Are Metal–Metal Interactions Involved in the Rising Enthalpies

Aug 28, 2012 - An alternate explanation for the rising enthalpies is also proposed, involving a .... Tuan K. A. Hoang , Leah Morris , Jing Sun , Miche...
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Are Metal−Metal Interactions Involved in the Rising Enthalpies Observed in The Kubas Binding of H2 to Hydrazine-Linked Hydrogen Storage Materials? Claire V. J. Skipper,† David M. Antonelli,*,‡ and Nikolas Kaltsoyannis*,† †

Department of Chemistry, University College, London, 20 Gordon Street, London WC1H OAJ, United Kingdom Sustainable Environment Research Centre, University of Glamorgan, Pontypridd CF37 1DL, United Kingdom

‡

S Supporting Information *

ABSTRACT: Models of two linked M(III) and M(II) (M = Ti, V, Cr) binding sites in hydrazine-linked hydrogen storage materials have been studied quantum chemically using density functional theory. The results compare favorably with previous experimental and computational results. Strong evidence is observed that the H2 molecules bind to the metal in a Kubas manner. As seen previously in monometallic analogues,1,2 altering the transition metal across the first row of the periodic table reduces the number of H2 molecules that can be bound, and replacing a hydrazide ligand with a hydride increases the MH2 interaction energy. Evidence is presented for metal−metal interactions, which can influence the H2 binding enthalpy and may help to explain the observed metallic properties and rising H2 binding enthalpies with coverage of the experimental materials. An alternate explanation for the rising enthalpies is also proposed, involving a pressure-induced deformation of the structure with concomitant twisting of the bonds into conformations that allow more optimal binding of an H2 ligand. a Kubas fashion. A Kubas interaction9,10 is consistent with a lengthening of the H−H bond without breakage and involves σdonation from the filled H−H σ-bonding orbital into an empty d orbital of a metal and simultaneous π-back-donation from a filled metal d orbital into the vacant σ* antibonding orbital of the H2 molecule. This is similar to the synergic bonding described by the Dewar−Chatt−Duncanson model for the interaction of, for example, CO with transition metals.11,12 The fabrication of solidstate materials that use the Kubas interaction to store hydrogen is a great challenge because it is difficult to synthesize a material that has both a high concentration of low-valent, low-coordinate binding sites (transition metals in the solid state prefer to be sixcoordinate in most cases, making Kubas binding in a solid state structure virtually impossible) and is lightweight and of sufficient porosity to allow hydrogen to diffuse through the structure. Previously we have investigated, both experimentally and computationally, hydrogen storage materials with first-row transition metals in the +3 and +2 oxidation states.1,2,7,13−19 Our computational studies have been based on an experimentally confirmed mesoporous silica with benzyl titanium binding sites13 and hydrazine-based systems containing vanadium or chromium binding sites.18,19 This latter system is of particular interest because the excess volumetric densities at 77 K (60 kgm−3) are greater than that of even the best-performing MOFs. In both the

1. INTRODUCTION The storage of hydrogen within a compact system of low density remains a problem for small road vehicles. The United States Department of Energy (DOE) has established targets to be met by 2015 for such storage systems. These include a gravimetric storage density of 5.5 wt %, a volumetric storage capacity of 40 g/ L, and a 3.3 min refuelling time for a 5 kg tank.3 After discounting liquid storage, due to the required cooling of the hydrogen and the losses during boil off, and very high pressures (in excess of 300 bar) where the tanks need to be made of specialist materials, it has been proposed to incorporate within high-pressure tanks a hydrogen storage material to which the hydrogen can bind, to increase the storage capacity of the tank at a lower pressure. It is thought that a storage material−hydrogen binding enthalpy of between 20 and 30 kJ mol−14,5 would give the best balance between storage capacity and the energy required to release the hydrogen. This is higher than that of physisorption materials such as zeolites or carbon-based frameworks that bind to the H2 through weak van der Waals forces (3−6 kJ mol−1)6 and have low storage capacities at room temperature, and lower than that of chemisorption materials, like metal hydrides, that bind to the H atoms with a strong covalent bond (40−80 kJ mol−1).7,8 These have high storage capacities at room temperature, but energy is required to cool and heat the material during hydrogen uptake and release, respectively, and this drastically cuts into the overall performance of the system. To achieve an enthalpy in the desired range, metals may be incorporated into the storage materials, to which H2 may bind in © 2012 American Chemical Society

Received: May 28, 2012 Revised: July 27, 2012 Published: August 28, 2012 19134

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rising H2 binding enthalpy with increased coverage and propose an alternative explanation for this effect.

silica and hydrazine systems, the experimental enthalpies are in the 20−40 kJ mol−1 range, and our calculations demonstrated that the H2 binds to the transition metals via the Kubas interaction.1,2,16 In our experimentally characterized systems, we observe a trend of rising H2 binding enthalpy with increased coverage, opposite to the behavior seen during physisorption. For the silica-based systems, this was rationalized through a frontier molecular orbital analysis; the binding of one hydrogen molecule alters the energy of the frontier orbitals of the binding site such that the HOMO and LUMO are closer in energy to the HOMO and LUMO of free H2, making the binding of the next H2 molecule more favorable.16 By contrast, for the hydrazine-linked materials, an analogous molecular orbital analysis proved inconclusive. We suggested that the rising enthalpy trends may be due to cooperativity between the metals of adjacent binding sites, which is thought to be possible due to the metallic conductivity observed in these materials, but the calculations did not include these effects.1,2 In this picture, H2 is considered to be an n-type dopant perturbing the band structure of the material and changing the position of the Fermi level such that subsequent H2 molecules experience a progressively different binding potential. Rising enthalpies have also been observed recently in KC24 and attributed to lattice expansion effects, so similar effects in these hydrazides must also be considered.20 Here we have included the effect of a single adjacent metal binding site by modeling hydrazine-based dimers (a molecule of two linked binding sites) of metals in the +3 and +2 oxidation states. In this way, we hoped to assess the extent to which the adjacent metals in the hydrazine-linked gel interact with each other and, by binding hydrogen to these model systems, whether any such interaction could account for the experimentally observed rising enthalpies. The hydrazine-linked systems are mainly amorphous, and the coordination number and geometry about the metal centers is unconfirmed experimentally, as is the way that the hydrazine links the metal centers together. The amorphous structure, paramagnetism, and air-sensitive nature of these materials preclude many spectroscopic techniques, as does the fact that substantial H2 binding is observed only at higher pressures. However, X-ray photoelectron spectroscopy (XPS) on the Cr(II) hydrazine-linked system shows that whereas the binding mode of the hydrazine and the way that it links the binding sites together vary, it mostly links in a -NH-NH2fashion.19 There is also evidence for nitrogen bound to more than one metal; so typically, two nitrogen environments are observed in the XPS, one most likely corresponding to a nitrogen bound to one metal and the second at lower binding energy being assigned to a nitrogen bound to two metal atoms. Our previous calculations on molecules representing single binding sites showed that four-coordinate metal binding site representations (BSRs) best represent the experimental data1,2 and so four coordinate dimers have been investigated here. Because the mode of linking the metal centers together is not known with any certainty, different modes and combinations of linking modes are initially screened, and, subsequently, the lowest energy H2-free systems and those lying within 20 kJ mol−1 are studied further by binding hydrogen to them. We analyze the geometric structures and energetics of the resulting complexes and study their electronic structures using orbital and charge analysis as well as the topology of their electron densities via the atoms-in-molecules (AIM) approach. Finally, we summarize the performance of our frontier orbital-based rationalizations of the

2. COMPUTATIONAL DETAILS Spin-unrestricted DFT with the Perdew−Burke−Ernzerhof (PBE)21,22 exchange correlation functional was used throughout. This functional was chosen because of its success in our previous studies on the benzyl titanium binding sites of a mesoporous silica16 and on the vanadium and chromium binding sites of hydrazine-based materials,1,2 and because it has been shown by Sun et al. to be the best functional to balance computational speed and accuracy when looking at dihydrogen bound to metal centers.23 It is definitely a commonly used functional in this area of research.24−33 In all cases the state with the highest possible spin multiplicity was calculated (based on the number of formally metal 3d-based electrons). The spin multiplicity data are provided in the Supporting Information for all species studied, together with the formal and calculated values of . The latter indicate that very little spin contamination is present, with the largest deviation from the formal value being 0.01 (for compound Cr(III) D13). The Gaussian 09 code 34 was used for all geometry optimizations, and the 6-311++G** basis35−41 sets were used on all atoms. An ultrafine integration grid was used, and the rms force geometry convergence criterion was set to 0.000667 au using IOP 1/7. Stationary points were analyzed by performing analytical frequency calculations. AIM calculations were performed using the AIMALLPro42 program on the electron densities at the Gaussian optimized geometries, employing formatted Gaussian checkpoint files as input. Partial atomic charges were quantified using the Mulliken, Voronoi, and Hirshfeld scales. These were calculated at the Gaussian-optimized geometries using the amsterdam density functional (ADF) program,43−45 with the PBE functional, TZ2P basis sets46−50 on all of the atoms and the parameter controlling the integration grid set to 6.0. Mulliken charges were also calculated using the Gaussian code, and AIM charges were taken from the AIMALLPro output. The average energy of interaction between the metal and the H2 units (M-H2) was calculated in ADF as follows. Using the same calculation settings employed for the partial charges, a single-point calculation on the geometry of the BSR with H2 molecules bound (BSR(H2)n) was performed. Two further single-point calculations were then performed breaking the molecule into two fragments: the metal-containing fragment (spin-unrestricted) and the (H2)n fragment (spin restricted). The average energy of interaction between the metal and the H2 units was calculated as E Hint2 =

E BSR(H2)n − E BSR − E(H2)n n

E for all species was taken as the SCF energy. This fragment method of calculating the energy of the M-H2 interaction was used successfully in our analysis of the amorphous silica-based hydrogen storage materials16 and the hydrazine-based hydrogen storage materials.1,2̀

3. RESULTS AND DISCUSSION 3.1. Screening of Potential Modes of Linking the Metal Centers. Several possible dimer structures representing two linked binding sites in the gel were initially considered, all 19135

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Figure 1. Schematic representations of the dimers with metals in the +2 oxidation state that were selected for H2 binding studies. A−E are dimers 1, 2, 5, 6, and 8 with only hydrazine-based ligands. “M” indicates that a low-energy dimer was obtained for all three metals Ti, V, and Cr, whereas a specific metal symbol indicates that the structure was of low energy only for that metal. F is dimer 2 with Ti and one hydride ancillary ligand per metal. All dimers were initially calculated for all metals, except only Ti was studied with hydride ancillary ligands.

Figure 2. Schematic representations of the dimers with metals in the +3 oxidation state that were selected for H2 binding studies. A−D are dimers 1, 7, 12, and 14 with only hydrazine-based ligands. “M” here indicates that a low-energy dimer was obtained for two metals V and Cr, whereas a specific metal symbol indicates that the structure was of low energy only for that metal. E and F are dimers 2 and 7 with Ti and one hydride ancillary ligand per metal. All dimers were initially calculated for all metals, except only Ti was studied with hydride ancillary ligands.

either +3 or +2. From experimental findings19 it is thought that the NH-NH2 ligand can link the metal centers in either an η2

maintaining the coordination geometry of the metal centers as four-coordinate and the oxidation state of the metals as 19136

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3.2. Binding of the H2 to Dimeric BSRs and Comparison with Previous Computational Results. Comparing the M-H2 interaction energies of the lowest energy dimers (Tables 3 and 4) with those of the four-coordinate monometallic BSRs for the M(II)2 and M(III)1 systems does not reveal a strong correlation. There are cases where the interaction energies are extremely similar, for example, with two H2 bound to Ti(III), the values are −18.15 and −19.80 kJ mol−1 for the dimer and monometallic BSR, respectively, and cases where the energies are rather more different, for example, with two H2 bound to V(II) the respective values are −32.40 and −8.93 kJ mol−1. An increase in the M-H2 interaction energy as more H2 molecules are bound has been seen in the experimental systems.18,19 For the present dimers, the change in the interaction energy as more H2 are bound depends on the metal and its oxidation state, and there are cases of it decreasing, increasing, and staying approximately the same (Tables 3 and 4). However, the experimental systems studied feature Cr(II) and V(III), and in both of these cases the computational M-H2 interaction energy increases as more H2 are bound. The Kubas interaction is characterized experimentally by a lengthening of the H−H bond without breakage and a reduction in its stretching frequency. In all systems studied the H−H bond increases from its computational free value of 0.752 to 0.770− 0.831 Å, with a simultaneous reduction in its stretching frequency of 4317 to 4012−3052 cm−1 (Tables 3 and 4). Molecular spin− orbitals showing the σ-donation and π-back-donation components of the Kubas interaction between the H2 and the metal are presented for V(II) D2 with one bound H2 in Figure 3. We have previously studied the M-H2 interaction via AIM theory and benchmarked our analysis against prototypical Kubas systems.1 In AIM theory, two atoms are considered to be bonding when there is a bond critical point (BCP) between them. The BCP is the minimum on the line of maximum electron density connecting two nuclei (the bond path) and is a maximum in a plane perpendicular to the bond path. The electron density at the BCP is correlated with the strength of the bond. We found the density at the BCP of the H−H bond of the bound H2 molecule for the classically Kubas systems to be between 0.202 and 0.219 e bohr−3.1 Here the values are between 0.207 and 0.247 e bohr−3 (Tables 3 and 4), showing that some of the interactions are of a similar strength to the classically Kubas systems and some are weaker. (A higher H−H BCP density implies a stronger H− H bond and hence weaker Kubas binding.) The values of the H−H stretching frequency, bond length, and BCP electron density are similar to those of the monometallic BSRs.1,2 However, the range of the values is broader for the dimers indicating that introducing just one other binding site increases the variety in the interactions that occur. Extrapolating the amorphous bulk solid may well have a greater range of Kubas interaction strengths. In the four-coordinate monometallic analogues, analysis of the partial charges on the metal centers suggested that the overall interaction of the H2 with the metal is generally σ-donation for the metals in the +3 oxidation state. This was also found to be the case for Cr(II), whereas for Ti(II) and V(II) there is a more balanced interaction.1,2 Here there generally tends to be a decrease in the partial charge on the metal directly bound to H2 as one H2 is bound for metals in the +3 oxidation state and a slight increase for all metals in the +2 oxidation state; for Ti examples, see Figures 4 and 5, with all values collected in the Supporting Information (Tables S5−S8). This generally agrees with the results from the monometallic systems, but the trends

fashion with each metal bound to one of the nitrogen atoms or that it can act as an μ2 bridging ligand with the NH end of the ligand bound to both metals and that a maximum of two ligands would link the two metals. The metals considered are Ti, V, and Cr to link to experiment and previous computational studies, and only hydrazine-based ligands are probed, except in the case of Ti where one hydride ligand on each metal not acting as a bridging ligand is considered, as hydride ligands have shown higher adsorption enthalpies than π-accepting ligands.1,2,16 The initial aim was to find the lowest energy dimers and hence the most likely method of linking the metals in the solid. During geometry optimization of these structures it became clear that some of the structures were at a lower energy than others and that some of the M(III) dimers had lower energy structures with three hydrazine ligands linking the two metal centers. This would leave one of the metal centers as five-coordinate and the other as fourcoordinate. These dimers were also considered as possible representations of the experimental systems. All of these initial structures are shown schematically in the Supporting Information (Figures S1−S4), which also gives the Cartesian coordinates and SCF energies. The lowest energy dimers and those within 20 kJ mol−1 were selected for H2 binding studies and are shown schematically in Figures 1 and 2. The lowest energy dimer for all of the studied M(II) systems is dimer 2 (D2) (Figure 1B,F, Table 1), where the two metal Table 1. Relative Energy of the +2 Oxidation State H2-Free Dimers with Respect to the Lowest Energy Dimer for Each Metala relative energy/kJ mol−1 dimer

Ti(II)

V(II)

Cr(II)

Ti(II)H

2 6 8 5 1

0 14.14

0 0.59 11.95 14.31

0 3.99

0

9.80

Only dimers within 20 kJ mol−1 of the lowest energy dimer are included. Ti(II)H = dimer with hydride ancillary ligands.

a

centers are bridged by one hydrazide ligand in a μ2 fashion through its ‘NH’ nitrogen atom. This is a much more open structure compared with the lowest energy structures of the M(III) centers where for Ti the metal centers are bridged by two hydrazides in an μ2 fashion (D7 Figure 2B,F, Table 2), and for V and Cr where the metal centers are linked by three hydrazides, two of which bridge in a μ2 fashion and one of which links in a η2 fashion (D12 Figure 2C, Table 2). Table 2. Relative Energy of the +3 Oxidation State H2-Free Dimers with Respect to the Lowest Energy Dimer for Each Metala relative energy/kJ mol−1 dimer

Ti(III)

7 12 14 1 2

0

V(III)

Cr(III)

Ti(III)H 0

0 4.94

0 14.16 6.57

Only dimers within 20 kJ mol−1 of the lowest energy dimer are included. Ti(III)H = dimer with hydride ancillary ligands.

a

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0.823

/

0.786 0.789 0.809 /

Cr(II) 3188 3590 3406 3635 3332 3405 3989 3619 3568 3127

0.818 0.831

Ti(II)

0.803 0.807 0.814 0.788 0.810 0.817 0.789 0.800

Ti(II)H

3529 3475

3431 3655 3460 3714 3485 3467 3764. 3747

V(II)

/

3750 3692 3368 /

Cr(II)

3229 3052

3439 3381 3273 3694 3339 3221 3653 3477

Ti(II)H

H−H stretching frequencies/cm−1

−36.49 (−34.71)

−32.40

−34.61 (/)

−30.69

V(II) −44.3 −34.85

−42.33 −29.03

Ti(II)

/

/

−28.13 −32.09

Cr(II)

Ti(II)H

−47.42

−26.40 (−32.47)

−40.10 −38.71

M-H2 interaction energies/kJ mol−1 0.218 0.233 0.227 0.223 0.234 0.227 0.246 0.234 0.232 0.215

Ti(II) 0.227 0.235 0.229 0.237 0.229 0.229 0.239 0.238 0.231 0.229

V(II)

/

0.238 0.223 0.236 /

Cr(II)

0.228 0.226 0.222 0.236 0.225 0.219 0.235 0.229 0.221 0.214

Ti(II)H

H−H BCP densities/e bohr−3

19138

2 and 2

0.771 0.771 0.779 0.770 0.779 0.780 /

V(III)

/

0.779 0.774 0.775 /

Cr(III) 0.772 0.808 0.810 0.781 0.797 0.805 0.790 0.792 0.796 0.809

Ti(III)H 3956 3787 3603 4009 3899 3757 3911 3841 3769 3664

Ti(III) 3971 3985 3852 4012 3836 3817 /

V(III)

/

3847 3936 3936 /

Cr(III) 3969 3397 3369 3798 3535 3414 3646 3604 3522 3370

Ti(III)H

H−H stretching frequencies/cm−1

−18.15

/

−14.16 (−16.97)

−14.50 (−14.20)

V(III) −9.97 −18.28

−12.03 −16.82

Ti(III)

/

/

−16.83 −13.47

Cr(III)

M-H2 interaction energies/kJ mol−1 Ti(III)H

−29.87

−24.44 (−26.42)

−47.83 −31.2

0.246 0.240 0.233 0.246 0.244 0.239 0.244 0.242 0.239 0.236

Ti(III)

0.245 0.246 0.242 0.247 0.241 0.241 /

V(III)

/

0.242 0.244 0.244 /

Cr(III)

0.207 0.226 0.225 0.240 0.231 0.227 0.234 0.239 0.230 0.225

Ti(III)H

H−H BCP densities/e bohr−3

Number of H2 molecules bound shows the number bound to each of the metals separately. The M-H2 interaction energies in brackets is the average energy of binding of all three H2 molecules. The interaction energy not in brackets in the same box is the average energy of the binding of two H2 molecules to one of the metals. / = calculation not computationally accessible. Ti(III)H = dimer with hydride ancillary ligands.

a

0.773 0.782 0.791 0.769 0.775 0.782 0.774 0.778 0.782 0.788

1 and 0 1 and 1

1 and 2

Ti(III)

no. of H2 bound

H−H bond lengths/Å

Table 4. H−H Bond Lengths, Frequencies and BCP Densities and Average M-H2 Interaction Energies for the Lowest Energy Dimers with Metals in the +3 Oxidation Statea

Number of H2 molecules bound shows the number bound to each of the metals separately. The M-H2 interaction energies in brackets are the average energy of binding of all three H2 molecules. The interaction energy not in brackets in the same box is the average energy of the binding of two H2 molecules to one of the metals. / = calculation not computationally accessible. Ti(II)H = dimer with hydride ancillary ligands.

a

0.801

0.789 0.810 0.803 0.771 0.791 0.794

1 and 2

2 and 2

0.817 0.817

1 and 0 1 and 1

V(II)

0.809 0.790 0.801 0.787 0.801 0.801 0.784 0.784 0.799

Ti(II)

no. of H2 bound

H−H bond lengths/Å

Table 3. H−H Bond Lengths, Frequencies and BCP Densities and Average M-H2 Interaction Energies for the Lowest Energy Dimers with Metals in the +2 Oxidation Statea

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which favored a balanced interaction in the monometallic analogues, was attributed to the fact that the metal d orbitals stablize across the periodic table such that for chromium the highest occupied molecular orbital (HOMO) was lower and of less favorable energy for π-back-donation to the H2.2 Here the interaction between the two metal centers broadens the range of frontier orbital energies and increases the HOMO energies of the dimers compared with the single metal BSRs (Table 5). Table 5. Predominantly d-Based Molecular Orbital Energies for the Lowest Energy M(II) Dimers and Four Coordinate Mono-Metallic BSRs18 with No H2 Molecules Bound orbital energy/eV metal

orbital

dimer

monometallic

Ti

LUMO HOMO HOMO-1 HOMO-2 HOMO-3 LUMO HOMO HOMO-1 HOMO-2 HOMO-3 HOMO-4 HOMO-5 LUMO HOMO HOMO-1 HOMO-2 HOMO-3 HOMO-4 HOMO-5 HOMO-6 HOMO-7

−1.396 −1.821 −2.208 −2.366 −2.696 −1.539 −1.908 −2.088 −2.150 −2.501 −2.653 −3.057 −1.593 −2.675 −2.963 −3.159 −3.397 −3.501 −3.546 −3.666 −3.866

−1.221 −2.132 −2.406

V

Figure 3. Orbitals of D2 with V(II) and one H2 bound showing (A) the ball-and-stick structure, (B) HOMO-3 (π-back-donation), and (C) HOMO-61 (σ-donation). Note that the orbital numbering includes both spin α and spin β levels and that global HOMO-61 is α HOMO-32.

Cr

−1.145 −2.401 −2.585 −2.678

−1.264 −2.801 −3.053 −3.421 −3.618

Therefore, the Cr(II) dimer has a higher HOMO that is more able to π-back-donate to the H2. This suggests that in the bulk there would be bands of frontier orbitals, many of which would be high enough in energy to take part effectively in π-backdonation. The partial charge on the metal not directly bound to the H2 does alter upon H2 binding, but there is not a strong trend in these changes across the studied systems. Previously, in the monometallic BSRs, it was observed that altering the metal across the periodic table reduced the number of H2 molecules that could be bound to the metal center as the number of empty d orbitals for the H2 molecule to donate into decreased.1,2 This is also observed in the dimeric models (Tables 3 and 4). We also noted previously that altering the ancillary ligand bound to the metal to poorer π-acceptors increased the MH2 interaction energy as more electron density could be donated back to the H2 molecule instead of to the ancillary ligand.1,2 Here we have changed a hydrazine ligand to a hydride ligand for the Ti case and also seen that the M-H2 interaction energy does generally increase (Tables 3 and 4). This is more pronounced when the Ti is in the +3 oxidation state. 3.3. Metal−Metal Interaction? To probe whether 3d-based metal−metal (M-M) interactions affect the binding of the H2, the M-H2 interaction energies were also calculated when the metal to which the H2 is not bound was altered to either Al(III) in the case of the M(III) systems or Ca(II) in the case of M(II). In this way,

Figure 4. Partial charges of the metal that binds directly to the first H2 molecule for D7 with Ti(III) and hydride ligands.

Figure 5. Partial charges of the metal that binds directly to the first H2 molecule for D2 with Ti(II) and hydride ligands.

are less pronounced, presumably due to the perturbation of one H2 molecule having a smaller effect on a larger system. The Cr(II) now also seems to favor π-back-donation over σ-donation. Its preference for σ-donation, compared with Ti(II) and V(II), 19139

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Table 6. M-H2 Interaction Energies of Binding the First H2 molecule with and without the Other Metal As Ca, and the Change between the Two for the +2 Metalsa M-H2 interaction energies/kJ mol−1

M-H2 interaction energies with Ca/kJ mol−1

change in M-H2 interaction energies/kJ mol−1

dimer

Ti(II)

V(II)

Cr(II)

Ti(II)H

Ti(II)

V(II)

Cr(II)

Ti(II)H

Ti(II)

V(II)

Cr(II)

Ti(II)H

2 6 8 5 1

−42.33 −43.85

−44.30 −63.36 −65.05 −32.15

−28.13 −33.68

−40.10

−40.22 −28.02

−46.30 −61.80 −42.77 −30.63

−29.36 −36.05

−42.85

+2.11 +15.83

−2.00 +1.56 +22.28

−1.23 −2.37

−2.75

−37.5

+0.21

a

Ti(II)H = dimer with hydride ancillary ligands. The values highlighted in italics indicate where altering the metal had a significant effect on the MH2 interaction energy.

Table 7. M-H2 Interaction Energies of Binding the First H2 Molecule with and without the Other Metal as Al and the Change between the Two for the +3 Metalsa M-H2 interaction energies/kJ mol−1 dimer

Ti(III)

7 12 14 1 2

−12.03

V(III) −9.97 −26.54

Cr(III)

M-H2 interaction energies with Al/kJ mol−1

Ti(III)H

Ti(III)

−47.83

−8.07

−16.83

V(III) −12.64 −27.39

−17.08

Cr(III)

Ti(III)H

Ti(III)

−38.73

+3.96

−17.78 −17.77

−15.37

change in M-H2 interaction energies/kJ mol−1 V(III)

Cr(III)

−2.67 −0.85

−0.95

Ti(III)H +9.10

−0.69 −11.36

+4.01

a

Ti(III)H = dimer with hydride ancillary ligands. The values highlighted in italics indicate where altering the metal had a significant effect on the MH2 interaction energy.

the valence d orbitals were removed but the size of the metal atom remained approximately the same. In most cases this alteration had little effect on the M-H2 interaction energies suggesting that in such cases the M-H2 interaction is a local interaction (Tables 6 and 7). However, in a few cases it significantly reduced the M-H2 interaction energy suggesting that the second metal is significant in the bonding of the H2. Further analysis reveals that the second metal affects the M-H2 interaction only when an M-M interaction is present in the orbital that is π-back-donating to the H2, and where the second metal contributes atomic orbitals of the same type as the first metal. For example, with D6 and Ti(II), the molecular orbital showing the most π-back-donation to the H2, HOMO-2, also shows an M-M interaction (Figure 6 B) and includes

Figure 7. D6 with a Ti(II) and a Ca(II) with one H2 bound showing (A) the ball-and-stick structure and (B) HOMO-1.

6.29% dx2−y2 from the V bound directly to the H2 and 12.38% dz2 and 11.52% dxz from the second V (Figure 8 B). With more d

Figure 8. D8 with two V(II) with 1 H2 bound showing (A) the ball-andstick structure and (B) HOMO-5.

Figure 6. D6 with two Ti(II) with one H2 bound showing (A) the balland-stick structure and (B) HOMO-2.

electrons in the V system than the Ti, the situation is more complicated because there are also three other orbitals showing π-back-donation to the H2, but these either do not have a M-M bonding component or the second V does not contribute the same type of functions as the V bound directly to the H2. Of the M(III) systems, there is only one example of M-M bonding affecting the binding of the first H2, and that is Ti(III) D7 with hydride ancillary ligands. Here the M-H2 interaction is dominated by σ-donation from the H2 (Figure 9). Before the second Ti is substituted for Al there are two orbitals showing a

contributions of 20.08% dxy and 16.15% dx2−y2 from the Ti bound directly to the H2 and 7.32% dx2−y2 and 7.22% dxy from the second Ti. The corresponding orbital showing the most π-backdonation in the case where the second Ti is replaced with Ca, HOMO-1, does not have a contribution from the Ca atom or an M-M interaction (Figure 7 B). Similarly with D8 and V(II) there is a molecular orbital, HOMO-5, showing a strong π-backdonation component to the H2 as well as a strong M-M interaction, and the orbital contributions include 27.96% dxz and 19140

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interaction in some cases, this could also contribute to the rising adsorption enthalpies with increasing H2 coverage seen experimentally. The binding of H2 at one center could affect the ease of binding at an adjacent center through the interaction of the metals. Indeed, for Cr(II) and V(III) (the metals used in the experimental systems), the average M-H2 interaction energy is higher when there is one H2 bound to each metal rather than when only one H2 is bound to one metal (Tables 3 and 4). 3.4. Further Observations on the Experimentally Observed Rising Enthalpies with Increased H2 Coverage. In both the silica and hydrazine systems we have studied computationally,1,2,16 we find evidence that frontier orbital effects may well-contribute to the experimentally observed rising enthalpies with increased H2 coverage. However, it is also clear that such arguments do not provide a comprehensive explanation of the experimental data. This may, of course, be due to oversimplifications arising from modeling the binding sites of amorphous systems as molecules and specifically the limitations that such an approach imposes. We would, therefore, like to propose an alternative explanation for the observed rising enthalpies that more broadly fits the experimental data. Observations of the isotherms show that in these hydrazides little or no H2 binds at low pressure, suggesting that either the binding enthalpies of the sites are either unfavorable or that such sites are inaccessible or do not exist in the material. However, in the case of Cr hydrazides and V oxamides, Raman evidence under 1 bar H2 pressure has demonstrated a bathochromic shift to frequencies in the region of 2300 cm−1, suggesting that a small number of strong binding sites exists in these materials at this pressure but not enough to affect significantly the adsorption properties of the bulk material. At higher pressures, hydrogen binding becomes universally more favorable in all materials studied by our group in which Kubas binding is suspected or demonstrated, indicating that binding sites exist at higher pressure which are not present or accessible at lower pressure. The fact that isosteric enthalpies as high as 40 kJ mol−1 are observed at high pressure but that H2 desorbs spontaneously with a drop of pressure suggests that other effects must be at play. Such a high enthalpy would not be expected to desorb H2 spontaneously unless a structural change of some kind accompanied this drop in pressure and facilitated rupture of the M-H2 bond. Because these materials are largely amorphous and amorphous materials readily undergo significant volume changes, necessitating a change in local bond angles, on exposure to pressures as low as 10 bar,51 it is possible that such a structural deformation occurs with an increase in pressure in these hydrogen storage systems. In the ground state at 1 bar there are few available binding sites, and pressure-induced deformation of the structure forces a change in local geometry, essentially opening up new binding sites or providing more optimal overlap for H2 in existing binding sites, leading to increased H2 adsorption and a perceived increase in binding enthalpy. When saturation is reached, reduction of pressure allows the structure to recoil like a spring into its ground state, essentially driving off bound H2 ligands. This would explain the spontaneous desorption of hydrogen on reduction of pressure. To obtain some measure of the energetic penalty associated with distorting the local geometry around the binding sites to accommodate incoming H2, we present, in Table 10, the energy of the H2-free BSRs of the experimentally studied V(III) and Cr(II) systems at their geometries in the H2-bound structures, relative to the energy of the BSR before any H2 binding occurs. For V(III), the BSR must distort by 20 kJ mol−1 to bind the first

Figure 9. D7 with two Ti(III) and one hydride ancillary ligand with 1 H2 bound showing (A) the ball-and-stick structure, (B) HOMO, (C) HOMO-1, and (D) HOMO-33.

strong M-M interaction, HOMO and HOMO-1, that are not present afterward (Figures 9B,C and 10). The greater delocalization of the electron density when the Ti is present, aided by a M-M interaction, may be stabilizing the mainly σ Kubas interaction in this case.

Figure 10. D7 with a Ti(III) and a Al(III) and a hydride ancillary ligand with one H2 bound showing (A) the ball-and-stick structure and (B) HOMO.

Orbitals showing some sort of M-M interaction may be observed in dimers where altering the second metal does not affect the M-H2 interaction (e.g., Figure 11), but these do not show a π-back-donating component to the H2 or the second metal is not contributing the same type orbitals as the metal bound directly to the H2.

Figure 11. D6 with two V(II) with one H2 bound showing (A) the ball and stick structure and (B) HOMO-3.

The M-M distance tends to lengthen as more H2 molecules are bound (Tables 8 and 9), and this is probably due to the increased coordination. Whether the second metal affects the M-H2 interaction does not seem to depend on the M-M distance and so is not a proximity effect. The above evidence for the participation of adjacent metals in the same orbitals could account for the experimentally observed metallic properties of the material,18,19 and, because the presence of two transition metals has been shown to strengthen the M-H2 19141

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Table 8. M-M Distance with Zero and One H2 Bound for the M(II) Dimersa M-M bond length with no H2 bound/Å

a

M-M bond length with H2 bound/Å

dimer

Ti(II)

V(II)

Cr(II)

Ti(II)H

Ti(II)

V(II)

Cr(II)

Ti(II)H

2 6 8 5 1

2.865 3.012

3.008 3.063 2.759 3.026

3.335 3.160

2.628

3.094 3.063

2.947 3.344 2.875 2.976

3.072 3.294

2.704

4.033

4.218

Ti(II)H = dimer with hydride ancillary ligands. The values highlighted in italics indicate where the M-M distance shortens upon binding H2.

Table 9. M-M Distance with Zero and One H2 Bound for the M(III) Dimersa M-M bond length with no H2 bound/Å

a

dimer

Ti(III)

7 12 14 1 2

2.723

V(III)

Cr(III)

2.760 2.668

M-M bond length with H2 bound/Å Ti(III)H

Ti(III)

2.773

2.732

2.948 4.619

V(III)

Cr(III)

2.845 2.730

3.003

Ti(III)H 2.748

4.434 2.900

2.975

Ti(III)H = dimer with hydride ancillary ligands. The values highlighted in italics indicate where the M-M distance shortens upon binding H2.

Table 10. Relative Energies (kJ mol−1) of the H2-Free BSRs for V(III) and Cr(II) at Their Geometries in the H2-Bound Structures V(III) no. of H2 bound

relative energy

relative energy change per additional H2

0 and 0 1 and 0 1 and 1 1 and 2

0 20.47 55.52 92.72

20.47 35.05 37.20

recorded under equilibrium conditions, behave as if adsorption and desorption is close to thermodynamically neutral, with only pressure changes and no temperature swing required to effect the position of equilibrium. So in this picture the structural deformation essentially acts like a spring, buffering the enthalpies of adsorption and desorption during the cycle. Energy in the form of pressure is required for adsorption to occur, buffering heat release on formation of the M-H2 bond, whereas the exothermic relaxation of the structure to the ground state provides the driving force to push the otherwise endothermic desorption from the binding sites. So in essence, this internal spring provides the same function as the heat management system used in most commercial metal hydride tanks. Whereas this mechanism is not proven, the degree of computation, calorimetry, and spectroscopy required going beyond the scope of this study, it does appear to fit the data better than a purely frontier orbital-based explanation and will be the subject of later more detailed experimental and computational studies by our group.

Cr(II) relative energy

relative energy change per additional H2

0 44.57 86.73

44.57 42.16

H2, whereas for subsequent H2 binding, and for Cr(II), the energetic cost is a little higher, between 35 and 45 kJ mol−1 per additional H2. These energies, while not negligible, are sufficiently small so as not to invalidate our proposed pressureinduced deformation model. In fact, in the experimental systems, no more than two H2 ligands per metal have been observed under the conditions of study, and the isosteric enthalpies rise from 20− 40 kJ mol−1 on increase of pressure; these numbers are in close agreement with the energetic penalties of distortion, suggesting that the twisting almost exactly offsets the binding of H2, making the systems close to thermodynamically neutral. This explains the spontaneous absorption and desorption of H2 at 298 K with increasing or decreasing pressure, respectively, without any apparent need for cooling or heating on cycling. The possibility that high enthalpy sites already exist and a pressure-induced phase change makes them kinetically more accessible can also be considered; however this does not explain the spontaneous desorption of H2 from 40 kJ mol−1 binding sites with loss of pressure because the distortion-induced reclosing of internal kinetic pathways to these binding sites after initial adsorption would, if anything, retard hydrogen desorption, as the hydrogen molecules would be trapped within the structure. The fact that the Kubas interaction is very sensitive to local binding geometry for optimal π-back bonding with the directional metal d orbitals is consistent with this pressureinduced distortion mechanism, as is the fact that H2 metal binding energies in our computations are very sensitive to ligand geometry and environment. This explanation also fits with the observation that these systems, whose isotherms have been

4. CONCLUSIONS Dimers of two linked metal binding sites in hydrazine-based hydrogen storage materials have been modeled computationally with Ti, V, and Cr in the +2 and +3 oxidation states. The lowest energy H2-free dimer structures of the metals in the +3 oxidation state have a higher metal coordination and are less open, with more shared ligands, compared with the +2 oxidation state. There is not a strong correlation between the M-H2 interaction energies of the dimeric models and the previously studied monometallic BSR analogues. As with the monometallic BSRs, there is strong evidence that the H2 binds to the metals through the Kubas interaction and that for the metals in the +3 and +2 oxidation states the interaction is biased toward the σ-donation and π-back-donation, respectively. Compared with the monometallic BSRs, the ranges of M-H2 interaction energies and the frontier orbital energies both increase. Extrapolating, the bulk solid would have an even broader range of energies. As for the monometallic systems, the number of H2 molecules that can be bound to the metal centers reduces as the metal is altered across 19142

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the first-row transition metals, and the M-H2 interaction energy increases as the ancillary ligand is altered to a poorer π-acceptor. The experimentally observed rising enthalpies with increasing H2 coverage have been reproduced computationally only in some cases. There is evidence that the participation of the adjacent metals in molecular orbitals that take part in the π-back-donation to H2 affects the strength of the M-H2 interaction in some cases and may be a contributory factor to the metallic properties and rising absorption enthalpies. Because this explanation does not completely fit all of our data a new explanation involving pressure-induced deformation of the structure is proposed for the focus of future spectroscopic and computational studies.

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ASSOCIATED CONTENT

* Supporting Information S

Schematic representations of all initially considered dimeric structures representing linked binding sites, metal partial charges on lowest energy Ti(II) and V(II) dimers as a function of the number of bound H2, and Cartesian coordinates, SCF energies and spin data of all optimized structures. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS We are grateful to the UCL Graduate School for a scholarship to CVJS and for computing resources via UCL’s Research Computing “Legion” cluster and associated services. We also thank the EPSRC for computing resources via its National Service for Computational Chemistry Software (http://www. nsccs.ac.uk).

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