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Study of Guest Molecules in Metal-Organic Frameworks by Powder X-ray Diffraction: Analysis of Difference Envelope Density Andrey A Yakovenko, Zhangwen Wei, Mario Wriedt, Jian-Rong Li, Gregory J Halder, and Hong-Cai Zhou Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/cg500525g • Publication Date (Web): 29 Sep 2014 Downloaded from http://pubs.acs.org on October 5, 2014

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Crystal Growth & Design 1

Study of Guest Molecules in Metal-Organic Frameworks by Powder X-ray Diffraction: Analysis of Difference Envelope Density Andrey A. Yakovenko,1,2* Zhangwen Wei,1 Mario Wriedt,1,3 Jian-Rong Li,4 Gregory J. Halder,2 and Hong-Cai Zhou1* 1

Department of Chemistry, Texas A&M University, College Station, Texas 77843, United States X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, Argonne IL 60439, United States 3Department of Chemistry & Biomolecular Science, Clarkson University, Potsdam, NY 13699, United States, 4Department of Chemistry & Chemical Engineering, Beijing University of Technology, Beijing, 100124, P. R. China 2

A successful technique for structural studies of guest molecules inside metal-organic framework (MOF) has been designed. It was shown that important structural information can be extracted using Structure Envelopes, which can be readily generated from the structure factors of a few (1 to 10) of the most intense low index reflections. By taking difference between structure envelope densities produced from X-ray powder diffraction pattern and that calculated from the desolvated MOF structure, the Difference Envelope Density (DED) can be prepared. DED can provide information about position, shape and approximate occupancy of molecules in the MOF pores. In comparison to regular Fourier difference density maps, generation of DED maps do not require large number of reflections with known structure factor phases. As such, DED maps can be readily obtained from routine powder X-ray diffraction data. In this article the use of DED maps for studies of solvent molecules location, porosity activation and gas loading are described.

*Corresponding Authors: Dr. Andrey A. Yakovenko X-ray Science Division, Advanced Photon Source, ANL 9700 South Cass Ave Argonne, IL 60439 USA Phone: 630-252-0325 Fax: 630-252-5391 Email: [email protected]

Dr. Hong-Cai Zhou Dept. of Chemistry, 3255 TAMU College Station, TX 77843, USA Phone:979-845-2936 Fax: 979-845-4719 Email:[email protected]

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Study of Guest Molecules in Metal-Organic Frameworks by Powder X-ray Diffraction: Analysis of Difference Envelope Density Andrey A. Yakovenko,1,2* Zhangwen Wei,1 Mario Wriedt,3 Jian-Rong Li,4 Gregory J. Halder,2 and Hong-Cai Zhou1* 1

3

Department of Chemistry

2

X-ray Science Division,

Texas A&M University

Advanced Photon Source

3255 TAMU

9700 South Cass Ave

College Station, TX 77843

Argonne National Laboratory, IL 60439

USA

USA

Department of Chemistry &

4

Department of Chemistry &

Biomolecular Science

Chemical Engineering

Clarkson University

Beijing University of Technology

8 Clarkson Ave

Beijing, 100124

Potsdam, NY 13699

P. R. China

USA

Tel.: +1 (630) 252-0325 Fax: +1 (630) 252-5391 Email: [email protected], [email protected]

Keywords: Metal-Organic Frameworks, Structure Envelope, Difference Envelope Density, Structure Determination from Powder Diffraction, Guest Molecules Location,


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ABSTRACT The structural characterization of metal-organic frameworks (MOFs) by powder X-ray diffraction can be challenging. Even more difficult are studies of guest solvent or gas molecules inside the MOF pores. Hence, recently we successfully designed several new approaches for structural investigations of porous MOFs. These methods use Structure Envelopes, which can be easily generated from the structure factors of a few (1 to 10) of the most intense low index reflections. However, the most interesting results have been found by using Difference Envelope Density (DED) analysis. DED can be produced by taken the difference between observed and calculated structure envelope densities. The generation and analysis of DED maps are straightforward, but allow studying guest molecules in the pores of MOFs by using routine powder X-ray diffraction data. Examples of DED used for studies of solvent molecule location, porosity activation and gas loading are presented herein. We show that DED analysis is an important technique in the study of host-guest properties in MOFs by providing position, shape and approximate occupancy of molecules in the MOF pores.



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INTRODUCTION Over the last 10 years, Metal-Organic Frameworks (MOFs) have become one of the fast growing areas in chemistry and materials science.1-5 Because of their high surface areas together with many other physical-chemical properties, these materials have a large number of applications in many fields, including gas storage,6-10 separation11,12 and sensoring.13,14 One of the main advantages of these porous materials is their crystallinity, which enables structural investigations via X-ray and/or neutron diffraction measurements. As the field of MOFs has been growing, standard procedures for structure determinations and verification have been developed. For example, the structure determination of MOFs is primarily performed by single-crystal X-ray diffraction analysis, while verification of materials bulk purity or stability is usually performed by powder X-ray diffraction (PXRD) measurements. At the same time, MOF researchers mainly use powder diffraction data only for comparison of diffraction peak positions to get limited structural insights of the materials. The reflection intensities, however, are usually largely ignored. In fact, crystal structures of new MOF materials are usually determined by single-crystal diffraction analysis of solvated crystals. During the structure refinement, one of the standard procedures is to “SQUEEZE”15,16 the disordered solvent molecules out of the structure leaving just the framework. This solvent-free MOF structure is used to simulate a powder pattern which is compared with the experimental patterns of as-synthesized and/or activated (solvent removed) MOFs. However, this approach provides evidence that only the material's framework is intact, while the full structure of the MOF, which includes solvent guest molecules, might differ dramatically. In fact, during the activation process, MOFs are treated extensively by solvent exchange reactions and thermal treatments to remove solvent molecules from pores, likely leading to changes in the structures which have rarely been studied.17-20 In general, MOF researchers appear to overlook structural studies of solvent molecules position and amount before and after activation reactions, yet they are at the core of the all-important porous properties. Thus, the porosity/sorption studies are sometimes performed on materials of a poorly defined structure. On the other hand, studies of positions and amount of small-molecule guests (e.g. CO2, H2, CH4) in the pores of frameworks are of great interest.21-28 They provide detailed insights in


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guest-framework interactions and help to understand gas sorption properties and thus, allow the design of materials with better gas sorption or separation capacities. However, these structural studies are limited due to complicated experimental setup and difficulty of structure determination. Understandable, PXRD measurements can provide information about gas or solvent guest location and amount in the framework via differences in the reflection intensities. Such information can sometimes be extracted by Rietveld refinements. However, MOFs usually have large lattice parameters and the guest molecules are often highly disordered in the pores, which leads to extreme peak overlaps and very weak diffraction intensities at high 2θ angles. Therefore, such analysis is usually not possible even with synchrotron powder diffraction data. The absence of easy and routine technique for guest position location is very likely the main reason for the small number of detailed guest molecule studies in MOFs. In recent years, the area of structure determination from powder diffraction has progressed dramatically.29-33 Particularly, in the case of structure determination of zeolites where McCusker and Baerlocher34 have shown that it is possible to forward structure solution by finding the regions in the structure which almost certainly contain atoms. Indeed, by assigning correct structure factor phases ϕhkl to structure factor amplitudes |Fhkl| by selecting a few (1 to 10) low-order, intense and not overlapping reflections in the powder pattern, a surface that divides regions with high and low electron density can be produced. This surface is named the structure envelope (SE)35,36 and can be generated by using the Fourier transformation similar to the electron density formula

ρ ( x, y, z ) = ∑ Fhkl cos(2π (hx + ky + lz ) − ϕ 'hkl ) (1). hkl

In this equation ρ(x,y,z) is called envelope density, and since summation in equation (1) is done for only a small number of reflections, envelope density might have positive and negative values. The three dimensional surface when ρ(x,y,z) = 0 will yield the structure envelope. Recently, we have shown that SEs can be easily generated for MOFs materials from PXRD data, and describe the pore system of material, with the framework atoms located on the positive side of the ρ(x,y,z). We also have shown that application of SEs in Charge Flipping calculations dramatically simplifies MOFs structure determination from powder diffraction.37



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In this article we introduce a new function – difference envelope density (DED). We will show, that generation and analysis of DED for MOFs is relatively straightforward, but it provides important information for the study of guest related properties in porous MOF materials, including solvent location, the activation process and gas loading. In our opinion DED analysis can become a critical method for the study of porous MOF materials by powder diffraction.

RESULTS AND DISCUSSION

Difference Envelope Density (DED). SEs can be also used for the structural identification of MOFs by powder diffraction data. This approach is based on the idea that if two MOF materials have identical structures, their structure envelopes should be the same. This statement can be used as the basis for a simple method of identification and/or conformation that the powder diffraction pattern corresponds to structure of a MOF material determined previously (e.g. via single-crystal diffraction). In fact, if the crystal structure of a MOF material is known, it is very easy to calculate calc calc ideal structure factor amplitudes Fhkl and phases ϕ hkl for the structure envelope determining

reflections. SE density calculated via equation (1) generated from this information we call ideal or calculated envelope density ρcalc. Structure factor amplitudes extracted via Pawley or Le Bail techniques from powder diffraction patterns Fhklobs can be used to generate observed envelope calc density ρobs. For this process the previously calculated structure factor phases ϕ hkl can be used.

It can be stated, that if a powder diffraction pattern precisely correspond to the structure of a MOF, the difference between observed and calculated envelope densities should be approximately equal to zero

ρobs − kρcalc ≈ 0 (2) where k is the scaling factor. This is a very simple way to identify that the structural model exactly corresponds to the structure of a MOF material of which powder data was collected. The word exactly in this case


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means, that all atoms in the structure of the bulk MOF material, including metal cluster – secondary building unit (SBU), organic linker and the pore guests have absolutely the same types, coordinates and occupancies as in the model MOF structure which has been used for generation of ρcalc. However, if one or several of these structural parameters are different, then equation (2) will not be equal to zero and difference between ρobs and ρcalc will produce difference envelope density (DED)ρ∆.

ρ∆ = ρobs − kρcalc (3) This density shows the rough difference between the actual structure of a MOF and its assumed model, in other words DED is a type of low resolution difference electron density map. Understandable that if such difference is large, the values of ρ∆ are meaningless. However, if the actual structure is close to the model (e.g. the structure of MOF framework is the same) then ρ∆ can provide vital structural information about the MOF and/or pore guests, such as solvent location, activation, gas loading, interpenetration, ligand substituents locations and MOF structural changes, etc. In this article we will describe the use of DEDs for the analysis of guest molecules in MOF pores. For such issues we assume that the structure of the framework, its crystallographic symmetry and unit cell parameters do not change upon addition or removal of the guest molecules to the MOF pores. The structure factor phases for envelope determining reflections for both guest loaded and empty MOFs will likely be the same while the structure factor amplitudes calc calc calc will differ. Hence, by using the combinations of Fhklobs , ϕ hkl and Fhkl , ϕ hkl via equation (1)

observed ρobs and calculated ρcalc can be generated. The difference between these two densities (equation (3)) results in the difference envelope densityρ∆, which corresponds to the envelope density of the guest molecules. Understandably, if the guest molecules do not contain heavy atoms, the maximums of

ρobs and ρcalc should be located at the same positions of the metal cluster SBUs. In this case it is easy to calculate the scale factor k by equation (3), which can be estimated as the division between values at maximums of these two envelope densities.

ρ = (4) ρ



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Plotting of DED will identify the position, shape and approximate occupancy of the guest molecules. In the following we will describe how to use this approach to study solvent position location, activation processes and gas loadings of MOFs. Solvent position location. It is well-known, that MOF syntheses are usually performed in polar solvents, which typically have high boiling points. As a result, solvent molecules are frequently trapped in the pores of the synthesized materials. Knowing the location of these guest molecules might provide important information about newly synthesized MOFs, such as stability, polarity of the cavities, and activation procedures. However, location of solvent molecules is rarely studied due to the high disorder, which prevents the accurate determination of their position or number. Thus, researchers “squeeze” those molecules from the structures and primarily study the framework itself.15,16 At the same time, this “squeeze” procedure provides an ideal set up for the determination of the solvent molecules position. Indeed, the structure determination of MOFs via single crystal diffraction and its refinement with the squeezed data yields a solvent free model which can be used for the generation of calculated envelope densities ρcalc. The powder diffraction measurement provides the intensities of the envelope determining reflections needed for building the observed envelope densities ρobs. Hence, the missing solvent molecular positions from the initial structural model obtained by single crystal databe easily determined by generating ρ∆ and overlapping it with the structure of the MOF material. The use of DEDs for the determination of solvent position is shown by examples of two well-known MOFs: HKUST-138 and UiO-6639 (Figures 1 and 2). Both MOFs crystallize in the cubic space group F m͞3m with the unit cell parameters close to 26 and 21 Å respectively. To show that DEDs provide useful data with any type of X-ray radiation, we collected powder diffraction data of an as-synthesized sample of HKUST-1 on a regular home diffractometer with Cu Kα radiation, while data of an activated and exposed to the air sample of UiO-66 was collected at beamline 1-BM of the Advance Photon Source, Argonne National Laboratory (Argonne, IL, USA) with a wavelength of 0.6057 Å. Pawley40 whole pattern decomposition for both MOFs were performed with the software TOPAS 4.2.41 Unit cells parameters are consistent with previous results and systematic absences


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correspond to the cubic F crystal system. Refinements converged with satisfactory R-values (see supporting information Table 1S) and final plots are presented in Figures 1a and 2a. From the powder data, reflections with indexes {420}, {422}, {200}, {220}, {222}, {440} for HKUST-1 and {111}, {200}, {220}, {311}, {222} and {400} for UiO-66 were selected as the most intense and non-overlapping reflections for SE generations.

Figure 1. (a) Final Pawley whole pattern decomposition plot of HKUST-1, (b) its observed structure envelope based on ρobs, (c) its calculated structure envelope based ρcalc, and (d) its difference envelope density ρ∆ overlapped with its structural model.

Solvent free structures of HKUST-1 and UiO-66 determined by single crystal X-ray diffraction were used to calculate ideal intensities and structure factor phases needed for generation of ρcalc. Calculated SEs which correspond to these model densities are presented in Figures 1c and 2c. It can be seen that the pore structure and shape of these envelopes completely repeats the MOFs structures itself, which confirms the correct nature of the envelopes.



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Combination of calculated structure factor phases with intensities determined from Pawley refinement were used to generate observed envelope densities ρobs. Corresponding SEs are shown in Figures 1b and 2b. The shape and structure of the observed envelopes are very similar to the calculated ones, however, it can be clearly seen that they contain more density in the pore regions.

Figure 2. (a) Final Pawley whole pattern decomposition plot of UiO-66, (b) its observed structure envelope based on ρobs, (c) its calculated structure envelope based ρcalc, and (d) its difference envelope density ρ∆ overlapped with its structural model.

The ρ∆ densities were generated with the software USF Chimera,42 their overlap with the HKUST-1 and UiO-66 structures are presented in Figures 1d and 2d. It can be clearly seen that in case of HKUST-1 the most intense peaks of the DED are located in all pore regions (Figure 1d). We can find one large peak in the middle of the octahedral cavity, while the cuboctahedral pores contain large peaks on each side of the cavity plus one in the middle. Since the HKUST-1 sample was synthesized from a reaction mixture containing diethylformamide (DEF) as solvent, we can speculate that these large peaks of ρ∆ represent the DEF molecule locations in the MOF


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pores. This assumption is probably correct due to the fact that these large peaks are located in both the octahedral and cuboctahedral cavities and have approximately the same size. The cuboctahedral pores also contain smaller peaks located on the side of the cavity close to the benzene tricarboxylate ligands. These peaks might represent smaller molecules trapped inside the pores during synthesis, such as water or other DEF molecules which have lower occupancies. On the other hand, DEDs made for UiO-66 (Figure 2d) contain only small peaks located close to the Zr-cluster. Since the sample of the UiO-66 was already activated and exposed to the air environment, these peaks probably correspond to the position of water molecules adsorbed from air moisture. It can be clearly seen that the position of these polar water molecules is very logical since they are located close to the most polar fragment in the cavity. With these two simple examples we have shown that DEDs can be very efficient in finding the position and approximate amount of solvent molecule trapped in different cavities of MOFs. Additionally, the size of the ρ∆ density peaks is seen to correspond to the size and/or occupancy of the guest molecules. This indicated that the DEDs can be used to study MOF activation processes. Study of MOF activation. The solvent removal from pores (activation) is extremely important as it influences the gas sorption properties of the MOF; hence, the study of activation processes should be of great interest to the MOF community. The activation process is usually studied either by gas sorption43 or thermoanalytical measurements.44,45 These methods allow the estimation of the amount of solvent molecules removed from the pores, however, direct evidence of what happens with particular solvent molecules during their removal is not provided. Powder X-ray diffraction measurements are usually performed for activated samples, but mainly for the purpose of determining stability of the framework material after activation, by comparison of diffraction peak positions in powder data for activated and as synthesized MOFs. However, there has traditionally not been intent to use such powder diffraction data to determine how many solvent molecules are left inside the pores at different temperatures and what happens to these molecules during the MOF activation process. These studies are rarely performed using single crystal diffraction data due challenges in the refinement of solvent molecules.46,47 However, generation and analysis of DEDs might be a



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very simple alternative for activation studies, since it can be performed using routine X-ray powder diffraction data obtained from home-lab diffractometers. To show how the generation of ρ∆ will help to study the activation of MOFs, we studied the activation of MAMS-4,48 which helps us to explain its unique selective adsorption properties. MAMS-4 is a 2D-layered MOF, which is formed by copper(II) paddlewheel SBUs connected by 4′-tert-butyl-biphenyl-3,5-dicarboxylate (BBPDC) ligands, having mesh-adjustable molecular sieve properties. The mesh size (size of the pore opening) can be easily changed by heating or cooling this material, which allows MAMS-4 to selectively separate a wide range of gases. Activation studies of MAMS-4 by different applied heating programs have been published in detail.48 A freshly synthesized sample of MAMS-4 was heated in a dynamic vacuum to 130 °C followed by heating in 10 °C increments to 180 °C, every single heating process was followed by a one hour isothermal step at each temperature. After each temperature step the O2 and N2 sorption properties were investigated. It was found that MAMS-4 does not have any significant oxygen or nitrogen uptake with activation temperatures below 150 °C; however, after its activation at 150 °C, the material has selective oxygen over nitrogen separation properties. Heating the material to higher temperatures leads to the loss of selectivity, while overall gas uptake increases, reaching a maximum at 170-180 °C (see supporting information Figure 1S). Based on this data we can clearly see that gas sorption properties of MAMS-4 highly depend on the activation conditions. To study this in detail, X-ray powder diffraction data was collected on three samples of MAMS-4: as-synthesized, activated at 150 °C, and activated at 180 °C; the two activated samples were collected in an inert atmosphere. All data were collected on home-based X-ray powder diffractometer using a Cu Kα radiation source. Pawley refinements of the diffraction data (Figure 3) show that all three samples crystallize in P3c1 space group with similar unit cell parameters close to a = 18 and c = 22 Å. Extracted intensities of 8 reflections ({010}, {002}, {110}, {012}, {020}, {202}, {112}, {302}) in each case were used for generation of ρobs and corresponding SEs (Figure 2Sb-d). The solvent free structure of MAMS-4 was used to calculate structure factor phases, and ideal intensities for envelope determining reflections which were used for generation of ρcalc and calculated SE (Figure 2Sa).


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We also re-determined crystal structure of as-synthesized MAMS-4 via single crystal Xray diffraction analysis, to investigate actual DMF solvent positions in the pores of the framework. The structural model for the freshly synthesized MOF is presented on Figure 4a. The structure reveals that the hydrophilic pores of the as-synthesized sample are blocked by disordered dimethylformamide (DMF) molecules, while the majority of these solvent molecules are coordinated to copper centers of the Cu-SBU.

Figure 3. Final Pawley whole pattern decomposition plots for (a) as-synthesized, (b) activated at 150 °C and (c) activated at 180 °C samples of MAMS-4.

DEDs were calculated via equation (3) and ρ∆ plots for each MAMS-4 sample are presented in Figures 4b-d. The comparison of the largest DED peaks for the as-synthesized sample with the shape and position of DMF molecules in the pore determined by single-crystal diffraction clearly reveals their similarity (Figures 4a,b). Hence, it confirms that the major peaks of ρ∆ indeed correspond to disordered solvent molecules in the pores. In case of the activated samples, the overall amount of the DED is decreasing with increasing activation temperature,



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which corresponds to the partial solvent removal from the cavities (Figures 4c,d). Almost no strong ρ∆ peaks remain in the middle of the pore in the case of the sample activated at 180 °C, hence it should have no solvent molecules left in the pores. This is in agreement with gas sorption data, since this activation temperature gives the highest O2 and N2 uptake.

Figure 4. (a) Crystal structure of as-synthesized MAMS-4, and difference envelope density ρ∆ plots generated for (b) as-synthesized, (c) activated at 150 °C and activated at 180 °C samples overlapped with their structural model. Second position of coordinated DMF molecule removed for clarity.

Meanwhile, the ρ∆ for MAMS-4 activated at 180 °C contains small peaks at the positions of oxygen atoms coordinated to Cu-based SBUs. These peaks probably originated from oxygen atoms of DMF molecules in the second orientation, which are located between the hydrophilic channels of the framework (The full description of the DMF solvent molecules disorder presented in supporting information). It probably requires additional energy and time to remove these DMF molecules. However, presence of these molecules does not block the main pores of the framework.


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Similar peaks can be observed in ρ∆ plot for the MAMS-4 sample activated at 150 °C (Figure 4c), therefore the strong peaks and surfaces in the middle of the pore likely correspond to non-coordinating DMF molecules. Based on this data it can be speculated, that the unique selective gas sorption properties for MAMS-4 can be attributed to partial presence of DMF molecules in the hydrophilic channels. Upon increase of the activation temperature the majority of solvent molecules leave the pore and the gas sorption selectivity of the MOF is lost. However, since the pores become less occupied, the overall gas uptake increases. It was shown that, DED generated from routine X-ray powder diffraction data can be used for detailed studies of MOF activation processes. The ρ∆ plot allowed not only tracking the amount of solvent molecule removed, but also their position in the pores at each particular temperature. Similar analysis of DED can be used in the investigation of another important process in MOF research, the gas loading into the pores.

Study of gas loading into MOF pores by “Benchmarking”. As described earlier, the most promising applications of MOFs involve gas storage and separation. In this context the study of gas sorption sites is crucial to understand and design MOF materials with unique adsorption properties. Experiments to locate gas molecules inside MOF cavities have been performed for almost a decade by using single crystal X-ray diffraction,23,24,49 powder X-ray diffraction,22,50 single crystal neutron diffraction25 and powder neutron diffraction21,26-28 techniques. However, all these studies required high quality data collection coupled with often complex data refinement and analysis. In our approach, generation and analysis of DEDs has been successfully used to identify gas molecule position, shape and approximate occupancy in MOF pores. For our experiment we choose to investigate the carbon dioxide loading of PCN-200, recently investigated in our lab.45,51 In this communication we have already mentioned the use of DEDs for finding CO2 molecules positions in the framework pores, however, here we describe specifics of ρ∆ plot generation and analysis, which led to identification of the gas molecule positions. PCN-200 is built from copper(II) tetrazolate-5-carboxylate and 1,3-di(4pyridyl)propane forming a 3D-network with pore openings equal to 4.4 Å in its activated form.



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In situ synchrotron-based powder diffraction experiments were performed at the 1-BM

beamline of the Advance Photon Source in Argonne National Laboratory (Argonne, IL, USA) from a PCN-200 sample contained in a polyimide capillary and using a flow-cell setup.52 The incident X-ray wavelength was 0.6065 Å. The sample was heated to 373 K in a dynamic helium atmosphere to generate the activated phase of PCN-200 followed by a CO2 loading process at 1atm and 200 K. Moderate-resolution diffraction data were collected using a flat panel area detector over a 2θ range of 1-25° (dmin = 1.4 Å). The Pawley refinements plots of the activated and CO2-loaded phases are presented in Figure 5. Refinements showed that both phases crystallize in the monoclinic space group C 2/c with unit cell parameters close to a = 28, b = 9, c = 9 Å and β = 116°. Reflections {2 0 0}, {1 1 1}, {3 1 0}, {3 11}, {511}, {5 1 0}, {3 1 1}, {2 0 2} and {621} were chosen for SE densities generation in all cases. The intensities of these reflections from Pawley whole pattern decompositions were used in generation of ρobs and corresponding SEs (see supporting information Figures 3Sb,c).

Figure 5. Final Pawley whole pattern decomposition plots for (a) activated and (b) CO2-loaded PCN-200 phases.

The ρ∆ plots for the CO2-loaded and activated phase of PCN-200 are presented in Figure 6 and 7a,b. For the generation of these plots we used the activated structure of PCN-200 as basis for the calculation of ideal structure envelope density ρcalc (see supporting information Figure


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3Sa). The peaks in the DED of the CO2-loaded phase have size and shape very similar to carbon dioxide molecules (Figure 6) and is located exactly in the center of the pores on a center of inversion (Figure 7a). However, the ρ∆ plot of the activated PCN-200 phase also contains major peaks at the same positions as in CO2-loaded phase (Figure 7b). Assuming that that we should not see any strong peaks of DED in the pore environment of the completely activated phase, these peaks might be attributed to errors and/or artifacts. Thus, it is likely that the peaks which were attributed to carbon dioxide molecules might also be artifacts. Hence, an additional evaluation of DED peaks validity is needed. To perform such a test we developed a benchmarking procedure. Well-known that, a benchmark in geodetic surveying is the point with a precisely known relationship to the level of the datum of an area, for example sea-level.53,54 In our case, such a benchmark can be one of the light atoms (O, C or N) in the structure of the main framework with known occupancy. This occupancy will provide us the known level of the datum to evaluate approximate occupancy for peaks in the DED. To use this technique, we selected one of the oxygen atoms in the tetrazolate-5-carboxylate ligand as our benchmark atom. This atom has full occupancy equal to 1 and can be used for the evaluation of other peaks in the DED. In the first step this atom was removed from the structural model of PCN-200, and this O-less-structure was used for the generation of a new calculated SE density ρ ͞ calc (see supporting information Figure 3Sd). New DEDs ͞ρ∆ were generated for both activated and CO2-loaded phases by subtracting from previously generated ρobs of the newly calculated O-less ρ ͞ calc. ͞ρ∆ = ρobs − k ͞ρcalc

(5)

In this case, ͞ρ∆ is now combined from two parts: first it contains peaks of the guest molecules inside the pores, and second it contains peaks Figure 6. Close-up view of the DED plot generated for the CO2-loaded phase of PCN-200.

corresponded to the missing oxygen atom, which we call benchmark density ρbm(O):



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͞ρ∆ = ρguest + ρbm(O)

(6)

If the occupancy of the guest molecule corresponding peaks will be much smaller than the occupancy of the oxygen atoms, then only the benchmark peaks will be present in a ρ ͞ ∆ plot. Figure 7c shows that in the newly generated DED plot for the CO2-loaded PCN-200 phase the benchmark peaks, located at carboxylate oxygen atom positions, and very strong CO2-molecule peaks in the middle of the pores are present, while in the ͞ρ∆ plot of the activated PCN-200 phase only benchmark ρbm(O) peaks remain (Figure 7d).

Figure 7. Difference envelope density ρ∆ plots generated for (a) CO2-loaded phase and (b) activated phase of PCN-200. Benchmarked difference envelope density ͞ρ∆ plots generated for (c) CO2-loaded phase and (d) activated phase of PCN-200.

Through the benchmarking procedure we were able to confirm the presence and positions of carbon dioxide molecules in the pores of the CO2-loaded phase. Also, because the intensity of


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the benchmark and CO2 peaks are close to each other, the occupancy of the CO2 molecules is probably around 100%. In the case of the activated PCN-200 phase it was confirmed that no guests are present in the pores and the peaks which were seen in the original ρ∆ plot are insignificant and probably related to errors. Possible Limitations. It is very important to understand that DEDs are affected by errors. There are two major sources of errors. First, is the number of the reflections used for generation of ρ∆. Understandable, that if more structure factors is used calculation of DED it becomes similar to regular difference Fourier electron density map and information about guest molecules becomes much clearer. Therefore in case of low symmetry MOFs greater number of the reflections should be used for generation of DED to minimize this error. Another error can arise due to the structural changes of porous framework during the experiment. In fact, change in temperature, pressure or atmosphere around the MOF sample not just affects the guest molecules, but MOF structure itself. Therefore the framework part of ρobs and ρcalc will be quite different which would lead to formation of error peaks in DED map. To minimise this error structural changes or their approximations may be introduced to the structure of MOF which used for calculation of ρcalc. It is includes not only changes in the atomic positions, but also changes in displacement parameters and occupies of the framework atoms. In addition, experimental artifacts such as absorption effects and preferred orientation effects might distort the correct estimates of important analysis factors (e.g., Fobs values). This would lead to the distortion of the ρobs and meaningless DED maps. These issues can be avoided by overlapping the resulted SE generated from observed data with the known structural model of MOF to confirm that the envelope corresponds to the framework model. Comparison to Low Resolution Fourier Difference Density Maps. In some cases,ρ∆ maps could be very similar to low resolution difference Fourier density maps (Fobs-Fcalc) built using reducing the angular range used in the refinement within regular Rietveld refinement software. Indeed such maps for UiO-66, HKUST-1, as synthesized MAMS-4 and carbon dioxide loaded phase PCN-200 contain some similar features and shapes which can be found in the DED maps for the same materials (Figure 6S). However, only for the case of UiO-66, where the difference between the calculated and observed powder patterns is small (Figure 7Sa), do both difference



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maps techniques produce a truly comparable result (Figures 2d and 6Sa).For each of the other materials, the the difference between observed and calculated patterns is significant (Figures 7Sb-d) and the resulting Fobs-Fcalc Fourier maps contain extra peaks which are not present in ρ∆ maps. It can be clearly seen, that in case of HKUST-1, MAMS-4 and PCN-200 (Figure 6Sb-d) the highest peaks in difference Fourier density maps are located on or near metal atom positions. This effect is due to inappropriate values for the scale factors and the atomic displacement parameters for the metal sites. Refinement by the Rietveld method will not provide the correct values for these parameters unless the composition of the structural phase is estimated correctly, which includes knowledge of the guest molecules positions and occupancies. Without this knowledge the low resolution Fobs-Fcalc Fourier maps have either additional error peaks in the void area of the MOF (MAMS-4, Figure 6Sc) and/or the size and shape of the guest peaks are greatly distorted (HKUST-1 and PCN-200, Figures 6Sb,d). For DED maps, the scale factor can be easily estimated by using equation (3) with maximums for ρobs and ρcalc, as long as guest molecule do not contain any atoms heavier than in the framework. This produces “cleaner” difference maps compared to simplistic low resolution Fobs-Fcalc Fourier maps, and greatly simplifies the estimation of guest molecule location and

shape. This is most clearly demonstrated by comparing the low resolution Fobs-Fcalc Fourier and DED maps for CO2-loaded phase of PCN-200; for the difference Fourier map, large peaks persist near the Cu-atom and two isolated peaks are observed in the MOF cavity (Figure 7Sd), while for the DED map, features are only present in the MOF cavity and distinctly reveal the a shape consistent with a single CO2 molecule (Figure 7a).

CONCLUSION Generation and use of difference envelope densities (DEDs) for analyzing host-guest properties of metal-organic frameworks has been described. It was shown that, DED can be easily generated from routine X-ray powder diffraction measurement and require only few nonoverlaping reflection peaks, however, it can provide detailed information about guest molecules located inside MOF pores. In fact, ρ∆ plot can be used for solvent position location, for tracking the solvent removal from pores upon activation, or for following the gas loading into the MOF


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pores. In our opinion, analysis of DEDs may become an important and routine technique for in situ powder diffraction studies of MOF activation and/or gas loading processes. In our future

work we will demonstrate the use of DEDs in the analysis of host MOF structures.

MATERIALS AND METHODS Synthesis of MOFs All chemicals were purchased from Alfa Aesar and Sigma-Aldrich and used as received. HKUST-1. A solution of Cu(NO3)2·2.5H2O (500 mg, 2.150 mmol) and benzene-1,3,5tricarboxylic acid (H3BTC) (250 mg, 1.195 mmol) in N,N-diethylformamide (DEF) (50 mL) were distributed in 25 glass tubes (2 mL solution in each tube). The tubes were sealed under vacuum, and placed in conventional microwave. Microwaving for 1 min at 770 W power produced blue precipitates of HKUST-1 in each tube. Resulting precipitates were combined and centrifuged, washed with fresh portions of DEF (3x 10 mL) and dried at 70 ºC for 12 h. Yield: 0.54 g. The purity of HKUST-1 was confirmed by a powder X-ray diffraction and Pawley refinement. UiO-66. Synthesis and activation of UiO-66 was performed according to the references.55,56 After activation was completed material was exposed to the air for 14 days before powder X-ray diffraction data was collected confirming its purity and Pawley refinement. MAMS-4 and PCN-200 were synthesized following procedures previously reported.45,48 The purities were confirmed by a powder X-ray diffraction and Pawley refinements.

Single-Crystal X-ray Diffraction Analysis Crystal data, details of data collection and structure refinement parameters for as-synthesized MAMS-4 are presented in Table 2S. The X-ray diffraction experiment was carried out with a Bruker SMART APEX II diffractometer with a CCD area detector (graphite monochromated Mo Kα radiation, λ = 0.71073 Å, ω-scans with a 0.5o step in ω) at 110 K. The semiempirical method



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SADABS57 was applied for absorption correction. The structures were solved by direct methods and refined by the full-matrix least-squares technique against F2 with the anisotropic temperature parameters for all non-hydrogen atoms. All H atoms were geometrically placed and refined in riding model approximation. Data reduction and further calculations were performed using Bruker SAINT+58 and SHELXTL59 program packages. The description of the disorder refinement of N,N-dimethylformamide (DMF) solvent molecules and t-Bu-groups in the 4′-tertbutyl-biphenyl-3,5-dicarboxylate ligand is presented in the supporting information. Powder X-ray Diffraction Experiments Powder X-ray diffraction (PXRD) patterns of HKUST-1, all MAMS-4 samples were obtained on a Bruker-AXS D8 Advanced Bragg-Brentano X-ray Powder Diffractometer using Cu-Kα (λ = 1.5406 Å) radiation, while PXRD data for UiO-66 and PCN-200 samples were recorded on 1BM beamline at the Advance Photon Source, Argonne National Laboratory (Argonne, IL, USA). The incident X-ray wavelength was 0.6057 Å for the UiO-66 sample and 0.6065 Å in the case of the PCN-200. Data were collected using a Perkin-Elmer flat panel area detector (XRD 1621 CN3-EHS) over the angular range 1-25° 2-Theta MAMS-4 activation study. Gas adsorption measurements were performed using an ASAP 2020 volumetric adsorption analyzer. A high-purity grade of oxygen and nitrogen gases was used throughout the adsorption experiments. Before adsorption and ex situ PXRD measurements 120 mg of a freshly synthesized MAMS-4 sample was dried under a dynamic vacuum (

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