Towards More Complete Descriptors of Reactivity in Catalysis by Solid Acids

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1 Supporting Information Towards More Complete Descriptors of Reactivity in Catalysis by Solid Acids Prashant Deshlahra 1 1, 2, * and Enrique Iglesia 1 Department of Chemical Engineering, University of California at Berkeley, and 2 Chemical Sciences Division, E.O. Lawrence Berkeley National Laboratory Berkeley, CA S1. Details of density functional theory (DFT) methods Periodic gradient-corrected DFT as implemented in Vienna ab initio Simulation Package (VASP) S1 was used to optimize structures and calculate energies of bare and deprotonated POM and MFI clusters, intermediates and transition states (for H + shuttling, CH 3 OH dehydration, C 3 H 6 methyl-shift and C 6 H 10 ring contraction) on these acids, and isolated cationic forms of the transition states. The plane wave basis set with energy cutoff of 396 ev was used to describe valence electrons along with ultrasoft pseudopotentials S2 to describe electron-core interactions. Calculations were performed using PW91 functional and using vdw-df2 method S3 of Langreth et al., S4 which implements the rpw86 exchange functional S5 and also includes van der Waals interactions. POM and MFI clusters were simulated inside cubic periodic supercells of edge lengths 2 nm and 2.5 nm, respectively k-point mesh was used to sample the first Brillouin zone. Charged supercells corresponding to cation and anion systems were simulated using a compensating uniform charge that allows maintaining overall charge-neutrality required in periodic calculations. The interactions of this uniform charge distribution with that of cations and anion were removed using energy corrections implemented within VASP. S6 Dipole/quadrupole * To whom correspondence should be addressed: iglesia@berkeley.edu. 1

2 corrections were used for all systems to eliminate long-range electrostatic interactions and thus allow simulation of isolated clusters within periodic boundaries of VASP. S2. Structures of MFI clusters Atomic coordinates of large MFI clusters used as solid acids in this work were derived from converged periodic MFI calculations as described here. Atomic coordinates and unit cell parameters ( x x nm3 and α = β = γ = 90 ) of orthorhombic MFI were determined from XRD. S7 XRD lattice constants were used without relaxation because relaxation led to negligible changes in adsorption energies. S8 One tetravalent Si atom in this unit cell was replaced by a trivalent Al atom and accompanying H atom to generate the Al1-O1(H) Brønsted acid site (numbered according to convention S9) located at the intersection of straight and sinusoidal channel voids. The unit-cell with this acid site was structurally relaxed at RPBE/PAW level and extended by doubling the (shortest) z-dimension as shown in Figure S1 (a, b, d, e). This extended unit cell was modified by translating all atoms in order to move the strainght MFI channel containing Al1-O1(H) site near the center of the periodic supercell. The atoms were then separated from periodic neighbors by introducing vacuum regions. Some extra Si and O atoms (distant from the straight channel containing active site) were deleted, all terminal Si atoms were frozen, and terminal Si-O bonds were replaced with frozen Si-H bonds of length nm. [S10] This method led to clusters for MFI framework with one Al-OH acid site, 65 fully relaxed Si and its neighboring O atoms, and 62 frozen Si atoms terminated with Si-H bonds (Figure S1 c, f). The same cluster geometry and location of active site was used for all calculations with MFI acids, by replacing the Al heteroatom with Ga, Fe or B and relaxing unfrozen atoms for each case. This conversion from periodic to cluster MFI geometry was performed in order to calculate 2

3 deprotonation energies (DPE), its ionic and covalent components, and transition state geometries on the same structure. Periodic systems do not allow accurate DPE calculations without ad-hoc correction to errors associated with charged supercells, S9 and our classical electrostatic calculations used to derive ionic and covalent components of ion-pair interactions have only been implemented for non-periodic systems. Figure S1. Conversion of a periodic Al-MFI unit cell structure (a, d) to an extended unit cell (b, e) and a MFI cluster (c, f). Blue boxes reflect periodic supercell boundaries in VASP calculations. Views through straight (a, b, c) and sinusoidal (d, e, f) MFI channels are shown. S3. Calculation of electrostatic interaction energy between ions DFT derived charge densities are obtained as a three-dimensional mesh spanning one unit of the periodic supercell. We denote each element of this mesh as a mesh-cell. Electrostatic 3

4 interaction energy (E es ) between a cation and an anion charge distribution is calculated as the sum of repulsion between atom cores (i.e., nucleus and inner electrons treated as a point charge at the center) and valence electrons of cation and anion species, and attraction between cation atom cores and anion electrons, as well as, anion atom cores and cation electrons, E es 1 Z Z ( ρ V )( ρ V ) Z ( ρ V ) ( ρ V ) Z = N M T S T M S N A C A C A C A C πε 0 C= 1 A= 1 rca C= 1 A= 1 rca C= 1 A= 1 rca A= 1 C= 1 rca (S1) Here, ε 0 is the permittivity of free space, Z A and Z C are charges of atom-cores of the anion and cation, ρ A and ρ C are cation and anion electron densities at a given mesh-cell, V is the volume of a mesh-cell, r CA reflects distance between the atom-cores and mesh-cells in anion and cation distributions, M and N are total numbers of atom-cores in the anion and the cation, and S and T are total number of mesh-cells in the anion and the cation, respectively. Charge distributions were calculated on meshes for 2 nm cubic unit cells of POM clusters (yielding nm cubic mesh-cells), and a mesh for 2.5 nm cubic unit cells of MFI clusters ( nm cubic mesh-cells). E es calculation from Equation S1 requires partitioning of the unit-cell volume into cation and anion regions to avoid terms with r ac = 0, (except when the cation is just a point charge, as in the case of a proton); this partitioning was achieved by adding charge distributions of isolated cations and anions, followed by separation using the Bader method, S11, S12 (Figure S2). The charges in the partitioned cation and anion regions were near +1 and -1, respectively (i.e., > 0.98 in magnitude) for all POM clusters, suggesting that the overlap between the two densities and is negligible and a clean partitioning was achieved using the Bader method. The electrostatic interactions described by equation S1 were calculated using VASP CHGCAR files as input to a c++ program. The charge separations described by Scheme S2 were performed using the -p sum_atom option in the Bader program developed by the Henkelman group. S12 4

5 Figure S2. Illustration of the partitioning of a 2 nm cubic VASP supercell into cation and anion regions prior to performing electrostatic calculation using Equation S1. The cation (CH 3 OH dehydration TS +, yellow) and anion (H 2 PW 12 O 40 -, blue) charge distributions are shown using isosurfaces at a charge density of 200 e nm -3. The outer surfaces (after partitioning) show the boundary between cation-and anion Bader volumes using iso-surfaces at charge densities of 3 e nm -3. S4. Ionic and covalent components of DPE and ion-pair interactions at transition states Classical electrostatic interaction energies are calculated using equation S1 at varying cationanion distances. Such interaction energies for an Al-MFI (AlO - ) anion and a proton (H + ) are shown in Figure S3. The energy first decreased with decreasing distance, reached a minimum and then increased again. The distance at minimum energy reflects the equilibrium distance that the two ions can achieve without relaxation of their structure and electron distribution. The interaction energy corresponding to this distance reflects ionic component of total interaction energy. The covalent component can be calculated by subtracting this ionic component from the total interaction energy derived from DFT calculations. 5

6 Figure S3. Electrostatic interaction energy between a proton and the Al-MFI anion as a function of the distance, calculated using Equation S1. Tables S1 through S5 show DFT-derived DPE and ion-pair interaction energies for H + transfer, CH 3 OH dehydration, C 3 H 6 methyl shift and C 6 H 10 (cyclohexene) ring contraction, as well as their ionic and covalent components derived from electrostatic calculations on (Mo,W) POM and MFI clusters. Table S1. DPE and its ionic and covalent components on (Mo,W) POM and MFI clusters. Acid DPE (kj mol -1 ) H E + ion (kj mol -1 ) E + (kj mol -1 ) H 2 SMo 12 O H 3 PMo 12 O H 4 SiMo 12 O H 5 AlMo 12 O H 6 CoMo 12 O H 2 SW 12 O H 3 PW 12 O H 4 SiW 12 O H 5 AlW 12 O H 6 CoW 12 O Hal(Si 127 O 219 H 74 ) HGa(Si 127 O 219 H 74 ) HFe(Si 127 O 219 H 74 ) HB(Si 127 O 219 H 74 ) H cov 6

7 Table S2. Ion-pair interaction energy for H + shuttling TS and its ionic and covalent components on (Mo,W) POM. Acid TS E int (kj mol -1 ) TS E + ion (kj mol -1 ) TS E + cov (kj mol -1 ) H 2 SMo 12 O H 3 PMo 12 O H 4 SiMo 12 O H 5 AlMo 12 O H 6 CoMo 12 O H 2 SW 12 O H 3 PW 12 O H 4 SiW 12 O H 5 AlW 12 O H 6 CoW 12 O Table S3. Ion-pair interaction energy for CH 3 OH dehydration TS and its ionic and covalent components on (Mo,W) POM. Acid TS E int (kj mol -1 TS ) E + ion (kj mol -1 TS ) E + cov (kj mol -1 ) H 2 SMo 12 O H 3 PMo 12 O H 4 SiMo 12 O H 5 AlMo 12 O H 6 CoMo 12 O H 2 SW 12 O H 3 PW 12 O H 4 SiW 12 O H 5 AlW 12 O H 6 CoW 12 O Table S4. Ion-pair interaction energy for C 3 H 6 methyl shift TS and its ionic and covalent components on (Mo,W) POM. Acid TS E int (kj mol -1 TS ) E + ion (kj mol -1 TS ) E + cov (kj mol -1 ) H 2 SMo 12 O H 3 PMo 12 O H 4 SiMo 12 O H 5 AlMo 12 O H 6 CoMo 12 O H 2 SW 12 O H 3 PW 12 O H 4 SiW 12 O H 5 AlW 12 O H 6 CoW 12 O

8 Table S5. Ion-pair interaction energy for C 6 H 10 ring contraction TS and its ionic and covalent components on (Mo,W) POM. Acid TS E int (kj mol -1 TS ) E + ion (kj mol -1 TS ) E + cov (kj mol -1 ) H 2 SMo 12 O H 3 PMo 12 O H 4 SiMo 12 O H 5 AlMo 12 O H 6 CoMo 12 O H 2 SW 12 O H 3 PW 12 O H 4 SiW 12 O H 5 AlW 12 O H 6 CoW 12 O S5. DFT-derived HOMO-LUMO gaps in POM and MFI clusters Wider HOMO-LUMO gaps reflect more insulating character of the oxide in the solid acid. The values of these gaps derived from DFT (PW91/USPP) calculations are shown in Table S6. Table S6. HOMO-LUMO gaps of intact (Mo, W) POM and MFI clusters derived from DFT (PW91/USPP) calculations. Acid HOMO-LUMO gap (ev) H 2 SMo 12 O H 3 PMo 12 O H 4 SiMo 12 O H 5 AlMo 12 O H 6 CoMo 12 O H 2 SW 12 O H 3 PW 12 O H 4 SiW 12 O H 5 AlW 12 O H 6 CoW 12 O Hal(Si 127 O 219 H 74 ) 5.62 HGa(Si 127 O 219 H 74 ) 5.61 HFe(Si 127 O 219 H 74 ) 5.65 HB(Si 127 O 219 H 74 ) 5.93 S6. Calculations of enthalpies and entropies using statistical mechanics treatments 8

9 The enthalpy (H) of a given molecule/structure is given by the sum of its DFT-derived electronic energy (E 0 ), its zero-point vibrational energy (ZPE) and thermal contributions from its vibrational, translational and rotational degrees of freedom (H vib, H trans and H rot, respectively): H = E0+ ZPE+ H vib+ H trans+ H rot (S1) Similarly, the entropy (S) of this molecule is given by: S = S0+ Svib + Strans + Srot (S2) and the Gibbs free energy (G) at a given temperature (T) by: G= H TS (S3) Vibrational contributions to H and S in Equations S1 and S2 depend on DFT-derived vibrational frequencies (ν) as shown by Equations S4 through S6. 1 ZPE= hν 2 i i (S4) H vib hνi kt hνie = hνi (S5) i kt 1 e hνi kt hν i hνi / T e kt Svib = k ln(1 e ) hνi (S6) i kt 1 e Translational and rotational contributions to H and S for gas-phase reactants products and transition states were calculated using equations S7 through S11: Htrans 5 = kt (S7) 2 H rot 3 = kt (S8) 2 9

10 3/2 2πmkT 5 Strans = k ln V + 2 h 2 (S9) S rot 1/2 1/2 3 π T 3 = k ln + σ θxθyθz 2 (S10) h θ x/ y/ z = 2 8 π I 2 x/ y/ z k (S11) where, I x, I y, I z are the moments of inertia about x, y or z axes, respectively, and σ is the rotational symmetry number. Equations S1through S11 were used to calculate enthalpies (H) and free energies (G) of bare POM clusters, gaseous reactants and transition states for C 6 H 10 ring-contraction, C 3 H 6 methyl shift, CH 3 OH dehydration and H 2 O assisted H + shuttling on POM clusters at 433K and 1 bar pressure of each gaseous reactant molecule. While calculating vibrational contributions the H and G for transition states involved in these reactions, some low frequency vibrational modes (typically < 150 cm -1 ) were removed from calculations, and their contributions were substituted by translational and rotational modes of corresponding gaseous analogs of transition states for more accurate H and G estimates, as previously describe elsewhere. S13 Such substitutions were performed uniformly by removing same number of low frequency modes for a given transition state on all solid-acids. Electronic energies (E 0 ) and H and G values for each species were used to calculate activation energies, enthalpies and free energies for each reaction relative to gaseous reactants and bare POM clusters. Figure S4 shows E TS, H TS and G TS values for C 6 H 10 ringcontraction, C 3 H 6 methyl shift, CH 3 OH dehydration and H 2 O assisted H + shuttling on W and Mo POM clusters with S, P, Si, Al and Co central atoms as a function of DPE. Table S7 shows 10

11 regressed slopes and distances (offsets) between the trend-lines for Mo and W POM clusters for the data shown in Figure S4. These slopes and offsets have similar values for E TS, H TS and G TS calculations, suggesting that the trends in reactivity remain unaffected by incorporation of thermal and entropic factors and that the pre-exponential factors in rate equations are constant for a give type of reaction. (a) (b) (c) (d) (e) (f) 11

12 (g) (h) (i) (j) (k) (l) Figure S4. Electronic energies (a, d, g, j), enthalpies (b, e, h, k) and Gibbs free energies (c, f, i, l) for kinetically-relevant transition-state relative to gaseous reactants and bare acids for C 6 H 10 ring-contraction (a, b, c), C 3 H 6 methyl shift (d, e, f), CH 3 OH dehydration (g, h, i) and H 2 O assisted H + shuttling (j, k, l) at 433K and 1 bar reactant pressure as a function of DPE on Mo and W POM clusters with S, P, Si, Al and Co central atoms. Table S7. Slopes of E TS, H TS and G TS values and offsets between trends for Mo and W POM clusters shown in Figure S4. Uncertainties represent 95% confidence intervals. Quantity Slope Offset C 6 H 10 ring-contraction E TS (Fig. S4a) 0.65 ( ± 0.08) 7.3 (± 3.4) H TS (Fig. S4b) 0.67 ( ± 0.13) 5.8 (± 5.6) G TS (Fig. S4c) 0.62 ( ± 0.16) 6.5 (± 7.0) C 3 H 6 methyl shift E TS (Fig. S4d) 0.59 ( ± 0.07) 8.0 (± 2.9) H TS (Fig. S4e) 0.58 ( ± 0.07) 7.4 (± 3.4) G TS (Fig. S4f) 0.54 ( ± 0.09) 7.5 (± 3.7) CH 3 OH dehydration E TS (Fig. S4g) 0.32 ( ± 0.06) 15.4 (± 2.5) H TS (Fig. S4h) 0.29 ( ± 0.05) 16.0 (± 2.4) G TS (Fig. S4i) 0.29 ( ± 0.12) 16.6 (± 5.4) 12

13 H + shuttling E TS (Fig. S4j) 0.04 ( ± 0.14) 15.4 (± 6.0) H TS (Fig. S4k) ( ± 0.17) 12.7 (± 7.3) G TS (Fig. S4l) ( ± 0.18) 11.6 (± 7.7) S7. Summary of procedures for determining ion-pair interactions (with their ionic-covalent components) and using them for predictive guidance on reactivity trends S7.1. Steps for calculating ionic and covalent components of DPE or ion-pair interactions a. Obtain energies of fully relaxed combined ion-pair (e.g, intact acid or transition state) and of fully-relaxed isolated ions using DFT. Cations for transition states are fully relaxed saddle points for organic fragment with full +1 charge and analogous structure to the ionpair transition state. b. Calculate ion-pair interaction energies (DPE or E int, scheme 1, main text) using the difference between the DFT energies obtained in a. c. Determine charge distributions of isolated cations and anions from DFT and calculate their electrostatic interaction energy at different separations between ions using steps in section S3. The minimum electrostatic energy is denoted as the ionic component of the ion-pair interaction (E ion ). d. The covalent component (E cov ) of the ion-pair interaction is then obtained by subtracting E ion from DPE or E int. S7.2. Qualitative guidance for reactivity trends a. Solid-acids with larger HOMO-LUMO gap typically have smaller covalent and larger ionic fraction of the DPE. b. Ion-pair transition states recover much larger fractions of the ionic component of DPE then ionic component. Therefore, at the same DPE, acids with larger covalent component stabilize the transition state cation less, leading to higher activation energy. c. Larger cations typically recover lower DPE fractions, leading to less stable transition states. The absolute transition state energies, however, also depend of the gas-phase protonation energies independently of acids. S7.3. Developing acid descriptors and predicting activation energies on new acids a. Calculate DPE and its ionic and covalent components ( E +, H ion H E + cov ) using steps in section S7.1 (descriptors of acid). b. Use E prot, f ion and f cov values (acid independent descriptors of transition states) from Table 1 with Equation 6 (in the main text) to predict activation energy. c. Accuracy of the prediction may be tested by comparing them with DFT derived activation energies. 13

14 S7.4. Developing descriptors of intermediates or transition states a. Obtain ion-pair interaction energies and its ionic and covalent components for intermediates or transition states (using steps in section S7.1) on a given acid with known DPE components (values in Table S1). b. Use the components and Equations 7 and 8 (in the main text) to calculate f ion and f cov. c. E prot can be obtained using the difference between DFT derived energy of the cationic gaseous analog of intermediate or transition state and of isolated proton and gaseous reactants. References (S1) a) G. Kresse, J. Hafner, Physical Review B 1993, 47, ; b) G. Kresse, J. Furthmüller, Comput. Mater. Sci. 1996, 6, 15-50; c) G. Kresse, J. Furthmüller, Physical Review B 1996, 54, ; d) G. Kresse, J. Hafner, Physical Review B 1994, 49, ; e) G. Kresse, D. Joubert, Physical Review B 1999, 59, (S2) D. Vanderbilt, Phys. Rev. B 1990, 41, (S3) J. Klimes, D. R. Bowler, A. Michelides, J. Phys.: Condens. Matter 2010, 22, :1-5. (S4) K. Lee, É. D. Murray, L. Kong, B. I. Lundqvist, D. C. Langreth, Physical Review B 2010, 82, (S5) É. D. Murray, K. Lee, D. C. Langreth, J. Chem. Theory Comput. 2009, 5, (S6) G. Makov, M. C. Payne, Phys. Rev. B 1995, 51, (S7) H. Van Koningsveld, H. Van Bekkum, J. C. Jansen, Acta Crystallographica Section B 1987, 43, (S8) A. J. Jones, S. I. Zones, E. Iglesia, J. Phys. Chem. C 2014, 118, (S9) A. J. Jones, E. Iglesia, ACS Catal. 2015, 5, (S10) A. J. Jones, R. T. Carr, S. I. Zones, E. Iglesia, J. Catal. 2014, 312, (S11) Bader, R. Atoms in Molecules: A Quantum Theory, Oxford University Press, New York, (S12) a) G. Henkelman, A. Arnaldsson, H. Jónsson, Comput. Mater. Sci. 2006, 36, b) E. Sanville, S. D. Kenny, R. Smith, G. Henkelman, J. Comput. Chem. 2007, 28, (S13) P. Deshlahra, E. Iglesia, J. Phys. Chem. C 2014, 118,

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