Ab initio Wavefunction-based Determination of ... - ACS Publications

Subscriber access provided by Kaohsiung Medical University

Spectroscopy and Excited States

Ab initio Wavefunction-based Determination of Element Specific Shifts for the Efficient Calculation of X-Ray Absorption Spectra of Main Group Elements and First Row Transition Metals Agisilaos Chantzis, Joanna K. Kowalska, Dimitrios Maganas, Serena DeBeer, and Frank Neese J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.8b00249 • Publication Date (Web): 12 Jun 2018 Downloaded from http://pubs.acs.org on June 14, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Journal of Chemical Theory and Computation

Ab initio Wavefunction-based Determination of Element Specific Shifts for the Efficient Calculation of X-Ray Absorption Spectra of Main Group Elements and First Row Transition Metals Agisilaos Chantzis1, 2, Joanna K. Kowalska1, Dimitrios Maganas1, 2, Serena DeBeer1, and Frank Neese1 ,2* 1

Max-Planck Institute for Chemical Energy Conversion, Stiftstrasse 34-36, D-45470

Mülheim an der Ruhr, Germany 2

Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470

Mülheim an der Ruhr, Germany

[email protected]

ACS Paragon Plus Environment

1

Journal of Chemical Theory and Computation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 47

RECEIVED DATE (to be automatically inserted after your manuscript is accepted if required according to the journal that you are submitting your paper to)


2

Page 3 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


ABSTRACT In this study, a detailed calibration of the performance of modern ab initio wavefunction methods in the domain of X-ray absorption spectroscopy (XAS) is presented. It has been known for some time, that for a given level of approximation, e.g. using time-dependent density functional theory (TD-DFT) in conjunction with a given basis set, there are systematic deviations of the calculated transition energies from their experimental values that depend on the functional, the basis set, and the chosen treatment of scalar relativistic effects. This necessitates a linear correlation for a given element/functional/basis set combination to be established before chemical applications can be performed. This is a laborious undertaking since it involves sourcing trustworthy experimental data, lengthy geometry optimizations, and detailed comparisons between theory and experiment. In this work, reference values for the element-specific shifts of all the first-row transition metal atoms and the main-group elements C, N, O, F, Si, P, S and Cl have been computed by using a protocol that is based on the complete active space configuration interaction in conjunction with second order Nelectron valence state perturbation theory (CASCI/NEVPT2). It is shown that by extrapolating the results to the basis set limit of the method and taking into account scalar relativistic effects via the second-order Douglas-Kroll-Hess (DKH2) corrections, the predicted element shifts are on average less than 0.75 eV across all the absorption edges and a very good agreement between theory and experiment in all the studied XAS cases is observed. The transferability of these errors to molecular systems is thoroughly investigated. The constructed CASCI/NEVPT2 database of element shifts is used to evaluate the performance and to automatically calibrate prior to comparison with the experiment two commonly used methods in X-ray spectroscopy namely DFT/Restricted open shell configuration interaction singles (DFT/ROCIS) and TD-DFT methods.


3


Page 4 of 47

1 Introduction X-ray absorption spectroscopy (XAS) has been established as a powerful tool for the understanding of the geometric and electronic structure of matter. Consequently, X-ray based techniques play a prominent role for studying the functionality, dynamics and reactivity of systems relevant to inorganic and bioinorganic chemistry, homogeneous and heterogeneous catalysis, and solid-state chemistry.1-16 Moreover, given the rapidly increasing availability of in-house X-ray spectrometers,17-22 together with the equally rapidly advancing sophistication of experimental techniques,23 it is anticipated that X-ray based techniques will gain significant popularity in the near future. For first-row transition metal complexes, the XAS spectra are categorized based on the energy range of the radiation field employed.24 K-edge XAS spectra are obtained in the region of ~5-10 keV, and correspond to the selective excitation of a core 1s electron, while lower energies of ~500-1000 eV and ~50-100 eV, respectively, are used to record L- and M-edge XAS spectra corresponding to excitations of 2p and 3p electrons. In combination, these techniques can be used to obtain information on the identity of the excited transition metal atom, as well as the covalency, oxidation state, spin state, local geometry of the studied complexes. Modern quantum chemical methods can provide valuable insights and interpretations of the experimental XAS measurements and aid in the correlation of experimental data to the geometrical and electronic structure of the studied systems. A large variety of methods are employed to calculate XAS spectra ranging from empirical multiplet methodologies,24-28 to various particle/hole based theories,29-33 as well as wavefunction-based approaches.34-47 Semi-empirical Ligand-Field Multiplet (LFM) models24-28 have been used to simulate numerous cases of experimental X-ray absorption spectra of highly symmetric chemical systems with considerable success. However, for low-symmetry environments or systems


4

Page 5 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


with high degrees of covalency, the number of empirical parameters quickly grows and fits to the experimental data are no longer unique. Recent studies employing ab initio ligand field theory (AILFT)48 to parameterize the LFM model have been proven successful in simulating complicated X-ray absorption spectra of chemical systems with lower symmetry.49 Particlehole theories, and in particular the linear response variant of Time-Dependent Density Functional Theory (TD-DFT), have shown great performance in calculating K-edge XAS spectra.

1-2, 4-12, 15, 43, 50-71

On the other hand, the computation of metal M- and L-edge XAS

spectroscopies presents additional complications since in addition to covalency and ligand field effects one has to also explicitly treat the final state multiplet and spin-orbit coupling (SOC) effects. Hence, these spectra can be best calculated by using computational methods that are grounded in first-principles electronic structure theory.34-35,

37-40, 72-74

Recently,

truncated Configuration Interaction (CI) techniques on the basis of restricted active space configuration interaction methods (RASSCF, or RASCI) in which the missing dynamic correlation is partially recovered perturbatively through, for example, the RASSCF/RASPT2 protocol75-81 have been used to treat various X-ray spectroscopic problems on medium size molecules. An alternative approach is provided by the Restricted Open shell Configuration Interaction Singles (ROCIS) and its parameterized version, DFT/ROCIS (also referred to as ROCIS/DFT), which has been developed in order to combine the strengths of the existing methods. Namely, ROCIS provides the correct description of the ground-state bonding (or covalency) in transition metal complexes by employing DFT orbitals, a proper Configuration Interaction (CI) description of the many particle character of excited states and their mixing by the SOC interaction, as well as a favorable scaling of the computational cost with the size of the system. However, as the DFT/ROCIS method is based on a high-spin coupled restricted open-shell determinant, complicated systems, such as antiferromagnetically aligned solids, cannot be treated by this method. Nevertheless, the ROCIS methods have been used as


5


Page 6 of 47

‘black-box’ tools. Their predictive power and efficiency to treat X-ray spectroscopy problems has been validated over a diverse set of systems, ranging from small mononuclear transition metal complexes to extended solid clusters.3,

41-42, 82-88

Recently, by using the pair natural

orbital (PNO) machinery, the PNO-ROCIS and PNO-ROCIS\DFT variants have been developed.89 These methods show spectacular performance increases relative to the original ROCIS methods for large, ‘real-life’, chemical systems, while providing results that are virtually indistinguishable from the original ROCIS predicted spectra. In practice, there are two criteria on which the applied theoretical methods are evaluated for their ability to predict the experimental X-ray absorption spectra. The first refers to the shape of the spectrum, which involves the broadening of the spectral lines mainly due to the finite lifetimes of the excited states. Although a proper theoretical treatment would require the dynamics of the molecule along the various radiative and non-radiative decay mechanisms to be taken into account, it is common practice to assign a constant, predetermined width to the calculated absorption peaks that matches the resolution obtained in the experiment. The second issue concerns the errors present in the theoretically estimated absolute excitation energies. These errors arise from: 1) limitations of the one-electron basis set employed in the core region, 2) the shortcomings of the chosen quantum chemical method that is used to treat vertical excitations, and 3) deficiencies in the description of spin-free relativistic effects. These errors are usually highly systematic and in fact all of these factors can (for a given basis set and density functional) be taken into account by introducing an element−dependent shift.

1-2, 4, 50, 90

It has been shown that a simple linear regression is

sufficient to establish predictive accuracy in the calculated transition energies for any given element.4, 12, 42, 50, 91 The concept of element specific shifts can serve also as a useful single measure of the performance of a given level of theory in reproducing the experimental absolute excitation energies collectively for all the studied complexes of a particular


6

Page 7 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


transition metal or ligand atom. Clearly, there is the need for the construction of a reference quality database of theoretically determined element specific shifts that will be used for the evaluation of the performance of the various theoretical methods without the need for individual calibrations. However, the construction of such a database, to the best of our knowledge, has never been attempted. To this end, we present in this work an ab initio wavefunction-based reference library of calculated metal and ligand K-, L- and M- edge excitation energies for an atomic series including main group and first row transition metal elements (C, N, O, F, P, S, Cl and ScCu). These energies are computed on the basis of the complete active space configuration interaction CASCI92-93 in conjunction with N-electron valence perturbation theory to second order (NEVPT2)94-95 and are compared with the available experimental data. It will be shown that the CASCI/NEVPT2 reference database of all edges is universal and expandable to elements for which no experimental atomic data are available. Hence it can be used to automatically calibrate or evaluate the performance of any other theoretical method that is employed to calculate X-ray absorption spectra of atoms and molecules.


7


Page 8 of 47

2 Experimental spectroscopic data 2.1 Atomic Absorption and X-ray Absorption Spectra In order to arrive in a consistent atomic set of X-ray absorption spectra we focus on gasphase literature data. The library of the experimental gas-phase atomic data of the valence absorption excitation energies for the atomic series from Sc to Cu, as well as the X-ray absorption K-edge spectra of neutral and charged C, N, and O main group elements and Cr, Mn and Cu transition metals were taken from the NIST database96 and the related literature.97-100 It should be noted that for the row four atomic series (Sc-Cu) the available NIST K-edge XAS experimental values referring to solid-state experiments were not included in our analysis. Reference quality experimental gas-phase atomic metal L- and Medge XAS spectra for the row four periodic series Sc-Cu have been collectively reported by M. Martins, P. Wernet et., al.,101 while the individual cases are discussed in the related literature.102-109

2.2 Molecular X-ray Absorption Spectra A library of experimental ligand K-edge and metal K-, L- and M- edge X-ray absorption spectra was constructed by collecting literature data for the following 55 complexes: TiIVCl4 (1)110, TiIVCpCl3 (2)110, TiIVCp2Cl2 (3)110, K4[CrII(CN)6] (6)111,

V(III)(acac)3 (4)91, V(IV)O(acac)2 (5)91,

[CrII(tacn)2]Cl2 (7)111, K3[CrIII(CN)6] (8)111, [CrIII(tacn)2]Br3 (9)111,

(PPh4)2[MnVN(CN)4] (10)112, (NMe4)2Na[MnVN(CN)5] (11)112, PPh4[MnV(taml)O] (12)112, (Et4N)2[FeIICl4] (13)113,

K4[FeIICN6] (14)113, [Fe(III)Cl6] (15)117, Fe(III)(salen)Cl (16)12,

K3[CoIII(CN)6] (17)114,

[CoIII(NH3)6]I3 (18)114, [CoIII(phen)3](ClO4)3 (19)114, CoIII(dtc)3

(20)114, [NiII(Im)6](BF4)2 (21)115, (Et4N)[NiII(Py2S)3] (22)115, (Et4N)2[NiII(pdtc)2] (23)115, [NiII(ttcn)3](BF4)2 (24)115,

Cs2[CuIICl4] (D2d) (25)50, V(IV)O(TPP) (26)42, V(IV)O(salen)


8

Page 9 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(27)116, [V(V)O2(R,R'L1)] , R=H, R'=Me (28)116, R=H, R'=Ph (29)116, R=H, R'=4O2NPh (30)116, R=Me, R'=Ph (31)116, Cr(III)(acac)3 (32), Mn(III)(acac)3 (33), [Fe(II)Cl6] (34)117, Fe(III)(acac)3 (35), Fe(III)(tacn)3 (36)118, Co(III)(acac)3 (37), Ni(II)(H2O)2 (38)77, Ni(II)(diene)2 (39)119, Ni(II)(pdtc)2 (40)119, [CuIICl4] (D4h) (41)120, CuII(Pc) (42)121, VIVO(Pc) (43)122, Na2[CrIVO4] (44)123, KMnVIIO4 (45)123, (Et4N)[FeIIICl4] (46)50, NiII(Pc)

(48)124,

NiII(BSE)

(49)10,

NiII(DACO)

(Ph3MeAs)2[CoIICl4] (47)50, (50)10,

NiII(MSE)

(51)10,

(Ph3MeAs)2[NiIICl4] (52)50, [FeIITren(Py)3](PF6)2 (53)125, [FeIITren(6-MePy)3](PF6)2 (54)125, CoII(Tp)2 (55)125. The following chemical abbreviations have been used for the ligands: Cp, cyclopentadienyl; acac, acetylacetonate; tacn, 1,4,7-triazacyclononane; taml, tetra-amido macrocyclic ligand; salen, N,N′-bis(salicylidene)ethylendiamine; phen, 1,10-phenanthroline; dtc, diethyldithiocarbamate ion; Im, imidazole; Py2S, pyridine-2-thiolate; pdtc, pyridine-2,6bis(thiocarboxylate); ttcn, 1,4,7 trithiacyclononane; TPP, 5,10,15,20-tetraphenylporphine; L1, oxyoxime;

tacn,

1,4,7-triazacyclononane;

diene,

5,7,7,12,14,14-hexamethyl-1,4,8,11-

tetraazacyclotetradeca-4,11-diene; Pc, phthalocyanine; BSE, N,N′-bis(2-sulfinatoethyl)-1,5diazacyclooctanato; DACO, N,N′-bis(2-mercaptoethyl)-1,5-diazacyclooctanato; MSE, N,N′2-mercaptoethyl-2-sulfinatoethyl-1,5-diazacyclootanato; ylmethylene)amino)ethyl)amine; ylmethylene)amino)ethyl)amine;

Tren(Py)3,

Tren(6-MePy)3, Tp,

tris(2-((pyridin-2-

tris(2-((6-methylpyridin-2-

hydrotris(pyrazolyl)borato].

In

situ

NEXAFS

measurements for complexes 4, 31, 32, 33, 35 and 37 were collected at DEIMOS beamline at the SOLEIL synchrotron facility in France. Additional experimental details can be found in the Supporting Information.

2.3 Energy calibration and intensities normalization of the XAS data As described in previous publications, the energy scales of the atomic XAS spectra were calibrated by using well-known photoelectron and Auger lines of noble gases.102-109 The respective XAS spectra of the molecular set were calibrated by using well defined molecular


9


Page 10 of 47

systems as external references. In both the atomic and the molecular data normalization of the XAS spectra was performed at the edge jump K-edge, the higher intensity L3-edge and the lower energy M-edge features.

3 Computational details All calculations were performed with the ORCA suite of quantum chemistry programs.126 For geometries and frequencies the BP86127-128 functional was used together with the Grimme’s dispersion correction129-130 in conjunction with the all-electron version of the def2-TZVP triple-zeta quality basis set of the Ahlrichs group.66,67 X-ray absorption spectra of the isolated atoms were computed on the basis of state averaged complete active space (SA-CASSCF) wavefunctions92-93 and second-order N-electron valence perturbation

theory (NEVPT2)94-95 theory by using the strongly contracted (SC) NEVPT2 algorithm (referred to as SC-NEVPT2). In all the calculations, in order to obtain a balance description between core and valence orbitals, decontracted versions of the correlation-consistent triplezeta quality one-electron basis sets (cc-pVTZ) have been chosen for the transition metal atoms and main group elements, respectively. All the calculations were performed using the

second-order Douglas-Kroll-Hess correction (DKH2)131-132 to account for the scalar relativistic effects, employing the finite nucleus model.133 The XAS spectra were calculated by first optimizing the valence active space orbitals in the framework of SACASSCF calculations, including valence excited states in the range between 6 to 15 eV. In a second step the relevant core orbitals were rotated into the active space and the CASCI/NEVPT2 problem was solved in the space of individually defined singly core-excited electronic configurations using the previously optimized sets of orbitals. For example, along the atomic series Sc-Cu two sets of orbitals involving the 3d, 4s, 4p and 4d or the 3d, 4s and 4d orbitals were initially included in the active space to calculate the valence excitation


10

Page 11 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


energies. In following, the first optimized set of orbitals was used to calculate the K-edge XAS spectra, while the second set was used to calculate the respective L- and M-edge XAS spectra with an exception to Cu. In fact for Cu likewise to the Sc-Cu K-edge XAS spectra the first optimized set of orbitals was used to calculate the Cu L and M-edge XAS spectra respectively. In fact preliminary results showed that inclusion of the 4p orbitals in the active space might influence the energy positions and the relative intensities of the calculated Sc-Cu K-edge and Cu L- and M-edge XAS spectra considerably, while this was not the case in the respective Sc-Ni L- and M-edge XAS spectra. On this basis, the configuration state

functions (CSFs) were constructed by considering all possible excitations within the (4s, 3d) and (4s, 3d, 4p) shells while single excitations were considered from 3d or 4s shells into the 4d shell. On the other hand the CASCI/NEVPT2 XAS spectra on molecules where performed by considering all possible singly core-excited electronic configurations within the 2p, 3d shell as well as all possible electronic configurations within the 3d shell. In all the molecular cases extensions beyond this active space was not found to be necessary and the CASCI/NEVPT2 problem was solved in the space of singly core-excited electronic configurations within the (2p, 3d) shell, without further restrictions. Further details of how

to individually select reference configurations are provided in the ORCA manual. Details with respect to the number of states/multiplicity that was included in the CASCI/NEVPT2 calculations for the atomic and the molecular sets are provided in the supporting information (Tables S16, S17). The DFT/ROCIS and TD-DFT XAS spectra were computed by employing the B3LYP127, 134-135 functional. For the atomic XAS spectra, the decontracted cc-pVTZ one-electron basis was used throughout, while for the complexes both the def2-TZVP and the decontracted cc-pVTZ were employed. The resolution of the identity (RI)136-137 approximation was employed to accelerate the calculations by utilizing the def2/J and the cc-pVTZ/C auxiliary basis sets, respectively. Transition intensities were


11


Page 12 of 47

obtained by a multipole expansion up to 1st order to include electric dipole, magnetic dipole and electric quadrupole contributions to the absorption transition rate.50 Constant Gaussian broadenings 1.5 eV, 0.8 eV and 2 eV, for the complexes and 1.5 eV, 0.4 eV and 0.3 eV for the atoms were used to the calculated transitions for the metal M-, L- and K-edge XAS spectra, respectively. The statistical error analysis was performed on the basis of the Mean Signed and Absolute Errors (MSE and MAE), as well as the Maximum Absolute Errors (MaxAE).

4 Non-relativistic SA-CASSCF/NEVPT2 calculations 4.1 Valence excited states Prior to the calculation of the core excited spectra, we first evaluated the performance of the SA-CASSC/NEVPT2 protocol by calculating the experimental valence excited state energies between the multiplets of the atomic series Sc-Cu. As discussed above, the experimental multiplet energies were taken from the NIST tables.96 As we do not yet include spin-orbit coupling in the calculations, the experimental values refer to degeneracy-

weighted multiplet averages138 according to:

E(L,S) =

∑

J

(2J + 1)E(J , L,S )

∑

J

(2J + 1)

The results are summarized in Table 1 for the Sc atom and tables S1-S8 for the Ti-Cu atomic series. As it is seen, the mean absolute errors range between 0.06 and 0.09 eV for Sc, Ti, V, Fe, Co and Ni to about 0.2 and 0.4 eV for Cr, Mn, and to about 0.87 eV for Cu transition metal atoms, respectively. These results are consistent with the performance of SACASSCF/NEVPT2 in calculating the valence vertical excitation energies in organic molecules or transition metal complexes. 48, 139-140


12

Page 13 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 1. Selection of average experimental versus SA-CASSCF/NEVPT2 non-relativistic calculated valence excited energies for the Sc atom. Spectroscopic Term

Experimental Average ( E(L, S) ) Energies (eV)

SA-CASSCF/NEVPT2 (eV)

4

F

1.44

1.43

2

F

1.86

1.94

4

F

1.97

2.05

4

D

2.00

2.07

2

D

1.99

2.08

2

D

2.11

2.21

4

P

2.14

2.21

4

P

2.30

2.35

2

P

2.33

2.39

MSE

0.09

MAE

0.09

MaxAE

0.28

5 Relativistic CASCI/NEVPT2 calculations 5.1 Complete Basis set limit In the next step, we investigated the convergence of the calculated shifts with respect to the employed one-electron basis set. In an effort to ensure that the calculated shifts are close to the complete basis set limit (CBS) and the calculated spectral shapes are converged with respect to that, the atomic K-edge XAS spectra of neutral O and S as well as the L- and M-Edge XAS spectra for neutral Sc, Cr and Co have been chosen as examples. C and S are second- and third-row main group elements, while Sc, Cr and Co contain a less than half-


13


Page 14 of 47

filled, half-filled and more than half-filled d shell, respectively, and thus, they constitute representative cases for all the atoms studied herein. The decontrancted versions of the correlation consistent cc-pVXZ (X = D, T, Q, 5) basis set series have been used to monitor convergence of the CASCI/NEVPT2 excitation energies. The active space used to construct the SC-NEVPT2 reference values for the atoms has also been used, for consistency. The calculated shifts for the energetically lowest absorption maximum for K-edges and the L3 and M3-edge maxima for L- and M-edges are shown in Table 2. In all the studied cases, the differences between the cc-pVTZ basis set and the largest basis set studied (cc-pV5Z) range between ~ 0.1 to 0.4 eV. Besides the energies, the total integrated intensity of each spectrum has been used as a useful measure of convergence. In all the examined cases, the spectral shapes calculated using a cc-pVTZ basis set or larger are found to be essentially identical (e.g. the spectral shape deviations are below 0.1%). Clearly the cc-pVTZ basis set represents an optimal choice, providing the best accuracy/performance ratio. Hence, this basis set was adopted for all the SA-CASSCF/NEVPT2 and CASCI/NEVPT2 calculations. Addition of a set of diffuse functions to the cc-pVTZ basis set, leading to the aug-cc-pVTZ variant, does not alter the results. Table 2. CASCI/NEVPT2 energies of the lowest energy absorption peak of the K-edge XAS

spectra of neutral C and S atom and the L- and M-edge XAS spectra of the neutral Sc, Cr and Co atoms calculated with different correlation consistent cc-pVXZ (X = D, T, Q, 5) basis sets. Atom C(0) S(0)

Sc(0)

ESC-NEVPT2 (eV) ESC-NEVPT2 (eV)

ESC-NEVPT2

cc-pVDZ 285.42

cc-pVTZ 285.05

K-Edge cc-pVQZ 284.95

cc-pV5Z 284.92

aug-cc-pVTZ 285.03

2465.84

2464.48

2464.40

2463.91

2464.63

cc-pVDZ 401.91

cc-pVTZ 401.97

L-Edge cc-pVQZ 401.75

cc-pV5Z 401.66

aug-cc-pVTZ 401.88


14

Page 15 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Cr(0) Co(0)

Sc(0) Cr(0) Co(0)

(eV) ESC-NEVPT2 (eV) ESC-NEVPT2 (eV)

ESC-NEVPT2 (eV) ESC-NEVPT2 (eV) ESC-NEVPT2 (eV)

574.63

574.51

574.19

573.85

574.47

778.89

779.09

778.72

778.67

779.21

cc-pVDZ 29.61

cc-pVTZ 29.62

M-Edge cc-pVQZ 29.30

cc-pV5Z 29.17

aug-cc-pVTZ 29.59

39.56

39.55

39.52

39.51

39.52

60.46

60.40

60.26

60.20

60.38

5.2 Influence of the active space on the XAS spectra Entering the discussion of the XAS spectra, we first investigate the impact of the chosen active space on the calculated CASCI/NEVPT2 XAS spectra. As an example, we discuss below the case of the atomic Co L-edge XAS spectrum. The neutral Co atom has a ground state with 2p64s23d7 electron configuration. The CASCI/NEVPT2 calculations were performed by considering three active spaces (13, 8), (15, 9) and (15, 14) which involve the 2p, 3d, the 2p, 4s, 3d and the 2p, 4s, 3d and 4d orbitals, respectively. The results are shown in Figure 1. As it is seen, the relative intensities of the L3 and L2-edge regions as well as the number of the experimental spectral features are correctly reproduced only when the 4s orbital is included in the active space as in the case of the (15, 9) and (15, 14) CASCI/NEVPT2 XAS spectra. In terms of calculated spectral energy positions, the best agreement with experiment is observed only when the 4d orbitals are included in the active space. In fact only the (15, 14) CASCI/NEVPT2 XAS spectrum energetically matches the energy position of the experimental features with deviations of about ~0.3 eV. On the other hand, the (13, 8) CASCI/NEVPT2 and (15, 9) CASCI/NEVPT2 XAS spectra are


15


Page 16 of 47

approximately 8 and 5 eV to lower energies, respectively. The final active spaces used in all the atomic CASCI/NEVPT2 calculations are presented in Table 3.

Figure 1. Experimental black versus calculated CASCI/SC-NEVPT2 atomic Co L-edge XAS spectra with active spaces (13, 8) green, (15, 9) blue and (15, 14) red

Table 3. Final active spaces used in the atomic CASCI/NEVPT2 calculations. Atom

K-Edge

L-Edge

M-Edge

C(1) N(1) O(0) O(1) F(0) Si(0) P(0) S(0) Cl(0) Sc Ti

CAS(5,9) CAS(6,9) CAS(6,8) CAS(5,8) CAS(7,8) CAS(6,9) CAS(7,9) CAS(6,8) CAS(7,8) CAS(5,15) CAS(6,15)

CAS(9,14) CAS(10,14)

CAS(9,14) CAS(10,14)


16

Page 17 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


V Cr Mn Fe Co Ni Cu

CAS(7,15) CAS(8,15) CAS(9,15) CAS(10,15) CAS(11,15) CAS(12,15) CAS(13,15)



6 RESULTS. 6.1 Database of ab initio NEVPT2 element-specific shifts 6.1.1 K-edges of main group elements C, N, O, F, Si, P, S and Cl The CASCI/NEVPT2 calculated main absorption band for each of the K-edge XAS spectra of the main group elements C, N, O, F, Si, P, S and Cl in oxidation states 0 and 1 along with the corresponding experimental values (when available) are provided in Table 4. As it is seen, the mean average SC-NEVPT2 error is about 0.83 eV. Analysis shows that all the bands are dominated by states characterized by single electron excitations with electron configurations 1s12s22pn+1 (for C, N, O and F) and 1s13s23pn+1 (for Si, P, S and Cl).

Table 4. Theoretical transition energies, dominant terms and electronic configurations calculated at the CASCI/NEVPT2//cc-pVTZ//DKH2 level of theory for the maxima of the energetically lowest K-edge absorption peak of selected neutral and cationic second- and third-row main group atoms along with the corresponding experimental values.

Element C(1) N(1) O(0) O(1) F(0)

Term 4

P D 3 P 4 P 2 S

5

Configuration 1s12s22p2 1s12s22p3 1s12s22p5 1s12s22p4 1s12s22p6

K-Edge ESC-NEVPT2 (eV) 289.05 400.56 526.87 530.94 678.52

EExp. (eV) 288.14 399.84 527.85 531.65 –

ESC-NEVPT2–EExp. (eV) 0.91 0.72 -0.98 -0.71 –


17


Si(0) P(0) S(0) Cl(0) MSE MAE MaxAE

3

S P 3 P 2 S 4

1s13s23p3 1s13s23p4 1s13s23p5 1s13s23p6

1836.92 2140.22 2464.60 2813.59

– – – –

Page 18 of 47

– – – – -0.02 0.83 0.98

6.1.2 X-ray absorption edges of transition metal elements Sc-Cu The CASCI/NEVPT2 calculated main absorption band of the metal K-edge XAS spectra of the neutral Sc-Cu atomic series, together with the corresponding experimental values are provided in Table 5. The mean absolute error amounts to about 0.74 eV. For the light elements Sc-Cr, analysis of the nature of the states dominating the main pre-edge spectral features (Table 6) shows that the dominating absorption bands involve mainly single electron excitations with 1s14s23dn+1 electron configuration. In addition, double electron excitations with electron configurations 1s14s13dn+2 and 1s14s03dn+3 are also contributing approximately 5-15% to the intensity of pre-edge spectral features. Moving to the Mn-Cu series (Table 7), the number of multiplets present in the K-edge spectral features is reduced and states with a 1s14s13dn+2 electron configuration dominate. The CASCI/NEVPT2 calculated metal L- and M-Edge XAS spectra for the Sc-Ni series, together with their respective experimental spectra are visualized in Figures 2 and 3. The respective Cu L- and M-edge experimental XAS spectra were excluded from the direct spectra comparison due to somewhat lower spectra quality. Nevertheless, the main experimental bands were included in the analysis below. In all cases, very good agreement between theory and experiment is observed in terms of the number, the energy position and the relative intensities of the spectral features. The energy position and the nature of the selected (enumerated) spectral features shown in Figure 2 and 3 are analyzed in Tables 5, S9, 6 and 7. As shown in Tables 5 and S9, by comparing the energy position of the first band


18

Page 19 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


with respect the experiment, the mean absolute errors along the atomic series Sc-Cu are 0.23 eV (M-edge) and 0.39 eV (L-edge). Slightly larger errors (0.62 and 0.57 eV) are observed when all the selected bands are taken into account. As it is shown in Tables 6 and 7, in all the cases, the low energy features are dominated by single and double electron excitations with electron configurations 2/3p54s23dn and 2/3p54s13dn+1, while at higher energies electron excitations with electron configurations 2/3p54s03dn+2 are also contributing. It should be emphasized that in both the calculated K, L and M-edge XAS spectra electron configurations (1s14s13dn+14d1, 1s14s03dn+24d1, 2/3p54s13dn+14d1, 2/3p54s03dn+24d1) which involve significant 4s → 3d → 4d doubles excitation character contribute up to 10% to all the calculated features. As it was shown above, these additional electron correlation effects are essential for achieving the best possible agreement with the experiment.


19


Page 20 of 47

Figure 2. Experimental and theoretical CASCI/NEVPT2//cc-pVTZ//DKH2 L-Edge XAS spectra of the first-row transition metal atoms Sc-Ni. All spectra are normalized with respect to the corresponding absorption maxima to unity to facilitate comparisons.


20

Page 21 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



21


Page 22 of 47

Figure 3. Experimental and theoretical CASCI/NEVPT2//cc-pVTZ//DKH2 M-Edge spectra of the first-row transition metal atoms Sc-Ni. All spectra are normalized with respect to the corresponding absorption maxima to unity to facilitate comparisons.

Table 5. CASCI/ NEVPT2//cc-pVTZ//DKH2 calculated K-, L- and M-edge XAS energies of the 1st band along the Sc-Cu atomic series together with the respective mean signed error (MSE), mean absolute error (MAE) and maximum absolute error (MaxAE) analysis.

Element

Band

K-Edge EExp. ENEVPT2 (eV) (eV)

∆E (eV)

Band

L-Edge EExp. ENEVPT2 (eV) (eV)

∆E (eV)

Band

M-Edge EExp. ENEVPT2 (eV) (eV)

∆E (eV)

Sc

1

-

4492.12

-

1

399.36

399.55

0.19

1

29.66

29.62

0.04

1

-

4970.21

-

1

453.95

453.38

-0.57

1

33.35

32.82

0.53

1

-

5471.87

-

1

512.25

511.07

-1.18

1

35.94

36.24

-0.3

1

5990.78

5990.55

-0.23

1

573.54

574.51

0.97

1

39.21

38.78

0.43

1

6545.88

6546.52

0.72

1

639.55

638.99

-0.56

1

48.04

47.61

0.43

1

--

7120.06

-

1

707.30

707.42

0.12

1

53.61

53.72

-0.11

1

-

7719.56

-

1

776.47

776.45

-0.02

1

57.70

57.74

0.04

1

-

8139.19

-

1

850.60

850.91

0.31

1

65.11

64.92

-0.19

1

8982.71

8981.45

-1.26

1

929.16

928.32

-0.84

1

67.31

67.31

0.01

Ti V

Cr Mn Fe

Co Ni Cu MSE (1st Band) MAE (1st Band) MaxAE (1st Band)

-0.25 0.74 1.26

0.13 0.23 1.53

0.11 0.39 1.18


22

Page 23 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 6. Selected bands from the CASCI/ NEVPT2//cc-pVTZ//DKH2 calculated K-, L- and Medge XAS spectra along the Sc-Cr atomic series together with the dominant electronic configurations.

Element

Band

K-Edge Configuration

Band

L-Edge Configuration

Band

M-Edge Configuration

Sc

1 2

1s14s23d2 1s14s03d4

1 2 3 4

2p54s23d2 2p54s13d2, 2p54s23d3 2p54s23d2, 2p54s13d3, 2p54s03d4 2p54s23d2, 2p54s03d4 5

1

3

1 2 3 4

3p54s23d2, 3p54s13d3 3p54s23d2, 3p54s13d3 3p54s23d2, 3p54s13d3, 3p54s03d4 3p54s23d2, 3p54s13d3, 3p54s03d4 3p54s23d2, 3p54s13d3, 3p54s03d4 3p54s23d2, 3p54s13d3, 3p54s03d4

6

2p 4s 3d , 2p54s23d2, 2p54s03d4 2p54s13d3

7 8 9

2p54s03d4 2p54s03d4 2p54s03d4

1 2

1 2

3p54s23d3 3p54s23d3, 3p54s13d4

3 4 5

2p54s23d3, 2p54s13d4 2p54s23d3, 2p54s13d4, 2p54s93d5 2p54s13d4, 2p54s03d5 2p54s23d3, 2p54s03d5 2p54s23d3, 2p54s03d5

3 4 5

3p54s23d3 3p54s13d4, 3p54s03d5 3p54s23d3, 3p54s03d5

5

5 6

Ti

1 2

1s14s23d3, 1s14s03d5

V 1 2

1s14s23d4, 1s14s03d6

1 2 3 4 5 6 7 8

2p54s23d4, 2p54s13d5 2p54s23d4 2p54s23d4 2p54s23d4, 2p54s13d5 2p54s23d4, 2p54s13d5 2p54s23d4, 2p54s13d5 2p54s23d4 2p54s23d4

1 2 3 4 5 6

3p54s23d4, 3p54s13d5 3p54s23d4 3p54s23d4, 3p54s13d5 3p54s23d4, 3p54s13d5 3p54s23d4, 3p54s13d5 3p54s23d4, 3p54s13d5

1 2

1s14s13d6 1s14s03d7

1 2 3 4 5

2p54s23d5, 2p54s13d6 2p54s23d5, 2p54s13d6 2p54s13d6 2p54s13d6 2p54s13d6, 2p54s23d5

1 2 3 4 5 6

3p54s23d5 3p54s23d5 3p54s23d5 3p54s13d6 3p54s13d6 3p54s13d6

Cr


23


Page 24 of 47

Table 7. Selected bands from the CASCI/ NEVPT2//cc-pVTZ calculated K-, L- and M-edge XAS spectra along the Mn-Cu atomic series together with the dominant electronic configurations.

Element

Band

K-Edge Configuration

Band

L-Edge Configuration

Band

M-Edge Configuration

Mn

1

1s14s23d6

1 2 3 4 5

2p54s23d6 2p54s23d6 2p54s23d6, 2p54s13d7 2p54s23d6, 2p54s23d6

1 2 3

3p54s23d6 3p54s23d6 3p54s23d6

4

3p54s23d6, 3p54s13d7

2p54s23d7, 2p54s13d8 2p54s23d7 2p54s13d8 2p54s23d7, 2p54s13d8 2p54s13d8

1

3p54s23d7

2 3 4

3p54s23d7 3p54s23d7 3p54s23d7, 3p54s13d8

2p54s23d8 2p54s23d8 2p54s23d8, 2p54s13d9 2p54s23d8, 2p54s03d10 2p54s23d8, 2p54s03d10 2p54s23d8, 2p54s03d10

1 2 3

3p54s23d8 3p54s23d8 3p54s23d8, 3p54s13d9

2p54s23d9 2p54s23d9 2p54s23d9 2p54s23d9, 2p54s13d10 2p54s23d9, 2p54s13d10

1 2

3p54s23d9, 3p54s13d10

2p54s23d10 2p54s23d10

1 2

3p54s23d10 3p54s23d10

Fe

1

1s14s23d7

1 2 3 4 5

Co

1

1s14s23d8

1 2 3 4 5 6

Ni

1

1s14s23d9

1 2 3 4 5

Cu

1

1s14s13d10

1 2


24

Page 25 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


6.2 CASCI/NEVPT2 Reference Database of Element-Specific Shifts It was shown above that the CASCI/NEVPT2 protocol can deliver very good energetics for the atomic K-, L- and M-edge XAS spectra of the main group elements and first row transition metals. Hence, these results can serve as a reference database of the element specific shifts. By analyzing collectively the data presented in tables 4, 5 and S9, the mean absolute error (MAE) in the calculated energies is about 0.74 eV with a maximum absolute error (MaxAE) about 1.8 eV. These differences may be attributed to shortcomings of the computational protocol, however, we also note that energy calibration procedures differ among different research groups and different beamlines also show variations in both their calibration procedures and energy stabilities. Such differences can easily account for 0.5-1 eV differences and a more rigorous comparison would require all the data to be measured under precisely the same conditions.141 Comparing with the CASSCF/NEVPT2 performance for calculating excitations energies in the visible region the NEVPT2 transitions energies in the core excited regions are slightly higher (about 0.2-0.3 eV) than those reported for the vertical excitations in organic molecules or the d-d excitation energies in transition metal complexes.48, 139-140 On the other hand, these errors are quite similar to the errors reported for the energies of charge transfer (CT) type of excitations. 47, 121

6.3 Evaluation of the Performance of TD-DFT and DFT/ROCIS for Atoms In this section, the CASCI/NEVPT2 reference database is used to evaluate the performance of two methods that are widely used in simulating X-ray absorption spectra, namely the DFT/ROCIS and the TD-DFT in conjunction with the B3LYP functional. The


25


Page 26 of 47

comparisons are performed at the energy position of the first band for the K- and M-edge XAS spectra and the maximum intensity L3 band in the respective XAS spectra. In fact, at these positions in both the CASCI/NEVPT2, DFT/ROCIS and TD-DFT calculations, the character of the contributing excited states can be clearly identified. The results are presented in Tables 8-10. In general it is expected that particle/hole type of methods like TD-DFT, or single reference type of methods like ROCIS/DFT are expected to perform worst in comparison to multiconfiguational type of methods like CASCI/NEVPT2 when dealing with atomic or molecular cases featuring near orbital degeneracy. This is reflected to the calculated absolute transition energies. In particular the absolute errors introduced by the DFT/ROCIS and TDDFT methods with respect to the CASCI/NEVPT2 energies depend strongly on the edge region. The larger errors are observed in the K-edge region of the main group elements and the 1st row transition metals. The mean absolute errors are about 64.78 and 66.69 eV (MaxAE ~ 108.40 eV and 105.85 eV) for B3LYP/ROCIS/cc-pVTZ//DKH2 and TDDFT/B3LYP//cc-pVTZ//DKH2 methods in comparison to the CASCI/NEVPT2//ccpVTZ//DKH2 reference energies. On the other hand, the B3LYP/ROCIS//cc-pVTZ//DKH2 metal L-edge calculated energies are characterized by significantly lower errors (MAE ~14.5 eV, MaxAE ~ 17.98 eV). The smaller errors are observed for the B3LYP/ROCIS//ccpVTZ//DKH2 M-edge calculated energies (MAE ~1.27 eV, MaxAE ~ 1.90 eV). As shown in Tables S10-S12, similar error ranges are observed when the B3LYP/ROCIS and TDDFT/B3LYP calculations were performed by using the def2-TZVP and including DKH2 relativistic corrections. On the other hand exclusion of the relativistic corrections results in errors that are about 1.2 times larger in magnitude. (Tables S13-S15).


26

Page 27 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 8. Comparison between the reference CASCI/NEVPT2//cc-pVTZ, B3LYP/ROCIS//ccpVTZ//DKH2 and TD-DFT/B3LYP//cc-pVTZ//DKH2 K-edge transition energies for selected neutral and cationic second- and third-row main-group elements and all the neutral first-row transition metal atoms.

Element

Band

C(+1) N(+1) O(0) O(+1) S(0) Cl(0) Sc Ti V Cr Mn Fe Co Ni Cu MSE MAE MaxAE

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

ENEVPT2 (eV) 289.05 400.56 526.87 530.94 2479.16 2831.52 4492.12 4970.21 5471.87 5990.55 6547.03 7120.06 7719.56 8341.19 8985.42

ETD-DFT/B3LYP (eV) 276.47 387.11 512.91 516.34 2418.15 2779.98 4421.44 4893.74 5389.98 5906.87 6407.13 7026.64 7617.67 8239.18 8881.61

K-Edges EB3LYP/ROCIS (eV) 276.17 385.59 509.95 512.68 2416.15 2761.02 4421.64 4893.74 5390.57 5906.95 6456.16 7026.67 7617.60 8239.24 8881.61

ETD-DFT/B3LYP- ENEVPT2 (eV) -12.58 -13.45 -13.96 -14.6 -61.01 -51.54 -70.68 -76.47 -81.89 -83.68 -90.90 -93.42 -101.89 -102.01 -103.81 -64.78 64.78 103.81

EB3LYP/ROCIS- ENEVPT2 (eV) -12.88 -14.97 -16.92 -18.26 -63.01 -70.50 -70.48 -76.47 -81.3 -83.6 -90.87 -93.39 -101.96 -101.95 -103.81 -66.69 66.69 103.81

Table 9. Comparison between the reference CASCI/NEVPT2//cc-pVTZ, B3LYP/ROCIS//ccpVTZ and TD-DFT/B3LYP//cc-pVTZ//DKH2 L-edge transition energies for all the neutral first-row transition metal atoms.

Element

Band

Sc Ti V Cr Mn Fe Co Ni Cu MSE MAE MaxAE

4 2 2 1 1 1 4 3 1

ENEVPT2 (eV) 401.97 456.25 512.59 574.51 638.99 707.42 779.09 852.44 928.32

L-Edges EB3LYP/ROCIS (eV) 389.48 443.86 501.85 558.31 623.64 691.11 761.11 835.31 915.68

EB3LYP/ROCIS- ENEVPT2 (eV) -12.49 -12.39 -10.74 -16.2 -15.35 -16.31 -17.98 -17.13 -12.64 -14.54 14.54 17.98


27


Table

10.

Comparison

between

the

reference

Page 28 of 47

CASCI/NEVPT2//cc-pVTZ,

B3LYP/ROCIS//cc-pVTZ//DKH2 and TD-DFT/B3LYP//cc-pVTZ//DKH2 M-edge transition energies for all the neutral first-row transition metal atoms.

Element

Band

Sc Ti V Cr Mn Fe Co Ni Cu MSE MAE MaxAE

1 1 1 1 1 1 1 1 1

ENEVPT2 (eV) 28.67 32.87 36.24 39.55 48.61 53.72 57.74 64.92 67.31

M-Edges EB3LYP/ROCIS (eV) 29.76 33.63 37.80 38.97 46.98 51.88 57.53 63.07 69.21

EB3LYP/ROCIS- ENEVPT2 (eV) 1.09 0.76 1.56 -0.58 -1.63 -1.84 -0.21 -1.85 1.90 -0.09 1.27 1.90

6.4 CASCI/NEVPT2 XAS edges for molecules In a further step, we evaluated the performance of the CASCI/NEVPT2 protocol on selected XAS spectra cases chosen from the molecular dataset presented in section 2. In particular, the M(III)(acac)3 (M=V, Cr, Mn, Fe and Co) family of complexes was chosen and the CASCI/NEVPT2 metal K, L and M-edge XAS spectra were calculated for all cases where experimental data are available. Representative spectra are visualized in Figure 4. In accordance with the performance of the CASCI/NEVPT2 calculated XAS spectra for atoms, the CASCI/NEVPT2 calculated XAS spectra for all complexes studied provide very good agreement with respect to experiment.


28

Page 29 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 4. Representative experimental (black) versus calculated CASCI/NEVPT2//ccpVTZ//DKH2 metal L-Edge spectra for complexes V(III)(acac)3 (4), Cr(III)(acac)3 (32) and Fe(III)(acac)3 (35). In Table 11 the error analysis is performed on the experimental versus the CASCI/NEVPT2 calculated energy positions of the pre-edge K-edge feature for complex 4, the higher intensity L3-edge features of complexes 4, 32, 33, 34 and 37 and the lower energy M-edge feature of complex 37. As it is seen in all cases, the errors are very similar to the ones observed in the atomic series with the same protocol (Tables 4, 5 and S9). This implies that the very good performance of the CASCI/NEVPT2 protocol for calculating the atomic XAS spectra across the edges is entirely transferable to the molecular set studied in this section. Table 11 Calculated CASCI/NEVPT2//cc-pVTZ//DKH2 ENEVPT2 versus experimental Eexp metal K-, L-, and M-edge XAS spectra of M(III)(acac)3, (M=V, Cr, Mn, Fe and Co) family of complexes. Molecule

Element

2SGS+1

Eexp (eV)

ENEVPT2(eV)

∆ENEVPT2 (eV)

5467.1

0.3

516.62 577.6 639.8 707.5 777.9

0.28 0.4 0.33 0.5 0.42

K-edge 4

V(III)

3

5467.51

L-edge 4 32 33 34 37

V(III) Cr(III) Mn(III) Fe(III) Co(III)

3 4 5 6 1

516.90 578.00 640.13 708.00 778.32 M-edge


29


37 MSE MAE MaxAE

Co(III)

1

64.96

64.56

Page 30 of 47

0.4 0.37 0.37 0.5

6.5 B3LYP/ROCIS and TD-DFT/B3LYP XAS edges for molecules. In this section, B3LYP/ROCIS and TD-DFT/B3LYP methods together with the def2TZVP basis sets are employed to calculate the ligand and metal K-edge and the metal L- and M-edge XAS spectra across the molecular training set. The results are summarized in Tables 12-14. Once again, the ligand and metal K-edges contain larger errors for both B3LYP/ROCIS and TD-DFT/B3LYP to MAE = ~101 eV (MaxAE ~197 eV). On the other hand the B3LYP/ROCIS metal L-edge calculated energies are characterized by significantly lower errors (MAE ~14.61 eV, MaxAE ~19.49 eV) while the B3LYP/ROCIS M-edge calculated energies (MAE ~1.70 eV, MaxAE ~2.12 eV) contain the smallest errors. It should be noted that these errors follow the general trends of the core ionization energies in the different spectral areas. For example in the sequence of the main group elements C, N, O, S and Cl the errors increase from C to Cl, in line with the increase of the respective core ionization energies.96 Similar comparisons can be made for the increase of errors in the sequence metal M-edge, metal L-edge, ligand K-edge and metal K-edge XAS spectra. On average these errors amount to about 4%, 2.5% and 1.4% of the 3p, 2p and 1s core ionization energies.

Table 12. Experimental Eexp versus calculated B3LYP/ROCIS//def2-TZVP//NoRel and TDDFT/B3LYP//def2-TZVP//NoRel metal and ligand pre-edge K-edge energy positions for the complexes of the training set 1−25 and 41-52 respectively. The oxidation state of each transition metal atom in each complex is shown inside brackets, following the name of the


30

Page 31 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


element. The ground state multiplicities 2SGS+1 of all the studied systems are also shown. NoRel denotes that the calculations presented here in employed no relativistic corrections.

Molecule

Element

2SGS+1

Eexp (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Ti(IV) Ti(IV) Ti(IV) V(III) V(IV) Cr(II) Cr(II) Cr(III) Cr(III) Mn(V) Mn(V) Mn(V) Fe(II) Fe(II) Fe(III) Fe(III) Co(III) Co(III) Co(III) Co(III) Ni(II) Ni(II) Ni(II) Ni(II) Cu(II)

1 1 1 3 2 3 5 4 4 1 1 1 5 1 6 6 1 1 1 1 3 3 3 3 2

4969.10 4968.13 4968.74 5463.15 5468.25 5990.54 5988.36 5991.03 5990.40 6541.32 6542.67 6541.62 7111.71 7112.95 7112.80 7112.93 7708.30 7707.80 7707.29 7706.52 8341.60 8339.40 8340.10 8339.80 8978.40

1 2 3 3 13 14 25 41 42 43 44 45 46 47 48 48 49 50 51 52 MSE MAE MaxAE

Cl Cl C Cl Cl N Cl Cl N O O O Cl Cl C N S S S Cl

1 1 1 1 5 1 2 2 2 2 1 1 6 4 1 1 1 1 1 3

2821.96 2821.92 284.04 2821.27 2823.22 399.98 2820.24 2820.61 406.38 530.48 529.47 528.24 2820.60 2822.69 292.49 406.46 2475.82 2470.64 2470.63 2821.61

EB3LYP/ROCIS ETD-DDT/B3LYP (eV) (eV) Metal K-edge 4863.29 4862.49 4863.09 5350.04 5353.64 5861.59 5861.29 5861.79 5862.09 6403.44 6404.13 6403.51 6958.15 6962.85 6958.30 6959.05 7547.35 7545.95 7545.45 7545.55 8150.07 8150.17 8150.47 8150.57 8781.08

∆EB3LYP/ROCIS (eV)

∆ETD-DFT/B3LYP (eV)

4862.97 4862.19 4863.02 5353.65 5354.53 5866.10 5864.88 5865.60 5864.48 6403.44 6404.37 6403.49 6961.09 6962.65 6961.66 6962.23 7547.00 7545.44 7545.71 7545.42 8152.01 8152.23 8152.27 8150.57 8781.08

-105.81 -105.64 -105.65 -113.11 -114.61 -128.95 -127.07 -129.24 -128.31 -137.88 -138.54 -138.11 -153.56 -150.10 -154.50 -153.88 -160.95 -161.85 -161.84 -160.97 -191.53 -189.23 -189.63 -189.23 -197.32

-106.13 -105.94 -105.72 -109.50 -113.72 -124.44 -123.48 -125.43 -125.92 -137.88 -138.30 -138.13 -150.62 -150.30 -151.14 -150.70 -161.30 -162.36 -161.58 -161.10 -189.59 -187.17 -187.83 -189.23 -197.32

2757.92 2757.53 274.59 2757.24 2758.00 387.59 2755.15 2755.45 385.91 516.88 517.05 515.44 2756.58 2757.63 273.54 386.18 2418.12 2413.52 2413.46 2756.45

-64.04 -64.40 -10.26 -64.03 -67.66 -13.15 -66.08 -66.09 -21.17 -13.60 -13.85 -13.06 -67.00 -67.65 -19.37 -21.29 -57.70 -57.17 -57.22 -67.23 -101.76 101.76 197.32

-64.04 -64.39 -9.45 -64.03 -65.22 -12.39 -65.09 -65.16 -20.47 -13.60 -12.43 -12.80 -64.02 -65.06 -18.95 -20.28 -57.70 -57.12 -57.17 -65.16 -101.60 101.60 197.32

Ligand K-edge 2757.92 2757.52 273.78 2757.24 2755.56 386.83 2754.16 2754.52 385.21 516.88 515.62 515.18 2753.60 2755.04 273.12 385.17 2418.12 2413.47 2413.41 2754.38

Table 13. Experimental Eexp versus calculated B3LYP/ROCIS//def2-TZVP//NoRel metal Ledge energy positions of the most intense L3 –edge feature for the complexes of the training set 2, 4, 5 and 26-42 respectively. The oxidation state of each transition metal atom in each complex is shown inside brackets, following the name of the element. The ground state


31


Page 32 of 47

multiplicities 2SGS+1 of all the studied systems are also shown. NoRel denotes that the calculations presented here in employed no relativistic corrections.

System

Element

2SGS+1

Eexp (eV)

EB3LYP/ROCIS (eV)


2 4 5 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 MSE MAE MaxAE

Ti(IV) V(III) V(IV) V(IV) V(IV) V(V) V(V) V(V) V(V) Cr(III) Mn(III) Fe(II) Fe(III) Fe(III) Co(III) Ni(II) Ni(II) Ni(III) Cu(II) Cu(II)

1 3 2 2 2 1 1 1 1 4 5 5 6 2 1 3 1 2 2 2

458.73 516.90 517.20 517.25 517.20 518.50 518.20 518.30 518.40 578.00 640.13 706.64 708.00 709.30 778.32 853.14 853.82 855.09 931.37 931.20

447.07 504.13 504.60 504.33 504.13 505.93 505.85 505.90 505.55 564.69 624.13 690.61 692.45 695.44 765.01 833.96 836.99 838.15 911.88 912.64

-11.66 -12.77 -12.60 -12.92 -13.07 -12.57 -12.35 -12.40 -12.85 -13.31 -16.00 -16.03 -15.55 -13.86 -13.31 -19.18 -16.83 -16.94 -19.49 -18.56 -14.61 14.61 19.49

Table 14. Experimental Eexp versus calculated B3LYP/ROCIS//def2-TZVP//NoRel metal Medge energy positions of the lower energy M3 –edge feature for the complexes 37, 53-55 of the training set. The oxidation state of each transition metal atom in each complex is shown inside brackets, following the name of the element. The ground state multiplicities 2SGS+1 of all the studied systems are also shown. NoRel denotes that the calculations presented here in employed no relativistic corrections. Molecule

Element

2SGS+1

Eexp. (eV)

EB3LYP/ROCIS (eV)


53 54 55 37 MSE MAE MaxAE

Fe(II) Fe(II) Co(II) Co(III)

1 5 4 1

53.79 53.37 58.55 58.96

51.67 51.44 57.74 57.01

-2.12 -1.93 -0.81 -1.95 -1.70 1.70 2.12

As in the case of the molecular CASCI/NEVPT2 calculations, these errors are very similar with the errors of the atomic B3LYP/ROCIS and TD-DFT/B3LYP energies when


32

Page 33 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


compared against the reference atomic CASCI/NEVPT2 database of element shifts (Tables S13-S15). This implies that for a given calculation protocol in terms of the chosen basis set and inclusion (or exculsion) of relativistic effects, the element shifts of any method that is calibrated against the CASCI/NEVPT2 reference database can be used to shift the calculated spectra prior to comparisons with the experiment.


33


Page 34 of 47

Figure 5. Representative experimental (black) versus calculated B3LYP/ROCIS//def2TZVP//DKH2 metal K-Edge XAS spectra for complex (a): Ti(IV)Cp2Cl2 b), ligand K-Edge XAS spectra for complexes (b): Ni(II)(BSE) and (c): [Mn(VII)O4]1-, metal L-Edge XAS spectra


34

Page 35 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


for complexes (d): V(IV)O(acac)2, (e): Ni(II)(diene)2 (f): Ni(II)(pdtc)2 and (g): [Fe(II)Cl6]4- as well as metal M-Edge XAS spectrum for complex (h): Co(II)(Tp)2 .

An example is presented in Figure 5 in which a selection of DFT/ROCIS//def2-TZVP//DKH2 calculated versus experimental XAS spectra are visualized. In all the cases, the DFT/ROCIS spectra are shifted by a reference shift that is obtained by comparing atomic DFT/ROCIS calculations against the CASCI/NEVPT2 reference database (Tables S10-S12). As it is seen in all cases, the main calculated features of the shifted spectra deviate from the respective experimental ones by 0.1-0.4 eV. Hence a direct comparison of the calculated versus the experimental XAS spectra can be performed. In all cases, very good agreement with respect to experiment is observed in terms of the number as well, as the relative intensities of the calculated spectral features. This indicates that the calibrated (against the CASCI/NEVPT2 reference database) DFT/ROCIS method can deliver first principles quality calculated XAS spectra that are directly comparable to the experiment over a large variety of chemical systems and across both K-, L- and M- edge energy ranges of X-ray absorption core spectroscopy.

7 CONCLUSIONS In this work, a detailed study on the concept of the element-specific energy shifts in K-, L- and M-edge X-ray absorption spectroscopy has been performed. A database of reference-quality theoretical element-specific shifts has been constructed based on detailed and thorough comparisons between CASCI/NEVPT2 calculations and literature reference experimental K-, L- and M-edge XAS spectra of all the neutral first-row transition metal atoms and selected second- and third-row main-group elements. In all examined cases, very good agreement between theory and experiment was observed. The mean absolute error ACS Paragon Plus Environment

35


Page 36 of 47

between the theoretical CASCI/NEVPT2 energies and the corresponding experimental ones is about 0.74 eV across all the edges. This finding applies to both the atomic and molecular XAS cases studied. In principle, the CASCI/NEVPT2 calculation protocol would be the method of choice for calculating the XAS spectra of molecules. However, the applicability of the method is presently limited by the size of the studied systems. On this basis, the constructed database serves as a unique global reference for the assessment of the accuracy of any theoretical method used to calculate XAS spectra. In this respect, two commonly used methods in the field of X-ray absorption spectroscopy, namely the B3LYP/ROCIS, and the TD-DFT/B3LYP were evaluated against the CASCI/NEVPT2 reference database of the element specific shifts. It was found that in both methods the errors follow the general trends of the core ionization energies in the different spectral areas. Hence, the larger errors were observed for the metal K-edge XAS spectra which range between ~65 and ~90 eV depending mostly whether the calculations include relativistic corrections and much less to the type of the chosen basis set. These error ranges were shown to be transferable across the edges over a large molecular set consisting of 55 transition metal complexes. Taken together, we believe that the computed reference-quality element-specific shifts database introduced in this study will aid future computational efforts in the field of X-ray absorption spectroscopy. Importantly the present studies provide a basis for more meaningful and rigorous comparison between theoretical and experimental results. The described approach can also serve as a performance evaluation tool of the employed theoretical methods. Further investigations are currently under way in our laboratory to generate data beyond the fourth row of the periodic table and to further evaluate the performance of the CASCI/NEVPT2 protocol in challenging molecular applications in the field of X-ray absorption spectroscopy. This requires a) making the CASCI/NEVPT2 protocol more usable,


36

Page 37 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


including more efficient implementations that will provide access to larger active spaces and possible expansion towards linear scaling methods and b) improving on the CASCI/NEVPT2 protocol with even more accurate multireference (MR) methods.

8 ASSOCIATED CONTENT A complete list of the molecular training set their xyz coordinates, representative analysis Tables are provided in the Supporting Information.

9 ACKNOWLEDGMENT FN, SD, DM and AC and JKK gratefully acknowledge financial support of this work by the Max Planck Society. We acknowledge SOLEIL for provision of synchrotron radiation facilities and we would like to thank Dr. Edwige Otero for assistance in using beamline DEIMOS. Dr. M. Martins and Dr. P. Wernet are kindly acknowledged for providing the atomic reference experimental L and M-edge XAS spectra. The reviewers of the manuscript are acknowledged for their constructive comments.

10 ABBREVIATIONS XAS, element-specific shifts, DFT/ROCIS, NEVPT2, ab initio, transition metal complexes, computational spectroscopy


37


Page 38 of 47

11 REFERENCES 1. DeBeer George, S.; Neese, F., Calibration of Scalar Relativistic Density Functional Theory for the Calculation of Sulfur K-Edge X-Ray Absorption Spectra. Inorg. Chem. 2010, 49, 1849-1853. 2. Lee, N.; Petrenko, T.; Bergmann, U.; Neese, F.; DeBeer, S., Probing Valence Orbital Composition with Iron Kβ X-Ray Emission Spectroscopy. J. Am. Chem. Soc. 2010, 132, 9715-9727. 3. Roemelt, M.; Maganas, D.; DeBeer, S.; Neese, F., A Combined DFT and Restricted Open-Shell Configuration Interaction Method Including Spin-Orbit Coupling: Application to Transition Metal L-Edge X-Ray Absorption Spectroscopy. J. Chem. Phys. 2013, 138, 204101. 4. Roemelt, M.; Beckwith, M. A.; Duboc, C.; Collomb, M.-N.; Neese, F.; DeBeer, S., Manganese K-Edge X-Ray Absorption Spectroscopy as a Probe of the Metal–Ligand Interactions in Coordination Compounds. Inorg. Chem. 2011, 51, 680-687. 5. Lancaster, K. M.; Roemelt, M.; Ettenhuber, P.; Hu, Y.; Ribbe, M. W.; Neese, F.; Bergmann, U.; DeBeer, S., X-Ray Emission Spectroscopy Evidences a Central Carbon in the Nitrogenase Iron-Molybdenum Cofactor. Science 2011, 334, 974-977. 6. Ament, L. J. P.; van Veenendaal, M.; Devereaux, T. P.; Hill, J. P.; van den Brink, J., Resonant Inelastic X-Ray Scattering Studies of Elementary Excitations. Rev. Mod. Phys. 2011, 83, 705-767. 7. Solomon, E. I., Spectroscopic Methods in Bioinorganic Chemistry: Blue to Green to Red Copper Sites. Inorg. Chem. 2006, 45, 8012-8025. 8. DeBeer George, S.; Metz, M.; Szilagyi, R. K.; Wang, H.; Cramer, S. P.; Lu, Y.; Tolman, W. B.; Hedman, B.; Hodgson, K. O.; Solomon, E. I., A Quantitative Description of the Ground-State Wave Function of Cua by X-Ray Absorption Spectroscopy: Comparison to Plastocyanin and Relevance to Electron Transfer. J. Am. Chem. Soc. 2001, 123, 5757-5767. 9. Solomon, E. I.; Szilagyi, R. K.; DeBeer George, S.; Basumallick, L., Electronic Structures of Metal Sites in Proteins and Models: Contributions to Function in Blue Copper Proteins. Chem. Rev. 2004, 104, 419-458. 10. Dey, A.; Jeffrey, S. P.; Darensbourg, M.; Hodgson, K. O.; Hedman, B.; Solomon, E. I., Sulfur K-Edge Xas and DFT Studies on NiII Complexes with Oxidized Thiolate Ligands: Implications for the Roles of Oxidized Thiolates in the Active Sites of Fe and Co Nitrile Hydratase. Inorg. Chem. 2007, 46, 4989-4996. 11. Solomon, E. I.; Hedman, B.; Hodgson, K. O.; Dey, A.; Szilagyi, R. K., Ligand KEdge X-Ray Absorption Spectroscopy: Covalency of Ligand–Metal Bonds. Coord. Chem. Rev. 2005, 249, 97-129. 12. DeBeer George, S.; Petrenko, T.; Neese, F., Prediction of Iron K-Edge Absorption Spectra Using Time-Dependent Density Functional Theory. J. Phys. Chem. A. 2009, 112, 12936. 13. Rees, J. A.; Bjornsson, R.; Schlesier, J.; Sippel, D.; Einsle, O.; DeBeer, S., The Fe–V Cofactor of Vanadium Nitrogenase Contains an Interstitial Carbon Atom. Angew. Chem. 2015, 127, 13447-13450. 14. Goswami, M.; Lyaskovskyy, V.; Domingos, S. R.; Buma, W. J.; Woutersen, S.; Troeppner, O.; Ivanović-Burmazović, I.; Lu, H.; Cui, X.; Zhang, X. P., et al., Characterization of Porphyrin-Co(III)-‘Nitrene Radical’ Species Relevant in Catalytic Nitrene Transfer Reactions. J. Am. Chem. Soc. 2015, 137, 5468-5479. 15. Castillo, R. G.; Banerjee, R.; Allpress, C. J.; Rohde, G. T.; Bill, E.; Que, L.; Lipscomb, J. D.; DeBeer, S., High-Energy-Resolution Fluorescence-Detected X-Ray


38

Page 39 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Absorption of the Q Intermediate of Soluble Methane Monooxygenase. J. Am. Chem. Soc. 2017, 139, 18024-18033. 16. Kowalska, J. K.; Nayyar, B.; Rees, J. A.; Schiewer, C. E.; Lee, S. C.; Kovacs, J. A.; Meyer, F.; Weyhermüller, T.; Otero, E.; DeBeer, S., Iron L2,3-Edge X-Ray Absorption and X-Ray Magnetic Circular Dichroism Studies of Molecular Iron Complexes with Relevance to the FeMoco and FeVco Active Sites of Nitrogenase. Inorg. Chem. 2017, 56, 8147-8158. 17. Mann, K., Near-Edge X-Ray Absorption Fine Structure Measurements Using a Laboratory-Scale XUV Source. In Short Wavelength Laboratory Sources: Principles and Practices, The Royal Society of Chemistry: 2015; pp 407-413. 18. Mantouvalou, I.; Lachmann, T.; Singh, S. P.; Vogel-Mikus, K.; Kanngiesser, B., Advanced Absorption Correction for 3d Elemental Images Applied to the Analysis of Pearl Millet Seeds Obtained with a Laboratory Confocal Micro X-Ray Fluorescence Spectrometer. Anal. Chem. 2017, 89, 5453-5460. 19. Mantouvalou, I.; Witte, K.; Martyanov, W.; Jonas, A.; Grotzsch, D.; Streeck, C.; Lochel, H.; Rudolph, I.; Erko, A.; Stiel, H., et al., Single Shot near Edge X-Ray Absorption Fine Structure Spectroscopy in the Laboratory. Appl. Phys. Lett. 2016, 108. 20. Peth, C.; Barkusky, F.; Mann, K., Near-Edge X-Ray Absorption Fine Structure Measurements Using a Laboratory-Scale Xuv Source. J. Phys. D: Appl. Phys. 2008, 41. 21. Sakurai, K.; Guo, X. M., Recent Performance of Laboratory-Scale X-Ray Absorption Fine Structure Instruments. Spectrochim. Acta, Part B 1999, 54, 99-107. 22. Seidler, G. T.; Mortensen, D. R.; Remesnik, A. J.; Pacold, J. I.; Ball, N. A.; Barry, N.; Styczinski, M.; Hoidn, O. R., A Laboratory-Based Hard X-Ray Monochromator for HighResolution X-Ray Emission Spectroscopy and X-Ray Absorption Near Edge Structure Measurements. Rev. Sci. Instrum. 2014, 85. 23. Koziej, D.; DeBeer, S., Application of Modern X-Ray Spectroscopy in Chemistry— Beyond Studying the Oxidation State. Chem. Mater. 2017, 29, 7051-7053. 24. de Groot, F. M. F.; Kotani, A., Core Level Spectroscopy of Solids. CRC Press: 2008. 25. de Groot, F. M. F., X-Ray Absorption and Dichroism of Transition Metals and Their Compounds. J. Electron. Spectrosc. Relat. Phenom. 1994, 67, 529-622. 26. de Groot, F. M. F., Multiplet Effects in X-Ray Spectroscopy. Coord. Chem. Rev. 2005, 249, 31-63. 27. Thole, B. T.; van der Laan, G., Branching Ratio in X-Ray Absorption Spectroscopy. Phys. Rev. B: Condens. Matter 1988, 38, 3158-3171. 28. van der Laan, G.; Thole, B. T.; Sawatzky, G. A.; Verdaguer, M., Multiplet Structure in the L2,3 X-Ray-Absorption Spectra: A Fingerprint for High- and Low-Spin Ni2+ Compounds. Phys. Rev. B: Condens. Matter 1988, 37, 6587-6589. 29. De Francesco, R.; Stener, M.; Fronzoni, G., Computational Investigation of the L2,3Edge Spectra of Bulk and (110) Surface of Rutile TiO2. Surf. Sci. 2011, 605, 500-506. 30. Fronzoni, G.; Stener, M.; Decleva, P.; Wang, F.; Ziegler, T.; van Lenthe, E.; Baerends, E. J., Spin–Orbit Relativistic Time Dependent Density Functional Theory Calculations for the Description of Core Electron Excitations: TiCl4 Case Study. Chem. Phys. Lett. 2005, 416, 56-63. 31. Landmann, M.; Rauls, E.; Schmidt, W. G., The Electronic Structure and Optical Response of Rutile, Anatase and Brookite TiO2. J. Phys.: Condens. Matter 2012, 24, 195503. 32. Laskowski, R.; Blaha, P., Understanding the L2, L3 X-Ray Absorption Spectra of Early 3d Transition Elements. Phys. Rev. B: Condens. Matter 2010, 82, 205104. 33. Vinson, J.; Rehr, J. J., Ab Initio Bethe-Salpeter Calculations of the X-Ray Absorption Spectra of Transition Metals at the L-Shell Edges. Phys. Rev. B: Condens. Matter 2012, 86. 34. Brik, M. G.; Ogasawara, K.; Ikeno, H.; Tanaka, I., Fully Relativistic Calculations of the L2,3-Edge Xanes Spectra for Vanadium Oxides. Eur. Phys. J. B. 2006, 51, 345-355.


39


Page 40 of 47

35. Ikeno, H.; Mizoguchi, T.; Koyama, Y.; Kumagai, Y.; Tanaka, I., First-Principles Multi-Electron Calculations for L2,3 ELNES/XANES of 3d Transition Metal Monoxides. Ultramicroscopy 2006, 106, 970-5. 36. Ikeno, H.; Mizoguchi, T.; Tanaka, I., Ab Initio Charge Transfer Multiplet Calculations on the L2,3 XANES and ELNES of 3d Transition Metal Oxides. Phys. Rev. B: Condens. Matter 2011, 83, 155107. 37. Ikeno, H.; Tanaka, I., Effects of Breit Interaction on the L2,3 X-Ray Absorption NearEdge Structures of 3d Transition Metals. Phys. Rev. B: Condens. Matter 2008, 77, 075127. 38. Ikeno, H.; Tanaka, I.; Koyama, Y.; Mizoguchi, T.; Ogasawara, K., First-Principles Multielectron Calculations of Ni L2,3 NEXAFS and ELNES for LiNiO2 and Related Compounds. Phys. Rev. B: Condens. Matter 2005, 72, 075123. 39. Kumagai, Y.; Ikeno, H.; Oba, F.; Matsunaga, K.; Tanaka, I., Effects of Crystal Structure on Co-L2,3 X-Ray Absorption Near-Edge Structure and Electron-Energy-Loss NearEdge Structure of Trivalent Cobalt Oxides. Phys. Rev. B: Condens. Matter 2008, 77, 155124. 40. Ogasawara, K.; Iwata, T.; Koyama, Y.; Ishii, T.; Tanaka, I.; Adachi, H., Relativistic Cluster Calculation of Ligand-Field Multiplet Effects on Cation L2,3 X-Ray-Absorption Edges of SrTiO3, NiO, and CaF2. Phys. Rev. B: Condens. Matter 2001, 64, 115413. 41. Maganas, D.; Roemelt, M.; Havecker, M.; Trunschke, A.; Knop-Gericke, A.; Schlögl, R.; Neese, F., First Principles Calculations of the Structure and V L-Edge X-Ray Absorption Spectra of V2O5 Using Local Pair Natural Orbital Coupled Cluster Theory and Spin-Orbit Coupled Configuration Interaction Approaches. Phys. Chem. Chem. Phys. 2013, 15, 7260-76. 42. Maganas, D.; Roemelt, M.; Weyhermuller, T.; Blume, R.; Havecker, M.; KnopGericke, A.; DeBeer, S.; Schlögl, R.; Neese, F., L-Edge X-Ray Absorption Study of Mononuclear Vanadium Complexes and Spectral Predictions Using a Restricted Open Shell Configuration Interaction Ansatz. Phys. Chem. Chem. Phys. 2014, 16, 264-76. 43. Roemelt, M.; Neese, F., Excited States of Large Open-Shell Molecules: An Efficient, General, and Spin-Adapted Approach Based on a Restricted Open-Shell Ground State Wave Function. J. Phys. Chem. A 2013, 117, 3069-83. 44. Wenzel, J.; Wormit, M.; Dreuw, A., Calculating Core-Level Excitations and X-Ray Absorption Spectra of Medium-Sized Closed-Shell Molecules with the AlgebraicDiagrammatic Construction Scheme for the Polarization Propagator. J. Comput. Chem. 2014, 35, 1900-1915. 45. Zhang, Y.; Biggs, J. D.; Healion, D.; Govind, N.; Mukamel, S., Core and Valence Excitations in Resonant X-Ray Spectroscopy Using Restricted Excitation Window TimeDependent Density Functional Theory. J. Chem. Phys. 2012, 137, 194306. 46. Besley, N. A., Fast Time-Dependent Density Functional Theory Calculations of the X-Ray Absorption Spectroscopy of Large Systems. J. Chem. Theory Comput. 2016, 12, 5018-5025. 47. Myhre, R. H.; Coriani, S.; Koch, H., Near-Edge X-Ray Absorption Fine Structure within Multilevel Coupled Cluster Theory. J. Chem. Theory Comput. 2016, 12, 2633-2643. 48. Atanasov, M.; Ganyushin, D.; Sivalingam, K.; Neese, F., A Modern First-Principles View on Ligand Field Theory through the Eyes of Correlated Multireference Wavefunctions. In Molecular Electronic Structures of Transition Metal Complexes II, Mingos, D. M. P.; Day, P.; Dahl, J. P., Eds. Springer Berlin Heidelberg: Berlin, Heidelberg, 2012; pp 149-220. 49. Van Kuiken, B. E.; Hahn, A. W.; Maganas, D.; DeBeer, S., Measuring Spin-Allowed and Spin-Forbidden D–D Excitations in Vanadium Complexes with 2p3d Resonant Inelastic X-Ray Scattering. Inorg. Chem. 2016, 55, 11497. 50. DeBeer George, S.; Petrenko, T.; Neese, F., Time-Dependent Density Functional Calculations of Ligand K-Edge X-Ray Absorption Spectra. Inorg. Chim. Acta 2008, 361, 965-972.


40

Page 41 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


51. Besley, N. A.; Noble, A., Time-Dependent Density Functional Theory Study of the X-Ray Absorption Spectroscopy of Acetylene, Ethylene, and Benzene on Si(100). J. Phys. Chem. C 2007, 111, 3333-3340. 52. Bjornsson, R.; Delgado-Jaime, M. U.; Lima, F. A.; Sippel, D.; Schlesier, J.; Weyhermuller, T.; Einsle, O.; Neese, F.; DeBeer, S., Molybdenum L-Edge Xas Spectra of MoFe Nitrogenase. Z. Anorg. Allg. Chem. 2015, 641, 65-71. 53. Casarin, M.; Finetti, P.; Vittadini, A.; Wang, F.; Ziegler, T., Spin-Orbit Relativistic Time-Dependent Density Functional Calculations of the Metal and Ligand Pre-Edge Xas Intensities of Organotitanium Complexes: TiCl4, Ti(eta5-C5H5)Cl3, and Ti(eta5-C5H5)2Cl2. J. Phys. Chem. A 2007, 111, 5270-5279. 54. Daly, S. R.; Keith, J. M.; Batista, E. R.; Boland, K. S.; Clark, D. L.; Kozimor, S. A.; Martin, R. L., Sulfur K-Edge X-Ray Absorption Spectroscopy and Time-Dependent Density Functional Theory of Dithiophosphinate Extractants: Minor Actinide Selectivity and Electronic Structure Correlations. J. Am. Chem. Soc. 2012, 134, 14408-14422. 55. do Couto, P. C.; Hollas, D.; Slavicek, P., On the Performance of Optimally Tuned Range-Separated Hybrid Functionals for X-Ray Absorption Modeling. J. Chem. Theory Comput. 2015, 11, 3234-3244. 56. Donahue, C. M.; McCollom, S. P.; Forrest, C. M.; Blake, A. V.; Bellott, B. J.; Keith, J. M.; Daly, S. R., Impact of Coordination Geometry, Bite Angle, and Trans Influence on Metal-Ligand Covalency in Phenyl-Substituted Phosphine Complexes of Ni and Pd. Inorg. Chem. 2015, 54, 5646-5659. 57. Donahue, C. M.; Pacheco, J. S. L.; Keith, J. M.; Daly, S. R., Sulfur K-Edge X-Ray Absorption Spectroscopy and Time-Dependent Density Functional Theory of Arsenic Dithiocarbamates. J. Chem. Soc., Dalton Trans. 2014, 43, 9189-9201. 58. Frank, P.; Szilagyi, R. K.; Gramlich, V.; Hsu, H. F.; Hedman, B.; Hodgson, K. O., Spin-Polarization-Induced Preedge Transitions in the Sulfur K-Edge Xas Spectra of OpenShell Transition-Metal Sulfates: Spectroscopic Validation of Sigma-Bond Electron Transfer. Inorg. Chem. 2017, 56, 1080-1093. 59. Fronzoni, G.; Francesco, R.; Stener, M.; Causa, M., X-Ray Absorption Spectroscopy of Titanium Oxide by Time Dependent Density Functional Calculations. J. Phys. Chem. B 2006, 110, 9899-9907. 60. Fronzoni, G.; Stener, M.; Reduce, A.; Decleva, P., Time-Dependent Density Functional Theory Calculations of Ligand K Edge and Metal L Edge X-Ray Absorption of a Series of Oxomolybdenum Complexes. J. Phys. Chem. A 2004, 108, 8467-8477. 61. Lee, K.; Wei, H. C.; Blake, A. V.; Donahue, C. M.; Keith, J. M.; Daly, S. R., Ligand K-Edge XAS, DFT, and TDDFT Analysis of Pincer Linker Variations in Rh(I) PNP Complexes: Reactivity Insights from Electronic Structure. J. Chem. Soc., Dalton Trans. 2016, 45, 9774-9785. 62. Lee, Y. W.; Hsu, I. J., Theoretical Analysis of Fe K-Edge Xanes on Mononitrosyl Iron Complex (NO)Fe(S2C6H4)2 PNP. J. Chin. Chem. Soc. 2013, 60, 935-941. 63. Lestrange, P. J.; Nguyen, P. D.; Li, X. S., Calibration of Energy-Specific TDDFT for Modeling K-Edge XAS Spectra of Light Elements. J. Chem. Theory Comput. 2015, 11, 29942999. 64. Liang, W.; Fischer, S. A.; Frisch, M. J.; Li, X. S., Energy-Specific Linear Response TDHF/TDDFT for Calculating High-Energy Excited States. J. Chem. Theory Comput. 2011, 7, 3540-3547. 65. Lima, F. A.; Bjornsson, R.; Weyhermuller, T.; Chandrasekaran, P.; Glatzel, P.; Neese, F.; DeBeer, S., High-Resolution Molybdenum K-Edge X-Ray Absorption Spectroscopy Analyzed with Time-Dependent Density Functional Theory. Phys. Chem. Chem. Phys. 2013, 15, 20911-20920.


41


Page 42 of 47

66. Loble, M. W.; Keith, J. M.; Altman, A. B.; Stieber, S. C. E.; Batista, E. R.; Boland, K. S.; Conradson, S. D.; Clark, D. L.; Pacheco, J. L.; Kozimor, S. A., et al., Covalency in Lanthanides. An X-Ray Absorption Spectroscopy and Density Functional Theory Study of LnCl6(X-) (X=3, 2). J. Am. Chem. Soc. 2015, 137, 2506-2523. 67. Minasian, S. G.; Keith, J. M.; Batista, E. R.; Boland, K. S.; Kozimor, S. A.; Martin, R. L.; Shuh, D. K.; Tyliszczak, T.; Vernon, L. J., Carbon K-Edge X-Ray Absorption Spectroscopy and Time-Dependent Density Functional Theory Examination of Metal-Carbon Bonding in Metallocene Dichlorides. J. Am. Chem. Soc. 2013, 135, 14731-14740. 68. Olson, A. C.; Keith, J. M.; Batista, E. R.; Boland, K. S.; Daly, S. R.; Kozimor, S. A.; MacInnes, M. M.; Martin, R. L.; Scott, B. L., Using Solution- and Solid-State S K-Edge XRay Absorption Spectroscopy with Density Functional Theory to Evaluate M-S Bonding for MS4(2-) (M = Cr, Mo, W) Dianions. J. Chem. Soc., Dalton Trans. 2014, 43, 17283-17295. 69. Peng, B.; Lestrange, P. J.; Goings, J. J.; Caricato, M.; Li, X. S., Energy-Specific Equation-of-Motion Coupled-Cluster Methods for High-Energy Excited States: Application to K-Edge X-Ray Absorption Spectroscopy. J. Chem. Theory Comput. 2015, 11, 4146-4153. 70. Salassa, L.; Ruiu, T.; Garino, C.; Pizarro, A. M.; Bardelli, F.; Gianolio, D.; Westendorf, A.; Bednarski, P. J.; Lamberti, C.; Gobetto, R., et al., EXAFS, DFT, LightInduced Nucleobase Binding, and Cytotoxicity of the Photoactive Complex Cis[Ru(bpy)2(CO)Cl]+. Organometallics 2010, 29, 6703-6710. 71. Spencer, L. P.; Yang, P.; Minasian, S. G.; Jilek, R. E.; Batista, E. R.; Boland, K. S.; Boncella, J. M.; Conradson, S. D.; Clark, D. L.; Hayton, T. W., et al., Tetrahalide Complexes of the [U(NR)2]2+ Ion: Synthesis, Theory, and Chlorine K-Edge X-Ray Absorption Spectroscopy. J. Am. Chem. Soc. 2013, 135, 2279-2290. 72. Bagus, P. S.; Freund, H.; Kuhlenbeck, H.; Ilton, E. S., A New Analysis of X-Ray Adsorption Branching Ratios: Use of Russell-Saunders Coupling. Chem. Phys. Lett. 2008, 455, 331-334. 73. Miedema, P. S.; Ikeno, H.; Groot, F. M. F. d., First Principles Multiplet Calculations of the Calcium L2, 3 X-Ray Absorption Spectra of CaO and CaF2. J. Phys.: Condens. Matter 2011, 23, 145501. 74. Haverkort, M. W.; Zwierzycki, M.; Andersen, O. K., Multiplet Ligand-Field Theory Using Wannier Orbitals. Phys. Rev. B: Condens. Matter 2012, 85, 165113. 75. Josefsson, I.; Kunnus, K.; Schreck, S.; Föhlisch, A.; de Groot, F.; Wernet, P.; Odelius, M., Ab Initio Calculations of X-Ray Spectra: Atomic Multiplet and Molecular Orbital Effects in a Multiconfigurational SCF Approach to the L-Edge Spectra of Transition Metal Complexes. J. Phys. Chem. Let. 2012, 3, 3565-3570. 76. Wernet, P.; Kunnus, K.; Schreck, S.; Quevedo, W.; Kurian, R.; Techert, S.; de Groot, F. M. F.; Odelius, M.; Föhlisch, A., Dissecting Local Atomic and Intermolecular Interactions of Transition-Metal Ions in Solution with Selective X-Ray Spectroscopy. J. Phys. Chem. Let. 2012, 3, 3448-3453. 77. Kunnus, K.; Josefsson, I.; Schreck, S.; Quevedo, W.; Miedema, P. S.; Techert, S.; de Groot, F. M. F.; Odelius, M.; Wernet, P.; Föhlisch, A., From Ligand Fields to Molecular Orbitals: Probing the Local Valence Electronic Structure of Ni2+ in Aqueous Solution with Resonant Inelastic X-Ray Scattering. J. Phys. Chem. B 2013, 117, 16512-16521. 78. Wernet, P.; Kunnus, K.; Josefsson, I.; Rajkovic, I.; Quevedo, W.; Beye, M.; Schreck, S.; Grubel, S.; Scholz, M.; Nordlund, D., et al., Orbital-Specific Mapping of the Ligand Exchange Dynamics of Fe(CO)5 in Solution. Nature 2015, 520, 78-81. 79. Bokarev, S. I.; Khan, M.; Abdel-Latif, M. K.; Xiao, J.; Hilal, R.; Aziz, S. G.; Aziz, E. F.; Kühn, O., Unraveling the Electronic Structure of Photocatalytic Manganese Complexes by L-Edge X-Ray Spectroscopy. J. Phys. Chem. C 2015, 119, 19192-19200.


42

Page 43 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


80. Kunnus, K.; Josefsson, I.; Rajkovic, I.; Schreck, S.; Quevedo, W.; Beye, M.; Weniger, C.; Grübel, S.; Scholz, M.; Nordlund, D., et al., Identification of the Dominant Photochemical Pathways and Mechanistic Insights to the Ultrafast Ligand Exchange of Fe(CO)5 to Fe(CO)4EtOH. Struct. Dyn. 2016, 3, 043204. 81. J. Schlappa, K.; Wohlfeld, K.; J. Zhou; Mourigal, M.; M. W. Haverkort; V. N.Strocov; Hozoi, L.; Monney, C.; Nishimoto, S.; Singh, S., et al., Spin-Orbital Separation in the Quasi 1d Mott-Insulator Sr2CuO3. arXiv:1205.1954. 82. Maganas, D.; Kristiansen, P.; Duda, L.-C.; Knop-Gericke, A.; DeBeer, S.; Schlögl, R.; Neese, F., Combined Experimental and Ab Initio Multireference Configuration Interaction Study of the Resonant Inelastic X-Ray Scattering Spectrum of CO2. J. Phys. Chem. C 2014, 118, 20163-20175. 83. Maganas, D.; Trunschke, A.; Schlogl, R.; Neese, F., A Unified View on Heterogeneous and Homogeneous Catalysts through a Combination of Spectroscopy and Quantum Chemistry. Faraday Discuss. 2016, 188, 181-197. 84. Carlotto, S.; Sambi, M.; Sedona, F.; Vittadini, A.; Bartolome, J.; Bartolome, F.; Casarin, M., L2,3-Edges Absorption Spectra of a 2d Complex System: A Theoretical Modelling. Phys. Chem. Chem. Phys. 2016, 18, 28110-28116. 85. Carlotto, S.; Sambi, M.; Vittadini, A.; Casarin, M., Theoretical Modeling of the L2,3Edge X-Ray Absorption Spectra of Mn(acac)2 and Co(acac)2 Complexes. Phys. Chem. Chem. Phys. 2016, 18, 2242-2249. 86. Walroth, R. C.; Lukens, J. T.; MacMillan, S. N.; Finkelstein, K. D.; Lancaster, K. M., Spectroscopic Evidence for a 3d10 Ground State Electronic Configuration and Ligand Field Inversion in [Cu(CF3)4]1–. J. Am. Chem. Soc. 2016, 138, 1922-1931. 87. Xiao, J.; Golnak, R.; Atak, K.; Pfluger, M.; Pohl, M.; Suljoti, E.; Winter, B.; Aziz, E. F., Assistance of the Iron Porphyrin Ligands to the Binding Interaction between the Fe Center and Small Molecules in Solution. J. Phys. Chem. B 2014, 118, 9371-9377. 88. Atak, K.; Golnak, R.; Xiao, J.; Pfluger, M.; Brandenburg, T.; Winter, B.; Aziz, E. F., Co(III) Protoporphyrin Ix Chloride in Solution: Spin-State and Metal Coordination Revealed from Resonant Inelastic X-Ray Scattering and Electronic Structure Calculations. Phys. Chem. Chem. Phys. 2015, 17, 3409-3414. 89. Maganas, D.; DeBeer, S.; Neese, F., A Pair Natural Orbitals Restricted Open Shell Configuration Interaction (PNO-ROCIS) Approach for Calculating X-Ray Absorption Spectra of Large Chemical Systems. J. Phys. Chem. A 2018. 90. Beckwith, M. A.; Roemelt, M.; Collomb, M.-N. l.; DuBoc, C.; Weng, T.-C.; Bergmann, U.; Glatzel, P.; Neese, F.; DeBeer, S., Manganese Kβ X-Ray Emission Spectroscopy as a Probe of Metal–Ligand Interactions. Inorg. Chem. 2011, 50, 8397-8409. 91. Rees, J. A.; Wandzilak, A.; Maganas, D.; Wurster, N. I. C.; Hugenbruch, S.; Kowalska, J. K.; Pollock, C. J.; Lima, F. A.; Finkelstein, K. D.; DeBeer, S., Experimental and Theoretical Correlations between Vanadium K-Edge X-Ray Absorption and Kβ Emission Spectra. J. Biol. Inorg. Chem. 2016, 21, 793-805. 92. Roos, B. O.; Taylor, P. R.; Siegbahn, P. E. M., A Complete Active Space SCF Method (CASSCF) Using a Density-Matrix Formulated Super-CI Approach. Chem. Phys. 1980, 48, 157-173. 93. Siegbahn, P. E. M.; Almlof, J.; Heiberg, A.; Roos, B. O., The Complete Active Space SCF (CASSCF) Method in a Newton-Raphson Formulation with Application to the HNO Molecule. J. Chem. Phys. 1981, 74, 2384-2396. 94. Angeli, C.; Cimiraglia, R.; Evangelisti, S.; Leininger, T.; Malrieu, J.-P., Introduction of N-Electron Valence States for Multireference Perturbation Theory. J. Chem. Phys. 2001, 114, 10252-10264.


43


Page 44 of 47

95. Angeli, C.; Cimiraglia, R., Multireference Perturbation Configuration Interaction V. Third-Order Energy Contributions in the Møller–Plesset and Epstein–Nesbet Partitions. Theor. Chem. Acc. 2002, 107, 313-317. 96. P.J. Linstrom and W.G. Mallard; Eds., Nist Chemistry Webbook, Nist Standard Reference Database Number 69. National Institute of Standards and Technology, Gaithersburg 2017; Vol. 20899. 97. Müller, A.; Borovik, A.; Buhr, T.; Hellhund, J.; Holste, K.; Kilcoyne, A. L. D.; Klumpp, S.; Martins, M.; Ricz, S.; Viefhaus, J., et al., Observation of a Four-Electron Auger Process in Near K-Edge Photoionization of Singly Charged Carbon Ions. Phys. Rev. Lett. 2015, 114, 013002. 98. Gharaibeh, M. F.; Bizau, J. M.; Cubaynes, D.; Guilbaud, S.; Hassan, N. E.; Shorman, M. M. A.; Miron, C.; Nicolas, C.; Robert, E.; Blancard, C., et al., K-Shell Photoionization of Singly Ionized Atomic Nitrogen: Experiment and Theory. J. Phys. B: At., Mol. Opt. Phys. 2011, 44, 175208. 99. Kawatsura, K.; Yamaoka, H.; Oura, M.; Hayaishi, T.; Sekioka, T.; Agui, A.; Yoshigoe, A.; Koike, F., The 1s–2p Resonance Photoionization Measurement of O + Ions in Comparison with an Isoelectronic Species Ne 3+. J. Phys. B: At., Mol. Opt. Phys. 2002, 35, 4147. 100. Arp, U.; Lagutin, B. M.; Materlik, G.; Petrov, I. D.; Sonntag, B.; Sukhorukov, V. L., K-Absorption Spectra of Atomic Ca, Cr, Mn and Cu. J. Phys. B: At., Mol. Opt. Phys. 1993, 26, 4381. 101. Michael, M.; Kai, G.; Tobias, R.; Philippe, W.; Peter, Z., Open Shells and MultiElectron Interactions: Core Level Photoionization of the 3d Metal Atoms. J. Phys. B: At., Mol. Opt. Phys. 2006, 39, R79. 102. Whitfield, S. B.; Kehoe, K.; Wehlitz, R.; Krause, M. O.; Caldwell, C. D., Photoelectron Spectrometry of Atomic Scandium in the Region of the 3p→3d Giant Resonance. Phys. Rev. A 2001, 64, 022701. 103. Whitfield, S. B.; Krosschell, B. D.; Wehlitz, R., Photoelectron Spectrometry of Atomic Chromium in the Region of the 3p → 3d Giant Resonance. J. Phys. B: At., Mol. Opt. Phys. 2004, 37, 3435. 104. Feist, H.; Feldt, M.; Gerth, C.; Martins, M.; Sladeczek, P.; Zimmermann, P., 3pPhotoionization Resonances of Atomic Fe, Co, and Ni Studied by the Observation of Singly and Doubly Charged Photoions. Phys. Rev. A 1996, 53, 760-765. 105. Costello, J. T.; Kennedy, E. T.; Sonntag, B. F.; Clark, C. W., 3p Photoabsorption of Free and Bound Cr, Cr+, Mn, and Mn+ . Phys. Rev. A 1991, 43, 1441-1450. 106. Richter, T.; Godehusen, K.; Martins, M.; Wolff, T.; Zimmermann, P., Interplay of Intra-Atomic and Interatomic Effects: An Investigation of the 2p Core Level Spectra of Atomic Fe and Molecular FeCl2. Phys. Rev. Lett. 2004, 93, 023002. 107. Godehusen, K.; Richter, T.; Zimmermann, P.; Martins, M., 2p Photoionization of Atomic Ni: A Comparison with Ni Metal and Nio Photoionization. Phys. Rev. Lett. 2002, 88, 217601. 108. Nagata, T.; Kawajiri, K.; Kosugi, S.; Suzuki, N.; Kemmotsu, M.; Nandi, T.; Sokell, E.; Azuma, Y.; Koike, F., Photoion Spectroscopy on Isolated Mn Atoms in the 2p → 3d Excitation Region: I. Total Photoion-Yield Spectrum. J. Phys. B: At., Mol. Opt. Phys. 2014, 47, 185006. 109. Diehl, S.; Cubaynes, D.; Bizau, J. M.; Wuilleumier, F. J.; Kennedy, E. T.; Mosnier, J. P.; Morgan, T. J., New High-Resolution Measurements of Doubly Excited States of Li +. J. Phys. B: At., Mol. Opt. Phys. 1999, 32, 4193.


44

Page 45 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


110. DeBeer George, S.; Brant, P.; Solomon, E. I., Metal and Ligand K-Edge XAS of Organotitanium Complexes: Metal 4p and 3d Contributions to Pre-Edge Intensity and Their Contributions to Bonding. J. Am. Chem. Soc. 2005, 127, 667-674. 111. Scarborough, C. C.; Sproules, S.; Weyhermüller, T.; DeBeer, S.; Wieghardt, K., Electronic and Molecular Structures of the Members of the Electron Transfer Series [Cr(Tbpy)3]N (N = 3+, 2+, 1+, 0): An X-Ray Absorption Spectroscopic and Density Functional Theoretical Study. Inorg. Chem. 2011, 50, 12446-12462. 112. Hall, E. R.; Pollock, C. J.; Bendix, J.; Collins, T. J.; Glatzel, P.; DeBeer, S., Valenceto-Core-Detected X-Ray Absorption Spectroscopy: Targeting Ligand Selectivity. J. Am. Chem. Soc. 2014, 136, 10076-10084. 113. Chandrasekaran, P.; Stieber, S. C. E.; Collins, T. J.; Que, J. L.; Neese, F.; DeBeer, S., Prediction of High-Valent Iron K-Edge Absorption Spectra by Time-Dependent Density Functional Theory. J. Chem. Soc., Dalton Trans. 2011, 40, 11070-11079. 114. Sano, M., Xanes Study at the Co-K Absorption Edge in a Series of Cobalt(Iii) Complexes. Inorg. Chem. 1988, 27, 4249-4253. 115. Colpas, G. J.; Maroney, M. J.; Bagyinka, C.; Kumar, M.; Willis, W. S.; Suib, S. L.; Mascharak, P. K.; Baidya, N., X-Ray Spectroscopic Studies of Nickel Complexes, with Application to the Structure of Nickel Sites in Hydrogenases. Inorg. Chem. 1991, 30, 920928. 116. Collison, D.; David Garner, C.; Grigg, J.; M. McGrath, C.; Frederick W. Mosselmans, J.; Pidcock, E.; D. Roper, M.; M. W. Seddon, J.; Sinn, E.; A. Tasker, P., et al., X-Ray Absorption Fine Structure Study of the Bound State Electronic Transitions at the Vanadium K and L Edges in Low Symmetry, Molecular, Vanadium-(IV) and -(V) Complexes with Oxyoxime and Oxyoximate Ligands. J. Chem. Soc., Dalton Trans. 1998, 2199-2204. 117. Wasinger, E. C.; de Groot, F. M. F.; Hedman, B.; Hodgson, K. O.; Solomon, E. I., LEdge X-Ray Absorption Spectroscopy of Non-Heme Iron Sites: Experimental Determination of Differential Orbital Covalency. J. Am. Chem. Soc. 2003, 125, 12894-12906. 118. Hocking, R. K.; Wasinger, E. C.; de Groot, F. M. F.; Hodgson, K. O.; Hedman, B.; Solomon, E. I., Fe L-Edge XAS Studies of K4[Fe(CN)6] and K3[Fe(CN)6]: A Direct Probe of Back-Bonding. J. Am. Chem. Soc. 2006, 128, 10442-10451. 119. Wang, H.; Ralston, C. Y.; Patil, D. S.; Jones, R. M.; Gu, W.; Verhagen, M.; Adams, M.; Ge, P.; Riordan, C.; Marganian, C. A., et al., Nickel L-Edge Soft X-Ray Spectroscopy of Nickel−Iron Hydrogenases and Model Compoundsevidence for High-Spin Nickel(Ii) in the Active Enzyme. J. Am. Chem. Soc. 2000, 122, 10544-10552. 120. George, S. J.; Lowery, M. D.; Solomon, E. I.; Cramer, S. P., Copper L-Edge Spectral Studies: A Direct Experimental Probe of the Ground-State Covalency in the Blue Copper Site in Plastocyanin. J. Am. Chem. Soc. 1993, 115, 2968-2969. 121. Nardi, M. V.; Detto, F.; Aversa, L.; Verucchi, R.; Salviati, G.; Iannotta, S.; Casarin, M., Electronic Properties of CuPc and H2Pc: An Experimental and Theoretical Study. Phys. Chem. Chem. Phys. 2013, 15, 12864-12881. 122. Zhang, Y.; Learmonth, T.; Wang, S.; Matsuura, A. Y.; Downes, J.; Plucinski, L.; Bernardis, S.; O'Donnell, C.; Smith, K. E., Electronic Structure of the Organic Semiconductor Vanadyl Phthalocyanine (VO-Pc). J. Mater. Chem. 2007, 17, 1276-1283. 123. Minasian, S. G.; Keith, J. M.; Batista, E. R.; Boland, K. S.; Bradley, J. A.; Daly, S. R.; Kozimor, S. A.; Lukens, W. W.; Martin, R. L.; Nordlund, D., et al., Covalency in Metal– Oxygen Multiple Bonds Evaluated Using Oxygen K-Edge Spectroscopy and Electronic Structure Theory. J. Am. Chem. Soc. 2013, 135, 1864-1871. 124. De Francesco, R.; Stener, M.; Fronzoni, G., Theoretical Study of Near-Edge X-Ray Absorption Fine Structure Spectra of Metal Phthalocyanines at C and N K-Edges. J. Phys. Chem. A 2012, 116, 2885-2894.


45


Page 46 of 47

125. Zhang, K.; Lin, M.-F.; Ryland, E. S.; Verkamp, M. A.; Benke, K.; de Groot, F. M. F.; Girolami, G. S.; Vura-Weis, J., Shrinking the Synchrotron: Tabletop Extreme Ultraviolet Absorption of Transition-Metal Complexes. J. Phys. Chem. Let. 2016, 7, 3383-3387. 126. Neese, F., The Orca Program System. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2012, 2, 73-78. 127. Becke, A. D., Density-Functional Exchange-Energy Approximation with Correct Asymptotic-Behaviour. Phys. Rev. A 1988, 38, 3098-3100. 128. Perdew, J. P., Density-Functional Approximation for the Correlation-Energy of the Inhomogeneous Electron-Gas. Phys. Rev. B 1986, 33, 8822-8824. 129. Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H., A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. AIP: 2010; Vol. 132, p 154104. 130. Grimme, S.; Ehrlich, S.; Goerigk, L., Effect of the Damping Function in Dispersion Corrected Density Functional Theory. J. Comput. Chem. 2011, 32, 1456-1465. 131. Douglas, M.; Kroll, N. M., Quantum Electrodynamical Corrections to the Fine Structure of Helium. Annals of Physics 1974, 82, 89-155. 132. Hess, B. A., Relativistic Electronic-Structure Calculations Employing a TwoComponent No-Pair Formalism with External-Field Projection Operators. Phys. Rev. A 1986, 33, 3742-3748. 133. Visscher, L.; Dyall, K. G., Dirac–Fock Atomic Electronic Structure Calculations Using Different Nuclear Charge Distributions. At. Data Nucl. Data Tables 1997, 67, 207224. 134. Becke, A. D., Density‐Functional Thermochemistry. Iii. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648. 135. Lee, C.; Yang, W.; Parr, R. G., Lyp Functional. Phys. Rev. B 1988, 37, 785. 136. Feyereisen, M.; Fitzgerald, G.; Komornicki, A., Use of Approximate Integrals in Ab Initio Theory. An Application in MP2 Energy Calculations. Chem. Phys. Lett. 1993, 208, 359. 137. Kendall, R. A.; Früchtl, H. A., The Impact of the Resolution of the Identity Approximate Integral Method on Modern Ab Initio Algorithm Development. Theor. Chem. Acc. 1997, 97, 158. 138. Neese F.; Petrenko T.; Ganyushin D.; Olbrich G., Advanced Aspects of Ab Initio Theoretical Optical Spectroscopy of Transition Metal Complexes: Multiplets, Spin-Orbit Coupling and Resonance Raman Intensities. Coord. Chem. Rev. 2007, 251, 288. 139. Duboc, C.; Ganyushin, D.; Sivalingam, K.; Collomb, M.-N.; Neese, F., Systematic Theoretical Study of the Zero-Field Splitting in Coordination Complexes of Mn(III). Density Functional Theory Versus Multireference Wave Function Approaches. J. Phys. Chem. A 2010, 114, 10750-10758. 140. Schapiro, I.; Sivalingam, K.; Neese, F., Assessment of N-Electron Valence State Perturbation Theory for Vertical Excitation Energies. J. Chem. Theory Comput. 2013, 9, 3567-3580. 141. van Schooneveld, M. M.; DeBeer, S., A Close Look at Dose: Toward L-Edge XAS Spectral Uniformity, Dose Quantification and Prediction of Metal Ion Photoreduction. J. Electron. Spectrosc. Relat. Phenom. 2015, 198, 31-56.


46

Page 47 of 47 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46



Ab initio Wavefunction-based Determination of ... - ACS Publications

Recommend Documents