Uncovering the Origin of Divergence in the CsM(CrO4)2 (M = La, Pr, Nd, Sm, Eu; Am) Family through Examination of the Chemical Bonding in a Molecular Cluster and by Band Structure Analysis

Uncovering the Origin of Divergence in the CsM(CrO4)2 (M = La, Pr, Nd, Sm, Eu; Am) Family through Examination of the Chemical Bonding in a Molecular Cluster and by Band Structure Analysis Shane S. Galley,1 Alexandra A. Arico,1 Tsung-Han Lee,2 Xiaoyu Deng,2 Yong-Xin Yao,3 Joseph M. Sperling,1 Vanessa Proust,1 Julia S. Storbeck,1 Vladimir Dobrosavljevic,4,5 Jennifer N. Neu,5,6 Theo Siegrist,5,6 Ryan E. Baumbach,5 Thomas E. Albrecht-Schmitt1,* Nikolas Kaltsoyannis,7,* Nicola Lanatà5,*


Introduction
Actinides beyond plutonium often have 5f electrons that are largely localized as evidenced by the superconducting behavior of americium metal. 1,2 In contrast, earlier actinides from at least uranium to plutonium display itinerant 5f electron behavior in their metallic states that extends to molecules where hybridization of 5f orbitals with ligand orbitals and delocalization of 5f electrons can occur. [3][4][5][6][7][8][9] This situation is further complicated by several factors that include the near degeneracy and greater radial extension of empty 6d orbitals, additional frontier orbitals coming into play (6p, 7s, and 7p), and reorganization of all of these orbitals upon complexation. [8][9][10][11][12][13] Relativistic effects and spinorbit coupling (SOC) dominate the electronic structure in these heavy elements, [14][15][16][17][18][19] and the magnitude of crystal-and ligand-field splitting lies between that found in the 4f series and 5d transition metals.
This situation is often termed the intermediate coupling regime. 14 Taken together, understanding the chemistry and physics of 5f elements represents the outer limits of current experimental and theoretical approaches. These challenges must be undertaken nevertheless for fundamental reasons that include understanding the evolution of electronic structure across the periodic table, and for practical applications, such as mitigating the environmental effects of the Cold War and improving the utilization of nuclear energy.
There are radiologic and reaction-scale challenges that are inherent to working with actinides that lie beyond uranium that often force the use of benign analogs for these elements. Examples of this include replacing Pu IV with Ce IV or Am III with Eu III . [20][21][22][23][24][25][26][27][28][29] These substitutions are often based on similarities between ionic radii. 20 However, the aforementioned changes in electronic structure and the increased involvement of frontier orbitals in the actinides creates dissimilarities between the 4f and 5f series that manifests in unexpected coordination chemistry, electronic properties, and reactivity.
For example, the reactivity and coordination environments of cerium and plutonium diverge in 4 phosphonates, 23,25 carboxypyridinonates, 30,31 and hydroxypyridinonates. 21,[32][33][34] The enthalpy of complexation of Am III by softer donors ligands is notably stronger than it is for Eu III and can be exploited for separating Am III from lanthanides in used nuclear fuel recycling. 10 Te; R = Ph, iPr, H) that are consistent with enhanced covalency in An-E bonds versus that found with lanthanides. 41 Variance occurs not only between the 4f and 5f series, but also between early and late actinides. 19,[42][43][44][45][46][47][48][49][50] Recent studies on the reduction of An III cyclopentadienyl complexes to An II have shown bifurcation in the ground states of the resultant species with U II existing in a 5f n 6d 1 (5f 3 6d 1 ) state; whereas Pu II adopts a 5f n+1 6d 0 (5f 6 ) configuration. [51][52][53] These differences in bonding between actinides are further illustrated by U IV and Pu IV β-ketoiminates where contributions from both 7s and 6d orbitals were found in the U-O bonds; whereas the only metal-based orbitals participating in the Pu-O bonds are the 6d orbitals. 11 Rare examples of studies on the complexation of Bk III and Cf III have shown that the more negative bond enthalpies are the result of increased covalency, and that part of the origin of this effect is driven by the degeneracy of actinide 5f orbitals and ligand orbitals. 44,46,[55][56][57] While many of the aforementioned examples have been pursued in order to provide a basic understanding of structure and bonding in f-element compounds, some of these materials are of practical importance and play roles in mitigating the environmental legacy of the Cold War. Among the components of nuclear waste of particular concern are large amounts of the mutagen, chromate, that is present in waste tanks because of its use in antiquated separations methods such as REDOX, 58 and as a corrosion inhibitor for the tanks themselves. Complicating matters further, chromates also form undesirable inclusions in the form of spinels during vitrification of nuclear waste. 59 Th IV and U VI chromates have been the subject of numerous investigations and show a vast array of structural 5 topologies. [60][61][62][63][64][65][66] However, both of these actinide cations are 5f 0 , and therefore lack many of the interesting electronic characteristics found in later actinide compounds. Large, well-faceted gold or yellow-orange offset prisms were isolated for CsLa(CrO4)2 and CsPr(CrO4)2, respectively. The crystals of CsNd(CrO4)2 and CsSm(CrO4)2 form green columns and gold plates, respectively. These reactions were then scaled down to appropriate levels for work with 243 Am. The reactions were carried out again to ensure that crystal growth still occurs. Once this was verified, the work with americium was conducted. Reactions were performed on the exact scale described below for all of the lanthanides described in this work. It should also be noted that reactions 7 were also carried out with Eu through Lu. These reactions result in the formation of Ln(OH)(CrO4) (Ln = Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, or Lu). Europium represents the crossover in this system and the europium reactions appears to contain a mixture of products. Studies on these compounds will be reported elsewhere. Reactions with Ce III starting materials result in an immediate redox reaction prior to heating with a corresponding color change to black and formation of amorphous black and green solids. Alternatively, all of these compounds can be prepared by reactions between Cs2CrO4 and Ln(NO3)3·nH2O in 2:1 ratio using the same hydrothermal conditions described above. This results in improvement in crystal quality, purity, and yield. Typical yields are ~70% based on the lanthanide content. Furthermore, this latter method allows one to isolate pure β-CsLn(CrO4)2 (Ln = Nd, Sm, Eu, Gd, Tb, Dy, and Ho); whereas using the former conditions the products are mixtures that also contain the aforementioned Ln(OH)(CrO4) compound beginning at europium. All in cases except for Am, SEM-EDS data were obtained that help to confirm the 1:1:2 ratio of Cs:Ln:Cr. hours with a 48-hour cooling period. Very dark red (nearly black) rods ~200 μm in length were isolated directly from the mother liquor. β-CsAm(CrO4)2 was instead prepared with a hydrous AmCl3 starting 8 material on a larger scale. A 24-hour digestion of 0.0358 mmol of AmO2 with 500 μL of 5 M HCl at 150 °C yielded a solution of Am III . This solution was fumed to dryness with a heat lamp, after which 0.0179 mmol of Cs2CrO4 and 0.0179 mmol of Cs2Cr2O7 and 500 μL of water were loaded into a 10 mL autoclave. The same heating profile was followed as used in the synthesis of α-CsAm(CrO4)2.
Crystallographic Studies. Single crystals of all compounds were adhered to Mitogen loops with immersion oil and then mounted on a goniometer under a cold stream set at 100 K. The crystals were then optically aligned on a Bruker D8 Quest X-ray diffractometer using a digital camera.
Diffraction data were obtained by irradiating the crystals with an IμS X-ray source (Mo Kα, λ = 0.71073 Å) with high-brilliance and high-performance focusing multilayered optics. Bruker software was used for determination of the unit cells, data collection, and integration of the data. Lorentz, polarization, and absorption corrections were also applied. A hemisphere of data was collected for all crystals. The structures were solved by direct methods and refined on F 2 by full-matrix least-squares techniques using the program suite SHELXTL. 72 Structure factors for americium were not present in the SHELX software at the time of these studies were performed, but were recently added by G. M.
Sheldrick. Thus a new SFAC command had to be added to the instructions file that defines the scattering factors for americium. This procedure no longer has to be done if one uses the most recent version of SHELX. Some of these compounds crystallize in less common space groups and the solutions were checked for missed symmetry using PLATON. 73 The Crystallographic Information  Table S1. We have simplified the formula to CsM(CrO4)2. In some cases, the formulae are more correctly (crystallographically) expressed as Cs2M2(CrO4)4.

UV−Vis-NIR Spectroscopy.
Single crystals of each compound were placed on quartz slides under medium-viscosity Krytox oil. A Craic Technologies microspectrophotometer was used to collect optical data in the UV-vis-NIR region. Irradiation of the samples was performed with a mercury light source. Absorption spectra of β-CsSm(CrO4)2 and β-CsEu(CrO4)2 are provide in Figure   S1. These data reveal band gaps from these materials of 2.462 and 2.435 eV for β-CsSm(CrO4)2 and β-CsEu(CrO4)2, respectively.

Magnetic Susceptibility Measurements.
Magnetism measurements were performed on polycrystalline samples of α-CsAm(CrO4)2, β-CsNd(CrO4)2, and β-CsEu(CrO4)2 using a Quantum Design MPMS under an applied field of 10 kOe for 4 K < 300 K. Plots of these data for β-CsNd(CrO4)2, and β-CsEu(CrO4)2 are provided in the Figure S2. The americium sample was sealed inside two, different, custom-built Teflon capsules. The first capsule has a piston design and fits inside of the second capsule that screws closed and is also taped to ensure that it cannot open during data collection. Datasets were collected with the capsules both empty and full, and the background from the sample holder was subtracted from the signal. Appropriate diamagnetic corrections were also applied. Data for α-CsAm(CrO4)2 are not provided because the sample was nonmagnetic over the entire temperature range studied.  Figure S1 shows the temperature dependences of χ, χΤ, and χ -1 , respectively. As shown in panel a, the curves for both compounds are weakly temperature dependent on the range 25 -300 K. In panel b we show χΤ, which will approach 10 the Curie-constant in the high temperature limit if Curie-Weiss behavior occurs (χΤ ≈ 0.09 cm 3  basis set plus the 46-electron relativistic pseudopotential for Cs. 75 Dunning's cc-pVTZ basis set was used for Cr and O. The PBE0 functional 77 was used in conjunction with the ultrafine integration grid. The SCF convergence criterion was set to 10 -6 , and the geometry convergence criterion was relaxed slightly from the default using iop(1/7=667) that produces 10 -3 au for the maximum force.
QTAIM analyses were performed using the AIMALL program package, 78 with .wfx files generated in Gaussian 09 used as input. NBO analyses were performed with the NBO6 code. 79 Band-Structure Calculations of α-CsAm(CrO4)2.
The electronic structure of α-CsAm(CrO4)2 was investigated utilizing the Local Density Approximation (LDA) 80 in combination with dynamical mean field theory (LDA+DMFT) [81][82][83] and in combination with the Gutzwiller 11 Approximation (LDA+GA). [84][85][86] Both of these computational approaches are powerful tools widely used to study strongly-correlated electron systems that enables us to take into account the strong Am-5f electron correlations in α-CsAm(CrO4)2. We utilize the DFT code WIEN2K, [87][88][89] and employ the standard fully-localized limit form for the double-counting functional. The LAPW interface between LDA and DMFT/GA employed in our calculations was implemented as described in Ref. [89]. The The Ln III centers are nine-coordinate with an approximate muffin geometry in CsLn(CrO4)2 (Ln = La, Pr). 91 The coordination environment contains nine oxygen atoms donated from CrO4 2units, 12 as shown in Figure 2a.  Table S1.
Gradual symmetry reduction and ultimately collapse of the layers occurs as the Ln III ionic radii diminish. Beginning at Nd III the crystallographic symmetry is lowered to P2/c. However, the structures remain quite similar as shown in Figure 3. The rubidium analogs have been previously reported, but do not adopt the same structure type as those reported here. 92 As the ionic radii continue to contract the Ln III coordination number decreases from nine to eight, and Nd III , Sm III , and Eu III cations are found within LnO8 trigonal dodecahedra. 21 A view of the local coordination environment around these cations is shown in Figure 2b.  Table S2.
Polymorphism in α-CsAm(CrO4)2 and β-CsAm(CrO4)2 is likely representative of small energetic differences between different structure types in this system. Similar polymorphism is also observed in M(IO3)3 (M = La -Lu, Am, Cm, Bk, Cf). 98-108 α-CsAm(CrO4)2 is triclinic and not isotypic with any of the other compounds described in this work. In contrast, β-CsAm(CrO4)2 is isomorphous with β-CsLn(CrO4)2 (Ln = Nd, Sm, Eu). The ionic radius of Am III most closely matches that of Nd III , and this latter result is expected. 20 Even though α-CsAm(CrO4)2 possesses lower symmetry than β-CsAm(CrO4)2, both structures contain one crystallographically unique Am III site. However, the reduced symmetry of α-CsAm(CrO4)2 does give rise to two crystallographically-unique chromium centers rather than one, and this alters the topology of the layers from that observed in β-CsAm(CrO4)2.
The layers in β-CsAm(CrO4)2 have already been described because they are isomorphous with Selected bond distances are provided in Table 1, and additional distances are given in the SI.  16 Over the last few years there has been much debate about the nature of covalency in the 5f series. Perturbation theory holds that, to first order, the mixing of molecular orbitals and is governed by the mixing coefficient (1) : where the off diagonal elements of the Hamiltonian matrix are related to the overlap between the orbitals, and the denominator is the difference between the corresponding energies. Thus, large orbital mixings can arise when and are close in energy, without there necessarily being significant spatial orbital overlap. The actinide community is now cognisant of the distinction between the more traditional overlap-driven covalency and energy-driven covalency that arises from the near degeneracy of metal and ligand orbitals. 109,110 The latter is common in the transuranic elements; as the actinide series is crossed the 5f orbitals become energetically stabilized and radially more contracted. Thus, at a certain point (dependent on the metal and the supporting ligand set) they become degenerate with the highest lying ligand based functions, yet are too contracted for there to be significant spatial overlap.
The atomic orbital (AO) contributions to the 20 highest occupied α spin canonical Kohn-Sham molecular orbitals (MOs) are shown in SI (Table S4). They are composed of Am f and oxygen p character, and there is extensive mixing of metal and ligand AOs in many MOs. This is illustrated in Figures 7 and 8 which show, respectively, MOs 266α and 262α. These images suggest that Am(CrO4)7Cs11 is a good example of energy-driven covalency; there are many atomic orbital contributions to the two molecular orbitals shown, but little or no spatial overlap of the individual atom-centered orbitals. This conclusion is reinforced by Natural Bond Orbital (NBO) analysis. The NBO approach is an orbital localization procedure that attempts to recast the canonical Kohn-Sham orbital structure in terms of more chemically intuitive localized orbitals, emphasizing the Lewis-like molecular bonding pattern of electron pairs. Applying the technique to Am(CrO4)7Cs11 yields no Am-O NBOs. Furthermore, the NBO calculation yields six α spin orbitals that are all greater than 99.9% Am 5f in character, i.e., they are the six unpaired 5f electrons expected for an Am 3+ center at the scalar relativistic level. This picture is very different from the delocalized nature of the Kohn-Sham orbitals, and suggests highly ionic Am-O bonding. In support of this, the Natural and Mulliken spin densities are 5.93 and 6.02 respectively (very close to the 6 expected for an Am 3+ ion). Furthermore, the expectation value of the 2 operator is ⟨ 2 ⟩ = 12.01; a pure heptet state would have is ⟨ 2 ⟩ = 12.
Hence, these results indicate essentially zero spin contamination in the wavefunction.
In principle, there is an infinite number of orbital representations we could choose to analyze.
By contrast, the Quantum Theory of Atoms in Molecules (QTAIM) focuses not on orbitals but on the topology of the electron density, and allows us to analyze actinide covalency in an alternative way, ideally distinguishing energy-driven from overlap-driven effects; the former will not lead to a significant build-up of electron density in the internuclear region, while the latter should do so. 12,[111][112][113][114] The QTAIM states that there is a bond critical point (BCP) between every two atoms bonded to each other, with the BCP located at the minimum in the electron density along the bond path, the line of maximum electron density between the two atoms. The values of the electron and energy densities and , and 2 , at the BCP can be used in analyzing the nature of the bond. Large values are associated with covalent bonds, and is negative for interactions with sharing of electrons, with its magnitude indicating the covalency of the interaction. 2 is also generally significantly less than zero for covalent bonds. The delocalization index between two bonded atoms indicates the bond order between them.
As expected, QTAIM analysis of Am(CrO4)7Cs11 finds eight bond paths terminating at the Am center, one from each of the nearest neighbour O atoms. BCP data for these are given in Table 2 In the Introduction, we noted that the enthalpy of complexation of Am III by softer donors can be larger than for Eu III . This is sometimes attributed to marginally larger covalency in the 5f complexes. To compare directly the Am-O and Eu-O bonding in our system, we have replaced the Am center with Eu and recomputed the electronic structure and QTAIM metrics; the data are given in Table 2. Consistent with reduced covalency, all of the Eu QTAIM metrics are a little smaller in an absolute sense than their Am counterparts. We stress, however, the highly ionic nature of both Am-O and Eu-O bonding that Table 2 presents; rather than say the lanthanide system is less covalent than the actinide, a better description is that the Eu-O bonds are marginally more ionic than the already highly ionic Am-O analogues.
In summary, the extent or otherwise of Am-O covalency in our Am(CrO4)7Cs11 cluster depends on one's definition of the term. The canonical orbitals show extensive mixing between Am-5f and O-2p orbitals, but there is no significant overlap between them. There is thus very little buildup of electron density in the internuclear region, and QTAIM analysis points to a very ionic picture. This view is reinforced by the NBO data, which find six fully localized 5f electrons and no Am-O bonding orbitals. We conclude that there is very little overlap-driven Am-O covalency, though degeneracydriven covalency is clearly present in the electronic structure. We will now show that this degeneracydriven covalency plays a major role in the properties of α-CsAm(CrO4)2. Furthermore, the SOC was not included in the cluster calculations presented above; as we are going to see in the next section, our 19 band-structure calculations demonstrate that the SOC substantially influences the electronic structure of this material.  Table 3, the Am-5f electronic structure is dominated by a singlet with N = 6 electrons and total angular momentum = 0, whose probability weight is 0 ∼ 0.88. We note that Tr�0̂2� = Tr�0 � 2 �∼ 2.25 × (2.25 + 1). Similarly, as shown in Table 4, also the Eu-4f electronic structure is dominated by a singlet with N = 6 and = 0, where the corresponding probability weight is 0 = 0.92, and Tr�̂0̂2� = Tr�0 � 2 �∼ 2.8 × (2.8 + 1). Finally, as shown in Table 5, the Sm-4f electronic structure is dominated by a 6-fold degenerate multiplet with N = 5 and = 5/2, whose probability

Conclusions
We have prepared and characterized a series of f-block chromates, CsM(CrO4)2 (M = La, Pr, Nd, Sm, Eu; Am), and noted pronounced differences between the Am III derivative and its lanthanide analogs. In order to investigate the origin of these differences, we have theoretically analyzed the examined. Interestingly, we also observed that the covalency effects in the Am III compounds are not present because of significant orbital overlap, but rather because of the degeneracy of the Am III and oxygen 5f and 2p orbitals, and because the large SOC prevents the formation of an Am-5f local moment.      Table 5. Parameters of the Sm-5f reduced density matrix in CsSm(CrO4), computed employing LDA+GA assuming U=6 and J=0.7, see Eq. 2. Largest probability weights , corresponding quantum labels (number of electrons) and (total angular momentum).   In the former case the Am III polyhedron is best approximated by a bicapped trigonal prism (C2v);

 ASSOCIATED CONTENT
whereas in the latter it is closer to a trigonal dodecahedron (D2d). Moreover, in αthere is only one chelating CrO4 2anion, while in βthere are two.