doi.org/10.26434/chemrxiv.8209304.v1

Electrically Enhanced Hydrogen Adsorption in Metal-OrganicFrameworksLiviu Zarbo, Marius Oancea, Emmanuel Klontzas, Emmanuel Tylianakis, Ioana G. Grosu, George E.Froudakis

Submitted date: 31/05/2019 • Posted date: 03/06/2019Licence: CC BY-NC-ND 4.0Citation information: Zarbo, Liviu; Oancea, Marius; Klontzas, Emmanuel; Tylianakis, Emmanuel; Grosu, IoanaG.; Froudakis, George E. (2019): Electrically Enhanced Hydrogen Adsorption in Metal-Organic Frameworks.ChemRxiv. Preprint.

Using a multiscale approach, we show that applied electric field does not affect significantly the hydrogenuptake of weakly polarizable metal-organic frameworks (MOFs). Nonetheless, we show that, for large MOFpolarizabilities, the hydrogen uptake can double in applied electric field. We propose searching for a novelclass of hydrogen storage materials, that of highly polarizable porous MOFs. Hydrogen uptake in suchmaterials would be controlled by electric field, a much easier to adjust parameter than pressure ortemperature.

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Electrically Enhanced Hydrogen Adsorption inMetal-Organic Frameworks

Liviu P. Zârbo,∗,† Marius A. Oancea,†,‡ Emmanuel Klontzas,¶,§ EmmanuelTylianakis,‖,¶ Ioana G. Grosu,† and George E. Froudakis¶

†Mol & Biomol Phys Dept, Natl Inst Res & Dev Isotop & Mol Technol, RO-400293Cluj-Napoca, Romania.

‡Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg1, D-14476 Potsdam, Germany

¶Department of Chemistry, University of Crete, Voutes Campus, P.O. Box 2208, 71003Heraklion, Crete, Greece

§Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation,Vass. Constantinou 48, GR-11635 Athens

‖Materials Science and Technology Department, University of Crete, Vassilika Voutes,P.O. Box 2208, Heraklion, Greece

E-mail: liviu.zarbo@itim-cj.roPhone: +40-264-584037/196

AbstractUsing a multiscale approach, we show that ap-plied electric field does not affect significantlythe hydrogen uptake of weakly polarizablemetal-organic frameworks (MOFs). Nonethe-less, we show that, for large MOF polarizabil-ities, the hydrogen uptake can double in ap-plied electric field. We propose searching for anovel class of hydrogen storage materials, thatof highly polarizable porous MOFs. Hydrogenuptake in such materials would be controlled byelectric field, a much easier to adjust parameterthan pressure or temperature.

1 IntroductionOne of the top priorities of the moderneconomies is to secure the power sources anddevelop the extended energy distribution net-works to satisfy the ever increasing energy de-mands. Nowadays and in the near future, fossilfuels are expected to play dominant role in pro-

viding the required energy for our needs mostlyby converting to electricity or heat, since therelative technology has reached maturity and isused to power the vast majority of our daily ac-tivities. The restricted access to the resourcesof fossil fuels, coupled with the inevitable deple-tion of the underground reserves has spurredthe quest for the development of alternativeenergy technologies. There are several alterna-tive energy resources with economic potential,such as solar, wind, marine, geothermal andbiomass. These provide energy for static ap-plications, but they are inherently fluctuating,so they cannot fully replace traditional powerplants. Efficient and cost effective high densityenergy storage solutions are intensely soughtas the key for regularizing the output of al-ternative energy sources. But, such solutionswould open the way for emission free mobileapplications, sensibly reducing their environ-mental footprint. Among the possible highdensity energy storage solutions, using hydro-gen as an energy carrier is regarded as one ofthe most promising. Hydrogen releases almost

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three times more energy per unit of mass thangasoline,1 and its combustion produces mainlywater, which makes it ideal for environmentallyfriendly applications.The exploitation of hydrogen in mobile appli-

cations includes three basic steps, namely theproduction of hydrogen, the storage of hydro-gen and the conversion of hydrogen to power.The latter involves the fuel cell technologyfor splitting hydrogen molecule and producingpower and water with high efficiency. There arethree hydrogen storage technologies. The mostmature ones, involving hydrogen storage as acompressed gas or as a liquid at cryogenic tem-peratures, seem to have reached their full po-tential. The third technology involves the stor-age of hydrogen in atomic or molecular formin the structure of materials. For reasons ex-plained elsewhere,1 hydrogen storage in mate-rials has been intensely investigated as a po-tentially safer and more energy efficient alter-native to the first two. Specific targets havebeen established concerning the reversible hy-drogen capacity of materials containing storagetanks. To enable a driving range exceeding 300miles for the hydrogen powered vehicles, DOEset targets2 of 5.5% H2 for the gravimetric, and40g/L for the volumetric capacity of the wholeon-board storage system. This means the de-liverable uptakes of the material in the tankshould exceed the capacities mentioned above.Physical adsorption of molecular hydrogen

in porous materials has been proposed as themost promising approach to reaching the DOEtargets for hydrogen storage on-board of vehi-cles. Physisorption has the advantage of highreversibility and fast adsorption-desorption ki-netics during the loading cycles. A varietyof porous materials have been proposed3 andstudied both theoretically and experimentally,the most promising of them belonging to thefamily Metal-Organic Frameworks4 (MOFs).These materials have been the subject of in-tense research over the last fifteen years be-cause of their physico-chemical properties, suchas high surface area, large pore volumes, andtunable chemical properties, identified as cru-cial for achieving high H2 storage capacities. Ithas been proven that surface area and pore vol-

ume affect the H2 storage capacities and theireffect is more pronounced in different pressureranges of the adsorption isotherms of the ex-amined materials. A third important factor isthe binding affinity of the molecular hydrogento the pore surface. In contrast to the caseof hydrides where hydrogen is absorbed in theatomic form with high absorption enthalpy (40-100kJ/mol), in physical adsorption H2 interactsmainly through weak van der Waals interac-tions with the surface leading to weak adsorp-tion enthalpies (4-12kJ/mol). Such low adsorp-tion enthalpies prevent large capacities of ad-sorption at room temperature. Room temper-ature adsorption capacities are of the order of1-2%wt, while at 77K and high pressures, thecapacities are close to the established targets.5It has been estimated,6,7 that for adsorption en-thalpies in the range of 10 kJ/mol to 30kJ/mol,the DOE targets are attainable. The adsorp-tion enthalpy can be enhanced by designingmaterials with certain pore sizes in the rangeof nanoporous materials and by controlling thechemical functionality of the pore surface andmost of the efforts are focused on enhancing ad-sorption enthalpy. One must have in mind thatthe overall H2 capacity would be a compromiseof more than the three factors that have beenmentioned above as has been shown recentlyby the construction of quantitative structure-property relationship (QSPR) models.8Several routes have been proposed to enhance

the adsorption strength of H2 in physisorptionmaterials. In the case of MOFs, these routes9,10include doping with species that can polarizeH2, such as lithium cations, the functionaliza-tion of linkers, the existence of open metal siteseither on the inorganic building blocks or onthe linker, the pore size control either by se-lecting linkers with various lengths or by cate-nation. Another route, that has not been con-sidered yet in the case of MOFs, is the enhance-ment of the binding energy by applying an ex-ternal electric field. Directly increasing the H2binding to sorbent materials via electric fieldshas been proposed only recently11 and is stilla largely unexplored area in hydrogen storage.The original proposal showed11 that the hydro-gen adsorption capacity of a BN sheet can be

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tuned and enhanced by a sufficiently large ap-plied electric field to meet the DOE require-ments. Under the applied electric field, bothH2 and the adsorbent’s surface get polarized,and the dipole-dipole interaction between thetwo induced dipoles enhances the binding. Theidea originated from an earlier work12 relatedto polarization-mediated binding of hydrogento metal atoms. Subsequent theoretical inves-tigations under applied electric field were per-formed on systems such as: i) carbon nanotubesdecorated with metals,13,14 SiC nanotubes,15ii) atomic clusters such as C12N12 isomers16 or(MgO)9 metal oxide clusters,17 and iii) two-dimensional nanosheets such as graphene deco-rated with metals,18–21 graphyne doped or dec-orated with metals,22,23 B/C/N sheets,24 AlNsheets25 and metal decorated silicene.26 To ourknowledge, no one has approached this prob-lem in MOFs, although there has been a pro-posal for building a three dimensional structure,a π-stacked organic crystal27 with enhanced ad-sorption properties in electric field.In this paper, we have chosen to investigate

the adsorption of H2 in IRMOF-1 in appliedelectric field. IRMOF-1 is one of the mostinvestigated MOFs and its H2 adsorption hasbeen extensively studied both experimentallyand theoretically. Theoretical investigations in-cluding quantum mechanics calculations andGrand Canonical Monte Carlo (GCMC) sim-ulations have been performed to find the opti-mal configurations and the corresponding bind-ing energies of hydrogen in the different adsorp-tion sites of the material and to predict the ad-sorption capacity in different thermodynamicconditions. Literature reports28,29 concerningquantum mechanics calculations can be dividedin two groups based on the model that wasused to represent IRMOF-1, either by perform-ing calculations on fragments of various sizestaken from the crystal structure, or by takinginto account the crystal with the correspond-ing periodic boundary conditions. It has beenshown28–30 that the strongest adsorption site islocated on Zn4O corner (known as the “cup”site, labeled31 α) with an enthalpy of adsorp-tion of -7.1kJ/mol, in good agreement with theavailable experimental value at 77K. The sites,

labeled31 β and δ, located on the Zn4O cor-ner and the site located on top of the phenylring, respectively, were found to be isoener-getic with a enthalpy of adsorption of -4.1 to-4.6kJ/mol. GCMC simulations on IRMOF-1have been mainly performed at 77K and 298Kand pressure ranges up to 150bar and were re-cently summarized by Durette et al.32 The pre-dicted uptakes showed small deviations fromthe value of 1.3%wt at 77K and 1 bar wherelarger deviations has been found for higher pres-sures (5.2 to 7.2%wt at 20bar). It was shownthat quantum corrections are essential at 77Kwhere the addition of partial charges was foundto overestimate the uptake in some cases.The rest of the paper is structured as fol-

lows. In Sec. 2, we provide the computationaldetails used in our calculations. In Sec. 3 wepresent the results of our calculations. We jus-tify the computational model used to obtain theH2 uptake in electric field by quantum chem-istry calculations on finite size IRMOF-1 mod-els as presented in Sec. 3.1. Using results fromperiodic density functional (DFT) calculations,we parametrize a simple model used for GCMCcalculations of H2 adsorption isotherms in elec-tric field, as presented in Sec. 3.2. We concludein Sec. 4.

2 Computational DetailsTo investigate the adsorption in electric field onIRMOF-1, we employed a multiscale methodol-ogy33 that was modified to include electricallyinduced polarization effects. Our approach wasas follows. i) We performed ab initio calcu-lations of the binding energy vs the distanceof H2 to the binding sites of IRMOF-1, withand without electric field. In these calculations,the binding sites were represented by finite sizefragments containing these sites. ii) We per-formed periodic structure DFT simulations ofthe IRMOF-1 unit cell with and without elec-tric field to obtain: optimized lattice parame-ters, Born effective charges for each atom andthe atomic positions in unit cell. iii) Using thedata from the ab initio calculations, GCMCsimulations were performed to obtain the H2

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uptake at 77K and 300K.The calculations i) are described in Sec.3.1.

Each binding site was modeled by a finite frag-ment of IRMOF-1. We formed dimers in whichone monomer is the MOF fragment, and theother is a H2 molecule. The binding energiesof H2 to a binding site were computed with re-spect to the distance between that site and thecenter of the H2 molecule. Each monomer is re-laxed with and without electric field, and thenthe dimer binding energies are computed. Thecalculations were done at the B3-LYP34 level oftheory with the def2-TZVP35 basis set. Disper-sion corrections36 with Becke-Johnson damp-ing37 were taken into account. We also cor-rected for the basis set superposition errors us-ing the counterpoise method.38 The energy andgeometrical tolerance criteria, for the structureoptimizations of monomers and dimers, carriedout in this work and its attached Supplemen-tary Information (SI), have been set to 10−8a.u.and 10−4a.u., respectively. The cluster calcula-tions have been performed using the TURBO-MOLE software package.39The GCMC calculations of the adsorption

isotherms used data from ii) periodic structureDFT calculations, performed using the softwareCRYSTAL09.40 The calculations were done atGGA-PBE41 level using all electron Gaussianbasis sets. We considered the basis pob-TZVP,42 which is based on def2-TZVP. Thischoice of functional/basis set is justified be-cause: a) the Born effective charges (or atomicpolarizations) computed for Zn and O in thestructure agree to those of ZnO, b) the staticdielectric constant (permittivity) κ = 1.41 isin very good agreement with the value κ =1.37 estimated using the Clausius-Mossotti ap-proach,43 and c) the calculated electronic bandgap Eg = 3.6 eV only slightly overestimates theexperimental44 value Eg = 3.4 eV. As previ-ously shown,45,46 the dynamical Born effectivecharges are not very sensitive to the differentexchange-correlation functionals used to esti-mate them.The optimized lattice constants and Born

charges were computed using a 6 × 6 × 6 k-point grid in the Brillouin zone of the IRMOF-1 fcc cell with 106 atoms/cell. For consistency,

in the GCMC simulations, we used the lat-tice parameters obtained from our calculations.Those are a = b = c = 26.06Å for zero fieldand c = 26.07Å in applied field. These val-ues are slightly larger than the experimentalones as GGA-PBE typically overestimates thelattice parameters. The atomic relaxations, inthe presence of the field, are performed usinga 2 × 2 × 1 mesh of k-points in the Brillouinzone of 1 × 1 × 2 cubic supercell following anapproach45 proposed for periodic system relax-ation in electric field.The self-consistent-field periodic structure

calculations were considered to be convergedwhen the energy changes between interactionswere smaller than 10−8a.u. An extra-largepredefined pruned grid consisting of 75 ra-dial points and 974 angular points was usedfor the numerical integration of charge den-sity. Full optimizations of the lattice con-stants and atomic positions have been per-formed with the optimization convergence of5 × 105Hartree/Bohr in the root-mean squarevalues of forces and 1.2 × 103Bohr in the root-mean square values of atomic displacements.The level of accuracy in evaluating the Coulomband exchange series is controlled by five param-eters.40 The values used in our calculations are7, 7, 7, 7, and 14.The adsorption isotherms were computed

performing iii) GCMC simulations using theRASPA2 program.47 The program was modi-fied to allow for the inclusion of the H2 dipoleinteraction with the applied electric field. Theframework is considered immobile for bothcases, with and without applied electric field.The cut-off radius is set to 12.8Å, the latticeconstants and positions are those obtained fromthe periodic structure calculations. For non-bonded interactions we use the Lennard-Jonespotential with the parameters taken from theDREIDING48 force field for all the frameworkatoms. The partial charges for the frameworkatoms and H2, as well as the Lennard-Jones co-efficients are listed in SI. The atomic positionsand Born charges, also listed in SI, were ob-tained from the ii) periodic structure calcula-tions discussed above.

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3 Results and discussionThe magnitude of the H2 uptake increase inMOF will depend on the magnitude of the ap-plied field. In our calculations, we included theeffects of polarization on both the adsorbateand the adsorbent. H2 is weakly polarizableand possesses no permanent dipole moment.49IRMOF-1 is also weakly polarizable, with anestimated permittivity43 κ = 1.37. Thus, oneneeds a large electric field to significantly in-crease the uptake. However, too large appliedfields E = 0.045 a.u. = 23 GV/m, as those con-sidered in the original study11 on BN sheets,would cause the Zener breakdown of the MOF.An upper limit for the Zener breakdown fieldof IRMOF-1 can be estimated50 at ∼ Eg/a =13 GV/m, where Eg = 3.4 eV is the experimen-tal value of the band gap,44 and a is the latticeconstant of the cubic IRMOF-1 cell. Therefore,we choose E0 = 0.005 a.u. = 2.57 GV/m as themagnitude of the applied electric field through-out our simulations.In our model, we consider a spherical IRMOF-

1 crystallite on which we apply the electric fieldE0z. The adsorbed gas feels the effect of thefield through the local field inside of the pore.The contributions to the local field inside thepore are51 the applied field E0, the depolar-ization and the Lorentz fields, plus the field ofthe atomic charges. For a spherical MOF crys-tallite, the Lorentz and the depolarization fieldcancel each other. Thus, we can approximatethe field in the center of the pore by E0. Tosimplify our treatment, in all our subsequentcalculations, we assumed that the electric fieldinduced inside the MOF pores was constant,equal to the applied field E0. As a result, themolecule of H2 inside the pore would be sub-jected to a field equal to E0 plus the contribu-tions of the charge distribution inside the MOF.

3.1 Quantum chemistry calcula-tions

We perform DFT simulations to obtain the in-teraction energy between the H2 molecules andtheir binding sites as a function of distance inapplied electric field E0 = 0.005a.u.. We con-

Figure 1: Potential energy curves for H2 ad-sorbed at a) the δ-site at the center of the BDClinker, b) the α “cup” site, c) the β site. Thepositive direction is considered z-direction. Theelectric field is color coded red for positive andblue for negative. The horizontal axis of thegraph represents the distance between the cen-ter of the H2 molecule and a) center of the ben-zene ring on the linker, b) the µ3-O atom inthe center of the SBU, c) the Zn atom abovethe µ3-O from the center of the SBU. The Zn,C, O and H atoms of the fragments are coloredpurple, gray, red and white, respectively. Theadsorbed H2 is colored green.

sider the three adsorption sites31 referenced atthe end of Sec. 1 for the hydrogen in MOF: theδ-site above the center of the benzene dicar-boxylate (BDC) linker, and the α “cup” andβ adsorption sites, located on the secondarybuilding unit (SBU), as shown in Fig. 1. Ourscans are performed for ±E0z field and the re-sults are compared to the ones in the zero fieldcase. The hydrogen molecule is parallel to thez-axis in the case presented in Fig. 1. The MOFfragments (clusters) used in this calculation areshown next to each plot in Fig. 1a the linker andtwo hydrogen terminated SBU units, in Fig. 1bthe SBU unit modeling the “cup” site, and inFig. 1c) the SBU unit modeling the β site.

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The potential energy curves in Fig. 1 showthat the binding energy is either enhanced,or decreased depending on the field direc-tion. This effect has been noticed in previouswork on Li-decorated carbon nanotubes13 andgraphene.18 Induced dipole-dipole interactiondoes not explain this feature, as both H2 andMOF dipoles are odd functions of the electricfield, so the dipole-dipole interaction is even. Ithas been argued52 that the binding of H2 to thesites in IRMOF-1, in zero field, is mostly due todispersion forces. This suggests that the energydifferences seen in Fig. 1 can be explained byconsidering polarization effects. We do so be-low, but only for the electrostatic energies andnot for exchange and correlation.To show this, we calculate the lowest order

terms in the multipole expansion of the electro-static energy for the system formed by the BDClinker and H2. The benzene ring (monomer A)is representative for the BDC fragment and itscenter is the origin. The H2 molecule (monomerB) is above the center of the ring as in Fig. 1aat position R = Rz. The field is ±E0z.We compute the components of the dipole

pA,Bα and quadrupole ΘA,Bαβ moments in the ap-

plied field for each isolated monomer from wave-functions. The applied field E0 induces a dipolein each monomer, but is too small to affect sig-nificantly the quadrupole moments (see the SIfor more details). Thus, the additional electro-static energy terms due to the polarization in-duced by electric field are a dipole-dipole term(DD) and two quadrupole-dipole terms (DQand QD). This follows from the multipole ex-pansion53 of the electrostatic energy for twomonomers A, and B

UAB = DD + DQ + QD= −TABαβ pAαpBβ−1

3TABαβγ(p

AαΘB

βγ −ΘAαβp

Bγ ) + . . . ,

(1)where TABαβ...ν = ∇α∇β . . .∇ν1/R in a.u. TheGreek letters label the x-, y-, or z-axes.Using Eq. (1), we compute the electrostatic

energy terms DD, DQ, and QD. The results areshown in Fig. 2a. The dipole-dipole term is al-ways attractive, but the DQ and QD terms arerepulsive if the field is positive and attractive for

Figure 2: Electrically induced electrostatic in-teraction energy between benzene and H2 vs.distance: a) calculated dipole-dipole (DD) anddipole-quadrupole (DQ, QD) terms of Eq. (1),b) pictorial explanation of the result. The DDterms are always attractive (negative), but toosmall compared to the QD and DQ terms whichswitch the sign if the electric field direction isreversed. As a result, the total electrostatic en-ergy is repulsive for field E0z and attractive andslightly larger for field −E0z. This is consistentwith what is seen in Fig. 1a. The benzene isoriented as BDC in Fig. 1a, and its center isthe origin, while H2 position is Rz.

negative electric field. This is consistent withthe result in Fig. 1a. For the small fields consid-ered, the DD interaction is one order of mag-nitude smaller than QD and DQ interactionssimply because the induced dipole is too small.This is true despite the fact that DD ∼ 1/R3

while DQ, QD ∼ 1/R4. The results of Fig. 1b,c, can be similarly explained, but one has touse atomic site-resolved charges and multipoles,rather than the global multipoles, for the shortrange interactions.We performed additional tests by repeating

the calculations presented in Fig. 1 with a meta-

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GGA functional, namely M06-2x,54 recentlytested on IRMOF-1.29 As discussed in SI, andsimilar to the result in Fig. 1, the binding en-ergies in the electric field increase or decreasedepending on the orientation of the field. But,in the case of some binding sites, the sign ofthe binding energy change with respect to thezero field case is opposite to the result obtainedemploying B3-LYP. This result is also oppositeto what we expect from our electrostatics con-siderations. This could stem from the largerpercentage of Hartree-Fock exchange M06-2xcompared to B3-LYP, or could be an artifactof the meta-GGA functionals being constructedwith the aid of electron density gradients. How-ever, further benchmarking studies are neededto clarify what are the ideal functionals to usewhen studying metal-organic systems in electricfield.

3.2 GCMC calculations in elec-tric field

Paragraph 20 Based upon the insight offeredby the ab initio calculations, we make a modelfor the adsorbent-adsorbate system formed byIRMOF-1 and H2 gas in electric field. As dis-cussed above, inside the pores of IRMOF-1 thefield can be approximated as being equal tothe applied field E0z. In our GCMC simula-tions, the adsorbent is represented by a peri-odic fcc IRMOF-1 unit cell of 424 atoms (seeSI for details). Though relatively small, the ap-plied electric field considered slightly deformsand polarizes the unit cell. Since the deforma-tion of the unit cell is small compared to thecell size, we expect it not to affect significantlythe H2 uptake. The induced dipole moment ofthe unit cell is expected to influence the adsorp-tion, so each atom in the model of IRMOF-1 forthe GCMC calculation will carry both a partialcharge and a dipole, as explained below. Thehydrogen, on the other hand, will be weakly po-larized by the field inside the pores. We modelit as gas whose molecules can be polarized ei-ther parallel, or perpendicular to their axes.Without the applied electric field, our modelreduces to the one previously used in GCMCsimulations of H2 adsorption on IRMOF-1.55

To make a polarized model for the adsorbate,we start from the unpolarized model, and in-troduce the polarization. The unpolarized H2molecule is modeled as56 a quadrupole withcharge q ≈ 0.468e on the H sites and −2q atits center. In electric field, this molecule be-comes polarized, depending on its orientationwith respect to the field in the pore.49 To ac-count for this effect, we consider the adsorbateas made of two components: H2

‖ with a con-stant polarization along its axis and H2

⊥ with aconstant polarization perpendicular to its axis.In the field E0 present in the pores, the adsor-bate molecule oriented along the field H2

‖ hasa dipole p‖ = 0.033a.u., and the molecule per-pendicular to the field H2

⊥ possesses a momentp⊥ = 0.013a.u.. To account for these dipoles,we place additional charges ±δq on the H sitesof H2

‖, chosen to reproduce p‖. For H2⊥, only

the center of H2 is displaced perpendicular tothe axis of the molecule by δd chosen to repro-duce p⊥. The numerical values of charges anddistances for this model are given in the SI.As in the case of the adsorbate, the polarized

model for IRMOF-1 starts from the unpolarizedmodel typically used in GCMC simulations. Inthe unpolarized model, each atom i is placedat the position Ri in the 424 atom unit cell.These positions are obtained, as explained inSec.2, by optimizing the crystalline structure.To each atom i we assign a partial charge qiand two Lennard-Jones coefficients Ci

6,12.In the polarized model, each atom is displaced

by the electric field to a new position Ri(E0).These positions are also obtained by performingperiodic structure optimization calculations inelectric field. From the calculated value of theBorn charge Z∗i for each atom i, we can find thedipole moment acquired under the effect of theelectric field as pi = Z∗i (Ri(E0)−Ri). The sim-plest way to introduce these moments into thecalculation, is by placing dummy charge sitesnext to each atom i, the charge of each sitebeing labeled Qi. Thus, we assign the chargeqi−Qi and position Ri to the atomic site i, andplace the dummy charge Ri at Ri+di. The dis-tance di and the charge Qi > 0 are chosen sothat pi = Qidi. We take |di| = 0.27Å, which isan order of magnitude less than the equilibrium

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Figure 3: Absolute uptake for IRMOF-1 in applied electric field (red). The dotted line is theisotherm in the absence of electric field. The blue and green lines represent the cases with 25 and40-fold increase of polarizability, respectively.

distances between H2 and its adsorption sites,so we do not expect large spurious effects fromthe quadrupole-H2 dipole terms. The dispersioncoefficients are approximated to be identical tothe ones in the zero field case.We compute first the isotherms in zero

field. Then, we use the polarized models forthe adsorbate and IRMOF-1 to compute theisotherms at 300K and 77K in electric field.The positions Ri of atoms i are identical, in re-duced coordinates, for both zero and non-zerofield. The cut-off radius is set to 12.8Å. Duringthe simulations, translation, rotation, insertionand deletion moves are performed on the H2molecules. The moves are modified to includethe additional −E ·PH2 term which arises whenthe electric field is applied. As explained above,the local field in the pore is approximately E0z.The adsorption isotherms, shown in Fig. 3,

are very close to the reference values withoutelectric field. This is expected as only theinduced dipole-dipole interaction increases thebinding energy. As suggested by the results pre-sented in Fig. 1, larger quadrupole-dipole termsare present, but according to our pictorial ex-planation of Fig. 2b, they cancel out. For eachbinding site in IRMOF-1, one could generate anidentical binding site by a reflection operation.Assume a H2 binds at the top of the first site,and another H2 binds at the bottom of the sec-

ond, where bottom-top is the z-direction. Asin Fig. 2a, the dipole quadrupole contributionsto the energy (DQ, QD) for the first site wouldhave the opposite sign to the ones for the sec-ond (see SI for a more detailed explanation).Thus, the overall contribution to the uptake isonly given by the dipole-dipole interaction, de-spite the optimistic expectations suggested bythe results of Fig. 1. This contribution is small,as it is proportional to the square of the appliedfield.As the electric field cannot be increased in a

practical device too far beyond the already largevalue E0 considered, one should search for morepolarizable porous MOFs whose uptake can beelectrically enhanced. To test this idea, we scaleup the Born charges of IRMOF-1 25 and 40times and repeat the GCMC simulations. Asshown in Fig. 3, the hydrogen uptake at roomtemperature almost doubles for the 40-fold in-crease in polarizability. Such polarizable MOFsdo exist,57 but they are usually not porous. Forporous isoreticular MOFs, lower permittivities,up to κ = 1.94, were estimated.43 More researchis needed to find a MOF that is both polarizableand highly porous.

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4 ConclusionsWe have chosen IRMOF-1 to test the poten-tial of applied electric field to enhance H2 up-take in MOFs. We provided an extension tothe multiscale approach33 previously used bysome of us for adsorption simulations, whichenables the inclusion of polarization effects inthe GCMC simulations. We found that, apartfrom the expected induced dipole-dipole contri-bution to the interaction, higher order terms,such as dipole-quadrupole, contribute to theextra-binding in electric field. However, theseterms change sign with the field direction, sothey cancel out in the adsorption simulations.We have chosen the applied field as large aspossible without causing the dielectric break-down of the MOF. It appears that even thisfield is too low to significantly affect the hydro-gen uptake. However, we showed that a 40-foldincrease in IRMOF-1 polarizability would leadto an almost doubling of the uptake at roomtemperature. Thus, we believe that the onlyway to make further progress, in enhancing thehydrogen uptake in MOFs via electric fields, isto search for materials with both large poresand polarizability. Through this work, we pro-pose opening a new research direction, that ofelectrically controlled adsorption in highly po-larizable porous MOFs.

Acknowledgement L. P. Z. has been fundedby a grant of the Romanian National Au-thority for Scientific Research and Innovation,CNCS-UEFISCDI, project number PN-II-RU-TE-2014-4-1309. E. K. has been funded byState Scholarships Foundation (SSF), grantnumber 2016-050-0503-8189, and co-financedby the European Union (European Social Fund-ESF) and Greek national funds through theaction entitled “Reinforcement of PostdoctoralResearchers”, in the framework of the Opera-tional Programme “Human Resources Develop-ment Program, Education and Lifelong Learn-ing” of the National Strategic Reference Frame-work (NSRF) 2014-2020. I. G. G. has beenfinancially supported by the Romanian Na-tional Authority for Scientific Research andInnovation (ANCSI) through the Core Pro-

gram, Project PN19-35-02-02. L. P. Z. thanksGabriela Blăniţă, Dan Lupu, Atilla Bende,Claudiu Filip and Alston J. Misquitta for stim-ulating discussions, and David Dubbeldam forcorrespondence.

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5 Supporting Informationfor Electrically EnhancedHydrogen Adsorption inMetal-Organic Frame-works

We include additional ab initio simulations tosupport the idea that the dipole-dipole inter-action is the most important contribution toelectrically induced uptake, while higher ordercontributions cancel out when statistical aver-aging is performed. We show PES scans for H2with perpendicular orientation with respect tothe binding sites, and we compute the bindingenergies of H2 to these sites. We also presentadditional benchmarking of the cluster calcu-lations for the binding energies with differentfunctionals. We include the parameters used inthe GCMC simulations such as charges, Borncharges, dispersion coefficients. We add a pic-torial explanation of the polarized model forIRMOF-1 used in the simulations.

Figure 4: Models used for calculations of thebinding energies of H2 at the sites α, β and δin IRMOF-1. The direction of the applied fieldE0z is perpendicular to the binding positions.The Zn, C, O and H atoms of the fragmentsare colored purple, gray, red and white, respec-tively. The adsorbed H2 is colored green.

5.1 Quantum chemistry calcula-tions

We have computed the binding energies of H2at the sites α, β and δ in IRMOF-1 under theinfluence of applied electric field and comparedthe results with the case of zero field. For thebinding energy calculations, we considered, aspreviously done in the literature,28 the modelspresented in Fig. 4. In the figure, the z-axis isthe direction joining the center of H2 moleculeto the each binding site.The electric field is considered along the z-

axis. The dimer formed by the IRMOF-1molecular fragment and H2 is relaxed until thehydrogen reaches its equilibrium position. Tomake sure the optimized structures correspondto an energy minimum, the dimers are opti-mized with the hydrogen initially oriented ei-ther along the z-axis or in the horizontal xy-plane. After structural optimization is per-formed, the calculations are corrected for BSSEerrors using the counterpoise method.

Table 1: Binding energies in kJ/mol forthe three IRMOF-1 binding sites consid-ered in our calculations. Note that thebinding energy for one direction of ap-plied field is larger than the zero fieldvalue, while for the opposite direction ofthe field tends to be smaller (the differ-ence seen for the β site is due to the dis-placement of H2 from the initial position.The results in 0-field are consistent withpreviously reported calculations.28–30

Field (a.u.) EαB Eβ

B EδB

0.0 -7.4 -3.9 -3.8-0.005 -7.1 -4.8 -4.10.005 -8.4 -3.9 -3.5

The models shown in Fig. 4 for the α, β sitesare used in the structural optimizations becausethe 6 benzene arms prevent the molecule frommoving to the site α during the geometry op-timization steps. The benzene arms can be re-placed by hydrogen atoms in the case of poten-tial energy scans done to obtain the dependenceof the energy on the distance to the binding site,along the z-axis as in the main text.

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The binding energies, obtained for the opti-mized structures, are presented in the Table 1.The superscript corresponding to each energyin the table references the subsection which liststhe XYZ-file containing the optimized structureof each dimer.As in the main text, the ab initio calcula-

tions are performed at the B3-LYP34 level oftheory with the def2-TZVP35 basis set. Disper-sion corrections36 with Becke-Johnson dampingare taken into account. We also correct for thebasis set superposition errors using the coun-terpoise method.38 The structural optimiza-tions of monomers and dimers have considered10−8a.u. tolerance for the energy convergenceand 10−4a.u. for the geometry convergence.The calculations are performed using the TUR-BOMOLE software package.39Similar to Fig. 1 in the main text, we have

performed ab initio simulations in the case theH2 is perpendicular to the z-direction. In Fig. 5,the positive direction for the applied field is con-sidered the z-direction. The horizontal axis ofthe graph represents the distance between thecenter of the H2 molecule and a) center of thebenzene ring, b) the µ3-O atom in the center ofthe SBU, c) the Zn atom above the µ3-O fromthe center of the SBU.As it is shown in Fig. 5, the qualitative be-

havior of the binding energy in applied electricfield persists. In other words, for a field di-rection the binding is enhanced, while for theother, is lower. To explain this behavior, wecan follow the same qualitative argument as inthe main text: the dipole-dipole (DD) contri-bution is small but always attractive, while thedipole-quadrupole (DQ and QD) contributionsare larger, but change sign with the electricfield. It is important to mention here that theH2 dipole is smaller if the field is perpendicularto it. Therefore, the dipole-dipole interaction,between H2 and binding sites, is smaller thanfor H2 oriented parallel to the z-axis.Quadrupoles in electric field. As discussed

in the main text, H2 quadrupole changes onlyslightly as electric field is applied. This jus-tifies the approximation we used to estimatethe additional electrostatic interaction energybetween hydrogen and the binding sites on

Figure 5: Potential energy curves for H2 per-pendicular to the z-axis adsorbed above a) theδ-site on the BDC linker, b) the α-site, c) theβ-site on the SBU. As in the main text, themodels used in the calculations for the α andβ sites are next to the graphs. But, the modelused for the δ site calculation is the one shownin Fig. 4c, which contains the two hydrogen ter-minated SBUs connected by the linker. The Zn,C, O and H atoms of the fragments are coloredpurple, gray, red and white, respectively.

IRMOF-1 in the presence of the applied elec-tric field. The H2 traceless quadrupole in zerofield is Θ = diag(−0.20447,−0.20447, 0.40894).For field parallel to the H2 axis, the quadrupoleis Θ = diag(−0.20423,−0.20423, 0.40846), andif the field E0 is perpendicular to the H2axis Θ = diag(−0.204465,−0.20465, 0.408930).The quadrupoles of the MOF fragments arealso insensitive to the applied field. Thetraceless quadrupole of benzene, which is rep-resentative for the BDC linker, is, in zerofield, Θ ≈ diag(2.87112, 2.87226,−5.74338),where we neglected the off-diagonal terms thatare four orders of magnitude smaller thanthe diagonal. Applying electric field perpen-dicular to the center of the benzene, this

14

quadrupole changes only slightly to Θ ≈diag(2.87976, 2.88074,−5.76050).Additional benchmarking: the choice of func-

tionals. Functionals such as PBE and B3-LYPhave been previously used in studying hydro-gen adsorption in IRMOF-1.28,30,52 Recently, abenchmarking study,29 performed on IRMOF-1, concluded that the meta-GGA functionalM06-2x54 gives more precise results than theother two. Thus, we repeated the calculationsof the binding energy of the H2 to the bind-ing sites considered in Fig. 1 of the manuscript.These calculations were performed using TUR-BOMOLE at the M06-2x/def2-TZVP level ofthe theory. The calculations use the counter-poise method to correct for the BSSE errors.Dispersion corrections are also taken accountin the simulation. Fig. 6 presents these resultsside by side with the results of Fig. 1 in themanuscript, which were obtained using the B3-LYP functional. To perform these energy vsdistance scans, the monomers (H2 and MOFfragments) were optimized prior the calculationwith the same functional and electric field usedin the scans.Comparing the two panels of Fig. 6, we can

see that the results differ both quantitativelyand qualitatively. To explain the quantita-tive differences one should carry out additionalbenchmarking calculations in electric field us-ing more computationally demanding, but alsomore precise methods such as MP2. For thecalculations performed with the M06-2x func-tional, shown in the right panel of Fig. 6a, thebinding energy for the δ-site increases for pos-itive electric field, and decreases for negativeelectric field. Qualitatively, this is the oppositeof the result obtained using the B3-LYP func-tional, and expected from the electrostatics ar-guments invoked in the manuscript. Nonethe-less, if the same calculation is performed on asimpler model of the α-site, the results are qual-itatively the same as expected from the electro-statics considerations. In this case, presented inFig. 7, the results obtained from the GGA func-tionals PBE and B3-LYP agree with the resultsobtained for the meta-GGA functionals M06-2xand M06.The GCMC calculations presented in the pa-

per are consider only the induced polarization(effective Born charges) effect of the electricfield on the MOF. The effect of the electricfield on the exchange-correlation terms of theinteraction between the MOF and H2 is notincluded, as the Lennard-Jones dispersion po-tential is parametrized in the absence of theelectric field. This parametrization works wellin the zero field case. However, if strongerpolarization effects are present, this simplemodel should be revised to include i) more pre-cise calculations of the effective Born charges,ii) a field-dependent parametrization of theexchange-correlation effects. The latter couldprove a daunting task due to the asymmetryintroduced by the electric field.

5.2 Parameters for the GCMCsimulations

Parameters for H2. In zero field, the H2 is mod-eled56 as a quadrupole with q ≈ 0.468e on thehydrogen atoms and −2q charge in the centerof the molecule. For H2 parallel to the appliedfield, the charges are q±δq on the H atoms and−2q in the center of the molecule. δq = 0.023eis chosen so that the dipole of H2 along its axisis p‖ = 0.033a.u.. The model for H2 polarizedperpendicular to its axis has the same chargesas the unpolarized model, but its center chargeis displaced perpendicular to the molecule’s axisby δd = 0.0074Å. This is chosen to reproducethe dipole moment p⊥ = 0.013a.u. induced byelectric field E0 perpendicular to the molecule’saxis.

Parameters of the unpolarized IRMOF-1model. There are 7 inequivalent atoms inIRMOF-1 unit cell. Each of these has a partialcharge qi. The corresponding Lennard-Jonescoefficients Ci

6, Ci12 are taken from the DREID-

ING force field parameters48 Table 2a containsthe partial charges and Lennard-Jones coeffi-cients used in our calculations for IRMOF-1.The position of the other 417 equivalent atomsin the IRMOF-1 unit cell can be obtained by ap-plying symmetry transforms S from the spacegroup 225 of IRMOF-1.

15

Figure 6: The binding energy as a function of the distance of H2 to a) the δ-site located abovethe benzene ring of the BDC linker, b) the α-site and the c) β-site on the SBU. The left panelcontains the data presented in Fig. 1 of the main manuscript which was obtained with the B3-LYPfunctional, while the right panel represents the results of the same calculation performed using theM06-2x functional. The Zn, C, O and H atoms of the fragments are colored purple, gray, red andwhite, respectively. The adsorbed H2 is colored green.

Parameters of the polarized IRMOF-1 model.The polarized IRMOF-1 model uses the par-tial charges and Lennard-Jones coefficients pre-sented in Table. 2a. To include the polariza-tion effects, we computed the Born charges Z∗ifor each of the inequivalent MOF atoms, as ex-plained in the main text. The point dipole cor-responding to an atom i is pi = Z∗i (Ri(E0) −Ri), whereRi is the atomic position of the atomin zero field, whileRi(E0) is the atomic positionof the atom i in field E0z. As the Born chargeis a tensor, the induced dipole of the atom i isnot necessarily parallel to the field. The calcu-lated Born charges are shown in Table 3 for the7 inequivalent atoms in the IRMOF-1 fcc unitcell. From these Born charges, one can obtainthe Born charges for any equivalent atoms inthe unit cell using the symmetry operations S

from the space group 225 of IRMOF-1. If Z∗i ofatom i is known, Z∗j = SZ∗i S

† for the equivalentatom j. The periodic system DFT calculations,from which we obtained Born charges, atomicpositions, and lattice constants, discussed in thenext section, were performed using the softwareCRYSTAL40 as described in the main text.IRMOF-1 model for GCMC simulations. The

GCMC simulations were performed by consid-ering a 424-atom fcc IRMOF-1 cell. In this cell,each atom has its charge qi as shown in Ta-ble 2a. To create a model for IRMOF-1 that in-cludes the electrically induced polarization, weplace a dummy atomic site next to each atom asshown in Fig. 8. In this model, charges Qi > 0are placed on the dummy site and qi − Qi areplaced on the atomic site i. Ri is the positionof the site i as obtained by lattice relaxation inzero field. The dummy site is placed at Ri+di,

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Table 2: Parameters for GCMC in zero field case. a) Lennard-Jones coefficients andpartial charges for the inequivalent atoms in IRMOF-1 unit cell. The reduced coor-dinate for these atoms are given, where a = b = c for IRMOF-1 cubic cell. b) partialcharges and Lennard-Jones coefficients for the adsorbate. Note that the IRMOF-1atoms only interact with the center of mass HCOM of the H2 via Lennard-Jones disper-sion potentials.

(a) IRMOF-1Label Type x/a y/b z/c Charge C6 C12

Zn1 Zn 0.2936 0.2064 0.2064 1.5332 27.6760 4.0454O1 O 0.2500 0.2500 0.2500 -1.8572 48.1562 3.0337O2 O 0.2809 0.2191 0.1331 -0.7817 48.1562 3.0337C1 C 0.2500 0.2500 0.1105 0.7364 47.0000 3.4726C2 C 0.2500 0.2500 0.0534 0.0882 47.8600 3.4700C3 C 0.2828 0.2172 0.0265 -0.1504 47.8600 3.4700H1 H 0.3082 0.1918 0.0481 0.1634 7.6500 2.8500(b) H2Hatom H - - - 0.4680 - -HCOM H - - - 0.9360 36.7000 2.9580

Table 3: The Born charges obtained for the IRMOF-1 atoms as discussed in the maintext.

Label Type Z∗xx Z∗xy Z∗xz Z∗yx Z∗yy Z∗yz Z∗zx Z∗zy Z∗zzZn1 Zn 2.15 0.22 0.22 0.22 2.15 -0.22 -0.22 -0.22 2.15O1 O -1.85 0.0 0.0 0.0 -1.85 0.0 0.0 0.0 -1.85O2 O -0.99 0.44 -0.47 0.44 -0.99 0.47 -0.64 0.64 -2.07C1 C 1.18 -0.91 0.0 -0.91 1.18 0.0 0.0 0.0 3.18C2 C -0.03 0.06 0.0 0.06 -0.03 0.0 0.0 0.0 -1.1C3 C -0.03 -0.06 0.17 -0.06 -0.03 -0.16 -0.06 0.06 -0.03H1 H 0.06 0.06 -0.03 0.06 0.06 0.03 -0.06 0.06 0.11

where the vector di is chosen so that pi = Qidi.The distance between the dummy position andits corresponding atom i has been chosen con-stant di = 0.27Å. One can see from the figurethat the dummy atoms are not only displacedalong the z-axis with respect to the positions oftheir corresponding atoms. This is consistentwith the fact that the polarization induced bythe applied field is not necessarily parallel tothe applied field since the Born charge is a ten-sor with off-diagonal components. The GCMCsimulations are performed with the RASPA2software.47 For the zero field case, we use the424-atom fcc unit cell of the MOF, while for thefield along z-axis, we use the unit cell with theextra 424 dummy sites as shown in Fig. 8.Cancellation of the quadrupole-dipole effects

on adsorption. We argued in the main textthat the dipole-quadrupole contributions to theinteraction energy between H2 and its bindingsites in IRMOF-1 do not affect the uptake. InIRMOF-1, and any MOF with reflection sym-metry, we can obtain an identical site to a givensite by simply performing a reflection. Assumethe electric field is turned on and is perpen-dicular to the reflection plane. The hydrogencan bind to both sites, the first site, and theone obtained by reflection. On one of the sites,the dipole-quadrupole interaction will have onesign, while on the other, it will have the oppo-site sign. Note that the dipole-dipole contribu-tion would always have the same sign on bothsites.The algorithm for the GCMC simulations58

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Figure 7: Comparison of the binding energy ofH2 to the δ-site on the BDC linker, calculatedwith a) PBE, b) B3-LYP, c) M06-2x, and d)M06 functionals. The results are BSSE cor-rected. All the calculations use a H2 moleculeand a BDC fragment initially optimized withB3-LYP in zero electric field. The C, O andH atoms of the MOF fragment modeling theδ-site are colored gray, red and white, respec-tively. The adsorbed H2 is colored green.

implies the generation of a starting configura-tion for the H2 present in the MOF cell. Oncethat is generated, a number N of cycles are per-formed, until, on average, the energy and thenumber of particles inside the selected MOFcell does not change anymore. During a cycle,moves such as insertion, deletions, translationsand rotations of H2 molecules are performed.The averaging is done every n cycles, over thelast n cycles, including the current one. Averageenergies and number of adsorbate particles arecomputed. If these averages do not differ signif-icantly from the previous averages, the GCMCcalculation is converged.Assume we perform n cycles and compute av-

erage densities and energies at the end. Letus consider a site, for instance, the site α of

Figure 8: Pictorial representation of the polar-ized model for IRMOF-1. The Zn, C, O andH and dummy atoms are colored purple, grey,red, white, and magenta, respectively.

IRMOF-1 as in Fig. 4. Another identical siteα′ can be obtained by performing a reflectionoperation allowed by the crystal symmetry. Wewill have configurations in which i) none of thetwo sites is occupied, ii) only one of the sites isoccupied, iii) both sites are occupied. The sit-uation i) is equally probable for both directionsof the applied electric field E.In the situation ii) for one field direction, we

have either site α, or site α′ occupied. Let us la-bel the binding energy at these sites Eα

B(E), orEα′B (E). Neglecting the relatively small dipole-

dipole interaction, we have EαB(E) ≈ Eα′

B (−E),as the main contribution to the energy comingfrom the dipole-quadrupole interaction changessign with electric field. That means the config-uration with electric field E and site α occupiedis as probable as the one with electric field −Eand site α′ occupied, if we neglect the dipole-dipole interactions. As a result, there will be anequal number of configurations with one of thesites occupied for both directions of the appliedfield.In the situation iii), in which both sites are

occupied, we can argue that the probability toarrive at such configuration, from a configura-tion in which they are unoccupied is, for a given

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direction of the field, P (E) = Pα(E)Pα′(E),where the probability to occupy the site byperforming a move is58 Pα(E) = e−βE

αB(E).

Then, the probability of obtaining a configura-tion with both sites occupied is equal for bothfield directions, and very close to the one ob-tained for zero field, if the dipole-dipole inter-action is weak.

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