Isolation of a Californium(II) Crown-Ether Complex
Californium (Z = 98) is the first member of the actinide series displaying metastability of the 2+ oxidation state. Understanding the origin of this chemical behavior requires characterizing Cf II materials, but isolating a complex with this state has remained elusive. The source of its inaccessibility arises from the intrinsic challenges of manipulating this unstable element as well as a lack of suitable reductants that do not reduce Cf III to Cf 0 . Herein we show that a Cf II crown-ether complex, Cf(18-crown-6)I2, can be prepared using an Al/Hg amalgam as a reductant. While spectroscopic evidence shows that Cf III can be quantitatively reduced to Cf II , rapid radiolytic reoxidation back to the Cf III parent occurs and co-crystallized mixtures of Cf II and Cf III complexes are isolated if the crystallization is not conducted over the Al/Hg amalgam. Quantum chemical calculations show that the Cf-ligand interactions are highly ionic and that 5f/6d mixing is absent, 2 resulting in remarkably weak 5f→5f transitions and an absorption spectrum dominated by 5f→6d transitions.
INTRODUCTION<!>RESULTS AND DISCUSSION<!>CONCLUSION<!>Notes<!>Acknowledgements.<!>Experimental<!>Synthesis of [Cf
<p>Recent advances in heavy element chemistry spurred by innovative molecular design, new spectroscopic techniques, and relativistic theory have evolved our understanding of the divergence between the chemistries of 5f elements and their 4f counterparts. Historically the primary distinction between these two series has been that early actinides display facile redox chemistry compared to lanthanides with the exception of those with special electronic configurations such as Eu II (4f 7 ) and Yb II (4f 14 ). 1 This key attribute is largely lost in all trans-plutonium elements (excluding nobelium) where the most stable oxidation state is 3+ akin to lanthanides. 2 This has led to the notion that their chemistries are lanthanide-like. The combination of this bias with their scarcity, short half-lives, and need for specialized research facilities has further stymied progress in understanding these elements. However, it has been known for several decades that actinides from californium to nobelium have accessible 2+ oxidation states. 3 In fact, electro-and thermochemical measurements have shown a progressive stabilization of the 2+ state ultimately revealing that No II is more stable than No III by 1.45 V. [4][5][6] Of late significant efforts have been dedicated to isolating complexes containing f-elements in either new or rare oxidation states for the purpose of determining their electronic configurations, bonding trends, spectroscopic features, and reactivity. Using strong reductants such as KC8 and low-temperature reaction conditions, the first examples of Th II , U II , Np II , and Pu II triscyclopentadienyl derivatives such as [Pu(Cp')3] 1− (Cp' = trimethylsilylcyclopentadienyl) have been prepared, characterized, and their reactivities explored. [7][8][9][10] These studies inspired the pursuit of other molecular scaffolds for stabilizing U II such as the U II bis(amidate arene) [U(TDA)2] 1− (TDA = N-(2,6-di-isopropylphenyl)pivalamido) that acts as U I synthon because of the non-innocence of the ligand, as well as the monoarene [U(( Ad,Me ArO)3mes)] that exhibits stabilization of U II via backbonding. 11,12 These reductive methods can also yield compounds whose oxidation states are difficult to describe such as [K(18-crown-6)(THF)2]2[U(η 6 -C14H10)(η 4 -C14H10)(μ-OMe)]2•4THF. 13 Likewise, Cf II complexes have been prepared in the gas phase as exemplified by reductive elimination of CH3SO2 from Cf III (CH3SO2)4 − to yield Cf II (CH3SO2)3 − . 14 The issue with applying the above synthetic methods to the preparation of low-valent transplutonium complexes is that unlike early actinides the standard reduction potential for An III → An II can be quite similar to the potential for An III → An 0 . In fact, even with uranium the reaction of UCl4 with LiC10H8 results in the formation of U 0 nanoparticles. 15 Thus, it would be expected that the reactions of alkali metal-based reagents with Cf III should result in the formation of Cf 0 unless the supporting ligands prevent over reduction because the potential for Cf III → Cf II is −1.525 V, whereas the Cf III → Cf 0 potential is −2.01 V. 16,17 Moreover, for americium the potential for Am III → Am II is −2.28 V versus Am III → Am 0 at −2.00 V, rendering the formation of Am 0 at lower energy than Am II . 18 Reagents such as KC8 are expected to yield ca. 2.93 V of reduction potential and thus are anticipated to be too strong for preparing most trans-plutonium An II complexes.</p><p>Lastly, one cannot neglect that all trans-plutonium isotopes have high specific activities and that both their ionizing radiation and concomitant formation of radiolysis products will influence the longevity of certain oxidation states. For example, radiolysis products rapidly reduce Bk IV to Bk III , but instead oxidize Cf II I2 to Cf III OI via the stunning -particle induced abstraction of oxide from silica reaction vessels. 19,20 The latter provides an excellent illustration of the energetic differences between nuclear and chemical reactions. Taken together, there are two hurdles to overcome to successfully isolate a Cf II complex. First, a reductant must be identified that is strong enough to reduce Cf III to Cf II but does not over reduce it to Cf 0 . Second, synthetic methodologies must be developed that allow for rapid complexation, reduction, and crystallization before radiolytic re-oxidation occurs. Herein, we show that Al/Hg amalgams can be used to achieve the proper reduction potential, and that crown ether ligands are appropriate for rapid crystallization of Cf II complexes.</p><!><p>Synthesis. We have previously shown that when Sm II is coordinatively saturated by large crown-ether ligands such as dibenzo-30-crown-10 that the resultant complex is stable in aqueous media for days. 21 This is somewhat surprising because Sm II normally reduces water and forms {Sm III 2O2} oxo-or hydroxo-dimers. From electrochemical measurements it has been affirmed that the stability of Sm II crown-ether complexes is kinetic in origin. This chemistry has been used to guide our synthetic efforts for Cf II because of the similarities between the Sm III to Sm II standard reduction potential (−1.66 V) with that of californium. 16 Given the difficulties in preparing soluble and anhydrous trans-plutonium starting materials, this former observation suggests that a route that is tolerant to a small amount of water might be initially more flexible than strictly moisture and air-free methods.</p><p>After optimizing the following reaction with both samarium and americium as well as with dicyclohexano-18-crown-6, the desired Cf II crown-ether complex, Cf II (18-crown-6)I2, was prepared via the reaction of CfI3•nH2O (n ≤ 6) with 18-crown-6 in the presence of</p><p>over a large excess of Al/Hg amalgam in anhydrous acetonitrile. Solubility issues with the [Cf III (18-crown-6)(H2O)(CH3CN)I]I2 complex that initially forms were eliminated by adding</p><p>[NBu4][BPh4] to the reaction mixture to inhibit ion pairing as was done in other Sm II reactions. 22 It is important to note that while the CfI3•nH2O (n ≤ 6) is obviously hydrated that this material has been dried in vacuo, and this process is known to convert hexahydrates to monohydrates.  few minutes to a peach-brown color as shown in Figure 1C. We have evidence that [Cf III (18crown-6)(H2O)(CH3CN)I]I2 is first reduced to [Cf II (18-crown-6)(H2O)2(CH3CN)]I2, and that the water is lost to the amalgam to yield the desired Cf(18-crown-6)I2 complex. It should be noted that if the mother liquor is removed from the amalgam at this stage its color will revert back to the original yellow-green color of the starting solution. While crystals can be isolated from this solution, they contain a mixture of Cf II and Cf III in the form of [Cf(18-crown-</p><p>This issue is circumvented by growing crystals over the amalgam itself via vapor diffusion of a 1:1 mixture of diethyl ether and pentane into the mother liquor at 0 ºC. Red-brown crystals of Cf(18-crown-6)I2 primarily grow (in surprisingly high yield) between the amalgam and the wall of the glass vial as shown in Figure 1D. Even with this crystal growth method where a large excess of reductant is always present, these samples degrade at room temperature, 0 ºC, and even at −173 ºC in less than 16 hours because of radiolytic effects.</p><p>It should be noted that KC8 can be used in the place of the Al/Hg amalgam, but as we discussed above, over reduction can occur rendering these reactions unpredictable. When this takes place, the californium becomes intercalated into the graphite and is difficult to extract. Given the scarcity of 249 Cf, the herculean efforts required to recycle it, and the real external radiation hazards that it poses to researchers even on small scales (ca. 5 mg), it is ill advised to utilize these overly strong reductants to prepare Cf II .</p><p>Structure. Single crystal X-ray diffraction studies reveal that Cf(18-crown-6)I2 (Figure 2B) adopts a structure-type first established with Ln II cations (Ln II = Eu, Sm, Yb, Dy, Tm) that has been the subject of recent investigations for single molecule magnetism with Tm(18-crown-6)I2. 22,24,25 The Cf(18-crown-6)I2 molecule consists of a Cf II cation bound within the cavity of the crown ether by the six etheric oxygen atoms and by two trans iodide anions. This yields a slightly distorted hexagonal bipyramidal environment where the Cf II cation is located on an inversion center. Cf-O bond distances range from 2.685(5) to 2.666(5) Å and are slightly shorter than those found with Eu(II), but longer than those of Dy(II) as shown in Figure 2C. Although the Cf-O and Cf-I bonds are mostly ionic, there is a small covalent contribution to these bonds where the 5forbital participation is essentially negligible. The Cf-I bond distance is 3.1563(4) Å which is notably shorter than that of Eu II -I, but statistically longer than that observed for Dy II -I. 22 The shortening of this bond is ascribed to the mixing of iodide 4pz orbitals with Cf II 6𝑑 z 2 orbitals (Figure 3A). Seeing as this is the first condensed-matter Cf II molecule that has been isolated and characterized, these bond metrics help bracket the upper and lower limits of the ionic radius of Cf II , which is currently not established. As previously mentioned, crystals can be obtained in low yield from reaction mixtures where the mother liquor has been removed from the amalgam. These crystals, while complex in nature, shed some light on the reductive process. X-ray diffraction studies show that these crystals are composed of [Cf(18-crown-6)(H2O)2-x(CH3CN)Ix]I2 as shown in Figure 2. The structure contains a mixture of an intermediate Cf II complex, [Cf(18-crown-6)(H2O)2(CH3CN)]I2, and the Cf III parent [Cf(18-crown-6)(H2O)(CH3CN)I]I2. The key difference between these two complexes exists primarily in the apical position that can be occupied by either a H2O molecule or an iodide anion. The structure refinement shows that the occupancy of the superimposed atomic positions are 0.6865 (15) for the oxygen atom and 0.3135 (15) for the iodide anion. In short, it contains ~69%</p><p>Cf II and 31% Cf III .</p><p>Given that the solution spectrum did not show the presence of Cf III and that O2 has been excluded, two possible oxidants remain: water and radiolysis. In this study, the amount of water is low with no more than six equivalents of water present in the initial reaction, and any remaining water after the CfI3•nH2O is placed under vacuum is removed via reduction by the amalgam. Thus, we conclude from six replications of this experiment and numerous others, that radiolytic oxidation occurs and is the primary cause of oxidation. This latter result is expected given the high specific activity of 249 Cf. 3 The presence of an oxygen atom in the apical position of [Cf(18-crown-6)(H2O)2(CH3CN)]I2 does not necessarily mean that it is a water molecule. It could be a hydroxide anion instead, which would yield a Cf III complex. However, computational analyses (Extended Data Table 1) show that a Cf III -OH bond distance would be 2.098 Å resulting in a weighted bond distance of 2.407 Å for Cf III -L (L = 69% OH -, 31% I -), which is much shorter than the observed distances of 2.705(11) and 2.742(2) Å for water and iodide, respectively. The same calculated weighted bond distance for Cf II -L (L = 69% H2O, 31% I -) is 2.791 Å, which is in much better agreement with experimental data. This type of substitutional disorder is well precedented in general (e.g. the origin of the bond shift isomerization misidentification), but is also known from numerous actinide halide compounds such as Pu2[B12O18(OH)4Br2(H2O)3]•0.5H2O and Cm2[B14O20(OH)7(H2O)2Cl] where Br -/H2O or Cl -/H2O disorder occurs. 26,27 The present system is somewhat different from the latter of these examples and better parallels that of the Mo=O/Mo-Cl averaging where two different molecules are present in the same crystal structure on the same crystallographic sites. 28 The structure of [Cf(18-crown-6)(H2O)2(CH3CN)]I2 consists of a nine-coordinate Cf II ion within a hula-hoop geometry. Similar to the Cf(18-crown-6)I2 structure, the "hoop" is formed from six approximately co-planar etheric oxygen atoms from the 18-crown-6 ligand. The apex is occupied by the aforementioned water molecule, and the two positions below the plane are filled by an acetonitrile molecule and a second water molecule as shown in Figure 2 with two outersphere iodide anions rounding out the asymmetric unit. This structure type is well established from lanthanide crown ether complexes and from this present study with Am III . 29 Spectroscopy. Room temperature solid-state absorption studies of single-crystals of Cf(18-crown-6)I2 yield broadband transitions in the UV-visible region as shown in Figure 4A. By comparison, typical solid-state absorption spectra of Cf 3+ -containing compounds are dominated by distinct 5f→5f transitions. 30,31 Based on reported absorption data for Cf 2+ binary halides, it is anticipated that compounds containing Cf 2+ would also exhibit characteristic 5f→5f transitions. 20,[32][33][34] However, the broadband features observed in the experimental absorption spectra reported here are, in fact, 5f→6d transitions (Figure 4), and there is a notable lack of expected 5f→5f transitions. For comparison with the experimental data presented here as well as relevant literature data, Ligand-field DFT calculations were used to predict the absorption spectrum for this system (Figure 5). It is worth mentioning that the 5f→6d transitions reported in the literature for CfCl2 and CfBr2 in particular are higher in energy than the 5f→6d transitions exhibited by Cf(18-crown-6)I2. The expected 5f→5f transitions in this region are not observed as a result of either (or both) the presence of a formal inversion center in the molecule or masking of the Laporte forbidden transitions by the electric dipole allowed 5f→6d transitions.  and 20,368 cm −1 . These bands are produced by the excitation from different 5f orbitals to the lowest lying 6d orbitals, which in this case correspond to the 6dyz and 6dxz (Extended Data Figure 1). In addition, a shoulder resolves on the peak centered at 20,368 cm −1 . This shoulder is indicative of the oxidation of Cf 2+ . Under the N2 atmosphere of the temperature-controlled stage used for solidstate measurements, this oxidation is slowed such that reliable measurements can be obtained before complete oxidation of Cf 2+ occurs. At room temperature, the oxidation occurs more rapidly under ambient conditions indicated by the increased intensity of the observed shoulder at 20,829 cm −1 and the gradual decrease of the 5f→6d transitions in the visible region as shown in Figure 4B.</p><p>The observed Cf 2+ 5f→6d transitions are further supported by photoluminescence measurements of single crystals at 93.15 K. As shown in Figure 4C, excitation of these crystals with 546 nm (18,315 cm −1 ) light yields broadband emission at 14,087 cm −1 (710 nm) which corresponds to emission of the first group of 5f→6d transitions (16,303 cm −1 ). Compared to the photoluminescence observed from the isomorphous Sm(18-crown-6)I2 under the same conditions, the emission exhibited by Cf(18-crown-6)I2 is far less intense. 22 The solution-phase absorption spectrum for this system corroborates the presence of Cf 2+ prior to crystallization. As shown in Figure 4D, the absorption spectrum of [Cf (18-crown-6)x] 2+ in acetonitrile exhibits several broad features between 32,500 and 15,000 cm −1 . Most of these features can be attributed to the transitions identified in the solid-state absorption spectra of Cf(18-crown-6)I2. However, there are notable differences in the spectra obtained from these two phases that are likely the result of competing coordination environments of the [Cf(18-crown-6)x] 2+ ion. An example of this is an observed color change that is dependent on the concentration of [Cf(18crown-6)x] 2+ in solution. The more concentrated solution from which Cf(18-crown-6)I2 crystallizes is a dark peach-brown color, but the color of this solution shifts dramatically when diluted with acetonitrile resulting in a blue-green solution (Figure 6). In the presence of excess acetonitrile, it is probable that the more labile iodide ions would be displaced by solvent molecules. Given the possibility of different coordination environments in solution, the allowance of 5f→5f transitions cannot be overlooked. However, the pseudo-axial symmetry imposed by the coordination of the 18-crown-6 molecule restricts the overall intensity of these transitions compared to the dipoleallowed 5f→6d transitions (Extended Data Figure 2).</p><p>When the solution containing [Cf(18-crown-6)x] 2+ is exposed to oxygen, a vivid color change from blue-green to bright yellow is observed resulting in the spectrum shown in Figure 6.</p><p>Similar to studies with Sm 2+ , the introduction of oxygen to this system rapidly oxidizes the divalent species to [Cf(18-crown-6)x] 3+ . The solution absorption spectrum obtained following this color change shows that the low energy features exhibited by the reduced species in acetonitrile are notably absent, and a broad, intense feature is observed at 27,758 cm −1 (360 nm) instead. This latter feature is comparable to the high energy transition displayed by [Cf(18-crown-6)(H2O)2-</p><p>x(CH3CN)Ix]I2 in the same region (Extended Data Figure 3). Overall, the ambiguity of the solutionphase absorption data obtained for the divalent and trivalent species highlights the necessity for reliable solid-state structural evidence of the presence of Cf 2+ in systems like the one reported here.</p><!><p>The isolation of Cf(18-crown-6)I2 establishes an important precedent for stabilization of the 2+ oxidation state in the later actinides (Z ≥ 98) in condensed-matter, molecular systems.</p><p>Although radiolytic re-oxidation of Cf 2+ is a significant hurdle to overcome, we have shown that the use of a more suitable reductant in the form of an Al/Hg amalgam is sufficient to reduce and maintain stability of the divalent state as well as prevent potential oxidants like water from Samantha Justiniano: 0000-0001-6117-4432</p><p>Thomas E. Albrecht-Schönzart: 0000-0002-2989-3311</p><p>Cristian Celis-Barros: 0000-0002-4685-5229</p><!><p>The authors declare no competing financial interest.</p><!><p>This research was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Heavy Elements Chemistry Program, under Award DE-FG02-13ER16414. Materials. The 249 CfCl3 used in this experiment was isolated as a solid residue following purification procedures. The 243 AmCl3 used in this experiment was acquired from an Am stock solution in 2M HCl. DyI2 (Sigma-Aldrich, 99%) was used as received. 18-crown-6 (Sigma-Aldrich, 99%) and tetrabutylammonium tetraphenylborate (Sigma-Aldrich, 99%) were used as received. Dicyclohexano-18-crown-6 (98%) was acquired as a mixture of cis-isomers from Sigma-Aldrich. The cis-syn-cis and cis-anti-cis isomers were separated from one another using the procedure established by Izatt and coworkers. 1 Hydroiodic acid (contains no stabilizer, distilled, 57 wt. % in H2O, 99.99% trace metals basis, Sigma-Aldrich) was stored in a freezer at less than 0 °C until it was used. Ammonium hydroxide (28% NH3 in H2O, ≥ 99.99% trace metals basis, Sigma-Aldrich) was used as received. Diethyl ether (VWR, anhydrous ≥ 99.0% stabilized) was used as received for all manipulations on the benchtop. For manipulations in the glovebox, diethyl ether and acetonitrile (Sigma-Aldrich, anhydrous, 99.8%) were dried over sodium (Sigma-Aldrich, cubes, contains mineral oil, 99.9% trace metals basis) and benzophenone (Sigma-Aldrich, 99%)</p><!><p>and CaH2 (Sigma-Aldrich, reagent grade, 95% (gas-volumetric)), respectively, before being stored in a glovebox under an argon atmosphere over activated molecular sieves (3 Å, 4-8 mesh, Sigma-Aldrich). The Al/Hg amalgam was prepared as follows: Aluminum (Sigma-Aldrich, beads, 5-15 mm, 99.9% trace metals basis) was charged in a 100 mL Schlenk flask and submerged in concentrated HCl. Vigorous bubbling occurred as the oxide coating was stripped from the aluminum beads. The flask was stirred vigorously by hand for five minutes. The solution was then carefully decanted. The aluminum beads were washed 3 times with diethyl ether and then the entire flask was placed under vacuum overnight. The flask was then pumped into a glovebox under and argon atmosphere. In a 20 mL scintillation vial, enough Hg metal (Sigma-Aldrich, ≥ 99.99% trace metals basis) to just cover the bottom of the vial was added. Three aluminum beads were removed from the Schlenk flask and careful placed over the mercury. The vial was capped and placed on a hot plate and heated to 250 °C. The amalgam was kept heated overnight and stirred occasionally.</p><p>Eventually, aluminum began to dissolve in the mercury forming a dull gray, liquid Al/Hg amalgam. Preparation of Dy (18-crown-6)I2. In a glovebox under an argon atmosphere, a 20 mL glass scintillation vial was charged with 20.0 mg of DyI2. Then, 3 mL of cold (−30 °C) DME was added to the vial and swirled to encourage dissolution of the DyI2. The dissolution process was slow, and the solution began to turn a shade of dark green. The reaction vial was stored in a glovebox freezer at −30 °C to maintain stability of Dy 2+ in solution. Every 10 minutes, the vial was removed from the freezer and a metal spatula was used to grind the remaining solid to encourage further dissolution of the DyI2. The solution was then gently swirled and replaced in the freezer for another 10-minute period. This was repeated until all solids dissolved, resulting in a dark green solution.</p><!><p>Separately, 12.7 mg of 18-crown-6 was dissolved in 3 mL of cold (−30 °C) toluene to create a stock solution and then stored in a glovebox freezer at −30 °C to maintain the temperature of the solution. Once both solutions were prepared and chilled to −30 °C, they were removed from the glovebox freezer. A disposable glass pipette was used to transfer 3 drops of the toluene solution containing 18-crown-6 to the DME solution containing DyI2. Neither solution was stirred. Both solutions were then carefully (avoiding agitation of the solution) replaced in the glovebox freezer to maintain a solution temperature of −30 °C. Both solutions were allowed to sit in the freezer for 5 minutes untouched. Then, the solutions were carefully removed from the freezer to avoid agitation, and 3 drops of the toluene stock solution containing 18-crown-6 was again added to the solution containing DyI2. This process was repeated continually avoiding agitation of the DyI2 solution at all costs. Additions of the 18-crown-6 stock solution yielded a dark brownish-green precipitate almost immediately. After the slow, dropwise addition of almost half of the stock solution described previously, dark green microcrystals began to form on the walls of the glass scintillation vial. Slow, dropwise addition of the ligand solution sometimes resulted in crystals of Dy(18-crown-6)I2 large enough for single-crystal x-ray diffraction studies, but total crystalline yield was low (< 20%). Further characterization and interpretation of Dy(18-crown-6)I2 will reported elsewhere, but the crystal structure is crucial to the bond length comparisons for Cf(18crown-6)I2.</p><p>Crystallography. Crystals of all three compounds were isolated in a glovebox under an argon atmosphere and placed on a glass slide under immersion oil before being transferred to a microscope on the benchtop. Single crystals were then mounted on 75 μm inner diameter MiTeGen loops before being transferred to the goniometer of a Bruker D8 Quest Single Crystal X-ray Diffractometer with a IμS X-ray source (Mo Kα; λ = 0.71073 Å). A stream of N2 gas was flowed over the crystals to preserve crystallinity and regulate the temperature of the sample. All collections were performed at 100.00 K. Subsequent data integration was performed using APEXIII software, and space group determination was performed using xprep. The following structure refinement was completed with the SHELXTL suite using the OLEX2 GUI. Extended Data Table 1 shows a comparison between the experimental and theoretical bond lengths with and without the inclusion of the surrounding iodide ions. Our theoretical structures suggest that the oxygen in the apical position corresponds to a water molecule because a hydroxide anion should display a significantly shorter experimental bond length.</p><p>These calculations were performed in the ADF engine of AMS2021. 4 The generalized gradient approximation (GGA) PBE functional was used for this task along with the Slater-type orbital (STO)-DZ basis set for H, N, and C atoms, and STO-TZP for Cf, O, and I atoms. Scalar relativistic effects were included using the ZORA approximation as implemented in ADF. 5 For those calculations involving surrounding counter ions, the position of iodide anions were constrained to simulate the crystal packing.</p><p>Ligand Field DFT (LFDFT). The LFDFT approach has been used widely to reproduce the electronic structure of f-element complexes of mostly lanthanides but has also been applied to actinide complexes. [6][7][8][9] The inability of TD-DFT to predict multiplet electronic structure due to the lack of static correlation makes the LFDFT a more appropriate model, which account for both static and to a certain extent dynamic correlation.</p><p>The intensities associated with the excitation spectra were calculated using the oscillator strengths 𝑓 𝑎,𝑏 of an a → b electron transition, with a and b representing the initial final electronic states (in atomic units): 𝑓 𝑎,𝑏 = 2 3 ∆𝐸 𝑎,𝑏 ⟨𝑎|𝝁|𝑏⟩ 2 , where the electric transition dipole moments were formulated in the dipole-length form (𝝁 = −𝑟). The non-zero oscillator strengths for 5f-5f transitions arise from the mixing between actinide 5f states and 6d or other ligand states in a noncentrosymmetric ligand-field regime. The ligand states for the actinide complexes are referred to the one-electron ligand-to-metal charge transfer states that possess large parentage of ligands 2p orbitals. We note that we use a static model somewhat equivalent to the Judd-Ofelt model, 10,11 where non-zero oscillator strengths existed through parity mixing that is due to the coordination geometry of the actinide ion. Thus, dynamical effects (eg. vibrations) were not considered in our calculations.</p><p>The calculated ligand field parameters for Cf(18-crown-6)I2 in a 5f 10  Molecular orbital localization. The Kohn-Sham orbitals obtained from single point calculations were used to obtain the Natural Localized Molecular Orbitals using the NBO module included in ADF. 12 The single point calculation was performed using the hybrid GGA PBE0 functional in conjunction with the STO-TZP basis set for all atoms except Cf and I, where the STO-TZ2P basis set was used.</p><p>Complete active space self-consistent field (CASSCF). Spin-orbit CASSCF calculations were performed in ORCA 5.0.2 at the PBE0/TZVP level of theory (except H atoms for which we used the small SVP basis set). 13 Scalar relativistic effects were included via the Douglas-Kroll-</p>