Dynamics of bound states of dihydrogen at Cu(I) and Cu(II) species coordinated near one and two zeolite framework aluminium atoms: A Combined Sorption, INS, IR and DFT study

e Ambient conditions sorption isotherms of dihydrogen in a series of various levels of Cu-exchanged ZSM-5 zeolites, with two different Si/Al ratios, namely 11.5 and 25, show the presence of different amount of Cu centres able to strongly bind H 2 . Although the isosteric heats of adsorption derived from these isotherms are rather similar, of the order of 30 kJ/mol H 2 , Inelastic Neutron Scattering (INS) of adsorbed dihydrogen and Fourier-Transformed Infra-Red (FTIR) spectroscopy measurements of adsorbed CO and NO reveal that copper is encountered in two oxidation states. At least two types of Cu(I) ions are clearly detected as well as some heterogeneity of the Cu(II) species. The number of these Cu species is different in the two investigated ZSM-5 materials and depends on the Cu exchange level. With the aid of DFT model cluster calculations we find that under different coordination environments, determined by the Al distribution, both mono- and divalent Cu ions could bind H 2 with a different strength. Unprecedentedly, we found that Cu-ions compensating two Al atoms, i.e. formally Cu(II) species, relatively far apart from each other, may behave very similarly to the monovalent Cu-species or alternatively viewed – as Cu(I) species that compensate for two framework Al-atoms. Such Cu- species also form stable η 2 dihydrogen complexes. Cu(I) coordination [45]. Strong interactions between Cu(II) and H 2 have not been reported yet. Known isosteric heats for the Cu(II)-H 2 complexes as well as IR red-shifts correspond to a physisorption regime, e.g. 5-7 kJ/mol and 60 cm -1 [45] in agreement with the observed INS lines, in the range 55 – 80 cm -1 [54, 58]. Our computational results, based on the T23-AlT1T4-Cu(II) cluster also suggest low binding energy, of the order of just a few kJ/mol H 2


Introduction
Due to their ability to stabilise metal ions in highly reactive electronic states, with low coordination number, within an open for various guest molecules pore structure, ZSM-5 zeolites continue to attract an intense scientific and industrial interest. Perhaps the most valuable merit of Cu-exchanged ZSM-5 is its high activity in reactions for NOx control, such as direct decomposition of NO [1] and selective reduction of NOx by hydrocarbons [2,3]. The catalytic properties of the Cu-ZSM-5 materials have been well established from a macroscopic point of view and the corresponding research work comprehensively reviewed [4]. One of the outputs is showing that the activity of the material depends on the Si/Al-ratio, the copper loading, and, to some extent, on the preparation conditions [4]. It has been suggested by early studies [5] that monovalent Cu ions are responsible for the observed high catalytic activity. The reducibility of the Cu ions in Cu-ZSM-5 in vacuum, H2, and CO, as well as the Cu(I)-ion sitting have been further investigated [6][7][8] by means of UV-vis photoluminescence and in situ NO Fourier-Transform Infra-Red (FTIR) spectroscopy. Two main types of Cu(I) species have been found [6][7][8], with concentration ratios depending on the Si/Al ratio and the Cu concentration correlating well to the observed catalytic activities. The Cu ion coordinated near a single Al-atom, presumably to two framework oxygen atoms only, has been suggested as an active site, in contrast to the second type of sites in which the Cu ion is coordinated to three framework oxygens, very likely in the vicinity of two Al-atoms [8]. The autoreduction process in which Cu(II) is reduced to Cu(I) by temperature treatment in vacuum as well as the Cu ion local coordination environment and activity have been further studied by X-ray spectroscopic techniques and in situ FTIR measurements of adsorbed NO and CO [9][10][11][12][13][14]. Thus, in highly siliceous samples e.g. Si/Al=25÷45, after vacuum activation at 673 K, more that 90% of the total Cu content has been found in a monovalent state in which the Cu(I) ion resides 2.00±0.03Å away from the nearby oxygen atom, with an average coordination number of 2.5±0.3 [9]. Under similar conditions, about 40% of the total Cu content has been reduced to Cu(I) for a Cu-ZSM-5 sample with Si/Al=14 [10]. Another study [12], concluded that for samples with higher Al content, Si/Al=11.9, 46% of the Cu ions are in the form of Cu(I) after evacuation at 673 K. The reduction process evidently continues with the increase of the temperature, reaching 56% at 773 K and 70% at 873 K [13]. For a very similar sample with Si/Al=11.9 the same group has reported an average coordination number of 2.8 and an average Cu-O distance of 1.98 Å [14]. The trend of increase of the Cu(I) coordination number and decrease of its fractional content with the increase of the Al-substitution is supported by other studies on Cu-exchanged mordenite material with Si/Al=5 [11]. In this case the coordination number varies from 4.1±0. 4 for Cu(II) to 2.9±0. 3 for Cu(I) after evacuation at 673K [11], with at least 30% of the Cu remaining in the divalent state. The above experimental observations [6][7][8][9][10][11][12][13][14] may be rationalised by assuming that various Cu coordination sites are associated with different aluminium tetrahedral site preferences. Following the notation of the nonequivalent Si(Al) crystallographic positions [15], and employing combined interatomic potential function for the periodic zeolite structure and ab initio quantum mechanical methods for the atoms defining the particular coordination site, Nachtigalová et al. [16] have evaluated the stability of Al substitution in each of the 12 possible non-equivalent tetrahedral positions (T-sites). More recently [20] the stability and energetic preference of formation of various combinations of framework Al-pairs has been computationally explored in a great detail. It has been experimentally established [21] that at low Cu loadings, e.g. below 1% wt, bare Cu(II) ions are abundant, compensating two framework Al-atoms. EXAFS data suggest the formation of oxygen bridged linear dinuclear Cu-species at higher loadings [21]. It has been computationally shown [22] that at high Culoadings even trinuclear Cu-species may be thermodynamically rather stable. This seems to have been again corroborated experimentally [21]. However, EXAFS studies on the distribution and dynamical structure of Cu-species in the Chabazite structure SSZ-13 demonstrate that equally good fits may be obtained by considering neighbouring Al(Si) tetrahedral atoms [23]. Yet again, in Cu -exchanged SSZ-13, similarly to the findings for Cu-exchanged ZSM-5 [21], EXAFS experiments [24] suggest possible formation of oxygen bridged binuclear Cuspecies only at high Cu loadings, e.g. 1.2 % wt Cu and only monomeric species for medium loadings of 0.5% wt Cu. The interest in the Cu-exchanged ZSM-5 zeolites, particularly for dihydrogen binding and storage, has been recently revived by reports on some extraordinarily strong interaction with dihydrogen [25,26] raising a fundamental interest in utilising this type of binding interactions as a prototype of solid state hydrogen storage media. In a previous work [27] we have confirmed that the hydrogen molecule is chemically bound to a low coordination number Cu-centre and forms a nonclassical η 2hydride, a.k.a Kubas's complex [28]. The observed spectroscopic features [27], a sharp peak centred at about 0.8 cm -1 and much broader bands at 1.4 and 1.7 cm -1 , appearing at higher loadings, were interpreted in terms of adsorption on Cu ions in various coordination environments, with only the lowest energy peak unambiguously modelled as an η 2 -Cu(I) complex coordinated at two framework oxygen atoms. Note the erroneous units given in the caption of Figure 1 of [27] -the correct units on the energy axis are cm -1 . The broad bands at around 1.4 and 1.7 cm -1 were tentatively assigned to dihydrogen on Cu(I) ions sitting in a very diverse coordination environment. Multiple dihydrogen binding at a single Cu(I) centre was rejected by the simulations [27]. Consequently, we have also measured and reported [29] dihydrogen adsorption isotherms at ambient temperatures and extracted the corresponding isosteric heats of adsorption in a broad concentration range covering about 40% of the isolated Cu-ions. For these we obtained isosteric heats starting at 80 kJ/mol H2 for the lowest concentrations, flattening out at e.g. 50-60 kJ/mol and then continuously dropping down to about 40 kJ/mol for the highest accessed loading corresponding to 0.4 H2/Cu. More recently, the possibility of storing hydrogen via chemical adsorption has been further explored in Cu(I) exchanged ZSM-5, SSZ-13 and SSZ-39 using only Cu(I) source such as CuCl in acetonitrile solution [30,31], thus achieving high loading of monovalent Cu-species, again assuming that isolated Cu(I) species are responsible for the extraordinarily strong binding of the adsorbed hydrogen. The strong binding was explored by other authors [32] aiming at quantum separation of hydrogen isotopes, owing to the large enough difference in the vibrational energies of the isotopes, a factor of 2 for H2 and D2 at the strong-binding sites. In the present work, we extend our studies on Cu-exchanged ZSM-5 zeolites focussing on low exchange levels, in different Sito-Al materials, aiming to shed more light on the details of dihydrogen binding and metal ion activities at isolated Cu-ions compensating either a single or two Al framework atoms at various distances from each other, positioned in a single or different zeolite rings. The dynamics of dihydrogen bound at such Cu species, as we will show not necessarily of oxidation state (I), is observed by high resolution INS and is able to explain the previously unassigned [27] peculiar broad bands in the corresponding low temperature INS spectra.

Materials and Synthetic procedures
The ammonium forms of ZSM-5 zeolites with Si/Al ratios of 11.5 and 25 (CBV2314G and CBV5524G), purchased from Zeolyst, USA, were converted into the corresponding protonated forms by calcinations at 823 K for about 2 hours. Copper ion exchange was performed in aqueous solutions of copper acetate with concentrations between 0.002 and 0.023 M in a single step process. The exchanged materials were filtered out, washed and dried at 393 K for about 16 hours. The total copper content in each sample was determined by Atom Absorption Spectroscopy (AAS). Research grade dihydrogen gas (99.9995%) was used throughout all measurements. Carbon monoxide (> 99.5 % purity) was supplied by Merck. Before adsorption, the CO gas was passed through a liquid nitrogen trap. Nitrogen monoxide was provided by Messer Griesheim GmbH, and had a purity of > 99.0%. Prior to the adsorption procedure the NO gas was purified by fraction distillation. text of the article should appear here with headings as appropriate.

Techniques
Dihydrogen adsorption isotherms were measured with a Sieverts type volumetric gas handling rig. The samples were placed in a stainless steel reactor for activation and isotherm measurement. Details of this experimental set up have previously been given [27,29]. The activation and isotherm measurement procedures reported Please do not adjust margins Please do not adjust margins before [29] were followed here as well; with the only difference that now we used larger samples of the order of 10 g each. Isotherms at three different temperatures were measured for each sample in order to determine the corresponding isosteric heats of adsorption. Additionally, at the same three temperatures, dihydrogen adsorption isotherms of the two 'blank' H-ZSM5 materials, CBV2314G and CBV5524G, were also measured. Their fourth power polynomial interpolants were consequently subtracted from the isotherms of their Cu-containing counterparts in order to obtain isotherms corresponding to adsorption on Cu ions only, as shown in the SI material. FTIR investigations were carried out using a Nicolet Avatar 360 spectrometer, at a spectral resolution of 2 cm -1 , by accumulating 64 scans per spectrum. Self-supporting pellets ( 10 mg cm -2 ) were prepared by pressing the sample at 10 4 kPa and were always treated in situ in the purpose-built IR cell. The latter was connected to a vacuum apparatus with a residual pressure of about 10 -3 Pa. Prior to the adsorption measurements, the sample was activated by heating for 1 h at 723 K under oxygen followed by evacuation for 1 h at the same temperature. INS spectra of dihydrogen adsorbed in large batches of the same samples were collected on the time-of-flight direct geometry chopper spectrometers IN5 [33] and TOF TOF [34]. Prior to the INS experiments each Cu-ZSM5 sample was activated in a stainless steel container at up to 823K, in a dynamic vacuum of the order of 10 -6 Torr, then transferred to an aluminium scattering cell attached to a centre stick equipped with gas capillaries. The transfer procedures were accomplished in a He-filled glove bag. In situ dihydrogen dosing was performed with the same gas handling rig as for the adsorption isotherm measurements. After recording a blank spectrum for each sample i.e. with no dihydrogen, at 4K, using neutrons with wavelengths of 2 Å and 7 Å, calibrated amounts of dihydrogen gas were introduced into the scattering cells at around 100 K. After each pressure equilibration step, the temperature was decreased again to 4 K and the corresponding spectra were measured using the same neutron wavelengths. One reference INS spectrum of 20 cc (STP) H2 per gram, adsorbed in a H-ZSM-5 sample (Si/Al=25), was also measured at 4K.

Computational details
Dihydrogen rotational dynamics and adsorption site strengths were studied using clusters cut out from the original MFI structure, consisting of 23 Si(Al)O4 tetrahedra, closely resembling Cu-sites at the intersection of the straight and sinusoidal channels for both Cu(I) and Cu(II) ions. The results were checked against similar accuracy periodic model DFT calculations based on the Chabazite structure as a test bed. The multiprocessor version of Gaussian 09 computational package [35] was used for the cluster simulations while the Abinit package, version 8, was employed for the periodic model studies. Full details of the computational setups are provided in the Supporting Information.

Results and discussion
The following nomenclature was adopted in order to label the investigated samples: the approximate Si-to-Al ratio in each sample was abbreviated as SAX, X=Si/Al ratio, i.e. SA12 and SA25 for our two bare zeolite materials; the Cu-to-Al exchange level is given shortly as CuX, X=Cu/Al ratio. Thus, where the Cu/Al ratio, as determined by Atomic Absorption Spectroscopy (AAS) is 0.25, the corresponding part of the sample's label is Cu0.25. The full label of a sample with Si/Al of 25 and Cu/Al=0.25 thus becomes SA25Cu0.25. Table 1 and 2 summarise some physical and chemical properties of our samples with the two different Si/Al ratios of 11.5 and 25, accordingly.

Volumetric dihydrogen adsorption
The isosteric heats of dihydrogen adsorption at low coverage in the H-form of the two parent ZSM-5 materials are shown in Fig. 1. The corresponding adsorption isotherms measured at the three experimental temperatures namely 273, 294, and 314 K, are given in the Supporting Information along with the isotherms of each of the two zeolites exchanged with different amount of copper ions.     The average isosteric heats of adsorption of the two H-ZSM-5 samples are almost equal within their estimated errors and may be compared to the 6.0 kJ/mol H2 heats of adsorption of dihydrogen in silicalite [36] as well as in Na-and K-exchanged ZSM-5 [37] namely 10.3 and 9.1 kJ/mol H2. Thus, there is about 50% increase in the adsorption heat on going from the neutral pure silica to the protonated Al-containing zeolite form. Further, as seen in Fig. 2, the replacement of the acidic protons by Cu ions, most likely both di-and monovalent as will be shown later, leads to a three to four-fold increase in the corresponding isosteric heat. The average all data points on each curve in Fig. 2 is reported in the Qst columns in Tables  1 and 2 accordingly. It may also be noted that for the SA25Cu0.25 samples, for which we have also shown the Qst curve, resulting from H-ZSM-5 unsubtracted isotherms, there is a clear and significant drop of the adsorption heat down to about 10 kJ/mol H2 at about 0.5 H2/Cu that is very close to the values for the non-exchanged zeolite materials. This indicates that at these H2 concentrations most of the dihydrogen is adsorbed at the weaker Cu(II) sites and the rest of the zeolite framework.
In all the presently investigated samples, the measured isosteric heat of adsorption at the lowest loadings is on average lower than that determined for H2 in the over-exchanged Cu-ZSM-5 material [29]. The experimental Qst values are, however, similar near the middle of the accessed concentration range where the adsorption heat of H2 in the over-exchanged material [29] settles near 40 kJ/mol, before dropping down to about 30 kJ/mol at loadings of about 0.5 H2/Cu. These observations may suggest that in the over-exchanged material some additional and stronger adsorption sites must be present.

FTIR characterisation
IR spectroscopy of probe molecules e.g. CO and NO was used for an additional and independent identification of the different copper species.

CO adsorption
FTIR spectroscopy of adsorbed CO is a powerful frequently used technique for the characterization of Cu(I) species. The Cu(I)-CO bond is relatively strong due to the synergism between its -and components [41]. In addition, the formation of -back bonding enhances the C-O extinction coefficient which allows detection of relatively small amounts of Cu(I) sites. It has been reported that Cu(I)-CO species in Cu-ZSM-5 are characterized by an unusual high frequency [38][39][40][41] (2158 cm -1 ) as compared to carbonyls formed with oxide-supported copper [41][42][43] and this has been attributed to the enhanced -component of the Cu(I)-CO bond [41]. It has also been found that, at room temperature and in the presence of CO in the gas phase, the monocarbonyls tend to be converted to dicarbonyl species [38][39][40][41][42]: Cu(I)-CO + CO  Cu(I)(CO)2 (1) These dicarbonyls manifest themselves by IR features at s(CO) at 2178 cm -1 and as(CO) at 2151 cm -1 , symmetric and antisymmetric intramolecular C-O stretches accordingly. Zecchina et al. [39] reported that at low temperature conversion of di-to tricarbonyl species also takes place: Cu(I)(CO)2 + CO  Cu(I)(CO)3 (2) It has been concluded that the tricarbonyls are characterised by two bands at 2191 and 2167 cm -1 . In addition, a band at 2137 cm -1 , coinciding in position with the band characterizing physisorbed CO, has been proposed to be due to the same complex [39]. The authors noted, however, this was a tentative assignment and that not all dicarbonyl species could be converted into tricarbonyls. There is currently no consensus in the literature about the possibility of detection of Cu(II) sites in zeolites by CO [37]. In any case, the Cu(II)-CO bond is much weaker compared to the Cu(I)-CO bond. For that reason, Cu(II) sites may be detected using CO only at low temperatures. Contrary to CO, NO forms relatively strong complexes with Cu(II) ions [46] while the Cu(I)-NO bond is rather weak and these complexes are formed at lower temperatures [47]. However, highly coordinatively unsaturated Cu(I) cations in zeolites can form nitrosyls even at room temperatures while at low temperature these species are converted to dinitrosyls [48]. In this work we initially exploited the capabilities of IR spectroscopy of adsorbed CO to characterize the Cu(I) ions formed during autoreduction of Cu(II) on several Cu-ZSM-5 zeolites differing in copper loading and Si : Al ratio. Data on the fractions of Cu(I) sites able to form tricarbonyls were obtained. Further, NO was used as a molecular probe to obtain information on the ratio between Cu(II) and Cu(I) species. Four samples were selected for the FTIR studies: SA25Cu0.19, SA25Cu0.25, SA12Cu0.15 and SA12Cu0. 19. The background IR spectra of these activated samples, in the OH region, are presented in Fig. 3. The spectrum of SA25Cu0.19 contains three main bands at 3744, 3655 and 3612 cm -1 (Fig. 3, spectrum a). A shoulder around 3726 cm -1 is also visible. In addition, a broad absorbance, centred on 3500 cm -1 , can be distinguished too. The band at 3744 cm -1 is known to arise from external silanol groups and that at 3726 cm -1 to internal silanols [49]. The band at 3612 cm -1 corresponds to zeolite acidic hydroxyls and indicates an incomplete ion-exchange which is consistent with the low Cu:Al ratio (see Table  1). In any case, the band is reduced in intensity as compared to the parent zeolite. The band at 3665 cm -1 is associated with Al-OH groups and evidences the existence of EFAL species [49]. Finally, the broad band around 3500 cm -1 is due to H-bonded hydroxyls. The spectrum of SA25Cu0.25 shows the same features (Fig. 3, spectrum b). In this case, however, the band due to bridged hydroxyls is less intense, which indicates a higher exchange degree and is consistent with the higher copper concentration in the sample.
The spectrum of SA12Cu0.15 is noisier (Fig. 3, spectrum c). This is due to the fact that the transmission of the sample in the region is rather low, which is attributed to a larger particle size and enhanced light scattering. In any case, the same features as with samples 1 and 2 can be distinguished. As expected, the spectrum of SA12Cu0.19 (based on the same parent zeolite) is also noisy. In this case, the OH bands are poorly resolved and less intense. This indicates that some copper species have reacted not only with the acidic hydroxyls, but with the other OH groups.

Adsorption of CO on SA25Cu0.19
Carbonyl species in this material showed rather exciting behaviour and their characterisation was published in a separate article [50]. In summary, these results confirmed the formation of Cu(I)-CO species on Cu-ZSM-5 that may be converted into dicarbonyls, and part of them, even to tricarbonyls. Some Cu(II) species were also detected at low temperature by a carbonyl band at 2194 cm -1 . In order to obtain information on the conversion of di-to tricarbonyls, the intensities of the characteristic bands at 2191 and 2151 cm -1 were analized as a function of the coverage. It was found that about 45 % of the Cu(I) sites in this sample that are in cationic positions are able to coordinate up to three CO molecules, while the  remaining 55 % of the sites can form only dicarbonyls [50] The results of these studies is now reflected in the corresponding lines integral intensity ratios R1 and R2 in Tables 1 and 2. In addition to the carbonyl bands associated with copper, there were bands due to CO-OH interaction: CO polarized by the zeolite acidic hydroxyls at 2175 cm -1 ; CO interacting with aluminol groups, at 2170 cm -1 , and CO affected by the silanol groups -around 2155 cm -1 .

Comparison of CO adsorption features on all samples
The carbonyl spectra detected after CO adsorption on SA25Cu0.25 are similar to those already described with SA25Cu0.19 (Fig. 4, spectrum b). The most important differences are: • The band at 2175 cm -1 is less intense, which is consistent with the lower concentration of bridged hydroxyls on the sample.

•
The band at 2170 cm -1 appears with enhanced intensity in agreement with the more important concentration of Al-OH species in this sample.
• All bands assigned to copper carbonyls and polycarbonyls are more intense in line with the higher concentration of copper.
In agreement with the established highest copper content in SA12Cu0.19, the carbonyl spectra, registered after CO adsorption here, show the highest intensity of the band due to tricarbonyls (Fig.  4, spectrum d). In addition, the highest level of conversion from dito tricarbonyls was detected for this sample. Some amount of EFAL Lewis acid sites were also detected by an Al 3+ -CO band at 2220 cm -1 . Interestingly, the FWHM of the 2158 cm -1 monocarbonyl band with the two SA25Cu samples is 8 cm -1 while with the samples SA12Cu, 12 cm -1 . This suggests a more homogeneous copper distribution in the samples SA25Cu.

Adsorption of NO
The IR spectra of NO (1.6 kPa equilibrium pressure) adsorbed on the samples are shown on Fig. 5.
The bands above 1850 cm -1 are usually assigned to Cu(II)-NO species while the bands below this frequency originate from nitrosyls of Cu(I) [46]. The band at 1910 cm -1 is assigned to NO adsorbed on isolated Cu(II) sites. Clearly, all samples contain significant amount of isolated Cu(II) sites. A careful analysis of the related NO spectra reveals that these sites have slightly different coordination environments. The band at 1811 cm -1 is typical of Cu(I)-NO species in Cu-ZSM-5 [48]. A negligible fraction of these species are converted into dinitrosyls at the conditions used, being evidenced by the weak relatively broad band at around 1740 cm -1 . A shoulder of the main band (1811 cm -1 ) appears at around 1827 cm -1 . Note that, in agreement with the CO adsorption results, the Cu(I)-NO bands with the SA12Cu samples are broader thus again indicating a larger inhomogeneity of the Cu(I) sites in this higher Al-content material.

In situ Inelastic Neutron Scattering of adsorbed dihydrogen
Owing to its large neutron scattering cross section, about an order of magnitude larger than that of other chemical substances, as well as the relatively large rotational constant, B=59 cm -1 , dihydrogen is a very sensitive and convenient probe for studying diverse adsorption sites, their strengths, and spatial shapes. Such data provides a unique detailed microscopical description of porous-materials internal surfaces and their heterogeneity. This is achieved by observing the spectrum of lowest energy rotational states of the adsorbed molecules. In comparison to that in the free state, this spectrum is strongly modified by the local adsorption potential, depending on each site size, shape, and the local interactions strengths. In the rotationally free state, at low temperatures, and in thermodynamic equilibrium all molecules are in the spherically symmetric singlet state J=0. Being composed of half-spin particles, dihydrogen obeys Fermi-Dirac statistics. In order to preserve the required antisymmetric character of the total molecular wavefunction, with respect to the two nuclei interchange, neutron scattering processes  The spectra are background corrected. Please do not adjust margins Please do not adjust margins leading to rotational excitations to the triply degenerate spatially antisymmetric J=1 state (as well as any other transition between even and odd J states) is necessarily accompanied by a nuclear spin flip. The intensities of such transitions are proportional to the very large incoherent scattering cross section of hydrogen. The transition to the first excited state in the gas phase, is expected at about 119 cm -1 . In physisorption systems such as Grafoil the first rotational transition of the adsorbed dihydrogen, at concentrations corresponding to the commensurate 3 phase, has been observed at 117 cm -1 as a single sharp line [51]. On the contrary, the same feature appears split into a doublet and a singlet for H2 adsorbed in Single-Wall Carbon Nanotubes [52] while a complex broad spectrum, extending between 80 and 140 cm -1 , has been observed for dihydrogen adsorbed in microporous activated carbon [51]. In Metal-Organic Framework (MOF) compounds with unsaturated metal sites such as HKUST-1 [53], containing Cu(II) centers coordinated to four oxygen atoms in a planar arrangement, the corresponding rotational component has been found at 72 cm -1 [54] and 100 cm -1 [55]. In CPO-27-M, (M =Mg 2+ , Ni 2+ , and Co 2+ ) a material with high density of the metal centres, in a square pyramidal coordination, the lowest excited H2 rotational state has been observed between 52 and 60 cm -1 [56] for H2 adsorbed only at the metal centre. For this set of equivalent topology metal-ion sorption sites, with similar coordination environments, the binding energy follows a relatively simple monotonic trend, with the position of the centre of the gravity of the corresponding rotational transitions [55,56], which could serve as a miscroscopic indicator of the relative adsorptive site strengths. However, in general the interpretation of the data is more complicated due to the influence of steric interactions, for instance with host structural fragments, shaping the adsorption potential at a particular site. Thus, the most favourable sorption site in the [Zn(trz)(tftph)] MOF was identified, with aid of simulations, to be in the vicinity of a metal-coordinated H2O molecule, an exposed fluorine atom, and a framework carboxylate oxygen. These coordination environments give rise to a rotational transition at 43.6 cm -1 and a measured adsorption heat of c.a. 8 kJ/mol [50]. In an yttrium-based Y-FTZB MOF (containing Y 3+ open sites), on the other hand, the rotational transition has been observed at an even lower energy, e.g. 19.4 cm -1 , but with a similar isosteric heat of 9 kJ/mol H2 [58]. This value is close to the lowest heats observed in the CPO-27-M materials [55,56] too, but showing a much stronger rotational hindrance. In over-exchanged, predominantly Cu(I)-containing ZSM-5, due to the very strong interactions between the H2 and the Cu(I) ions, an η 2 -H2 complex has been observed involving significant π back-bonding to the metal, [27] with the corresponding rotational line shifted even further down near 1 cm -1 , lowest to date with respect in any other porous material.
The above examples demonstrate the prospective of high resolution INS technique as a very sensitive and useful technique for probing the local adsorption site topology. However, the observation of the ground-to-first excited rotational transition of adsorbed dihydrogen, while representing a strong microscopic piece of information, cannot on its own serve as a definitive measure of the individual site adsorptive strength and therefore computational methods and/or complementary methods must be employed. The rotational spectra of dihydrogen, adsorbed in the under-exchanged Cu-ZSM-5 materials of this study, are shown in Fig. 6 a, b, c, and d. In all cases, features previously observed in the Cu(I)-η 2 -H2 complex [27] are observed here too. Additionally, a useful differentiation of the signal is apparent too.   Tables 1 and 2, respectively. .

Cluster models of the ZSM-5 MFI structure
The results from our cluster based calculations are presented n Tables 3 and 4. All rotational frequencies in Tables 3 and S2 were computed numerically, following the procedure as described in [27,46], assuming a 1D rigid rotor model, using the zeolitic model clusters shown in Fig. 8. In Table 4 we present the NBO formal charges of the Cu atoms in different fragments, with and without adsorbed H2, along with the corresponding Natural Atomic Orbital (NAO) configuration and the electronic population in the bonding and antibonding H2 orbitals. The model structures, used in the calculations, were chosen so as to reconstruct in a simple and efficient way the positions and the corresponding coordination environment of the Cu atoms most easily accessible for guest species. The number of SiO4 tetrahedrons in each model cluster allows for a realistic reproduction of the Si/Al ratios in the samples and the local electrostatic fields experienced by the adsorbed H2. Inspection of Table 3 does confirm previous findings [25][26][27][28], based on small clusters, that monovalent Cu-species, represented here by the much larger clusters T23-AlT1-Cu(I), T23-AlT1HT4-Cu(I), and T23-AlT1HT7-Cu(I) bind dihydrogen strongly, resulting in a strongly hindered rotation [27]. The present larger structural clusters demonstrate again the dominant importance of the local coordination geometry of the Cu(I) species. Coordination to two framework oxygen atoms is associated with a more stable Cu(I)-H2 complex, with a substantially stronger rotational hindrance of the H2 ligand as compared to the four O-atom coordinated Cu(I)-ions for which both the binding energy and the barrier to rotation are reduced by factors of nearly 2 and 8, respectively. We recall that from a theoretical point of view, the dihydrogen rotational transition largely depends on the mode of binding at the metal centre and in particular to the electronic state of the metal ion, its coordination state, as well as the electrostatic and steric interactions with neighbouring framework fragments. Orbital interactions, leading to electron charge transfers and redistribution, are known to be essential in the η 2 metal-dihydrogen complexes [24] and this is intact with our results in Tables 3 and 4. The dispersive interactions, totalling to only about 10% of the binding energy, are expected to be rather isotropic, hence not significantly contributing to the bound-H2 rotational barrier, and consequently have negligible effect on the rotational dynamics. The computed Cu-H2 distances agree well to those previously observed in various 3d metal-dihydrogen complexes [28]. Notably, at coordinatively unsaturated Cu(II) species, orbital interactions are totally absent and the observed Cu(II)-H2 distances increase to 2.3-2.8 Å, with the dihydrogen ligand freely rotating in the plane parallel to the Cu(II) square coordination plane [54,55]. According to the NBO analyses here, Table 4, the very low rotational barrier in 4O-coordinated Cu(I)-ions is because, in contrast to 2O-coordinated Cu(I), the two different Cu 3d-orbitals involved in the back bonding, both in the equilibrium and in the transition state, are now of very similar shape and at similar energies. Thus, both orbitals are equally able to donate electrons, with the same magnitude of the corresponding energetic effect leading to a rather isotropic rotational potential. Comparing the data in Tables 3  and 4, becomes clear that the height of the barrier to rotation indeed depends on the amount of the electron π-back donation from the Cu 3d orbital to the H2 σ * antibonding orbital. There is a direct dependence of the barrier height on the difference between the electron back bonding in the equilibrium state and that rotated by 90° (i.e. the rotational transition state).     Moreover, as most of the M-H2 bond strength depends on the H2 to M σ-bond (not affecting the barrier to rotation due to its symmetry) there is only an indirect relationship between the positions of the observed rotational transitions and the measured isosteric heat of absorption. The back donation of electrons from the Cu 3dπ orbitals into the H2  * orbital, leads to the expected H-H bond weakening [28], causing the red shift the H-H vibrational frequency. According to the calculations, the T23-AlT1-Cu(I) cluster with a Cu(I) atoms coordinated to two framework oxygens is the most likely candidate as the origin of the sharp rotational line at about 0.8 cm -1 . Nearly identical result is obtained for the T23-AlT1HT4-Cu(I) cluster, Fig. 8 and Ref. [27]. Weaker binding and much lower rotational hindering is found for H2 at the 4O-atom coordinated Cu(I) in the T23-AlT1HT7-Cu(I) for the reasons discussed above. However, our INS spectra do not indicate the presence of the latter types of structures. Three and four oxygen-coordinated Cu(I) species at defect sites in the Cu-MOF-74(CPO-27-Cu) structure were recently anticipated and investigated computationally, again showing a decreasing H2 binding power with increasing of the Cu(I) coordination [45]. Strong interactions between Cu(II) and H2 have not been reported yet. Known isosteric heats for the Cu(II)-H2 complexes as well as IR red-shifts correspond to a physisorption regime, e.g. 5-7 kJ/mol and 60 cm -1 [45] in agreement with the observed INS lines, in the range 55 -80 cm -1 [54,58]. Our computational results, based on the T23-AlT1T4-Cu(II) cluster also suggest low binding energy, of the order of just a few kJ/mol H2.  Table 5, and a typical Cu(II) chemistry, in terms of 3d9 electronic structure, large half-filled 3dz 2 orbital, and relatively low reactivity. Correspondingly, the H2 rotational tunnelling transition for this structure is predicted at about 44 cm -1 , Table 3, only marginally lower than that observed for the paddle-wheel Cu-sites in HKUST-1 [54]. Such 4O-coordinated Cu(II) ions may logically be expected as the most stable divalent species, that would hardly undergo autoreduction even at 873 K. We argue then that INS bands in the range 40-70 cm -1 originate from H2 forming electrostatic adducts with Cu(II). Thanks to the larger size of the zeolitic clusters, we were additionally able to explore the extra framework Cu-ion electronic state and H2 binding in configurations containing two Al atoms, where one of the framework Al-atoms was moved further away from the other one: structures T23-AlT1AlT4-Cu(II) and T23-AlT1AlT23Cu(II). As seen in Fig. 8 e and f, the Cu atoms in such structures appear coordinated to only 2 oxygen atoms and their formal oxidation state, Table 4, formally is +1, very similar to the Cuspecies T23-AlT1-Cu(I) and T23-AlT1HT4-Cu(I) (with and without adsorbed H2). The binding energy and correspondingly the rotational hindrance at these sites are visibly reduced, Table 3, with tunnelling frequencies predicted in the range between 1.7 and 3.4 cm -1 , depending on the Al-Al distance.
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Chabazite periodic models
The effect of neighbouring second framework Al atoms, at a different distances from the coordinated Cu-centre, in the same and different zeolite rings scenario was additionally tested by periodic structure calculations based on the Chabazite (CHA) zeolite type framework, using projector augmented plane wave representation of the electronic density in DFT. This structure was chosen due to its similarities with the MFI structure of ZSM-5 and the smaller unit cell, making the calculations feasible for the available computational power.
For all periodic calculations we used the conventional Bravais unit cell of the CHA structure, containing a total of 130 atoms. It must be pointed out that although the CHA structure contains only one crystallographically inequivalent site for Si (all SiO4 equivalent), the local environment of the vicinal coordinated Cu-ions, compensating for Al-atoms replacing a Si atom is quite different. The diversity in environments becomes even larger if a second Al atom is introduced in the place of a silicon. The original structure of the CHA framework (https://america.iza-structure.org/IZA-SC/framework.php?STC=CHA) was first fully optimized, i.e. all atomic coordinates and lattice parameters were allowed to vary. Then for the model with Al-substitutions and Cu centres we removed all symmetry restrictions, except the translational invariance of the unit cell, by reducing the original space group symmetry, R-3m, to group P1. The unit cell of the structure depicting the now inequivalent 36 tetrahedral sites occupied by Si, which could all individually or in different combination be replaced by Al atoms, is shown in Figure 9a. During the optimisation of the Al-substituted structures, with Cu-centres, with or without adsorbate guests, we allowed all atomic coordinates to be varied, along with isotropic lattice vectors change, i.e. the shape of the unit cell was kept constant to minimize effect of artificial Al(Cu-sites) long range ordering. When the Al-atom is in a T12 position, the extra framework Cu-ion may coordinate differently: i) near two oxygen atoms, in the 8MR as in Fig. 9b, ii) above the 6MR as shown in Fig. 10, iii) above the nearby 4 MR -in Fig. 11. There is another, slightly higher energy site formed on the 4 MR, at the other side of the Cu-centre, where the nearest oxygen atom is below the plane defined by the four tetrahedrals. Consequently, the Cu-ion is coordinated to two oxygen atoms bridging the two 6MRs as shown in Fig. 12a. In the same figure, Fig.12b, is shown another site that is practically equivalent to the one in Fig. 11. For high Si/Al ratios, at low metal exchange levels, these sites represent the three possible types of sites for the extra framework Cu-ions and the corresponding dihydrogen complexes. It is worth noting that they reside very closely, a few Å away from each other, and especially when there is dihydrogen adsorbed, are quite similar in energy, Table S1, differing by just a few kJ/mol. This implies that the formed Cu(I) -dihydrogen complex may be rather mobile in the CHA structure, at moderate temperatures. Note that the adsorption of hydrogen is expected to be quite exothermic and local framework overheating is very likely. Fast hydrogen loadings may cause isolated copper ions aggregation and reduction to metallic clusters. The sites at the 4 membered rings are specific for the CHA structure while the position in the 8 MR, being large enough is generally representative of isolated Cu-ions, coordinated to two framework oxygens and could be used as a model site describing the dynamics of dihydrogen complexes formed in the 12MR, at the intersection of the straight and the sinusoidal channels of the MFI(ZSM-5) structure. The site at the 6 membered ring is similar to the Z6 ring in the MFI structure of ZSM-5, for instance.
Next we turn to a structure with two Al -atoms: one again in the T12 position and second just opposite on the 8MR, which is actually a part of the lower 6MR if considering the same unit cell, in T30, Fig. 13 and Fig. 9 a . The charge on the second Al-atom, in T30, was compensated by a H-atom bound at the near O. In this coordination environment the Cu(I)-H2 complex has the typical geometry features and stability, Tables S1 and S2. Notably, when the charge balancing proton, near the second Al in position T30, is removed the Cu -H distances in the complex are increased, the stability decreased by a few kJ/mol and the corresponding tunnelling frequency is substantially increased from 0.55 cm -1 in the Cu(I) complex up to 0.81 cm -1 for the formally designated as Cu(II) complex. It is worth noting that the corresponding dihydrogen complex is again diamagnetic, Table S1, specifying that in all two Al-atoms containing structures the two spin channels were treated separately. Other examples from Table S1 are illustrated in Figure 14, with Al -atoms in T12 and T4, the latter again balanced by a proton, Fig. 14a, leading to a diamagnetic Please do not adjust margins Please do not adjust margins Cu(I) species in either with or with no bound H2, and a corresponding tunneling transition expected at 0.44 cm -1 . Fig. 14 b shows a structure with Al-atoms even further apart -in T12 and T34 and no charge balancing proton, i.e. expectedly a Cu(II) species. However, in this case too, the binding energy is significant, 69 kJ/mol, similar to that for the AlT4HT12Cu+H2 structure -82 kJ/mol H2. The frequency of the tunnelling transition in AlT12T34 -coordination is shifted upwards at 1.38 cm -1 .
The weakest Cu-dihydrogen interactions occur at the 6MR where two Al-atoms reside in the ring as shown in Fig. 15, and the Cu-centre manifests a typical Cu(II) chemistry, with the usual halfempty 3d9 orbital, atomic magnetic moment of about 0.8 Bohr, in a nearly square planar coordination. Interaction with H2 leads to a typical physisorption adduct with binding energy of just below 18 kJ/mol and Cu-H distances about 2.5 Å, Tables S1 and S2. The corresponding rotational tunnelling transition is expected near 46 cm -1 , similarly to the cases of dihydrogen in HKUST-1 [54] and CPO-27-Cu [55] Furthermore, we explored the binding of dihydrogen at dual Cuspecies [21][22][23][24], of the types [Cu-O-Cu] and [Cu-OO-Cu] in the 8MR, as depicted in Fig. 16. Such structures could not be a priori ignored, particularly for the SA12 samples with relatively high Al-content and higher Cu-loadings, e.g. >1 %wt. The interactions between such structures, Fig. 16, and dihydrogen, however, turns out from our calculations, of purely dispersive origin, resulting in binding energies of about 14 kJ/mol H2, and Cu-H distances of 2.8 Å, like those in the CPO-27-Cu-dihydrogen system [55]. These appear equivalent to planar triangular and square Cu(II) species, as far the interactions with dihydrogen are concerned.
Various configurations of single and double aluminum atom substituted CHA structures, with one Cu-centre and where the second Al-atom is or not balanced by a proton, are detailed in Tables S1 and S2. These results show that the energetics and dynamics of the bound hydrogen is scattered over a broad range of energies, spanning typical physisorption values, c.a. 10 kJ/mol H2, passing through an intermediate region of mixed contribution e.g. 30 kJ/mol, and reaching typical covalent interactions as strong as 80 kJ/mol H2. In all cases, these binding energies are overestimated as compared to the experimental adsorption heats shown in Tables 1 and 2. The corresponding H2 ligand rotational transitions are correspondingly covering the whole range of transition energies from just fractions of a cm -1 , for H2 on Cu-species with low coordination number, e.g. 2, either near one Al atom or two, where the second is charge balance by a compensating proton. It is quite remarkable that such species seem to manifest themselves by appearing all at very similar energies corresponding to the relatively sharp rotational feature in the INS spectra of high silica samples, at about 0.8 cm -1 [27], within both the cluster MFI-derived and the periodic Cha models, and in the present data, Fig. 6 a and b. Further up with the transition energy, 1 to a few cm -1 , come those sites where two framework Al-atoms are balanced by a single Cucentre, lying in the larger zeolite rings e.g. the AlT30T12Cu 2+ 8MR, AlT4T12Cu 2+ 8MR, AlT29T12Cu 2+ 8MR, AlT34T12Cu 2+ 8MR, Table S1 and S. This sort of Cu-coordination must be responsible for the scattered intensity into the broad spectrum of rotational energies experimentally seen for the overexchanged ZSM-5 [27] and here in Fig. 6. On the smaller rings e.g. the Z6 rings in ZSM-5, here the double 6MR and the 4MR, the Cu-center is in the vicinity of a larger number of atoms from the framework and the corresponding Cu-H2 complexes are less stable, e.g. AlT12Cu + 6MR and AlT12Cu + 4MR, AlT30HT12Cu + 6MR, for which the rotational transitions fall above a few and below 10 cm -1 . No significant intensity in that range was observed neither in the present studies nor in our earlier experiments [27]. Fig. 7, however, displays, quite significant inelastic intensity in the range 40 ÷ 70 cm -1 . An inspection of Table S2 leads to the conclusion that these must originate from structures in which the Cu-dihydrogen complex is coordinated to a larger number of nearby oxygen atoms e.g. 4, with model representatives AlT18T12Cu 2+ 6MR, the AlT27T12Cu 2+ 6MR in Fig. 15, AlT29T12Cu 2+ 6MR, AlT30T12Cu 2+ 6MR, AlT33T12Cu 2+ 6MR. A further important note to make, based on the total electronic energies data reported in Table S1, is that the stability of the Cu-sites, and the corresponding dihydrogen complexes are rather similar from site to site, differing by a few and up to a few tens of kJ/mol. Notably the monovalent Cu-species on the six membered ring with Al-atom in the T12 position is by about 60 kJ/mol more stable than above the 4MR and 38 kJ/mol more stable with respect to Cu(I) in the 8MR. Quite remarkably, when the corresponding dihydrogen complex is formed, the site above the 6MR becomes destabilized with respect to the neighbouring sites being higher in energy by 8kJ/mol with respect to the Cu(I)-H2 complex in the 8MR. This latter site can be reached via the appearing as an intermediated state 4MR at just 26 kJ/mol higher than for the Cu-H2 complex at the 6MR. Considering the relatively large isosteric heat released during the formation of the corresponding Cu-dihydrogen complexes, and the poor heat conductivity of the porous zeolite framework, one must expect large enough local adsorption related temperature jumps, leading to Cuspecies and Cu-H2 moieties migration withing the framework, possibly even Cu-ion reduction and clustering in extreme cases. Thus, even at low Cu exchange levels one may expect to find the Cu-centres in all possible coordination environments around the framework Alatoms. This is particularly true when the Cu-exchanged material has been in contact with strong ligands as CO, NOx, etc., which interact via significant covalent interactions with the Cu-centers and exert strong trans effects weakening the bonding between the centre and the framework, but may also happen during initial activation stages of water desorption, for instance. However, it is the Al-distribution in the parent zeolite framework that is the prerequisite of materials of different properties/activities. Indeed, the sitting and distribution of framework Al-atoms has already been established as a major factor in the catalytic activity of various zeolite structures and the reactivity  Please do not adjust margins Please do not adjust margins of the extra framework ions [60]. Recently two types of Cu-species have been anticipated in Cu-exchanged SSZ-13 [61] too, where only one crystallographic type of site has previously been detected by direct microscopic methods [62,63]. Contrary to the earlier results a more recent synchrotron X-ray spectroscopy study showed [62] that only up to 20% of Cu(II) ions reside in the 6 membered rings of CHA zeolite with a Si-to Al ratio of 15.5 and Cu-to-Al loading of 0.45, while the rest 80% are located in 8-mebered rings. In this latter case, although crystallographically similar, the sites for the Cu-ion, and respectively the cation activity on these sites, would differ depending on the relative Al-Al distribution, as shown in our model calculations.
Our simulations results support the idea that all of the above experimental results, at the macro- [60] and microscopic level [62,63] are not contradictive, but simply observe different distribution of the Cu-species in the vicinity of the framework Al-atoms in various coordination environments -a distribution that could be influenced by different sample treatments and activation procedures. It is worth noting, that in practical applications, as in automotive catalytic converters for instance, these materials operate at elevated temperatures, e.g. 250 ÷ 350 o C, where the zeolitic framework internal surface potential corrugation would be further reduced by the temperature and the heat effects of the interactions with the incoming gas constituents and products. Thus, it makes sense to anticipate that many of the above studied Cu-species contribute to the experimentally observed catalytic activities either as individual centres and/or in a cooperative manner. Furthermore, these findings point to the perspective of molecular dynamics studies on the mobilities of the above species, capable of elucidating the processes behing catalyst degradation and deactivation.

Conclusions
Adsorption isotherms of dihydrogen were measured at ambient temperatures, in two types of ZSM-5 zeolites with Si-to-Al ratios of 11.5 and 25. For both Si-to-Al ratios tested, the isosteric heats of adsorption increase 3 to 4 folds as compared to the bare H-ZSM-5, from about 8-9 kJ/mol H2 to 24 -37 kJ/mol H2 remaining still much lower than those previously found in the same zeolite type, but with a high copper exchange level [29]. From the room temperature measured dihydrogen sorption capacities becomes clear that higher fraction of strongly binding sites can be formed for higher Cu-exchange levels and higher Si-to-Al ratio.
The materials were also characterized by FTIR spectroscopy of in situ adsorbed CO (for characterization of Cu(I) sites) and NO (for characterization of Cu(II) sites). In all samples two types of Cu(I) species were found, able to coordinate up to two and up to three CO molecules, respectively. The relative concentrations of these sites depend on the parent zeolite local structure and copper loading. NO adsorption revealed the presence of isolated Cu(II) sites in all samples too, showing some degree of inhomogeneity .
Using DFT cluster and periodic model calculations, we have also shown that the observed INS bands may be explained in terms of two different types of Cu(I) species representing two relatively strong binding sites. The first group being the already known Cu(I) species coordinated to two oxygen atoms only. The broader INS feature is now suggested to originate from H2 adsorbed on Cu-centres that compensate two framework Alatoms, relatively far apart from each other so that after the activation process the compensating Cu-ions remain coordinated to only two O-atoms, near one of the Al-atoms. The activation of these sites must involve only thermal desorption of H2O molecules, coordinated at Cu species during the exchange procedures, without the formation of bridging hydroxyls. Judging from the integral area of the INS peak at ~ 0.8 cm-1 and the broad band centred at ~ 1.4 cm-1, the amount of such Cu(I) centres, in place of the expected Cu(II) ones, must be quite significant and, possibly, even represent the majority of the strongly binding (reactive) Cu sites. Moreover, there must be a relatively broad spread of such Cu-species, replicating a variety of Al-Al distances in the MFI zeolite framework, offering even a larger possible spread than the studied here model CHA structure.
The non-reduced Cu(II) species, most likely coordinated to 4 O-atoms, bind H2 weakly, with adsorption energies in the range typical for physisorption as also previously observed for Cu-containing MOFs and zeolites. Our study supports the view that depending on the Al content and relative disposition, a variety of both divalent and monovalent Cu-species may be present. Both species represent quite different activities towards guest molecules, ranging from typical physisorption to strong chemisorption, depending on the coordination mode. Hence, key feature, underlying the activity towards guest molecules of the various Cu-species in these zeolites, via their coordination environment and electronic states, possibly also readiness for switching between electronic states, is the Al content and relative geometric Al -Al configuration in the zeolite structure.

Conflicts of interest
There are no conflicts to declare.

Acknowledgements
The computational work benefits from support by the project

Dihydrogen adsorption isotherms in the H and Cu-exchanged forms of ZSM-5 zeolites
CBV2314G with Si/Al=11.5 and CBV5524G with Si/Al=25 Figure S1. H2 adsorption isotherms, measured at 273K, in the H-form, Cu/Al=0, and Cuexchanged SA12 (CBV2314G) samples. The total amount of adsorbed dihydrogen at STP per gram material is shown in the left block while on the right side block is shown the subtracted adsorption isotherms, corresponding to the extra adsorption due to the presence of Cu-ions.

DFT calculations
The multiprocessor version of Gaussian 09 computational package S1 (revision A.02) has been used throughout the cluster model calculation in these studies. The total energy of each structural fragment has been calculated using the B3LYP S2  Calculations involving periodic zeolite clusters were performed using the Abinit software package S6,S7 version 8. The PBE parametrization of GGA was used for the total energy calcualtion. Spatially isotropic, i.e. angles between the lattice vectors were kept fixed, geometry optimizations for all investigated structures, with the Bravai unit cell of the Chabazite structure, with the space group reduced to P1, were done until the forces on all atoms were reduced to below 1 meV/Å. The projector augmented pseudopotential method S8 was used to model the electronic wave function and electron-ion interactions, with an energy cut off on the plane wave part of 820 eV. Additionally, a Hubbard U correction on the energy of Cu 3d electrons was applied with a magnitude of 9 eV and a correlation part J of 1 eV, computed for a free Cu + -ion, using the standard Abinit procedure (macro_uj=1), treating the two spin channels separately as in all other calculations. The double counting term, calculated using the atomic limit method S9 was used in all periodic calculations. This set up was used for both types of Cu-species in the model periodic structures. It is worth noting that the binding energy of H2 and corresponding dynamics depends on the choice of U. Thus, with U=0, the binding energy of H2 on Cu(I) in the CHA model CHA-Cu(I)Al1 rises up to 143 kJ/mol H2 from 80.8 kJ/mol H2 with U=9 eV. The method is however well suited for large scale calculations, especially on larger systems and behaves suitably for the calculation of the binding in porous Metal-Organic frameworks(MOFs), for instance, of zero spin molecules. S10 Our fixed U -value is relatively high, but falls very close to previously calculated and tested values for the Cu2O, Cu4O3, and CuO materials. S11 Dispersive interactions between the Cucenters and the H2 molecules were taken into account with use of the Grimme's D3 correction S12.

Dihydrogen rotational tunneling frequencies
The barrier to rotation, V2, for H2 molecules adsorbed at each type of Cu-species was calculated as the difference between the equilibrium state and the one in which the corresponding H2 molecule is rotated by 90 o . The corresponding Schrödinger equation in one dimension, the rotational angle , with a perturbation potential V of the form: is reduced to the well-known Mathieu equation which was solved numerically to obtain the rotational tunnelling frequencies, Ωt, given in Table S2.