ORIGINAL PAPER Electronic structure and stabilities of Ni-doped germanium nanoclusters: a density functional modeling study Kapil Dhaka & Ravi Trivedi & Debashis Bandyopadhyay Received: 19 June 2012 / Accepted: 12 November 2012 # Springer-Verlag Berlin Heidelberg 2012 Abstract The present study reports the geometry, elec- tronic structure, growth behavior and stability of neutral and ionized nickel encapsulated germanium clusters containing 1–20 germanium atoms within the frame- work of a linear combination of atomic orbital density functional theory (DFT) under a spin polarized gener- alized gradient approximation. In the growth pattern, Ni-capped Ge n and Ni-encapsulated Ge n clusters appear mostly as theoretical ground state at a particular size. To explain the relative stability of the ground state clusters, variation of different parameters, such as aver- age binding energy per atom (BE), embedding energy (EE) and fragmentation energy (FE) of the clusters, were studied together with the size of the cluster. To explain the chemical stability of the clusters, different parameters, e.g., energy gap between the highest occu- pied and lowest unoccupied molecular orbitals (HO- MO– LUMO gap), ionization energy (IP), electron affinity (EA), chemical potential (μ), chemical hardness (η), and polarizability etc. were calculated and are dis- cussed. Finally, natural bond orbital (NBO) analysis was applied to understand the electron counting rule applied in the most stable Ge 10 Ni cluster. The impor- tance of the calculated results in the design of Ge-based superatoms is discussed. Keywords Clusters and nanoclusters . Binding energy . Density functional theory . Electron affinity . Embedding energy . Ionization potential Introduction The study of the electronic structure and properties of nano- clusters is an extremely active area of research due to its importance in nanoscience and nanotechnology. In the past 10–12 years, a considerable amount of research has focused on semiconductor based nanomaterials [1–8]. Recently, small and medium size metal encapsulated semiconductor clusters have been investigated due to the potential interest of the physical and chemical processes taking place at the metal–semiconductor interface [9–13]. In general, pure semiconductor clusters are chemically reactive [14] and it is a challenging job to model and verify experimentally physically and chemically stable semiconductor nanoclus- ters. Among different possibilities, encapsulation of a tran- sition metal (TM) in a pure semiconductor cage-like structure is currently the most popular and effective method. Such clusters enhance stability because the TM atom absorbs the dangling bonds present on the semiconductor cages [15, 16]. Simultaneously, the cluster exhibits a wide range of electronic properties by varying the doping ele- ments. The first experimental contribution to this field was made by Beck [17, 18], who used a laser vaporization supersonic expansion technique and found that TMs such as Cr, Mo W, etc., in Si clusters enhanced the stability of the doped clusters. Hiura et al. [7] reported the formation of a series of Si cages with TM atoms Hf, Ta, W, Re, Ir, etc. Ohara et al. [19] used photoelectron spectroscopy and a chemical-probe method to study the geometric and electron- ic structures of negatively charged Tb doped Si n clusters, and found that Tb atom always remains encapsulated inside the Si clusters of size n 0 10. Recently, Bandyopadhyay [20–28] reported an extensive study of the electronic struc- ture, growth behavior, and different physical and chemical properties of pure and TM-doped semiconductor nanoclus- ters (TM@M, TM0 Ti, Zr, Hf, Ni, Cu, Sc and V, M0 Si or K. Dhaka : R. Trivedi : D. Bandyopadhyay (*) Department of Physics, Birla Institute of Technology and Science, Pilani, Rajasthan 333031, India e-mail: debashis.bandy@gmail.com J Mol Model DOI 10.1007/s00894-012-1690-y