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The Journal of Physical Chemistry

Unraveling Electronic Structure of Photocatalytic Manganese Complexes by L-edge X-ray Spectroscopy Sergey I. Bokarev*a, Munirah Khanb, Mahmoud K. Abdel-Latifc, Jie Xiaob, Rifaat Hilald, Saadullah G. Azizd, Emad F. Azizb, Oliver Kühna

E-mail: [email protected] a

Institut für Physik, Universität Rostock, 18051 Rostock, Germany.

b

Joint Ultrafast Dynamics Lab in Solutions and at Interfaces (JULiq), Institute of

Methods for Material Development, Helmholtz Zentrum Berlin für Materialien und Energie, Albert-Einstein-Strasse 15, 12489 Berlin, Germany. c

Chemistry Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt.

d

Chemistry Department, Faculty of Science, King Abdulaziz University, 21589 Jeddah, ,

Saudi Arabia.

Abstract X-ray absorption (XAS) and resonant inelastic scattering (RIXS) of a number of Mn2+,3+,4+ complexes relevant for photo-electrooxidation of water is studied theoretically using the RASSCF/RASSI approach. This enables us to quantify spin-orbit coupling induced mixing of states with different multiplicities in the valence- and core-excited electronic states, evidencing the mostly spin-forbidden character of transitions in RIXS spectra. The notably different patterns of spectroscopic features in this series of substances not only provide insight into their electronic structure, but open the possibility for tracing redox evolution by means of X-ray spectroscopy. Specific findings deduced from the analysis of the shape of the RIXS spectra concern the gap between the ground and first excited valence states relevant for catalytic activity. This gap is substantially lower for Mn3+ as compared to the even oxidation states.

Keywords: X-ray spectroscopy, multi-reference methods, water oxidation, manganese complexes, spin-orbit coupling ACS Paragon Plus Environment


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Introduction Metal ion-coordinated ligand interactions govern a large fraction of processes in everyday life. Therefore, unraveling their underlying mechanisms is of key importance for chemistry, biochemistry, catalysis, and material sciences.1,2 To address such interactions, a number of experimental and theoretical techniques can be applied. Tracing the changes of the vibrational and electronic levels upon ion-ligand coupling, spectroscopy is one of the most powerful tools. Hard and soft X-ray spectroscopic techniques attract special attention because they allow for an atom-specific electronic excitation due to the energetic separation of the core levels of different elements.3,4 As a consequence of the localized nature of the core-orbitals the dipole transition operator acts locally and that is why X-ray excitation probes the local electronic structure of a particular atom. This is in contrast to UV/vis spectroscopy, where transitions generally occur between delocalized molecular orbitals (MO). For the studies of transition metal complexes in solutions, the L-edge spectra enjoy popularity.4,5 The L-edge absorption corresponds to excitations of electrons from 2p core to unoccupied MOs (Fig. 1). The dipole selection rules allow excitations to s-type orbitals and more importantly to the frontier 3d orbitals containing information on the nature of metal-ligand or metal ion-solute interaction, thus being rather rich in features. The additional complexity of L-edge spectra stems from strong spin-orbit coupling, triggered upon core-hole formation and within the 3d states themselves. Along with X-ray absorption spectra (XAS), resonant inelastic X-ray scattering (RIXS) originating from radiative decay of the core-excited states to the manifold of valence-excited states gives valuable information on electronic structure (Fig. 1, state picture). Specifically, it provides insight into the character of the deeper occupied orbitals (Fig. 1, orbital picture). Combination of X-ray absorption and emission together with photoelectron studies, in principle, could be a very powerful suite of tools to address electronic structure.4-6 However, interpretation of complex experimental spectra or spectra with unresolved bands (common in soft-matter) is a non-trivial task and insights from theoretical simulations are mandatory.

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Figure 1. Left panel: The sketch of processes relevant to X-ray spectroscopy in the orbital and many-electron state representations. Different types of RIXS transitions are shown, i.e. elastic, local d-d reorganization, and charge-transfer (CT) together with the corresponding MOs (see also Fig. 3). Right panel: General view of the 2D RIXS spectrum as calculated for [MnII (H2O)6]2+ showing different features as indicated.

The multi-reference approach to X-ray spectroscopy utilizing the restricted active space self-consistent field (RASSCF) technique together with second-order perturbation correction (RASPT2) the state interaction method (RASSI) for spin-orbit coupling 7 was shown to be quite effective, accurate, and well suited for the investigation of valence excited states of transition metal complexes

8,9

. These systems are known for their multi-reference character sometimes

even in the ground electronic state. In case of X-ray spectroscopy, the dipole selection rules allow keeping the active spaces quite compact, since only MOs with substantial d-character need to be considered. This approach was recently successfully applied for unraveling the nature of different transitions in both XAS and RIXS.10-17 However, other techniques such as singlereference TDDFT (see, e.g., Refs.

18-20

) and RODFT-CIS

performance.


21

method also showed good


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The present study is motivated by L-edge XAS and RIXS spectroscopic investigations of the redox evolution of manganese systems relevant to the photo-electrooxidation of water.22,23 These manganese-based nanostructured catalysts are exploiting the similarity to the natural water-oxidation systems

24,25

and have attracted much attention.24-29 The L-edge X-ray

spectroscopy revealed the important role of the MnIII oxidation state and correlation of the local HOMO-LUMO gap at the Mn sites with the catalytic activity.22,23 In view of these experimental findings, the purpose of this article is twofold. First, since the catalytic activity is sensitive to the oxidation state of Mn ions,22,23,25,29 the detailed assignment of spectral features of manganese in different oxidation states is warrant. Second, manganese complexes in different oxidation states are convenient objects for a methodological study of the capabilities of RASSCF/RASSI method. The application of this approach for description of core-excited states of transition metal compounds was proposed recently 10-17 and yet not enough tested on different systems. For the theoretical investigations the species depicted in Fig. 2 have been chosen. These are the reduced (II) and oxidized (III) forms of the manganese hexa-aqua complex ([MnII/III(H2O)6]2+/3+) and its analogue ([MnII/III(H2O)4N2]0/+) with two mono-coordinated CF3SO3– ions (denoted as N) modeling a Nafion environment, corresponding to doping precursors into Nafion polymer matrix in the experiments.22,23 In addition, complexes [MnIIIL(AcO)N2]0

and

[MnIVL(OMe)3]+,

where

L

denotes

1,4,7-trimethyl-1,4,7-

triazacyclononane, were considered. These compounds correspond to the precursors, intermediate and product forms produced in course of doping, and electro-photooxidation as proposed in the ex situ X-ray spectroscopic studies.22,23 In all these complexes (apart from [MnII(H2O)6]2+), Mn has a distorted octahedral coordination sphere of O and N atoms.


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Figure 2. Structures of manganese complexes which were studied. N denotes mono-coordinated CF3SO3– ions modeling a Nafion polymer matrix and L is a 1,4,7-trimethyl-1,4,7triazacyclononane. Atom color code: grey - Mn, black - C, green - N, red - O, yellow - F, dark yellow –S, and blue - H.

Computational details The equilibrium geometries of the species shown in Fig. 2 of the main text for high-spin ground states with the highest possible point group symmetry were obtained at the BLYP/LANL2DZ (Mn atom)30 and 6-311+G(d) (H, F, O, N, and C atoms)31 level using the Gaussian 09 program package.32 The interpretation provided in present paper is based on isolated cluster calculations which is justified due to high locality of the core-excitation process where only first coordination shell of the target atom is of primary importance. Different types of X-ray spectra were calculated at the first principles multi-reference RASSCF level with the revised version of the relativistic ANO-RCC-VTZ basis set for all atoms.33,34 This method should provide reliable results for transition metal compounds, where static electron correlation could play an important role. Its high accuracy was demonstrated for the prediction of L-edge spectra for a number of compounds.

10-17

MOs were first optimized in a state-averaged complete active

space calculation for five lowest valence states (apart from MnII where only one state was possible). In subsequent calculations, all occupied MOs except for the active ones were kept



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frozen. Spin-orbit coupling was treated in the LS-coupling scheme within the state-interaction (RASSI-SO) method 7 and including directly interacting S and S±1 states, where S is the spin of the ground state. Because of the weak field of the ligands the ground states correspond to S=5/2 (sextet) for Mn2+, S=2 (quintet) for Mn3+, and S=3/2 (quartet) for Mn4+ complexes. For the present choice of active space, octet states (S=7/2) were not included for MnII systems. Scalar relativistic

effects

were

considered

within

the

Douglas-Kroll-Hess

approach.35,36

RASSCF/RASSI calculations were performed with the MOLCAS 8.0 program suite.37 The RASSCF calculations implied no symmetry.

Figure 3. Orbitals included in the active spaces used for RASSCF/RASPT2 calculations.

3p5d space contains three 2p, three 3d, and two ∗ 3 orbitals. 3p2σ5d includes in addition two

3 orbitals. Note that ∗ 3 orbitals are localized mostly on ligands and thus correspond to CT

transitions in RIXS.

Since the choice of the active space is the most crucial step in RASSCF calculations, a number of active spaces were tried to model Mn L-edge XAS and RIXS spectra. The simplest one (denoted as 3p5d) included three Mn 2p (one hole is allowed) and five 3d orbitals 3 ACS Paragon Plus Environment

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and ∗ 3 (full CI) if octahedral symmetry is assumed, see Fig. 3 of main text, allowing for the description of XAS spectrum consisting of dipole-allowed 2p→3d transitions. This is the universal active space applied to all species under study allowing unambiguous comparison of spectra. However, the 3 orbitals should be included in addition to ∗ 3 (active space

3p2σ5d) to account for possibly important correlation effects.38 These orbitals are also needed to describe charge-transfer 2 ← 3 transitions in RIXS spectra, which are fingerprints of

metal-ligand interaction and orbital mixing.12,15 Because of high computational demands, the

extended active space 3p2σ5d was applied only to [MnII/III(H2O)6]2+/3+ species. For MnII, two holes were allowed for 3p2σ orbitals and full configuration interaction for 5d MOs, however only singly excited core-states were considered. To decrease the number of electronic states for the MnIII case, only one hole was allowed for 3p2σ subspace. Different active spaces for different oxidation states of Mn atoms resulted in about 200-800 spin-free states and 800-3400 spin-orbit electronic states comprising both valence and core-excited states, for details see Table S1. The effect of dynamic correlation was included only for active space 3p5d via second order perturbation theory (RASPT2) with an imaginary level shift of 0.4 Hartree to avoid intruder states. For active spaces comprising σ3d orbitals, it was not possible to find a reasonable universal complex level shift to get rid of intruder states for valence and core-excited states simultaneously, that is why results of RASPT2 are not presented. The 1s, 2s, 3s, 3p orbitals of Mn as well as 1s of C, N, and O were kept frozen in these calculations. The energy corrections from RASPT2 were applied to the diagonal of the spin-orbit Hamiltonian within the SO-RASSI procedure, while off-diagonal couplings were obtained at the RASSCF level. The XAS spectrum was calculated according to a Golden Rule expression:

Ω = , + − Ω, Γ .

RIXS intensities accounting for electronic coherence effects were estimated according to the Kramers-Heisenberg expression 39:



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Γ( * + "#Ω$ % = , & ' & - % + + − − Ω. , / . ) % + + − − , Γ(

+

Here, Ω and % denote incoming and emitted photon energies; indices 0, , , and refer to

the initial, core-excited intermediate, and valence-excited final states (0 ∈ {}), see Fig. 1 state

picture; * and are polarization vectors of emitted and absorbed photon. A Gaussian profile (- Ω. , / = 1//√2) exp −Ω − Ω. /2/ ) centered at the incoming photon energy Ω.

with /=0.25 eV resembling the experimental excitation pulse width and Lorentzian lifetime

broadening (Γ( =0.26 eV for L3-edge states and 0.43 eV for L2-edge states) were assumed. The

same broadening parameters were used for XAS, where + − Ω, Γ = Γ/) + −

Ω + Γ ;* is the Lorentzian lineshape function. The XAS and RIXS spectra were additionally convoluted with a 0.5 eV Gaussian to mimic experimental inhomogeneous linewidths due to the

Nafion environment. Here we assume that influence of surrounding leads only to broadening of bands, however, environmental dynamical effects could potentially lead to changes in first coordination shell essential for XAS and RIXS spectra. To account for the random orientation of the target complexes in polymer matrices, the effect of polarization dependent detection was 40

included according to Ref. experimental conditions

;

* and were chosen to be perpendicular corresponding to

. Transitions from multiple initial 0 states, corresponding to zero

22,23

field splitting of the open shell ground states were taken into account and weighted with the corresponding Boltzmann factor , for T=300 K. To fit the experimental spectra the energy offset of several eV was applied to both XAS and RIXS, see Table S2. This absolute shifts are partially discussed in Ref. 10 and can be attributed to, e.g., insufficient flexibility of the basis in the core-region and frozen relaxation of a fraction of valence orbitals upon core hole formation. The details for the experimental results discussed in the present work are reported elsewhere.22,23


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Results and discussion

XAS. In the experiments,22,23 the [MnII(H2O)6]2+, [Mn2IIIOL2(AcO)2]0, and [MnIVL(OMe)3]+ precursors were doped into the Nafion matrix and a bias voltage and light irradiation were applied. It was shown that the original forms were reduced to MnII upon doping independent of the precursor species. Further, it can be oxidized upon application of a bias and reduced again under the visible light illumination. In addition, a disordered manganese oxide (birnessite) phase is obtained. Thus, the measured samples represent mixtures of Mn complexes in different oxidation states. Figure 4 shows the experimental absorption spectra recorded in total electron yield (TEY) mode for MnII and MnIII precursors after doping into Nafion matrix (denoted as doped) and application of a voltage (denoted as biased). The spectrum of the doped MnIII compound is not shown because it very closely resembles that of the MnII doped sample, see Ref. 22. The spectra are aligned according to the energies of corresponding transitions. In Fig. 4, the calculated XAS spectra for different complexes using the RASSCF and RASPT2 methods for different active spaces are presented. For visual clarity, some of spectra are omitted and can be found in Fig. S1 of the Supporting Information. The fact that in the experiment one has mixture of different forms complicates the comparison with theoretical results. However, it can be clearly seen from Figs. 4 and S1, that XAS of doped MnII and MnIII samples is dominated by the reduced MnII species, whereas MnII and MnIII after applying bias could be attributed to predominant MnIII and MnIV species, respectively. All spectra consist of two band systems L3 and L2 (3/2 and 1/2 total angular momentum of the core hole), with the L3/L2 energy splitting corresponding to the core hole spin-orbit coupling. The values of this splitting are about 11 eV and thus the SOC constant is approximately 7.3 eV. This values are nearly the same for all species and for different L3 and L2 states, being the intrinsic property of the 2p core hole which is quite insensitive to the structure of valence levels. As illustrated in Fig. 5 and discussed below, core-excited states with



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different spin, S-1, S, S+1, strongly mix; here S denotes the spin of the ground state. The unambiguous analysis of character of both valence and core-excited states is further hindered by strong multi-configurational nature of the states. Therefore, below a simplified picture based on the occupation numbers of natural orbitals is presented. Due to multi-configurational character, these occupation numbers are in general non-integer and the core electron can be distributed over several MOs. The complexes with different oxidation states of the central Mn ion show distinct differences in their absorption spectra. In [MnII(H2O)6]2+ (group II in Fig. 4), the low energy shoulder (a) of the L3 band consist of weak almost purely spin-allowed S→S transitions predominantly of 2p→3d(t2g) character. The main band (b) besides S→S has a notable admixture of S→S-1 character as seen in Fig. 5. The nature of the electronic transitions is of mixed 2p→3d(t2g) and 2p→3d(eg) type, with the latter having larger intensity. The next two peaks denoted as c in Fig. 4, are mostly spin-forbidden S→S-1 transitions of mixed t2g/eg character borrowing some intensity through mixing with the S states of the main spin series. The corresponding groups of states (a-e) are also shown in Fig. 5. The L2 band has similar assignment although spin mixing is even stronger. Coordination of two Nafion-like ligands (group IIb in Fig. S1) leads only to very minor changes if compared to [MnII(H2O)6]2+. The low-energy shoulder (d) of the L3 edge in the [MnIII(H2O)6]3+ spectrum (group III in Fig. 4) is due to S→S/S+1 excitations, mostly to eg orbitals. The corresponding transitions at the L2 edge gain more intensity due to stronger spin-orbit coupling giving rise to more pronounced features in the 647-650 eV range. Starting from the main peak (b) the S/S-1 state mixing plays a role and for the post-peaks (c) it has already predominant spin forbidden character. The electronic character of the most intense transitions across the whole MnIII spectrum corresponds to 2p→3d(eg) excitations. Remarkably, already at the main band the shake-up effects are prominent, i.e. the 2p→3d(eg) excitations are accompanied by 3d(t2g)→3d(eg) transitions. This effect becomes more pronounced for the c bands (especially for the second one at 645 eV) and


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the last peak of L2 band (653 eV). These shake-up bands have lower intensities than one-electron transitions, but their density is large giving rise to notable features. Coordination of CF3SO3ligands (spectrum IIIb in Fig. S1) has a bit more pronounced influence on the XAS spectra of

Figure 4. Experimental (see text) and calculated (RASSCF and RASPT2 methods and different active spaces) XAS spectra of Mn complexes: group II is [MnII(H2O)6]2+; group III is [MnIII(H2O)6]3+; and group IV is [MnIVL(OMe)3]+. For spectra of [MnII/III(H2O)4N2]0/+ and [MnIIIL(AcO)N2]0 model complexes see Fig. S1 in Supporting Information. For assignment of ae features see text and Fig. 5. Bands A, B, C, and D denote excitation energies at which RIXS spectra are analyzed (see Figs. 6 and S2 and Table S2 in the Supporting Information). ACS Paragon Plus Environment


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Figure 5. Contributions of states with ∆S=0,±1 to the spin-orbit coupled wave functions for [MnII(H2O)6]2+ (top), [MnIII(H2O)6]3+ (middle), and [MnIVL(OMe)3]+ (bottom) ions obtained


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with the RASSCF method and the 3p5d active space. The labels on top of each panel correspond to bands in Fig. 4.

MnIII complex than for MnII one. However, the assignment for both [MnIII(H2O)4N2]+ and [MnIIIL(AcO)N2]0 (spectrum IIIc in Fig. S1) stays the same as for [MnIII(H2O)6]3+. The MnIV spectrum has an assignment similar to MnIII. As peculiarities one can consider the prevailing 2p→3d(t2g) character of d shoulder and notable contributions from the sextet states (S+1) for b, d, and e features (Fig. 4). Shake up effects are even more pronounced in this case.

RIXS. The experimental RIXS spectra for doped and biased MnII and MnIII precursors are plotted in Fig. 6 together with the results of theoretical simulations. As for XAS, the results for complexes including CF3SO3– ligand can be found in Fig. S2 of Supporting Information. The experimental excitation energies correspond to the bands denoted as A (640.4 eV), B (642.0 eV), C (644.0 eV), and D (652.6 eV) in Fig. 4. These energies vary slightly for different complexes and methods in theoretical simulations, for details see Table S2 of the Supplement. In general, the shapes of the theoretical RIXS spectra are in good agreement with the experiments. Specific features of these spectra are discussed in the following. In MnII systems, both t2g and eg orbitals are equally populated in the ground sextet state. Additionally, all final valence excited states except for the ground one belong to the quartet spin manifold within the 3p5d active space. This means that apart from the elastic peak all other features for this model correspond to the change of the multiplicity, see below. The lowest excited valence state of MnII lies about 2.8 eV above the ground state. In total for the 3p5d active space, valence states cover range up to 6.5 eV (or -6.5 eV loss energies). The inelastic transitions in MnII RIXS can be divided into three groups. They start from the pairing of electrons from eg to t2g orbitals, which corresponds to the shoulder at -2.7 − -3.2 eV loss energies. The main peak at -



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4.1 – -4.3 eV and the less intense feature at about -6.3 eV are assigned to reverse electron redistribution t2g→eg. Due to complex multi-configurational nature of the wave function the loss/excess of electrons is usually almost equally redistributed within t2g or eg orbitals. The third group, present only for the 3p2σ5d active space, corresponds to relaxation of electrons from σ3d(eg) orbitals filling the core hole. These transitions have substantial CT character, because the core-hole is strongly localized on the Mn atom and σ3d orbitals have predominant ligand localized character, see Fig. 3. The coordination of Nafion (spectrum IIb in Fig. S2) has very minor effect on the RIXS spectrum, similar to the case of XAS. MnIII RIXS demonstrates a more specific behavior due to the appearance of the valence hole in the eg orbitals. Here, the first excited valence state occurs at 0.7 eV having eg→eg nature. The gap between ground and first excited states is smaller than the combined lifetime and inhomogeneous broadening, that is why, the elastic peak is not resolved from the inelastic bands. In contrast to MnII, in MnIII the quintet states are present in the valence manifold, however, the triplet states still dominate and most inelastic features correspond to formally spin-forbidden S→S-1 transitions. The next feature at about -1.6 eV is attributed to a number of intertwined t2g→eg and eg→t2g transitions having nearly the same energy and intensity. The feature at -2.9 eV corresponds to redistributing electrons within t2g or eg orbitals that is t2g→t2g and eg→eg excitations. The range -3.9 – -8.6 eV can be assigned to t2g→eg transitions possessing notable amount of double electron shake up character. In contrast to MnII, [MnIII(H2O)4N2]+ (and similarly [MnIIIL(AcO)N2]0, see Fig. S2) demonstrates an increase of intensity at about -2 eV, this can be caused by stronger covalent interactions for the higher charged MnIII. The nature of the electronic transitions in the case of the MnIV complex is quite homogeneous. All transitions representing inelastic features with appreciable intensity are of t2g→eg character; some of them possess considerable double excitation character. Mainly, these are transitions in the ranges -3.0 – -3.9 eV and below -5.0 eV. Noteworthy, inelastic features are


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of both S→S and S→S-1 character, with the amount of S→S intense transitions decreasing from A to D excitation lines, which is in accord with increase of spin-mixing, see Fig. 5.



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Figure 6. RIXS spectra of different Mn complexes at excitation energies of 640.4 (A), 642.0 (B), 644.0 (C), and 652.6 (D) eV as obtained from experiment and different computational approaches. See also Fig. S2 in Supporting Information. Spectra II-IV are the same as in Fig. 4. The CT bands (-15 - 25 eV) consisting of σ3d(eg)→3d(t2g) and σ3d(eg)→σ*3d(eg) transitions tend to have 7-10 eV lower loss energies than in experiment, showing notably more bound σ3d orbitals. Probably, the inclusion of dynamic correlation could improve the agreement with experiments here. Note that for both [MnII(H2O)6]2+ and [MnIII(H2O)6]3+ with 3p2σ(1hole)5d active space the intensities of CT bands are quite low for all excitation energies (see Fig. S3 in Supplement). Only if two holes are allowed for σ-orbitals, the intensity of CT becomes large for D excitation similar to experiments. This effect cannot be attributed solely to the contribution of two-electron transitions; obviously the correlation introduced by allowing two holes is also important. Comparing RIXS spectra for systems with different oxidation states of the manganese ion shows that MnIII differs most prominently from MnII and MnIV. It has a very small gap between ground and first excited state of 0.7 eV, while both even oxidation states have a gap of 2.8 and 1.8 eV, respectively. Since under experimental conditions one has a mixture of different Mn ions, the contribution from MnIII leads to the appearance of inelastic features at lower energies as it was observed in the experiments

22

and is shown in Fig. 6. However, the signal is dominated

by the MnII contribution. In addition, the XAS spectra seem to be more sensitive to the Mn oxidation state than RIXS spectra.

Dynamic correlation effects Concerning the effect of the computational method, the PT2 correction overstabilizes the ground state if compared to other valence and core-excited states. This is reflected both in the XAS and RIXS. For XAS this corresponds to a shift of the spectrum as a whole to higher energies. The offset for the comparison with experiments substantially increases upon inclusion


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of the PT2 correction (see Table S2). The same effect corresponds to the shift of inelastic RIXS features to more negative loss energies (Fig. 6 of main text), e.g. for MnII this shift is 0.6 eV. The structure of the inelastic bands stays almost intact upon such shift, again evidencing that it is mostly due to the effect on the ground state. In a series MnII-MnIII-MnIV the effect of PT2 increases, what can be explained by stronger covalent interaction of highly charged ions with ligands and thus increasing importance of inclusion of dynamic correlation. Note that PT2 adds ion-ligand inter-correlation effects on top of mostly inner-atomic correlation in RASSCF (due to the choice of the active space). In general, PT2 correction does not change much in spectra and their interpretation. In this respect the extension of active space including strongly interacting ion-ligand σ3d orbitals seems to be more important. Unfortunately, PT2 experiences severe intruder states problems, when these orbitals are included. Thus, although inclusion of dynamic correlation is important, especially for highly charged ions it cannot be regarded as a universal remedy when deeper orbitals need to be considered. The description of charge-transfer 2 ← 3 transitions might require larger active spaces. However, RASPT2 demonstrated good performance for aqueous ions with simple 2p5d active space 10,11,13,14 and could be recommended in this case.

Spin-orbit coupling. The spin-orbit mixing is illustrated in Fig. 5, which provides the collective contributions of states of different multiplicities to the wave function of the spin-orbit coupled states in the LS coupling scheme. The labels on top of each panel correspond to bands in Fig. 4. The strength of mixing systematically increases with the state energy and along with the increase of the charge of central ion, being the largest for MnIV. For the valence manifold, states from main spin progression S usually have the lowest energies; S-1 states have intermediate and S+1 states have the highest energies. Interestingly, in the case of MnIII and MnIV for the core manifold, the S+1 states (septets and sextets, respectively) occur right after the core-excitation threshold. Thus, the



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order of spin-states changes to S+1

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