B₁₂X₁₁(H₂)⁻: exploring the limits of isotopologue selectivity of hydrogen adsorption

Abstract

We study the isotopologue-selective binding of dihydrogen at the undercoordinated boron site of B₁₂X₁₁⁻ (X = H, F, Cl, Br, I, CN) using ab initio quantum chemistry. With a Gibbs free energy of H₂ attachment reaching up to 80 kJ mol⁻¹ (ΔG at 300 K for X = CN), these sites are even more attractive than most undercoordinated metal centers studied so far. We thus believe that they can serve as an edge case close to the upper limit of isotopologue-selective H₂ adsorption sites. Differences of the zero-point energy of attachment average 5.0 kJ mol⁻¹ between D₂ and H₂ and 2.7 kJ mol⁻¹ between HD and H₂, resulting in hypothetical isotopologue selectivities as high as 2.0 and 1.5, respectively, even at 300 K. Interestingly, even though attachment energies vary substantially according to the chemical nature of X, isotopologue selectivities remain very similar. We find that the H–H activation is so strong that it likely results in the instantaneous heterolytic dissociation of H₂ in all cases (except, possibly, for X = H), highlighting the extremely electrophilic nature of B₁₂X₁₁⁻ despite its negative charge. Unfortunately, this high reactivity also makes B₁₂X₁₁⁻ unsuitable for practical application in the field of dihydrogen isotopologue separation. Thus, this example stresses the two-edged nature of strong H₂ affinity, yielding a higher isotopologue selectivity on the one hand but risking dissociation on the other, and helps define a window of adsorption energies into which a material for selective adsorption near room temperature should ideally fall.

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Introduction

As the element with the lowest mass, hydrogen has the most pronounced isotope effect of all elements. This leads to numerous applications of heavy hydrogen isotopes, deuterium (²H = D) and tritium (³H = T): in spectroscopy; structural analysis and the elucidation of reaction mechanisms, especially in biochemistry and pharmaceutical research;^1,2 and – more recently – even in pharmaceuticals,^3,4 where an effort is ongoing to exploit the slower rate of reaction of deuterated compounds to delay or alter metabolic pathways in order to increase potency and/or reduce side effects.

The continuous need for heavy hydrogen for energy production, science and medicine has motivated a revision of state-of-the-art separation processes⁵ by employing nanostructured materials. In a relatively recent approach, penetration and tunneling through two-dimensional materials such as graphene or hexagonal boron nitride are used to separate hydrogen isotopes.^6,7 Other separation techniques involve kinetic sieving in the interstitial space of layered materials⁸ or in apertures in metal–organic frameworks (MOFs),⁹ or isotopologue-selective adsorption (chemical affinity quantum sieving, CAQS)¹⁰ at strong metal sites in MOFs^11–13 and zeolites.^14,15

CAQS relies on the different zero-point energies of the H₂ isotopologues, which approximately correlate with the square root of the mass of the isotopologue. This leads to a stronger adsorption of the heavier isotopes and results in higher selectivities when the zero-point energy of adsorption is higher. The adsorption energy itself also positively correlates with the selectivity (albeit more loosely), because a higher adsorption energy leads to a steeper potential energy surface, which in turn increases the zero-point energy. (Although the stretching of the H–H bond decreases the frequency of the corresponding vibrational mode and thereby the zero-point energy, this effect is overcompensated by the contributions from other modes.^16,17).

Recent progress has been made to enable CAQS significantly above the boiling temperature of liquid nitrogen. For example, Cu(I)-MFU-4l with an H₂ adsorption enthalpy on the order of 30–35 kJ mol⁻¹ and a zero-point energy difference of 2.5–3.0 kJ mol⁻¹ between D₂ and H₂ reaches a D₂/H₂ selectivity of 10 at 100 K. However, since both selectivity and uptake decline with increasing temperature, operating temperatures must remain well below 200 K.¹² Nevertheless, these experiments raised hopes that an appreciable selectivity at or near room temperature could be achieved if materials or adsorption sites with higher adsorption energies could be found. With this publication, we want to make a contribution towards the search of such materials.

B₁₂X₁₁⁻ is a fascinating ion. Derived from the highly stable^18–20 dianion B₁₂X₁₂²⁻ by abstraction of X⁻, its reactivity is driven by the strong preference for a double negative charge.^21,22 Despite its negative charge, the monoanion is therefore highly electron-deficient. The partial positive charge at the undercoordinated boron atom would be expected to lead to strong H₂ attraction in a way similar to undercoordinated metal cations.¹⁷ The significant interaction between the undercoordinated boron site and noble gas atoms reported by experiment and theory^21–24 suggests that this system will also strongly bind dihydrogen, and that gas-phase experiments addressing this interaction should be feasible. A particularly attractive feature of these systems is the prospect of modifying the substituents X in order to form a cavity that sterically confines the bound dihydrogen to further increase isotopologue selectivity. For these reasons, we consider B₁₂X₁₁⁻ a suitable model system to study the limits of isotopologue-selective H₂ adsorption.

In this article, we computationally study H₂ attachment at B₁₂X₁₁⁻ (X = H, F, Cl, Br, I, CN). Using ab initio methods, we calculate thermodynamic parameters of the attachment reaction, analyze the influence of X on these parameters and of the different vibrational modes on the isotopologue selectivity. Furthermore, we investigate entropy effects, calculate isotopologue selectivities of the hypothetical adsorption of molecular H₂ and examine potential dissociation pathways for H₂ bound at B₁₂X₁₁⁻. Therefore, the present study highlights a wide range of aspects that are useful for the rational design of materials for dihydrogen isotopologue separation, including some rather surprising findings on the relation of attachment energy and selectivity, parameters that can be adjusted to enhance selectivity, and obstacles such as dihydrogen dissociation.

Methods

B₁₂X₁₁⁻ (with X = H, F, Cl, Br, I and CN) and their H₂ adducts have been optimized with hybrid density functional theory using the PBE0 (ref. 25) functional. Dispersion interactions have been accounted for with Grimme's D3 approach and Becke–Johnson damping, commonly referred to as D3(BJ).²⁶ Equilibrium structures, their energies and Hirshfeld charges have been obtained using geometry optimization employing Ahlrich's def2-QZVP split-valence quadruple-zeta basis set.²⁷ Potential energy surface scans have been performed using the smaller def2-TZVP basis set from the same series. For all DFT calculations we have made use of the resolution-of-identity and chain-of-spheres approximations, RIJCOSX,²⁸ in conjunction with the def2/J²⁹ auxiliary basis.

Thermal and zero-point energy contributions to enthalpies and entropies have been calculated at the above-mentioned DFT level using numerical harmonic vibrational frequency analysis. Standard increments of 0.005 Bohr have been used except for B₁₂H₁₁(H₂)⁻ and B₁₂F₁₁(H₂)⁻ where this led to imaginary frequencies; 0.002 and 0.001 Bohr, respectively, have been used in those cases to ensure consistent treatment in thermodynamic calculations by ORCA. The Gibbs free energy has been calculated using the quasi-rigid-rotor-harmonic-oscillator (QRRHO) approximation³⁰ as implemented in ORCA. This approximation treats the entropy (but not internal energy) contributions of low-frequency vibrational modes as free internal rotations by default. In line with such treatment, the zero-point and thermal vibrational contributions of the internal rotation to the internal energy have been subtracted from the value calculated by ORCA and ½RT has been added instead. Finally, entropy contributions have been corrected for an external symmetry number of 5 for B₁₂X₁₁⁻ and an internal symmetry number for B₁₂X₁₁(H₂)⁻: 10 for homoisotopic cases and 5 for heteroisotopic ones.³¹ For the B₁₂X₁₁(H₂)⁻ species, the Gibbs energies have been calculated for both symmetrical orientations of H₂ with respect to B₁₂X₁₁⁻ and the average has been used subsequently.

The hypothetical separation factors between two isotopologues of H₂ (below referred to as i and j) have been calculated from the Gibbs energies of attachment of H₂ (for the reaction leading to the local minima with undissociated H₂) via the respective equilibrium constants:

Correlated single-point calculations have been performed using the DLPNO-CCSD(T)^32,33 method as implemented in ORCA in conjunction with the def2-QZVPP and def2-QZVPP/C³⁴ basis sets based on a Hartree–Fock calculation with VeryTightSCF settings. SCF convergence issues, which arose in some cases, have been cured using the SlowConv setting and employing the SOSCF algorithm late in the SCF procedure (SOSCFStart 0.0001). For X = H, NormalPNO and TightPNO³⁵ settings have been compared and found to give almost identical results; NormalPNO has therefore been used throughout. Similarly, def2-TZVPP, def2-QZVPP, aug-cc-pVTZ and aug-cc-pVQZ basis sets have been found to yield very similar reaction energies for X = H, which has been taken as justification for using def2-QZVPP results without further refinement or correction for basis set effects.

Calculations employed ORCA³⁶ version 4.2.1, except for energy decomposition analysis (EDA). The latter calculations have been performed with the Amsterdam Density Functional (ADF) program from the Amsterdam Modeling Suite (AMS), version 2019.104 (r76620),^37,38 performing single-point calculations at the PBE0-D3(BJ) level in conjunction with scalar ZORA³⁹ for relativistic effects and the TZ2P⁴⁰ basis set with native Slater-type orbitals.

Results and discussion

Structure of B₁₂X₁₁⁻ and B₁₂X₁₁(H₂)⁻

The structure of B₁₂X₁₁⁻ (X = F, Cl, Br, I, CN) with and without attached noble gas atoms has been computationally investigated several times^21–23 and discussed in detail recently:²⁴ Compared to B₁₂X₁₂²⁻, the undercoordinated boron atom (B⁰) in B₁₂X₁₁⁻ moves toward the center of the cluster. Meanwhile, the substituents X of the surrounding boron atoms slightly bend towards B⁰, thereby decreasing the angle α(X–Ctr–B⁰) between X, the center of the cluster (Ctr) and B⁰ from 63.4° to 60.5°. Upon binding of noble gas atoms, this angle remains practically unchanged.

Given the similar size of He, Ne and H₂, one might expect B₁₂X₁₁(H₂)⁻ to behave similarly to B₁₂X₁₁He⁻ and B₁₂X₁₁Ne⁻. However, the latter two complexes show distinct differences in their B⁰–noble gas bond length. Moreover, H₂ has a much higher HOMO, lower LUMO and is more polarizable. Therefore, it should bind much more strongly to B₁₂X₁₁⁻. This expectation is reflected in the B⁰–H₂ distances, which are much shorter than those of B⁰–He despite similar sizes.

The structure of B₁₂X₁₁(H₂)⁻ is shown in Fig. 1. For all X investigated, the H–H bond is elongated by more than 9 pm, that is at least 3 pm more than for H₂ coordinated at (C₄H₈O₂)Cu⁺ (C₄H₈O₂ = 1,4-dioxane; calculated value from ref. 17). A comparison of the geometric parameters, which are listed in Table 1, reveals that X = F is an outlier with a much longer H–H bond length and a shorter B⁰–H₂ distance, which has consequences for the thermodynamic properties and isotopologue selectivity as discussed below.

Fig. 1 Illustration of B₁₂X₁₁⁻ with H₂ attached. B⁰ is the boron atom which is undercoordinated in B₁₂X₁₁⁻ and to which H₂ is bound in B₁₂X₁₁(H₂)⁻.

Table 1 Characteristic geometric parameters of B₁₂X₁₁(H₂)⁻: H–H bond length (minimum on the potential energy surface at the PBE0-D3(BJ) level) and distance between B⁰ and center of H₂. All distances in pm

X	r(H–H)	R(B^0–H2)
(Free H2)	74.4
H	85.0	125.7
F	91.0	119.6
Cl	85.2	125.2
Br	84.5	126.4
I	84.1	127.6
CN	84.2	127.3

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Analysis of the dihydrogen–B₁₂X₁₁⁻ interaction

Attachment energies for H₂ coordinating side-on at B₁₂X₁₁⁻ are shown in Table 2 and have, with the exception of X = H, a magnitude of ≈100 kJ mol⁻¹, which is much stronger than for most interactions of H₂ with undercoordinated metal sites.^11,12 As would be expected from the significantly elongated H–H bonds, the title compounds are predicted to strongly attract H₂. However, the order CN ≈ F > Cl ≳ Br > I ≫ H from strongest to weakest interaction differs from what would be expected from the bond lengths (Table 1). This surprising lack of correlation, which is shown in Fig. 2a, is contrary to systems where undercoordinated metal sites serve as attractors and where bond length and binding energy are evidently correlated.

Table 2 Internal energies of H₂ and D₂ attachment at B₁₂X₁₁⁻ calculated for 0 K, difference of this energy between D₂ and H₂ (which is equivalent to the difference in zero-point energy), Gibbs energies of attachment for 300 K, its difference between D₂ and H₂ and the resulting D₂/H₂ selectivity at 300 K. All energies are in kJ mol⁻¹; selectivities in units of one

X =	ΔadU (H2)	ΔadU (D2)	ΔΔE0	ΔadG (H2)	ΔadG (D2)	ΔΔG	S (D2/H2)
H	−36.6	−41.5	−4.9	−9.1	−10.8	−1.72	1.99
F	−110.0	−114.6	−4.6	−81.3	−82.6	−1.31	1.69
Cl	−101.4	−106.6	−5.2	−72.5	−74.3	−1.81	2.06
Br	−98.5	−103.6	−5.2	−70.1	−71.9	−1.77	2.04
I	−90.4	−95.4	−5.1	−62.0	−63.7	−1.67	1.96
CN	−108.5	−113.9	−5.3	−80.0	−81.8	−1.87	2.12

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Fig. 2 Correlation of (a) the H₂ attachment energy and (b) the red-shift of H–H stretch frequency Δν(H–H) with the H–H bond length elongation Δr(H–H) w.r.t. free H₂ in B₁₂X₁₁⁻ and dioxane complexes. (c): Comparison of H₂ attachment energies and differences of zero-point energies of attachment ΔΔE₀ between D₂ and H₂. Experimental values for MOFs are from ref. 12,13,41, calculated values for dioxane complexes (C₄H₈O₂M⁺) are from ref. 17.

Interestingly, the H–H bond is much more elongated for X = F compared to other X, despite a binding energy which is only slightly higher. Conversely, X = H shows a substantially lower binding energy (36 kJ mol ⁻¹ vs. > 90 kJ mol ⁻¹) despite geometric parameters which are very similar to X = Cl. Furthermore, X = CN, which has the second-highest H₂ binding energy after X = F, lies in between the least strongly binding halogens X = Br and X = I in terms of the H–H bond length. Only for X = Cl, Br, I does the binding energy follow the trend expected from the DFT-predicted bond lengths, that is: among the three, B₁₂Cl₁₁(H₂)⁻ has the highest binding energy, the shortest B⁰–H₂ distance and the most elongated H–H bond, followed by B₁₂Br₁₁(H₂)⁻ with B₁₂I₁₁(H₂)⁻ being last.

If the interaction between H₂ and all investigated B₁₂X₁₁⁻ was mainly driven by σ bonding (from H₂ to B⁰), one would expect a strong correlation between the charge at B⁰ and the H₂ attachment energy. At least for Cl, Br and I, a reasonable correlation between attachment energy and Hirshfeld charge at B⁰ is found (see ESI; Fig. S1†). However, the correlation is poor for other X and different charge trends are obtained when using orbital-based charges such as NPA charges (Fig. S2†). Furthermore, this does not explain the significant elongation of the H–H bond for X = F.

Since these unintuitive findings warrant a deeper investigation of the underlying binding properties, we have performed energy decomposition analysis (EDA) of the Gibbs energy of the attachment reaction of H₂ at B₁₂X₁₁⁻. Results are shown in Table 3: With one exception (ΔE_def of B₁₂X₁₁⁻, for discussion see below), the contributions of dispersion interaction and geometry deformation of the reactants as well as zero-point and thermal contributions are very similar.

Table 3 Contributions to the Gibbs free energy of attachment (300 K) of H₂ at B₁₂X₁₁⁻ from energy decomposition analysis (EDA): Pauli repulsion energy ΔE_Pauli, electrostatic interaction (including nuclear repulsion) ΔE_elstat, orbital interaction ΔE_oi, explicit dispersion correction ΔE_disp, geometry deformation ΔE_def of B₁₂X₁₁⁻ and H₂, Born–Oppenheimer energy ΔE_el (sum of electronic and nuclear contributions, i.e. all of the aforementioned ones), zero-point energy ΔE₀, thermal contributions ΔE_therm at 300 K (mostly entropy) and total Gibbs energy ΔG (sum of ΔE_el, ΔE₀ and ΔE_therm). ΔG values differ from Table 2 because EDA is at the DFT level; values in Table 2 are expected to be more accurate. All energies in kJ mol ⁻¹

X =	ΔEPauli	ΔEelstat	ΔEoi	ΔEdisp	ΔEdef (B12X11^−)	ΔEdef (H2)	ΔEel	ΔE0	ΔEtherm	ΔG
CN	400	−166	−402	−10	13	19	−146	22	29	−95
Cl	435	−185	−405	−10	16	16	−134	22	29	−84
Br	444	−185	−406	−11	14	14	−130	21	28	−81
I	476	−192	−420	−13	13	13	−122	21	28	−73
H	490	−205	−385	−7	15	19	−72	21	27	−23
F	480	−213	−462	−7	34	18	−150	23	29	−99

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The greatest variability is afforded by the Pauli repulsion term, which results from the antisymmetry requirement of the wave function and closely matches the intuitive understanding of steric repulsion. For CN, Cl, Br and I, Pauli repulsion is the dominating contributor to the overall trend in the reaction Gibbs energies. It is partly compensated by the electrostatic interaction, which may sound surprising at first, but is justified given the well-known fact⁴² that molecules attract each other more strongly the more diffuse their charge clouds are.

EDA shows two main reasons for the B₁₂X₁₁⁻–H₂ interaction being weakest for X = H. One is the weaker orbital interaction. The other is the stronger Pauli repulsion, which is caused by the larger electron density at B⁰ due to the less electron-withdrawing nature of X = H (see also ESI; Fig. S3†).

Finally, the case of X = F is characterized by a substantially stronger orbital interaction with H₂. This is unlike what has been observed for the attraction of noble gas atoms, which is weakest for X = F. This striking difference is in line with results from a recent publication,⁴³ which compared the binding of noble gases, N₂ and CO at B₁₂X₁₁⁻. It was found that X = F shows the weakest binding of noble gas atoms but the strongest binding of N₂ and CO due to π-like backbonding from B⁰ into the antibonding σ* orbitals of the attached molecule (something which is not possible for noble gases). This binding of N₂ and CO for X = F is unlike the strong binding for X = CN, which is based almost solely on strong σ bonding, a binding mode which is much weaker for X = F. We expect similar behavior for the binding of H₂, i.e. strong σ bonding and weak backbonding with modest H–H elongation for X = CN (and to a lesser degree Cl, Br, I) and weaker σ bonding but strong backbonding for X = F. The stronger backbonding would also explain the much greater elongation of the H–H bond for X = F.

Very similar zero-point energies of attachment

Previous studies of undercoordinated metal sites show a substantial (albeit sublinear) increase of the adsorption zero-point energy with the adsorption energy in paddlewheel MOFs¹⁶ and zeolites¹⁷ (see also Fig. 2c). By contrast, all B₁₂X₁₁⁻ investigated here have very similar zero-point energies of attachment, which are almost independent of X (see Fig. 2c).

In the case of X ≠ H, this could be interpreted as entering a region of saturation where an increase in the attachment energy yields smaller and smaller gains in the selectivity. However, this does not explain the case of X = H, where a lower zero-point energy of attachment would have been expected.

An explanation is given by the ZPE contributions of the different vibrational modes (see below for a detailed discussion). The greatest ZPE variability is afforded by the asymmetrical B⁰–H stretch mode, which works in favor of the overall selectivity. However, most of this contribution is compensated by the weakening of the H–H bond with an opposite contribution (see Fig. 3b).

Fig. 3 (a) Calculated isotopologue selectivities for the H₂ attachment at B₁₂X₁₁⁻ using X = Cl as example. Very similar selectivities are obtained for X = H, Br, I, CN and lower ones for X = F (see ESI; Table S1†). (b) Contribution of vibrational modes to zero-point energy difference between D₂ and H₂ isotopologues for free (unbound) dihydrogen in the gas phase (left bar) and when coordinated at the various B₁₂X₁₁⁻.

Vibrational modes in detail

When discussing the vibrational modes of B₁₂X₁₁⁻, the internal rotation (φ in previous publications^12,17) of H₂ about the B⁰–H₂ axis is of some interest. The combination of five-fold symmetry of B₁₂X₁₁⁻ and two-fold symmetry of H₂ results in a ten-fold internal rotational symmetry (36° period) about the B⁰–H₂ axis³¹ for homoisotopic H₂ (five-fold internal rotational symmetry for heteroisotopic H₂). The high symmetry leads to an exceptionally flat potential energy surface for this mode, which is confirmed by a scan of the potential energy surface using DFT: the obtained differences between highest and lowest energy are below 0.02 kJ mol⁻¹ in all cases, which is indistinguishable from numerical noise (see NEB paths for the internal rotation in the ESI†). A comparison of the vibrational behavior of B₁₂X₁₁(H₂)⁻ for φ = 0° and φ = 90° (equivalent to φ = 18°) shows almost identical results for the frequencies of the other modes (differences of less than 5 cm⁻¹). These small differences suggest that the coupling between the quasi-free rotational mode along φ and the remaining vibrational modes is negligible. This allows for treatment of the other modes independent of φ and thereby greatly simplifies the calculation of the ZPE and of the thermal contributions to the Gibbs energies.

H₂ coordinated at B₁₂X₁₁⁻ exhibits a vibrational behavior that qualitatively matches that observed in previous studies of highly attractive metal centers.^12,16 The highest-frequency mode is the H–H stretch vibration (ν_HH along r), which is strongly red-shifted with respect to the free molecule. It is followed by the asymmetrical B⁰–H stretch vibration (ν_BH,asym, which in the case of weaker interaction would have been denoted as rotation of H₂ in the B⁰–H₂ plane along the angle ϑ) and the (symmetrical) stretch vibration of the B⁰–H₂ bond (ν_BH,sym along R).

As shown in Fig. 2b, the frequency shift of the H–H stretch vibration correlates almost linearly with the H–H distance, not only for different B₁₂X₁₁⁻, but also when expanding the dataset using data from different (C₄H₈O₂)M⁺ calculated in ref. 17. Near-linearity holds true even across different classes of compounds and breaks down only at extreme elongations (H₂ at B₁₂F₁₁⁻ and C₄H₈O₂Au⁺; the latter is not shown in Fig. 2b because of the extreme values of Δr = 100 pm and Δν = 3722 cm⁻¹). These cases, where the H–H stretch frequency approaches zero and the H–H distance goes to infinity, however, are still very well described by Badger's rule,⁴⁴ which implies ν ∝ r^−3/2 for H₂.

Likewise, it could be expected that the frequencies of the B⁰–H stretching modes correlate with the B⁰–H₂ distance. This is indeed the case for ν_BH,asym, but surprisingly not for ν_BH,sym.

The two remaining degrees of freedom, which can be interpreted as the hindered translations of H₂ perpendicular to the B⁰–H₂ axis, are expected to correlate more with the degree of steric hindrance than with the attractiveness of the undercoordinated site itself. Unfortunately, the substituents X are too far away from the H₂ binding site to exert any significant influence leading to little variation in the frequencies of these modes.

Zero-point energies of attachment, entropies and high predicted D₂/H₂ selectivities

Although H₂ attachment energies at B₁₂X₁₁⁻ vary widely with X, the differences between the Gibbs energies of attachment of H₂ and D₂ for a given X and therefore the selectivities are in a very narrow range (with X = F being a slight outlier). This may be surprising at the face of it, but is in line with the very similar zero-point energies of attachment of all species.

The entropy of H₂ attachment is negative because the translational and rotational entropies of the free H₂ are higher than the vibrational entropy of the bound H₂, an effect which is more pronounced the higher the temperature. This fight against entropy is one of the key obstacles towards adsorptive H₂ isotopologue sieving at high temperatures. Therefore, the high predicted D₂/H₂ selectivity – which is approximately 2.0 at 300 K for X = H, Cl, Br, I, CN – is truly remarkable. Selectivities of about 2.9 and 5.1 are predicted for 250 K and 200 K, respectively. Note, that the selectivities at 250 K and 200 K are much higher than would be expected based on the room temperature value if only the direct influence of temperature T on the separation factor via α = exp(-ΔΔG/RT) was considered. This is because most of the selectivity loss at higher temperatures is due to the above-mentioned entropy effects, which result in lower absolute values of ΔΔG as temperature increases and therefore lower selectivities.

HD/H₂ selectivities are predicted to be about 1.4 at 300 K, 1.8 at 250 K and 2.4 at 200 K. Even at 200 K, T₂/D₂ and DT/D₂ selectivities are much lower at around 1.7 and 1.3, respectively. More information is given in Fig. 3a and in the ESI (Table S1†).

Heterolytic dissociation of H₂ at B₁₂X₁₁(H₂)⁻

Given the high H₂ binding energies, one might expect that the title compounds show a substantial propensity towards dissociation of coordinated H₂. Indeed, we found local minimum structures with a negatively polarized H⁻ at B⁰ and a positively polarized H⁺. As shown in Fig. 4, that H⁺ can coordinate at one X (for X = F, CN), between two X (for X = Cl, Br, I) or directly at the boron core (preferred only for X = H, F), behavior which is in line with observations on B₁₂X₁₂H⁻ (X = F, Cl, Br, I)⁴⁵ and B₁₂X₁₁RH⁻ (R = alkyl group).⁴⁶

Fig. 4 Potential energy surface of H₂ bound at B₁₂X₁₁⁻. The (local) minima in the middle (a) correspond to undissociated H₂, the other ones (b–e) to heterolytically dissociated H₂ (with H⁻ at B⁰). The minima on the left (b) have H⁺ bound at the B₁₂ cage. For the minima on the right, H⁺ either binds to one X – which is a local minimum for X = F (c) and X = CN (e) – or between two X, which is a local minimum for X = Cl, Br, I (d). The curve for X = H does not show the right side as structures (a) and (c) would be equivalent in that case. Except for X = F, the two transition states shown are similar not only in energy but also in structure. The zero level of the energy corresponds to the unbound state (infinite distance between H₂ and B₁₂X₁₁⁻). Energies for local minima are given at the DLPNO-CCSD(T)//PBE0-D3(BJ) level, other points are interpolated using PBE0-D3(BJ) data. Colors: B pinkish, H white, X green, C gray, N blue.

The dissociation behavior of H₂ at B₁₂X₁₁⁻ is, however, unlike what has been observed in the case of undercoordinated metal sites. In a previous publication we have predicted particularly strong H₂ interaction at zeolitic Au⁺ sites¹⁷ and observed strong elongation of the H–H bond to the point of dissociation using local coupled-cluster calculations. However, dissociation was homolytic in that case and attempts to create structures with H⁺/H⁻ polarization failed (geometry optimization reverted to structures with equivalent H atoms). This shows the uniquely strong ability of B₁₂X₁₁⁻ to polarize H₂ and stabilize a H⁻ ion at the B⁰ site.

For H₂ bound at B₁₂X₁₁⁻, the activation energy for heterolytic dissociation is below (or only slightly above in the case of X = H) the H₂ attachment energy, which means that an incoming H₂ would have enough energy to overcome the barrier and dissociate. We therefore expect that B₁₂X₁₁(H₂)⁻ (X = F, Cl, Br, I, CN) will not be observed in experiment and a technological application requiring multiple adsorption cycles is not realistic. As indicated by its potential energy surface, B₁₂H₁₁(H₂)⁻ may be somewhat metastable against dissociation and it could therefore be interesting to study the dynamic behavior of this ion at low temperatures. Harmonic values of characteristic vibrational frequencies are given in the ESI (Table S2†).

Compared to other X, the potential energy surface for X = F is much flatter towards H₂ dissociation and the formation of the structure shown in Fig. 4(b), which is in line with the much longer H–H bond length in this case.

It is interesting to note that the heterolytic dissociation of heteronuclear H₂ isotopologues (i.e. HD, HT and DT) shows a preference for the heavier nucleus to occupy the position where the vibrational frequency of the corresponding stretch frequency is higher, thereby minimizing the overall zero-point energy. Especially for B₁₂X₁₁HD⁻ with X = Cl, Br and I, this results in a pronounced preference for D to occupy the H⁻ position (coordinated at B⁰ as D⁻) and for H to take the H⁺ position between two X as the latter is characterized by a very shallow potential energy surface. Equilibrium constants are given in Table S3.†

Related species

Preliminary calculations on related species (B₁₂X₁₁²⁻, B₁₂X₁₀²⁻ and B₁₂X₁₀⁻) showed a similar propensity towards dissociative binding of H₂, albeit with even lower dissociation barriers. Given the added computational expense of treating radical systems and/or multiple isomers, they have not been studied in detail.

For the octahedral B₆X₅⁻, no local minimum structure with undissociated H₂ has been found at all. Their smaller structures lead to smaller B–B–B angles, stronger pre-hybridization and therefore much stronger interaction.

Conclusion

We have investigated the interaction of B₁₂X₁₁⁻ with H₂ with a special focus on the different interaction strengths of H₂ and D₂. Internal energies of attachment are highest for X = CN and X = F (ΔU (¹H₂) = −110 kJ mol⁻¹ at 0 K), decrease with increasing mass for the halogens (down to −90 kJ mol⁻¹ for X = I) and are lowest for X = H (−36 kJ mol⁻¹). Despite widely varying attachment energies, zero-point energy differences between D₂ and H₂ attachment are very similar at ≈5.0 kJ mol⁻¹ (in contrast to results from other materials where a positive correlation between both parameters was typically found). Gibbs energies for different isotopologues are reported as well, corresponding to D₂/H₂ selectivities of ≈2.0 at 300 K.

Unfortunately, the strong H₂ activation leads to heterolytic dissociation with activation energies below the interaction energy; that is, H₂ approaching the cluster has enough kinetic energy to overcome the activation barrier and form a compound with dissociated H₂. This highlights the very high electrophilicity of B₁₂X₁₁⁻ despite its negative charge, even exceeding that known from many strong H₂-adsorbing metals like Au⁺ in zeolitic environments.

Although heterolytic dissociation likely precludes experimental investigation of B₁₂X₁₁(H₂)⁻ (with undissociated H₂) and practical application for hydrogen isotopologue separation, the example is instructive as it shows the limits of increased adsorption energy with regards to enhancing isotopologue selectivity: not only do higher adsorption energies run the risk of leading to H₂ dissociation, but there also seems to be a limit to the adsorption zero-point energy between H₂ and D₂ of around 5 kJ mol⁻¹. However, already this 5 kJ mol⁻¹ difference is very encouraging as it leads to predicted D₂/H₂ separation factors of 2.0 at 300 K and 3.0 at 250 K, figures that might be further enhanced by steric confinement and would even be high enough to enable HD/H₂ separation if a suitable material could be found that does not lead to H₂ dissociation.

Outlook

Since the smaller B₆X₅⁻ show much stronger H₂ affinity than B₁₂X₁₁⁻, we would expect higher closo-borates to bind H₂ less strongly. Therefore, it could be interesting to investigate clusters like B₁₆X₁₅⁻, B₃₂X₃₁⁻ and B₄₂X₄₁⁻ (which derive from polyhedra dual to C₂₈, C₆₀ and C₇₀, respectively).^47,48 Unfortunately, the synthesis of higher closo-borates is faced with huge thermodynamic and kinetic obstacles.⁴⁹ To the best of our knowledge, none of these compounds have been synthesized to date, leaving little prospect for eventual application.

Nevertheless, we believe that the two known cases of Cu(I)-MFU-4l (adsorption enthalpy of ≈35 kJ mol⁻¹ and appreciable selectivity around 200 K) and B₁₂X₁₁(H₂)⁻ (internal energy adsorption of ≈110 kJ mol⁻¹ and appreciable selectivity at 300 K for X = CN, but dissociation and saturation of zero-point energy of adsorption) give us an estimate of the window of adsorption energies within which the search for materials enabling isotopologue-selective adsorption should be focused.

Author contributions

JW proposed to investigate the H₂ affinity of B₁₂(CN)₁₁⁻. TW performed all calculations and prepared the first draft of the manuscript. The authors jointly discussed results and revised the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

TW thanks the European Social Fund for a PhD fellowship. JW is grateful to a Freigeist Fellowship of the Volkswagen foundation. We thank the Center for Information Services and High Performance Computing (ZIH) at TU Dresden for computational resources.

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Footnote

† Electronic supplementary information (ESI) available: Additional tables and figures as quoted in the article (PDF); sample input files (TXT); atomic coordinates and NEB paths (XYZ); and vibration files (7-column XYZ, which can be read and visualized e.g. with Jmol⁵⁰ using tools → vibrate). See DOI: 10.1039/d1ra06322g

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