Structural and Electronic Effects on the Properties of Fe 2 (dobdc) upon Oxidation with N 2 O

Transcription

1 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-1 Structural and Electronic Effects on the Properties of Fe (dobdc) upon Oxidation with N O oshua Borycz, 1, oachim Paier, 3,* Pragya Verma, 1, Lucy E. Darago,,4 Dianne. Xiao,,4 Donald G. Truhlar, 1,, * effrey R. Long,,4-6 and Laura Gagliardi 1,, * 1 Department of Chemistry, Minnesota Supercomputing Institute, and Chemical Theory Center, University of Minnesota, 07 Pleasant Street SE, Minneapolis, Minnesota , USA. Nanoporous Materials Genome Center, University of Minnesota, 07 Pleasant Street SE, Minneapolis, Minnesota , USA. 3 Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, Germany. 4 Department of Chemistry, University of California, Berkeley, California , USA. Department of Chemical and Biomolecular Engineering and Chemistry, University of California, Berkeley, California , USA. 6 Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 9470, USA. * To whom the correspondence should be addressed: gagliardi@umn.edu, joachim.paier@chemie.hu-berlin.de, truhlar@umn.edu

2 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S- Table of Contents 1. Lattice Parameters S-. Equilibrium Structure Comparison S-3 3. Convergence Tests and Grids S-4 4. Elastic Properties S-6. Infrared Spectra S-8 6. Orbital Projected Density of States (OP-DOS) S-9 7. Magnetic constants computed assuming z = 3 S Doubled Unit Cell Calculations S Cluster Calculations S Optimized Periodic Structures (VASP Format) S- 11. Cluster Model Structures (xyz Format) S-4 1. Charges and spin populations S Curie-Weiss Fit S References S-9 1. Lattice Parameters Table S1: Lattice parameters for Fe (dobdc), Fe (O) (dobdc), and Fe (OH) (dobdc). method a (Å) b (Å) c (Å) α ( ) β ( ) γ ( ) volume (Å 3 ) Fe (dobdc) PBE PBE+U PBE+U+D HSE HSE+D Expt. a Fe (O) (dobdc) PBE PBE+U PBE+U+D HSE HSE+D Fe (OH) (dobdc) PBE PBE+U PBE+U+D HSE HSE+D Expt. a a Taken from ref 1.

3 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-3. Equilibrium Structure Comparison Table S gives the equilibrium structures of the three MOFs studied here. In the case of Fe (dobdc) there is good agreement between the bond distances and angles computed with all the methods and experiment, with the exception of PBE, which significantly underestimates the Fe Fe distances and the Fe O c Fe angle. These findings are expected based on previous calculations with PBE and Fe (dobdc)., 3 The good agreement of GAM+U, PBE+U, and HSE06 for Fe (dobdc) is quite encouraging. Table S shows that after oxidation to Fe(III), the experimental Fe Fe distance increases by Å. If we ignore PBE due its clear underestimation of the Fe Fe distance in Fe (dobdc), the density functional calculations predict that there is an increase in the Fe Fe distance between 0. and 0.8 Å. This consistency indicates that the geometrical parameters are predicted reasonably accurately. The comparison of theory and experiment may be complicated by the presence of Fe(II) in the experimental Fe (OH) (dobdc) sample, leading to structural disorder of the Fe(II) and Fe(III) sites. The discrepancies may also be the result of the structural averaging that takes place when performing refinements from X-ray powder diffraction data. For the Fe(IV) case, the various calculations are in good agreement with one another, but there is no experimental data for comparison. The only structural parameter that is improved significantly by including Hartree Fock exchange is the unit cell volume (Table S1). Changes in the equilibrium volumes are small upon inclusion of molecular mechanics damped dispersion ( 0.% to 1%). This is reasonable based on the strong covalent bonds making up these MOFs. Volumes obtained using HSE06 are approximately % to 3% smaller than the volumes obtained using PBE+U.

4 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-4 Table S: Bond distances and angles for the nearest-neighbor iron and oxygen atoms in Fe (dobdc), Fe (O) (dobdc), and Fe (OH) (dobdc) computed using periodic DFT. All geometries presented were optimized in the FM spin state. Fe Fe Fe O Fe O a1 Fe O a Fe O b Fe O c1 Fe O c Fe O a Fe Fe O c Fe method length (Å) angle (deg.) Fe(II) case: Fe (dobdc) PBE PBE+U PBE+U-D HSE HSE06-D GAM+U Expt. (PXRD) a Fe(III) case: Fe (OH) (dobdc) PBE PBE+U PBE+U-D HSE HSE06-D GAM+U Expt.(PXRD) b Expt.(EXAFS) b c Fe(IV) case: Fe (O) (dobdc) PBE PBE+U PBE+U-D HSE HSE06-D GAM+U a ref 1, 4 b ref 1 c Average equatorial Fe-O distance 3. Convergence Tests and Grids For the PBE+U calculations, Table S3 reports our findings showing that the energies and structural parameters of Fe (dobdc) are well converged using a x x 4 k-point grid. For the HSE06 calculations, we did a number of separate tests to check convergence of the energy with respect to the number of k-points used to sample the Fock potential. To reduce the computational cost we tested the effect of reducing the k-point grid for the Fock potential to 1 x 1 x. 6 For Fe (dobdc), this resulted in a total energy change of 0.08 ev in the ferromagnetically (FM) ordered case. For the antiferromagnetically (AFM) ordered Fe (O) (dobdc) we found a change in energy of only ev with a 1 x 1 x k-point mesh. Thus, the HSE06 calculations employ the full k-point mesh for Fe (dobdc) and a reduced mesh for Fe (O) (dobdc) and Fe (OH) (dobdc). The grid reduction was not performed for Fe (dobdc) because it has unique metamagnetic character 7 that requires a dense k-point grid to

5 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S- be modeled accurately. For the density of states (DOS) calculations the number of grid points was increased to 001 with the NEDOS tag in VASP, and single-points were performed on the optimized PBE+U and HSE geometries. Table S3: Convergence of total energies and structural parameters of Fe (dobdc) with respect to the number of k-points to sample the BZ. Method: Dudarev s 8 DFT+U (PBE+U, U = ev; energy cut-off = 00 ev; ISIF = 3). #k points E 0 /UC [ev] a [Å] b [Å] c [Å] α [ ] β [ ] γ [ ] V UC [Å 3 ] 1x1x xx xx x4x

6 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-6 4. Elastic Properties 4.1. Methods The bulk modulus measures the response of a crystal to uniform pressure, i.e. the hardness of the material. The bulk moduli of each species were computed with PBE+U by incrementally expanding and shrinking the unit cell and optimizing the ionic positions. A total of eleven points were used for each volume scan (±30% of the equilibrium volume), and the computed curves were used to fit the Birch-Murnaghan equation of state (BM-EOS). 9 The bulk modulus and third-order BM-EOS are defined by the equations, = = (S1) (S) where V is the deformed volume, V 0 is the equilibrium volume, P is pressure, and B 0 is the first derivative of the bulk modulus with respect to pressure. The BM-EOS is commonly used to compute the bulk moduli of MOFs, and can provide a reasonable estimate of the relative hardness of the materials studied as well as an indication of the accuracy of the computed unit cell volumes, because it provides an estimation of the effect of anharmonicity. 4.. Results The curves used to predict the bulk moduli of the studied species are provided in Figure S1, and the ground state unit cell volumes and bulk moduli are presented in Table S4. The BM- EOS and PBE+U computed unit cell volumes are within Å 3 ( 0.4%), i.e. a perfect match, in the case of Fe (dobdc). These volumes are within 0 Å 3 ( +1.%) for Fe (O) (dobdc) and Fe (OH) (dobdc). Volumes obtained using BM-EOS for Fe (O) (dobdc) and Fe (OH) (dobdc) are larger than the volumes optimized using the stress tensor, and hence indicate some degree of anharmonicity in the E(V) curve shown in Figure S1. Since the bulk modulus is a measure of the pressure needed to change the unit cell volume, it was expected that adding O and OH to Fe (dobdc) would result in larger bulk moduli values.

7 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-7 Figure S1: Bulk moduli of Fe (dobdc) and Fe (OH) (dobdc) computed using PBE+U and using the BM-EOS. Note that Fe (O) (dobdc) curves are not shown for clarity. The energy of the equilibrium geometry was set to zero. Table S4: Minimum volumes and bulk moduli of Fe (dobdc), Fe (O) (dobdc), and Fe (OH) (dobdc) as predicted by PBE+U and by the BM-EOS. VASP V 0 (Å 3 ) BM V 0 (Å 3 ) B 0 (GPa) Fe (dobdc) Fe (O) (dobdc) Fe (OH) (dobdc)

8 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-8. Infrared Spectra Figure S: Above are the experimental and theoretical infrared spectra of Fe (dobdc) and below are the same for Fe (OH) (dobdc). All spectra were normalized based on the highest peak. The experimental spectra were taken from ref 1. To test the effect that freezing the carbon atoms has on the IR spectra, each plot shows the spectrum resulting from the vibrations of Fe and O and that arising from the vibrations of Fe, O, and Ca. The C a O stretches seem to have a negligible effect on the Fe O stretches and bends. For both Fe (dobdc) and Fe (OH) (dobdc) there are two C O peaks that are red-shifted from experiment by approximately 1 cm 1. When C a was unfrozen these peaks shifted towards the organic C O region and a new C C stretch appeared in the aromatic region).

9 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-9 6. Orbital Projected (Local) Density of States (OP-DOS) The OP-DOS comparison between Fe (dobdc), Fe (O) (dobdc), and Fe (OH) (dobdc) at the PBE+U level is provided in Figure S3. The same comparison with HSE06 is provided in Figure S4. Figure S shows the projection of an (Fe O) unit in both Fe (dobdc) and Fe (O) (dobdc). Figure S3. PBE+U orbital projected densities of states of (a) Fe (dobdc), (b) Fe (O) (dobdc), and (c) Fe (OH) (dobdc) in their respective ground spin state. Densities given as positive are those for the majority spin, and densities shown as negative are those for the minority spin.

10 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-10 Figure S4. HSE06 orbital projected densities of states of (a) Fe (dobdc), (b) Fe (O) (dobdc), and (c) Fe (OH) (dobdc) in their respective ground spin states (see Table 1). Densities given as positive are those for the majority spin, and densities shown as negative are those for the minority spin. Figure S: OP-DOS of an (Fe O) unit in Fe (dobdc) (upper panel) and Fe (O) (dobdc) (lower panel).

11 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-11 By virtue of the very good agreement between PBE+U and HSE06 structural parameters, we found that it is efficient to simply rescale the volume by a factor of 0.97 in total, in particulr by 0.99 in each of the spatial directions, and do single-point HSE06 calculations on top of the rescaled PBE+U structures to compute the HSE06 magnetic coupling parameters. DOS obtained using this protocol agree well with the OP-DOS obtained by the more computationally expensive full optimizations using HSE06. The Fe (dobdc) OP- DOS for the ferromagnetic (FM), intrachain antiferromagnetic (AFM1), and interchain antiferromagnetic (AFM) spin states with both PBE+U and an HSE single-point upon scaling to PBE+U volume to the HSE optimized volume are provided in Figures S6-S8. The same quantities for Fe (O) (dobdc) and Fe (OH) (dobdc) are provided in Figures S9-S11 and S1-S14, respectively. Figure S1 shows a comparison of the Fe (dobdc), HSE OP-DOS with the HSE OP-DOS of the PBE+U geometry scaled to the HSE unit cell volume. Figure S16 shows the same for Fe (O) (dobdc). Figure S6: FM-ordered Fe (dobdc) OP-DOS.

12 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-1 Figure S7: AFM1-ordered Fe (dobdc) OP-DOS. Figure S8: AFM-ordered Fe (dobdc) OP-DOS.

13 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-13 Figure S9: FM-ordered Fe (O) (dobdc) OP-DOS. Figure S10: AFM1-ordered Fe (O) (dobdc) OP-DOS.

14 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-14 Figure S11: AFM-ordered Fe (O) (dobdc) OP-DOS. Figure S1: FM-ordered Fe (OH) (dobdc) OP-DOS.

15 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-1 Figure S13: AFM1-ordered Fe (OH) (dobdc) OP-DOS. Figure S14: AFM-ordered Fe (OH) (dobdc) OP-DOS. Fe (dobdc):

16 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-16 Figure S1: Upper panel: HSE OP-DOS at the corresponding fully optimized structure (+ volume) of Fe (dobdc) in FM ordering. Lower panel: HSE OP-DOS performed on PBE+U optimized coordinates that were scaled to the HSE unit cell volume. Fe (O) (dobdc) Figure S16: Upper panel: HSE OP-DOS at the corresponding fully optimized structure (+ volume) of Fe (O) (dobdc) in AFM ordering. Lower panel: HSE OP-DOS performed on PBE+U optimized coordinates that were scaled to the HSE unit cell volume.

17 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S Magnetic coupling values computed assuming z = 3 Table S: Periodic DFT isotropic exchange and coupling energies of the iron centers for each studied MOF. The NN and IC coupling values represent the nearest-neighbor and the interchain metal-metal couplings, respectively. All coupling values were extracted using geometries optimized with the FM spin state. method E AFM1 E b FM / b E AFM E FM NN ( NNN ) z IC b E AFM3 E FM cm 1 Fe(II) case: Fe (dobdc) PBE PBE+U-108 b 6.6/ (0.3) 1.9 PBE+U PBE+U-D HSE HSE06-D Expt. a Fe(III) case: Fe (OH) (dobdc) PBE PBE+U-13 b 316.0/ ( 1.1) 6.3 PBE+U PBE+U-D HSE HSE06-D Fe(IV) case: Fe (O) (dobdc) PBE PBE+U-10 b 0.6/ ( 0.9) 1.3 PBE+U PBE+U-D HSE HSE06-D a Taken from ref 7. b E FM is the electronic energy of the ferromagnetic state, E AFM1 is the electronic energy of antiferromagnetic state 1, and E AFM is the electronic energy of antiferromagnetic state.

18 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S Doubled Unit Cell Calculations Figure S17 provides a picture of the Fe (dobdc) extended unit cell (supercell with 108 atoms) as well as the spin states computed to extract the magnetic coupling values. Equations S3-S6 are the Heisenberg-Dirac-Van Vleck (HDV) Hamiltonian equations for the extended unit cell calculations. The terms of the equations are similar to the ones described in the main paper. In particular this section assumes the full interchain coupling model. Figure S17: Extended unit cell (108 atoms) and spin configurations used to compute the magnetic coupling values of Fe (dobdc), Fe (O) (dobdc), and Fe (OH) (dobdc) at the PBE+U level. This unit cell is double the size of the primitive unit cell (4 atoms) along the c-axis. Blue atoms are iron, red are oxygen, gray are carbon, and white are hydrogen. Red and blue circles indicate the upward or downward spin of the high-spin iron ions. The entirely ferromagnetic (FM), intrachain antiferromagnetic (AFM1), interchain antiferromagnetic (AFM), and nearest-neighbor antiferromagnetic (AFM3) spin states were considered with this unit cell. Equations for computing the values of the 108-atom cell of Fe (dobdc) and the 10-atom cell of Fe (O) (dobdc) are shown below:, H HDV, = E, = [1 NN +1 NNN +1 IC ], H HDV, = E, = [ 1 NN +1 NNN +6 IC ], H HDV, = E, = [ 4 NN 4 NNN +1 IC ], H HDV, = E, = [1 NN +1 NNN 1 IC ] (S11) IC = 1 19 E E,,

19 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-19 NN = 1 19 E, E, 1 4 IC NNN = 1 18 E, E, NN (S1) Equations for computing the values of the doubled cell of Fe (OH) (dobdc) are shown below: ] 1 1 [1,, IC NNN NN, HDV + + = = E H ] [,, IC NNN NN, HDV + + = = E H ] [,, IC NNN NN, HDV + = = E H ] 18 1 [1,, IC NNN NN, HDV + = = E H (S13) [ ],, IC E E = [ ] IC,, NN E E = [ ] NN,, NNN 00 1 E E = (S14)

20 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-0 9. Cluster Calculations Three iron cluster models The coordinates for the cluster models used to compute the nearest-neighbor coupling values are provided in Section S1. The equations used to compute the NN coupling values are provided by eqs S1 and S16. The equations for the Fe (dobdc) and Fe (O) (dobdc) three iron cluster model are, HHDV = E= [ NN ] HHDV = E = [ NN ] NN = 1 [ 3 E E ] (S1) and the equations used for Fe (OH) (dobdc) are, H H NN HDV HDV = 1 0 E = E = [ = E = [ E NN NN ] ] (S16) The equations used to extract both NN and NNN coupling values using the cluster models are as follows: For Fe (dobdc) and Fe (O) (dobdc), H HDV = E = [ NN1 + NN + NNN ] H HDV = E = [ NN1 NN NNN ] H HDV = E = [ NN1 NN + NNN ] H HDV = E = [ NN1 + NN NNN ] (S17) NN1 = 1 3 [ E E + E E ] [ E E ] NN = 16 NN1

21 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S-1 ] [ 1 NN NN1 NN + = [ ] NN NNN E E = (S18) For Fe (OH) (dobdc) they are, ] [ NNN NN NN1 HDV + + = = E H ] [ NNN NN NN1 HDV = = E H ] [ NNN NN NN1 HDV + = = E H ] [ NNN NN NN1 HDV + = = E H (S19) + = NN1 0 1 E E E E + = NN1 NN 16 1 E E ] [ 1 NN NN1 NN + = = NN NNN 16 1 E E (S0) NN1 and NN refer to the two nearest-neighbor interactions in the cluster models. NN is obtained by taking average of NN1 and NN.

22 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S- Two iron cluster models The equations used to compute only NN coupling values are provided by eqs S1 and S. The equations for the Fe (dobdc) two iron cluster model is, NN = 1 16 E E (S1) The equations for the Fe (OH) (dobdc) two iron cluster model is, NN = 1 E E (S)

23 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S Optimized Periodic Structures (VASP Format) Fe (dobdc)-hse O C H Fe Direct

24 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S Fe (dobdc)-hse-d O C H Fe Direct

25 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S Fe (dobdc)-pbe O C H Fe Direct

26 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S Fe (dobdc)-pbe+u

27 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S O C H Fe Direct

28 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S Fe (dobdc)-pbe+u-d O C H Fe Direct

29 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S Fe (O) (dobdc)-hse O O C H Fe Direct

30 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S

31 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S Fe (O) (dobdc)-hse-d O O C H Fe Direct

32 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S Fe (O) (dobdc)-pbe O O C H Fe Direct

33 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S Fe (O) (dobdc)-pbe+u

34 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S O O C H Fe Direct

35 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S Fe (O) (dobdc)-pbe+u-d O O C H Fe Direct

36 Supporting information for paper in Inorganic Chemistry, April 11, 016, page S Fe (OH) (dobdc)-hse O O C H Fe Direct