Bounding [AnO 2 ] 2+ (An=U, Np) covalency by simulated O K-edge and An M-edge X-ray absorption near-edge spectroscopy

Restricted active space simulations are shown to accurately reproduce and characterise both O K-edge and U M4,5-edge spectra of uranyl in excellent agreement with experimental peak positions and are extended to the Np analogue. Analysis of bonding orbital composition in the ground and O K-edge core-excited states demonstrates that metal contribution is underestimated in the latter. In contrast, An M4/5-edge core-excited states produce bonding orbital compositions significantly more representative of those in the ground state. Quantum Theory of Atoms in Molecules analysis is employed to explain the discrepancy between K- and M-edge data and demonstrates that the location of the core-hole impacts the pattern of electron localisation in core-excited states. An apparent contradiction to this behaviour in neptunyl is rationalised in terms interelectronic repulsion between the unpaired 5f electron and the excited core-electron.

Unless stated otherwise, all spectra in this supporting document are unshifted, meaning energies (eV) are those taken directly from RASSI calculations.All theoretical XANES curves are generated from fitting Lorentzian functions across all intense states with a full-width at half-maximum value of 0.80 eV and 1.00 eV for ligand-and metal-edge XANES simulations respectively., is obtained by taking the first root of the Ag singlet wavefunctions in both ligand-and metal-edge simulations.The [NpO 2 ] 2+ ground-state takes the form of a degenerate pair of Kramers doublets (a result of the half-integer total spin) and are obtained via a spin-orbit coupling of the first roots of the four spin-free RASSCF ungerade (u) irreducible representations of the doublet wavefunctions.These spin-free states represent the four possible ways of arranging a single electron across the set of non-bonding 5f orbitals.The [NpO 2 ] 2+ spin-orbit coupled ground-state in both the degenerate Kramers pair for O K-edge RAS(SD) XANES can be expressed as: The [NpO 2 ] 2+ spin-orbit coupled ground-state in both the degenerate Kramers pair for Np M 4/5 -Edge RAS(S) XANES can be expressed as: with weights taken from RASSI calculations.

Additional Considerations for O K-Edge XANES Simulations:
The active space for both [AnO 2 ] 2+ systems (figure S1) comprise the occupied linear combination of oxygen 1s orbitals in RAS1 (2 orbitals), the occupied valence bonding orbitals in RAS2 (6 orbitals), and the formally non-bonding 5f orbitals and empty anti-bonding orbitals in RAS3 (10 orbitals).For [UO 2 ] 2+ , RAS(S) and RAS(SD) wavefunctions are generated by allowing up to 1 or 2 electrons across RAS3 respectively.For [NpO 2 ] 2+ , RAS3 is allowed up to 2 or 3 electrons for RAS(S) and RAS(SD) wavefunctions respectively, set in order to account for the single unpaired 5f electron.For [UO 2 ] 2+ both the non-bonding and anti-bonding orbitals are vacant of electrons in the GS and the RAS3 space reflects this.[NpO 2 ] 2+ also has an empty set of anti-bonding orbitals in the GS but contains a single unpaired electron across the non-bonding 5f orbitals.To generate core-excited states at both the RAS(S) and RAS(SD) levels, a single core-hole is enforced across RAS1 for both systems usings the HEXS keyword.Core-excitations for [UO 2 ] 2+ can take the form of singlet or triplet wavefunctions depending on the spin-alignments of electrons.Both the singlet ground-state, and set of singlet and triplet core-ESs, are spin-orbit coupled through the RASSI module.[NpO 2 ] 2+ core-excitations take the form of doublet or quartet wavefunctions, which are spin-orbit coupled through the RASSI module along with the first roots of A u , B 1u , B 2u and B 3u symmetry which couple to generate the [NpO 2 ] 2+ degenerate Kramer ground-states.In both cases, the resulting spin-orbit coupled energies (converted to electron-volts) and dipole-oscillator strengths between the core-states and the ground-states are plotted to generate the various O K-Edge XANES transition sticks.For [NpO 2 ] 2+ , both the degenerate Kramer ground-states and their dipole-oscillator strengths with the various core-ESs are plotted as transition sticks and contribute to the overall XANES curve.Lorentzian functions are fitted to all intense states using a full-width at half maximum (FWHM) value of 0.80 eV, to generate the overall XANES curves for RAS(S) and RAS(SD) simulations.
Tables S1-7 show the number of RASSCF state-averages performed out of the total number of theoretically possible corestates.Tables also report the number roots from these state-averages that went on to be used in state-interaction calculations (RASSI).At the RAS(SD) level of theory, the Laporte selection rule for centrosymmetric systems is applied to reduce the number of states supplied to the state-interaction calculation.Which aids in reducing computational cost.Making use of this selection rule is shown to be valid by comparing the generated spectra of both [UO 2 ] 2+ and [NpO 2 ] 2+ with and without applying the selection rule when choosing which states were included in RASSI calculations.The results of which are shown in figure S3 and indicate that the selection rule has no notable effect on the spectrum generated.Additionally, at the RAS(SD) level of calculation, maximum energy cutoffs were also used to inform which spin-free states would be included in RASSI calculations, these were 553eV and 547eV cutoffs for [UO 2 ] 2+ and [NpO 2 ] 2+ states respectively.Values were chosen with the desired goal of restricting the final spectrum to the 525-545eV energy range and to reduce the number of states supplied to RASSI to reduce computational cost.

Additional Considerations for An M 4/5 -Edge XANES simulations:
The active space for both [AnO 2 ] 2+ systems (figure S1) at the RAS(S) level of theory comprise the occupied set of metal core 3d orbitals in RAS1 (5 orbitals), the full set of valence bonding orbitals in RAS2 (6 orbitals), and only the ungerade set of anti-bonding orbitals and non-bonding 5f-orbitals in RAS3 (7 orbitals).At the higher RAS(SD) level of theory, the RAS2 set of orbitals is reduced (3 orbitals) to comprise only those bonding orbitals that pair with the anti-bonding set in RAS3.This was done to reduce computational cost and the simulation results are those presented in the main text.The active space is setup such that it will fulfill the Laporte selection rule, with the set of 3d orbitals spanning the gerade irreps and the antibonding orbitals of interest spanning the ungerade irreps, thus capturing the expected core-excitations responsible for the M 4/5 -edge spectra.
For [UO 2 ] 2+ , RAS(S) and RAS(SD) wavefunctions are generated by allowing up to 1 or 2 electrons across RAS3 respectively.For [NpO 2 ] 2+ , RAS3 is allowed up to 2 or 3 electrons for RAS(S) and RAS(SD) wavefunctions respectively, set in order to account for the single unpaired 5f electron.For [UO 2 ] 2+ both the non-bonding and anti-bonding orbitals are vacant of electrons in the GS and the RAS3 space reflects this.[NpO 2 ] 2+ also has an empty set of anti-bonding orbitals in the GS but contains a single unpaired electron across the non-bonding 5f orbitals.At the RAS(S) and RAS(SD) levels of theory, a single core-hole is enforced across RAS1.To generate core-excited states at both the RAS(S) and RAS(SD) levels, a single core-hole is enforced across RAS1 for both systems usings the HEXS keyword.Core-excitations for [UO 2 ] 2+ can take the form of singlet or triplet wavefunctions depending on the spin-alignments of electrons.Both the singlet ground-state, and set of singlet and triplet core-ESs, are spin-orbit coupled through the RASSI module.[NpO 2 ] 2+ core-excitations take the form of doublet or quartet wavefunctions, which are spin-orbit coupled through the RASSI module, along with the first roots of A u , B 1u , B 2u and B 3u ground-states which couple to generate the [NpO 2 ] 2+ degenerate Kramer ground-states.In both cases, the resulting spin-orbit coupled energies (converted to electron-volts) and dipole-oscillator strengths between the core-states and the ground-states are plotted to generate the various An M 4/5 -Edge XANES transition sticks.For [NpO 2 ] 2+ , both degenerate Kramer ground-states and their dipole-oscillator strengths with the various core-ESs are plotted as transition sticks and contribute to the overall XANES curves.Lorentzian functions are fitted to all intense states with a full-width at half maximum (FWHM) value of 1.00 eV utilized to generate the overall XANES curves for RAS(S) simulations.
Tables S1-7 show the number of RASSCF state-averages actually performed out of the total number of theoretically possible core-states and further reports the number roots from these state-averages that went on to be used in stateinteraction calculations.To reduce the computational cost of state-interaction calculations, spin-free spectra for both systems at the RAS(S) level of theory, figure S2, were utilized to inform a maximum energy cutoff for spin-free states supplied to RASSI calculations at the RAS(SD) level.Energy cutoffs of 3657 eV and 3773 eV were chosen for M 4 -edge for [UO 2 ] 2+ and M 5 -edge for [NpO 2 ] 2+ .Figure S4, shows the validity of this approach, as the RAS(S) M 5 -edge spectra for [NpO 2 ] 2+ when including all possible core-ESs and when reducing the number of states according to the energy cutoff, both generate spectra that are qualitatively identical.Thus, the same energy cutoffs were used to inform the size of production level RASSI calculations.

Core-ES Singlets
State-Average Performed:

Core-ES Triplets
State-Average Performed:

QTAIM Analysis:
Table S10: Changes in delocalisation and localisation ∆(,) indexes between the ground-and core-excited states.∆()   occupation at a greater level above that of all other states.Peak 4 contains a core-excitation responsible for generating the peak, assigned to core-excitation into the orbital.Overall, the same core-excitation assignments for peaks 1-4 can be  *  made here at the RAS(SD) level as compared with RAS(S).Detailed assignments are given in table S20.The RAS(SD) simulated O k-edge spectrum of [NpO 2 ] 2+ , figure S10, contains the correct three-peak structure in the 525-545 eV energy range.To make simulation tractable, a 545 eV energy cut-off was utilized when performing the state-interaction (RASSI) calculation.Therefore, peak 4 captured at the RAS(S) level, is neglected here as it does not fall within the energy threshold.The overall assignments for peaks 1-3, are the same as those made at the RAS(S) level of theory.Peak 1 is assigned to a core-excitation into , peak 2 into and peak 3 into .Peak 1 contains a higher density of states  *   *   *  compared to RAS(S), with transitions labelled 1.5 -1.13 containing significant occupation.States 1.1 -1.4 which  *  contribute to a small intensity shoulder on the first peak are assigned to core-excitations into the non-bonding 5f orbitals.
Peak 2 contains a number of transitions, 2.1 -2.5, which contain significant occupancy.State 2.3 is the most intense of  *  these and corresponds to the state with the highest occupancy.For these states, there is also significant additional  *  occupancy of the non-bonding 5f orbitals and to a lesser degree occupancy.Peak 3 contains states presenting higher  *  degrees of multiconfigurational character.The high density of states is labelled 3.1 -3.12, of which 3.4, 3.5, 3.7 and 3.8, contain higher than the background level occupation of the orbitals.States continue an emerging trend for these  *  RAS(SD) simulations, shared for [UO 2 ] 2+ and [NpO 2 ] 2+ O k-edge, as higher energy core-states tend to utilize occupation of lower energy orbitals to optimize states.The exception to this being for peak 4 which has near single electron occupancy of the orbital.Detailed assignments given in table S21. *  Table S21: Assignments for [NpO 2 ] 2+ oxygen K-edge XANES RAS(SD) simulation.

[UO 2 ] 2+ U M 4/5 -Edge RAS(SD) XANES:
Figure S12 shows the U M 4 -edge simulated XANES spectrum at the RAS(SD) level of theory consisting of three peaks 1-3.The same overall peak assignments made for the RAS(S) spectrum are utilized to inform and aid in the assignments made here, as states present more multiconfigurational character, making assignments more difficult.However, we find that the assignments made here are in agreement with the RAS(S) simulations, with peaks 1, 2 and 3 corresponding to coreexcitations into the non-bonding 5f, , and orbitals respectively, and further agree with those made by Vitova et al. .While transitions 3.9 -3.16 (except 3.15), show  *  low level occupation of the , these are found to be higher than the background level occupancy, which combined with  *  RAS(S) findings, allows for the conclusion that these states represent core-excitations into the .Transitions 3.9 and 3.16  *  present core-states with the greatest occupancy at 0.14 and 0.17 respectively.Detailed assignments given in table S22. *  Figures S13-14 show the U M 5 -edge RAS(SD) simulated XANES spectrum consisting of two main peaks.Peak 1 contains a number of transitions labelled 1.1 -1.10 show non-bonding 5f and orbital occupancy.Natural populations therefore  *  indicate that peak 1 contains core-states with an admixture of both non-bonding 5f and occupancy.Transitions labelled  *  2.1 -2.6, also show the same occupancy pattern.Transitions 2.7 -2.17 all show clear occupancy above the background  *  level, with states 2.10, 2.12 and 2.17 all having the highest degrees of occupation at 0.34, 0.35 and 0.41 respectively. *  Detailed assignments given in table S23.S22.S23. Figure S15 presents the simulated RAS(SD) Np M 5 -edge XANES spectrum of [NpO 2 ] 2+ with a two peak profile consistent with experiment.Peak 1 contains a small shoulder with transitions labelled 1.1 -1.4 in figure S16 which are assigned to core-transitions into the non-bonding 5f orbitals, followed by the set of transitions 1.5 -1.12 under the main peak which correspond to core-excitations into the orbitals.Across these transitions, occupancy ranges between 0.01 -0.03  *   *  and is considered unoccupied.In comparison the second intense peak labelled 2, contains a large number of low intensity transitions which in combination generate the full XANES peak intensity.A selected sample of intense transitions labelled 2.1 -2.5 are assigned to core-excitations into the .While occupation of the orbital is low, ranging from 0.08 -0.12,  *   *  these values are above the background level seen in transitions 1.1 -1.12 and assignment of peak 2 to core-excitation into the would agree with transitions found at the RAS(S) level of simulation, were core-state multiconfigurational nature is  *  less pronounced.To represent the overall assignment of peak 1, the highest intensity transition labelled 1.8 is chosen, and the corresponding degenerate pair of states for this transition are taken for additional covalency analysis.For peak 2, the highest intensity transition 2.5 is chosen out of those sampled and corresponds to the highest natural occupation of the  *  out of the set at 0.12.S24.

Additional Theoretical Spectra & Assignments at the RAS(S) Level of Theory:
Due to the wavefunction constraints at the RAS(S) level, generated core-states will only involve electrons entering the RAS3 space from the core-orbitals in RAS1.This allows for a clear assignment of peaks to distinct core-excitations.S25.The simulated oxygen k-edge XANES spectrum in figure S17(b) contains a four peak structure akin to that of [UO 2 ] 2+ .In the ground-state of [NpO 2 ] 2+ , a single unpaired electron occupies the non-bonding 5f orbitals.All core-excitations also retain this single electron, which continues to span the four non-bonding 5f orbitals, this is the case for all states labelled and characterized in Table S26.The additional electron occupying the set of non-bonding 5f orbitals generates an increased number of possible electronic configurations when compared to uranyl, thus it is not surprising that the XANES spectrum has a greater density of states contributing to each peak.This is clear to see in peaks 1 and 3 for example.Peaks 2 and 4 contain distinct high-intensity transitions labelled 2.7 and 2.8 for peak 2, and a single state labelled 4.2 for peak 4.  S26. Figure S18 shows the spin-orbit splitting between the M 5 -and M 4 -edges for both systems.The simulated U M 4 -edge spectrum of [UO 2 ] 2+ is labelled in figure S19(a).The spectrum consists of a three-peak structure (peaks 1-3) in agreement with experiment. 2 Full natural orbital occupations for labelled transitions are contained within Table S27.Peak 1 contains four labelled transitions which can be assigned to core-excitations into the non-bonding 5f orbitals.Peak 2 contains five labelled transitions which can all be assigned to core-excitations into the orbitals, and  *  peak 3 contains three transitions which can be assigned to core-excitations into the orbital.These assignments agree  *  with those made by Vitova et al. 2   The simulated U M 5 -edge Spectrum of [UO 2 ] 2+ was also generated and labelled in figure S19(b).The spectrum has a threepeak structure, with a potential shoulder on the first peak.Peak 1 consists of two high intensity transitions labelled 1.2 and 1.3, each corresponding to core-excitations into the non-bonding 5f orbitals.A low intensity transition labelled 1.1 also corresponds to a core-excitation into the non-bonding 5f orbitals.Peak 2 contains four states labelled 2.1 -2.The simulated Np M 5 -edge spectrum of [NpO 2 ] 2+ is shown in figure S20(b).The spectrum reproduces the two-peak structure expected from experiment, but with the addition of a shoulder on peak 1.Additional plots Figure S20(e) and S20(f) show the labelled transitions under peaks 1 and 2 respectively.The highest intensity transition under peak 1 is labelled 1.9 and can be assigned to a core-excitation into orbitals.Lower intensity transitions (1.4 -1.12) either side of  *  1.9 can also be assigned to core-excitations into the orbitals with varying degrees of natural occupations.Smaller  *  intensity transitions under the shoulder on peak 1, labelled 1.1 -1.3, correspond to core-excitations into the non-bonding 5f orbitals.In simulation, we find that the core-excitations into the non-bonding 5f orbitals and into the are  *  energetically separable, with the core-states involving the non-bonding 5f orbitals coming first, followed by those states of higher intensity for the main peak into the .Peak 2 has four labelled transitions 2.1 -2.4,all corresponding to core- *  excitations into the orbital.Detailed assignments are given in table S29. *

𝑢
The simulated Np M 4 -edge spectrum of [NpO 2 ] 2+ was also generated and labelled in figure S20(a).The spectrum consists of a three-peak structure, with a select number of states labelled in additional plots in figure S20(c) and S20(d).Peak 1 contains several transitions labelled 1.1 -1.7.These states are assigned to core-excitations into the non-bonding 5f

Figure S1 :
Figure S1: Active spaces for XANES RASSCF simulations.1.2Ground-states for both O K-Edge and An M 4/5 -Edge XANES:Ground-states were obtained through state-averaging, which was found to stabilize the active-spaces.The [UO 2 ] 2+ groundstate,, is obtained by taking the first root of the Ag singlet wavefunctions in both ligand-and metal-edge Ψ GS = 1 (  ) 1

Figure S2 :
Figure S2: Spin-free RAS(S) spectra for (a) U M 4 -edge of [UO 2 ] 2+ and (b) Np M 5 -edge of [NpO 2 ] 2+ used to inform the energy cut-off values utilized to restrict RAS(SD) states utilized in RASSI calculations.Spin-free spectra were generated from stateinteraction of GS and only irreps of singlet multiplicity for [UO 2 ] 2+ and doublets for [NpO 2 ] 2+ .The number of states is recorded in tables S3 and S4.

Figure S3 :
Figure S3: Oxygen K-edge XANES RAS(S) simulations for (a,b) [UO 2 ] 2+ and (c,d) [NpO 2 ] 2+ when (a,c) applying the Laporte selection rule and (b,d) without applying the rule, in order to inform the irreps supplied to RASSI calculations.

Figure
Figure S4: [NpO 2 ] 2+ Np M 5 -edge XANES RAS(S) simulations when (a) including all possible core-excited stats in the RASSI calculation, and (b) when restricting states included in RASSI calculations informed by the 3773 eV cut-off for spin-free states.Cut-off was informed from figure S2(b).

Figure S9 :
Figure S9: Theoretical oxygen K-edge [UO 2 ] 2+ RAS(SD) XANES spectrum annotated with peak and stick transition labels.The 525-555 eV (left) and a 535-538 eV (right) region is shown.Assignments of labelled transitions can be found in tableS20.
transitions labelled 1.1 -1.4 which are assigned to core-excitations into the non-bonding 5f orbitals.Peak 2 contains transitions labelled 2.1 -2.8, which show clear occupation of the orbitals, alongside partial occupation of the  *  non-boding 5f orbitals.Peak 3 contains a large density of states, transitions labelled 3.1 -3.8 consist of core-states with substantial partial occupations of both the non-bonding 5f orbitals and

Figure
Figure S12: (a) The theoretical RAS(SD) [UO 2 ] 2+ U M 4 -edge XANES spectrum and (b-d) peak regions.Spectra are annotatedwith peak and stick transition labels.Assignments of labelled transitions can be found in tableS22.
Transitions 2.7 and 2.8 are core-excitations into the orbital, and transition 4.2 corresponds to a core-excitation into the  *  orbital.Transitions 4.1 and 4.3 are lower intensity core-excitations into the .A number of transitions contribute to  labelled from 1.3 -1.9 in figure S17(b).All these core-excitations contain varying degrees of occupation. *  Meaning an overall assignment to peak 1 can still be made, which corresponds to a core-excitation into the orbital. *  Transitions labelled 1.2 and 1.3 present core-states with the majority of the excited electron from the core-1s orbitals residing across the non-bonding 5f orbitals, akin to the shoulder assigned in [UO 2 ] 2+ .Between peaks 1 and 2, transitions labelled 2.1 to 2.3 are found to be intermediate states between the two main core-excitations into the and the state.Peak 3 contains a number of states that contribute to the overall peak.All four transitions labelled 3.1 -3.4 contain clear core-excitations into the orbital, allowing this peak to be ascribed to this core-excitation  *  overall.On the whole, the peak assignments are characteristic of those made for [UO 2 ] 2+ , indicating a similar energy order of the anti-bonding orbitals found in [NpO 2 ] 2+ .Detailed assignments given in table
Figure S19: [UO 2 ] 2+ U M 4/5 -edge XANES RAS(S) simulated spectra showing the (a) M 4 -edge and (b) M 5 -edge spectra.Peak and stick transition labels for the M 4 -edge and M 5 -edges are also presented.Assignments can be found in tables S27 and S28.

Figure
Figure S20: [NpO 2 ] 2+ Np M 4/5 -edge XANES RAS(S) simulated spectra showing the (a) M 4 -edge and (b) M 5 -edge spectra.Peak and stick transition labels for the (b,c) M 4 -edge and (e,f) M 5 -edges are also presented.Assignments can be found in tables S29 and S30.

Table S1 :
Number of state-average RASSCF roots and states used in subsequent RASSI calculations for RAS(S) O K-edge [UO 2 ] 2+ XANES simulations.States in bold are those used when the Laporte selection rule was imposed.GS = Ground-State, Core-ES = Core-Excited State.

Table S2
: Number of state-average RASSCF roots and states used in subsequent RASSI calculations for RAS(S) O K-edge [NpO 2 ] 2+ XANES simulations.States in bold are those used when the Laporte selection rule was imposed.GS = Ground-State, Core-ES = Core-Excited State, VS = Valence State.

Table S5 :
Number of state-average RASSCF roots and states used in subsequent RASSI calculations for RAS(SD) O K-edge [UO 2 ] 2+ XANES simulations.A max energy cut-off of 553 eV was utilized to inform choice of states used in RASSI.GS = Ground-State, Core-ES = Core-Excited State.

Table S6
: Number of state-average RASSCF roots and states used in subsequent RASSI calculations for RAS(SD) O K-edge [NpO 2 ] 2+ XANES simulations.A max energy cut-off of 547 eV was utilized to inform choice of states used in RASSI.GS = Ground-State, Core-ES = Core-Excited State.

Table S7
: Number of state-average RASSCF roots and states used in subsequent RASSI calculations for RAS(SD) U M 4/5 -edge [UO 2 ] 2+ XANES simulations.A max energy cut-off of 3657 eV was utilized to inform choice of states used in RASSI.GS = Ground-State, Core-ES = Core-Excited State.

Table S8 :
Peak energy positions in electron volts for RAS(SD) O K-Edge XANES simulations (unshifted), compared to experimental values for [UO 2 ] 2+ taken from experiment. 1 No reported O K-edge XANES experimental values are known for [NpO 2 ] 2+ so only RAS(SD) values are reported.Theoretical peak energies were measured as shown in figureS5and S6, while state energies are taken from tables S20 and S21.Values reported in brackets are differences with respect to experimental peak positions.Detailed assignments of states and energies can be found in tables S20 and S21, and
2Theoretical peak energies were measured as shown in figureS7and S8, while state energies are taken from tables S22 and S24.Values reported in brackets are differences with respect to experimental peak positions.Detailed assignments of states and energies can be found in tables

Table S13 :
QTAIM data for ground-state (GS) and a select number of key core-excited states from the [UO 2 ] 2+ U M 4 -Edge RAS(SD) XANES simulation.The electron-density at the bond critical point in atomic units, delocalisation , and localisation indexes   (,) are reported.Changes in QTAIM metrics with respect to the GS are also reported ( ).

Table S14 :
QTAIM data for ground-state (GS) and a select number of key core-excited states from the [NpO 2 ] 2+ O K-Edge RAS(SD)

Table S15 :
QTAIM data for ground-state (GS) and a select number of key core-excited states from the [NpO 2 ] 2+ Np M 5 -Edge RAS(SD)

Table S20 :
Assignments for [UO 2 ] 2+ oxygen K-edge XANES RAS(SD) simulation.Table reports the natural populations of the spin-orbit natural orbitals for key core-states.Transitions correspond to assignments made in figureS9.States corresponds to the spin-orbit coupled state numbers assigned by the OpenMolcas RASSI calculation.Energy corresponds to the state energy in electron-volts.

RAS(SD) Assignments for Simulated Uranium M 4/5 -edge XANES:
Table reports the natural populations of the spin-orbit natural orbitals for key core-states.Transitions correspond to assignments made in figure S10.States corresponds to the spin-orbit coupled state numbers assigned by the OpenMolcas RASSI calculation.Energy corresponds to the state energy in electron-volts.

Table S22 :
Assignments for M 4 -edge XANES states for [UO 2 ] 2+ at the RAS(SD) level of theory.Table reports the natural populations of the spin-orbit natural orbitals for key core-states.Transitions correspond to assignments made in figure S12.States corresponds to the spin-orbit coupled state numbers assigned by the OpenMolcas RASSI calculation.Energy corresponds to the state energy in electron-volts.

Table S23 :
Assignments for M 5 -edge XANES for [UO 2 ] 2+ at the RAS(SD) level of theory.Table reports the natural populations of the spinorbit natural orbitals for key core-states.Transitions correspond to assignments made in figures S13 and S14.States corresponds to the spin-orbit coupled state numbers assigned by the OpenMolcas RASSI calculation.Energy corresponds to the state energy in electronvolts.

Table S24 :
Assignments for M 5 -edge XANES for [NpO 2 ] 2+ at the RAS(SD) level of theory.Table reports the natural populations of the spin-orbit natural orbitals for key core-states.Transitions correspond to assignments made in figures S15 and S16.States corresponds to the spin-orbit coupled state numbers assigned by the OpenMolcas RASSI calculation.Energy corresponds to the state energy in electron-volts.

Table S25 :
Assignments for [UO 2 ] 2+ oxygen K-edge XANES RAS(S) simulation.Table reports the natural populations of the spin-orbit natural orbitals for key core-states.Transitions correspond to assignments made in figureS17(a).States corresponds to the spin-orbit coupled state numbers assigned by the OpenMolcas RASSI calculation.Energy corresponds to the state energy in electron-volts.

Table S26 :
Assignments for [NpO 2 ] 2+ oxygen K-edge XANES RAS(S) simulation.Table reports the natural populations of the spin-orbit natural orbitals for key core-states.Transitions correspond to assignments made in figure S17(b).States corresponds to the spinorbit coupled state numbers assigned by the OpenMolcas RASSI calculation.Energy corresponds to the state energy in electronvolts.

Table S27 :
Assignments for M 4 -edge XANES for [UO 2 ] 2+ at the RAS(S) level of theory.Table reports the natural populations of the spin-orbit natural orbitals for key core-states.Transitions correspond to assignments made in figureS19(a).States corresponds to the spin-orbit coupled state numbers assigned by the OpenMolcas RASSI calculation.Energy corresponds to the state energy in electron-volts.

Table S28 :
Assignments for M 5 -edge XANES for [UO 2 ] 2+ at the RAS(S) level of theory.Table reports the natural populations of the spin-orbit natural orbitals for key core-states.Transitions correspond to assignments made in figure S19(b).States corresponds to the spin-orbit coupled state numbers assigned by the OpenMolcas RASSI calculation.Energy corresponds to the state energy in electron-volts.Peak 2 contains a high intensity transition labelled 2.5 for a core-excitation into the orbitals.Additional density  *  of states is present either side of this main excitation with varying degrees of orbital occupation.Peak 3 contains a  *  number of transitions labelled 3.1 -3.5 which all correspond to core-excitations into the orbital.Detailed assignments  *  are given in table S30.

Table S29 :
Assignments for M 5 -edge XANES for [NpO 2 ] 2+ at the RAS(S) level of theory.Table reports the natural populations of the spinorbit natural orbitals for key core-states.Transitions correspond to assignments made in figure S20.States corresponds to the spin-orbit coupled state numbers assigned by the OpenMolcas RASSI calculation.Energy corresponds to the state energy in electron-volts.

Table S30 :
Assignments for M 4 -edge XANES for [NpO 2 ] 2+ at the RAS(S) level of theory.Table reports the natural populations of the spinorbit natural orbitals for key core-states.Transitions correspond to assignments made in figureS20.States corresponds to the spin-orbit coupled state numbers assigned by the OpenMolcas RASSI calculation.Energy corresponds to the state energy in electron-volts.