ARTICLES

Growth behavior and electronic properties of Gen + 1 and AsGen (n = 1–20) clusters: a DFT study

M. Benaida1, , K. E. Aiadi1, S. Mahtout2, S. Djaadi1, W. Rammal3 and M. Harb4,

+ Author Affiliations

 Corresponding author: M. Benaida, Email: meriembenaida@gmail.com; M. Harb, moussab.harb@kaust.edu.sa

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Abstract: We present a systematic computational study based on the density functional theory (DFT) aiming to high light the possible effects of one As doping atom on the structural, energetic, and electronic properties of different isomers of Gen + 1 clusters with n = 1–20 atoms. By considering a large number of structures for each cluster size, the lowest-energy isomers are determined. The lowest-energy isomers reveal three-dimensional structures starting from n = 5. Their relative stability versus atomic size is examined based on the calculated binding energy, fragmentation energy, and second-order difference of energy. Doping Gen + 1 clusters with one As atom does not improve their stability. The electronic properties as a function of the atomic size are also discussed from the calculated HOMO–LUMO energy gap, vertical ionization potential, vertical electron affinity, and chemical hardness. The obtained results are significantly affected by the inclusion of one As atom into a Gen cluster.

Key words: density functional theoryAs–Ge clustersstructural propertieselectronic properties



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Fig. 1.  (Color online) Most favorable structures together with their corresponding isomers for Gen + 1 (n = 1–20) clusters.

Fig. 2.  (Color online) Most favorable structures and their corresponding isomers of AsGen (n = 1–20) clusters.

Fig. 3.  (Color online) Evolution of the binding energy per atom for the lowest energy structures of Gen + 1 and AsGen (n = 1–20) clusters as a function of cluster size.

Fig. 4.  (Color online) Evolution of the fragmentation energy of Gen + 1 and AsGen (n = 1–20) clusters as a function of cluster size.

Fig. 5.  (Color online) Evolution of the second-order difference of energy for the lowest energy structures of Gen + 1 and AsGen (n = 1–20) clusters as a function of cluster size.

Fig. 6.  (Color online) Evolution of the HOMO–LUMO gap for the lowest energy structures of Gen + 1 and AsGen (n = 1–20) clusters as a function of cluster size.

Fig. 7.  (Color online) Evolution of the vertical ionization potential (VIP) for the lowest energy structures of Gen + 1 and AsGen (n = 1–20) clusters as a function of cluster size.

Fig. 8.  (Color online) Evolution of the vertical electron affinity (VEA) for the lowest energy structures of Gen + 1 and AsGen (n = 1–20) clusters as a function of cluster size.

Fig. 9.  (Color online) Evolution of the chemical hardness η for the lowest energy structures of Gen + 1 and AsGen (n = 1–20) clusters as a function of cluster size.

Table 1.   Averaged bond length a, binding energy Eb, vertical ionization potential VIP, and vertical electron affinity VEA for Ge2, Ge3 and As2.

Symmetry Our work Bibliographic date[24-40]
a (Å) Eb (eV) VIP (eV) VEA (eV) a (Å) Eb (eV) VIP (eV) VEA (eV)
Ge2 2.503 1.445 7.362 1.473 2.450 1.446 7.844 1.900
2.413 ~1.430 7.627 1.751
2.540 1.620 7.934 1.549
2.610 1.812
2.570 ~1.350
2.420 1.410
2.440 1.320
2.421 1.230
2.625 1.280
Ge3 2.370 2.110 8.024 1.306 2.546 2.059 7.804 2.200
2.400 2.240
2.476 2.150
2.040
1.860
As2 2.143 1.686 9.677 0.132 2.189 1.763
2.103
2.192
DownLoad: CSV
Continued from Table 2
Cluster size (n) Symmetry Eb (eV/atom) ΔE (eV) VEA (eV) VIP (eV) η (eV) aGe–Ge (Å)
15 C2h 3.027 1.436 6.840 2.308 4.532 2.715
C1 3.020 0.883 6.555 2.494 4.061 2.755
C2 3.034 1.364 6.755 2.262 4.493 2.808
C2h 3.095 1.393 7.548 1.753 5.795 2.780
16 Cs 3.050 1.103 6.588 2.343 4.245 2.781
C1 3.043 1.254 6.696 2.428 4.268 2.772
C1 3.038 1.022 6.616 2.500 4.116 2.762
Cs 3.077 0.858 7.075 1.716 5.359 2.823
17 C2 3.014 0.864 6.493 2.590 3.903 2.869
Cs 3.013 0.948 6.537 2.537 4.000 2.790
Cs 3.009 0.555 6.400 2.815 3.585 2.782
C 3.062 1.452 7.152 1.486 5.666 2.729
18 C1 3.053 0.966 6.473 2.477 3.996 2.843
C1 3.019 0.779 6.516 2.728 3.788 2.771
C1 3.019 0.780 6.517 2.727 3.790 2.771
19 C1 3.046 0.828 6.387 2.596 3.791 2.735
C1 3.033 0.962 6.365 2.455 3.910 2.768
C1 3.001 0.828 6.418 2.650 3.768 2.781
20 C1 3.041 0.743 6.372 2.679 3.693 2.769
C1 3.061 3.061 6.403 2.845 3.558 2.735
C1 3.050 0.559 6.182 2.734 3.448 2.761
DownLoad: CSV

Table 2.   Group of symmetry, Eb, ΔE, VIP, VEA, η, and aGe–Ge for pure Gen + 1 (n = 1 – 20) clusters.

Cluster size (n) Symmetry Eb (eV/atom) ΔE (eV) VEA (eV) VIP (eV) η (eV) aGe–Ge (Å)
1 D∞h 1.445 0.265 7.362 1.473 5.889 2.503
2 D∞h 2.048 1.272 7.557 1.476 6.081 2.339
C2v 2.109 1.543 8.024 1.305 6.719 2.370
C2v 2.110 1.543 8.024 1.306 6.718 2.370
3 D4h 2.228 0.455 6.834 1.599 5.235 2.550
D2h 2.556 1.180 7.734 1.758 5.976 2.576
D2h 2.557 1.179 7.733 1.758 5.976 2.597
C3v 2.078 0.660 7.056 1.717 5.339 2.479
D∞h 2.061 1.169 7.114 2.102 5.012 2.346
4 C2 2.518 1.089 6.911 2.149 4.762 2.606
C2v 2.450 1.026 6.766 2.207 4.559 2.564
C2v 2.499 0.808 6.774 2.070 4.704 2.618
C2v 2.504 0.577 7.588 2.560 5.028 2.775
D3h 2.707 2.036 8.672 0.218 8.454 2.547
5 D4h 2.847 1.998 7.777 1.372 6.405 2.782
C2h 2.668 1.236 7.142 1.820 5.322 2.760
C2 2.672 1.386 7.172 1.790 5.382 2.606
C2v 2.848 1.957 7.742 1.359 6.383 2.710
6 D3v 2.877 2.350 7.460 1.064 6.396 2.734
C1 2.687 0.164 7.304 1.673 5.631 2.647
C2 2.843 1.170 7.034 1.749 5.285 2.754
D5h 2.974 1.836 7.875 1.774 6.101 2.747
C2 2.843 1.170 7.034 1.748 5.286 2.754
Cs 2.617 0.755 6.620 2.102 4.518 2.701
7 C2v 2.866 0.980 7.216 2.232 4.984 2.776
C2 2.735 0.977 6.937 2.194 4.743 2.658
Cs 2.739 0.708 6.556 2.212 4.344 2.730
Cs 2.422 0.431 6.194 2.805 3.389 2.651
8 C2v 2.985 1.654 7.126 1.570 5.556 2.782
C1 2.700 1.066 6.849 2.394 4.455 2.570
D3d 2.574 0.227 6.288 2.271 4.017 2.798
C3v 2.827 1.102 7.068 2.313 4.755 2.686
9 Cs 2.848 1.459 6.462 2.146 4.316 2.742
Cs 3.002 1.753 7.137 1.662 5.475 2.779
C2v 2.968 1.379 7.070 1.981 5.089 2.785
C3v 3.082 1.812 7.432 1.857 5.575 2.775
C1 2.953 1.295 6.900 1.913 4.987 2.738
Cs 3.013 1.015 7.152 2.393 4.759 2.794
Cs 3.003 1.547 7.410 1.383 6.027 2.771
10 C3v 2.792 1.063 6.402 2.364 4.038 2.714
D4h 2.715 0.793 6.326 1.975 4.351 2.816
Cs 2.907 0.962 6.605 2.084 4.521 2.748
Cs 2.892 0.990 6.820 2.318 4.502 2.724
Cs 3.029 1.258 7.107 1.332 5.775 2.770
11 Cs 2.936 0.803 6.852 2.547 4.305 2.798
C1 2.955 0.916 6.759 2.345 4.414 2.784
C1 2.964 1.059 6.696 2.175 4.521 2.801
Cs 2.979 0.370 6.656 2.780 3.876 2.793
C2v 3.032 1.793 7.402 1.258 6.144 2.744
12 C2v 3.050 1.181 8.243 1.290 6.953 2.760
C2 3.007 1.153 1.153 2.390 4.553 2.792
C1 3.015 0.945 6.785 2.412 4.373 2.835
Cs 2.990 1.130 6.608 2.102 4.506 2.769
C1 3.015 0.944 7.302 1.779 5.523 2.831
13 C3v 2.922 0.987 5.967 2.633 3.334 2.696
Cs 3.026 1.107 6.625 2.179 4.446 2.700
Oh 2.977 1.007 6.915 3.095 3.820 2.659
C1 2.986 1.036 6.471 2.127 4.344 2.784
Cs 3.092 1.628 7.486 1.539 5.947 2.797
14 D3d 2.864 0.495 6.726 2.977 3.749 2.666
C1 2.999 1.234 6.800 2.311 4.489 2.829
Cs 2.959 0.941 6.553 2.393 4.160 2.785
C1 3.022 1.149 6.579 2.178 4.401 2.812
C1 3.023 1.156 6.927 2.468 4.459 2.786
C2v 3.082 0.899 7.339 1.851 5.488 2.814
DownLoad: CSV

Table 3.   Group of symmetry, Eb, ΔE, VEA, VIP, η, and aGe–Ge, aAs–Ge for AsGen (n = 1–20) clusters.

Cluster size (n) Symmetry Eb (eV/atom) ΔE (eV) VEA (eV) VIP (eV) η (eV) aGe–Ge (Å) aAs–Ge (Å)
1 (a)C∞v1 1.426 0.171 2.175 8.142 5.967 - 2.350
2 (a)C2v 2.139 1.110 0.969 7.425 6.456 2.775 2.445
(b)C2v 2.139 1.109 0.778 8.198 7.410 2.775 2.445
3 (a)C2v 2.380 0.589 1.440 6.704 5.264 2.603 2.543
(b)C2v 2.418 1.266 1.726 7.377 5.651 2.661 2.473
4 (a)C2v 2.575 0.208 0.451 8.640 8.189 2.738 2.661
(b)C2v 2.641 0.917 0.124 8.809 8.685 2.692 2.734
5 (a)C4v 2.705 1.116 0.928 6.657 5.729 2.807 2.679
(b)C2v 2.702 1.058 1.088 6.951 5.863 2.782 2.706
6 (a)C2v 2.837 1.279 1.632 6.614 4.982 2.786 2.703
(b)C2v 2.837 1.278 1.632 6.615 4.983 2.786 2.704
7 (a)Cs 2.814 0.503 2.060 7.179 5.119 2.788 2.635
(b)C3v 2.835 0.743 1.701 7.022 5.321 2.821 2.567
8 (a)Cs 2.908 0.571 1.279 6.661 5.382 2.808 2.678
(b)Cs 2.909 0.571 1.279 6.661 5.382 2.808 2.678
9 (a)Cs 2.977 1.066 1.604 6.271 4.667 2.774 2.819
(b)Cs 2.977 1.064 1.603 6.271 4.668 2.774 2.819
10 (a)C1 2.949 0.759 1.051 6.663 5.612 2.793 2.697
(b)C1 2.949 0.898 0.884 6.953 6.069 2.774 2.716
11 (a)Cs 2.945 1.026 0.783 6.609 5.826 2.740 2.813
(b)Cs 2.940 0.773 1.305 6.481 5.176 2.775 2.596
12 (a)C1 2.993 0.393 1.019 8.052 7.033 2.788 2.693
(b)Cs 3.003 0.396 1.044 7.736 6.692 2.814 2.667
13 (a)C1 3.016 0.696 1.518 6.578 5.060 2.826 2.606
(b)C1 3.016 0.697 1.520 6.574 5.054 2.780 2.607
14 (a)C1 3.042 0.581 1.248 7.125 5.877 2.821 2.681
(b)Cs 3.046 0.797 1.174 6.946 5.772 2.828 2.783
15 (a)Cs 3.045 0.782 1.482 6.984 5.502 2.801 2.736
(b)C1 3.043 0.846 1.300 6.917 5.617 2.817 2.719
16 (a)C1 3.045 0.538 1.394 6.977 5.583 2.813 2.595
(b)Cs 3.035 0.810 1.547 6.823 5.276 2.830 2.593
17 (a)C1 3.031 0.623 0.763 7.031 6.268 2.766 2.566
(b)C1 3.030 0.390 0.453 7.310 6.857 2.747 2.556
18 (a)C1 3.017 0.627 1.867 6.346 4.479 2.777 2.629
(b)C1 3.024 0.594 2.000 6.361 4.361 2.803 2.592
19 (a)C1 3.023 0.559 1.916 6.098 4.182 2.769 2.581
(b)C1 3.029 0.519 1.667 6.834 5.167 2.732 2.580
20 (a)C1 3.065 0.667 1.961 6.558 4.597 2.739 2.573
(b)C1 3.059 0.579 1.870 6.937 5.067 2.745 2.601
DownLoad: CSV
[1]
Wang J, Han J G. The growth behaviors of the Zn-doped different sized germanium clusters: a density functional investigation. Chem Phys, 2007, 342: 253 doi: 10.1016/j.chemphys.2007.10.008
[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]
Schmude R W, Gingerich K A. Thermodynamic study of small silicon carbide clusters with a mass spectrometer. J Phys Chem A, 1997, 101: 2610 doi: 10.1021/jp964093b
[4]
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
[5]
Kingcade J Jr, Gingerich K. Knudsen effusion mass spectrometric investigation of palladium-germanium clusters. Inorg Chem, 1989, 28: 89 doi: 10.1021/ic00300a020
[6]
Yadav P S, Yadav R K. Ab initio study of the physical properties of binary SimCn (m + n ⩽ 5) nanoclusters. J Phys Cond Matter, 2006, 18: 7085. doi: 10.1088/0953-8984/18/31/004
[7]
Bandyopadhyay D, Kumar M. The electronic structures and properties of transition metal-doped silicon nanoclusters: a density functional investigation. Chem Phys, 2008, 353: 170. doi: 10.1016/j.chemphys.2008.08.017
[8]
Han J G, Hagelberg F. Recent progress in the computational study of silicon and germanium clusters with transition metal impurities. J Comput Theor Nanosci, 2009, 6: 257 doi: 10.1166/jctn.2009.1035
[9]
Bals S, Van Aert S, Romero C P, et al. Atomic scale dynamics of ultrasmall germanium clusters. Nat Commun, 2012, 3: 897. doi: 10.1038/ncomms1887
[10]
Siouani C, Mahtout S, Safer S, et al. Structure, stability, and electronic and magnetic properties of VGen (n = 1–19) clusters. J Phys Chem A, 2017, 121, 3540 doi: 10.1021/acs.jpca.7b00881
[11]
Brack M. The physics of simple metal clusters: self-consistent jellium model and semiclassical approaches. Rev Mod Phys, 1993, 65: 677. doi: 10.1103/RevModPhys.65.677
[12]
Han J G, Zhang P F, Lic Q X, et al. A theoretical investigation of GenSn (n = 1–4) clusters. J Mol Struct, 2003, 624: 257 doi: 10.1016/S0166-1280(02)00790-X
[13]
Singh A K, Kumar V, Kawazoe, Y. Thorium encapsulated caged clusters of germanium: The Gen, n = 16, 18, and 20. J Phys Chem B, 2005, 109: 15187 doi: 10.1021/jp053169d
[14]
Wang J, Han J G. A computational investigation of copper-doped germanium and germanium clusters by the density-functional theory. J Chem Phys, 2005, 123: 244303. doi: 10.1063/1.2148949
[15]
Zhao W J, Wang, Y X. Geometries, stabilities, and magnetic properties of MnGen (n = 2–16) clusters: density-functional theory investigations. J Mol Struct, 2009, 901: 18 doi: 10.1016/j.theochem.2008.12.039
[16]
Jaiswal S, Kumar V. Growth behavior and electronic structure of neutral and anion ZrGen (n = 1–21) clusters. Comput Theor Chem, 2016, 1075: 87 doi: 10.1016/j.comptc.2015.11.013
[17]
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    Received: 04 August 2018 Revised: 27 September 2018 Online: Accepted Manuscript: 08 January 2019Uncorrected proof: 09 January 2019Published: 01 March 2019

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      M. Benaida, K. E. Aiadi, S. Mahtout, S. Djaadi, W. Rammal, M. Harb. Growth behavior and electronic properties of Gen + 1 and AsGen (n = 1–20) clusters: a DFT study[J]. Journal of Semiconductors, 2019, 40(3): 032101. doi: 10.1088/1674-4926/40/3/032101 M Benaida, K E Aiadi, S Mahtout, S Djaadi, W Rammal, M Harb, Growth behavior and electronic properties of Gen + 1 and AsGen (n = 1–20) clusters: a DFT study[J]. J. Semicond., 2019, 40(3): 032101. doi: 10.1088/1674-4926/40/3/032101.Export: BibTex EndNote
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      M. Benaida, K. E. Aiadi, S. Mahtout, S. Djaadi, W. Rammal, M. Harb. Growth behavior and electronic properties of Gen + 1 and AsGen (n = 1–20) clusters: a DFT study[J]. Journal of Semiconductors, 2019, 40(3): 032101. doi: 10.1088/1674-4926/40/3/032101

      M Benaida, K E Aiadi, S Mahtout, S Djaadi, W Rammal, M Harb, Growth behavior and electronic properties of Gen + 1 and AsGen (n = 1–20) clusters: a DFT study[J]. J. Semicond., 2019, 40(3): 032101. doi: 10.1088/1674-4926/40/3/032101.
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      Growth behavior and electronic properties of Gen + 1 and AsGen (n = 1–20) clusters: a DFT study

      doi: 10.1088/1674-4926/40/3/032101
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