Tight-binding studies of bulk properties and hydrogen vacancies in KBH 4 A. Shabaev a , Khang Hoang a,b , D.A. Papaconstantopoulos a,⇑ , M.J. Mehl c , N. Kioussis d a Computational Materials Science Center, George Mason University, Fairfax, VA 22030, USA b Center for Computationally Assisted Science and Technology, North Dakota State University, Fargo, ND 58108, USA c Center for Computational Materials Science, Naval Research Laboratory, Washington, DC 20375, USA d Department of Physics, California State University, Northridge, CA 91330, USA article info Article history: Received 5 December 2012 Received in revised form 24 June 2013 Accepted 28 June 2013 Available online 19 August 2013 Keywords: Tight binding First principles Hydrogen storage Potassium borohydride Hydrogen vacancies abstract We present computational studies of the bulk properties and hydrogen vacancies in KBH 4 using tight- binding (TB) calculations. The NRL-TB method was used to construct a TB Hamiltonian by fitting the den- sity-functional theory (DFT) data for the electronic energies for the tetragonal and cubic phases of KBH 4 as a function of volume. Our approach allows for computationally efficient calculations of phonon fre- quencies and elastic constants, mean-square displacements, and formation energies of hydrogen vacan- cies using the static and molecular dynamics modules of the NRL-TB code. We find that the results for the bulk properties and hydrogen vacancies given by TB calculations are comparable to those given by DFT calculations. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction In the search for hydrogen storage materials, alkali borohy- drides (MBH 4 ; M = Li, Na, K) are especially attractive because of the light weight and high number of hydrogen atoms per metal atom [1]. These materials, however, have high thermodynamic sta- bility and exhibit limitations in hydrogen kinetics and/or revers- ibility, making them not very suitable for practical applications [2]. Computational studies of the structural, electronic, elastic, vibrational, and dynamic properties and the energetics of native defects are therefore needed in order to better understand the fun- damental properties of these complex hydrides and their hydrogen kinetics [3–9]. In this paper we focus on a tight-binding parametrization of KBH 4 using the Naval Research Laboratory tight-binding (NRL-TB) scheme [10,11]. In Section 2 we give the basic equations used in the NRL-TB method and discuss details of the procedure we fol- lowed to fit to a database of density-functional theory (DFT) results obtained with a pseudopotential code. Previously we had used lin- earized augmented plane wave (LAPW) results to derive a tight- binding Hamiltonian for palladium (Pd) and palladium–hydrogen systems (PdH x ) [12,13]. In these works, we showed that the NRL- TB scheme works well for a transition-metal-based hydride sys- tem, reproducing the LAPW total energies and band structures and extending to molecular dynamics (MD) simulations of large systems going beyond the standard capabilities of DFT. A tight-binding formulation of a borohydride such as KBH 4 pre- sents a challenge because it is a light and soft material with ener- getic differences as a function of volume that are very small. This requires a substantially lower target for root mean square (rms) fit- ting errors than those that were adequate for PdH x . KBH 4 is known to have a low temperature (LT) tetragonal phase which transforms into a high temperature (HT) partially filled face-centered cubic (fcc) phase at 65–70 K [14]. We performed DFT calculations as a function of volume for both the tetragonal and cubic phases and used them as an input to derive our TB parameters. Although the NRL-TB scheme can be applied with a non-orthogonal basis, the re- sults presented in this paper are using an orthogonal basis. We chose the orthogonal Hamiltonian in order to reduce the number of TB parameters and because we found that in this case non- orthogonality did not give us any significant improvement of the fit. Our TB matrix contains the K 4s orbital, the B 2p orbitals, and the H 1s orbital, hence we diagonalize an 8  8 matrix per formula unit which makes the calculation very fast despite the fact that we are using close to 1000 atoms in our MD simulations. Our TB re- sults reproduce the total energies of both the LT and HT phases very well as a function of volume, and produce an excellent agree- ment with independent (not included in the fit) results of the pho- non frequencies. Also our study of hydrogen vacancies gives a good agreement with separate DFT calculations. In general our DFT re- sults used in the TB fitting are consistent with those found by other groups [14–20]. 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.06.055 ⇑ Corresponding author. Tel.: +1 703 993 3624; fax: +1 703 993 9300. E-mail address: dpapacon@gmu.edu (D.A. Papaconstantopoulos). Computational Materials Science 79 (2013) 888–895 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci