Supporting Information for. Testing the Concept of Hypervalency: Charge Density Analysis of K 2 SO 4

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1 1 Supporting Information for Testing the Concept of Hypervalency: Charge Density Analysis of K 2 SO 4 Mette S. Schmøkel, a Simone Cenedese, b Jacob Overgaard, a Mads R. V. Jørgensen, a Yu-Sheng Chen, c Carlo Gatti, b * Dietmar Stalke, d* Bo B. Iversen a* a Center for Materials Crystallography, Department of Chemistry and inano, Aarhus University Langelandsgade 140, DK-8000 Aarhus C. Denmark b Istituto di Scienze e Tecnologie Molecolari del CNR (CNR-ISTM) and Dipartimento di Chimica Fisica ed Elettrochimica, Università di Milano, via Golgi 19, I-20133, Milano, Italy c ChemMatCARS, University of Chicago, Advanced Photon Source, Argonne, IL 60439, USA d Institut für Anorganische Chemie, Georg-August-Universität Göttingen, Tammannstrasse 4, Göttingen

2 2 Content SI.1: SI.2: SI.3: SI.4: SI.5: SI.6: Additional information on data reduction Additional information on the multipole modelling Full list of bond critical points (BCPs) Laplacian profiles for K-O and O-O interactions Topological analysis of the Laplacian of the erimental electron density Experimental source function contributions SI.1 DATA REDUCTION The data were integrated with the program SAINT+ found in the APEX2 software package. Two approached were taken concerning the box size used for the integration: one in which the box size was refined by the program and another where the box size was fixed at user defined values. In the latter case two different box sizes were used; one for the high order (HO) runs and one for the low order (LO) ones. The size of the box was based on the observation of the average peak shapes for each run found in the *._ls files. The box size was chosen so that the peaks were, as far as possible, just exactly contained in each box. The sizes of the refined and fixed boxes are tabulated below. Table S1. Box sizes used for the integration of each of the six batches. Rows 1-6 are the box sizes used when choosing the option of refining the boxes. Rows 7-8 are the fixed box sizes chosen for the low and high order data. Spot spread (deg) X Y Z Refined box, run Refined box, run Refined box, run Refined box, run

3 3 Refined box, run Refined box, run Fixed, LO (run 1-2) Fixed, HO (run 3-6) As can be seen, the fixed boxes are somewhat larger than the refined ones. According to Zhurov et al. i using integration box sizes that are too small can possibly lead to an underestimation of the strong reflections. For each of the data collections the runs were integrated separately and the resulting *.raw files were used for further data treatment. In addition an integration of all runs together was made and the resulting unit cell was used in the further data treatment. Each integration was performed at least three times updating the *.p4p file after each round. The data were integrated to a resolution in direct space of 0.37 Å corresponding to (sinθ/λ) max =1.35 Å -1. After integration the data was scaled in SADABS where several corrections were also made. First of all, SADABS performs a phi correction, taking into account the inhomogeneity of the beam, off-centering of the crystal, and the fact that the crystal is not entirely isotropic, by scaling the individual frames in each run to each other. Furthermore, an overall scaling of the individual runs against each other is performed making sure that all reflections are on the same arbitrary scale. An oblique incidence correction and an absorption correction are also carried out. Due to the fact that very small crystals, 30 µm, were used and thus very little absorption was ected, an isotropic absorption correction was assumed to suffice. It should be noted that SADABS will automatically manipulate/correct the erimental uncertainties by applying a so-called error-model. ii Such a redistribution of the uncertainties is not desirable in the case of accurate data to be used for charge density modelling. Therefore, the

4 4 application of the error model is avoided by setting g=0. This alone, however, is not enough since, in addition to adding a term (g<i c >)² to the uncertainties, all uncertainties within a certain batch are multiplied by a constant, K i, that is different for each batch. This means that the significance, I/σ(I), for the output from SADABS is different from the raw data. Therefore, the uncertainties within each run are divided by the proper scale factor, K i, given by SADABS and the significances of the raw data thus restored. Figure S1. Σ F O 2 /Σ F C 2 binned with respect to resolution shells and plotted against sinθ/λ from the multipole refinement using Model 1. Similar plots for the K+ model and Model 2 are in the main paper.

5 5 Figure S2. Residual density in the mirror plane for a model using a K + scattering factor with all data (left) and data with sinθ/λ < 0.9Å -1. The contour interval is 0.1 e/å 3. Positive contours are full, blue lines, while negative are dashed red lines. The zero contour is shown as black dotted lines. Figure S3. Scattering factor for the 4s valence electron on potassium as a function of sinθ/λ.

6 6 Figure S4. Residual density in the mirror plane for Model 1 using data with sinθ/λ < 0.9 Å -1 (left) and Model 2 using all data (right). Contours as in Figure S2. SI.2 MULTIPOLE REFINEMENT Additional information on the multipole refinements in XD2006 for the Model 1-2 is given below. Model 1 Model 2 K1 K2 S x (8) (8) y z (6) (6) U (18) (18) U (17) (17) U (16) (16) U (12) (12) x (8) (8) y z (6) (6) U (17) (17) U (17) (16) U (15) (15) U (11) (11) x (9) (9) y z (7) (7) U (2) (2) U (2) (2) U (19) (19)

7 7 O1 O2 O3 U (14) (14) x (4) (5) y z (3) (3) U (9) (10) U (8) (9) U (7) (8) U (5) (6) x (4) (5) y z (3) (4) U (8) (9) U (8) (9) U (8) (9) U (5) (6) x (3) (4) y (4) (5) z (2) (3) U (6) (7) U (5) (6) U (6) (6) U (5) (5) U (4) (5) U (4) (5) Monopole Populations, Radial Parameters and Net Atomic Charges Model 1. Atom P val κ P 00 κ Net charge K(1) 0.595(187) (187) K(2) 0.426(169) (169) S(1) 5.831(78) 0.943(4) (4) (78) O(1) 6.293(29) 0.983(2) (2) (29) O(2) 6.310(29) 0.983(2) (2) (29) O(3) 6.272(25) 0.983(2) (2) (25) Dipole Population Parameters Model 1. Atom D 11+ D 11- D 10 κ K(1) K(2) S(1) 0.036(20) (16) O(1) 0.021(9) (9) O(2) 0.082(10) (9) O(3) (7) 0.036(6) 0.049(7) Quadrupole Population Parameters Model 1. Atom Q 20 Q 21+ Q 21- Q 22+ Q 22- κ K(1) K(2) S(1) 0.024(19) (17) (17) O(1) 0.024(10) (8) (9) 0.983

8 8 O(2) 0.010(10) (9) 0.030(9) O(3) (6) 0.022(6) (7) (6) 0.009(6) Octupole Population Parameters Model 1. Atom O 30 O 31+ O 31- O 32+ O 32- O 33+ O 33- κ K(1) K(2) S(1) (19) (17) (15) (17) O(1) (9) (9) (9) 0.005(9) O(2) (10) (9) (9) 0.012(9) O(3) (7) 0.013(7) (7) 0.011(7) 0.005(7) (6) (6) Hexadecapole Population Parameters Model 1. Atom H 40 H 41+ H 41- H 42+ H 42- H 43+ H 43- H 44+ H 44- κ K(1) K(2) S(1) 0.088(18) (17) (17) (14) 0.104(15) O(1) O(2) O(3) Monopole Populations, Radial Parameters and Net Atomic Charges Model 2. Atom P val κ P 00 κ Net charge K(1) 0.875(198) (198) K(2) 0.350(170) (170) S(1) 5.782(103) 0.946(5) (18) (103) O(1) 6.250(37) 0.983(2) (70) (37) O(2) 6.280(38) 0.983(2) (70) (38) O(3) 6.231(35) 0.983(2) (70) (35) Dipole Population Parameters Model 2. Atom D 11+ D 11- D 10 κ K(1) K(2) S(1) 0.053(22) (18) O(1) 0.025(8) (8) O(2) 0.078(9) (8) O(3) (6) 0.035(6) 0.049(7) Quadrupole Population Parameters Model 2. Atom Q 20 Q 21+ Q 21- Q 22+ Q 22- κ K(1) K(2) S(1) 0.030(21) (19) (18) O(1) 0.021(9) (8) (8) O(2) 0.011(9) (9) 0.027(8) O(3) (6) 0.021(6) (6) (6) 0.010(6) 1.215

9 9 Octupole Population Parameters Model 2. Atom O 30 O 31+ O 31- O 32+ O 32- O 33+ O 33- κ K(1) K(2) S(1) (35) (28) (17) 0.443(33) O(1) (8) (8) (7) 0.003(7) O(2) (8) (8) (7) 0.011(7) O(3) 0.010(5) (6) 0.009(6) 0.002(6) (5) (5) (6) Hexadecapole Population Parameters Model 2. Atom H 40 H 41+ H 41- H 42+ H 42- H 43+ H 43- H 44+ H 44- κ K(1) K(2) S(1) 0.113(20) (19) (25) (17) 0.119(17) O(1) O(2) O(3) Figure S5. Static deformation density in the O3-S-O3 plane for Model 1 (left) and Model 2 (right). The contour intervals are 0.05 e Å -3. Full, blue lines are positive contours, dashed red lines are negative SI.3 BOND CRITICAL POINTS

10 10 Table S1. Topological parameters for the different chemical bonds based on the erimental (first line) and theoretical (second line) charge density. d is the bond distance between the two atoms. AIL (Å) is the length of the atomic interaction line, split in the contributions from the BCP to either one or the other bonded atom. ρ is the electron density (e/å 3 ), 2 ρ the Laplacian (e/å 5 ) and ε the ellipticity of the bond. The labels B1 to B19 are used to identify the various BCPs in the Figures. S-O1 (B14) S-O2 (B12) S-O3 (B13) O1-O3 (B15) O1-O3 (B16) O2-O2 (B17) O2-O3 (B18) O3-O3 (B19) K1-O2 (B1) K1-O1 (B2) K1-O3 (B3) K1-O3 (B4) K1-O3 (B5) K2-O1 (B6) K2-O3 (B7) K2-O3 (B8) K2-O1 (B9) K2-O2 (B10) d (Å) AIL A-BCP (Å) AIL BCP-B (Å) ρ (e/å 3 ) 2 ρ (e/å 5 ) ε theo theo theo theo theo theo theo theo theo theo theo theo theo theo theo theo theo theo

11 11 K2-O2 (B11) theo

12 12 SI.4 LAPLACIAN PROFILES Figure S6. Laplacian profiles (theoretical electron density) along the K-O (left) and O-O (right) internuclear axes in the crystal. The dotted vertical line marks the position of the BCP. On the x axes the distance from the origin (in the left picture the K atom is placed at the origin) is reported.

13 13 SI.5 LAPLACIAN TOPOLOGY Laplacian topology for the erimental density No. - 2 ρ (e/å 5 ) ρ (e/å 3 ) d VSCC-O (Å) O O O

14 14 Figure S7. Three-dimensional plots of the Laplacian for the erimental electron density at contour levels of: -95 (top left), -100 (top right), -105 (bottom) e/å 5, respectively. It is clearly seen that one region of charge accumulation on O2 is broader and at higher - 2 ρ values than the other region on O2 and the regions of the other oxygen atoms. SI.6 EXPERIMENTAL SOURCE FUNCTION CONTRIBUTIONS There is a problem with charge integration in the TOPINT feature in XDPROP, which appears to be related to the potassium atoms. This gives %SF values that are inaccurate. However, the same trends for the S and O source function contributions are observed in the erimental values as in the theoretical values discussed in the main text.

15 15 Bond S O1 O2 O3 S-O S-O S-O i Zhurov, V. V.; Zhurova, E. A.; Pinkerton, A. A. J. Appl. Crystallogr. 2008, 41, ii Jørgensen, M. R V.; Svendsen, H.; Schmøkel, M. S.; Overgaard, J., Iversen, B. B. Acta Crystallogr. Sect. A 2012, 68, in press.