Small Rhodium Clusters: A HF and DFT Study–III

Conference paper
Part of the Progress in Theoretical Chemistry and Physics book series (PTCP, volume 31)

Abstract

Small neutral and ionic Rhodium clusters Rhn (n = 6, 8, 13) are investigated by ab initio molecular orbital calculations with full optimization at the Restricted Open Shell Hartree-Fock (ROHF) level with a LANL2DZ basis set, and with the methods based on Density Functional Theory, B3LYP/MWB, B3LYP/PBE. The clusters are found favor close-packed icosahedron structures in contrast to previous theoretical predictions that rhodium clusters should favor cubic motifs. A range of spin multiplicities are investigated for each cluster and we present the minimum energy conformation along with the vertical and adiabatic ionization potentials.

Keywords

Rhodium clusters ROHF calculations Transition metal Ionization potential 

References

  1. 1.
    Cox AJ, Louderback JG, Bloomfield LA (1993) Experimental observation of magnetism in rhodium clusters. Phys Rev Lett 71:923–926CrossRefGoogle Scholar
  2. 2.
    Cox AJ, Louderback JG, Apsel SE, Bloomfield LA (1994) Magnetism in 4d-transition metal clusters. Phys Rev B 4:12295–12298CrossRefGoogle Scholar
  3. 3.
    Schmid G (2004) Nanoparticles from theory to applications. Wiley-VCH. ISBN 3527305076Google Scholar
  4. 4.
    Wei J, Iglesia E (2004) Structural requirements and reaction pathways in methane activation and chemical conversion catalized by rhodium. J Catal 225:116–127CrossRefGoogle Scholar
  5. 5.
    Nolte P, Stierle A, Jin-Phillipp NY, Kasper N, Schulli TU, Dosch H (2008) Shape changes of supported Rh nanoparticles during oxidation and reduction cycles. Science 321:1654–1658CrossRefGoogle Scholar
  6. 6.
    Loferty PJ (2013) Commodity report: platinum group metals. United States Geological SurveyGoogle Scholar
  7. 7.
    Heldings FM, Capka M (2003) Rhodium complexes as catalyst for hydrosilylation crosslinking of silicone ruber. J Appl Polymer Sci 30(5):1837Google Scholar
  8. 8.
    Halligudi SB et al (1992) Hydrogenation of bencene to cycloexene catalized by Rhodium(I) complex supported on montmorillonite clay. React Kinet Catal Lett 48(2):547–552CrossRefGoogle Scholar
  9. 9.
    Cramer Stepen S Jr, Covino, Bernard (1990) ASM handbook materials park OH: ASM international report pp 393–396Google Scholar
  10. 10.
    Harding DJ, Gruene P, Haertelt M, Meijer G, Fielicke A, Hamilton SM, Hopkins WS, Mackenzie RS, Neville SP, Walsh TR (2010) Probing the structures of gas-phase rhodium cluster cation by far-infrared spectroscopy. J Chem Phys 133:214304–214313CrossRefGoogle Scholar
  11. 11.
    Harding DJ, Walsh TR, Hamilton SM, Hopkins WS, Mackenzie SR, Gruene P, Haertelt M, Maijer G, Fielicke F (2010) Comunications: the structure of Rh8+ in the gas phase. J Chem Phys 132:011101–011104CrossRefGoogle Scholar
  12. 12.
    Knickelbin MB (2005) Phys Rev B 71:18444Google Scholar
  13. 13.
    Apsel SE, Emmert JW, Deng J, Bloomfield LA (1996) Surface-enhanced magnetism in nickel clusters. Phys Rev Lett 76:1441CrossRefGoogle Scholar
  14. 14.
    Douglas DC, Bucher JP, Bloomfield LA (1992) Magnetic studies of free ferromagnetic clusters. Phys Rev B 45:6341–6344CrossRefGoogle Scholar
  15. 15.
    Knickelbein MB (2001) Experimental observation of superparamagnetism in manganese clusters. Phys Rev Lett 86:5255–5257CrossRefGoogle Scholar
  16. 16.
    Knickelbein MB (2004) Magnetic ordering in manganese clusters. Phys Rev B 70:014424CrossRefGoogle Scholar
  17. 17.
    Xu X, Yin S, Moro R, de Herr WA (2005) Magnetic moments and adiabatic magnetization of free cobalt clusters. Phys Rev Lett 95:237209CrossRefGoogle Scholar
  18. 18.
    Reddy BV, Khanna SN, Dunlap BI (1993) Giant magnetic moments of 4d clusters. Phys Rev Lett 70:3323–3326CrossRefGoogle Scholar
  19. 19.
    Bae YC, Kumar V, Osanai H, Kawazoe Y (2005) Cubic magic clusters of rhodium stabilized with eight-center bonding: magnetism and growth. Phys Rev B 72:115427–115432CrossRefGoogle Scholar
  20. 20.
    Chang CM, Chou MY (2004) Alternative low-symmetry structure for 13-atoms metal clusters. Phys Rev Lett 93:133401–133404CrossRefGoogle Scholar
  21. 21.
    Aguilera-Granja F, Rodríguez-López JL, Michaelian K, Berlanga-Ramírez EO, Vega A (2002) structure and magnetism of small rhodium clusters. Phys Rev B 66:224410–224419CrossRefGoogle Scholar
  22. 22.
    Wang LL, Johnson DD (2007) Density functional study of structural trends for late-transition-metal 13-atoms clusters. Phys Rev B 75:235405–235409CrossRefGoogle Scholar
  23. 23.
    Sun Y, Zhang M, Fournier R (2008) Periodic trends in the geometric structures of 13-atoms metal clusters. Phys Rev B 77:0754435Google Scholar
  24. 24.
    Jinlong Y, Toigo F, Kelin W (1994) Structural electronic, and magnetic properties of small rhodium clusters. Phys Rev B 50:7915–7924CrossRefGoogle Scholar
  25. 25.
    Reddy BV, Nayak SK, Khanna SN, Rao BK, Jena P (1999) Electronic structure and magnetism of Rhn (n = 2-13) clusters. Phys Rev B 59:5214–5222CrossRefGoogle Scholar
  26. 26.
    Guirado-López R, Villaseñor-González P, Dorantes-Dávila J, Pastor GM (2000) Magnetism of Rhn clusters. J Appl Phys 87:4906CrossRefGoogle Scholar
  27. 27.
    Aguilera-Granja F, Montejano-Carrizales JM, Guirado-López RA (2006) Magnetic properties of small 3d and 4d transition metal clusters: the role of a noncompact growth. Phys Rev B 73:115422CrossRefGoogle Scholar
  28. 28.
    Bae YC, Osansi H, Kumar V, Kawazone Y (2004) Nonicosahedral growth and magnetism behavior of rhodium clusters. Phys Rev B 70:195413–195419CrossRefGoogle Scholar
  29. 29.
    Rogan J, García G, Loyola C, Orellana W, Ramírez R, Kiwi M (2006) Alternative search strategy for minimal energy nanocluster structures: the case of rhodium, palladium, and silver. J Chem Phys 125:214708–214712CrossRefGoogle Scholar
  30. 30.
    Joswig JO, Springborg M (2003) Generic algorithms search for global minima of aluminium clusters using Sutton-Chen potential. Phys Rev B 68:085408CrossRefGoogle Scholar
  31. 31.
    Zhan L, Chen JZY, Montejano-Carrizalez JM, Guirado-López RA (2006) Phys Rev B 73:115422CrossRefGoogle Scholar
  32. 32.
    Aprá E, Ferrando R, Fontunelli A (2006) Density-functional global optimization of gold clusters. Phys Rev B 73:205414CrossRefGoogle Scholar
  33. 33.
    Wales DJ, Doye JPK (1997) Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. J Phys Chem A 101:5111–5116CrossRefGoogle Scholar
  34. 34.
    Kim HG, Choi SK, Lee HM (2008) New algorithm in the basin-hopping Monte Carlo to find the global minimum structure of unary and binary metallic nano clusters. J Chem Phys 128:144702CrossRefGoogle Scholar
  35. 35.
    Erkoc S, Saltaf R (1999) Monte Carlo computer simulations of copper clusters. Phys Rev A 60:3053CrossRefGoogle Scholar
  36. 36.
    Cheng J, Fournier R (2004) Structural optimization of atomic clusters by Tabu search in descriptor spaces. Theor Chem Acc 112:7–15CrossRefGoogle Scholar
  37. 37.
    Baletto F, Ferrando R (2005) Structural properties of nanoclusters: energetic, thermodynamic, and kinetic effects. Rev Mod Phys 77:371CrossRefGoogle Scholar
  38. 38.
    Piotrowsky MJ, Piquini P, Da Silva JLF (2010) Density functional theory investigation of 3d, 4d, and 5d 13-atom metal clusters. Phys Rev B 81:155446–155459CrossRefGoogle Scholar
  39. 39.
    Piotrowski MJ, Piquini P, Odashima MM, DaSilva JLF (2011) Transition-metal 13-atom clusterts assessed with solid and surface-biased functionals. J Chem Phys 134:134105–134110CrossRefGoogle Scholar
  40. 40.
    Hay PJ, Wadt WR (1985) Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi. J Chem Phys 82:270CrossRefGoogle Scholar
  41. 41.
    Wadt WR, Hay PJ (1985) Ab initio effective core potentials for molecular calculations. Potentials for the transition metal atoms Sc to Hg. J Chem Phys 82:284Google Scholar
  42. 42.
    Hay PJ, Wadt WR (1985) Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals. J Chem Phys 82:299CrossRefGoogle Scholar
  43. 43.
    Wood JH, Boring AM (1978) Improved Pauli Hamiltonian for local-potential problems. Phys Rev B 18:2701CrossRefGoogle Scholar
  44. 44.
    Perdew JP, Burke K, Ernzerhof M (1996) General gradient approximation made simple. Phys Rev Lett 77:3865CrossRefGoogle Scholar
  45. 45.
    Perdew JP, Burke K, Ernzerhof M (1997) General gradient approximation made simple [Phys Rev Lett 77:4884(1996)] Phys Rev Lett 78:1396Google Scholar
  46. 46.
    Peng C, Ayala PY, Schelegel HB, Frish MJ (1996) Using redundant internal coordinates to optimize equilibrium geometries and transition states. J Comput Chem 17:49CrossRefGoogle Scholar
  47. 47.
    Peng C, Schelegel HB (1994) Combining synchronous transit and quasi-Newton methods to find transit states. Israel J Chem 33:449CrossRefGoogle Scholar
  48. 48.
    Beltrán MR, Buendía Zamudío F, Chanhan V, Sen P, Wang H, Ko YJ, Bowen K (2013) Ab initio and anion photoelectron studies of Rhn (n = 1-9) clusters. Eur Phys J D 67:63–70CrossRefGoogle Scholar
  49. 49.
    Bertin V, Lopez-Rendón R, del Angel G, Poulain E, Avilés R, Uc-Rosas V (2010) Comparative theoretical study of small Rhn nanoparticles (2 ≤ n ≤ 8) using DFT methods. Int J Quantum Chem 110:1152–1164Google Scholar
  50. 50.
    Harding DJ, Davies RDL, Mackenzie SR, Walsh TR (2008) Oxides of small rhodium clusters: theoretical investigation of experimental reactivities. J Chem Phys 129:124304–124310CrossRefGoogle Scholar
  51. 51.
    Mora MA, Mora-Ramírez MA, Rubio-Arroyo Manuel F (2010) Structural and electronic study of neutral, positive and negative small rhodium clusters [Rhn, Rhn+, Rhn-]. Int J Quantum Chem 110:2541–2547Google Scholar
  52. 52.
    Li ZQ, Yu JZ, Ohno K, Kawazoe Y (1999) Calculations on the magnetic properties of rhodium clusters. J Phys Condens Matter 7:47–53CrossRefGoogle Scholar
  53. 53.
    Hang TD, Hung HM, Thiem LN, Nguyen HMT (2015) Electronic structure and thermochemical properties of neutral and anionic rhodium clusters Rhn, n = 2-13. Evolution of structures and stabilities of binary clusters RhmM (M = Fe Co, Ni; m = 1-6). Comput Theor Chem 1068:30–41CrossRefGoogle Scholar
  54. 54.
    Chien CH, Blaisten-Barojas E, Pedersen MR (1998) Magnetic and electronic properties of rhodium clusters. Phys Rev A 58:2196–2202CrossRefGoogle Scholar
  55. 55.
    Harding D, Mackenzie SR, Walsh TR (2006) Structural isomers and reactivity for Rh6, Rh6+. J Phys Chem B 110:18272–18277CrossRefGoogle Scholar
  56. 56.
    Da Silva JLF, Piotrowski MJ, Aguilera-Granja F (2012) Phys Rev B 86:125430–125435CrossRefGoogle Scholar
  57. 57.
    Sun Y, Fournier R, Zhang M (2009) Structural and electronic properties of 13-atom 4d transition-metal clusters. Phys Rev B 79:043202–043211CrossRefGoogle Scholar
  58. 58.
    Lee C, Yang W, Parr RG (1988) Development Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B 37:785CrossRefGoogle Scholar
  59. 59.
    Miehlich B, Sabin A, Stoll H, Preus H (1989) Results obtained with the correlation energy density functional of Becke and Lee, Yang and Parr. Chem Phys Lett 157:200–206CrossRefGoogle Scholar
  60. 60.
    Futschek T, Marsman M, Hafner J (2005) Structural and magnetic isomers of small Pd and Rh clusters: an ab initio functional study. J Phys Condens Matter 17:5927–5963CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Depto. de QuímicaUniversidad Autónoma MetropolitanaMexico, D. F.Mexico
  2. 2.Depto. Fisicomatemáticas, Facultad de C. QuímicasBenemérita Universidad Autónoma de PueblaPueblaMexico

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