Linker Functionalization in MIL-47(V)R MetalOrganic Frameworks: Understanding the Electronic Structure
CONTENTS S1. Computational details S1 S2. Structure information S2 S3. Atomic charges S3 S4. Electronic Structure S4 References S7 S1. COMPUTATIONAL DETAILS For the series of structures under study we perform ab-initio density functional theory (DFT) calculations within the projector augmented wave (PAW) method as implemented in the Vienna ab-initio Package (VASP) program using the generalized gradient approximation (GGA) functional as constructed by Perdew, Burke and Ernzerhof (PBE). 1-5 The
... of (PBE). 1-5 The plane wave kinetic energy cutoff is set to 500 eV. Due to the large difference in lattice vector lengths for the structures a Monkhorst-Pack special k-point grid of 2 × 2 × 6 k-points is used to sample the Brillouin zone. 6,7 Dispersive interactions, which play an important role in the flexibility of the crystal structure of MOFs, are included through the DFT-D method as suggested by Grimme et al., including Becke-Johnson damping.     . To obtain an accurate picture of the electronic structure, hybrid functional, HSE06+D, 12-14 calculations are performed on the PBE optimized geometries, as this was previously shown to give very accurate estimates of the experimental band gap in MOFs. 15 The atomistic model used in our DFT calculations consisted of a conventional unit cell containing four formula units (i.e. containing 72 to 88 atoms). Figure 1 shows a ball-and-stick representation of the large pore MIL-47(V) structure (a super cell is shown). Starting from the experimental lattice parameters and volumes the structures are optimized under the constraint of constant volume to allow for direct comparison to the experimental results. 7 Ionic positions and cell shape are optimized simultaneously using a conjugate gradient method, and convergence is set to the difference in energy between subsequent steps becoming smaller than 1.0 × 10 −7 eV. After full relaxation, the forces on the ions were found to be below 0.002 eV/Å. As each of the four vanadium atoms (two V atoms on each vanadyl chain in the conventional unit cell) contributes one unpaired electron to the system, and it is known that the configuration of these unpaired spins has a strong influence on the electronic structure and mechanical properties of flexible MOFs, 16 we considered two different spin configurations for each of the structures: the anti-ferromagnetic (AF) ground state configuration 17 and the ferromagnetic (FM) configuration. The presence of both configurations in experimental samples has been derived from X-Ray Diffraction data. 18 The different spin configurations are manually imposed upon initialization of the structure optimization by setting the initial magnetic moment for each atom in the cell (MAGMOM keyword). For each following calculation the atomic magnetic moments are checked, and it is verified that the imposed spin configuration is retained. If this is not the case, the magnetic moment is reinitialized and the structure optimization is continued from this point. The atomic charges of the systems are calculated using the iterative Hirshfeld-I approach 19 as implemented in our in house developed code HIVE. 20-22 Our implementation makes use of the grid stored (pseudo) electron density distributions which are standardly obtained from VASP. 21, 22 The atom centered spherical integrations are done using Lebedev-Laikov grids of 1202 grid points per shell, and a logarithmic radial grid. 23,24 The iterative scheme is considered converged when the largest difference in charge of a system atom is less than 1.0 × 10 −5 electron in two consecutive iterations.