We present wannier90, a program for calculating maximally-localised Wannier functions (MLWF) from a set of Bloch energy bands that may or may not be attached to or mixed with other bands. The formalism works by minimising the total spread of the MLWF in real space. This done in the space of unitary matrices that describe rotations of the Bloch bands at each k-point. As a result, wannier90 is independent of the basis set used in the underlying calculation to obtain the Bloch states. Therefore, it may be interfaced straightforwardly to any electronic structure code. The locality of MLWF can be exploited to compute band-structure, density of states and Fermi surfaces at modest computational cost. Furthermore, wannier90 is able to output MLWF for visualisation and other post-processing purposes. Wannier functions are already used in a wide variety of applications. These include analysis of chemical bonding in real space; calculation of dielectric properties via the modern theory of polarisation; and as an accurate and minimal basis set in the construction of model Hamiltonians for large-scale systems, in linear-scaling quantum Monte Carlo calculations, and for efficient computation of material properties, such as the anomalous Hall coefficient. wannier90 is freely available under the GNU General Public License from http://www.wannier.org/.

Abstractwannier90 is a program for calculating maximally-localised Wannier functions (MLWFs) from a set of Bloch energy bands that may or may not be attached to or mixed with other bands. The formalism works by minimising the total spread of the MLWFs in real space. This done in the space of unitary matrices that describe rotations of the Bloch bands at each kpoint. As a result, wannier90 is independent of the basis set used in the underlying calculation to obtain the Bloch states. Therefore, it may be interfaced straightforwardly to any electronic structure code. The locality of MLWFs can be exploited to compute band-structure, density of states and Fermi surfaces at modest computational cost. Furthermore, wannier90 is able to output MLWFs for visualisation and other post-processing purposes. Wannier functions are already used in a wide variety of applications. These include analysis of chemical bonding in real space; calculation of dielectric properties via the modern theory of polarisation; and as an accurate and

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Mechanochemical synthesis using CeCl 3 -MBH 4 (M = Li, Na or K) mixtures are investigated and produced a new compound, LiCe(BH 4 ) 3 Cl, which crystallizes in a cubic space group I4̅ 3m, a = 11.7204(2) Å. The structure contains isolated tetranuclear anionic clusters [Ce 4 Cl 4 (BH 4 ) 12 ] 4− with a distorted cubane Ce 4 Cl 4 core, charge-balanced by Li + cations. Each Ce atom coordinates three chloride ions and three borohydride groups via the η 3 −BH 3 faces, thus completing the coordination environment to an octahedron. Combination of synchrotron radiation powder X-ray diffraction (SR-PXD), powder neutron diffraction and density functional theory (DFT) optimization show that Li cations are disordered, occupying 2/3 of the 12d Wyckoff site. DFT calculation indicates that LiCe(BH 4 ) 3 Cl is stabilized by higher entropy rather than lower enthalpy, in accord with the disorder in Li positions. The structural model also agrees well with the very high lithium ion conductivity measured for LiCe(BH 4 ) 3 Cl of 1 × 10 −4 Scm −1 at T = 20°C. In situ SR-PXD reveals that the decomposition products consist of LiCl, CeB 6 and CeH 2 . The Sieverts measurements show that 4.7 wt % H 2 is released during heating to 500°C. After rehydrogenation at 400°C and p(H 2 ) = 100 bar for 24 h an amount of 1.8 wt % H 2 is released in the second dehydrogenation. The 11 B MAS NMR spectra of the central and satellite transitions for LiCe(B(D/H) 4 ) 3 Cl reveal highly asymmetric manifolds of spinning sidebands from a single 11 B site, reflecting dipolar couplings of the 11 B nuclear spin with the paramagnetic electron spin of the Ce 3+ ions.