Geometric and electronic properties of titanium clusters studied by ultrasoft pseudopotential Jijun Zhao a, * , Qi Qiu a , Baolin Wang b , Jinlan Wang b , Guanghou Wang b a Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3255, USA b National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, People's Republic of China Received 11 December 2000; received in revised form 5 January 2001; accepted 31 January 2001 by H. Akai Abstract The structural and electronic properties of titanium clusters are studied by the plane-wave ultrasoft pseudopotential method with the generalized gradient approximation. The equilibrium geometries Ti n (n  2±14, 19, 55) clusters are determined by optimizing the bond length of various structural isomers under a symmetric constraint. Pentagonal growth patterns are found for small Ti n clusters and the theoretical binding energies are in reasonable agreement with experimental results on Ti n 1 . The electron density of state of Ti n clusters shows a rapid convergency towards bulk bands, which agrees with the photoelectron spectra of Ti clusters. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: A. Nanostructures; D. Electronic band structures; E. Photoelectron spectroscopies PACS: 36.40.Cg; 36.40.Mr; 71.24. 1 q The structures and properties of transition metal clusters have been intensively studied during the past two decades [1±6]. It is of fundamental importance to illustrate the evolution from the molecular to bulk behavior with increas- ing cluster size. Due to the existence of d electrons, the physical and chemical properties of transition-metal (TM) clusters show remarkable size-dependent variations that cannot be explained by the shell model of s valence elec- trons [7]. Instead, the in¯uence of d electrons as well as geometric effects such as a coordination number must be considered [4±6]. Among the 3d TM clusters, the atomic structures and physical properties of titanium clusters are much less studied and understood. The outer electron con®guration of free Ti atom is 3d 2 4s 2 . With only two 3d electrons, the electronic structures of Ti cluster are expected to be different from those of the later 3d TM clusters. Besides the homonuclear Ti dimer [1,8,9], experimental studies on titanium clusters include only collision-induced dissociation on Ti n 1 (n  2±22) [10], size-selected anion photoelectron spectra of Ti n 2 (n  3±65) [11], and time of ¯ight mass spectrometry of Ti n with up to 30 atoms [12]. Although there are certain differences in the structures and electronic properties between neutral clusters and cluster ions, experi- mental conditions in mass spectrometric studies can still roughly re¯ect the properties of neutral clusters. From the mass spectra [12] and bond energies [10], the `magic number' cluster ions with signi®cant high stability are found at Ti 7 1 , Ti 13 1 , Ti 19 1 , Ti 25 1 , which implies a pentagonal growth pattern of the corresponding neutral clusters. Photo- electron spectra of Ti n show that the 3d band emerges at n  8 and then gradually broadens and evolves towards the bulk band [9]. On the theoretical side, within our knowledge, there are no accurate quantum chemistry studies on the electronic properties of Ti clusters except for a very early extended Hu Èckel molecular orbital calculations for Ti 2±6 [13]. Thus, ®rst-principles calculation is important to illustrate the structural and electronic properties of Ti clusters. In this paper, we report our density functional results on the electronic properties of Ti n up to 55 atoms. Density functional electronic calculations on Ti n (n  2± 14, 19, 55) clusters have been performed by using the Solid State Communications 118 (2001) 157±161 0038-1098/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S0038-1098(01)00044-8 PERGAMON www.elsevier.com/locate/ssc * Corresponding author. Tel.: 11-919-962-1386; fax: 11-919- 962-0480. E-mail address: zhaoj@physics.umc.edu (J. Zhao).