Structural and electronic properties of thin chains of Ag Michael Springborg* Physical Chemistry, University of Saarland, 66123 Saarbru ¨cken, Germany Pranab Sarkar † Physical Chemistry, University of Saarland, 66123 Saarbru ¨cken, Germany and Department of Chemistry, Visva-Bharati University, Santiniketan, India Received 4 April 2003; published 31 July 2003 Results of first-principles, density-functional, full-potential calculations on four different types of chains linear, zig–zag, double-zig–zag, and tetragonal of Ag are reported. In particular, structural degrees of free- dom are optimized, and the band structures and electron densities reported and discussed. Some discrepancies with earlier theoretical works are found and it is suggested that the effects of an organic matrix, inside which Ag chains have been synthesized, are stronger than previously assumed. The bond lengths are found to be between those of the Ag 2 dimer and those of crystalline Ag, and for the nonlinear systems the bond angles are in all cases somewhat larger than 60°. All chains are found to be metallic, except for the linear chain where a bond-length alternation opens up a gap at the Fermi level. As expected, spin–orbit couplings have only minor effects on the results. DOI: 10.1103/PhysRevB.68.045430 PACS numbers: 61.46.+w, 68.65.La, 73.22.-f I. INTRODUCTION One of the central issues of chemistry, physics, and mate- rials science is to control, vary, exploit, and understand the dependence of materials properties on their structure and composition. With the development of experimental tech- niques for artificially producing low-dimensional materials new possibilities for varying the materials properties have opened up, and in some cases also new phenomena are ob- served that are absent in the materials found in Nature. Quantum dots form one class of such materials, as also do the materials of the present work, quantum wires. There are different ways of experimentally producing nanowires. In one approach, they are grown at steps on crys- tal surfaces, whereby the structure of the nanowires to a large extent is dictated by that of the underlying substrate. Alter- natively, they may be synthesized inside some crystalline host that contains sufficiently long and wide channels for hosting the nanowires. Also in this case the host material dictates partly the structure of the nanowire. Third, in break- junction experiments nanowires of limited length form the ultimate junction just before breaking. In this case, the struc- ture is rather an intrinsic property of the material of the nano- wire, but the nanowire is often of only very limited length. The present work was motivated by progress in the last two categories. Thus, ultrathin silver wires with a width of 0.4 nm were synthesized inside the pores of self-assembled calix4hydroquinone nanotubes by Hong et al. 1 By perform- ing a structural analysis, Hong et al. found that the structure of the Ag chain is related to the tetragonal structure of Fig. 1. Moreover, recently the intense research activity in break- junctions of Au was extended to other metals, including Ag. 2,3 In this case the structure of the nanowire is rather like that of the linear chain of Fig. 1. For the case of complete- ness we add that slightly thicker Ag nanowires have been considered by Tosatti et al. 4 and by Rodrigues et al. 5 The materials of those studies are, however, not the topic of the present work. Motivated by experimental work on Au nanojunctions 6,7 we have earlier studied the structural properties of a linear chain of Au atoms. 8 Moreover, in another work 9 we studied the different structures of Fig. 1 for chains of Tl, Pb, or Bi following an experimental work by Romanov 10 on the syn- thesis of such chains inside the channels of a zeolite. Thus, besides giving relevant and interesting information on the material of interest, Ag, the present study can be considered a very natural and relevant extension of our earlier studies on monatomic, metallic nanowires. We have applied a density-functional method for the infi- nite, periodic structures of Fig. 1. This method will be briefly outlined in Sec. II. The results are presented in Sec. III, and a brief summary is offered in Sec. IV. II. CALCULATIONAL DETAILS The computational method 11,12 we are using is based on the Hohenberg-Kohn density-functional formalism 13 in the formulation of Sham and Kohn. 14 The single-particle equa- tions h ˆ eff  i  r   -  2 2 m  2 +V  r   i  r = i  i  r 1 are solved by expanded the eigenfunctions in a set of aug- mented waves. These are spherical waves that inside non- overlapping, atom-centered, so-called muffin-tin spheres are augmented continuously and differentiably with numerically represented functions. The spherical waves are spherical Hankel functions times spherical harmonics, h l (1)   | r-R|  Y lm  r -R   , 2 where R specifies the atom where the function is centered, |  | is a decay constant (  is imaginary, and ( l , m ) describes PHYSICAL REVIEW B 68, 045430 2003 0163-1829/2003/684/0454305/$20.00 ©2003 The American Physical Society 68 045430-1