SCC-DFTB Parametrization for Boron and Boranes Bernhard Grundkö tter-Stock, † Viktor Bezugly, ‡,§ Jens Kunstmann, ‡ Gianaurelio Cuniberti, ‡,§ Thomas Frauenheim, † and Thomas A. Niehaus* ,∥ † Bremen Center for Computational Materials Science, Universitä t Bremen, Am Fallturm 1, 28359 Bremen, Germany ‡ Institute for Materials Science and Max Bergmann Center of Biomaterials, Dresden University of Technology, 01062 Dresden, Germany § Division of IT Convergence Engineering, POSTECH, Pohang 790-784, Republic of Korea ∥ Department of Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany ABSTRACT: We present the results of our recent parametrization of the boron−boron and boron−hydrogen interactions for the self-consistent charge density-functional-based tight-binding (SCC-DFTB) method. To evaluate the performance, we compare SCC-DFTB to full density functional theory (DFT) and wave-function-based semiempirical methods (AM1 and MNDO). Since the advantages of SCC-DFTB emerge especially for large systems, we calculated molecular systems of boranes and pure boron nanostructures. Computed bond lengths, bond angles, and vibrational frequencies are close to DFT predictions. We find that the proposed parametrization provides a transferable and balanced description of both finite and periodic systems. 1. INTRODUCTION Since the discovery of the element boron, the structural features of pure boron and boron hydrogen systems have been investigated intensely due to their distinction from the bonding situation found in organic compounds and related systems. 1−3 The diversity is attributed to the electron poorness of boron, meaning that the number of valence orbitals exceeds the number of valence electrons, giving rise to bonds formed by two electrons between three centers, so-called 2e3c bonds. One of the best known examples of this bonding scheme is found in diborane, B 2 H 6 , whose structure was subject to discussion for some time. 4 But also in other structures, uncommon bonding situations are found, so the whole series of boranes and borates are not properly described by Lewis structures but by concepts developed by Lipscomb, Wade, and Williams. 5−8 In addition to these fascinating molecular systems, stable quasi-planar and tubular clusters of elemental boron were first predicted 9,10 and later observed experimentally. 11−13 On the basis of these findings, the existence of more complex pure boron nanostructures like boron fullerenes, 14,15 nanotubes, and two-dimensional sheets has been predicted. 16−21 These nanostructures are expected to have interesting properties for application in future nanoscaled devices. Recently, first successes in the synthesis and characterization of boron nanotubes 22−24 and the first hints on their real atomic structure and electronic properties 23,25 have been reported. Also, in its bulk phases, boron exhibits a remarkable complexity. All elemental bulk modifications are based on a three-dimensional framework of slightly distorted B 12 icosahedra. The currently known elemental bulk phases are α-rhombohedral (α-B 12 ), 26,27 β-rhombohedral, 28 β-tetragonal, 29 and the γ-orthorhombic (γ- B 28 ) phases. 30−32 In all of these phases, boron is superhard and has semiconducting properties. Given that the structural features of these systems are outstanding and the size of nanostructures favor computation- ally less demanding methods than ab initio schemes, we propose here a parametrization for the boron−boron and boron−hydrogen interactions in the SCC-DFTB method. 33−35 This approximate DFT scheme is shortly introduced in section 2, which also contains computational details and information on the protocol followed to generate the present para- metrization. The results in section 3 cover both finite molecular systems and periodic nanostructures to illustrate the trans- ferability of the approach. A detailed comparison with respect to DFT and semiempirical methods applicable to boron systems is then provided, which is summarized in section 4. 2. METHODS 2.1. Density Functional-Based Tight Binding (DFTB). The SCC-DFTB method has already been the subject of several reviews 36,37 and will be described here only briefly. In order to derive the scheme, the total energy of DFT, which is a functional of the electron density n(r ⃗ ), is expanded up to second order around a given reference density n 0 (r ⃗ ) with n(r ⃗ )= n 0 (r ⃗ )+ δn(r ⃗ ): 35 ∬ ∫ ∬ ∑ = ⟨Ψ| ̂ |Ψ⟩ − ⃗ ⃗ ′ |⃗− ⃗′| ⃗ ′ ⃗ + − ⃗ ⃗ ⃗+ + |⃗− ⃗′| − δ δ ⃗ δ ⃗′ ×δ ⃗ δ ⃗′ ⃗ ⃗′ ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ E Hn n r n r r r r r E n V n r n r r E r r E nr nr nr nr r r [ ] 1 2 () ( ) d d [ ] [ ]( ) ()d 1 2 1 () ( ) () ( )d d i i i n tot occ 0 0 0 xc 0 xc 0 0 ii 2 xc 0 (1) Here, H ̂ [n 0 ] is the usual Kohn−Sham Hamiltonian evaluated at the reference density. E xc and V xc denote the exchange- Received: October 13, 2011 Published: February 1, 2012 Article pubs.acs.org/JCTC © 2012 American Chemical Society 1153 dx.doi.org/10.1021/ct200722n | J. Chem. Theory Comput. 2012, 8, 1153−1163