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1 Electronic Supplementary Material (ESI) for CrystEngComm. This journal is The Royal Society of Chemistry 2014 Electronic Supplementary Information Configurational and energetical study of the (100) and (110) surfaces of the MgAl 2 O 4 spinel by means of quantum-mechanical and empirical techniques Francesco Roberto Massaro, 1 Marco Bruno, 2 Fabrizio Nestola 1 1 Dipartimento di Geoscienze Università di Padova, via G. Gradenigo 6, I Padova, Italy 2 Dipartimento di Scienze della Terra - Università di Torino, via Valperga Caluso 35, I Torino, Italy. (100) configurations cut1 Figure S1. The (100) cell configuration of the cut1. Blue is for Mg ion. The symmetry elements (the two-fold axes and the m planes) are reported as well. cut2 1 cut2 2 cut2 3 1
2 cut2 1 cut2 2 cut2 3 cut2 a1 cut2 a2 cut2 a3 cut2 b1 cut2 b2 cut2 b3 cut2 c1 cut2 c2 cut2 c3 cut2 d1 cut2 d2 cut2 d3 2
3 cut2 a1 cut2 a2 cut2 a3 cut2 b1 cut2 b2 cut2 b3 cut2 c1 cut2 c2 cut2 c3 cut2 d1 cut2 d2 cut2 d3 cut2 e1 cut2 e2 cut2 e3 3
4 cut2 f1 cut2 f2 cut2 f3 cut2 g1 cut2 g2 cut2 g3 cut2 a1 cut2 a2 cut2 a3 cut2 b1 cut2 b2 cut2 b3 cut2 c1 cut2 c2 cut2 c3 4
5 cut2 d1 cut2 d2 cut2 d3 Figure S2. The fifty-one (100) cell configurations of the cut2. The colors stand: red for the O bonded to Mg (O1), purple for the O bonded only to Al (O2) and greenish for the Al. The symmetry elements (the two-fold axes and the m planes) are reported as well. 5
6 (110) configurations cut1 Figure S3. The (110) cell configuration of the cut1. The colors stand: red for the O bonded to Mg (O1), purple for the O bonded only to Al (O2), greenish for the Al and blue for the Mg ions. The m plane is reported as well. cut2 1 cut2 2 cut2 3 cut2 1 cut2 2 cut2 3 6
7 cut2 a1 cut2 a2 cut2 a3 cut2 b1 cut2 b2 cut2 b3 cut2 c1 cut2 c2 cut2 c3 cut2 d1 cut2 d2 cut2 d3 7
8 cut2 a1 cut2 a2 cut2 a3 cut2 b1 cut2 b2 cut2 b3 cut2 c1 cut2 c2 cut2 c3 cut2 d1 cut2 d2 cut2 d3 8
9 cut2 e1 cut2 e2 cut2 e3 cut2 f1 cut2 f2 cut2 f3 cut2 g1 cut2 g2 cut2 g3 cut2 h1 cut2 h2 cut2 h3 9
10 cut2 a1 cut2 a2 cut2 a3 cut2 b1 cut2 b2 cut2 b3 cut2 c1 cut2 c2 cut2 c3 cut2 d1 cut2 d2 cut2 d3 Figure S4. The fifty-four (110) cell configurations of the cut2. The colors stand: red for the O bonded to Mg (O1), purple for the O bonded only to Al (O2), greenish for the Al and blue for the Mg ions. The symmetry elements (the two-fold axes and the m planes) are reported as well. 10
11 Computational details (CRYSTAL09) The ab initio CRYSTAL09 code 1,2 was employed, which implements the Hartree-Fock and Kohn- Sham self-consistent field (SCF) method for the study of periodic systems. 3 The crystal surfaces were simulated by using the 2D periodic slab model, consisting of a film formed by a set of atomic layers parallel to the hkl crystalline plane of interest. 4 All the calculations were performed at the DFT (Density Functional Theory) level. In the Density Functional approach, the B3LYP Hamiltonian was adopted, 5-7 which contains a hybrid Hartree-Fock/Density-Functional exchange term and already shown to provide accurate results for structural and dynamical properties of garnet end members. 8 In CRYSTAL the multi-electronic wave-function is constructed as an anti-symmetrized product (Slater determinant) of mono-electronic crystalline orbitals (COs) which are linear combinations of local functions (i.e.: atomic orbitals, AOs) centered on each atom of the crystal. In turn, AOs are linear combinations of Gaussian-type functions (GTF, the product of a Gaussian times a real solid spherical harmonic to give s-, p- and d-type AOs). In this study, two different Gaussian basis sets reproducing the multi-electronic wave-function were adopted: (i) BS1, where aluminum, oxygen, and magnesium were described by (8s)-(511sp)-(1d), (8s) (411sp) (1d), and (8s) (511sp) (1d) contractions, respectively; 9,10 (ii) BS2, with aluminum, oxygen, and magnesium described by (73211s)-(5111p)-(1d), (6211s)-(411p)-(1d) and (73211s)-(511p)-(1d) contractions, respectively. 11 The thresholds controlling the accuracy in the evaluation of Coulomb and exchange integrals (ITOL1, ITOL2, ITOL3, ITOL4 and ITOL5, see Dovesi et al. 2 ) were set to 10-8 (ITOL1 to ITOL4) and (ITOL5). The threshold on the SCF energy was set to 10-8 Hartree. In the adopted package the DFT exchange and correlation contributions are evaluated by numerically integrating functions of the electron density and of its gradient over the cell volume. The choice of the integration grid is based on an atomic partition method, originally developed by Becke. 12 In the present study, a pruned (75, 974) p grid was adopted (XLGRID in the code 2 ), which ensured a satisfactory accuracy in the numerically integrated electron charge density (the error is on the order of e on a total of 1120 e for all the considered surfaces). The reciprocal space was sampled according to a Monkhorst-Pack mesh 13 with shrinking factor 6, corresponding to 20 k points in the first irreducible Brillouin zone in both slabs e bulk, respectively. Structures were optimized by using the analytical energy gradients with respect to atomic coordinates and lattice parameters within a quasi-newton scheme, combined with the Broyden- Fletcher-Goldfarb-Shannon scheme for Hessian updating Convergence was checked on energy, gradient components and nuclear displacements. The threshold on energy between two subsequent 11
12 optimization steps was set to 10 7 Hartree; the thresholds on the root-mean-square of the gradient components and of the nuclear displacements were set to Hartree bohr -1 and bohr, respectively; those on the maximum components of the gradients and displacements were set to Hartree bohr -1 and bohr, respectively. References 1 R. Dovesi, R. Orlando, B. Civalleri, C. Roetti, V.R. Saunders, C.M. Zicovich-Wilson, Z. Kristallogr, 2005, 220, R. Dovesi et al., CRYSTAL09 User s Manual; University of Torino: Torino, Italy, C. Pisani, R. Dovesi, C. Roetti, Hartree-Fock ab-initio treatment of crystalline systems, Lecture Notes in Chemistry; Springer: Berlin, Heidelberg, New York, R. Dovesi, B. Civalleri, R. Orlando, C. Roetti, V.R. Saunders, In: Reviews in Computational Chemistry; B.K. Lipkowitz, R. Larter, T.R. Cundari Eds.; John Wiley & Sons, Inc.: New York, 2005, vol.1, p A.D. Becke, J. Chem. Phys., 1993, 98, C. Lee, W. Yang, R.G. Parr, Phys. Rev. B, 1998, 37, P.J. Stephens, F.J. Devlin, C.F. Chabalowski, M.J. Frisch, J. Phys. Chem., 1994, 98, R. Dovesi, M. De La Pierre, A.M. Ferrari, F. Pascale, L. Maschio, C.M. Zicovich-Wilson, American Mineralogist, 2011, 96, Y. Noel, M. Catti, P. D Arco, R. Dovesi, Phys. Chem. Min., 2006, 33, R. Demichelis, B. Civalleri, M. Ferrabone, R. Dovesi, Int. J. Quantum Chem., 2010, 110, M.F. Peintinger, D. Vilela Oliveira, T. Bredow, J. Comput. Chem., 2013, 34, A.D. Becke, Phys. Rev. A, 1998, 38, H.J. Monkhrost, J.D. Pack, Phys. Rev. B, 1976, 8, B. Civalleri, Ph. D Arco, R. Orlando, V.R. Saunders, R. Dovesi, Chem. Phys. Lett., 2001, 348, K. Doll, Comp. Phys. Commun., 2001, 137, K. Doll, V.R. Saunders, N.M. Harrison, Int. J. Quantum. Chem., 2001, 82, 1. 12
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