23. Sun Y, Zhang M, Fournier R (2008) Periodic trends in the geometric structures of 13-atoms
metal clusters. Phys Rev B 77:0754435
24. Jinlong Y, Toigo F, Kelin W (1994) Structural electronic, and magnetic properties of small
rhodium clusters. Phys Rev B 50:7915–7924
25. 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 59:5214–5222
26. Guirado-López R, Villaseñor-González P, Dorantes-Dávila J, Pastor GM (2000) Magnetism
of Rh n clusters. J Appl Phys 87:4906
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
73:115422
28. Bae YC, Osansi H, Kumar V, Kawazone Y (2004) Nonicosahedral growth and magnetism
behavior of rhodium clusters. Phys Rev B 70:195413–195419
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 125:214708–214712
30. Joswig JO, Springborg M (2003) Generic algorithms search for global minima of aluminium
clusters using Sutton-Chen potential. Phys Rev B 68:085408
31. Zhan L, Chen JZY, Montejano-Carrizalez JM, Guirado-López RA (2006) Phys Rev B
73:115422
32. Aprá E, Ferrando R, Fontunelli A (2006) Density-functional global optimization of gold
clusters. Phys Rev B 73:205414
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:
5111–5116
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
128:144702
35. Erkoc S, Saltaf R (1999) Monte Carlo computer simulations of copper clusters. Phys Rev A
60:3053
36. Cheng J, Fournier R (2004) Structural optimization of atomic clusters by Tabu search in
descriptor spaces. Theor Chem Acc 112:7–15
37. Baletto F, Ferrando R (2005) Structural properties of nanoclusters: energetic, thermodynamic,
and kinetic effects. Rev Mod Phys 77:371
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 81:155446–155459
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–
134110
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 82:270
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 82:284
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 82:299
43. Wood JH, Boring AM (1978) Improved Pauli Hamiltonian for local-potential problems. Phys
Rev B 18:2701
44. Perdew JP, Burke K, Ernzerhof M (1996) General gradient approximation made simple. Phys
Rev Lett 77:3865
45. Perdew JP, Burke K, Ernzerhof M (1997) General gradient approximation made simple [Phys
Rev Lett 77:4884(1996)] Phys Rev Lett 78:1396
46. Peng C, Ayala PY, Schelegel HB, Frish MJ (1996) Using redundant internal coordinates to
optimize equilibrium geometries and transition states. J Comput Chem 17:49
226
M. A. Mora and M. A. Mora-Ramírez
metal clusters. Phys Rev B 77:0754435
24. Jinlong Y, Toigo F, Kelin W (1994) Structural electronic, and magnetic properties of small
rhodium clusters. Phys Rev B 50:7915–7924
25. 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 59:5214–5222
26. Guirado-López R, Villaseñor-González P, Dorantes-Dávila J, Pastor GM (2000) Magnetism
of Rh n clusters. J Appl Phys 87:4906
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
73:115422
28. Bae YC, Osansi H, Kumar V, Kawazone Y (2004) Nonicosahedral growth and magnetism
behavior of rhodium clusters. Phys Rev B 70:195413–195419
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 125:214708–214712
30. Joswig JO, Springborg M (2003) Generic algorithms search for global minima of aluminium
clusters using Sutton-Chen potential. Phys Rev B 68:085408
31. Zhan L, Chen JZY, Montejano-Carrizalez JM, Guirado-López RA (2006) Phys Rev B
73:115422
32. Aprá E, Ferrando R, Fontunelli A (2006) Density-functional global optimization of gold
clusters. Phys Rev B 73:205414
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:
5111–5116
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
128:144702
35. Erkoc S, Saltaf R (1999) Monte Carlo computer simulations of copper clusters. Phys Rev A
60:3053
36. Cheng J, Fournier R (2004) Structural optimization of atomic clusters by Tabu search in
descriptor spaces. Theor Chem Acc 112:7–15
37. Baletto F, Ferrando R (2005) Structural properties of nanoclusters: energetic, thermodynamic,
and kinetic effects. Rev Mod Phys 77:371
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 81:155446–155459
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–
134110
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 82:270
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 82:284
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 82:299
43. Wood JH, Boring AM (1978) Improved Pauli Hamiltonian for local-potential problems. Phys
Rev B 18:2701
44. Perdew JP, Burke K, Ernzerhof M (1996) General gradient approximation made simple. Phys
Rev Lett 77:3865
45. Perdew JP, Burke K, Ernzerhof M (1997) General gradient approximation made simple [Phys
Rev Lett 77:4884(1996)] Phys Rev Lett 78:1396
46. Peng C, Ayala PY, Schelegel HB, Frish MJ (1996) Using redundant internal coordinates to
optimize equilibrium geometries and transition states. J Comput Chem 17:49
226
M. A. Mora and M. A. Mora-Ramírez