J Supercond Nov Magn DOI 10.1007/s10948-017-4234-y ORIGINAL PAPER First-Principle Calculations of Structural, Elastic, and Electronic Properties of Intermetallic Rare Earth R 2 Ni 2 Pb (R = Ho, Lu, and Sm) Compounds Y. Benkaddour 1 · A. Abdelaoui 2 · A. Yakoubi 1 · H. Khachai 1 · Y. Al-Douri 3,4 · S. Bin Omran 5 · A. Shankar 6 · R. Khenata 7 · C. H. Voon 8 · Deo Prakash 8 · K. D. Verma 9,10 Received: 3 May 2017 / Accepted: 28 June 2017 © Springer Science+Business Media, LLC 2017 Abstract The structural, elastic, and electronic properties of rare earth intermetallic R 2 Ni 2 Pb (where R = Ho, Lu, and  Y. Al-Douri yaldouri@yahoo.com 1 Laboratoire d’ ´ Etude des Mat´ eriaux and Instrumentations Optiques, D´ epartement Mat´ eriaux and D´ eveloppement Durable, Facult´ e des Sciences Exactes, Universit´ e Djillali Liab` es de Sidi Bel Abb` es, 22000, Sidi Bel Abb` es, Algeria 2 Laboratoire Mat´ eriaux de l’Ecole Nationale Polytechnique d’Oran, 31000, Algiers, Algeria 3 Nanotechnology and Catalysis Research Center (NANOCAT), University of Malaya, 50603 Kuala Lumpur, Malaysia 4 Physics Department, Faculty of Science, University of Sidi-Bel-Abb` es, 22000, Sidi Bel Abb` es, Algeria 5 Department of Physics and Astronomy, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia 6 Department of Physics, Kurseong College, Darjeeling 734013, India 7 Laboratoire de Physique Quantique et de Mod´ elisation Math´ ematique (LPQ3M), D´ epartement de Technologie, Universit´ e de Mascara, 29000, Mascara, Algeria 8 Institute of Nano Electronic Engineering, University Malaysia Perlis, 01000 Kangar, Perlis, Malaysia 9 School of Computer Science and Engineering, Faculty of Engineering, SMVD University, Kakryal, Katra, J&K, 182320, India 10 Material Science Research Laboratory, Department of Physics, S. V. College, Aligarh, U.P. 202001, India Sm) compounds were investigated with the density func- tional theory (DFT) calculations. The calculations are per- formed using the full potential-linearized augmented plane wave (FP-LAPW) method within the framework of local density approximation (LDA). The calculated values of the equilibrium lattice constants were in agreement with the available experimental values. The elastic constants (C ij ) were also calculated to understand the mechanical proper- ties and structural stability of the compounds. Furthermore, the density of states and the charge density distributions of the compounds were calculated to understand the nature of the bonding in the material. The calculated results are in accordance with the available data in the literature. Keywords Intermetallic R 2 Ni 2 Pb compounds · Density functional theory · Crystal structure · Elastic constants · Electronic properties 1 Introduction Over the last few years, the intermetallic compounds with rare earth elements have become a subject of intensive studies due to their intriguing physical properties, which have promising potential in both fundamental and applied researches [1]. Gulay et al. [2–4] have synthesized a new series of ternary intermetallic compounds R 2 Ni 2 Pb (where R = Ho, Lu, and Sm). These plumbide 2-2-1 compounds crystallize in AlB 2 F 2 structure with space group, Cmmm [5]. In this space group (Cmmm) with the orthorhombic structure, all the R atoms are equivalent and occupy the same crystallographic position at 4(j ) (0, y 1 , 0.5). The R atoms are surrounded by non-magnetic elements in the crystal unit cell; however, there exists a significant crys- talline magnetic anisotropy in the compound. Whereas, the