Article pubs.acs.org/cm
Contradistinct Thermoresponsive Behavior of Isostructural MIL-53 Type Metal−Organic Frameworks by Modifying the Framework Inorganic Anion Chompoonoot Nanthamathee,†,§ Sanliang Ling,‡ Ben Slater,‡ and Martin P. Attfield*,† †
Centre for Nanoporous Materials, School of Chemistry, The University of Manchester, Brunswick Street, Manchester, M13 9PL, United Kingdom ‡ Department of Chemistry, University College London, 20 Gordon Street, London, WC1H 0AJ, United Kingdom S Supporting Information *
ABSTRACT: The influence of simple framework inorganic anions on the thermoresponsive behavior of the isostructural MIL-53 type metal−organic frameworks [AlF(bdc)] and [Al(OH)(bdc)] has been determined using a combination of diffraction and computational techniques. [AlF(bdc)] has an orthorhombic large pore structure from 500 to ∼175 K at which point it undergoes a subtle distortion to form a monoclinic large pore structure that remains stable to 11 K. The orthorhombic large pore form of [AlF(bdc)] exhibits negative thermal expansion from 175−500 K. [Al(OH)(bdc)] has an orthorhombic large pore structure from 500 to 125 K at which point it undergoes a displacive phase transition, a breathing effect, to form a nonporous monoclinic structure. The orthorhombic large pore form of [Al(OH)(bdc)] exhibits positive thermal expansion from 150 to 500 K. The presence of a breathing effect in [Al(OH)(bdc)], and not [AlF(bdc)], is related to the additional contributions to attractive interactions across the shortest dimension of the pore provided by the presence of the hydroxide groups. The display of positive or negative thermal expansion of the orthorhombic large pore structure of either material is related to the rigidity of the constituent corner-sharing chain of AlO4X2 octahedra with the more rigid AlO4F2 octahedra favoring one type of static or dynamic displacement and the less rigid AlO4(OH)2 octahedra favoring a different type of static displacement. Formation of metal−organic frameworks with controlled expansion and displacive phase transition properties, or simultaneously containing mixed thermoresponsive properties, is predicted through control of the identity and amount of the simple inorganic anions in this family of material. The work indicates the importance of considering the simplest species when designing the thermo-mechanical properties of metal−organic frameworks.
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[M(OH)(bdc)] where M = Al,8 Cr,9 Ga,10,11 V(III),12 Fe(III)/ V(III)13 and bdc = 1,4-benzenedicarboxylate. Such thermoresponsive behavior has important potential implications for MOFs in the formation of composites of controlled thermal expansivity, for instance, to prevent microcracking during formation of thermosets,14 influencing adsorption of gases,15 and forming thermally responsive sensors or flow controllers. One of the materials that exhibits a thermoresponsive “breathing effect” is [Al(OH)(bdc)]16 for which conversion from the very narrow pore (np) form (unit cell volume = ∼864 Å3) to the large pore (lp) form (unit cell volume = ∼1428 Å3) displays significant temperature hysteresis over the range 125− 375 K.8 Although the structural behavior encompassing the phase transition temperature range has been reported, the thermoresponsive behavior of the framework of the lp-form itself is unknown. This is surprising as the framework has
INTRODUCTION Metal−organic frameworks (MOFs) exhibit a vast array of interesting properties and functionalities.1 One such property that is receiving significant attention is the thermoresponsive behavior of the framework.2 As for any crystalline material, the framework of a MOF can expand, contract, or undergo a displacive phase transition as temperature is varied. The negative thermal expansion (NTE) behavior and displacive phase transitions exhibited by certain MOFs are of particular note. For example, certain metal cyanides 3 and metal carboxylates4 have been reported to exhibit overall NTE behavior of magnitude similar to or surpassing that of one of the prototypical NTE materials ZrW2O8,5 with Ag3Co(CN)6 exhibiting colossal NTE behavior.6 A particularly significant displacive phase transition behavior of certain MOFs is their ability to exhibit a “breathing effect” in which the framework unit cell volume varies by a considerable amount in response to a simple external stimulus such as pressure7 or temperature.8 Noteworthy examples of MOFs that undergo such a thermally induced breathing effect are members of the MIL-53 family © XXXX American Chemical Society
Received: September 8, 2014 Revised: November 24, 2014
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[Al(OH)(bdc)]. The evacuated sample was flame-sealed under vacuum. The synthesis of [AlF(bdc)] was developed from the previously reported method19 with replacement of the solvent dimethylformamide (DMF) by DEF. AlF3 (0.0084 g) was dissolved in 10 mL DEF followed by addition of H2bdc (0.996 g). The mixture was then loaded into a 23 mL Teflon-lined stainless steel autoclave that was heated at 220 °C for 4 days. The mother liquor was removed by suction filtration leaving a white fine powder product that was washed with 20 mL of DMF prior to being stirred overnight in 15 mL of methanol. The powder was recovered by filtration and dried at 70 °C before being calcined in static air at 300 °C for 24 h in order to remove any occluded guest molecules from the framework. Successful synthesis of [AlF(bdc)] is indicated by the powder X-ray diffraction pattern (see Supporting Information Figure SI3) and thermogravimetric analysis data (see Supporting Information Figure SI4). A sample of [AlF(bdc)] was packed into a 0.5 mm diameter borosilicate capillary tube and evacuated at 2.1 × 10−1 mbar at 200 °C for 24 h to obtain a fully evacuated sample of ortho-lp-[AlF(bdc)]. The evacuated sample was flame-sealed under vacuum. Another sample of [AlF(bdc)] was packed into a 0.5 mm diameter aluminum capillary tube and evacuated at 2.1 × 10−1 mbar at 200 °C for 24 h to obtain a fully evacuated sample of ortho-lp-[AlF(bdc)]. The evacuated sample was sealed under vacuum by crimping the aluminum tube and further sealing it with super glue. Powder X-ray Data Collection, Structure Refinement, and Determination. Synchrotron X-ray data were collected on samples of lp-[Al(OH)(bdc)] and ortho-lp-[AlF(bdc)] contained in glass capillary tubes mounted on the high resolution X-ray powder diffractometer, equipped with a multianalyzing crystal-detector configuration, at station I11, Diamond Light Source, U.K. The incident X-ray wavelength was 0.825993(3) Å, and the capillary tube was spun during data collection to minimize preferred orientation and sampling effects. Data were collected from 3 to 140° 2θ with a step size of 0.001° 2θ and a total collection of 30 min. The powder patterns were rebinned subsequently with a 2θ step size of 0.003°. Diffraction data were collected at 25 K intervals in the temperature range of 100−500 K using an Oxford Cryosystems’ Cryostream Plus. Synchrotron X-ray data were also collected from a sample of ortho-lp-[AlF(bdc)] contained in a sealed aluminum tube using a similar diffractometer configuration but at temperatures of 11 K, 40 K, 70 K, 100 K, 150 K, 200 K, 250 K, and 290 K attained through use of a Oxford Cryosystems’ PheniX cryostat. The incident X-ray wavelength for these data sets was 0.827154(1) Å, and the capillary tube was rocked during data collection. The diffraction data for lp-[Al(OH)bdc] were initially fitted using the Le Bail method20 to obtain accurate lattice parameters and starting peak shape profile coefficients. These refined parameters were subsequently used in Rietveld refinement. The starting model for the lp-[Al(OH)(bdc)] was taken from the literature.16 Profile analysis was performed on data in the range 5−40° 2θ, and the first highly asymmetrical peak was excluded from the pattern. The background was fit using linear interpolation between manually designated background points. The peak shape profile function used was a modified pseudo-Voigt function that allows for the effect of microstrain and microsize. The final cycle of least-squares refinement consisted of 28 refined parameters including the scale factor, detector zero point, unit cell parameters, peak profile parameters, atomic coordinates, and isotropic atomic displacement parameters of all six atoms in the asymmetric unit. The isotropic atomic displacement parameters of the O atoms were constrained to have the same value, as were those of the C atoms. All the data sets from 150−500 K were refined using an identical procedure. Evidence of the presence of np-[Al(OH)(bdc)] was identified in the diffraction patterns at 100 and 125 K which reflects the displacive phase transition behavior reported previously for the lp- to np[Al(OH)(bdc)] transition.8 The thermoresponsive behavior of phase pure lp-[Al(OH)(bdc)] will only be included in this study to remove any possible influence on the results of the np-[Al(OH)(bdc)] phase. A nearly identical refinement procedure was pursued for data collected from the ortho-lp-[AlF(bdc)] sample contained in the glass
features such as an open pore structure, a wine rack type lattice, and the inclusion of fully coordinated bdc groups that are features present in other MOFs that exhibit interesting thermoresponsive behavior.4 Indeed, recently the concept of directing the design of the mechanical properties of MOFs via consideration and inclusion of certain mechanical building units, called XBUs, within the framework has been proposed for which the lp-[Al(OH)(bdc)] form is predicted to exhibit NTE/ PTE behavior.17,18 Another member of the MIL-53 family to be reported is [AlF(bdc)] for which the structure of the framework at 300 K is found to be isostructural with that of lp-[Al(OH)(bdc)] even when exposed to a variety of guest molecules including water.19 The thermoresponsive behavior of this material has not been reported, but the simple difference in chemical composition of the framework anion, OH− or F−, is seen to produce a profound difference in the response of the framework to external stimuli. In this work, we determine the thermoresponsive behavior of lp-[Al(OH)(bdc)] and [AlF(bdc)] to reveal a variety of structural elements displaying NTE behavior and a subtle displacive phase transition for [AlF(bdc)]. The contrasting thermoresponsive behavior of the materials is solely due to the difference in the simple framework anion and its effect on the dispersion interactions in the material and flexibility of the constituent chain of corner-sharing AlO4X2 octahedra as determined by experiment and simulation. The results indicate the importance of considering the simplest species when designing the thermo-mechanical properties of MOFs.
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EXPERIMENTAL SECTION
Materials and Methods. The reagents used to synthesize the materials were Al(NO3)3·9H2O (Sigma-Aldrich, 98%), AlF3 (SigmaAldrich, 99.9%), H2bdc (Sigma-Aldrich, 98%), N,N-diethylformamide (DEF) (TCI, 99%), and deionized water. All reagents were used without further purification. The magic angle spinning solid state nuclear magnetic resonance (MAS SSNMR) 19F MAS NMR spectrum was recorded using a Bruker AVANCE III 400 spectrometer operating at a frequency of 367.5 MHz and a sample spinning speed of 13 kHz, with recycle delays of 5 s and using adamantane as a standard prior to the data collection. Nitrogen adsorption isotherm data were collected at 77 K using a Micromeritics ASAP 2010 apparatus. The surface area was calculated using the BET method over the relative pressure range 0.02−0.2. Thermogravimetric analysis (TGA) data were collected using a TGA/DSC 1 Thermogravimetric Analyzer (Mettler Toledo) with the samples heated in open alumina crucibles under flowing nitrogen from 25 to 600 °C at a heating rate of 5 °C min−1. Room temperature X-ray diffraction patterns were collected using a Phillips X’Pert diffractometer employing Cu Kα1+2 radiation and a RTMS X’Celerator detector. Sample Preparation. [Al(OH)(bdc)]·0.70(H2bdc) was synthesized by following the procedure reported previously.16 Al(NO3)3· 9H2O (5.2 g) was dissolved in deionized water (20 mL) followed by addition of H2bdc (1.112 g) to the mixture which was then placed into a 40 mL Teflon-lined stainless steel autoclave. The mixture was heated to 220 °C for 3 days before being cooled to room temperature without quenching. The product was washed with deionized water and separated by suction filtration to reveal a white powdered solid. This product was calcined in a tube furnace under static air at 300 °C for 3 days to remove the unreacted and occluded H2bdc molecules producing monophasic [Al(OH)(bdc)]·H2O, as evidenced by the Xray powder pattern (see Supporting Information Figure SI1) and thermogravimetric analysis data (see Supporting Information Figure SI2). A sample of [Al(OH)(bdc)]·H2O was packed into a 0.5 mm diameter borosilicate capillary tube and evacuated at 2.1 × 10−1 mbar at 150 °C for 48 h to obtain a fully evacuated sample of lpB
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Chemistry of Materials and aluminum capillary tubes using the reported structure of ortho-lp[AlF(bdc)] as the starting model.19 The reflections arising from the aluminum capillary tube were excluded from the diffraction patterns prior to structural refinement. All the data sets from 175−500 K were refined using an identical procedure. The powder X-ray diffraction patterns from 11 to 150 K all displayed an additional set of diffraction peaks arising from subtle splitting of some of the diffraction peaks observed at temperatures >150 K, indicating a lowering of the crystal symmetry of ortho-lp-[AlF(bdc)] (space group Imma). Inspection revealed that orthorhombic space groups with lower symmetry were unable to account for the extra diffraction peaks, so monoclinic metric symmetry was considered by systematically allowing the unit cell angle α, β, or γ to vary to try to generate the additional diffraction peak positions. Refinement of γ was found to yield the correct peak positions corresponding to the extra diffraction peaks. The systematic absences of the diffraction pattern were found to be consistent with the monoclinic space group of I112/b that is also a maximal nonisomorphic subgroup of Imma. The new crystal structure model in monoclinic symmetry, designated as mono-lp-[AlF(bdc)], was determined from the Imma model by inspection and separating the atoms related in the general position in space group Imma into two sets of symmetry related atoms in space group I112/b. This model was then refined following the same procedure as that for the orthorhombic structures ortho-lp-[AlF(bdc)] and lp-[Al(OH)(bdc)]. All Le Bail fitting and Rietveld refinements were performed using the GSAS21 software package as implemented in the EXPGUI user interface.22 Final observed, calculated, and difference plots for representative Rietveld refinements of lp-[Al(OH)(bdc)], mono-lp[AlF(bdc)], and ortho-lp-[AlF(bdc)] are shown in Figure 1. Standard crystallographic data, final atomic coordinates, occupancies, isotropic atomic displacement parameters, and selected geometric parameters are given the CIF files for each refinement in the Supporting Information. Computer Simulations. The thermally induced displacive phase transition behavior of [AlF(bdc)] is found to be significantly different from that of [Al(OH)(bdc)]. In order to understand the physical origin of this difference, the relative energy of each observed phase of [Al(OH)(bdc)] and [AlF(bdc)], and hypothetical np-[AlF(bdc)] and np-/lp-[Al(OH)1−xFx(bdc)] phases was probed using computational methods. Calculations were based on the density functional theory (DFT)23,24 using the CP2K code which uses a mixed Gaussian/planewave basis set.25,26 We employed triple-ζ polarization quality Gaussian basis sets and a 1200 Ry plane-wave cutoff for the auxiliary grid, in conjunction with the Goedecker−Teter−Hutter pseudopotentials.27,28 The PBE density functional29 with Grimme’s “D3” dispersion correction, including the Axilrod−Teller−Muto three-body terms,30 was used for all structural optimizations and total energy calculations. This approach has been shown to give good results on energetic and structural properties of rare gas and molecular crystals.30,31 Full geometry relaxations, including all unit cell lengths, non-90° angles, and atomic positions were performed for all structures. The structural optimizations were considered converged if the maximum force on all atoms falls below 0.534 kcal mol−1 Å−1 (4.5 × 10−4 Hartree Bohr−1). Calculations of np and lp structures were performed with a 2 × 1 × 2 and a 2 × 1 × 1 multiplication of the primitive cell, respectively. The initial structures that were optimized were taken from the observed crystal structures for the respective phases and the np-[Al(OH)(bdc)]8 phase for the hypothetical np-[AlF(bdc)] phase. The appropriate observed crystal structures were used for the optimizations of the np-/ lp-[Al(OH)1−xFx(bdc)] structures.
Figure 1. Final observed (red crosses), calculated (green line), and difference (purple line) plot for Rietveld refinement of (a) lp[Al(OH)(bdc)] at 300 K, (b) mono-lp-[AlF(bdc)] at 100 K, and (c) ortho-lp-[AlF(bdc)] at 300 K. The tick marks are the calculated 2θ angles for the Bragg peaks.
function of temperature of the pure lp form are shown in Figure 2 and provided in Supporting Information Table SI1. A relatively linear decrease in a (−6.27 × 10−6 Å K−1) and b (−2.43 × 10−4 Å K−1) and a linear increase in c (3.10 × 10−4 Å K−1) is observed over the entire temperature range. Overall the positive expansion in the [001] direction outweighs the contraction in the [100] and [010] directions to give an overall linear positive volume expansion represented by V = 1.25 × 10−2T + 1.418 with a volume expansion coefficient αV = 8.78 × 10−6 K−1. The structure of [Al(OH)(bdc)] obtained from the refinement at 300 K is shown in Figure 3a. Structure refinements at each temperature provide some insight into the mechanism of the thermoresponsive behavior of the lp form. The chain of
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RESULTS AND DISCUSSION Thermoresponsive Behavior of lp-[Al(OH)(bdc)]. [Al(OH)(bdc)] was found to remain solely in the lp form as it was cooled from 500 to 150 K. At 125 K, small signs of the presence of the np form became evident, and at 100 K significant amounts of the lp and np form coexist within the sample. This behavior reflects that reported previously.8 The measured variations in lattice parameters and unit cell volume as a C
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Figure 2. Variation of lattice parameters and unit cell volume as a function of temperature of lp-[Al(OH)(bdc)].
corner-sharing AlO4(OH)2 lying along the a axis contracts upon heating. A plausible mechanism for contraction along the a-axis is shown in Figure 3b and involves a correlated rocking of the carboxylate groups about the major axis of the bdc linker that introduces a twisting motion about the Al−OH−Al linkage of the relatively rigid AlO4(OH)2 octahedra. The magnitude of the rocking and twisting motions will increase with temperature resulting in contraction of the structure along the a-axis. Such aspects of this mechanism have previously been deduced from single crystal studies for other dicarboxylate-based MOFs.4,32 The expected accompanying decreases in nonbonding adjacent Al···Al (see Supporting Information Figure SI5a) and carboxylate O1···O1 (see Supporting Information Figure SI5b) distances along the [AlO4(OH)]∞ chain support this mechanism, as do the near constant values of the Al−O2 (see Supporting Information Figure SI5c), C1−O1 (see Supporting Information Figure SI5d), and Al−O1 (see Supporting Information Figure SI5e) bond distances and Al−O2−Al (see Supporting Information Figure SI5f) bond angle and the slight decrease in O1−C1−O1 (see Supporting Information Figure SI5g) angle. The variation in the latter geometric parameters would be expected as the magnitude of the rocking or twisting motions of the carboxylate and Al-centered octahedra, and associated transverse vibrations of the O species, increase. However, the small magnitude of the changes in geometric parameters over the temperature range and the precision of the structure refinements limit full determination of the mechanism of contraction along the a-axis. Thermal expansion of the structure along the [001] direction and contraction along the [010] direction is observed over the temperature range studied. The mechanism behind this behavior may be explained by considering one of the rhombus-shaped channels in the (100) plane, as shown in Figure 3a, that is bounded by four bdc ligands with Al atoms at the vertices of the rhombus. The bdc linkers rotate around the −Al−OH−Al− chain running through the core of the cornersharing AlO4(OH)2 octahedra as the temperature increases and as shown schematically in Figure 3c. This process is reflected in the linear increase of the internal rhombus angle, α, defined in Figure 3a,c and shown in Figure 4a and the change of the internal O1−Al−O1 angles as shown in Supporting Information Figure SI5h,i. The sides of the rhombus remain fairly constant in length during this process with a distance, d(Al···Al) as defined in Figure 3a, decreasing from 10.5432(1) Å at 150 K to 10.5415(1) Å at 500 K. The connectivity of the framework means that these structural factors are coupled to give a linear
Figure 3. (a) Structure of lp-[Al(OH)(bdc)] viewed along the a-axis showing the rhombus-shaped channels in the (100) plane that are bounded by four bdc ligands linked by aluminum atoms at each vertex. The nonbonding Al···Al distance forming the sides of the rhombus, d(Al···Al), and the internal rhombus angle, α, are defined in the figure. (b) A schematic representing the possible mechanism for contraction along the a-axis consisting of a correlated rocking of the carboxylate groups about the major axis of the bdc linker, represented by black arrows, that introduces a twisting motion about the Al−OH−Al linkage of the AlO4(OH)2 octahedra, represented by blue arrows. The numbers on the arrows represent the different directions of the motions. (c) A schematic representing the rotation of the bdc linkers around the −Al−OH−Al− chain running through the core of the corner-sharing AlO4(OH)2 octahedra defined in terms of α and the burgundy arrows and the “knee cap” bending motion of the carboxylate group and the O1−Al−OH−Al−O1 unit about the O1···O1 vector of the carboxylate group defined in terms of ϕ and the blue arrows. The structures are represented in ball and stick mode with blue, red, and black balls representing the Al, O, and C atoms, respectively.
increase in the area of the rhombus-shaped channel, as shown in Figure 4b and a “wine rack” thermo-mechanical mechanism of expansion for lp-[Al(OH)(bdc)] in the (100) plane, similar to that reported for other noncarboxylate containing MOFs.33 The observation of such a mechanism demonstrates that the AlO4(OH)2 octahedra are not rigid octahedra in terms of angular deformation and rotation of the bdc linkers around the −Al−OH−Al− chain running through the core of the cornersharing AlO4(OH)2 octahedra is a lower energy process relative to the “knee cap”34 bending motion of the carboxylate groups and the O1−Al−OH−Al−O1 units about the O1···O1 vector of the carboxylate group by an angle ϕ as shown schematically in Figure 3c. D
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in Supporting Information Table SI2. Unlike [Al(OH)(bdc)], [AlF(bdc)] remains in a lp form over the temperature range 11−500 K indicating its stability in comparison to a np form. Structural refinements at each temperature data were collected and reveal that [AlF(bdc)] undergoes a structural distortion at ∼175 K from an orthorhombic lp form (ortho-lp) to a monoclinic lp form (mono-lp). The structure of the ortholp form is the same as that reported previously19 and that of lp[Al(OH)(bdc)] as shown in Figure 6a. The structure of the
Figure 4. Variation of the internal rhombus angle, α (a), and rhombus area (b) as a function of temperature. An equation for the linear fit, the goodness of fit (R2), and the estimated standard deviations are given on each plot.
The [Al(OH)(bdc)] becomes a more open structure over the full temperature range from its np to lp form and to a more open lp form. This change is driven by a reduction in internal energy as the internal O1−Al−O1 angles converge toward the more favorable regular values of 90° and possible associated entropic gains in the framework as the AlO4(OH)2 octahedra become more regular in the AlO4 plane. These results indicate that the thermo-mechanical behavior of [Al(OH)(bdc)] can be deconstructed into XBUs consisting of rigid bdc linker struts and Al2(OH)(CO2)2 hinges in a manner described recently17 providing possibilities to design the mechanical properties of MOFs. Thermoresponsive Behavior of [AlF(bdc)]. The measured variation of the unit cell volume as a function of temperature of [AlF(bdc)] is shown in Figure 5 and provided
Figure 6. Structure of (a) ortho-lp-[AlF(bdc)] and (b) mono-lp[AlF(bdc)] viewed along the [100] direction.
mono-lp form is shown in Figure 6b and is very similar except for the slight tilting of adjacent corner-sharing AlO 4F 2 octahedra relative to each other about the Al−F−Al core of the chain of corner-sharing AlO4F2 octahedra and the accompanying rotation of the bdc groups around the central C···C axis of the bdc linker. This is the most subtle distortion of any of the lp forms of the MIL-53 family to be reported, although other subtle distortions of more narrow pore forms of members of the MIL-53 family are known.35,36 The BET surface area of mono-lp-[AlF(bdc)], calculated from the N2 adsorption isotherm shown in Supporting Information Figure SI6 and collected at 77 K, is 1020(17) m2 g−1, a value similar to that reported for lp-[Al(OH)(bdc)].16
Figure 5. Variation of the unit cell volume as a function of temperature for lp-[AlF(bdc)]. The estimated standard deviations are given on the plot. Blue and red data points correspond to the diffraction data collected for the two different experiments covering the temperature ranges 11−290 K and 100−500 K, respectively. E
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Chemistry of Materials The final relaxed structure of theoretical np-[AlF(bdc)] is shown in Figure 7a, and the structure of each optimized phase
to the ortho-lp-[AlF(bdc)] phase at higher temperature, in a manner similar to that reported for the [Al(OH)(bdc)] system, as it will gain vibrational entropy within the structure. The total energy of the np-[AlF(bdc)] structure is higher than the other two lp-[AlF(bdc)] phases by ∼0.4 kcal mol−1 per Al center. This indicates that the np-[AlF(bdc)] structure is energetically disfavored, and this denser phase is not observed at any temperature because it will have both a lower entropy and a higher enthalpy than the lp forms and hence the free-energy of the np form is always higher than the lp forms. The thermoresponsive behavior in terms of displacive phase transitions reported here for [AlF(bdc)] is considerably different to that of [Al(OH)(bdc)].8 If lp-[AlF(bdc)] were to transform to np-[AlF(bdc)] then two opposed energy changes would occur during the transformation. An increase in the energy due to the distortion of the inorganic chains of cornersharing AlO4F2 octahedra and a decrease in energy arising from the more dispersion interactions between the organic linkers that are closer to each other in the np-form. These two energy changes can be quantified by deconstructing the relative total energy differences of the mono-lp-[AlF(bdc)] structure relative to the np structure into a relative dispersion energy difference and a relative nondispersive energy difference that are given in Supporting Information Table SI3. The PBE+D3 theoretical method used throughout this work accounts for the missing dispersion interactions in conventional DFT/PBE functions through additive terms and so enables the deconstruction of the relative total energy in this manner. The relative nondispersive energy difference reflects the change in the energy due to the distortion of the inorganic chains of corner-sharing AlO4F2 octahedra, and the relative dispersion energy difference reflects the change in energy as the dispersion interactions between the organic linkers varies. The values of the relative dispersion energy difference and the relative nondispersive energy difference of 6.01 and −6.42 kcal mol−1 per Al center respectively support the assertion that the decrease in energy arising from the more dispersion interactions between the organic linkers that are closer to each other in the np-form is smaller than the increase in the energy due to the distortion of the inorganic chains of corner-sharing AlO4F2 octahedra for [AlF(bdc)]. This implies that the energy to distort the inorganic chains in [AlF(bdc)] to adopt the np structure always outweighs the gain in dispersion interactions between the organic linkers indicating that the lp-/np-phase transition will not occur at any temperature. The behavior for [Al(OH)(bdc)] is complicated by the presence of the OH groups in the structure. Opposing energy changes occur during the transformation of lp-[Al(OH)(bdc)] to np-[Al(OH)(bdc)]; an increase in energy due to the distortion of the inorganic chains of corner-sharing AlO4(OH)2 octahedra occurs and a
Figure 7. Structure of (a) optimized np-[AlF(bdc)] and (b) optimized np-[Al(OH)(bdc)] viewed along the [100] direction. The structures are represented in ball and stick mode with blue, green, red, black, and tan balls representing the Al, F, O, C, and H atoms, respectively. Dotted lines in (b) represent H···O interactions.
is provided in the Supporting Information. The theoretically predicted lattice parameters and relative energies of the different phases, given in kcal mol−1 per Al center, are summarized in Table 1. The optimized structures are in very good agreement with the experimental structures as indicated by the small difference in unit cell parameters (
