Computational Study of Au Doped Cu Nano Alloy Clusters

Article Preview

Abstract:

Among several bimetallic nanoclusters, the compounds formed between Cu-Au have gained immense importance due to its remarkable optical, mechanical, electronic and catalytic behaviors. Density Functional Theory (DFT) is one of the most successful and popular approaches of quantum mechanics to explore electronic properties of materials. Conceptual DFT based descriptors have become indispensable tools for analyzing and correlating the experimental properties of compounds. In this venture, we have successfully investigated the physico-chemical properties of Au doped Cu nanoclusters invoking DFT methodology. Our results reveal that computed HOMO-LUMO gap of CunAu (n=1-7) nanoalloy clusters show pronounced even-odd alternation behavior. A close agreement between experimental and our computed data is observed.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

62-71

Citation:

Online since:

August 2017

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2017 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

* - Corresponding Author

[1] A. Z. Khosousi and A. A. Dhirani, Charge transport in nanoparticle assemblies, Chem. Rev. 108 (2008) 4072-4124.

DOI: 10.1021/cr0680134

Google Scholar

[2] M. C. Daniel and D. Astruc, Gold nanoparticles: assembly, supermolecular chemistry, quantum-size-related properties, and applications toward biology, catalysis, and nanotechnology, Chem. Rev. 104 (2004) 293-346.

DOI: 10.1021/cr030698+

Google Scholar

[3] S. K. Ghosh and T. Pal, Interparticle coupling effect on the surface plasmon resonance of gold nanoparticles: from theory to applications, Chem. Rev. 107 (2007) 4797-4862.

DOI: 10.1021/cr0680282

Google Scholar

[4] R. G. Chaudhuri and S. Paria, Core/shell nanoparticles: classes, properties, synthesis mechanisms, characterization, and applications, Chem. Rev. 112 (2012) 2373-2433.

DOI: 10.1021/cr100449n

Google Scholar

[5] A. P. Alivisatos, Semiconductor clusters, nanocrystals, and quantum dots, Science 271 (1996) 933-937.

DOI: 10.1126/science.271.5251.933

Google Scholar

[6] H. Q. Wang, X. Y. Kuang and H. F. Li, Density functional study of structural and electronic properties of bimetallic copper-gold clusters: comparison with pure and doped gold clusters, Phys. Chem. Chem. Phys. 12 (2010) 5156-5165.

DOI: 10.1039/b923003c

Google Scholar

[7] R. Ismail, Theoretical studies of free and supported nanoalloy clusters, Ph.D. Thesis, University of Birmingham, UK (2012).

Google Scholar

[8] A. Roucoux, J. Schulz, and H. Patin, Reduced transition metal colloids: a novel family of reusable catalysts?, Chem. Rev. 102 (2002) 3757-3778.

DOI: 10.1021/cr010350j

Google Scholar

[9] B. M. Munoz-Flores, B. I. Kharisov, V. M. Jimenez-Perez, P. E. Martinez and S. T. Lopez, Recent advances in the synthesis and main applications of metallic nanoalloys, Ind. Eng. Chem. Res. 50 (2011) 7705-7721.

DOI: 10.1021/ie200177d

Google Scholar

[10] R. W. Murray, Nanoelectrochemistry: metal nanoparticles, nanoelectrodes, and nanopores, Chem. Rev. 108 (2008) 2688-2720.

DOI: 10.1021/cr068077e

Google Scholar

[11] F. Yin, Z. W. Wang and R. E. Palmer, Formation of bimetallic nanoalloys by Au coating of size-selected Cu clusters, J. Nanopart. Res. 14 (2012) 1124.

DOI: 10.1007/s11051-012-1124-x

Google Scholar

[12] X. Teng, Q. Wang, P. Liu, W. Han, A. I. Frenkel, M. N. Wen, J. C. Hanson and J. A. Rodriguez, Formation of Pd/Au nanostructures from Pd nanowires via galvanic replacement reaction, J. Am. Chem. Soc., 130 (2008) 1093-1101.

DOI: 10.1021/ja077303e

Google Scholar

[13] R. Ferrando, J. Jellinek and R. L. Johnston, Nanoalloys: from theory to applications of alloy clusters and nanoparticles, Chem. Rev. 108 (2008) 845-910.

DOI: 10.1021/cr040090g

Google Scholar

[14] A. Henglein, Physicochemical properties of small metal particles in aqueous solution, J. Phys. Chem. 97 (1993) 5457-5471.

DOI: 10.1021/j100123a004

Google Scholar

[15] S. C. Davis and K. J. Klabunde, Unsupported small metal particles: preparation, reactivity and characterization, Chem. Rev. 82 (1982) 153-208.

DOI: 10.1021/cr00048a002

Google Scholar

[16] L. N. Lewis, Chemical catalysis by colloids and clusters, Chem. Rev. 93(1993) 2693-2730.

Google Scholar

[17] G. Schmid, Large clusters and colloids. Metal in the embryonic state, Chem. Rev. 92(1992) 1709-1727.

DOI: 10.1021/cr00016a002

Google Scholar

[18] G. Schon and U. Simon, A fascinating new field in colloid science: small ligand-stabilized metal clusters and possible application in microelectronics, Colloid. Polym. Sci. 273 (1995) 101-117.

DOI: 10.1007/bf00654007

Google Scholar

[19] H. Y. Oderji and H. Ding, Determination of melting mechanism of Pd24Pt14 nanoalloy by multiple histogram method via molecular dynamics simulations, Chem. Phys. 388 (2011) 23-30.

DOI: 10.1016/j.chemphys.2011.07.011

Google Scholar

[20] H. B. Liu, U. Pal, A. Medina, C. Maldonado and J. A. Ascencio, Structural incoherency and structure reversal in bimetallic Au-Pd nanoclusters, Phys. Rev. B 71, 075403 (2005).

DOI: 10.1103/physrevb.71.075403

Google Scholar

[21] F. Baletto and R. Ferrando, Structural properties of nanoclusters: Energetic, thermodynamic and kinetic effects, Rev. Mod. Phys. 77 (2005) 371-423.

DOI: 10.1103/revmodphys.77.371

Google Scholar

[22] J. A. Alonso, Electronic and atomic structure, and magnetism of transition-metal clusters, Chem. Rev. 100 (2000) 637-678.

DOI: 10.1021/cr980391o

Google Scholar

[23] I. Katakuse, T. Ichihara, Y. Fujita, T. Matsuo, T. Sakurai and H. Matsuda, Mass distributions of copper, silver and gold clusters and electronic shell structure, Int. J. Mass Spectrom. Ion Processes 67 (1985) 229-236.

DOI: 10.1016/0168-1176(85)80021-5

Google Scholar

[24] I. Katakuse, T. Ichihara, Y. Fujita, T. Matsuo, T. Sakurai and H. Matsuda, Mass distributions of negative cluster ions of copper, silver and gold, Int. J. Mass Spectrom. Ion Processes 74 (1986) 33-41.

DOI: 10.1016/0168-1176(86)85021-2

Google Scholar

[25] W. A. D. Heer, The physics of simple metal clusters: experimental aspects and simple models, Rev. Mod. Phys., 65 (1993) 611-676.

DOI: 10.1103/revmodphys.65.611

Google Scholar

[26] G. Gantefor, M. Gausa, K. H. Meiwes-Broer and H. O. Lutz, Photoelectron spectroscopy of silver and palladium cluster anions. Electron delocalization versus, localization, J. Chem. Soc., Faraday Trans. 86 (1990) 2483-2488.

DOI: 10.1039/ft9908602483

Google Scholar

[27] D. G. Leopold, J. Ho and W. C. Lineberger, Phoelectron spectroscopy of mass-selected metal cluster anions.I. Cun-, n=1-10, J. Chem. Phys. 86 (1987) 1715-1726.

DOI: 10.1063/1.452170

Google Scholar

[28] A. Lattes, I. Rico, A. D. Savignac and A. A. Z. Samii, Formamide, a water substitute in micelles and micromulsions xxx structural analysis using a diels-alder reaction as a chemical probe, Tetrahedron 43 (1987) 1725-1735.

DOI: 10.1016/s0040-4020(01)90284-4

Google Scholar

[29] F. Chen, G. Q. Xu and T. S. A. Hor, Preparation and assemble of colloidal gold nanoparticles in CTAB-stabilized reverse microemulsion, Mater. Lett. 57 (2003) 3282-3286.

DOI: 10.1016/s0167-577x(03)00048-x

Google Scholar

[30] A. Taleb, C. Petit and M. P. Pileni, Optical properties of self-assembled 2D and 3D superlattices of silver nanoparticles, J. Phys. Chem. B 102 (1998) 2214-2220.

DOI: 10.1021/jp972807s

Google Scholar

[31] H. Q. Liu, Y. Tian and P. P. Xia, Pyramidal, rodlike, spherical gold nanostructures for direct electron transfer of copper, zinc-superoxide dismutase: application to superoxide anion biosensors, Langmuir 24 (2008) 6359-6366.

DOI: 10.1021/la703587x

Google Scholar

[32] K. J. T. Noonan, B. H. Gillon, V. Cappello and D. P. Gates, Phosphorus-containing block copolymer templates can control the size and shape of gold nanostructures, J. Am. Chem. Soc. 130 (2008) 12876-12877.

DOI: 10.1021/ja805076y

Google Scholar

[33] T. Wang, X. G. Hu and S. J. Dong, Surfactantless synthesis of multiple shapes of gold nanostructures and their shape-dependent SERS spectroscopy, J. Phys. Chem. B 110 (2006) 16930-16936.

DOI: 10.1021/jp062486x

Google Scholar

[34] C. Majumder, A. K. Kandalam and P. Jena, Structure and bonding of Au5M (M=Na, Mg, Al, Si, P and S) clusters, Phys. Rev. B: Condens. Matter. Mater. Phys. 74 (2006) 205437.

Google Scholar

[35] X. Li, B. Kiran, L. F. Cui and L. S. Wan, Magnetic properties in transition-metal-doped gold clusters: M@Au6 (M=Ti, V, Cr), Phys. Rev. Lett. 95 (2005) 253401.

Google Scholar

[36] M. B. Torres, E. M. Fernandez and L. C. Balbas, Theoretical study of oxygen adsorption on pure Aun+1+ and doped MAun+ cationic gold clusters for M=Ti, Fe and n=3-7, J. Phys. Chem. A 112 (2008) 6678-6689.

Google Scholar

[37] J. H. Teles, S. Brode and M. Chabanas, Cationic gold (I) complexes: highly efficient catalysis for the addition of alcohols to alkynes, Angew. Chem. 110 (1998) 1475-1478.

DOI: 10.1002/(sici)1521-3773(19980605)37:10<1415::aid-anie1415>3.0.co;2-n

Google Scholar

[38] M. Valden, X. Lai and D. W. Goodman, Onset of catalytic activity of gold clusters on titania with the appearance of nonmetallic properties, Science 281 (1998) 1647-1650.

DOI: 10.1126/science.281.5383.1647

Google Scholar

[39] B. Yoon, H. Hӓkkinen, U. Landman, A. S. Wörz, J. –M. Antonietti, S. Abbet, K. Judai and U. Heiz, Charging effects on bonding and catalyzed oxidation of CO on Au8 clusters on MgO, Science 307 (2005) 403-407.

DOI: 10.1126/science.1104168

Google Scholar

[40] R. McRae, B. Lai, S. Vogt and C. J. Fahrni, Correlative microXRF and optical immunofluorescence microscopy of adherent cells labeled with ultrasmall gold particles, J. Struct. Biol. 155 (2006) 22-29.

DOI: 10.1016/j.jsb.2005.09.013

Google Scholar

[41] C. J. Ackerson, P. D. Jadzinsky, G. J. Jensen and R. D. Kornberg, Rigid, specific and discrete gold nanoparticle/antibody conjugates, J. Am. Chem. Soc. 128 (2006) 2635-2640.

DOI: 10.1021/ja0555668

Google Scholar

[42] C. F. Shaw III, Gold-based therapeutic agents, Chem. Rev. 99 (1999) 2589-2600.

Google Scholar

[43] M. Kabir, A. Mookerjee and A. K. Bhattacharya, Copper clusters: electronic effect dominates over geometric effect, Eur. Phys. J. D 31 (2004) 477-485.

DOI: 10.1140/epjd/e2004-00142-y

Google Scholar

[44] C. J. Heard and R. L. Johnston, A density functional global optimization study of neutral 8-atom Cu-Ag and Cu-Au clusters, Eur. Phys. J. D 67 (2013) 30601-30607.

DOI: 10.1140/epjd/e2012-30601-7

Google Scholar

[45] H. Hakkinen, M. Moseler and U. Landman, Supported magnetic nanoclusters: soft landing of Pd clusters on a MgO surface, Phys. Rev. Lett. 89 (2002) 176103.

DOI: 10.1103/physrevlett.89.176103

Google Scholar

[46] C. Massobrio, A. Pasquarello and R. Car, Structural and electronic properties of small copper clusters: a first principles study, Chem. Phys. Lett. 238 (1995) 215-221.

DOI: 10.1016/0009-2614(95)00394-j

Google Scholar

[47] J. C. Bauer, D. Mullins, M. Li, Z. Wu, E. A. Payzant, S. H. Overbury and S. Dai, Synthesis of silica supported AuCu nanoparticle catalysts and the effects of pretreatment conditions for the CO oxidation reaction, Phys. Chem. Chem. Phys. 13 (2011).

DOI: 10.1039/c0cp01859g

Google Scholar

[48] W. Bouwen, F. Vanhoutte, F. Despa, S. Bouckaert, S. Neukermans, K. L. Theil, H. Weidele, P. Lievens and R. E. Silverans, Stability effects of AunXm+ (X=Cu, Al, Y, In) clusters, Chem. Phys. Lett. 314 (1999) 227-233.

DOI: 10.1016/s0009-2614(99)01150-1

Google Scholar

[49] C. L. Bracey, P. R. Ellis and G. J. Hutchings, Application of copper-gold alloy in catalysis: current status and future perspectives, Chem. Soc. Rev. 38 (2009) 2231-2243.

DOI: 10.1039/b817729p

Google Scholar

[50] W. Chen, R. Yu, L. Li, A. Wang, Q. Peng and Y. Li, A seed-based diffusion route to monodisperse intermetallic CuAu nanocrystals, Angew. Chem. Int. Ed. 49 (2010) 2917-2921.

DOI: 10.1002/anie.200906835

Google Scholar

[51] X. Liu, A. Wang, L. Li, T. Zhang, C. Mou and J. Lee, Structural changes of Au-Cu bimetallic catalysts in CO oxidation: in situ XRD, EPR, XANES, and FT-IR characterizations, J. Catal 278 (2011) 288-296.

DOI: 10.1016/j.jcat.2010.12.016

Google Scholar

[52] C. N. R. Rao, G. U. Kulkarni, P. J. Thomas and P. P. Edwards, Metal nanoparticles and their assemblies, Chem. Soc. Rev. 29 (2000) 27-35.

Google Scholar

[53] B. Pauwels, G. V. Tendeloo, E. Zhurkin, M. Hou, G. Verschoren, L. T. Kuhn, W. Bouwen and P. Lievens, Transmission electron microscopy and monte carlo simulations of ordering in Au-Cu clusters produced in a laser vaporization source, Phys. Rev. B 63 (2001).

DOI: 10.1103/physrevb.63.165406

Google Scholar

[54] A. K. Sra and R. E. Schaak, Synthesis of automatically ordered AuCu and AuCu3 nanocrystals from bimetallic nanoparticle precursors, J. Am. Chem. Soc. 126 (2004) 6667-6672.

DOI: 10.1021/ja031547r

Google Scholar

[55] T. J. Toai, G. Rossi and R. Ferrando, Global optimization and growth simulation of AuCu clusters, Faraday Discuss. 138 (2008) 49-58.

DOI: 10.1039/b707813g

Google Scholar

[56] H. Yasuda and H. Mori, Cluster-size dependence of alloying behavior in gold clusters, Z. Phys. D: At, Mol. Clusters 31 (1994) 131-134.

DOI: 10.1007/bf01426588

Google Scholar

[57] F. Yin, Z. W. Wang and R. E. Palmer, Controlled formation of mass-selected Cu-Au core-shell cluster beams, J. Am. Chem. Soc. 133 (2011) 10325-10327.

DOI: 10.1021/ja201218n

Google Scholar

[58] A. Rapallo, G. Rossi, R. Ferrando, A. Fortunelli, B. C. Curley, L. D. Lloyd, G. M. Tarbuck and R. L. Johnston, Global optimization of bimetallic cluster structures.I. Size-mismatched Ag-Cu, Ag-Ni, and Au-Cu systems, J. Chem. Phys. 122 (2005).

DOI: 10.1063/1.1898223

Google Scholar

[59] A. M. Molenbroek, J. K. Norskov and B. S. Clausen, Structure and reactivity of Ni-Au nanoparticle catalysts, J. Phys. Chem. B 105 (2001) 5450-5458.

DOI: 10.1021/jp0043975

Google Scholar

[60] C. J. Cramer and D. G. Truhlar, Density functional theory for transition metals and transition metal chemistry, Phys. Chem. Chem. Phys. 11 (2009) 10757-10816.

DOI: 10.1039/b907148b

Google Scholar

[61] O. J. Wacker, R. Kümmel and E. K. U. Gross, Time-dependent density-functional theory for superconductors, Phys. Rev. Lett. 73 (1994) 2915-2918.

DOI: 10.1103/physrevlett.73.2915

Google Scholar

[62] F. Illas and R. L. Martin, Magnetic coupling in ionic solids studied by density functional theory, J. Chem. Phys. 108 (1998) 2519-2527.

DOI: 10.1063/1.475636

Google Scholar

[63] S. Kümmel and M. Brack, Quantum fluid dynamics from density-functional theory, Phys. Rev. A 64 (2001) 022506.

DOI: 10.1103/physreva.64.022506

Google Scholar

[64] R. Car and M. Parrinello, Unified approach for molecular dynamics and density-functional theory, Phys. Rev. Lett. 55 (1985) 2471-2474.

DOI: 10.1103/physrevlett.55.2471

Google Scholar

[65] M. Koskinen, P. Lipas and M. Manninen, Unrestricted shapes of light nuclei in the local-density approximation: Comparison with jellium clusters, Nucl. Phys. A 591 (1995) 421-434.

DOI: 10.1016/0375-9474(95)00209-j

Google Scholar

[66] R. N. Schmid, E. Engel and R. M. Dreizler, Density functional approach to quantum hadrodynamics: Local exchange potential for nuclear structure calculations, Phys. Rev. C 52 (1995) 164-169.

DOI: 10.1103/physrevc.52.164

Google Scholar

[67] R. G. Parr and W. Yang, density functional theory of the electronic structure of molecules, Annu. Rev. Phy. Chem. 46 (1995) 701-728.

DOI: 10.1146/annurev.pc.46.100195.003413

Google Scholar

[68] W. Kohn, A. D. Becke and R. G. Parr, Density functional theory of electronic structure, J. Phys. Chem. 100 (1996) 12974-12980.

DOI: 10.1021/jp960669l

Google Scholar

[69] S. Liu and R. G. Parr, Second-order density-functional description of molecules and chemical changes, J. Chem. Phys., 106 (1997) 5578-5586.

DOI: 10.1063/1.473580

Google Scholar

[70] T. Ziegler, Approximate density functional theory as a practical tool in molecular energetics and dynamics, Chem. Rev. 91(1991) 651-667.

DOI: 10.1021/cr00005a001

Google Scholar

[71] R. G. Parr and W. Yang, Editor, Density Functional Theory of Atoms and Molecules, Oxford University Press, Oxford (1989).

Google Scholar

[72] H. Chermette, Chemical reactivity indexes in density functional theory, J. Comput. Chem. 20 (1999) 129-154.

DOI: 10.1002/(sici)1096-987x(19990115)20:1<129::aid-jcc13>3.0.co;2-a

Google Scholar

[73] P. Geerlings, F. D. Proft and W. Langenaeker, Conceptual density functional theory, Chem. Rev. Washington, D.C. 103 (2003) 1793-1873.

DOI: 10.1021/cr990029p

Google Scholar

[74] P. Geerlings and F. D. Proft, Chemical reactivity as described by quantum chemical methods, Int. J. Mol. Sci. 3 (2002) 276-309.

DOI: 10.3390/i3040276

Google Scholar

[75] P. Ranjan, S. Dhail, S. Venigalla, A. Kumar, L. Ledwani and T. Chakraborty, A theoretical analysis of bi-metallic (Cu-Ag)n=1-7 nano alloy clusters invoking DFT based descriptors, Mater. Sci. -Pol. 33 (2015) 719-724.

DOI: 10.1515/msp-2015-0121

Google Scholar

[76] P. Ranjan, S. Venigalla, A. Kumar and T. Chakraborty, Theoretical study of bi-metallic AgmAun (m+n=2-8) nano alloy clusters in terms of DFT based descriptors, New Front. Chem. 23 (2014) 111-122.

DOI: 10.1515/msp-2015-0121

Google Scholar

[77] S. Venigalla, S. Dhail, P. Ranjan, S. Jain and T. Chakraborty, Computational study about cytotoxixity of metal oxide nanoparticles invoking Nano-QSAR technique, New Front. Chem. 23 (2014) 123-130.

Google Scholar

[78] P. Ranjan, A. Kumar and T. Chakraborty, Computational study of AuSin (n=1-9) nanoalloy clusters invoking DFT based descriptors, AIP Conf. Proc. 1724, (2016) 020072.

DOI: 10.1063/1.4945192

Google Scholar

[79] P. Ranjan, A. Kumar and T. Chakraborty, Theoretical analysis: Electronic and optical properties of gold-silicon nanoalloy clusters, Mat. Today Proc. 3, (2016) 1563-1568.

DOI: 10.1016/j.matpr.2016.04.043

Google Scholar

[80] P. Ranjan, A. Kumar and T. Chakraborty, Computational study of nanomaterials invoking DFT based descriptors, in Environmental Sustainability: Concepts, Principles, Evidences and Innovations, Edited G. C. Mishra, Excellent Publishing House, New Delhi (2014).

Google Scholar

[81] P. Ranjan, S. Venigalla, A. Kumar and T. Chakraborty, A theoretical analysis of bi-metallic AgAun (n=1-7) nano alloy clusters invoking DFT based descriptors, in Recent Methodology in Chemical Sciences: Experimental and Theoretical Approaches, Edited T. Chakraborty and L. Ledwani, Apple Academic Press and CRC Press, USA (2015).

DOI: 10.1515/msp-2015-0121

Google Scholar

[82] Gaussian 03, Revision C. 02, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, J. A. Montgomery, Jr., T. Vreven, K. N. Kudin, J. C. Burant, J. M. Millam, S. S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G. A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J. E. Knox, H. P. Hratchian, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, P. Y. Ayala, K. Morokuma, G. A. Voth, P. Salvador, J. J. Dannenberg, V. G. Zakrzewski, S. Dapprich, A. D. Daniels, M. C. Strain, O. Farkas, D. K. Malick, A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. V. Ortiz, Q. Cui, A. G. Baboul, S. Clifford, J. Cioslowski, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe, P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, C. Gonzalez, and J. A. Pople, Gaussian, Inc., Wallingford CT (2004).

Google Scholar

[83] R. O. Jones and O. Gunnarsson, The density functional formalism, its applications and prospects, Rev. Mod. Phys. 61(1989) 689-746.

DOI: 10.1103/revmodphys.61.689

Google Scholar

[84] A. Zupan, P. Blaha, K. Schwarz and J. P. Perdew, Pressure-induced phase transitions in solid Si, SiO2, and Fe: Performance of local-spin-density and generalized-gradient-approximation density functionals, Phys. Rev. B 58 (1998) 11266-11272.

DOI: 10.1103/physrevb.58.11266

Google Scholar

[85] J. Theilhaber, Quantum-molecular-dynamics simulations of liquid metals and highly degenerate plasmas, Phys. Fluids B 4 (1992) 2044-(2051).

DOI: 10.1063/1.860013

Google Scholar

[86] R. Stadler and M. J. Gillan, First-principles molecular dynamics studies of liquid tellurium, J. Phys.: Condens. Matter 12 (2000) 6053-6061.

DOI: 10.1088/0953-8984/12/28/304

Google Scholar

[87] N. Argaman and G. Makov, Density functional theory: An introduction, Am. J. Phys. 68 (2000) 69-79.

Google Scholar

[88] H. Xiao, J. T. Kheli, W. A. Goddard III, Accurate band gaps for semiconductors from density functional theory, J. Phys. Chem. Lett. 2 (2011) 212-217.

DOI: 10.1021/jz101565j

Google Scholar

[89] K. P. Huber and G. Herzberg, Constraints of Diatomic Molecules, Van Nostrand Reinhold Company, New York (1979).

Google Scholar

[90] V. Beutel, H. G. Kramer, G. L. Bhale, M. Kuhn, K. Weyers and W. Demtroder, High resolution isotope selective laser spectroscopy of Ag2 molecules, J. Chem. Phys. 98 (1993) 2699-2708.

DOI: 10.1063/1.464151

Google Scholar

[91] G. A. Bishea, J. C. Pinegar and M. D. Morse, The ground state and excited state d-hole states of CuAu, J. Chem. Phys. 95 (1991) 5630-5636.

DOI: 10.1063/1.461638

Google Scholar