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A Combined DFT and Restricted Open-Shell Configuration Interaction Method Including SpinOrbit Coupling: Application to Transition Metal LEdge X-Ray Absorption Spectroscopy Michael Roemelt,1 Dimitrios Maganas,1 Serena DeBeer 1,2 and Frank Neese 1a 1 Max-Planck Institute for Chemical Energy Conversion, Stiftstrasse 34-36, D-45470 Mülheim an der Ruhr, Germany 2 a Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853, USA Author to whom frank.neese@cec.mpg.de correspondence should be addressed: Electronic mail I. Matrix elements of the BO Hamiltonian S’ = S See Roemelt, M; Neese, F “Excited State of large open-shell molecules: An efficient, general and spin-adapted approach based on a restricted open-shell ground state wavefuntion” (in preparation) S’ = S -1 i t u Hˆ BO j A12 S ij FtuI tu FijO SOMO I I ij Ftu tw | uw tu Fij iw | jw wwtu SOMO SOMO ij | tu it | ju ij tu Tw | Tw T wt A22 S wu SOMO SOMO 1 tu ij | tu ij FtuO tv | uv tw | uw v u wt SOMO SOMO wv | wv ij tu wt v u SOMO SOMO A1 S A2 S 2 tu 1 it | ju tu iv | jv tu iw | jw v u wt t i SOMO b BO ˆ H u A1 S A3 S iu | tb A2 S A4 S it | ub 1 tu iu | tb wwtu i t b Hˆ BO j A1 S A5 S ij FbtI it | jb SOMO A1 S A6 S ij FbtO tu | ub ij | tb u SOMO A2 S A6 S ij FbtI ij | tb wt SOMO SOMO O 2 F 2 tw | wb tv | vb ij ij bt vw wt A2 S A7 S SOMO SOMO SOMO ij tu | ub 2 ij | tb u w t wt w u ta Hˆ BO ub A32 S tu FabI ab FtuO tu | ab SOMO 2 A3 S A4 S 1 tu ta | ub tu wa | wb wt SOMO SOMO O O F wa | wb F wt | wu wT | wT ab tu tu ab T wwtu SOMO SOMO 2 I A4 S 1 tu ab Ftu tu | ab ab wt | wu ab vt | vu wt v u SOMO SOMO SOMO ab wv | wv ta | ub tu | ab wt wt v u t a b Hˆ BO j A3 S A5 S ab FjtO jt | ab SOMO A3 S A6 S ab FjtI ab ut | uj jt | ab u SOMO A4 S A5 S ab FjtO 2 ta | jb jt | ab wt SOMO A4 S A6 S ab FjtI jt | ab wt ia Hˆ BO bj A52 S ij FabI ab FijI ij | ab SOMO 2 A5 S A6 S ab it | jt ij at | bt t SOMO A62 S 2 ij FabC 2 ab FijC 2 ij | ab t SOMO SOMO 2 A6 S A7 S 2 ab it | jt 2 ij ua | ub t u t SOMO SOMO 2 ij FabO 2 ab FijI 4 ij ta | tb 4 ab it | jt t w t 4 ij ab tw | tw 2 ij | ab A72 S SOMO SOMO SOMO SOMO SOMO SOMO 4 ij ab tw | tw 4 ij ab tT | tT w t u t t w t T u t where the spin coupling coefficients An S are given by A1 S A3 S 2S 1 2S 2 1 2S 2 2S 1 A2 S A4 S A5 S A6 S A7 S 2S 1 2S 3 S 1 2 S 2 1 S 1 2S 3 2S 2 2 2 1 S 1 2S 3 2 2S 2 2S 1 S’ = S + 1 ia Hˆ BO bj ij FabO ab FijI ij | ab II. Parameterized diagonal elements of the DFT/ROCIS matrix The parameterized diagonal elements of the CI matrix in the DFT/ROCIS method in the basis of CSF’s with S S are given by: O KS C KS ti Hˆ DFT / ROCIS it Ftt Fii c1 ii | tt c2 it | it SOMOs T Hˆ a t DFT / ROCIS a t O KS aa F C KS tt F 1 cHF tT | tT iT | iT 2 c1 tt | aa c2 ta | ta C KS C KS ia Hˆ DFT / ROCIS ia Faa Fii c1 ii | aa 2c2 ia | ia O KS O KS C KS O KS taiw Hˆ DFT / ROCIS atwi Faa Ftt Fii Fww c1 ii | ww c1 tt | aa c1 ii | tt c1 ww | tt c1 ii | aa c1 ww | aa 1 cHF tT | tT iT | iT 2 T 2 4 C KS C KS Faa Fii c1 tt | tt c1 ii | aa 2c2 it | it c2 ta | ta 3 3 SOMOs 1 2 c2 tT | tT cHF iT | iT 3 3 T (1.1) c2 it | it c2 wa | wa tait Hˆ DFT / ROCIS tiat SOMOs Off-diagonal matrix elements of two “trip-doublet“ basis functions tiat and uiau , that share the same internal and external labels i and a but have different active labels t and u, are treated as diagonal elements with respect to the parameterization. 1 1 1 1 2 tait Hˆ DFT / ROCIS uiau FaaC KS FiiC KS c2 it | it c2 iu | iu c2 tu | tu 3 3 3 3 3 1 1 1 c1 ii | aa c2 ta | ta c2 ua | ua 3 3 3 Likewise, the parameterized diagonal elements of CSF’s with S S 1 read to: ia Hˆ DFT / ROCIS ia FaaO KS FiiC KS c1 ii | aa SOMOs T 1 cHF iT | iT 2 Eventually, the parameterized diagonal elements with S S 1 are given by: ti Hˆ DFT / ROCIS ti FttO KS FiiC KS c1 ii | tt A12 S SOMOs 1 cHF tT | tT iT | iT 2 T FttO KS FiiC KS c1 ii | tt c1 tw | tw c2 it | it c2 iw | iw SOMOs 1 SOMOs wt c2 tT | tT cHF tT | tT cHF tT | tT A22 S 2 T SOMOs SOMOs c2 vw | vw v t wt 2 A1 S A2 S t a a c iw | iw wt 2 SOMOs O KS a O KS Hˆ DFT / ROCIS t A32 S Faa Ftt c1 tt | aa cHF TT | aa T O KS O KS F Ftt c2 tw | tw c1 tt | aa SOMOs aa SOMOs wt c2 ta | ta c2 wa | wa c2 wT | wT 2 A4 S T SOMOs SOMOs w c2 vw | vw v t 2 A3 S A4 S i SOMOs SOMOs c wa | wa wt 2 SOMO O KS a O KS Hˆ DFT / ROCIS i A52 S Faa Fii c1 ii | aa cHF Ta | Ta T 2 FaaC KS 2 FiiC KS 2c1 ii | aa SOMOs SOMOs t 2c2 tT | tT 2 A6 S T SOMOs SOMOs 2 c2 tu | tu t u F C KS F C KS c ii | aa c ta | ta c wa | wa ii 1 2 2 SOMOs SOMOs aa 2 A7 S 2 c2 iw | iw c2 it | it 2c2 tw | tw t wt SOMOs c2 wT | wT c2 tT | tT 1 cHF iT | iT T 2 2 A5 S A6 S SOMOs c it | it ta | ta 2 t 2 A6 S A7 S SOMOs SOMOs c iw | iw it | it wa | wa ta | ta t wt (1.2) 2 With the spin coupling coefficients A1 S A3 S 2S 1 2S 2 1 2S 2 2S 1 A2 S A4 S A5 S A6 S A7 S III. An S 2S 1 2S 3 S 1 2 S 2 1 S 1 2S 3 2S 2 2 2 1 S 1 2S 3 2 2S 2 2S 1 Experimental Details of Ti Data Collection [Cp2TiCl2] and [CpTiCl3] (99+%) were purchased from Strem Chemicals and were used without further purification. Samples were finely ground and spread across double-adhesive conductive carbon tape, which was attached to a copper paddle. Ti L-edge data were measured at Stanford Synchrotron Radiation Lightsource using the 31-pole wiggler beam line 10-1. A spherical grating monochromator was used for energy selection. The data were measured at room temperature as total electron yield spectra utilizing a Galileo 4716 channeltron electron multiplier as a detector. Three to four scans were measured in order to check reproducibility; the presented data represent a single scan. TiO2 was used as a calibration reference with the maximum of the L3 edge assigned to 458.2 eV and the highest energy L2 feature set to 465.8 eV. In all cases, a linear background was fit to the pre-edge region and was subtracted from the entire spectrum. Normalization was accomplished by fitting a straight line to the post-edge region and normalizing the edge jump to 1.0. Due to the presence of a significant oxygen background, at ~520 eV, there is a significant error in the absolute normalizations. IV. Reduced matrix elements of the SOC operator C01 0 zˆ m 0 SOMO m zTT T 1 0 0 zˆ m C z mju u j m C01 0 zˆ m bu zub C01 0 zˆ m bu 0 vj 2 m z jb 6 C01 0 zˆ m bu uj C01 ti zˆ m uj ij tu SOMO m zTT tu z mji ij ztum T 1 0 C zˆ t i m b u 0 C01 ti zˆ m bj 1 ij ztbm 2 C01 ti zˆ m bu ij tu zvbm vj C01 ti zˆ m bu uj 1 2 ij ztbm ij tu zubm 6 6 C01 ta zˆ m bu tu ab SOMO m m zTT tu zab zutm T C01 ta zˆ m bj 1 ab z mjt 2 C01 ta zˆ m bu ab tv z mju vj C01 ta zˆ m bu uj 2 1 ab z mju ab z mjt 6 6 SOMO 1 m C01 ia zˆ m bj ij ab zTT 2 T C01 ia zˆ m bu 0 vj C01 ia zˆ m bu uj 2 ij zabm ab z mji 12 C01 taiw zˆ m bu ij tu vw ab vj SOMO m zTT T z m ij vw ab tu m ij tu ab zvw m ij tu vw zab tu vw ab z mji C01 taiw zˆ m bu uj 2 m ij ab wu ztum ij ab tu zuw 6 4 SOMO m C01 tait zˆ m bu ij tu ab zTT zutm uj 6 T SOMO 2 m ij ab zTT 6 TT 4 m ij tu zab 6 4 ab tu z mji 6 b C1 0 zˆ m j z mjb C1 ti zˆ m bj ij ztbm C1 ta zˆ m bj ab z mjt C1 ti zˆ m bj ij ztbm C1 ia zˆ m bj 1 ij zabm ab z mji 2 C1 taiw zˆ m bj ij ab ztwm C1 tait zˆ m bj 2 1 1 ij ab zttm ij ab zabm ab z mji 6 6 6 1 0 C t i t SOMO m ˆz m uj A12 S ij tu zTT tu z mji ij ztum T SOMO SOMO m m m m tu ij tu zTT 2 ij tu zww tu z ji ij ztu T A22 S wwtu m 1 tu ij ztu C01 i b zˆ m u 0 C01 i b zˆ m j A1 S A5 S A1 S A6 S ij ztbm t SOMO A2 S A6 S 2 A2 S A7 S ij ztbm wt SOMO m m C01 ta zˆ m ub A32 S tu ab zTT ab zutm tu zab TT SOMO SOMO m m tu ab zTT tu ab 2 zutm ab zutm tu zab TT A32 S wwtu m 1 tu ab zut C01 t a b zˆ m j A3 S A5 S A3 S A6 S ab z mjt A4 S A6 S 2 A4 S A7 S ab SOMO wt z mjt SOMO m m C01 ia zˆ m bj A52 S ab ij zTT ab z mji ij zab T SOMO SOMO m A62 S ij ab 2 zTT 4 zttm t T SOMO SOMO SOMO m m m m A72 S ij ab 2 zTT 4 zttm 4 zww 2 ab z ji 2 ji zab T t wt u C1 0 zˆ m j A1 S z mju m C1 0 zˆ m bu A3 S zub C1 0 zˆ m uj A5 S z mjb SOMO m C1 ti zˆ m uj A1 S ij tu zTT tu z mji A2 S ij z mju T C1 ti zˆ m ub 0 b C1 ti zˆ m j A6 S ij ztbm C1 ta zˆ m uj 0 SOMO b m C1 ta zˆ m u A3 S tu zab A3 S ab tu zvvm ab zutm v u C1 ta zˆ m bj A6 S ab z mjt C1 ia zˆ m uj A1 S C1 ia zˆ m bu C1 ia zˆ m bj ij Cm zaum 2 A3 S 2 A5 S 2 ab zuim z ab z mji m ij ab m C1 itwa zˆ m uj A2 S ij tu zaw C1 itwa zˆ m ub A4 S ab uw ztim m C1 itwa zˆ m bj A7 S ij tu zaw C1 tait zˆ m uj b C1 tait zˆ m u C1 tait zˆ m bj A1 S 6 A3 S 6 ij zaum ab z 2 A2 S 6 2 A4 S 6 2 A5 S 2 A6 S 2 A7 S 6 1 tu ij zaum 1 tu ab zuim ab z mji ij zabm 6 2 A7 S 2 A6 S SOMO A5 S 6 ab z mji A5 S 2 ij u z mji u 6 A6 S SOMO 6 ab 6 m ab uu z ij zabm where 2S C01 S S 1 2 2S 1 2S 3 C1 C1 2 1 x y z pq iz pq 2 z pq1 z pq1 1 x y z pq iz pq 2 z z 0pq z pq and A1 S A3 S 2S 1 2S 2 1 2S 2 2S 1 A2 S A4 S A5 S A6 S A7 S 2S 1 2S 3 S 1 2 S 2 1 S 1 2S 3 2S 2 2 2 1 S 1 2S 3 2 2S 2 2S 1 Matrix elements between wavefunctions SM and SJ M are evaluated as follows: I 1,0,1 1 S m ˆ tot S M E S 1m C C S SM H I J IJ SS MM I I J zˆ M m M m where the summation of and is over all ROCIS basis functions. V. Coordinates of [CuCl4] in D2d and D4h symmetry D2d Cu Cl Cl Cl Cl -0.000031 -0.000016 -0.000234 2.146470 -0.000040 0.870967 -2.146442 0.000048 0.870932 -0.000043 2.146466 -0.870845 0.000046 -2.146458 -0.870819 D4h Cu Cl Cl Cl Cl 0.000008 2.336259 -2.336248 -0.000007 -0.000012 0.000011 -0.000012 -0.000017 2.336263 -2.336245 0.000000 0.000000 0.000000 0.000000 0.000000 VI. DFT/ROCIS spectra of D2d – [CuCl4]2- using ZORA Figure S1. DFT/ROCIS spectra of [CuCl4]2- in D2d symmetry using no relativistic correction (top), ZORA (middle) and ZORA including picture change effects (bottom). VII. Scalar Relativistic effect on L-edge of [FeCl4]2- Figure S2. DFT/ROCIS spectra of [FeCl4]2- using no relativistic correction (black), ZORA (red) and the DKH2 approximation (blue). VIII. Basis set dependence on SOC splitting Figure S3. ROCIS spectrum of [CuCl4]2- in D2d symmetry using the def2-TZVP (black), QZVP (red) and CP(PPP) basis set (blue). IX. Effect of density on the L-edge of [Cp2TiCl2] . Figure S4. DFT/ROCIS spectrum of [Cp2TiCl2] using the ground (red) and excited state (black) density for the evaluation of SOMF integrals. Both curves virtually overlay each other. X. Charges of effective core potentials and point charges for non-heme iron complexes Large supercells that contain a few thousand atoms were extracted from the crystal strctures of the non-heme iron complexes.1-3 The supercells were divided into three parts. The first part is the region that is treated by quantum chemical methods (QR) comprising the non-heme iron complex. The second part is the sphere of counterions, called boundary region, (BR) that are approximated by effective core potentials according to Fuentealbe and co-workers.4 The third part comprises a large number of point charges (PC) that mimicks the effect of the remaining part of the supercell. Three distribution of charges were applied to the effective core potentials, each obeying a set of boundary conditions. Two common boundary conditions of all three models are that the total charge of the supercell has to be close to zero (~10 -12-10-14 charge units) and that the charge of a given ion has to be as close as possible to its charge as defined in the sense of the electrostatic potential model introduced by Breneman and Wiberg.5 Model A has been chosen with regard to these conditions. For model B the charge of the QR plus the charge of the BR also has to equal zero. Model C is equivalent to model B but also applies the conductor-like screening model with an infinite dielectric.6 Model A: Atom Fe Cl N Na K Co [FeCl4]20.836 -0.709 1.000 - [FeCl6]42.042 -0.804 1.050 1.052 - [FeCl6]31.610 -0.778 0.386 0.689 [Fe(tacn)2]2+ 0.424 -0.982 0.220 - [Fe(tacn)2]3+ 0.588 -0.984 0.486 - [FeCl4]2-0.707 0.615 - [FeCl6]40.500 0.500 - [FeCl6]30.064 0.116 [Fe(tacn)2]2+ -0.500 - [Fe(tacn)2]3+ -0.5 - [FeCl4]20.837 -0.696 0.983 - [FeCl6]42.043 -0.802 1.050 1.054 - [FeCl6]31.609 -0.780 0.410 0.685 [Fe(tacn)2]2+ 0.426 -1.001 0.223 - [Fe(tacn)2]3+ 0.584 -0.979 0.496 - Model B: BR Atom Fe Cl N Na K Co PC Atom Fe Cl N Na K Co XI. Fitting of DFT/ROCIS parameters 18 mononuclear complexes were chosen for this study featuring a variety of metal centers in different coordination environments, oxidation- and spin states. The data set consist of the iron complexes [Fe(III)Cl6]3- (1) and Fe(II)(tacn)2 (2), the Titanium complexes Ti(IV)Cp2Cl2 (3) and Ti(IV)CpCl3 (4) and the Vanadium complexes K2[V(V)O(O2)2C5H4NCOO)] (5), V(V)O2(R,R’L1)] , R=Me, R’=Ph (6), R=H, R’=Me (7), R=H, R’=Ph (8), R=H, R’=4-O2NPh (9), V(IV)O(HRL2), R=H (10)7, Me (11), Et (12), Cl (13), V(IV)O(acac)2 (14), V(IV)O(acac)2Py (15) V(IV)O(salen) (16) , V(IV)O(TPP) (17) and V(III)(acac)3 (18). In the foregoing list the following abbreviations were used for the ligands: L1 = oxyoxime,8 L2 = salicylaldoxime,8 acac = acetylacetonato, salen = N, N’-bis(salecylidene)ethylendiamine and TPP = 5,10,15,20Tetraphenyl-21H,23H-porphine. Complexes 1-5, 14, 17-18 were purchased or synthesized according to common published procedures. Complexes 1-4 are discussed in this work, while further details will be given in an upcoming manuscript for complexes 5-18. V L-edge data for complexes 6-13, 15-16 have been reported previously8 and kindly offered from professor Nigel Young in a personal communication. The BP86/def2-TZVP(-f) optimized structures of the above complexes are presented in Figure S5. Figure S5. The BP86/def2-TZVP(-f) optimized structures of the eighteen model complexes used for the parameterization procedure. Description of the parameterization procedure In the course of the parameterization procedure a constrained multigaussian least square fitting on the experimental spectrum employing the Lavenberg-Marquardt algorithm was performed over the calculated transition energies (calculated spectra). The chosen gaussians have the general form: f x Amp 1 2 FWHM 2 e x Centroid 2 2 FWHM Where Amp is the amplitude, FWHM is the full width at half maximum and Centroid is the position of the defined Gaussian. Tight convergence criteria are used for the relative error in the approximate solution (xtol=10-8) as well as for the desired sum of squares (ftol=10-8). The The quality of the fit is measured with the aid of the following parameters: First, SSerr y gridpoints 2 exp i yimodel 2 i where SSerr , is the regression sum of the squares which is the sum of the squares of the deviations of the predicted values yimodel from the experimental values yiexp . Second, SStot y gridpoints model i y 2 i where SStot is the total sum of the squares of the deviation of the predicted values yimodel from the average experimental value yimodel and eventually R2 1 SSerr SStot where R2 is usually referred to as the coefficient of determination. It provides a measure for the goodness of fit and takes values between 0 and 1. In this work R2 is used as a normalized version of SSerr and is used as an indicator of the quality of the fitting throughout the parametrization procedure. Fitting protocol The parametrization was performed in three steps. At first, a one-digit fitting was performed in which c1, c2 and c3 parameters were varied in the range between 0.0-1.0 taking steps of 0.1 intervals. This step was followed by a second-digit fitting procedure in a more spotted region of c parameters. For all these calculations the def2-SVP basis set was used. A final refinement of the optimized parameters was performed with the larger def2-TZVP(-f ) basis set (2000 calculations/functional). The calculated spectra were generated with the orca_mapspec utility by applying a constant line shape gaussian broadening of 0.2 eV. All calculated spectra have been energy shifted in order to match the maximum experimental and calculated L3 intensity. (V(B3LYP)= 10.9 eV, V(BHLYP)= -4.8 eV, Fe(B3LYP)= 13.9 eV, Fe(BHLYP)= -3.9 eV, Ti(B3LYP)= 11.8 eV, Ti(BHLYP)= -2.8 eV). We should note that slightly different shifts are reported in the main text for iron and titanium in which the shifts refer to a linear correlation between experimentally observed and calculated transition energies. Such corresponding shifts for vanadium will be reported elsewhere. 1.00 1.00 0.98$ 0.98$ 0.98 0.98 0.98 0.98 0.97$ B3LYP$ 0.96 0.96 0.97 0.97 0.97 0.97 BHLYP$ 0.97$ 0.97$ 0.96$ 0.96$ 0.95 0.95 0.95 0.95$0.95 0.94 0.94 0.950.95 0.950.950.95 0.95 0.940.94 0.94 0.94 0.92$ R22 R 0.92 0.92 0.91$ 0.91$ 0.93 0.93 0.93 0.91 0.91 0.92$ 0.93 0.92 0.93$ 0.92 0.91$ 0.90 0.90 0.90 0.90 0.88 0.88 0.94$ 0.93$ 0.88$ 0.87$ 0.86 0.86 0.86 0.86 0.84 0.84 0.84 0.84 0.83$ 0.82 0.82 0.80 0.80 11 2 0.82 0.82 0.82 0.82 33 44 55 66 77 88 99 18 Average 1010 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 Average Figure S6. Best-fit values between experimental and calculated spectra expressed in terms of R2 for the data set. Blue and green columns visualize the individual contributions for B3LYP and BHLYP functionals, respectively along the data set, whereas red and purple columns represent the corresponding average contributions. XII. Comparison to RAS-PT2 results In a recent publication, Odelius and co-workers calculated the Ni L-edge of [Ni(H2O)6]2+ as well as the Fe L-edge of [Fe(tren(py)3)]2+ and its high spin analogue [Fe(tren(6-methyl-py)3]2+ with the RAS-PT2 methodology.9 In order to compare the performance of the RAS-PT2 method with DFT/ROCIS for the calculation of transition metal L-edges, analogous calculations were conducted with DFT/ROCIS. Prior to the L-edge calculations, geometry optimizations were carried out utilizing the BP86 functionalref together with the def2-TZVP(f) basis set.ref During the optimizations molecular charges were absorbed by the conductor- like screening model (COSMO).ref Transition energies and moments were calculated according to the computational setup introduced in section IIIB of the main manuscript. All DFT/ROCIS spectra are shifted by +17 eV (Ni) or 16.2 eV (Fe). Figure S7 presents a comparison of the experimental Ni L-edge of [Ni(H2O)6]2+ (top panel) with the calculated Ni L-edges as obtained from RAS-PT29 (middle panel) and DFT/ROCIS (bottom panel) calculations. Experimentally, the L3 edge exhibits a sharp main feature at 853.4 eV and a small satellite at higher energies (~855.5 eV). On the other hand, the L2 edge consists of two almost equally intense features at about 870.2 eV and 871.5 eV. The RASPT2 spectrum reproduces the relative energy and intensity of all spectral features with high accuracy. The DFT/ROCIS spectrum does not reach such a high degree of accuracy for the Ni L-edge. In the L3 edge, the small satellite feature is predicted much too close to the main feature and the calculated L2 edge has only a single band. Figure S7. Comparison of the Ni L-edge of [Ni(H2O)6]2+ (top panel) with the calculated Ni L-edges as obtained from RAS-PT29 (middle panel) and DFT/ROCIS (bottom panel) calculations. The octahedral [Fe(tren(py)3)]2+ complex has a 1A1g ground state while the corresponding methylated analogue [Fe(tren(6-methyl-py)3]2+ features a 5T2g ground state. As expected, the change of the spin state strongly influences the Fe L-edge of the complex. In Figure S8 the experimental Fe L-edges of [Fe(tren(py)3)]2+ and [Fe(tren(6-methyl-py)3]2+ (top panel) are compared to the calculated Fe L-edges as obtained from RAS-PT2 (middle panel) and DFT/ROCIS (bottom panel). In the experimental spectrum the L3 edge of [Fe(tren(py))3]2+ consists of an intense main band at 709.4 eV and two small satellite features that appear as shoulders at the low energy side of the main band around 711.4 eV and 713.2 eV. The shape of the L2 edge is similar to the shape of the L3 edge with the exception that the two shoulders have merged to a single feature. Upon introduction of methyl groups to the pyridine ligands and the concomitant change of the spin state of the Fe center, the Fe L-edge moves about 2 eV to higher energies. Furthermore, the two edges become broader, resulting in lower maximal intensities. At the lower energy side of the L3 edge, a shoulder appears around 706.0 eV. RAS-PT2 correctly predicts the shift in energy as well as the intensity loss in the L2 edge. In particular, the L2 edge is reproduced quite accurately. However, in contrast to the findings made for [Ni(H2O)6)]2+, the RAS-PT2 spectra of [Fe(tren(py)3)]2+ and [Fe(tren(6-methylpy)3)]2+ considerably deviate from the corresponding experimental spectra. For example, the loss in intensity in the L3 edge with the change of the spin state is not reproduced. Furthermore, the RAS-PT2 spectra of both species exhibit intense features at the low energy side of the main L3 band that are not experimentally observed. The DFT/ROCIS calculations on the other hand do not only correctly reproduce the shift in energy and intensity but also produce realistic spectral shapes for both Fe-complexes. In summary, we have found that while the RAS-PT2 calculations for [Ni(H2O)6]2+ are of higher accuracy than the corresponding DFT/ROCIS calculations, DFT/ROCIS yields better results for the two octahedral Fe complexes. Hence, on the basis of the obtained results none of the two approaches can be classified as the more (or less) reliable. In our opinion, both methods have their strengths and weaknesses arising from their different construction schemes. Most probable, the relative performance of the two methods will be case sensitive for future applications. Figure S8. Comparison of the Fe L-edge of [Fe(tren(py)3)]2+ and [Fe(tren(6-methyl-py)3]2+ (top panel) with the calculated Fe L-edges as obtained from RAS-PT29 (middle panel) and DFT/ROCIS (bottom panel) calculations. XIII. 1. 2. 3. 4. 5. 6. 7. References J. K. Beattie and C. J. Moore, Inorg. Chem. 21 (4), 1292-1295 (1982). J. C. A. Boeyens, A. Forbes, R. D. Hancock and K. Wieghardt, Inorg. Chem. 24 (19), 2926-2931 (1985). J. W. Lauher and J. A. Ibers, Inorg. Chem. 14 (2), 348-352 (1975). P. Fuentealba, H. Stoll, L. Szentpaly, P. Schwerdtfeger and H. Preuss, J. Phys. B 16, L323 (1983). C. M. Breneman and K. B. Wiberg, J. Comput. Chem. 11 (3), 361-373 (1990). A. Klamt and G. Schüürmann, Journal of the Chemical Society-Perkin Transactions 2 (5), 799-805 (1993). For complex 10 no reliable data were availiable (see ref 7). Hence for the calibration procedure experimental data were taken from the isostructural complex 11. 8. 9. D. Collison, C. D. Garner, J. Grigg, C. M. McGrath, J. F. W. Mosselmans, E. Pidcock, M. D. Roper, J. M. W. Seddon, E. Sinn and P. A. Tasker, J. Chem. Soc., Dalton Trans. (13), 2199-2204 (1998). I. Josefsson, K. Kunnus, S. Schreck, A. Föhlisch, F. M. F. de Groot, P. Wernet and M. Odelius, The Journal of Physical Chemistry Letters 3 (23), 3565-3570 (2012).