Location of Cu2+ in CHA zeolite investigated by X-ray diffraction using the Rietveld/maximum entropy method

Rietveld/MEM analysis applied to synchrotron powder X-ray diffraction data of dehydrated CHA zeolites with catalytically active Cu2+ reveals Cu2+ in both the six- and eight-membered rings in the CHA framework, providing the first complete structural model that accounts for all Cu2+. Density functional theory calculations are used to corroborate the experimental structure and to discuss the Cu2+ coordination in terms of the Al distribution in the framework.


S3. MEM
The unit cell for all samples was divided into 90x90x120 pixels in the a, b, and c direction, respectively, giving a grid size of ~0.15 Å. The relatively large grid size is chosen to lower the calculation time. A test calculation at high resolution with a grid size of ~0.05 Å showed no change in the conclusions drawn from the relatively low resolution calculations.
It is assumed the experimental errors on the absolute scale observed structure factors, |F obs (H ⃗⃗ i )|, are random with a Gaussian distribution, giving the goodness-of-fit/stopping criteria: N F is the number of observed structure factors F obs (H ⃗⃗ ), F MEM (H ⃗⃗ ) denotes the structure factors calculated for the current estimate of the EDD, and σ(F obs (H ⃗⃗ )) is the standard deviation of F obs (H ⃗⃗ ).
Normally the criterion for MEM convergence is χ 2 = 1, but the actual optimal χ 2 value depends on the Rietveld refinement program used and the quality of the data. The reason is the standard deviation determination, which differs with each program. To ensure the optimum χ 2 value, and the optimal MEM EDD, Residual Density Analysis (RDA) has been performed according to Bindzus and Iversen (2012), (Meindl & Henn, 2008).

S3.1. Residual Density Analysis
The fractal dimension distributions for different χ 2 aims of MEM electron density distributions (EDDs) of H-CHA data are shown in Figure S9. Coefficients of determination, R 2 , from these fits are shown in Figure S10, giving χ opt 2 = 1.51.   Figure S9 to a parabolic function, f(x) = c 1 x 2 +c 2 . In the inset further R 2 are shown, based on d f (ρ res )'s calculated around χ aim 2 = 1.50.

S3.2. MEM EDDs
To be able to compare the MEM EDDs, the isosurface level of electron density (ED) for all MEM EDD figures is set to 0.55 e/Å 3 . The MEM EDD of H-CHA is shown in Figure S11 and Figure S12. It is clear that no extra ED is found outside of the framework. The small densities found in the second EDD in Figure S11 belong to the framework of the next unit cell. The MEM EDD shows that the structural model for H-CHA is complete. It also shows how effective the dehydration technique is.
Since no ED is found outside the framework, any ED found outside the framework of the metal loaded CHA zeolites must be due to guest species.   The MEM EDD of Cu-CHA using the framework-only model displays a lot of non-framework features in the ED, see Figure S13 and Figure S14. It is especially visible when the isosurface level is lowered, see Figure S15.
In the following figures the MEM EDDs of Cu-CHA using the three different Cu 2+ ion models are shown. Below ( Figure S16) is also a close up of a 6-ring in the model incl. sites A, A', and B, where the isosurface level has been lowered in order to see the A and A' sites.

S4. DFT
All density functional theory (DFT) calculations were performed using a real space grid-based projector augmented wave method (GPAW) (Mortensen et al., 2005, Enkovaara et al., 2010 interfaced using the atomic simulation environment (ASE) (Bahn & Jacobsen, 2002). For all calculations, periodic boundary conditions were used and the RPBE functional applied. Additionally, for all calculations only the Γ-point of the Brillouin zone was sampled using 0.1 eV Fermi smearing, which was found sufficient based on convergence tests.
Initially the CHA unit cell with the R3 ̅ m space group was obtained from the IZA structure database (IZA-SC, 2007) and was optimized using a 0.15 Å grid spacing, where the number of grid points was kept constant. First, the purely siliceous unit cell was optimized based on the volume, whereupon both a and c parameters were varied independently. In all cases all atomic positions in the unit cell were allowed to relax and a force threshold of 0.03 eV/Å was applied. The obtained unit cell based on this optimization routine with lattice constants a = 13.87 Å and c = 15.12 Å was used as the basis for all further calculations.
In the optimized unit cell Al was isomorphously substituted with Si (all T-sites are initially equivalent by symmetry, so the choice of Si when only one Al is introduced is irrelevant). Cu as well as O and H, when needed, were also introduced and due to the presence of Cu, the calculations were done applying spin polarization. The grid spacing was increased to 0.20 Å in order to increase calculation speed. Besides this, all parameters remained the same as stated for the optimization of the unit cell.
In the case of replacing only one Si with an Al atom and introducing a single Cu atom, the Cu atom can be coordinated to any of the oxygen atoms surrounding the Al. Thus, a calculation was made for each of the possible Cu coordinations, where the atom positions were allowed to relax to an energy minimum. This procedure was followed for all cases after introduction of the Cu moieties in the unit cell.
When a single Al and a single Cu was introduced only two stable locations could be found, which corresponds to the Cu in the plane of the 6R and in the plane of the 8R. However, the site in the 6R was found to be 0.26 eV more favorable than the site in the 8R. The magnetic moment converged to a value of zero, indicating that this type of Cu species corresponds to the Cu ion in oxidation state +1, and is therefore considered less relevant for this specific study.
Similarly, Cu with an OH-ligand was also introduced, which has recently been suggested from spectroscopic investigations as a relevant Cu species in dehydrated zeolites (Giordanino et al., 2013).
This leads to a Cu complex where Cu is in oxidation state +2, as also witnessed by the converged nonzero magnetic moment. Again all possible initial locations were attempted, but after relaxation of the atom positions only two stable sites were found. These correspond to the [Cu(OH)] + complex located in the plane of the 8R and one where the [Cu(OH)] + complex is moved slightly out of the 6R and into the large CHA cage in between the 6R and the 8R. In this case the most stable configuration is the [Cu(OH)] + complex in the 8R, being 0.08 eV more favored than the other.
When two Al atoms are isomorphously substituted for Si into the unit cell many options exist for the location of the second Al atom, which is expected to obey Löwensteins rule (no Al-O-Al bridges). All options of locating the second Al atom as a next-nearest-neighboring atom were attempted in combination with the various possibilities of locating a Cu atom coordinated to the O-atoms surrounding the Al. After relaxation of the atomic positions, two cases stood out being most stable (by more than 0.5 eV than the second most stable configuration). These are the configurations where both Al atoms are located in a 6R; either diagonally across the 6R or separated by a single Si T-atom.
Again the +2 oxidation state of Cu was confirmed by the non-zero magnetic moment.
The most stable configurations found as mentioned in the text above is given in Figure 2 in the main text. Furthermore, chosen distances and angles are given in Table S3.