Supplemental Material: Experimental and Theoretical Investigations of the Electronic Band Structure of Metal-Organic Framework of HKUST-1 Type

Transcription

1 Supplemental Material: Experimental and Theoretical Investigations of the Electronic Band Structure of Metal-Organic Framework of HKUST-1 Type Zhigang Gu, a Lars Heinke, a,* Christof Wöll a, Tobias Neumann, b Wolfgang Wenzel, b Qiang Li, b Karin Fink, b Ovidiu D. Gordan, c Dietrich R.T. Zahn, c a Institut für Funktionelle Grenzflächen (IFG), Karlsruher Institut für Technologie (KIT), Hermannvon-Helmholtz-Platz 1,76344 Eggenstein-Leopoldshafen, Germany b Institute of Nanotechnology (INT), Karlsruher Institut für Technologie (KIT), Hermann-von- Helmholtz-Platz 1,76344 Eggenstein-Leopoldshafen, Germany c Semiconductor Physics, Technische Universität Chemnitz, Chemnitz, Germany 1

2 Supplemental Material 1: VASP calculations on HKUST-1 For the calculation of the density of states (DOS), the Γ-point approximation was compared to a sampling of the Brillouin zone on a (5x5x5) Monkhorst and Pack 1 k-point mesh. The total energy differed by 0.01 ev and the DOS produced with both k-point mesh and Γ-point approximation were virtually identical, as expected because of the large primitive unit cell which contains six paddle wheel units. Accordingly, no band-dispersion is observed in the calculations. The energy cut-off of the planewave basis was set to 550 ev; for the fast Fourier transform (FFT) mesh, VASPs default settings from the PAW potentials were used. In order to account for the open shell character of the Cu-3d shells, we performed spin polarized calculations with Coulomb correction for the strongly correlated Cu-3d electrons (DFT+U, U=5eV; ref. 2 and the references therein). The antiferromagnetic coupling of the singly occupied Cu-3d orbitals was considered in the broken symmetry approach 3. DFT+U HSE DOS E Fermi E-E Fermi / ev Band Gap at Gamma point: 1.88 ev Band Gap at Gamma point: 3.76 ev = 0.29 ev = 0.19 ev Figure S1. Comparison of the density of states of HKUST-1 obtained with DFT+U and HSE06. The structure of the DOS is rather similar for both functionals. As expected the band gap is significantly increased for the hybrid functional HSE06. For the VASP calculations, the primitive unit cell containing six Cu pairs was used (in contrast to 24 Cu pairs in the cubic FCC unit cell). Therefore the energy difference between high spin and broken symmetry state should be approximately six times larger than in the cluster calculation. The value of this energy splitting depends strongly on the percentage of exact exchange in the functional. The energy difference per Cu pair obtained with HSE06 (0.031 ev) is in reasonable agreement with the B3LYP35 obtained in the cluster calculations (0.024 ev). As expected for GGAs the PBE value significantly overestimates the coupling. 2

3 Supplemental Material 2: Details of the cluster calculations The geometry of the BTC ion was taken from the crystal structure of the MOF. The positions of the hydrogen atoms were reoptimized yielding a C-H bond distance of 1.08 Å (0.93 Å in the X-ray structure). Neither the HOMO-LUMO gap nor the calculated excitation energies are influenced by more than 0.02 ev by the change of the C-H bond length. In model 1 (Fig. S2a), the point charges which mimic the Cu centers are positioned at a distance of 4.0 Å from the oxygen atoms in the molecular plane. This distance, which is larger than the O-Cu-distance in the MOF, was chosen to prevent the artificial delocalization of the electrons when the point charges are placed too close to the molecule itself as the partial charges represent only the attractive part of the Coulomb interaction. For model 2, where one Cu paddle wheel was included in the calculation (Fig. S2b), the positions of all H atoms were also optimized, while all other atom positions were taken from the crystal structure. Here, the Cu(II) ions at the other two carboxylate groups were replaced by Zn large core pseudopotentials with the effective charge reduced to The excitation energies of the BTC molecule were calculated using the program package Turbomole 4, employing the def2-tzvp basis set. The HOMO-LUMO gap and excitation energies at the level of the time-dependent DFT theory (TDDFT) 5-7 were calculated using different functionals: PBE for comparability to the VASP calculations and furthermore the B3-LYP functional, 8 and the B3-LYP with 35% Hartree-Fock exchange. In addition, Hartree-Fock (HF) as well as calculations with the approximate coupled-cluster singles-and-doubles model CC were performed for comparison. Excitation energies and HOMO-LUMO gaps obtained with different quantum chemical methods for model 1 (BTC linker with point charges) are summarized in Table S1. The most accurate value for the excitation energy is obtained by the CC2 calculations. In average, the CC2 energies are slightly underestimating the binding energies. 13 For the BTC linker, the values obtained with the hybrid functional B3-LYP and the B3-LYP35 functional (same as B3-lyp but with 35% Hartree-Fock exchange) are in reasonable agreement with the CC2 value of 4.75 ev. As expected, HF overestimates the excitation energies because of missing correlation while the GGA functional. On the other hand, PBE significantly underestimates the excitation energy as well as the HOMO-LUMO gap because of the self interaction error. 14 We conclude that B3-LYP35 is the best choice for all further calculations because it yields slightly larger excitation energies than CC2. The excitation energy determined with the PBE functional (3.41eV) approximately matches the band gap calculated for the periodic Zn model system (3.2 ev) but is much larger than the value obtained for HKUST-1 in the VASP calculations. The differences can be traced back to the empty Cu-3d orbitals.therefore, we continued the TD-DFT calculations on the excitation energy spectra on model 2 (Figure S2 b) where the Cu paddle wheel unit is included. 3

4 Figure S2. HKUST-1 cluster models. (a) In model 1, the BTC ion is charged with -3.0 unit charges. To compensate the net charge, point charges carrying +0.5 unit charges (indicated as grey spheres) were placed near the oxygen atoms in a distances of 4.0 Å. (b) Model 2 consists of a Cu paddle wheel connected to the BTC linker and three formate groups. The C atoms are plotted green, O red, H white, Cu orange, charges and Zn effective core potentials grey. Table S1: Band gap and excitation energy of the BTC molecule (model 1) calculated with different methods. Functional Excitation energy (TDDFT) HOMO-LUMO gap (DFT) PBE 3.41 ev 3.40 ev B3-LYP 4.41 ev 5.44 ev B3-LYP 35% HF 4.93 ev 6.92 ev HF 5.43 ev ev CC ev Figure S3. (a) Spin density of the broken symmetry state. Contour value At each of the Cu centers, one d- orbital is singly occupied. (b) and (c) In most excitations at low energies, electrons are excited from occupied orbitals into the two singly occupied d-orbitals. 4

5 Supplemental Material 3: CASSCF calculations on the d-d excitations The calculations were performed with the Bochum CASSCF program 15. Model 2 (Fig. S2b) was simplified by substituting the carboxylate groups of the BTC linker which are not coordinated to the paddle wheel by hydrogen atoms and removing the point charges. The def2-tzvp basis set was applied on Cu and O while the C and H atoms were described by an SV basis set. In the active space, five 3d-orbitals at each Cu were taken into account. The orbitals were obtained by a state average calculation on the lowest 25 singlet states. These are all singlet states with 9 electrons at each Cu. Table S2: Energies of the CASSCF states in Hartree No energy spin oscillator strength

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7 Supplemental Material 4: Density of states and band structure of a Zn model system In order to highlight the role of the open shell character of the Cu-3d orbitals, additional calculations were performed on a model system where Cu was substituted by Zn. It should be noted that this Zn- HKUST-1 structure is a hypothetical structure which could not yet been synthesized as stable MOF. The band structure was calculated using VASP with the same protocol as for the Cu-MOF (except for the k-point setting) on 10 points along the high symmetry lines of the Brillouin zone of the Fm-3m space group from the L-point (0.5, 0.5, 0.5) over the Γ-point (0,0,0) and the X-point (0,1,0) to the W- point (0.5,1,0). The Brillouin zone was sampled on a (6x6x6) Monkhorst and Pack 1 k-point mesh. For density of states (DOS) calculations, the super-cells were sampled on weighted and Γ-centered k-points along the reciprocal lattice vectors. For the energy cut-off of the plane-wave basis and the fast Fourier transform (FFT) mesh, VASPs default settings from the PAW potentials supplied by VASP were used. The resulting DOS displayed in Fig. S4 shows similarities to the DOS calculated for HKUST-1, except for the missing first excitation of the Cu 3d orbitals. In addition to the DOS, the structure of the bands above the Fermi level were calculated (3.0 ev to 3.5 ev) and is displayed in Fig. S5. In this case, the dispersion of the band is below 0.1 ev, which is very small compared to the standard semiconductor silicon. The insulating behaviour of HKUST-1 MOFs (without any guest molecules), resulting from the large band gap and the flat band structure, was also found in conduction experiments. 16,17 Figure S4: DOS of a model system where Cu was replaced by Zn. Orange: total DOS. Blue: Zn bands. Green: Zn d-bands. The Zn 3d-bands are fully occupied. A band gap of 3.2 ev was observed. 7

8 Figure S5. Calculated band structure of the Zn model system of HKUST-1. The bands close to the Fermi level are rather flat (as shown in the inset). The band gap results to 3.2 ev. References H.J. Monkhorst and J.D. Pack, Physical Review B 13 (12), 5188 (1976). Z. Jiang, W. Zhang, W. Shangguan et al., The Journal of Physical Chemistry C 115 (26), (2011). L. Noodleman, The Journal of Chemical Physics 74 (10), 5737 (1981). R. Ahlrichs, M. Bär, M. Häser et al., Chemical Physics Letters 162 (3), 165 (1989). J.P. Perdew, K. Burke, and M. Ernzerhof, Physical Review Letters 77 (18), 3865 (1996). F. Weigend and R. Ahlrichs, Physical Chemistry Chemical Physics 7 (18), 3297 (2005). J.P. Perdew, K. Burke, and M. Ernzerhof, Physical Review Letters 78 (7), 1396 (1997). A.D. Becke, The Journal of Chemical Physics 98 (7), 5648 (1993). O. Christiansen, H. Koch, and P. Jorgensen, Chemical Physics Letters 243 (5-6), 409 (1995). C. Hattig and A. Kohn, Journal of Chemical Physics 117 (15), 6939 (2002). C. Hattig and F. Weigend, Journal of Chemical Physics 113 (13), 5154 (2000). F. Weigend, M. Haser, H. Patzelt et al., Chemical Physics Letters 294 (1-3), 143 (1998). A. Hellweg, S.A. Gruen, and C. Haettig, Physical Chemistry Chemical Physics 10 (28), 4119 (2008). J.P. Perdew, Chemical Physics Letters 64 (1), 127 (1979). U. Meier and V. Staemmler, Theoret. Chim. Acta 76 (2), 95 (1989). 8

9 16 17 A. Dragässer, O. Shekhah, O. Zybaylo et al., Chemical Communications 48 (5), 663 (2012). A.A. Talin, A. Centrone, A.C. Ford et al., Science 343 (6166), 66 (2014). 9