12 C1 2.771 0.435 0.995 7.086 C1 2.958 0.061 0.997 3.100
13 C1 2.836 0.535 0.992 7.139 C1 2.985 0.174 0.976 2.682
14 Cs 2.828 0.650 0.999 6.939 Cs 2.992 0.426 0.985 3.244
15 C2 2.829 0.635 0.994 7.046 C2 2.991 0.446 0.945 3.278
16 C1 2.854 0.343 0.991 6.824 C1 2.978 0.151 0.966 3.022
17 C1 2.834 0.194 0.969 6.960 C1 2.963 0.122 0.976 3.110
DownLoad: CSV
[1]
Samanta P N, Das K K. Electronic structure, bonding, and properties of SnmGen (m + n ≤ 5) clusters: a DFT study. Comput Theor Chem, 2012, 980: 123 doi: 10.1016/j.comptc.2011.11.038
[2]
Mahtout S, Tariket Y. Electronic and magnetic properties of CrGen (15 ≤ n ≤ 29) clusters: a DFT study. Chem Phys, 2016, 472: 270 doi: 10.1016/j.chemphys.2016.03.011
[3]
Shvartsburg A A, Liu B, Lu Z Y, et al. Structures of germanium clusters: where the growth patterns of silicon and germanium clusters diverge. Phys Rev Lett, 1999, 83(11): 2167 doi: 10.1103/PhysRevLett.83.2167
[4]
Burton G R, Xu C, Arnold C C, et al. Photoelectron spectroscopy and zero electron kinetic energy spectroscopy of germanium cluster anions. J Chem Phys, 1996, 104(8): 2757 doi: 10.1063/1.471098
[5]
Burton G R, Xu C, Neumark D M. study of small semiconductor clusters using anion photoelectron spectroscopy: germanium clusters (Gen, n = 2−15). Surf Rev Lett, 1996, 03(01): 383
[6]
Negishi Y, Kawamata H, Hayakawa F, et al. The infrared HOMO–LUMO gap of germanium clusters. Chem Phys Lett, 1998, 294(4): 370
[7]
Gingerich K A, Schmude Jr R, Baba M S, et al. Atomization enthalpies and enthalpies of formation of the germanium clusters, Ge 5, Ge 6, Ge 7, and Ge 8 by Knudsen effusion mass spectrometry. J Chem Phys, 2000, 112(17): 7443 doi: 10.1063/1.481343
[8]
Hostutler D A, Li H, Clouthier D J, et al. Exploring the Bermuda triangle of homonuclear diatomic spectroscopy: the electronic spectrum and structure of Ge2. J Chem Phys, 2002, 116(10): 4135 doi: 10.1063/1.1431281
[9]
Bals S, Aert S Van, Romero C, et al. Atomic scale dynamics of ultrasmall germanium clusters. Nat Commun, 2012, 3: 897 doi: 10.1038/ncomms1887
[10]
Haeck J De, Tai T B, Bhattacharyya S, et al. Structures and ionization energies of small lithium doped germanium clusters. PCCP, 2013, 15(14): 5151 doi: 10.1039/c3cp44395g
[11]
Deutsch P, Curtiss L, Blaudeau J P. Electron affinities of germanium anion clusters, Gen (n = 2–5). Chem Phys Lett, 2001, 344(1): 101 doi: 10.1016/S0009-2614(01)00734-5
[12]
Wang J, Wang G, Zhao J. Structure and electronic properties of Gen (n = 2–25) clusters from density-functional theory. Phys Rev B, 2001, 64(20): 205411 doi: 10.1103/PhysRevB.64.205411
[13]
Wang J, Yang M, Wang G, et al. Dipole polarizabilities of germanium clusters. Chem Phys Lett, 2003, 367(3): 448
[14]
Kikuchi H, Takahashi M, Kawazoe Y. Theoretical investigation of stable structures of Ge6 clusters with various negative charges. Mater Trans-JIM, 2006, 47(11): 2624 doi: 10.2320/matertrans.47.2624
[15]
Ma S, Wang G. Structures of medium size germanium clusters. J Mol Struct: THEOCHEM, 2006, 767(1): 75
[16]
Zhao W J, Wang Y X. Geometries, stabilities, and magnetic properties of MnGen (n = 2–16) clusters: density-functional theory investigations. J Mol Struct: THEOCHEM, 2009, 901(1): 18
[17]
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    Received: 30 July 2017 Revised: 27 October 2017 Online: Uncorrected proof: 24 January 2018Accepted Manuscript: 01 March 2018Published: 01 April 2018

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      Soumaia Djaadi, Kamal Eddine Aiadi, Sofiane Mahtout. First principles study of structural, electronic and magnetic properties of SnGen(0, ±1) (n = 1–17) clusters[J]. Journal of Semiconductors, 2018, 39(4): 042001. doi: 10.1088/1674-4926/39/4/042001 S Djaadi, K E Aiadi, S Mahtout. First principles study of structural, electronic and magnetic properties of SnGen(0, ±1) (n = 1–17) clusters[J]. J. Semicond., 2018, 39(4): 042001. doi: 10.1088/1674-4926/39/4/042001.Export: BibTex EndNote
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      Soumaia Djaadi, Kamal Eddine Aiadi, Sofiane Mahtout. First principles study of structural, electronic and magnetic properties of SnGen(0, ±1) (n = 1–17) clusters[J]. Journal of Semiconductors, 2018, 39(4): 042001. doi: 10.1088/1674-4926/39/4/042001

      S Djaadi, K E Aiadi, S Mahtout. First principles study of structural, electronic and magnetic properties of SnGen(0, ±1) (n = 1–17) clusters[J]. J. Semicond., 2018, 39(4): 042001. doi: 10.1088/1674-4926/39/4/042001.
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      First principles study of structural, electronic and magnetic properties of SnGen(0, ±1) (n = 1–17) clusters

      doi: 10.1088/1674-4926/39/4/042001
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      • Corresponding author: djaadi58@gmail.com
      • Received Date: 2017-07-30
      • Revised Date: 2017-10-27
      • Published Date: 2018-04-01

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