Supporting Information. for. Fe L-edge XAS studies of K 4 [Fe(CN) 6 ] and K 3 [Fe(CN) 6 ]: a direct probe of back-bonding

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1 Supporting Information for Fe L-edge XAS studies of K [Fe(CN) and K [Fe(CN) : a direct probe of back-bonding Rosalie K. Hocking, Erik C. Wasinger, Frank M. F. de Groot*, Keith O. Hodgson*,,, Britt Hedman*, and Edward I. Solomon*, Corresponding author address: edward.solomon@stanford.edu Department of Chemistry, Stanford University, Stanford, California 9 Department of Inorganic Chemistry and Catalysis, Utrecht University, Sorbonnelaan,, The Netherlands Stanford Synchrotron Radiation Laboratory, SLAC, Stanford University, Stanford, California 99 -S -

2 Complete reference () Baerends E.J.; Berces A.; Bo C.; Boerrigter P.M.; Cavallo L.; Deng L.; Dickson R. M.; Ellis D. E.; Fan L.; Fischer T. H.; Fonseca Guerra C.; van Gisbergen S.J.A.; Groaeneveld J. A.; Gritsenko O. V.; Harris F. E.; van den Hoek P.; Jacobsen H.; van Kessel G.; Kootstra F.; van Lengthe E.; Osinga V. P.; Philipsen P. H. T.; Post D.; Pye C. C.; Ravenek W.; Ros P.; Schipper R. T.; Schreckenbach G.; Snijders J. G.; Sola M.; Swerhone D.; tevelde G.; Vernooijs P.; Versluis L.; Visser O.; van Wezenbeek E.; Wiesenekker G.; Wolff S. K.; Woo T. K.; Ziegler T.: ADF Program System Amsterdam,, V.. -S -

3 σ*(e g ) π* (t g ) e g Dq t g σ bonding (e g ) [Fe(CN) - Figure S. Molecular orbitals for K [Fe(CN) calculated using BP/ADF BSIV. Deconvolution. σ-bonding (e g ) % (CN σ-bonding) (occ) + % (Fe-d x-y /d z ); t g % (Fed xy /d yz /d xz ) % π acceptor, % π-donor; eg % (Fe-d z /d x-y ) + % (CN σ donor) + % (CN-σ acceptor) π*(t g ) % (CN π-acceptor) + % (Fe-t g ). σ* 9% (CN σ- acceptor) + % (Fe-d x-y /d z ) -S -

4 σ * (e g ) π * (t g ) e g * Dq t g sigma (e g ) bonding alpha-spin [Fe(CN) - beta-spin Figure S. Molecular orbitals for K [Fe(CN) calculated using BP/ADF BSIV. Deconvolution. Alpha-spin: sigma bonding (e g ).% (CN σ-donor) + % (Fe-d x-y /d z ). t g % Fe(d xy /d yz /d xz ) %(CN- π acceptor) % CN π donor); (e g )* % Fe(d z /d x-y ), % CN σ donor + % CN acceptor. π* % CN-accepter + % Fe(d xy /d yz /d xz ). σ* 9% (σacceptor); %(Fe-d x-y /d z ) Beta-spin: sigma bonding (e g ).% CN donor + % (Fe-d x-y /d z ). t g % Fe(d xy /d yz /d xz ) %(CN- π acceptor) % (CN-π donor); e g * % Fe(d z /d x-y ), % (CN σ donor + % (CN σ acceptor). π* % (CN π accepter) + % Fe(d xy /d yz /d xz ). σ* 9% (σ-acceptor); %(Fe-d x-y /d z ) -S -

5 Population analysis performed at the crystal structure geometries Fe(II) (e g ) % (CN σ-donor) + % (Fe-d x-y /d z ). t g % Fe(d xy /d yz /d xz ) %(CN- π acceptor) % CN π donor); (e g )* % Fe(d z /d x-y ), % CN σ donor + % CN acceptor. π* % CN-accepter + % Fe(d xy /d yz /d xz ). σ* 9% (σ-acceptor); %(Fe-d x- y/d z ) Fe(III) Alpha-spin: sigma bonding (e g ) % CN donor + % (Fe-d x-y /d z ). t g % Fe(d xy /d yz /d xz ) %(CN- π acceptor) % (CN-π donor); e g * % Fe(d z /d x-y ), % (CN σ donor + % (CN σ acceptor). π* 9% (CN π accepter) + % Fe(d xy /d yz /d xz ). σ* 9% (σ-acceptor);%(fe-d x-y /d z ) Beta--spin: sigma bonding (e g ) % (CN σ-donor) + % (Fe-d x-y /d z ). t g % Fe(d xy /d yz /d xz ) %(CN- π acceptor) % CN π donor); (e g )* % Fe(d z /d x-y ), 9% CN σ donor + % CN acceptor. π* % CN-accepter + % Fe(d xy /d yz /d xz ). σ* 9% (σacceptor); %(Fe-d x-y /d z ) -S -

6 Ground State Excited State d L - d L d L - d L d d Figure S. Illustrates the relationship between configuration input files and the parameters defining them. Table S. Edge shifts between cyanide and tacn ligand sets. Main Feature p d Weighted Average Fe(II) K [Fe(CN) -[Fe(tacn) Cl Fe(III)-Fe(II). ev. ev. ev.9 ev [Fe(tacn) Cl -[Fe(tacn) Cl -S -

7 Table S. Comparison of experimental literature values for Dq, R eq and β. Compound R eq M-L distance (Å) Lit Dq (ev) β Fe(III) [Fe(tacn) Cl.99,,. - 9% K [Fe(CN).9(.).9 % Fe(II) [Fe(tacn) Cl.. - % K [Fe(CN).9(.).9 %..9 C N Distance (Å)..... CN - distance in NaCN.H O(Å) Fe(III) Fe(II) Fe-C Distance (Å) Figure S. Scatter plot of the geometric parameters of all [Fe(CN) -/- species reported to the CSD. Number is calculated from the average of all available crystal structures containing the fragments [Fe(CN) - and [Fe(CN) - respectively. Error given represents the confidence interval on the man value of the available structures. -S -

8 A K [Fe(CN) AD K [Fe(CN) B C K [Fe(CN) K [Fe(CN) K [Fe(CN) CF K [Fe(CN) BE Figure S. Two*two configuration simulations. (which include σ and π back-donation) Comparison of data and best simulations for Fe(II) and Fe(III) hexacyanides that only considers two configurations, for Fe(II) d + d L - (left, blue)for Fe(III) d + d L - (right, red). In the top spectra there is no nephelauxetic reduction over the free ion value, in spectra B and C it is reduced by % (*) and % (*). -S -

9 A Fit K [Fe(CN) D Fit K [Fe(CN) Fit B K [Fe(CN) Fit C K [Fe(CN) Fit F K [Fe(CN) Fit K [Fe(CN) E Figure S. The effect of adding donation to the two configuration simulations. The top spectra are two configuration simulations, the middle a the best simulation and C and F spectra with too much donation in them. -S 9 -

10 A B C pure d D F simulation [Fe(tacn) Erik's Data Cl E H simulation simulation Erik's [Fe(tacn) Data Cl K [Fe(CN) simulation G [Fe(tacn) Erik's Data Cl [Fe(tacn) Cl K [Fe(CN) simulation K [Fe(CN) simulation K [Fe(CN) mix J=/ J=/ Figure S. Effects of d-d spin orbit coupling extended to d, tacn and cyanide systems. I -S -

11 9 9 A B Experiment Experiment E F Experiment Experiment π back-donation π back donation + % neph. red. Figure SA. Blow up of s A, B, E and F given in Figure. -S -

12 Normalized Absorption 9 9 C D K [Fe(CN) Experiment Experiment G H K [Fe(CN) Experiment Experiment π back-donation + σ-donation π, σ back-donation + π, σ-donation Figure SB. Expansion of simulations C, D G and H given in Figure. Table S. Input parameters for a CN simulation with a small (. ev) D h distortion. EG EF EG EF d /d B d /d A d /d B d /d E Dq Ds Dt d /d d /d d /d d /d B A B E S -

13 Table S. Parameters for two configuration simulations of [Fe(tacn) Cl, [Fe(tacn) Cl, K [Fe(CN) and K [Fe(CN). Compound Dq EG EF i / f T(e g ) T(t g ) [Fe(tacn) Cl K [Fe(CN) / /.. [Fe(tacn) Cl..... K [Fe(CN). /. /.. 9 9% CN σ-acceptor + % Fe(d x-y /d z ) [Fe(CN) - σ* [Fe(CN) - σ* 9% CN σ-acceptor + % Fe(d x-y /d z ) % CN π-acceptor + % Fe(d xy /d yz /d xz ) % Fe(d x-y /d z ) + % CN σ-donor + % CN σ-acceptor % Fe(d xy /d yz /d xz ) + % CN π acceptor + % CN π donor π* e g LUMO Dq HOMO t g Dq π* e g LUMO POMO t g % CN π-acceptor + % Fe(d xy /d yz /d xz ) % Fe(d x-y /d z ) + % CN σ-donor + % CN σ-acceptor % Fe(d xy /d yz /d xz ) + % CN π-acceptor + % CN π-donor 9 9 σ-donor % (CN σ-donor) + % Fe(d x-y /d z ) σ-donor % (CN σ-bonding) + % Fe(d x-y /d z ) 9% (CN π-donor) + % (d xy /d yz /d xz ) π-donor π-donor % (CN π-donor) + % (d xy /d yz /d xz ) Figure S9. Frontier molecular orbitals of [Fe(CN) - and [Fe(CN) -. The orbital coefficients are given, offset to the left Fe(II) and to the right Fe(III). For [Fe(CN) - only the β-spin orbitals are given. The α-spin molecular orbitals are given in the Supporting Information. POMO stands for partially occupied molecular orbital, as the threefold degenerate β t g levels in Fe(III) low spin compounds contain electrons. -S -

14 Input files for configuration d n- L - + d n + d n+ L Multiplet Program For simulations: *.ban erange. NCONF N N DEF EG =. UNITY DEF EF =. UNITY DEF EG =. UNITY DEF EF = -. UNITY XMIX.... XMIX.... XHAM TRAN TRIADS ^ ^ ^ ^ ^- ^- ^+ ^- - + ^- - + ^- ^- ^+ ^- - -S -

15 *.rcg Input INTER 9.9. P D D D P D D D Fe+ Fe INTER 9.9. P D D P D D Fe+ Fe INTER 9.9. P D D9 P D D9 Fe+ Fe SHELL SPIN INTER 9.9. P D D D P D D D Fe+ p d....9.hr Fe+ p d..9...hr SHELL SPIN INTER 9.9. P D D P D D9 Fe+ p d..9...hr Fe+ p d HR SHELL SPIN INTER 9.9. P D D D P D D D Fe+ p d hr Fe+ p d..9...hr SHELL SPIN INTER 9.9. P D D P D D9 Fe+ p d..9...hr Fe+ p d.....9hr S -

16 For projection: *.ban erange. PRMULT NCONF N N DEF EG =. UNITY DEF EF =. UNITY DEF EG =. UNITY DEF EF =. UNITY DEF EG =. UNITY DEF EF =. UNITY XMIX.. XMIX.. XMIX.. XHAM.. XHAM.. TRAN TRIADS S+ - S- S+ - S- S+ - S- S+ - S- S+ - ^S- ^S+ - S- ^S+ - ^S- S+ - S- -S -

17 () Boeyens J. C. A.; Forbes A. G. S.; Hancock R. D.; Wieghardt K. Inorg. Chem. 9,, 9-9. () Marsh R. E. Acta Crystallogr 9, B, -. () Ventor D.; Wieghardt K.; Buber B.; Weiss J. Z. Z. Anorg. Allg. Chem. 9,, -. () Wieghardt K.; Schmidt W.; Herrmann W.; Kuppers H.-J. Inorg. Chem. 9,, 9-9. () Wieghardt K.; Kuppers H.-J.; Weiss J. Inorg. Chem. 9,, -. () Naiman C. S. J. Chem. Phys. 9,, -. () Bats J. W. Acta Cryst. 9, B, -. -S -

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