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1.
Phys Chem Chem Phys ; 25(35): 23753-23760, 2023 Sep 13.
Artigo em Inglês | MEDLINE | ID: mdl-37615175

RESUMO

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

2.
Phys Chem Chem Phys ; 25(29): 19453-19461, 2023 Jul 26.
Artigo em Inglês | MEDLINE | ID: mdl-37314003

RESUMO

We compare the stabilities and bonding nature of [Eu/Am(BTPhen)2(NO3)]2+ complexes to those previously reported for [Eu/Am(BTP)3]3+, and investigate whether more accurately reflecting the reaction conditions of the separation process by considering [Eu/Am(NO3)3(H2O)x] (x = 3, 4) complexes instead of aquo complexes increases the selectivity of the separation ligands BTP and BTPhen for Am over Eu. The geometric and electronic structures of [Eu/Am(BTPhen)2(NO3)]2+ and [Eu/Am(NO3)3(H2O)x] (x = 3, 4) have been evaluated using density functional theory (DFT) and used as the basis for analysis of the electron density through the application of the quantum theory of atoms in molecules (QTAIM). Increased covalent bond character for the Am complexes of BTPhen over Eu analogues was found, with this increase more pronounced than that found in BTP complexes. BHLYP-derived exchange reaction energies were evaluated using the hydrated nitrates as a reference and a favourability for actinide complexation by both BTP and BTPhen was found, with the BTPhen ligand found to be more selective, with relative stability ≈0.17 eV greater than BTP.

3.
Inorg Chem ; 61(23): 8955-8965, 2022 Jun 13.
Artigo em Inglês | MEDLINE | ID: mdl-35654478

RESUMO

Reaction of the uranium(III) bis(amidinate) aryl complex {TerphC(NiPr)2}2U(Terph) (2, where Terph = 4,4″-di-tert-butyl-m-terphenyl-2'-yl) with a strong reductant enabled isolation of isomeric uranium(III) bis(amidinate) aryl product {TerphC(NiPr)2}2U(Terph*) (3, where Terph* = 4,4″-di-tert-butyl-m-terphenyl-4'-yl). In terms of connectivity, 3 differs from 2 only in the positions of the U-C and C-H bonds on the central aryl ring of the m-terphenyl-based ligand. A deuterium labeling study ruled out mechanisms for this isomerization involving intermolecular abstraction or deprotonation of the ligand C-H bonds activated during the reaction. Due to the complexity of this rapid, heterogeneous reaction, experimental studies could not further distinguish between two different intramolecular C-H activation mechanisms. However, high-level computational studies were consistent with a mechanism that included two sets of unimolecular, mononuclear C-H oxidative addition and reductive elimination steps involving uranium(II/IV).

4.
J Am Chem Soc ; 143(33): 13184-13194, 2021 08 25.
Artigo em Inglês | MEDLINE | ID: mdl-34387466

RESUMO

Pentavalent uranyl species are crucial intermediates in transformations that play a key role for the nuclear industry and have recently been demonstrated to persist in reducing biotic and abiotic aqueous environments. However, due to the inherent instability of pentavalent uranyl, little is known about its electronic structure. Herein, we report the synthesis and characterization of a series of monomeric and dimeric, pentavalent uranyl amide complexes. These synthetic efforts enable the acquisition of emission spectra of well-defined pentavalent uranyl complexes using photoluminescence techniques, which establish a unique signature to characterize its electronic structure and, potentially, its role in biological and engineered environments via emission spectroscopy.

5.
Inorg Chem ; 60(14): 10614-10630, 2021 Jul 19.
Artigo em Inglês | MEDLINE | ID: mdl-34192465

RESUMO

In continuing to examine the interaction of actinide-ligand bonds with soft donor ligands, a comparative investigation with phosphorus and arsenic was conducted. A reaction of (C5Me5)2AnMe2, An = Th, U, with 2 equiv of H2AsMes, Mes = 2,4,6-Me3C6H2, forms the primary bis(arsenido) complexes, (C5Me5)2An[As(H)Mes]2. Both exhibit thermal instability at room temperature, leading to the elimination of H2, and the formation of the diarsenido species, (C5Me5)2An(η2-As2Mes2). The analogous diphosphido complexes, (C5Me5)2An(η2-P2Mes2), could not be synthesized via the same route, even upon heating the bis(phosphido) species to 100 °C in toluene. However, they were accessible via the reaction of dimesityldiphosphane, MesP(H)P(H)Mes, with (C5Me5)2AnMe2 at 70 °C in toluene. When (C5Me5)2AnMe2 is reacted with 1 equiv of H2AsMes, the bridging µ2-arsinidiide complexes [(C5Me5)2An]2(µ2-AsMes)2 are formed. Upon reaction of (C5Me5)2UMe2 with 1 equiv of H2PMes, the phosphinidiide [(C5Me5)2U(µ2-PMes)]2 is isolated. However, the analogous thorium reaction leads to a phosphido and C-H bond activation of the methyl on the mesityl group, forming {(C5Me5)2Th[P(H)(2,4-Me2C6H2-6-CH2)]}2. The reactivity of [(C5Me5)2An(µ2-EMes)]2 was investigated with OPPh3 in an effort to produce terminal phosphinidene or arsinidene complexes. For E = As, An = U, a U(III) cation-anion pair [(C5Me5)2U(η2-As2Mes2)][(C5Me5)2U(OPPh3)2] is isolated. The reaction of [(C5Me5)2Th(µ2-AsMes)]2 with OPPh3 does not result in a terminal arsinidene but, instead, eliminates PPh3 to yield a bridging arsinidiide/oxo complex, [(C5Me5)2Th]2(µ2-AsMes)(µ2-O). Finally, the combination of [(C5Me5)2U(µ2-PMes)]2 and OPPh3 yields a terminal phosphinidene, (C5Me5)2U(═PMes)(OPPh3), featuring a short U-P bond distance of 2.502(2) Å. Electrochemical measurements on the uranium pnictinidiide complexes demonstrate only a 0.04 V difference with phosphorus as a slightly better donor. Magnetic measurements on the uranium complexes show more excited-state mixing and therefore higher magnetic moments with the arsenic-containing compounds but no deviation from uncoupled U(IV) behavior. Finally, a quantum theory of atoms in molecules analysis shows highly polarized actinide-pnictogen bonds with similar bonding characteristics, supporting the electrochemical and magnetic measurements of similar bonding between actinide-phosphorus and actinide-arsenic bonds.

6.
J Am Chem Soc ; 140(51): 17977-17984, 2018 Dec 26.
Artigo em Inglês | MEDLINE | ID: mdl-30540455

RESUMO

Evaluating the nature of chemical bonding for actinide elements represents one of the most important and long-standing problems in actinide science. We directly address this challenge and contribute a Cl K-edge X-ray absorption spectroscopy and relativistic density functional theory study that quantitatively evaluates An-Cl covalency in AnCl62- (AnIV = Th, U, Np, Pu). The results showed significant mixing between Cl 3p- and AnIV 5f- and 6d-orbitals (t1u*/t2u* and t2 g*/eg *), with the 6d-orbitals showing more pronounced covalent bonding than the 5f-orbitals. Moving from Th to U, Np, and Pu markedly changed the amount of M-Cl orbital mixing, such that AnIV 6d - and Cl 3p-mixing decreased and metal 5f - and Cl 3p-orbital mixing increased across this series.

7.
Inorg Chem ; 57(17): 10518-10524, 2018 Sep 04.
Artigo em Inglês | MEDLINE | ID: mdl-30113163

RESUMO

In a systematic approach to comparing the molecular structure and bonding in homoleptic transition-metal and actinide complexes, a series of dithiocarbamates, M(S2CNiPr2)4 (M = Ti, Zr, Hf, Th, U, Np), have been synthesized. These complexes have been characterized through spectroscopic and X-ray crystallographic analysis, and their bonding has been examined using density functional theory calculations. Computational results indicate that the covalent character associated with the M-S bonds shows the trend of Hf < Zr < Th < Ti < U ≈ Np.

8.
Inorg Chem ; 57(5): 2714-2723, 2018 Mar 05.
Artigo em Inglês | MEDLINE | ID: mdl-29436823

RESUMO

Bending the linear uranyl (UO22+) cation represents both a significant challenge and opportunity within the field of actinide hybrid materials. As part of related efforts to engage the nominally terminal oxo atoms of uranyl cation in noncovalent interactions, we synthesized a new uranyl complex, [UO2(C12H8N2)2(C7H2Cl3O2)2]·2H2O (complex 2), that featured both deviations from equatorial planarity and uranyl linearity from simple hydrothermal conditions. Based on this complex, we developed an approach to probe the nature and origin of uranyl bending within a family of hybrid materials, which was done via the synthesis of complexes 1-3 that display significant deviations from equatorial planarity and uranyl linearity (O-U-O bond angles between 162° and 164°) featuring 2,4,6-trihalobenzoic acid ligands (where Hal = F, Cl, and Br) and 1,10-phenanthroline, along with nine additional "nonbent" hybrid materials that either coformed with the "bent" complexes (4-6) or were prepared as part of complementary efforts to understand the mechanism(s) of uranyl bending (7-12). Complexes were characterized via single crystal X-ray diffraction and Raman, infrared (IR), and luminescence spectroscopy, as well as via quantum chemical calculations and density-based quantum theory of atoms in molecules (QTAIM) analysis. Looking comprehensively, these results are compared with the small library of bent uranyl complexes in the literature, and herein we computationally demonstrate the origin of uranyl bending and delineate the energetics behind this process.

9.
Chemistry ; 23(10): 2290-2293, 2017 Feb 16.
Artigo em Inglês | MEDLINE | ID: mdl-28009936

RESUMO

The redox chemistry of uranium is burgeoning and uranium(III) complexes have been shown to promote many interesting synthetic transformations. However, their utility is limited by their reduction potentials, which are smaller than many non-traditional lanthanide(II) complexes. Thorium(III) has a greater redox potential so it should present unprecedented opportunities for actinide reactivity but as with uranium(II) and thorium(II) chemistry, these have not yet been fully realized. Herein we present reactivity studies of two equivalents of [Th(Cp'')3 ] (1, Cp''={C5 H3 (SiMe3 )2 -1,3}) with 4,4'-bipyridine or two equivalents of pyridine to give [{Th(Cp'')3 }2 {µ-(NC5 H4 )2 }] (2) and [{Th(Cp'')3 }2 {µ-(NC5 H5 )2 }] (3), respectively. As relatively large reduction potentials are required to effect these transformations we have shown that thorium(III) can promote reactions that uranium(III) cannot, opening up promising new reductive chemistry for the actinides.

10.
Phys Chem Chem Phys ; 19(11): 7546-7559, 2017 Mar 15.
Artigo em Inglês | MEDLINE | ID: mdl-28252123

RESUMO

A series of uranyl complexes with hexaphyrin ligands are investigated at the density functional level of theory and analysed using a variety of density-based techniques. A relationship is identified between the size of the ligand and the stability of the complex, controlled by the presence of meso-carbon centres in the porphyrin ring. The complex with the smallest ligand, cyclo[6]pyrrole, is found to have enhanced covalent character in equatorial U-N bonds as defined by the quantum theory of atoms in molecules (QTAIM), as well as enhanced stability, compared to the larger complexes. QTAIM data are supported by electron density difference distributions, integrated electronic properties and analysis of the reduced density gradient (RDG), which all show unambiguous evidence of electron sharing in all U-N bonds. In all complexes, a weakening of the covalent axial U-Oyl interaction in comparison to free uranyl is found, with evidence for a separation of electronic charge resulting in a more ionic interaction. A relationship between covalent character in the U-N bonds and the magnitude of uranyl charge redistribution is identified, where the greater the covalent character of the U-N interaction, the more ionic the U-Oyl interaction appears. The complex with the largest ligand, hexaphyrin(1.1.1.1.1.1), is found to have additional interactions with the uranyl oxygen centres, perturbing the U-Oyl interaction.

11.
Chemistry ; 22(50): 17976-17979, 2016 Dec 12.
Artigo em Inglês | MEDLINE | ID: mdl-27714966

RESUMO

Improving our comprehension of diverse CO2 activation pathways is of vital importance for the widespread future utilization of this abundant greenhouse gas. CO2 activation by uranium(III) complexes is now relatively well understood, with oxo/carbonate formation predominating as CO2 is readily reduced to CO, but isolated thorium(III) CO2 activation is unprecedented. We show that the thorium(III) complex, [Th(Cp'')3 ] (1, Cp''={C5 H3 (SiMe3 )2 -1,3}), reacts with CO2 to give the mixed oxalate-carboxylate thorium(IV) complex [{Th(Cp'')2 [κ2 -O2 C{C5 H3 -3,3'-(SiMe3 )2 }]}2 (µ-κ2 :κ2 -C2 O4 )] (3). The concomitant formation of oxalate and carboxylate is unique for CO2 activation, as in previous examples either reduction or insertion is favored to yield a single product. Therefore, thorium(III) CO2 activation can differ from better understood uranium(III) chemistry.

12.
Inorg Chem ; 55(2): 573-83, 2016 Jan 19.
Artigo em Inglês | MEDLINE | ID: mdl-26700790

RESUMO

The molecular structures of a series of uranyl (UO2(2+)) complexes in which the uranium center is equatorially coordinated by a first-row species are calculated at the density functional theory level and binding energies deduced. The resulting electronic structures are investigated using a variety of density-based analysis techniques in order to quantify the degree of covalency in the equatorial bonds. It is shown that a consideration of the properties of both the one-electron and electron-pair densities is required to understand and rationalize the variation in axial bonding effected by equatorial complexation. Strong correlations are found between density-based measures of the covalency and equatorial binding energies, implying a stabilizing effect due to covalent interaction, and it is proposed that uranyl U-Oyl stretching vibrational frequencies can serve as an experimental probe of equatorial covalency.

13.
Inorg Chem ; 55(20): 10034-10042, 2016 Oct 17.
Artigo em Inglês | MEDLINE | ID: mdl-27494549

RESUMO

The geometrical and electronic structures of Ln[(H2O)9]3+ and [Ln(BTP)3]3+, where Ln = Ce-Lu, have been evaluated at the density functional level of theory using three related exchange-correlation (xc-)functionals. The BHLYP xc-functional was found to be most accurate, and this, along with the B3LYP functional, was used as the basis for topological studies of the electron density via the quantum theory of atoms in molecules (QTAIM). This analysis revealed that, for both sets of complexes, bonding was almost identical across the Ln series and was dominated by ionic interactions. Geometrical and electronic structures of actinide (An = Am, Cm) analogues were evaluated, and [An(H2O)9]3+ + [Ln(BTP)3]3+ → [Ln(H2O)9]3+ + [An(BTP)3]3+ exchange reaction energies were evaluated, revealing Eu ↔ Am and Gd ↔ Cm reactions to favor the An species. Detailed QTAIM analysis of Eu, Gd, Am, and Cm complexes revealed increased covalent character in M-O and M-N bonds when M = An, with this increase being more pronounced in the BTP complexes. This therefore implies a small electronic contribution to An-N bond stability and the experimentally observed selectivity of the BTP ligand for Am and Cm over lanthanides.

14.
Phys Chem Chem Phys ; 18(25): 16830-9, 2016 Jun 22.
Artigo em Inglês | MEDLINE | ID: mdl-27279271

RESUMO

Calculations performed at the density functional level of theory have been used to investigate complexes of uranyl with the expanded porphyrin isoamethyrin and the bis-triazinyl-pyridine (BTP) ligands, the latter of which is well-known to be effective in the separation of trivalent lanthanides and actinides. Analysis has been performed using a range of density-based techniques, including the Quantum Theory of Atoms in Molecules (QTAIM), the Electron Localisation Function (ELF) and the reduced density gradient (RDG). The effects of peripheral alkyl substituents on UO2-isoamethyrin, known to be vital for proper replication of the experimental geometry, are considered. Evidence for comparable amounts of covalent character has been found in the largely ionic U-N bonds of UO2-isoamethyrin and [UO2(BTP)2](2+) and examination of the variation in the electronic characteristics of the uranyl unit upon complexation in both of these cases reveal striking similarities in the nature of the U-N bonding and the effect of this bonding on the U-Oyl interaction, as well as evidence of donation into the U-N bonding region from the uranyl unit itself.

15.
J Chem Phys ; 145(20): 204708, 2016 Nov 28.
Artigo em Inglês | MEDLINE | ID: mdl-27908144

RESUMO

Density functional theory (DFT) at the generalised gradient approximation level is employed within the periodic electrostatic embedded cluster method (PEECM) to model the brucite (0001) surface. Three representative studies are then used to demonstrate the reliability of the PEECM for the description of the interactions of various ionic species with the layered Mg(OH)2 structure, and its performance is compared with periodic DFT, an approach known to be challenging for the adsorption of charged species. The adsorption energies of a series of s block cations, including Sr2+ and Cs+ which are known to coexist with brucite in nuclear waste storage ponds, are well described by the embedded cluster model, provided that basis sets of triple-zeta quality are employed for the adsorbates. The substitution energies of Ca2+ and Sr2+ into brucite obtained with the PEECM are very similar to periodic DFT results, and comparison of the approaches indicates that two brucite layers in the quantum mechanical part of the PEECM are sufficient to describe the substitution. Finally, a detailed comparison of the periodic and PEECM DFT approaches to the energetic and geometric properties of differently coordinated Sr[(OH)2(H2O)4] complexes on brucite shows an excellent agreement in adsorption energies, Sr-O distances, and bond critical point electron densities (obtained via the quantum theory of atoms-in-molecules), demonstrating that the PEECM can be a useful alternative to periodic DFT in these situations.

16.
Inorg Chem ; 54(24): 11625-36, 2015 Dec 21.
Artigo em Inglês | MEDLINE | ID: mdl-26636609

RESUMO

We report a comparison of the molecular and electronic structures of dithio- and diselenophosphinate, (E2PR2)(1-) (E = S, Se; R = (i)Pr, (t)Bu), with thorium(IV) and uranium(IV) complexes. For the thorium dithiophosphinate complexes, reaction of ThCl4(DME)2 with 4 equiv of KS2PR2 (R = (i)Pr, (t)Bu) produced the homoleptic complexes, Th(S2P(i)Pr2)4 (1S-Th-(i)Pr) and Th(S2P(t)Bu2)4 (2S-Th-(t)Bu). The diselenophosphinate complexes were synthesized in a similar manner using KSe2PR2 to produce Th(Se2P(i)Pr2)4 (1Se-Th-(i)Pr) and Th(Se2P(t)Bu2)4 (2Se-Th-(t)Bu). U(S2P(i)Pr2)4, 1S-U-(i)Pr, could be made directly from UCl4 and 4 equiv of KS2P(i)Pr2. With (Se2P(i)Pr2)(1-), using UCl4 and 3 or 4 equiv of KSe2P(i)Pr2 yielded the monochloride product U(Se2P(i)Pr2)3Cl (3Se-U(iPr)-Cl), but using UI4(1,4-dioxane)2 produced the homoleptic U(Se2P(i)Pr2)4 (1Se-U-(i)Pr). Similarly, the reaction of UCl4 with 4 equiv of KS2P(t)Bu2 yielded U(S2P(t)Bu2)4 (2S-U-(t)Bu), whereas the reaction with KSe2P(t)Bu2 resulted in the formation of U(Se2P(t)Bu2)3Cl (4Se-U(tBu)-Cl). Using UI4(1,4-dioxane)2 and 4 equiv of KSe2P(t)Bu2 with UCl4 in acetonitrile yielded U(Se2P(t)Bu2)4 (2Se-U-(t)Bu). Transmetalation reactions were investigated with complex 2Se-U-(t)Bu and various CuX (X = Br, I) salts to yield U(Se2P(t)Bu2)3X (6Se-U(tBu)-Br and 7Se-U(tBu)-I) and 0.25 equiv of [Cu(Se2P(t)Bu2)]4 (8Se-Cu-(t)Bu). Additionally, 2Se-U-(t)Bu underwent transmetalation reactions with Hg2F2 and ZnCl2 to yield U(Se2P(t)Bu2)3F (6) and U(Se2P(t)Bu2)3Cl (4Se-U(tBu)-Cl), respectively. The molecular structures were analyzed using (1)H, (13)C, (31)P, and (77)Se NMR and IR spectroscopy and structurally characterized using X-ray crystallography. Using the QTAIM approach, the electronic structure of all homoleptic complexes was probed, showing slightly more covalent bonding character in actinide-selenium bonds over actinide-sulfur bonds.

17.
Angew Chem Int Ed Engl ; 54(14): 4255-8, 2015 Mar 27.
Artigo em Inglês | MEDLINE | ID: mdl-25655652

RESUMO

Deprotonation of the yttrium-arsine complex [Cp'3Y{As(H)2Mes}] (1) (Cp'=η(5)-C5H4Me, Mes=mesityl) by nBuLi produces the µ-arsenide complex [{Cp'2Y[µ-As(H)Mes]}3] (2). Deprotonation of the As-H bonds in 2 by nBuLi produces [Li(thf)4]2[{Cp'2Y(µ3-AsMes)}3Li], [Li(thf)4]2[3], in which the dianion 3 contains the first example of an arsinidene ligand in rare-earth metal chemistry. The molecular structures of the arsine, arsenide, and arsinidene complexes are described, and the yttrium-arsenic bonding is analyzed by density functional theory.

18.
Phys Chem Chem Phys ; 16(40): 22052-61, 2014 Oct 28.
Artigo em Inglês | MEDLINE | ID: mdl-25207882

RESUMO

The optical absorption spectra of magnesium oxide (MgO) nanoparticles, along with the atomic centres responsible, are studied using a combination of time-dependent density functional theory (TD-DFT) and coupled-cluster methods. We demonstrate that TD-DFT calculations on MgO nanoparticles require the use of range-separated exchange-correlation (XC-) functionals or hybrid XC-functionals with a high percentage of Hartree-Fock like exchange to circumvent problems related to the description of charge-transfer excitations. Furthermore, we show that the vertical excitations responsible for the experimentally studied range of the spectra of the MgO nanoparticles typically involve both 3-coordinated corner sites and 4-coordinated edge sites. We argue therefore that to label peaks in these absorption spectra exclusively as either corner or edge features does not provide insight into the full physical picture.

19.
Phys Chem Chem Phys ; 15(6): 2197-209, 2013 Feb 14.
Artigo em Inglês | MEDLINE | ID: mdl-23296122

RESUMO

The restricted-active-space self-consistent-field methodology is successfully applied to the study of free base- and regular metalloporphyrins, the latter containing magnesium and zinc central ions. It is shown that inclusion of all excitations involving the Gouterman frontier orbitals in the RAS2 subspace results in a numerically stable approach, producing highly accurate results at a fraction of the computational cost of the complete-active-space self-consistent-field method, whereas increasing RAS2 beyond this size leads to only modest improvement. Topological and orbital analysis shows that the approach is also able to give a highly accurate description of the electronic wavefunction. Inclusion of the entire π-conjugated subsystem in the active space results in more accurate excitation energies and a reduction in the dependence on the exact form of the perturbational Hamiltonian used to include dynamic correlation. The larger active space also resolves a quantitative disagreement in results obtained with and without the inclusion of dynamic correlation.

20.
RSC Adv ; 13(41): 28426-28433, 2023 Sep 26.
Artigo em Inglês | MEDLINE | ID: mdl-37771918

RESUMO

Despite increase in demand, capacity for the recycling of rare earth elements remains limited, partly due to the inefficiencies with processes currently utilised in the separation of lanthanides. This study highlights the potential use of expanded porphyrinoids in lanthanide separation through selective binding, dependent on the tailored pore size of the macrocycle. Each emerging trend is subjected to multi-factored analysis to decompose the underlying source. Results promote the viability of size-based separation with preferential binding of larger lanthanum(iii) ions to amethyrin and isoamethyrin macrocycles, while smaller macrocycles such as pentaphyrin(0.0.0.0.0) present a preferential binding of lutetium(iii) ions. Additionally, the porphyrin(2.2.2.2) macrocycle shows a selectivity for gadolinium(iii) ions over both larger and smaller ions. An upper limit of applicable pore size is shown to be ≈2.8 Å, beyond which the formed complexes are predicted to be less stable than the corresponding nitrate complexes.

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