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Systematic theoretical investigation of structures, stabilities, and electronic properties of rhodium-doped silicon clusters: Rh2Si q n (n = 1–10; q = 0, ±1)

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Abstract

A systematic investigation of rhodium-doped silicon clusters, Rh2Si q n with n = 1–10 and q = 0, ±1, in the neutral, anionic, and cationic states is performed using density functional theory approach at B3LYP/GENECP level. According to the optimum Rh2Si q n clusters, mostly equilibrium geometries prefer the three-dimensional structures for n = 2–10. When n = 10, one Rh atom in Rh2Si 0,±110 clusters completely falls into the center of Si frame, and cage-like Rh2Si 0,±110 geometries are formed. The Rh2Si +1,6–9 and Rh2Si 5,7,9 clusters significantly deform their corresponding neutral geometries, which are in line with the calculated ionization potential and electron affinity values. The relative stabilities of Rh2Si q n clusters for the lowest-energy structures are analyzed on the basis of binding energy, fragmentation energy, second-order energy difference, and HOMO–LUMO gaps. The theoretical results confirm that the Rh2Si6 , Rh2Si6, and Rh2Si6 + clusters are more stable than their neighboring ones. The natural population analysis reveals that the charges in Rh2Si q n clusters transfer from the Si atoms to the Rh atoms except Rh2Si+. In addition, the relationship between static polarizability and HOMO–LUMO gaps is discussed.

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References

  1. Grubisic A, Ko YJ, Wang HP, Bowen KH (2009) Photoelectron spectroscopy of lanthanide-silicon cluster anions LnSin- (3 ≤ n ≤ 13; Ln = Ho, Gd, Pr, Sm, Eu, Yb): prospect for magnetic silicon-based clusters. J Am Chem Soc 131(30):10783–10790

    Article  Google Scholar 

  2. Xie L, Li WL, Romanescu C, Huang X, Wang LS (2013) A photoelectron spectroscopy and density functional study of di-tantalum boride clusters: Ta2B x (x = 2–5). J Chem Phys 138(3):034308/1–034308/11

    Article  Google Scholar 

  3. Xu B, Liu JP, Zhao LL, Yan LL (2013) Theoretical study on the structure and stability of aluminum hydride (Al n H 3n ) clusters. J Mater Sci 48(6):2647–2658. doi:10.1007/s10853-012-7058-y

    Article  Google Scholar 

  4. Guo L (2010) Density functional study of structural and electronic properties of GaP n (2 ≤ n ≤ 12) clusters. J Mater Sci 45(12):3381–3387. doi:10.1007/s10853-010-4361-3

    Article  Google Scholar 

  5. Beyer MK, Knickelbein MB (2007) Electric deflection studies of rhodium clusters. J Chem Phys 126(10):104301/1–104301/7

    Article  Google Scholar 

  6. Götz DA, Heiles S, Schäfer R (2012) Polarizabilities of SiN (N = 8–75) clusters from molecular beam electric deflection experiments. Eur Phys J D 66:293/1–293/4

    Article  Google Scholar 

  7. Ju M, Lv J, Kuang XY, Ding LP, Lu C, Wang JJ, Jin YY, Maroulis G (2015) Systematic theoretical investigation of geometries, stabilities and magnetic properties of iron oxide clusters (FeO)nμ (n = 1–8, μ = 0, ±1): insights and perspectives. RSC Adv 5(9):6560–6570

    Article  Google Scholar 

  8. Koyasu K, Akutsu M, Mitsui M, Nakajima A (2005) Selective formation of MSi16 (M = Sc, Ti, and V). J Am Chem Soc 127(14):4998–4999

    Article  Google Scholar 

  9. Reveles JU, Khanna SN (2006) Electronic counting rules for the stability of metal-silicon clusters. Phys Rev B 74(3):035435/1–035435/6

    Google Scholar 

  10. Li YJ, Tam NM, Claes P, Woodham AP, Lyon JT, Ngan VT, Nguyen MT, Lievens P, Fielicke A, Janssens E (2014) Structure assignment, electronic properties, and magnetism quenching of endohedrally doped neutral silicon clusters, Si n Co (n = 10–12). J Phys Chem A 118(37):8198–8203

    Article  Google Scholar 

  11. Kong XY, Xu HG, Zheng WJ (2012) Structures and magnetic properties of CrSi n (n = 3–12) clusters: photoelectron spectroscopy and density functional calculations. J Chem Phys 137(6):064307/1–064307/9

    Article  Google Scholar 

  12. Hiura H, Miyazaki T, Kanayama T (2001) Formation of metal-encapsulating Si cage clusters. Phys Rev Lett 86(9):1733–1736

    Article  Google Scholar 

  13. Koyasu K, Atobe J, Akutsu M, Mitsui M, Nakajima A (2007) Electronic and geometric stabilities of clusters with transition metal encapsulated by silicon. J Phys Chem A 111(1):42–49

    Article  Google Scholar 

  14. Ngan VT, Gruene P, Claes P, Janssens E, Fielicke A, Nguyen MT, Lievens P (2010) Disparate effects of Cu and V on structures of exohedral transition metal-doped silicon clusters: a combined Far-Infrared spectroscopic and computational study. J Am Chem Soc 132(44):15589–15602

    Article  Google Scholar 

  15. Ngan VT, Janssens E, Claes P, Lyon JY, Fielicke A, Nguyen MT, Lievens P (2012) High magnetic moments in manganese-doped silicon clusters. Chem Eur J 18(39):15788–15793

    Article  Google Scholar 

  16. Li YJ, Lyon JT, Woodham AP, Fielicke A, Janssens E (2014) The geometric structure of silver-doped silicon clusters. Chem Phys Chem 15(2):328–336

    Google Scholar 

  17. Lu J, Nagase S (2003) Structural and electronic properties of metal-encapsulated silicon clusters in a large size range. Phys Rev Lett 90(11):115506/1–115506/4

    Article  Google Scholar 

  18. Miyazaki T, Hiura H, Kanayama T (2003) Electronic properties of transition-metal-atom doped Si cage clusters. Eur Phys J D 24(1):241–244

    Article  Google Scholar 

  19. Guo LJ, Zhao GF, Gu YZ, Liu X, Zeng Z (2008) Density-functional investigation of metal-silicon cage clusters MSi n (M = Sc,Ti,V,Cr,Mn,Ni,Cu,Zn; n = 8–16). Phys Rev B 77(19):195417/1–195417/8

    Article  Google Scholar 

  20. Ma L, Wang JG, Wang GH (2013) Site-specific analysis of dipole polarizabilities of heterogeneous systems: Iron-doped Si n (n = 1–14) clusters. J Chem Phys 138(9):094304/1–094304/9

    Article  Google Scholar 

  21. Ren ZY, Hou R, Guo P, Gao JK, Du GH, Wen ZY (2008) A density functional theoretical investigation of RhSi n (n = 1–6) clusters. Chin Phys B 17(6):2116–2123

    Article  Google Scholar 

  22. Chien CH, Blaisten-Barojas E, Pederson MR (1998) Magnetic and electronic properties of rhodium clusters. Phys Rev A 58(3):2196–2202

    Article  Google Scholar 

  23. Silva JLF, Piotrowski MJ, Aguilera-Granja F (2012) Hybrid density functional study of small Rh n (n = 2–15) clusters. Phys Rev B 86(12):125430/1–125430/6

    Article  Google Scholar 

  24. Wang YC, Lv J, Zhu L, Ma YM (2010) Crystal structure prediction via particle-swarm optimization. Phys Rev B 82(9):094116/1–094116/8

    Google Scholar 

  25. Wang YC, Lv J, Zhu L, Ma YM (2012) CALYPSO: a method for crystal structure prediction. Comput Phys Commun 183(10):2063–2070

    Article  Google Scholar 

  26. Wang YC, Miao, Lv J, Zhu L, Yin KT, Liu HY, Ma YM (2012) An effective structure prediction method for layered materials based on 2D particle swarm optimization algorithm. J Chem Phys 137(22):224108/1–224108/6

    Google Scholar 

  27. Luo X, Yang J, Liu H, Wu X, Wang Y, Ma YM, Wei SH, Gong X, Xiang H (2001) Predicting two-dimensional boron-carbon compounds by the global optimization method. J Am Chem Soc 133(40):16285–16290

    Article  Google Scholar 

  28. Lu SH, Wang YC, Liu HY, Miao MS, Ma YM (2014) Self-assembled ultrathin nanotubes on diamond (100) surface. Nat Commun 5(16):3666–3672

    Google Scholar 

  29. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Zakrzewski VG, Montgomery JA, Stratmann RE, Burant JC, Dapprich S, Millam JM, Daniels AD, Kudin KN, Strain MC, Farkas O, Tomasi J, Baron V, Cossi M, Cammi R, Mennucci B, Pomelli C, Adamo C, Clifford S, Ochterski J, Petersson GA, Ayala PY, Cui Q, Morokuma K, Malick DK, Rabuck AD, Raghava-chari K, Foresman JB, Cioslowski J, Ortiz JV, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Gomperts R, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Gonzalez G, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Andres JL, Gonzalez C, HeadGordon M, Replogle ES, Pople JA (2009) Gaussian 09, Revision C.01. Gaussian, Inc., Wallingford

    Google Scholar 

  30. Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic behavior. Phys Rev A 38(6):3098–3100

    Article  Google Scholar 

  31. Lee C, Yang W, Parr RG (1988) Development of the Colic-Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B 37(2):785–789

    Article  Google Scholar 

  32. Xiao CY, Hagelberg F, Lester WA Jr (2002) Geometric, energetic, and bonding properties of neutral and charged copper-doped silicon clusters. Phys Rev B 66(7):075425/1–075425/23

    Article  Google Scholar 

  33. Hossain D, Pittman CU Jr, Gwaltney SR (2008) Structures and stabilities of copper encapsulated within silicon nano-clusters: Cu@Si n (n = 9–15). Chem Phys Lett 451(1–3):93–97

    Article  Google Scholar 

  34. Han JG, Zhao RN, Duan YH (2007) Geometries, stabilities, and growth patterns of the bimetal Mo2-doped Si n (n = 9–16) clusters: a density functional investigation. J Phys Chem A 111(11):2148–2155

    Article  Google Scholar 

  35. Tam NM, Tai TB, Ngan VT, Nguyen MT (2013) Thermochemical properties, and growth sequence of aluminum-doped silicon clusters Si n Al m (n = 1–11, m = 1–2) and their anions. J Phys Chem A 117(31):6867–6882

    Article  Google Scholar 

  36. Guo LJ, Liu X, Zhao GF, Luo YH (2007) Computational investigation of TiSi n (n = 2–15) clusters by the density-functional theory. J Chem Phys 126(23):234704/1–234704/7

    Article  Google Scholar 

  37. Maroulis G (2012) Applying conventional ab initio and density functional theory approaches to electric property calculations. Quantitative aspects and perspectives. Struct Bond 149:95–130

    Google Scholar 

  38. Karamanis P, Maroulis G (2003) Single (C–C) and triple (C ≡ C) bond-length dependence of the static electric polarizability and hyperpolarizability of H–C ≡ C–C ≡ C–H. Chem Phys Lett 376:403–410

    Article  Google Scholar 

  39. Hohm U, Maroulis G (2004) Dipole-quadrupole and dipole–octopole polarizability of OsO4 from depolarized collision-induced light scattering experiments, ab initio and density functional theory calculations. J Chem Phys 121(21):10411–10418

    Article  Google Scholar 

  40. Maroulis G (2011) Charge distribution, electric multipole moments, static polarizability and hyperpolarizability of silene. Chem Phys Lett 505:5–10

    Article  Google Scholar 

  41. Maroulis G (2003) Electric (hyper)polarizability derivatives for the symmetric stretching of carbon dioxide. Chem Phys 291:81–95

    Article  Google Scholar 

  42. Gingerich KA, Cocke DL (1972) Thermodynamic confirmation for the high stability of gaseous TiRh as predicted by the Brewer–Engel metallic theory and the dissociation energy of diatomic rhodium. J Chem Soc, Chem Commun 1:536

    Article  Google Scholar 

  43. Huber KP, Herzberg G (1979) Constants of Diatomic Molecules. Van Nostrand Reinhold, New York, pp 125–128

    Google Scholar 

  44. Marijnissen A, Ter Meulen JJ (1996) Determination of the adiabatic ionization potentials of Si2 and SiCl by photoionization efficiency spectroscopy. Chem Phys Lett 263(6):803–810

    Article  Google Scholar 

  45. Zhu XL, Zeng XC, Lei YA, Pan B (2004) Structures and stability of medium silicon clusters. II. Ab initio molecular orbital calculations of Si12–Si20. J Chem Phys 120(19):8985–8995

    Article  Google Scholar 

  46. Reddy BV, Nayak SK, Khanna SN, Rao BK, Jena P (1999) Electronic structure and magnetism of Rh n (n = 2–13) clusters. Phys Rev B 59(7):5214–5222

    Article  Google Scholar 

  47. Arab A, Gobal F, Nahali N, Nahali M (2013) Electronic and structural properties of neutral, anionic, and cationic RhxCu4−x (x = 0–4) small clusters: a DFT study. J Clust Sci 24(1):273–287

    Article  Google Scholar 

  48. Beltrán, Zamudio FB, Chauhan V, Sen P, Wang HP, Ko YJ, Bowen K (2013) Ab initio and anion photoelectron studies of Rh n (n = 1–9) clusters. Eur Phys J D 67:63/1–63/8

    Article  Google Scholar 

  49. Wu ZJ, Su ZM (2006) Electronic structures and chemical bonding in transition metal monosilicides MSi (M = 3d, 4d, 5d elements). J Chem Phys 124(18):184306/1–184306/15

    Article  Google Scholar 

  50. Bruna PJ, Peyerimhoff SD, Buenker RJ (1980) Theoretical prediction of the potential curves for the lowest-lying states of the isovalent diatomics CN+, Si2, SiC, CP+, and SiN+ using the abinitio MRD-CI method. J Chem Phys 72(10):5437–5445

    Article  Google Scholar 

  51. Nigam S, Majunmder C, Kulshreshtha SK (2006) Structural and electronic properties of Si n , Si - n , and PSi n-1 clusters (2 ≤ n ≤ 13): Theoretical investigation based on ab initio molecular orbital theory. J Chem Phys 125(7):074303/1–074303/11

    Article  Google Scholar 

  52. Robles R, Khanna SN (2009) Stable T2Si n (T = Fe,Co,Ni, 1 ≤ n ≤ 8) cluster motifs. J Chem Phys 130(16):164313/1–164313/6

    Article  Google Scholar 

  53. Robles R, Khanna SN (2008) Stability and magnetic properties of T2Si n (T = Cr, Mn, 1 ≤ n ≤ 8) clusters. Phys Rev B 77(23):235441/1–235441/6

    Article  Google Scholar 

  54. Shao P, Kuang XY, Ding LP, Zhong MM, Wang ZH (2012) Density-functional theory study of structures, stabilities, and electronic properties of the Cu2-doped silicon clusters: comparison with pure silicon clusters. Phys B 407(21):4379–4386

    Article  Google Scholar 

  55. Jungnickel G, Frauenheim T, Jackson KA (2000) Structure and energetics of Si n N m clusters: growth pathways in a heterogenous cluster system. J Chem Phys 112(3):1295–1305

    Article  Google Scholar 

  56. Zdetsis AD (2009) Silicon-bismuth and germanium-bismuth clusters of high stability. J Phys Chem A 113(44):12079–12087

    Article  Google Scholar 

  57. Gao AM, Li GL, Chang Y, Chen HY, Finlow D, Li QS (2011) The structures and stabilities of small diarsenic-doped silicon clusters. Inorg Chim Acta 367(1):51–56

    Article  Google Scholar 

  58. Pouchan C, Bégue D, Zhang DY (2004) Between geometry, stability, and polarizability: density functional theory studies of silicon clusters Si n (n = 3–10). J Chem Phys 121(10):4628–4634

    Article  Google Scholar 

  59. Xu HG, Zhang ZG, Feng Y, Zheng WJ (2010) Photoelectron spectroscopy and density-functional study of Sc2Si n (n = 2–6) clusters. Chem Phys Lett 498(1–3):22–26

    Article  Google Scholar 

  60. Fielicke A, Lyon JT, Haertelt M, Meijer G, Claes P, De Haeck J, Lievens P (2009) Vibrational spectroscopy of neutral silicon clusters via far-IR-VUV two color ionization. J Chem Phys 131(17):171105/1–171105/4

    Article  Google Scholar 

  61. Haertelt M, Lyon JT, Claes P, De Haeck J, Lievens P, Fielicke A (2012) Gas-phase structures of neutral silicon clusters. J Chem Phys 136(6):064301/1–064301/6

    Article  Google Scholar 

  62. Vogel M, Kasigkeit C, Hirsch K, Langenberg A, Rittmann J, Zamudio-Bayer V, Kulesza A, Mitrić R, Möller T, Issendorff BV, Lau JT (2012) 2p core-level binding energies of size-selected free silicon clusters: Chemical shifts and cluster structure. Phys Rev B 85(19):195454/1–195454/5

    Article  Google Scholar 

  63. Tam NM, Tai TB, Nguyen MT (2012) Thermochemical parameters and growth mechanism of the boron doped silicon clusters, Si n Bq with n = 1–10 and q = −1, 0, +1. J Phys Chem C 116(37):20086–20098

    Article  Google Scholar 

  64. Liu Y, Li GL, Gao AM, Chen HY, Finlow D, Li QS (2011) The structures and properties of FeSi n /FeSi + n /FeSi n (n = 1–8) clusters. Eur Phys J D 64(1):27–35

    Article  Google Scholar 

  65. Lu C, Kuang XY, Lu ZW, Mao AJ, Ma YM (2011) Determination of structures, stabilities, and electronic properties for bimetallic cesium-doped gold clusters: a density functional theory study. J Phys Chem A 115(33):9273–9281

    Article  Google Scholar 

  66. Trivedi R, Dhaka K, Bandyopadhyay D (2014) Study of electronic properties, stabilities and magnetic quenching of molybdenum-doped germanium clusters: a density functional investigation. RSC Adv 4(110):64825–64834

    Article  Google Scholar 

  67. Zhou GD, Duan LY (2002) Structural chemistry basis. Peking University Press, Beijing, pp 178–186

    Google Scholar 

  68. Bhattacharjee D, Kr Mishra B, Ch Deka RA (2014) A DFT study on structure, stabilities and electronic properties of double magnesium doped gold clusters. RSC Adv 4(100):56571–56581

    Article  Google Scholar 

  69. Zhang XR, Ding XL, Dai B, Yang JL (2005) Density functional theory study of W n (n = 2–4) clusters. J Mol Struct: Theochem 757(1):113–118

    Google Scholar 

  70. Zhao YR, Kuang XY, Shao P, Li CG, Wang SJ, Li YF (2012) A systematic search for the structures, stabilities, and electronic properties of bimetallic Ca2-doped gold clusters: comparison with pure gold clusters. J Mol Model 18(4):1333–1343

    Article  Google Scholar 

  71. Brieger M, Renn A, Sodeik A, Hese A (1983) The dipole moment of 7LiH and 7LiD in the excited A 1Σ+ state: a test of the born-oppenheimer approximation. Chem Phys 75(1):1–9

    Article  Google Scholar 

  72. Brieger M (1984) Stark effect, polarizabilities and the electric dipole moment of heteronuclear diatomic molecules in 1Σ states. Chem Phys 89(2):275–295

    Article  Google Scholar 

  73. Bégué D, Merawa M, Pouchan C (1998) Dynamic dipole and quadrupole polarizabilities for the ground 21S and the low-lying 31S and 33S states of Be. Phys Rev A 57(4):2470–2473

    Article  Google Scholar 

  74. Fuentealba P, Simon-Manso Y, Chattaraj PK (2000) Molecular electronic excitations and the minimum polarizability principle. J Phys Chem A 104(14):3185–3187

    Article  Google Scholar 

  75. Wang JL, Yang ML, Wang GH, Zhao JJ (2003) Dipole polarizabilities of germanium clusters. Chem Phys Lett 367(3–4):448–454

    Article  Google Scholar 

  76. Vasiliev I, Ogut S, Chelikowsky JR (1997) Ab initio calculations for the polarizabilities of small semiconductor clusters. Phys Rev Lett 78(25):4805–4808

    Article  Google Scholar 

  77. Deng K, Yang JL, Chan CT (2000) Calculated polarizabilities of small Si clusters. Phys Rev A 61(2):025201/1–025201/4

    Article  Google Scholar 

  78. Jackson KA, Yang M, Chaudhuri I, Frauenheim T (2005) Shape, polarizability, and metallicity in silicon clusters. Phys Rev A 71(3):033205/1–033205/6

    Article  Google Scholar 

  79. Zhao YR, Kuang XY, Zheng BB, Li YF, Wang SJ (2011) Equilibrium geometries, stabilities, and electronic properties of the bimetallic M2-doped Au n (M = Ag, Cu; n = 1–10) clusters: comparison with pure gold clusters. J Phys Chem A 115(5):569–576

    Article  Google Scholar 

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 11304167 and 61306007), 973 Program of China (2014CB660804), 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).

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Zhang, S., Zhang, Y., Yang, X. et al. Systematic theoretical investigation of structures, stabilities, and electronic properties of rhodium-doped silicon clusters: Rh2Si q n (n = 1–10; q = 0, ±1). J Mater Sci 50, 6180–6196 (2015). https://doi.org/10.1007/s10853-015-9175-x

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