Electronic Structure of Third-Row Elements in Different Local

Article pubs.acs.org/IC

Electronic Structure of Third-Row Elements in Different Local Symmetries Studied by Valence-to-Core X‑ray Emission Spectroscopy Marko Petric,*,†,‡ Rok Bohinc,† Klemen Bučar,† Stanisław H. Nowak,§,⊥ Matjaž Ž itnik,†,∥ and Matjaž Kavčič*,† †

J. Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia Jozef Stefan International Postgraduate School, Jamova cesta 39, 1000 Ljubljana, Slovenia § Institute for Scientific Instruments GmbH, 12489 Berlin, Germany ⊥ Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, United States ∥ Faculty of Mathematics and Physics, University of Ljubljana, Jadranska ulica 19, SI-1000 Ljubljana, Slovenia ‡

S Supporting Information *

ABSTRACT: The electronic structure of phosphorus, sulfur, and chlorine in compounds with Td and C3v local symmetries was studied with high-resolution Kβ X-ray emission spectroscopy (XES) in the tender X-ray range. Measured spectra are compared to the results of ab initio quantum chemical calculations based on density functional theory (DFT). The spectral structure is reproduced by the model spectra of isolated XO4n− and XO3n− (X = P, S, or Cl) anions incorporating only the first coordination sphere around the central atom. The main spectral components can be explained by the molecular orbital theory. Finally, the potential of XES spectroscopy combined with DFT calculations to study the electronic structure of third-row elements in a slightly larger molecule is investigated.

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INTRODUCTION X-ray inner-shell spectroscopic methods are element specific and bulk sensitive and provide the most direct information on the local chemical environment of the central atom within different complex systems and materials. Nowadays, X-ray absorption near-edge structure (XANES) is a standard technique implemented at third-generation synchrotron facilities to study valence electronic structure. In case of third-row elements, K-edge XANES involving 1s → np electron transitions can provide information about bonding and local symmetry. However, complex spectral shape together with the high sensitivity of XANES spectra to the local structure around the central atom including higher coordination spheres may lead to severe difficulties in the interpretation of the measured spectra. This is additionally hampered by the experimental selfabsorption effect that can modify the fluorescence detected XANES spectra. Alternatively to XANES, high-resolution X-ray emission spectroscopy (XES) can be applied, providing complementary information about the valence electronic structure. The emission is a second-order process in which the inner-shell vacancy is subsequently filled with an electron from a higher occupied electronic state. In the case of nonresonant excitation at photon energies well above the corresponding absorption edge, XES spectra are not affected by © XXXX American Chemical Society

the target self-absorption. Since the relaxation process of the inner vacancy is independent from the excitation source, such analysis is not restricted to synchrotron beamlines but can be performed also with the laboratory excitation sources.1,2 When using an emission spectrometer operating in the dispersive mode, emission spectra can be recorded on the single-shot basis, and XES spectroscopy is therefore one of the most promising techniques to study electronic structure and molecular dynamics at the X-ray free electron laser (FEL) facilities.3 Within last years valence-to-core (VtC) XES in combination with density functional theory (DFT) has been established as one of the most important inner-shell X-ray spectroscopic techniques used to probe electronic structure and perform chemical speciation.4,5 It has been predominantly used to study 3d transition metal complexes.6−10 From the experimental point of view, the X-ray energy required to perform VtC XES is given by the binding energy of the 1s electron, which is in the case of 3d metals situated in the hard X-ray range. In order to fully develop the potential of VtC XES, the energy range should be extended further down toward the tender X-ray range (2−5 Received: February 6, 2016

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DOI: 10.1021/acs.inorgchem.6b00237 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

2 MeV protons for target excitation with the proton current in the range 50−100 nA. In both cases the same Johansson-type crystal spectrometer for high-resolution X-ray emission spectroscopy in the tender X-ray range was used.30 The experimental conditions used in this work were similar to those used in our previous works.24,31 In case of phosphorus samples the emitted X-ray photons were reflected in the first order by (101̅0) planes of the SiO2 crystal (2d = 8.510 Å), while in the case of sulfur and chlorine samples the first-order reflection on a Si(111) crystal (2d = 6.271 Å) was used. The Rowland circle radius of the crystal analyzers was 50 cm, but the sample holder was placed inside the Rowland circle at a distance of 42 cm from the analyzer crystal in order to reach the dispersive mode of operation. The diffracted photons were detected by a position-sensitive chargedcoupled device (CCD) detector. The energy bandwidth at the central Bragg angle corresponding to the Kβ emission line covered by the CCD width was 56, 39, and 71 eV for P, S, and Cl, respectively, so the full Kβ emission spectrum was recorded simultaneously without moving the detector and the crystal. The two-dimensional images recorded by the CCD were projected on the horizontal axis corresponding to the dispersion axis to obtain the final spectra. These position-dependent spectra were finally converted into an energy scale relative to the position of the Kβ1,3 line of the K3PO4, Na2SO4, and NaCl compounds with corresponding reference emission energies of 2138.0,12 2467.15,32 and 2815.1133 eV, respectively. The final experimental energy resolution was around 0.5−0.6 eV, depending on the Bragg angle corresponding to each measured element. The measurements were done on the pellets pressed from powder reference materials purchased on the global market. The overall acquisition time for synchrotron radiation induced spectra was 2500 s, whereas for proton excitation significantly lower count rates were achieved and the acquisition of the spectra lasted up to several hours. In order to avoid radiation damage during long measurements, accumulation of short exposures from several fresh target spots was used to reach reasonable statistics.

keV) containing K edges of chemically very relevant third-row elements, in particular P, S, and Cl. However, compared to the hard X-ray range, this tender range has so far not been exploited to the same extent. Some Kβ emission studies using laboratory excitation sources can be found in the literature for phosphate/phosphite,11−14 sulfate/sulfite,14−17 and (per)chlorate.17 Also some electronic structure calculations can be found,18,19 but only a few attempts were made to fully interpret the measured Kβ emission spectra.20−22 Only recently have more elaborate VtC XES studies employing synchrotron radiation and modern X-ray emission spectrometer combined with ab initio quantum chemical calculations appeared also in the tender X-ray range.23,24 Large Johann-type in-air X-ray emission end-stations, currently available at various synchrotron radiation facilities, are used extensively to perform VtC studies in the hard X-ray range. However, going down to lower X-ray energy enhanced X-ray absorption severely limits their performance. In order to perform VtC XES also in the tender X-ray range, a full in vacuo experimental environment is mandatory, requiring dedicated X-ray emission spectrometers. Experimentally, this is the most important distinction between tender and hard X-ray VtC and is the main reason that tender VtC XES has been scientifically much less exploited. In the present work, we have tried to fill this gap by performing a systematic experimental and theoretical VtC XES study of several third-row elements (P, S, and Cl) in compounds exhibiting two different types of local symmetries (Td and C3v). Besides serving as a case study to explore analytical capabilities of VtC spectroscopy in the tender X-ray range, the XO4n− and XO3n− anions studied here are certainly also chemically and biologically very important molecular fragments. For example, the phosphate group has an essential role in plant hormones that regulate plant growth and development.25 The adenosine triphosphate (ATP) molecule, being the reservoir of biochemical energy, is also based on phosphate groups.26 Sulfate molecules significantly affect the hydrological cycle and global climate.27 Perchlorate and chlorate compounds are ubiquitous all across Earth’s surface, and these species are involved in the oxidation process of organic matter.28 Recently, (per)chlorates were extracted also in nonplanetary samples.29 In order to characterize these particular groups of compounds and understand their role in chemical processes, a detailed knowledge of the chemical environment of central P, S, and Cl atoms is of prime importance. In our experiment, high-energy resolution Kβ emission spectra of selected P, S, and Cl compounds were recorded using an in-vacuum X-ray emission spectrometer. Experimental data were compared to the first-principles calculations based on the DFT approach and discussed in terms of the molecular orbital (MO) theory. Finally, the results obtained for these basic symmetry systems were extended further toward a more complex molecule (metabisulfite) in order to demonstrate a general approach for the interpretation of the Kβ emission spectra of third-row-element-containing compounds.

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CALCULATIONS Ab initio quantum chemical calculations of Kβ emission spectra were performed with the StoBe-deMon34 program package based on density functional theory.35 First, the geometry optimization was performed to reach the energy minimum of the system yielding the ground state for each molecule. For the optimization of the first coordination sphere around the center P, S, or Cl atom two sets of calculations were performed, one employing the full symmetry of the molecular ion and the second one without imposing the symmetry in the calculation. Both calculations yielded consistent values, so the final geometrical optimization of the neutral molecular system was performed without the symmetry restriction. The calculated distances between center P, S, and Cl atoms and neighboring oxygen atoms for XO4n− and XO3n− ions and also for the corresponding neutral molecules are collected in Table 1. The calculated values are in good agreement with the existing experimental data available in the literature, which are also tabulated in Table 1. The Kβ X-ray emission spectra were calculated in the ground-state approximation in which both the initial core-hole state and the final valence-hole state were represented by Kohn−Sham orbitals of the ground state.42,43 In this approximation the dipole transition moments were calculated as explicit one-electron transitions. In order to improve the accuracy of transition energies, individual optimization of each state was performed and the emission energies were calculated as differences in orbital energies of corresponding initial and final states. The same TZVP (73111/6111/1) orbital basis set was used for P, S, and Cl atoms. For O, Na, and K atoms (6311/311/1), (6321/411/1), and (63321/5211/1) basis sets

EXPERIMENTAL SECTION

Measurements of phosphorus photoexcited Kβ emission spectra were performed at the ID26 beamline of the European Synchrotron Radiation Facility. The incident photon beam was tuned to 3000 eV, and the flux on the target was ∼5 × 1012 photons/s. Measurements of sulfur and chlorine emission spectra were performed at the 2 MV tandem ion accelerator at the Jožef Stefan Institute in Ljubljana, using B


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Td Local Symmetry. High-resolution P, S, and Cl Kβ X-ray emission spectra measured from K3PO4, K2SO4, and KClO4 compounds are presented in the top part of Figure 2. The spectral structure is very similar for all three compounds, exhibiting two main characteristic peaks, commonly labeled Kβ′ and Kβ1,3. Besides these two major components two additional side peaks are observed on both sides of the Kβ1,3 line, usually labeled Kβx and Kβ″. In the case of the Cl spectrum the Kβ″ side peak is shifted on the low-energy side of the main Kβ1,3 peak. Measured spectra were fitted by a model spectrum composed of four Voigt profiles, also presented in Figure 2. The experimental energies and intensities of separate spectral components extracted from the fit are tabulated in Table 2. In order to understand the measured spectral shape, DFT calculations of the electronic transitions corresponding to the Kβ emission spectrum were performed. In the first approximation only the first coordination sphere around the center atom building the XO4n− anion was included in the calculations, and later on the calculations were expanded to model the neutral molecule. The final theoretical spectra were built from the calculated line spectra using Voigt profiles, and the results are presented in Figure 2. The width of the Voigt profiles was adjusted to match the experimentally observed line shape widths, and an overall shift of the calculated absolute energy scale of a few electronvolts was applied in order to match the experimental energies. The actual shifts of the absolute energy scale applied to separate XO4n− and XO3n− theoretical spectra are given in Table 3. As seen from Figure 2, there are no significant differences between the theoretical model spectra of the isolated XO4n− ion and the neutral molecule. As already observed in our previous work focused on phosphorus compounds,24 the metallic ligand is bound with an ionic bond to the PO43− ion and the valence electron from the ligand is transferred to the phosphate ion without significantly perturbing the electronic structure of the phosphate ion. The same behavior is now observed for all three elements studied here. Our DFT calculations therefore suggest that the influence of the cation on the Kβ emission spectral shape is almost negligible. The main characteristics of the emission spectrum can be reproduced with the model including only the first coordination sphere around the center atom. Experimentally, this could be verified by comparing measured emission spectra of several compounds with different metallic ligands bound to the XO4n− ion. Ultimately, one could even study these complexes in solutions using the liquid cell as in our recent VtC XES study of aqueous sulfuric acid.52 The DFT-calculated ground-state electronic configuration is the same for all three (XO4n−) ions. Fifty electrons are arranged through the MOs, which are labeled according to the irreducible representation of the Td point group: 1a21, 2a21, 1t62, 3a21, 2t62, 4a21, 3t62, 5a21, 4t62, 1e4, 5t62, and 1t61. The first five orbitals correspond to X 1s, O 1s, X 2s, and X 2p atomic orbitals, respectively. The valence molecular orbitals are built from the X 3s, 3p, and 3d and the O 2s and 2p atomic orbitals. According to the dipole selection rule, electron transitions to the 1s state are allowed only from the orbitals of t2 symmetry. On the basis of the structure of valence MOs, three spectral components could be anticipated, corresponding to dipole transitions from the 3t2, 4t2, and 5t2 MO, respectively. In our case the Kβ′ and Kβ1,3 main spectral components correspond to transitions from 3t2 and 4t2, while the calculated intensities for transitions from 5t2 were found practically negligible and do not contribute significantly to the theoretical spectra. In order to interpret

Table 1. DFT-Calculated Distances between Center P, S, and Cl Atoms and Neighboring Oxygen Atoms in XO4n− and XO3n− Ions and in Neutral Moleculesa distance between P, S, or Cl and O [Å] calculated by StoBe

a

molecule

ion

molecule

literature data

PO43−/K3PO4 SO42−/K2SO4 ClO4−/KClO4 PO33−/Na2HPO3 SO32−/Na2SO3 ClO3−/NaClO3

1.615 1.541 1.513 1.665 1.598 1.556

1.607 1.536 1.512 1.575 1.596 1.561

1.54236 1.48637 1.46038 1.52539 1.50040 1.48541

Existing literature crystallographic data are added for comparison.

were employed, respectively. In the StoBe-deMon calculation two auxiliary Gaussian basis sets are used to represent the Coulomb potential and exchange−correlation potential. The same (5,4;5,4) auxiliary basis set was used for all three elements. In this notation the two sets of numbers correspond to the number of Gaussian functions used to fit the Coulomb and the exchange−correlation potential44,45 of the inner and valence region, respectively. In all calculations the exchange functional by Becke, Be88,46 and the correlation functional by Perdew, PD91,47 were employed. In order to describe the character of the MOs in terms of atomic ones, the Mulliken population analysis48−51 was finally performed. While individually optimized initial and final states were used to calculate the emission spectra, the Mulliken population analysis was performed on the ground state of the molecule/ion.

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RESULTS AND DISCUSSION Within the conventional X-ray spectroscopy nomenclature of isolated atoms the Kβ emission refers to the electron dipole transition from the 3p to the 1s atomic orbital. In the case of the third-row-element-containing compounds these 3p electrons are involved in chemical bonding and the Kβ emission spectrum corresponds to electronic transitions from the occupied molecular-valence orbitals. Consequently, this valence-to-core emission spectrum should reflect the local symmetry and chemical environment of the central atom. In order to study the influence of local symmetry on the Kβ emission spectral shape, two sets of XO4n− and XO3n− (X = P, S, Cl) compounds with Td and C3v symmetries, respectively, were studied experimentally and theoretically. In the Td tetrahedral symmetry of the XO4n− anion the central atom is positioned in the center of the cube with four oxygen atoms situated in the opposite corners of the cube. In the XO3n− ion exhibiting C3v symmetry oxygen atoms are positioned in the corners of the equilateral triangle with the central atom positioned in the center of the triangle but slightly out of the plane formed by the oxygen atoms (Figure 1).

Figure 1. Presentation (left) of the Td local symmetry and (right) the C3v local symmetry. C


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Inorganic Chemistry

Figure 2. Experimental and theoretical Kβ emission spectra of phosphorus (left), sulfur (center), and chlorine (right) in Td local symmetry.

Table 2. Experimental Energies and Relative Intensities of Main Spectral Components for the K3PO4, K2SO4, and KClO4 Compoundsa K3PO4 energy [eV] intensity [%] K2SO4 energy [eV] intensity [%] KClO4 energy [eV] intensity [%] a

Kβ′

Kβx

Kβ1,3

Kβ″

Kβ′/Kβ1,3

2123.75(2) 23.1(0.5)

2134.4(2) 3.8(1.0)

2138.03(1) 67.4(2.3)

2140.45(6) 5.7(1.2)

0.34(0.01)

2453.10(4) 31.7(1.6)

2464.2(4) 6.3(1.9)

2467.236(5) 59.3(2.3)

2470.6(2) 2.7(1.4)

0.53(0.03)

2805.25(7) 34.1(2.3)

2815.5(5) 8.1(7.8)

2819.60(1) 44.0(5.6)

2817.8(2) 13.8(13.7)

0.77(0.11)

The error estimates from the fit are given in parentheses.

valence electronic structure in terms of atomic orbitals, Mulliken population analysis was performed for all three (XO4n−) systems, and the results are presented in Table 4. Tabulated results are in good agreement with the orbital composition obtained by Adachi and Taniguchi19 with discrete variational Xα cluster calculation. While the structure of the Kβ emission spectrum for all measured (XO4n−) systems is practically the same and is defined by the local symmetry, the Kβ′/Kβ1,3 intensity ratio shows an increasing trend on going from P to Cl. This trend, which is observed clearly in the experiment and also reproduced nicely by the theoretical

Table 3. Overall Shift of the Absolute Energy Scale Applied to Each Calculated XO4n− and XO3n− Spectrum calculated by StoBe molecule

ion

molecule

PO43−/K3PO4 SO42−/K2SO4 ClO4−/ KClO4 PO33−/Na2HPO3 SO32−/Na2SO3 ClO3−/NaClO3

−3.930 −0.992 0.891 −3.934 −1.115 0.979

−3.589 −1.053 0.802 −4.047 −1.089 1.219

Table 4. Ground-State Electronic Configuration of Separate XO4n− Ions with Td Local Symmetry Performed by Mulliken Population Analysisa

a

Contribution of a particular MO to the corresponding spectral components is noted in the first column. D


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C3v Local Symmetry. The same kind of analysis as for the Td symmetry was performed also for the XO3 molecular systems with C3v local symmetry. High-resolution P, S, and Cl Kβ X-ray emission spectra measured from Na2HPO3, Na2SO3, and NaClO3 compounds are presented in Figure 4. The measured emission spectra are composed of three main peaks in the case of S and Cl compounds. The same notations have been used for the two main and the two side peaks as for the XO4 molecular systems with Td symmetry, whereas the new peak at higher energies is labeled as Kβxx. In the case of the Na2HPO3 compound, the Kβxx component is absent from the spectrum. As before, the experimental spectra were fitted by a model spectrum composed of several Voigt profiles. The experimental energies and intensities of separate spectral components extracted from the fit are reported in Table 5. Besides the appearance of the additional Kβxx spectral component, a decrease of the Kβ′/Kβ1,3 intensity ratio compared to the measured spectra of XO4 molecular systems is observed for each of the three elements. Also in this case the DFT calculations of the electronic transitions corresponding to the Kβ emission spectrum were performed for the first coordination sphere around the center atom building the XO3n− anion and also for the neutral molecule. The final theoretical spectra were built from the calculated line spectra using Voigt profiles; the width of the Voigt profiles was adjusted to fit the experimental line widths. DFT model spectra for the XO3n− ion and the neutral molecule are also presented in Figure 4. All three theoretical spectra calculated for the neutral molecule are in very good agreement with the experimental data. In the case of S and Cl the theoretical spectra of the isolated XO3n− ion and the neutral molecule are practically the same, so the influence of the sodium atoms on the electronic structure of sulfite and chlorate is negligible. The theoretical spectrum of the PO3n− ion also exhibits three main spectral components including the Kβxx one similar to the S and Cl spectra. In agreement with the experimental data, the Kβxx line disappears from the spectrum when the neutral Na2HPO3 molecule is considered in the calculations. This is explained with the covalent bonding of the hydrogen atom directly to phosphorus, which modifies the electronic structure. In order to confirm this assumption, we have performed geometrical optimization of the neutral Na2HPO3 molecule and then increased the distance between the Na2PO3 molecular fragment and the hydrogen atom in steps of 0.5 Å, while all other atoms were kept at fixed initial position. The Kβ spectra calculated for each distance including just the Na2PO3− molecular fragment are presented in Figure 5. As we were only interested in the evolution of the Kβxx component, only the calculations in the ground-state approximation without energy correction were performed and an overall shift of the calculated absolute energy scale of 67.4 eV was applied in order to match the experimental energies. The results show clearly the decrease of the Kβxx intensity when the hydrogen atom is approaching its actual position within the Na2HPO3 molecule. The MOs of XO3n− molecular systems are labeled according to the irreducible representation of the C3v point group. The first six orbitals 1a21, 2a21, 1e4, 3a21, 2e4, and 4a21 correspond to core atomic-like orbitals. The calculated valence electronic structure for the PO33− and SO32− ions is the same, 5a21, 3e4, 6a21, 4e4, 7a21, 5e4, 6e4, 1a22, and 8a21, whereas the calculated valence electronic structure of ClO3− is slightly different, 5a21, 3e4, 6a21, 7a21, 4e4, 5e4, 6e4, 8a21, and 1a22. The results of Mulliken

spectra, can be explained with the results of the Mulliken population analysis. The ratio of the amount of atomic 3p character in the 3t2 and 4t2 MO increases with increased Z of the central atom in the (XO4n−) anion, resulting in an increased intensity ratio of the Kβ′ and Kβ1,3 peaks. Besides Mulliken population analysis we have also constructed the MO diagram and plotted schematically the corresponding 3t2 and 4t2 orbitals. Despite that the MO diagram might be slightly simplified, it can provide a very helpful concept in understanding molecular valence electronic structure. In a diatomic molecule the s-type orbitals can form two σ orbitals, in-phase (σg) and out-of-phase (σu). In a similar way, the four O 2s atomic orbitals in Td symmetry form two types of orbitals, one in-phase (2sg) with a1 symmetry and three out-of-phase (2su) orbitals with t2 symmetry. The X 3s orbital with the a1 symmetry together with the oxygen (2sg) orbital forms the MOs 4a1 and 5a1. On the other hand, the O (2su) orbitals with the same symmetry as X 3p orbitals form the 3t2 and 4t2 MO. The schematic MO diagram is presented in Figure 3. The electron transition from the 3t2 orbital contributes to the

Figure 3. (Left) Qualitative molecular diagram for the XO4n− ions. Only occupied MOs contributing to the spectrum are presented. (Right) Schematic presentation of the 4t2 and 3t2 MOs (top and bottom, respectively).

Kβ′ spectral component, and this peak directly reflects O 2s and X 3p bonding. The second main spectral component Kβ1,3 corresponds to electron transition from the 4t2 orbital. In the analysis of 4t2, MO mixing of O 2s and 2p orbitals needs to be included, which complicates the electronic structure and leads to different ratios of O 2s and 2p atomic orbitals. As seen from population analysis the 4t2 MO is composed mostly of O 2p and X 3p atomic orbitals. In order to arrange O 2p orbitals around X 3p, we will expand the picture from s-type orbitals in diatomic molecules also to the p-type orbitals. The p orbitals can form σ- and π-type MOs. The σg orbitals are composed of two O 2p orbitals along the x axis and another two along the y axis. Together with a perpendicular X 3p orbital along the z axis the final 4t2 MO is built as presented schematically in Figure 3 (top right). In this way both main spectral components of the Kβ emission spectrum can be explained. E


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Inorganic Chemistry

Figure 4. Experimental and theoretical Kβ emission spectra of phosphorus (left), sulfur (center), and chlorine (right) in C3v local symmetry.

Table 5. Experimental Energies and Relative Intensities of Main Spectral Components for the Na2HPO3, Na2SO3, and NaClO3 Compoundsa Kβ′ Na2HPO3 energy [eV] intensity [%] Na2SO3 energy [eV] intensity [%] NaClO3 energy [eV] intensity [%] a

Kβx

Kβ1,3

Kβ″

Kβxx

Kβ′/Kβ1,3

2123.33(5) 13.6(0.8)

2133.9(1) 4.2(1.4)

2137.46(1) 72.2(3.0)

2140.11(9) 10.0(1.8)

2452.13(8) 14.2(2.0)

2463.3(5) 9.6(5.4)

2466.00(1) 54.2(10.3)

2468.9(5) 8.9(15.4)

2472.20(3) 13.0(4.7)

0.26(0.06)

2803.9(1) 19.7(2.1)

2813.4(2.5) 9.8(24.6)

2817.90(4) 47.2(12.0)

2815.7(2) 11.2(38.5)

2824.24(8) 12.0(1.7)

0.42(0.11)

0.19(0.01)

The fitting errors are reported in parentheses.

from the orbitals with a1 and e symmetry. The electron transitions from the 3e MO contribute to the Kβ′ peak, their atomic orbital composition is similar to the 3t2 MO in Td symmetry, and the number of MOs is reduced from three to two. It is important to note that in Td symmetry all four O 2s orbitals contribute equally to the 3t2 MO, whereas in the case of C3v symmetry the O 2s contribution is not equal for each degenerate 3e set. The reduction of the MO can be explained by the geometrical structure of the molecule. In the case of Td symmetry all Cartesian axes are equivalent and X 3p orbitals have two O 2s orbitals on the top and two on the bottom side. In the case of C3v symmetry the center atom is much closer to the oxygen plane. Consequently, the overlap integral between the X 3pz and O 2s orbitals is negligible. In other words, the X 3pz and O 2s orbitals cannot build valence-type molecular orbitals. The schematic arrangement of both X 3pz and O 2s is presented in Figure 6. On the other hand, the X 3px,y orbitals form a MO with the oxygen 2s orbitals in the same way as in Td symmetry. The result is that an overall spectral composition is similar to that for the systems of Td symmetry, while the reduction of MOs contributing to the Kβ′ component results in a decrease of the Kβ′ relative intensity.

Figure 5. Theoretical P Kβ emission spectra of Na2HPO3 with different distances between the Na2PO3 molecular fragment and the hydrogen atom. The calculated stick spectra were convoluted with a 0.9 eV fwhm Gaussian function.

population analysis for each valence MO are presented in Table 6 and can be compared with the population analysis of molecules with Td symmetry. Within a molecule with C3v local symmetry electron dipole transitions to the 1s state are allowed F


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Inorganic Chemistry

Table 6. Ground-State Electronic Configuration of Separate XO3n− Ions with C3v Local Symmetry Performed by Mulliken Population Analysisa

a

Contributions of a particular MO to the corresponding spectral components are noted in the first column.

shown in the upper part of Figure 7. It exhibits five spectral components, which are labeled in the same way as for the measured XO3 compounds with C3v local symmetry.

Figure 6. (Left) Qualitative molecular diagram for the XO3n− ions. Only occupied MOs contributing to the spectrum are presented. (Right Bottom) Schematic arrangement of O s and the X p atomic orbitals producing zero overlap. (Right Top) Schematic presentation of the 7a1 MO.

Figure 7. (Top) Experimental and (bottom) theoretical S Kβ emission spectrum of the Na2S2O5 molecule, with a model of the Na2S2O5 molecule, where yellow, red, and brown represent S, O, and Na atoms, respectively.

The Kβ1,3 spectral component corresponds to electron transition from the 4e and 7a1 MOs. Looking at the results of population analysis presented in Table 6, we can notice that the two 4e orbitals have the same structure as the 4t2 in Td symmetry. These two 4e orbitals are built in the same way as in tetrahedral symmetry from two X 3p orbitals in the xy plane and O 2p orbitals. However, because of the geometry the X 3pz orbital cannot interact with the O 2p orbitals in the same way as in the Td symmetry, and the overlap integral between X 3pz and O 2px,y is zero. On the other hand, the 3pz orbital interacts with the O 2pz to form two types of MOs, the “π-bonding” and the “π-antibonding”. The π-bonding MO corresponds to 7a1 and contributes to the Kβ1,3 spectral component. The schematic arrangement of this orbital is also presented in Figure 6. The π-antibonding MO corresponds to the 8a1 orbital with slightly higher energy, and the electron transitions from this 8a1 orbital correspond to the additional peak Kβxx on the high-energy side of the main Kβ1,3 peak. Electronic Structure of Sodium Metabisulfite (Na2S2O5). So far we have restricted our analysis to small basic molecular systems with well-defined symmetries. Now we would like to expand this to a bit larger and more complex molecule of Na2S2O5. The measured S Kβ emission spectrum is

In order to build the theoretical spectrum, DFT calculations of the corresponding electronic transitions were performed for the neutral molecule. First the geometry optimization of the molecule was performed, and the calculated positions were found in good agreement with the published crystal structure of sodium metabisulfite.53 Two separate calculations for both S atoms were performed in the ground-state approximation without energy corrections and then summed together to reach the final result. An overall shift was applied to the absolute calculated energy scale in order to match experimental ones. The theoretical spectrum was built from the calculated stick spectra broadened by the Voigt profile in order to fit the experimental line widths and is also presented together with the experimental spectrum in Figure 7. The green and red bars represent the components calculated for the sulfur atom surrounded by two (SO2) and three (SO3) oxygen atoms, respectively. The theoretical spectrum is in very good agreement with the experimental one. In a previous analysis of the XO3 and XO4 systems the influence of metallic cations on the emission spectra was found G


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Inorganic Chemistry

emission spectroscopy in the tender X-ray range is one of the most promising techniques for the bulk chemical analysis of third-row-element-containing materials. It can be successfully performed even at excitation energies far above the K-hole threshold, which are readily available at the hard X-ray synchrotron beamlines. With dedicated tender X-ray end stations becoming available at several synchrotron facilities and upcoming new FEL facilities targeting exactly the tender Xray range, VtC XES will gain further importance and develop its full potential also in this particular energy range.

to be negligible. In addition, a relatively large distance between the two sulfur atoms (2.2172(11)53 Å) allows us to interpret the spectral structure with the help of SO2 and SO3 building blocks. The calculated emission spectrum of the SO3 block within the full Na2S2O5 molecule (red bars) has basically the same shape as already discussed in the previous section. Two MOs contributing to the Kβ′ component are built by the S 3px,y orbital interacting with the O 2s orbitals. The contribution in the Kβxx component is due to formation of a “π-antibonding” MO between the S 3pz and O 2pz orbitals. In the case of the calculated emission spectrum of the SO2 block (green bars) only one of the S 3p orbitals interacts with the O 2s to form the single MO contributing to the Kβ′ spectral component. Two components on the high-energy side of the main Kβ1,3 peak are due to formation of an MO between the S 3p and O 2p orbitals in a similar way as for the XO3 spectrum. While originally three MO contributions built from S 3p and O 2p orbitals are found in the main Kβ1,3 peak for each isolated block, several additional components are observed in the calculated Na2S2O5 spectrum. However, this is not due to the changed electronic structure of the SO2 and SO3 building blocks. Within the neutral molecule new additional MOs are being formed as a linear combination of MOs from SO2 and SO3 contributing to the Kβ1,3 spectral component for both S atoms. Besides the main spectral components interpreted as a sum of the SO2 and SO3 contributions, two additional minor spectral components are observed in the theoretical spectrum on the low-energy side of the main Kβ′ and Kβ1,3 components. The Mulliken population analysis of the MO contributing to these components reveals atomic character similar to the 4a1 and 5a1 orbitals for the XO4 system in Td symmetry (Table S1 of the Supporting Infomation). In a molecular system with pure Td symmetry electron transition from orbitals of a1 symmetry to the 1s atomic orbital are dipole forbidden. However, in a neutral molecule the atoms of a second coordinate sphere modify slightly the character of the a1 MO and electron transitions to 1s are no longer forbidden, resulting in these small additional spectral contributions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b00237. Example of StoBe-deMon code; calculated molecular orbitals of XO4n− and XO3n−; Mulliken population analysis of the MO of the Na2S2O5 molecule (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been supported by Marie Curie Actions−Initial Training Networks (ITN) as an Integrating Activity Supporting Postgraduate Research with Internships in Industry and Training Excellence (SPRITE) under EC contract no. 317169. S.H.N. acknowledges support from the Swiss National Science Foundation (SNSF), Project No. P2FRP2_148569. Finally, the authors acknowledge the support of the Slovenian Research Program P1-0112 and excellent assistance of the ID26 beamline staff in preparation of the synchrotron experiment.

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CONCLUSION A systematic experimental and theoretical study of the electronic structure of P, S, and, Cl oxides of different local symmetries performed by valence-to-core X-ray emission spectroscopy is presented. Measured high-energy resolution Kβ X-ray emission spectra directly reflect the p-type character of occupied MOs. DFT calculations combined with an MO theory were performed to interpret the experimental data. The local symmetry of the molecular system defines the electronic structure and exhibits the same behavior for all three studied third-row elements. The main spectral features are well reproduced by the calculations considering only the first coordination sphere around the central atom. The differences between the emission spectra of compounds exhibiting Td and C3v symmetry are explained with the MO theory. The experimentally observed decrease of Kβ′/Kβ1,3 intensity ratio for the compounds in C3v symmetry and the appearance of an additional Kβxx spectral component on the high-energy side of the main Kβ1,3 peak are explained through changes of the overlap integrals between atomic orbitals building the corresponding MO. Finally, the Kβ X-ray emission spectrum of a large oxide molecule is explained as a combination of smaller blocks with a well-defined symmetry. With its high sensitivity to the local electronic structure, valence-to-core

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Electronic Structure of Third-Row Elements in Different Local

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