Understanding the H 2 Sorption Trends in the M-MOF-74 Series (M = Mg, Ni, Co, Zn)

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1 Understanding the H 2 Sorption Trends in the M-MOF-74 Series (M = Mg, Ni, Co, Zn) Tony Pham, Katherine A. Forrest, Rahul Banerjee, Gisela Orcajo, Juergen Eckert, and Brian Space, Department of Chemistry, University of South Florida, 4202 East Fowler Avenue, CHE205, Tampa, FL , United States Physical/Materials Chemistry Division, CSIR-National Chemical Laboratory, Dr. Homi Bhabha Road, Pune , India Department of Chemical and Energy Technology, ESCET, Rey Juan Carlos University, C/Tulipán s/n, Móstoles, Madrid, Spain brian.b.space@gmail.com S1 Grand Canonical Monte Carlo Simulations of H 2 sorption in Mg-MOF-74, Ni-MOF-74, Co-MOF-74, and Zn-MOF-74 were performed using grand canonical Monte Carlo (GCMC) on a unit cell system of the respective MOFs. This method constrains the chemical potential (µ), volume (V ), and temperature (T ) of the MOF sorbate system to be constant while allowing other thermodynamic quantities to fluctuate. 1 The simulation involves randomly inserting, deleting, translating, or rotating a sorbate molecule with acceptance or rejection based on a random number generator scaled by the energetic favorability of the move. For each MOF, a macroscopic MOF environment was approximated by periodic boundary conditions with a spherical cutoff corresponding to half the shortest system cell dimension length. All MOF atoms were constrained to be rigid for the simulations. In GCMC, the average particle number was calculated by the following expression: 2,3 N = 1 Ξ { 3N e βµn N=0 i=1 } dx i Ne βu(x1,...x 3N ) (1) where Ξ is the grand canonical partition function, β is the quantity 1/kT (k is the Boltzmann constant), and U is the total potential energy. The chemical potential for hydrogen was determined using the BACK equation of state. 4 The total potential energy of the MOF sorbate system was calculated by summing the repulsion/dispersion energy, the electrostatic energy, and the many-body polarization energy. Once N was calculated, it was converted to a value that can be compared with experimentally. For the simulations of H 2 sorption at the temperatures considered in this work, quantum mechanical dispersion effects were included semiclassically through Feynman-Hibbs corrections to the fourth order according to the following equation: 5 U F H = U + (U β 2 + 2r ) 24µ U + β2 4 ( µ 2 r 3 U + 4 ) r U + U (2) where is the reduced Planck s constant and the primes indicate differentiation with respect to pair separation r. Note, in equation 2, µ corresponds to the reduced mass. The isosteric heat of adsorption (Q st ) values were calculated based on the fluctuations in the particle number and the total potential energy in the system through the following expression: 6 NU N U Q st = N 2 N 2 + kt (3) For all state points considered in each MOF, the simulations consisted of Monte Carlo steps to guarantee equilibration, followed by an additional steps to sample the desired thermodynamic properties. Simulations involving many-body polarization utilized a correlation time of steps in order to produce uncorrelated equilibrium configurations. All simulations were performed using the Massively Parallel Monte Carlo (MPMC) code, 7 which is currently available for download on Google Code.

2 S2 Many-Body Polarization An overview of the Thole-Applequist type polarization model 8 11 used in this work is given here. The induced dipole, µ, at site i can be calculated using the following equation: µ i = α i E stat i N T ij µ j (4) where αi represents the atomic point polarizability, E i stat is the static electric field felt at site i due to the presence of the MOF atoms and the sorbate molecules, µ j represents the induced dipole at site j, and T αβ ij is the dipole field tensor which is defined from first-principles as the following: 8 j i T αβ ij = α β 1 r ij (5) = δαβ r 3 ij 3xα x β r 5 ij where r ij is the distance between sites i and j. Equation 4 is a self-consistent field equation with respect to the dipoles and thus, the quantity µ i must be solved for using iterative methods for large systems. The iterative method employed herein was the Gauss Seidel relaxation technique. 12 This method consists of updating the current dipole vector set for the k th iteration step as the new dipole vectors become available via the following: 13 (6) µ k i = α i E stat i j i ˆT ij µ k 1+ζ j (7) ζ = { 0, if i < j 1, if i > j (8) In this equation, ˆT ij is the modified dipole field tensor that accounts for short range divergences in the polarization model, defined as: ˆT αβ ij = δ αβ r 3 ij [ 1 ( λ 2 r 2 ij 2 + λr ij + 1 ) e λrij ] 3xα x β r 5 ij [ 1 ( λ 3 r 3 ij 6 + λ2 r 2 ij 2 + λr ij + 1 ) e λrij ] (9) where λ is a parameter damping the dipole interactions near the regions of discontinuity. A value of was used for λ in this work, which is consistent with the work performed by B. Thole. 9 The many-body polarization energy for the MOF H 2 system was calculated by the following based on the work of Palmo and Krimm: 16 Upol k = 1 µ k i 2 i E stat i 1 2 µ k i i E k+1 i (10) Thus, the polarization energy was determined from the k th iteration dipoles and the (k + 1) th induced field.

3 S3 Lattice Parameters Table S1. The lattice parameters for the crystal structures of M-MOF-74 (M = Mg, Ni, Co, Zn) used in this work. The parameters for the crystal structures were taken from the Cambridge Structural Database (CSD). 17 Lattice Parameter Mg-MOF-74 Ni-MOF-74 Co-MOF-74 Zn-MOF-74 a (Å) b (Å) c (Å) α ( ) β ( ) γ ( )

4 S4 Hydrogen Potentials Table S2. Parameters used to characterize the H 2 potentials used in this work: Buch model, 18 Belof Stern Space (BSS) model, 19 Darkrim-Levesque (DL) model, 20 and polarizable Belof Stern Space Polar (BSSP) model. 19 COM corresponds to the center-of-mass site, H corresponds to the atomic locations of the hydrogen atoms, and PS corresponds to the phantom sites. Model Atomic Site r (Å) ɛ (K) σ (Å) q (e ) α (Å 3 ) Buch COM COM BSS H PS DL COM H COM BSSP H PS

5 S5 Quantum Rotation Calculations The two-dimensional quantum rotational levels for a hydrogen molecule sorbed about the M 2+ ion in each member of the M-MOF-74 series (M = Mg, Ni, Co, Zn) were calculated by diagonalizing the rotor Hamiltonian in the spherical harmonic basis, Y jm, which is the following: Ĥ = Bj 2 + V (θ, φ) (11) where B is the rotational constant for molecular hydrogen, which is equal to approximately K, 21 j 2 is the angular momentum operator, and V (θ,φ) is the potential energy surface for the rotation of the hydrogen molecule with its center-ofmass held fixed within the MOF H 2 system. Each matrix element, Y jm V (θ,φ) Y jm, was constructed using Gauss-Legendre quadrature 22 with a basis set consisting of ±m functions. 13 The potential was generated over a quadrature grid. The kinetic energy term, j(j + 1), was then added to the diagonal elements. The matrix was diagonalized using the LAPACK linear algebra package, 23 yielding the rotational energy eigenvalues and the eigenvector coefficients. All two-dimensional rotational levels were calculated with j = 7, leading to 64 basis functions. All calculations were performed using the MPMC code. 7

6 S6 H 2 Sorption Results in Mg-MOF-74 (a) (b) (c) Figure S1. Low-pressure (up to 1.0 atm) absolute H 2 sorption isotherms in Mg-MOF-74 at (a) 77 K and (b) 87 K for experiment (black), Buch model (blue), BSS model (green), DL model (orange), and BSSP model (red). (c) Isosteric heats of adsorption, Q st, for H 2 in Mg-MOF-74 plotted against hydrogen uptakes. The experimental data for Mg-MOF-74 were taken from reference 24.

S7 Figure S2. Molecular illustration of a sorbed H 2 molecule onto the Mg 2+ ion in Mg-MOF-74 as determined from simulation. The sorbate molecule is shown in orange.

7 S7 Figure S2. Molecular illustration of a sorbed H 2 molecule onto the Mg 2+ ion in Mg-MOF-74 as determined from simulation. The sorbate molecule is shown in orange. The Mg 2+ COM(H 2) distance was observed to be Å from simulated annealing. Atom colors: C = cyan, H = white, O = red, Mg = gray. Figure S3. The normalized H 2 dipole distribution for the BSSP model in Mg-MOF-74 at 77 K and various pressures.

8 S8 H 2 Sorption Results in Ni-MOF-74 (a) (b) (c) Figure S4. Low-pressure (up to 1.0 atm) absolute H 2 sorption isotherms in Ni-MOF-74 at (a) 77 K and (b) 87 K for experiment (black), Buch model (blue), BSS model (green), DL model (orange), and BSSP model (red). (c) Isosteric heats of adsorption, Q st, for H 2 in Ni-MOF-74 plotted against hydrogen uptakes. The experimental data for Ni-MOF-74 were taken from reference 24.

S9 Figure S5. Molecular illustration of a sorbed H 2 molecule onto the Ni 2+ ion in Ni-MOF-74 as determined from simulation. The sorbate molecule is shown in orange.

9 S9 Figure S5. Molecular illustration of a sorbed H 2 molecule onto the Ni 2+ ion in Ni-MOF-74 as determined from simulation. The sorbate molecule is shown in orange. The Ni 2+ COM(H 2) distance was observed to be Å from simulated annealing. Atom colors: C = cyan, H = white, O = red, Ni = lavender. Figure S6. The normalized H 2 dipole distribution for the BSSP model in Ni-MOF-74 at 77 K and various pressures.

10 S10 H 2 Sorption Results in Co-MOF-74 (a) (b) (c) Figure S7. Low-pressure (up to 1.0 atm) absolute H 2 sorption isotherms in Co-MOF-74 at (a) 77 K and (b) 87 K for experiment (black), Buch model (blue), BSS model (green), DL model (orange), and BSSP model (red). (c) Isosteric heats of adsorption, Q st, for H 2 in Co-MOF-74 plotted against hydrogen uptakes. The experimental data for Co-MOF-74 were taken from reference 24.

S11 Figure S8. Molecular illustration of a sorbed H 2 molecule onto the Co 2+ ion in Co-MOF-74 as determined from simulation. The sorbate molecule is shown in orange.

11 S11 Figure S8. Molecular illustration of a sorbed H 2 molecule onto the Co 2+ ion in Co-MOF-74 as determined from simulation. The sorbate molecule is shown in orange. The Co 2+ COM(H 2) distance was observed to be Å from simulated annealing. Atom colors: C = cyan, H = white, O = red, Co = silver. Figure S9. The normalized H 2 dipole distribution for the BSSP model in Co-MOF-74 at 77 K and various pressures.

12 S12 H 2 Sorption Results in Zn-MOF-74 (a) (b) (c) Figure S10. Low-pressure (up to 1.0 atm) absolute H 2 sorption isotherms in Zn-MOF-74 at (a) 77 K and (b) 87 K for experiment (black), Buch model (blue), BSS model (green), DL model (orange), and BSSP model (red). (c) Isosteric heats of adsorption, Q st, for H 2 in Co-MOF-74 plotted against hydrogen uptakes. The experimental data for Zn-MOF-74 were taken from reference 25.

S13 Figure S11. Molecular illustration of a sorbed H 2 molecule onto the Zn 2+ ion in Zn-MOF-74 as determined from simulation. The sorbate molecule is shown in orange.

13 S13 Figure S11. Molecular illustration of a sorbed H 2 molecule onto the Zn 2+ ion in Zn-MOF-74 as determined from simulation. The sorbate molecule is shown in orange. The Zn 2+ COM(H 2) distance was observed to be Å from simulated annealing. Atom colors: C = cyan, H = white, O = red, Zn = silver. Figure S12. The normalized H 2 dipole distribution for the BSSP model in Zn-MOF-74 at 77 K and various pressures.

14 S14 Inelastic Neutron Scattering Details For Zn-MOF-74 Inelastic neutron scattering (INS) spectra for Zn-MOF-74 were collected at a temperature of 10 K on the QENS spectrometer at the Intense Pulsed Neutron Source (IPNS) of Argonne National Laboratory. Successive loading of the material with amounts of H 2 related to the number of moles of metal sites in the sample was carried out in situ at 77 K after first obtaining a spectrum of the blank sample. The sample was equilibrated after loading before cooling to the data collection temperature of 10 K. The spectra shown in Figure 13 were obtained by subtracting the blank spectrum. Figure S13. Inelastic neutron scattering (INS) spectra for H 2 in Zn-MOF-74 at different loadings: 0.5 H 2/Zn (black), 1.0 H 2/Zn (red), 1.5 H 2/Zn (violet), 2.0 H 2/Zn (blue), and 2.5 H 2/Zn (maroon). The spectra were collected at T = 10 K on the QENS spectrometer at IPNS.

15 S15 Additional H 2 Sorption Results Figure S14. Percent contributions of energy components in Mg-MOF-74 (red), Ni-MOF-74 (blue), Co-MOF-74 (violet), and Zn- MOF-74 (green) at 77 K and pressures up to 1.0 atm, with solid lines corresponding to van der Waals (vdw) contributions, dashed lines corresponding to electrostatic (Elec) contributions, and squares corresponding to polarization (Pol) contributions.

16 S16 (a) (b) (c) Figure S15. Low-pressure (up to 1.0 atm) absolute H 2 sorption isotherms in Mg-MOF-74 (red) and Ni-MOF-74 (blue) at (a) 77 K and (b) 87 K for experiment (solid lines) and simulations in which the proper polarizability was used for the metal ion (squares) or in control cases where a different polarizability was used (triangles). (c) Isosteric heats of adsorption, Q st, for H 2 plotted against hydrogen uptakes. The experimental data for Mg-MOF-74 and Ni-MOF-74, and Co-MOF-74 were taken from reference 24.

17 S17 1 Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. N.; Teller, A. H.; Teller, E. Physics Letters B 1953, 21, McQuarrie, D. A. Statistical Mechanics; University Science Books: Sausalito, CA, 2000; pp Frenkel, D.; Smit, B. Understanding Molecular Simulation: From Algorithms to Applications; Academic Press: New York, 2002; pp Boublík, T. Fluid Phase Equilibria 2005, 240, Feynman, R. P.; Hibbs, A. R. Quantum Mechanics and Path Integrals; McGraw-Hill: New York, 1965; pp Nicholson, D.; Parsonage, N. G. Computer Simulation and the Statistical Mechanics of Adsorption; Academic Press: London, 1982; pp Belof, J. L.; Space, B. Massively Parallel Monte Carlo (MPMC). Available on Google Code, Applequist, J.; Carl, J. R.; Fung, K.-K. Journal of the American Chemical Society 1972, 94, Thole, B. Chemical Physics 1981, 59, Bode, K. A.; Applequist, J. The Journal of Physical Chemistry 1996, 100, McLaughlin, K.; Cioce, C. R.; Pham, T.; Belof, J. L.; Space, B. The Journal of Chemical Physics 2013, 139, Dinh, T.-L.; Huber, G. A. Journal of Mathematical Modelling and Algorithms 2005, 4, Belof, J. L. Theory and simulation of metal organic materials and biomolecules. Ph.D. thesis, University of South Florida, Belof, J. L.; Stern, A. C.; Eddaoudi, M.; Space, B. Journal of the American Chemical Society 2007, 129, , PMID: Forrest, K. A.; Pham, T.; McLaughlin, K.; Belof, J. L.; Stern, A. C.; Zaworotko, M. J.; Space, B. The Journal of Physical Chemistry C 2012, 116, Palmo, K.; Krimm, S. Chemical Physics Letters 2004, 395, Allen, F. H. Acta Crystallographica Section B: Structural Science 2002, 58, Buch, V. The Journal of Chemical Physics 1994, 100, Belof, J. L.; Stern, A. C.; Space, B. Journal of Chemical Theory and Computation 2008, 4, Darkrim, F.; Levesque, D. The Journal of Chemical Physics 1998, 109, Bigeleisen, J.; Mayer, M. G. Journal of Chemical Physics 1947, 15, Abramowitz, M. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables 1965, Chapt. 25, Sect. 4, pg Anderson, E.; Bai, Z.; Dongarra, J.; Greenbaum, A.; McKenney, A.; Du Croz, J.; Hammerling, S.; Demmel, J.; Bischof, C.; Sorensen, D. LAPACK: A portable linear algebra library for high-performance computers. Proceedings of the 1990 ACM/IEEE conference on Supercomputing. 1990; pp Dietzel, P. D. C.; Georgiev, P. A.; Eckert, J.; Blom, R.; Strassle, T.; Unruh, T. Chemical Communications 2010, 46, Rowsell, J. L. C.; Yaghi, O. M. Journal of the American Chemical Society 2006, 128, , PMID:

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