Supporting Information Medel et al. 10.1073/pnas.1100129108 SI Materials and Methods Theoretical Method. First-principles electronic structure investigations were carried out using a molecular orbital approach within a gradient corrected density functional framework. The molecular orbitals are expressed as linear combinations of atomic orbitals formed via a combination of Gaussian functions centered at the atomic sites. The exchange-correlation contributions are included within a gradient corrected (GGA) density functional as proposed by Perdew et al. (1). The actual calculations were carried out using the deMon2k software (2). For all the atoms we employed the gradient corrected optimized double zeta valence polarized basis set (3) and the GEN-A2 auxiliary function set. The exchange-correlation potential was calculated via a numerical integration on an adaptive grid from the orbital density (4). To determine the geometry and spin multiplicity of the ground state, the configuration space was sampled by starting from several initial configurations and spin multiplicities and optimizing the geometry employing the quasi-Newton Levenberg– Marquardt method (5). All structures were fully optimized in delocalized redundant coordinates without imposing any symmetry constraints, to allow for full variational freedom. The molecular

geometries and orbitals were plotted using the Molekel software (6). To eliminate any uncertainty due to the choice of the basis set and the numerical procedure one additional complimentary scheme was used. All electron calculations were carried out, using the Naval Research Laboratory Molecular Orbital Library (NRLMOL) developed by Pederson and coworkers (7–9). Here the Hamiltonian matrix elements are evaluated by numerical integration over a mesh of points. The basis sets, built from a variable number of primitive Gaussians, are based on a total-energy minimization for free atoms and are optimized for all electron density functional calculations (9). The basis sets were supplemented with a diffuse d Gaussian to allow further variational freedom. For details of the codes and the basis sets, the reader is referred to earlier papers (7–9). In general we found a very good agreement between the deMon2k and NRLMOL calculations. The results presented in the paper are based on the deMon2k calculations, with the exception of the ðFeMg8 Þ2 dimer for which the ferromagnetic and antiferromagnetic states were calculated with the NRLMOL code.

1. Perdew JP, Burke K, Enzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865–3868. 2. Koster AM, et al., (2006) deMon2k, V. 2.3.6 (The deMon Developers Community, Cinvestav, Mexico), available at www.deMon-software.com. 3. Calaminici P, Janetzko F, Köster AM, Mejia-Olvera R, Zuniga-Gutierrez B (2007) Density functional theory optimized basis sets for gradient corrected functionals: 3d transition metal systems. J Chem Phys 126:044108. 4. Köster AM, Flores-Moreno R, Reveles JU (2004) Efficient and reliable numerical integration of exchange-correlation energies and potentials. J Chem Phys 121:681–690.

5. Reveles JU, Köster AM (2005) Geometry optimization in density functional methods. J Comput Chem 25:1109–1116. 6. Flükiger P, Lüthi HP, Portmann S, Weber J. (2000) Molekel 4.0 (Swiss National Supercomputing Centre CSCS, Manno, Switzerland). 7. Pederson MR, Jackson KA (1990) Variational mesh for quantum-mechanical simulations. Phys Rev B Condens Matter 41:7453–7461. 8. Jackson K, Pederson MR (1990) Accurate forces in a local-orbital approach to the local-density approximation. Phys Rev B Condens Matter 42:3276–3281. 9. Porezag D, Pederson MR (1999) Optimization of Gaussian basis sets for densityfunctional calculations. Phys Rev A 60:2840–2847.

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Fig. S1. The one electron energy levels and orbital wavefunction isosurfaces (isoval ¼ 0.01 a:u:) in the TMMg8 clusters. (A) TM ¼ Sc, (B) TM ¼ Ti, (C) TM ¼ V, and (D) TM ¼ Cr. The majority and minority levels are shown. Continuous lines correspond to the filled levels, whereas the dotted lines correspond to the unfilled states. For each level, the angular momentum and their occupancy has been marked. The 2D occupied energy levels are highlighted in a dotted red box.

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Fig. S2. The one electron energy levels and orbital charge wavefunction isosurfaces (isoval ¼ 0.01 a:u:) in the TMMg8 clusters. (E) TM ¼ Mn, (F) TM ¼ Fe, (G) TM ¼ Co, and (H) TM ¼ Ni. See caption of Fig. S1.

Fig. S3. The lowest energy structure and next spin isomer of the ðFeMg8 Þ2 dimer. (A) The antiferromagnetic (0 μB ) and (B) the ferromagnetic state (4 μB ) state. Arrows indicate the direction of Fe local spin moments.

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Fig. S4. The density of states for the lowest energy structure and next spin isomer of the ðFeMg8 Þ2 dimer. (A) The antiferromagnetic (0 μB ) and (B) the ferromagnetic (4 μB ) state. The Fermi level is marked with a dotted line.

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