DFT Investigations of the Magnetic Properties of Actinide Complexes

magnetochemistry

Review DFT Investigations of the Magnetic Properties of Actinide Complexes

Lotﬁ Belkhiri 1,*,† , Boris Le Guennic 2,† and Abdou Boucekkine 2,*,†

1 Laboratoire de Physique Mathématique et Subatomique LPMS, Faculté des Sciences Exactes, Université des Frères Mentouri Constantine 1, Constantine 25017, Algeria 2 Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes) - UMR 6226, F-35000 Rennes, France; [email protected] * Correspondence: lotﬁ[email protected] (L.B.); [email protected] (A.B.); Tel.: +3-32-2323-6269 (A.B.) † Equal contribution.

Received: 4 January 2019; Accepted: 8 February 2019; Published: 17 February 2019

Abstract: Over the past 25 years, magnetic actinide complexes have been the object of considerable attention, not only at the experimental level, but also at the theoretical one. Such systems are of great interest, owing to the well-known larger spin–orbit coupling for actinide ions, and could exhibit slow relaxation of the magnetization, arising from a large anisotropy barrier, and magnetic hysteresis of purely molecular origin below a given blocking temperature. Furthermore, more diffuse 5f orbitals than lanthanide 4f ones (more covalency) could lead to stronger magnetic super-exchange. On the other hand, the extraordinary experimental challenges of actinide complexes chemistry, because of their rarity and toxicity, afford computational chemistry a particularly valuable role. However, for such a purpose, the use of a multiconfigurational post-Hartree-Fock approach is required, but such an approach is computationally demanding for polymetallic systems—notably for actinide ones—and usually simplified models are considered instead of the actual systems. Thus, Density Functional Theory (DFT) appears as an alternative tool to compute magnetic exchange coupling and to explore the electronic structure and magnetic properties of actinide-containing molecules, especially when the considered systems are very large. In this paper, relevant achievements regarding DFT investigations of the magnetic properties of actinide complexes are surveyed, with particular emphasis on some representative examples that illustrate the subject, including actinides in Single Molecular Magnets (SMMs) and systems featuring metal-metal super-exchange coupling interactions. Examples are drawn from studies that are either entirely computational or are combined experimental/computational investigations in which the latter play a significant role.

Keywords: actinides; uranium complexes; magnetochemistry; Super-exchange; SMM; DFT

1. Introduction During recent decades, the magnetochemistry of actinide complexes has gained an important impetus, not only at the experimental level, but also at the theoretical one [1–8]. Indeed, since the ﬁrst observation early in the 1990s of the antiferromagnetic (AF) coupling between uranium(V) centers in the para-imido [(MeC5H4)3U]2(µ-1,4-N2C6H4) complex by Rosen et al. [9], this class of binuclear actinide systems has been arousing interest [10–52]. Moreover, the discovery in 2009 of the slow magnetic relaxation for the mononuclear complex U(Ph2BPz2)3 [53], which is a signature of a single-molecule magnet (SMM) behavior, has motivated more research, even though lanthanide SMMs have been described in the literature for a longer time [54,55]. A growing number of uranium-containing systems [56–69]—mononuclear as well as binuclear species—have been

Magnetochemistry 2019, 5, 15; doi:10.3390/magnetochemistry5010015 www.mdpi.com/journal/magnetochemistry Magnetochemistry 2019, 5, 15 2 of 31 synthesized to develop SMMs; the results have been the subject of recent reviews [70–75]. Such systems are of great interest, owing to the well-known larger spin–orbit coupling for actinide than for lanthanide ions [72], and the more diffuse 5f orbitals (5f covalency) [63,76–78] than the lanthanide 4f ones, which could lead to strong magnetic super-exchange [53]. Therefore, these unique features of actinides relatively to transition metals and lanthanides open the way to the design of new actinide-based SMMs with high blocking temperatures [71,72,75]. Moreover, over the last twenty years, much effort has been devoted to investigating the magnetic properties of actinide complexes by quantum chemical methods [62–65,67,70–76,79–81]. Indeed, investigating the electronic structure of actinide complexes is essential to understanding their magnetic behavior [1,2,71–73]. However, for such a purpose, the use of a multiconfigurational post-Hartree-Fock approach is required, as stated by several authors [63,64,82,83], but such an approach is computationally demanding (vide infra) for polymetallic systems, notably for actinide ones, and usually simplified models are computed instead of the actual systems [63,64]. Thus, Density Functional Theory (DFT) appears as an alternative tool to compute magnetic exchange coupling and to explore the electronic structure and magnetic properties of actinide-containing molecules, especially when the considered systems are very large [6,8,21,37,60,79,80,84,85]. Indeed, DFT emerged in the early 2000s as a powerful technique, particularly when used in combination with the hybrid B3LYP functional [86,87] and the Broken-Symmetry (BS) Noodleman’s approach [88,89], for satisfactory simulations of magnetic properties. This is true not only in the case of d-transition metal systems [82,83,90–104], but also for actinide-containing molecules [105–107]. It is worth noting that actinide-based SMMs are multiconfigurational systems, and the use of the monodeterminantal approach with DFT is a subject of debate [63,108–110]. We present here a review of relevant achievements regarding DFT investigations of the magnetic properties of actinide complexes. This review will also deal with representative examples that illustrate the subject, including actinides in SMMs and systems featuring metal-metal exchange coupling interactions. We focus on studies that are either entirely computational or are combined experimental/computational investigations in which the latter play a significant role.

2. Survey of Molecules Potentially Exhibiting Magnetic Behavior

2.1. Magnetic Coupling Interactions Actinide complexes exhibiting magnetic exchange properties are rarely mentioned in the literature [1,2], relatively to the rich d-transition metal magnetochemistry. Most documented cases involve diuranium(V) systems [8,23–27,37,49–51,106,111–116], and only a few studies of magnetic coupling in diuranium(III) and (IV) complexes or mixed uranium(IV)–transition metal have been reported [46,52,105,107,117–122]. Among them, remarkable examples of unusual U(V)–U(V) coupling involving a pentavalent bis(imido) uranium dimer [106] and within diuranium(V) dioxo diamond cores [46,49,114–116,123–126] have been reported, which can exhibit Néel temperatures of up to 70 and even 110 K [23,24,27,114,115,127]. Magnetic coupling constants J were estimated in the 1990s for UV/UV dinuclear complexes such −1 as the AF [(MeC5H4)3U]2(µ-1,4-N2C6H4) species (J = −19 cm )[1,2,9], and later for ferromagnetic IV IV −1 U /U coupling in U2Co pyrazolate (cyclam)Co[(µ-Cl)U(Me2Pz)4]2 system (15 cm ≥ J ≥ 48 −1 Xy cm )[21] and in the arene-bridged uranium(IV) complex U[HC(SiMe2Ar)2(SiMe2-µ-N)](µ-Ar)U(Ts ) (J = 20 cm−1)[38]. As expected for the more ionic uranium(IV) species, reports of UIV/UIV couplings are rather scarce, being limited to few examples [33,105,107,122,128] discussing couplings which are mediated by either chalcogen bridges or aromatic spacers. Moreover, examples of uranium(IV)–copper(II) and uranium(IV)–nickel(II) couplings have been reported [43–45,117,118]. It is noteworthy that a successful strategy to promote interactions between paramagnetic actinide ions has been the use of covalently-linked bridging ligands [1,2]. Thus, a great variety of spacer ligands bearing two functionalized actinide centers have been tested, showing signiﬁcant metal-metal communication Magnetochemistry 2019, 5, 15 3 of 31

and magnetic interaction. For example, the linear bis(imido) (imido = 1,4-diimidobenzene) covalent

MagnetochemistryMagnetochemistrylinkage was the 20182018 ﬁrst,, 44,, xx one FORFOR used PEERPEERin REVIEWREVIEW the diuranium(V) para- and meta-bridged complexes (Figure1)[ 3 3 9 ofof]. 3131

UU NN NN UU

⋅⋅⋅ FigureFigure 1. 1. TheThe diuranium(V) diuranium(V) imido imido complex complex which which exhibits exhibits AF AF U U⋅⋅⋅···UU couplingcoupling [9].[9]. [9].

MoreMore recently, recently, reports reports ofof Kiplinger’sKiKiplinger’splinger’s group group [[106,112,128][106,112,128]106,112,128] on on ketimideketimide actinide-containingactinide-containing assemblies,assemblies, indicatedindicated thatthat the the 1,4-phenylenediketimide 1,4-phenylenediketimide ligandligand couldcould leadlead toto diverse diverse and and interesting interesting µ magneticmagnetic behavior.behavior. InIn theirtheirtheir study, study,study, bis(ketimide) bis(ketimide)bis(ketimide) [(C [(C[(C5Me55MeMe4Et)44Et)Et)2(Cl)An]22(Cl)An](Cl)An]2(22(µ-{N=CMe-(C(µ-{N=CMe-(C-{N=CMe-(C666HHH444)-MeC=N}))-MeC=N}) IV IV 62 binuclearbinuclear An AnIVIV/An/An/AnIVIV (Th,(Th,(Th, U)U) U) complexescomplexes complexes6262 werewerewere synthesizedsynthesized synthesized (Figure(Figure (Figure 2).2).2). TheThe authors authors reported reported that,that, IV IV 2 2 althoughalthough evidence evidence for for magneticmagneticmagnetic couplingcouplingcoupling betweenbetweenbetween metal metalmetal centers centerscenters in inin the thethe bimetallic bimetallicbimetallic U UUIVIV/U/U/UIVIV (5f(5f22–5f–5f22))) complexcomplex isisis ambiguous,ambiguous,ambiguous, the thethe complex complexcomplex displays displaysdisplays appreciable appreciableappreciable electronic electronicelectronic communication communicationcommunication between betweenbetween the metal thethe metalmetalcenters centerscenters through throughthrough the π system thethe ππ systemsystem of the of dianionicof thethe dianionicdianionic bis(ketimide) bis(ketimibis(ketimi dianionicde)de) dianionicdianionic bridging bridgingbridging ligand ligandligand [128]. [128].[128].

RR HH33CC NN AnAn XX CC CC X RR X CH AnAn NN AAnn == UU,, XX == CCl,l, RR == EEtt CH33 AAnn == TThh,, XX == BBrr,, RR == MMee

FigureFigure 2.2.2. StructureStructureStructure of ofof the thethe bis(ketimide)-bridged bis(ketimide)-bridgedbis(ketimide)-bridged [(C [(C[(C5Me55MeMe4Et)44Et)Et)2(Cl)An]22(Cl)An](Cl)An]2(22µ(µ-{N=CMe-(C(µ-{N=CMe-(C-{N=CMe-(C666HHH444)-MeC=N}))-MeC=N}) binuclearbinuclear An AnIVIV/An/An/AnIVIVIV (Th,(Th,(Th, U)U) U) complexescomplexes complexes (ketimide(ketimide (ketimide == 1,4-phenylenediketimide) =1,4-phenylenediketimide) 1,4-phenylenediketimide) [128].[128]. [128 ].

AnotherAnother kindkind kind ofof of bridging-spacerbridging-spacer bridging-spacer systemsystem system includesincludes includes inverted-sandwichinverted-sandwich inverted-sandwich systsyst systems,ems,ems, whichwhich which containcontain contain twotwo uraniumuraniumtwo uranium atomsatoms atomsbridgedbridged bridged byby aa cycliccyclic by aromatic aaromatic cyclic hydrocarbon aromatichydrocarbon hydrocarbon ligandligand e.g.e.g.,, ligandbenzene,benzene, e.g., toluenetoluene benzene, (Figure(Figure toluene 3)3) [9],[9], 7 8 (Figure3)[ 9], cycloheptatrienyl77 (η -C H ) or naphthalene and cyclooctatetraene88 (η -C H ), as recently cycloheptatrienylcycloheptatrienyl ((ηη -C-C77HH77)) oror naphthalenenaphthalene7 7 andand cyclooctatetraenecyclooctatetraene ((ηη -C-C88HH88),), asas recentlyrecently8 8 reviewedreviewed [127].[127].reviewed Indeed,Indeed, [127 CumminsCummins]. Indeed, andand Cummins Coll.Coll. [10][10] and reportedreported Coll. [ 10 inin] thethe reported 2000s2000s thethe in theX-rayX-ray 2000s structurestructure the X-ray ofof thethe structure firstfirst inverted-inverted- of the 6 6 η6 η6 µ η η sandwichsandwichﬁrst inverted-sandwich structuresstructures ofof differendifferen structurestt arenearene of different spacers,spacers, arene namelynamely spacers, thethe (µ-(µ- namelyη6::η6-C-C the77HH8 (8)[U(N[R]Ar))[U(N[R]Ar)- : -C7H282]])[U(N[R]Ar)22 complexcomplex (R(R2 ] ==2 C(CHC(CHcomplex33))33,, ArAr (R == 3,5-C3,5-C C(CH66HH3)333MeMe, Ar22)) (Figure(Figure = 3,5-C 3),63),H 3ininMe whichwhich2) (Figure aa toluenetoluene3), in moleculemolecule which a bridges toluenebridges two moleculetwo uraniumuranium bridges bis-amidobis-amido two 6 6 fragmentsfragmentsuranium bis-amido inin aa symmetricalsymmetrical fragments ηη66::ηη6 in6 mode,mode, a symmetrical involvinginvolving covalentηcovalent:η mode, deltadelta involving bonds.bonds. TheseThese covalent aromaticaromatic delta ligands,ligands, bonds. whichwhich These couldcouldaromatic exhibitexhibit ligands, richrich redoxredox which chemistrychemistry could exhibit forfor aa rich rangerange redox ofof reduciblereducible chemistry substrates,substrates, for a range havehave of been reduciblebeen proposedproposed substrates, toto promotepromote have intra-molecularintra-molecularbeen proposed toelectronicelectronic promote andand intra-molecular magneticmagnetic communicatcommunicat electronicionsions and magneticbetweenbetween uraniumuranium communications centerscenters [65]. between[65]. ThisThisuranium classclass ofof inverted-sandwichinverted-sandwichcenters [65]. This class structuresstructures of inverted-sandwich waswas enrichedenriched structuresinin 20112011 byby was thethe enriched firstfirst arene-bridarene-brid in 2011 bygedged the diuranium(III)diuranium(III) ﬁrst arene-bridged [{U-[{U- TMS 6 6 TMS μ η6 η6 µ η η (BIPM(BIPMdiuranium(III)TMSH)(I)}H)(I)}22(( [{U-(BIPMμ--η6::η6-C-C66HH55Me)]Me)]H)(I)} systemsystem2( - exhibitingexhibiting: -C6H5 SMMMe)]SMM system behaviorbehavior exhibiting [60].[60]. SMM behavior [60].

PhPh PhPh HH HH PhPh PhPh PP PP PhPh CC CC PhPh PhPh PhPh NN NN Ph UU UU PhPh PhPh MeMe SiSi NN SiMeSiMe33 Me33Si NN II II 3

SiMeSiMe3 MeMe33SiSi 3 CH CH33

TMSTMS 2 μμ ηη66 ηη666 6 6 5 FigureFigureFigure 3.3. 3. StructureStructureStructure ofof of thethe the arene-bridgedarene-bridged arene-bridged uranium(III)uranium(III) (BIPM(BIPM H)(I)}H)(I)}H)(I)}2((2(--µ-η:: :η-C-C-C6HH65HMe)]Me)]5Me)] SMMSMM SMM [60].[60]. [60].

TheThe formulationformulation ofof thethe metalmetal oxidationoxidation statestate inin ththisis speciesspecies couldcould eithereither bebe uranium(II)/neutraluranium(II)/neutral arene,arene, uranium(III)/dianionicuranium(III)/dianionic arene,arene, oror uraniuuranium(IV)/tetraanionicm(IV)/tetraanionic arene,arene, butbut spectroscopicspectroscopic characterizationcharacterization andand theoreticaltheoretical cocomputationsmputations favorfavor uranium(III)/diauranium(III)/dianionicnionic arenearene formulationformulation [127].[127]. CumminsCummins andand Coll.Coll. [11][11] havehave extendedextended thisthis ininverted-sandwichverted-sandwich seriesseries ofof complexescomplexes toto thethe Magnetochemistry 2019, 5, 15 4 of 31

The formulation of the metal oxidation state in this species could either be uranium(II)/neutral arene, uranium(III)/dianionic arene, or uranium(IV)/tetraanionic arene, but spectroscopic characterization and theoretical computations favor uranium(III)/dianionic arene formulation [127]. CumminsMagnetochemistry and 2018 Coll., 4, x FOR [11 ]PEER have REVIEW extended this inverted-sandwich series of complexes to 4 of the 31 6 6 t naphthalene-bridged M2(µ-η ,η -C10H8)[U(NC[ Bu]Mes)3]2 (M = K, Na; Mes = 2,4,6-C6H2Me3) and 8 8 t itsnaphthalene-bridged cyclooctatetraene (Mµ-2η(µ-,ηη6-C,η68-CH108)UH82)[U(NC[(NC[ Bu]Mes)tBu]Mes)6 congener.3]2 (M = K,As Na reported ; Mes = 2,4,6-C by these6H2 authors,Me3) and the its 8 8 2- 8 8 performedcyclooctatetraene DFT computations (µ-η8,η8-C8H on8)U the2(NC[ [(µt-Bu]Mes)η ,η -C106 Hcongener.8)U2(NCH As2)6 ]reportedand (µ -ηby,η these-C8H 8authors,)U2(NCH the2)6 IV 2 modelsperformed in theirDFT quintetcomputations state (Son =the 2) [(µ- areη consistent8,η8-C10H8)U with2(NCH the2)6] tetravalent2- and (µ-η U8,η8-C(5f8H8))U oxidation2(NCH2)6 statemodels of in the their metal quintet centers state [(S11 =]. 2) are The consistent C−C bond with lengths the tetravalent of the U bridgingIV (5f2) oxidation arene were state foundof the tometal be centers slightly [11]. lengthened The C−C comparedbond lengths to of those the bridging of free toluene, arene were and found with to the be helpslightly of lengthened theoretical calculations,compared to suggestedthose of freeδ-back-bonding toluene, and with between the help uranium of theoretical and the arenecalculations, ring. Insuggested 2004, William δ-back- J. Evansbonding and between Coll. [19 uranium] reported and the the structure, arene ring. reactivity In 2004, andWilliam DFT J. analysis Evans and of the Coll. two [19] arene-bridged reported the t 6 6 5 6 6 diuraniumstructure, reactivity [(Mes( Bu)N) and 2DFTU]2( analysisµ-η :η -C of7 Hthe8) two and arene-bridged [(η -C5Me5)2U] diuranium2(µ-η :η -C [(Mes(6H6) systems.tBu)N)2U] The2(µ- latterη6:η6- speciesC7H8) and was [( describedη5-C5Me5)2 asU] two2(µ-η U(III)6:η6-C6 covalentlyH6) systems. bonded The latter metals species to the arenewas described ligand via asδ ’symmetrytwo U(III) bondingcovalently molecular bonded metals orbital to (MO). the arene Ephritikhine ligand via and δ’symmetry Coll. [119 ,bonding120] had molecular previously orbital reported (MO). a 7 7 − uniqueEphritikhine bridged-cycloheptatrienyl and Coll. [119,120] diuranium had previously [U(BH4 )2reported(OC4H8) 5][(a µunique-η ,η -C bridged-cycloheptatrienyl7H7)[U(BH4)3]2] anionic 3− complex.diuranium It was[U(BH suggested4)2(OC4H that8)5][(µ- theη (C7,η7H7-C7)7H7ring)[U(BH should4)3]2]- be anionic described complex. as an aromaticIt was suggested planar group thatand the IV the(C7H metals7)3− ring as Ushouldions, be with described four highest as an aromaticδ’symmetry planar bonding group MOs. and Suchthe metals covalently as UIV bridged ions, with systems four byhighestδ-bonding δ’symmetry should bonding promote MOs. U···U Such electronic covalently and magnetic bridged communicationssystems by δ-bonding [1,2,35 should–38,60, 65promote,72,73]. AlthoughU⋅⋅⋅U electronic to our and knowledge magnetic no communications systematic theoretical [1,2,35− studies38,60,65,72,73]. have been Although reported to on our the knowledge magnetic behaviorno systematic of the theoretical latter complexes, studies it have seems been likely re thatportedδ-bonding, on the whichmagnetic dominates behavior the of bonding the latter in thecomplexes, inverse it sandwich seems likely unit, that could δ-bonding, favor metal-metal which dominates exchange the bonding coupling in as the stated inverse by sandwich recent reports unit, evidencingcould favor arene-bridged metal-metal exchange diuranium coupling SMM behavior as stated [60 by,72 recent,73]. Indeed, reports in evidencing their continual arene-bridged efforts to developdiuranium new SMM synthetic behavior routes [60,72,73]. to magnetic Indeed, actinide in systems, their continual S.T. Liddle’s efforts group to recentlydevelop (2017) new extendedsynthetic TIPS theirroutes investigations to magnetic actinide to crystal systems, ﬁeld and S.T. magnetic Liddle’s interactions group recently in diuranium (2017) extended [{U(Tren their)} investigations2(µ-E)] (E = S, IV IV Se,to crystal Te) bridged-chalcogenide field and magnetic complexesinteractions with in diuranium U –E–U [{U(Trencores (FigureTIPS)}2(µ-E)]4)[ 37 ],(E which = S, Se, exhibit Te) bridged- linearly U–E–Uchalcogenide linked complexes cores. with UIV–E–UIV cores (Figure 4) [37], which exhibit linearly U–E–U linked cores.

i Pr 3Si i i Pr 3Si SiPr 3 N N N U N E U N N N i Pr 3Si N i i SiPr 3 SiPr 3

IVIV IVIV TIPS FigureFigure 4.4. StructureStructure ofof thethe diuranium diuranium U U /U/U [{U(Tren[{U(Tren )})}22(µ-E)](µ-E)] (E (E = = S, S, Se, Se, Te) Te) bridged-chalcogenide bridged-chalcogenide systemssystems [[37].37].

PlotsPlots ofof the the magnetic magnetic susceptibility susceptibility vs. vs. temperature temperature of these of these linkages linkages present present shoulders shoulders that could that becould interpreted be interpreted as evidence as evidence of uranium–uranium of uranium–uranium magnetic magnetic exchange. exchange. However, However, a detailed a detailed study usingstudy CASSCFusing CASSCF computations computations of their of electronic their electronic structures structures revealed revealed that the that magnetic the magnetic properties properties of these of systemsthese systems can be can simply be simply correlated correlate to single-iond to single-ion crystal crystal ﬁeld (CF) field effects (CF) effects which which vary as vary the natureas the nature of the chalcogenof the chalcogen varies. varies. AsAs reviewedreviewed recentlyrecently [[71,72],71,72], aa successfulsuccessful routeroute toto super-exchangesuper-exchange effectseffects inin actinide-containing actinide-containing multinuclearmultinuclear species isis throughthrough cation–cationcation–cation interactionsinteractions (CCI)(CCI) [23[23–33−33,46,46–−5151,59,61,69,114,59,61,69,114–−116116,123],,123], + mostlymostly betweenbetween uranyl(V)uranyl(V) UOUO22+ of actinyl units. This linkage forms an oxo-bridgeoxo-bridge betweenbetween metalmetal V centerscenters affordingaffording aa greatgreat numbernumber ofof oxo-bridgedoxo-bridged systemssystems exhibitingexhibiting signiﬁcantsignificant couplingcoupling betweenbetween UUV V centerscenters [[27,49],27,49], mixed UUV/transition metal metal [28 [28−–32,111]32,111] or or lanthanide centers [[47,112,123],47,112,123], withwith thethe largestlargest actinide-basedactinide-based multinuclearmultinuclear complexcomplex affordingaffording thethe uniqueunique structurestructure ofof aa wheel-shaped clustercluster + II {[UO{[UO22(salen)](salen)]22Mn(Py)33}6 (Py(Py = pyridine) pyridine) which is assembled throughthrough UOUO22+ and Mn II interactionsinteractions [29]. [29]. Additionally, CCIs were observed between NpIV/NpV ions in neptunyl complexes [75]. Beside the great number of synthesized CCI systems, few theoretical studies of their magnetic properties have been carried out [1–4,7,8,37,60,63,64,71,72,80,81].

Magnetochemistry 2019, 5, 15 5 of 31

Additionally, CCIs were observed between NpIV/NpV ions in neptunyl complexes [75]. Beside the great number of synthesized CCI systems, few theoretical studies of their magnetic properties have beenMagnetochemistry carried out 2018 [1,, –4,4, xx,7 FORFOR,8,37 PEERPEER,60,63 REVIEWREVIEW,64,71 , 72,80,81]. 5 5 ofof 3131

2.2.2.2. SMM Behavior TheThe ﬁrstfirst actinideactinide systemsystem foundfound toto displaydisplay slowslow magneticmagnetic relaxationrelaxation waswas thethe mononuclearmononuclear uranium(III)uranium(III) [U{Ph [U{Ph22B(NB(N2C2C3H3H3)32})32]} 3complex] complex exhibiting exhibiting clear clear SMM SMM beha behaviorvior (Figure (Figure 5) [53].5)[ Since53]. Sincethen, then,a wide a range wide rangeof SMMs of SMMs based basedon uran onium(III, uranium(III, V) have V) been have reported been reported [56−59,62,127,129 [56–59,62,127−131],,129 which–131], whichare mainly are mainly supported supported by pyrazolylborate by pyrazolylborate ligands ligands as reviewed as reviewed recently recently [69−72,127]. [69–72 ,127].

N N

Ph2B U

N N 3

FigureFigure 5. 5.Structure Structure of of the the uranium(III) uranium(III) [U{Ph [U{Ph2B(N2B(N22CC33HH3)2}}33] ]SMM SMM [127]. [127].

InIn 2012, 2012, the the uranium uranium SMM SMM chemistry chemistry was was extended extended to the to thepentavalent pentavalent species species of U(V) of U(V) ions, ions,with withthe report the report of the of nanostructure the nanostructure wheel-shaped wheel-shaped [{(UO2 [{(UO[(CH2NCHC2[(CH26NCHCH4-2-O)6H2])42-2-O)(Mn[Py]2])23(Mn[Py])}6] complex3)}6] complex[61]. As reported, [61]. As reported, significant signiﬁcant magnetic magnetic interactio interactionsns between between the uranyl(V) the uranyl(V) and manganese(II) and manganese(II) ions ionswere were studied studied by susceptibility by susceptibility measurements. measurements. In 201 In3, the 2013, synthesis the synthesis of a terminal of a terminal uranium(V) uranium(V) mono- TIPS mono-oxooxo complex complex U(Tren U(TrenTIPS)(=O) )(=O)(Figure (Figure 6) 6supported) supported by by the the sterically demandingdemanding ligandligand i i TIPSTIPS N(CHN(CH2CHCH22NSiPrNSiPri3)33) 3(Tren(Tren(TrenTIPS) ligand) ligand was was reported reported by byS.T. S.T. Liddle Liddle and and Coll., Coll., [127] [127 revealing] revealing the first the ﬁrstexample example of an of uranium(V) an uranium(V) monometallic monometallic SMM. SMM.

Prii Si ii 3 SiPr 3 N N O U N N ii SiPr 3 FigureFigure 6.6. TheThe mononuclearmononuclear uranium(V)uranium(V) U(TrenU(TrenTIPSTIPS)(=O) SMM SMM [127]. [127].

3.3. DFT Investigations of Actinide Complexes MagnetismMagnetism 3.1. Theoretical Approaches for Computing Exchange Coupling Constants 3.1. Theoretical Approaches for Computing Exchange Coupling Constants Magnetic properties of species bearing unpaired electrons are driven by the manifold of states of Magnetic properties of species bearing unpaired electrons are driven by the manifold of states different spin multiplicities they exhibit, especially if the latter energies are close [82,83]. The calculation of different spin multiplicities they exhibit, especially if the latter energies are close [82,83]. The of magnetic properties of molecular systems, which necessitates a high accuracy of the computed calculation of magnetic properties of molecular systems, which necessitates a high accuracy of the energies, needs to properly take into account both static and dynamic electron correlation. Static computed energies, needs to properly take into account both static and dynamic electron correlation. correlation is generally well described by multiconfigurational (MC) treatments like CASSCF, whereas Static correlation is generally well described by multiconfigurational (MC) treatments like CASSCF, dynamical correlation can be recovered with MR-CI techniques or by perturbation using CASPT2 whereas dynamical correlation can be recovered with MR-CI techniques or by perturbation using technique, for instance [132–139]. However, CASSCF computations are drastically limited by the size of CASPT2 technique, for instance [132−139]. However, CASSCF computations are drastically limited the active space, so that such high-level computations can only be applied to relatively small molecules by the size of the active space, so that such high-level computations can only be applied to relatively or models [82]. DFT could offer the opportunity to estimate the magnetic properties of large systems at small molecules or models [82]. DFT could offer the opportunity to estimate the magnetic properties a low computational cost [80–83,90]. The exact wavefunctions which are eigenfunctions of the square of large systems at a low computational cost [80−83,90]. The exact wavefunctions which are spin operator Sˆ 2 with eigenvalues S(S + 1) can be written as expansion of Slater determinants each eigenfunctions of the square spin operator S2̂̂ withwith eigenvalueseigenvalues S(SS(S ++ 1)1) cancan bebe writtenwritten asas expansionexpansion of Slater determinants each of them being eigenfunction of the spin component Sẑ̂ [83]. Such exact descriptions of the electronic states of a molecule cannot be obtained using DFT, which is a ground state and single determinant theory; therefore, the exact determination of the electronic states energies cannot be obtained. Magnetochemistry 2019, 5, 15 6 of 31 of them being eigenfunction of the spin component Szˆ [83]. Such exact descriptions of the electronic states of a molecule cannot be obtained using DFT, which is a ground state and single determinant Magnetochemistry 2018, 4, x FOR PEER REVIEW 6 of 31 theory; therefore, the exact determination of the electronic states energies cannot be obtained. RegardingRegarding magneticmagnetic exchange, the usedused spinspin HamiltonianHamiltonian isis thethe Heisenberg–Dirac–vanHeisenberg−Dirac−van VleckVleck (HDvV) one, Hˆ = −ΣJ Sˆ ·Sˆ where Sˆ , Sˆ are the spin operators associated to the magnetic centers i, j (HDvV) one, H ̂ = −ΣJijSijî ·Sîj wherej Ŝi, Siĵ arej the spin operators associated to the magnetic centers i, j and and J the coupling constants between these centers [82,83,90,91]. Jij theij coupling constants between these centers [82,83,90,91]. Experimentally, the coupling constants J are derived from the magnetic susceptibility Experimentally, the coupling constants Jijij are derived from the magnetic susceptibility measurementsmeasurements by fittingfitting thethe experimentalexperimental curve.curve. ThisThis approach waswas successfullysuccessfully usedused byby RinehartRinehart 1 andand Coll.Coll.1 toto modelmodel thethe susceptibilitysusceptibility ofof thethe diuranium(V)diuranium(V) bis(imido)-bridgedbis(imido)-bridged complex. As shownshown inin − −1 FigureFigure7 7,, thethe bestbest fitfit of the the susceptibility’s susceptibility’s curve curve provides provides an an exchange exchange constant constant of ofJ = J− =19 cm19−1 cm[1,2]. [1,2].

χ FigureFigure 7. Temperature-dependentTemperature-dependent magnetic magnetic susceptibility susceptibility (blackχ (black symbols) symbols) of [(MeCp) of [(MeCp)3U]2(µ-1,4-3U]2 χ (Cµ6-1,4-CH4N2)6 Hand4N fits2) and (lines) ﬁts and (lines) the and magnetic the magnetic molar molarT versusχT T versus (blue) T of (blue) the magnetically of the magnetically isolated isolated analog analog[(MeCp) [(MeCp)3U]2(µ-1,3-C3U]2(µ6H-1,3-C4N2).6 HSusceptibility4N2). Susceptibility data (reprinted data (reprinted with with permission permission from from [2], [2], American ChemicalChemical Society,Society, 2010).2010).

EstimatingEstimating the coupling constant using DFT is made possible using the Broken Symmetry (BS) approachapproach proposedproposed first first by by Noodleman Noodleman et et al. al. [88 [88,89],,89], which which have have been been nicely nicely reviewed reviewed by Bencini by Bencini [82] and[82] and Neese Neese [83]. [83]. In theIn the case case of aof dinuclear a dinuclear system, system, it it consists consists of of evaluating evaluating the the magneticmagnetic couplingcoupling constantconstant JJijij from the energy difference between two main configurations, configurations, i.e., the high-spin state (HS) 1 1 ofof spinspin SSmaxmax = 1 (in the casecase ofof aa 5f5f1/5f/5f1 configuration)configuration) which which is is generally generally well well described by a singlesingle determinantdeterminant and thethe BSBS statestate determinantdeterminant whichwhich isis eigenfunctioneigenfunction ofof SˆSẑz withwith eigenvalueeigenvalue MMss == 0, butbut notnot ofof SˆS22̂ .. In In the the latter binuclear case, the HS determinantdeterminant bears thethe twotwo highesthighest singlysingly occupiedoccupied molecularmolecular orbitalsorbitals (SOMOs)(SOMOs) withwith spinsspins αα//α,, whereas whereas the the BS BS starting starting determinant, before running thethe SCFSCF process, isis simply produced fromfrom thethe HSHS determinantdeterminant byby aa spinflipspinflip ofof thethe electron leadingleading toto thethe αα/ββ configuration.configuration. Different Different formulas formulas for for the ca calculationlculation of the couplingcoupling constantconstant fromfrom thethe EEHSHS andand 42 EEBSBS energiesenergies have been proposed; 42 amongamong them, them, the the Yamaguchi Yamaguchi et et al. al. formula formula [140 [140−–142]:142]: 2 2 J12 = (EBS − EHS)/(HS2 − BS2) (1) J12 = (EBS − EHS)/(HS − BS) (1) where HS and BS are respectively the mean values of the squared spin operator for the HS and 2 2 whereBS states. HS and BS are respectively the mean values of the squared spin operator for the HS and BSThe states. validity of the BS approach has been discussed [143], and the reliability and accuracy of the obtainedThe validityresults have of the been BS approachlargely investigated has been discussed [82,83,93 [−14398,133], and−139]. the It reliability has been and shown accuracy that ofcomputations the obtained of results the magnetic have been coupling largely constants investigated at the [82 ,83B3LYP,93–98 level,133– 139[86,87]]. It generally has been lead shown to thatsatisfying computations results and of the good magnetic agreement coupling either constants with high at thelevel B3LYP post-HF level computations [86,87] generally or with lead toexperimental satisfying resultsmeasurements and good [89]. agreement For instance, either D. Ga withtteschi high and level Coll. post-HF [144] reported computations DFT calculations or with experimentalin 2009 considering measurements a mixed [89{3d–4f}]. For [Cu(II)Gd(III)] instance, D. Gatteschi complex and[L1CuGd(O Coll. [1442CCF] reported3)3(C2H5OH) DFT2] calculations (L1 = N,N′- bis(3-ethoxy-salicylidene)-1,2-diamino-2-methylpropanato), with the aim of assessing a suitable DFT functional to understand the mechanism of magnetic coupling and to develop magneto-structural correlations. Several GGA, meta-GGA and hybrid functional calculations with different percentages of HF exchange have been performed. The coupling J constant using the Ĥ = JŜGd·ŜCu spin Hamiltonian, was Magnetochemistry 2019, 5, 15 7 of 31

1 in 2009 considering a mixed {3d–4f} [Cu(II)Gd(III)] complex [L CuGd(O2CCF3)3(C2H5OH)2] (L1 = N,N0-bis(3-ethoxy-salicylidene)-1,2-diamino-2-methylpropanato), with the aim of assessing aMagnetochemistry suitable DFT 2018 functional, 4, x FOR PEER to understandREVIEW the mechanism of magnetic coupling and to develop 7 of 31 magneto-structural correlations. Several GGA, meta-GGA and hybrid functional calculations with ˆ differentextracted percentagesfrom the difference of HF exchangeenergy between have been the HS performed. state (ST = The 4) and coupling the BS J one, constant using using the following the H = ˆ ˆ Jequation:SGd·SCu spin Hamiltonian, was extracted from the difference energy between the HS state (ST = 4) and the BS one, using the following equation: 𝐸 − 𝐸 𝐽 = (2) E − E J = BS2𝑆𝑆HS (2) 2SGdSCu The DFT/BS model provides ferromagnetic J constant value of −5.8 cm−1 (in the used model, negativeThe DFT/BSJ value indicates model provides a ferromagnetic ferromagnetic charac J constantter), which value is ofin −excellent5.8 cm− 1agreement(in the used with model, the negativeexperimental J value value indicates of −4.42 acm ferromagnetic−1, the B3LYP functional character), being which recommended is in excellent [144]. agreement with the experimental value of −4.42 cm−1, the B3LYP functional being recommended [144]. 3.2. Magnetic Exchange Coupling in Actinide Bimetallic Systems 3.2. Magnetic Exchange Coupling in Actinide Bimetallic Systems The DFT/BS approach for computing and modeling the exchange coupling interactions faces situationsThe DFT/BS in actinide approach systems for which computing are different and modeling from the lanthanide the exchange ones coupling because interactions of their potential faces situationsfor more incovalent actinide systemsmetal-ligand which interactions are different especially from the lanthanidefor uranium ones [8,21,71 because− of73,75]. their Even potential so, fornumerous more covalent DFT/BS metal-ligand studies aiming interactions at rationalizing especially the forsign uranium and strength [8,21,71 of– 73the,75 exchange]. Even so, coupling numerous for DFT/BSvarious studiesbridged aiming diuranium at rationalizing by drawing the sign magneto-st and strengthructural of the exchangecorrelations coupling have forbeen various carried bridged out diuranium[105−110,145 by− drawing147]. magneto-structural correlations have been carried out [105–110,145–147]. 1 1 TheThe discovery of the firstfirst AF coupled 5f 1/5f/5f1 bis(imido)bis(imido) diuranium(V) diuranium(V) complex complex [({MeC [({MeC5H5H4}34U)}3U)2(μ2- µ (1,4-N-1,4-N2C62HC46)]H [9],4)] [9rationalized], rationalized later later [1,127], [1,127 was], was undo undoubtedlyubtedly a amilestone milestone in in the the field field of actinideactinide moleculesmolecules likelylikely to to exhibit exhibit magnetic magnetic exchange exchange coupling coupling [1– 3[1,2,3,6].,6]. One ofOne the of first the magnetic first magnetic systems systems which waswhich theoretically was theoretically investigated investigated by DFT/BS by computations, DFT/BS computations, is the bis(imido) is the pentavalent bis(imido) diuranium(V) pentavalent t t [U(Ndiuranium(V)Bu)2(I)( Bu [U(N2bpy)]tBu)22complex(I)(tBu2bpy)] reported2 complex by Kiplinger’s reported by group Kiplinger’s in 2009 [group106]. This in 2009 system [106]. exhibits This 1 1 significantsystem exhibits AF coupling significant between AF coupling the two between metallic 5fthe/5f twospin metallic centers, 5f1/5f as1 shownspin centers, by the as magnetic shown by molar the χ + + magneticversus T, molar through χ versus CCI betweenT, through [U(NR) CCI between2] moieties [U(NR) similar2]+ moieties to that observedsimilar to inthat poly-uranyl observed in [UO poly-2] systemsuranyl [UO [23–2]32+ systems,46–51,59 [23,61−,32,4669,114−–51,59,61,69,114116]. The authors−116]. carried The authors out B3LYP carried computations, out B3LYP employingcomputations, the Stuttgartemploying RSC the 1997 Stuttgart ECP basis RSC set1997 for ECP uranium. basis set The for geometries uranium. ofThe the geometries HS and BS of states the HS were and optimized BS states withwere nooptimized symmetry with constraints. no symmetry DFT constraints. calculations DFT show calculations that the axial show U=N that double the axial bond U=N (2.073 double Å) consistsbond (2.073 of one Å) σconsistsand one of πonebonds, σ and whereas one π bonds, the bridging whereas equatorial the bridging U− Nequatorial bond (2.384 U−N Å) bond is a single(2.384 bond,Å) is a as single depicted bond, in as Figure depicted8. in Figure 8.

~~But~~

~~N But tBu I But N N N U N U tBu N N But I N But~~

~~tBu~~

~~Figure 8. Structure of the U2N2 core [106]. Figure 8. Structure of the U2N2 core [106].~~

TheirTheir computationscomputations predicted predicted that that the the BS stateBS state is lower is lower in energy in energy thanthe than triplet the HStriplet state, HS leading state, toleading an AF to exchange an AF couplingexchange constant coupling J ofconstant−12 cm −J 1of, which−12 cm is− in1, which good agreement is in good with agreement the experimental with the ﬁttingexperimental of the susceptibility fitting of the measurements. susceptibility measurem As reportedents. [106 As], thereported weak AF[106], coupling the weak between AF coupling the two 5fbetween1 centers the is two due 5f not1 centers only to is the due long not U-N only distance, to the long but U-N also todistance, the fact but that also half to orbitals the fact consist that half of orbitals consist of antisymmetric combinations which place a node along the U-N bond. Theoretical insights into the AF interaction between metal centers were assessed using the [{U(NtBu)2(I)2(bpy)}2] model to investigate molecular orbital interactions in the U2N2 core. As reported by the authors [106], the B3LYP natural orbital analysis shows that the two unpaired SOMO and SOMO-1 are localized on the uranium centers corresponding to the 5f1ϕ/5f1ϕ configuration. Magnetochemistry 2019, 5, 15 8 of 31 antisymmetric combinations which place a node along the U-N bond. Theoretical insights into the AF interaction between metal centers were assessed using the [{U(NtBu)2(I)2(bpy)}2] model to investigate molecular orbital interactions in the U2N2 core. As reported by the authors [106], the B3LYP natural orbital analysis shows that the two unpaired SOMO and SOMO-1 are localized on the uranium centers 1 1 corresponding to the 5f ϕ/5f ϕ conﬁguration. Magnetochemistry 2018, 4, x FOR PEER REVIEW 8 of 31 One year later, Newell et al. [107] reported in 2010 on the para and meta dinuclear IV IV 0 0 0 tetravalentOne year U later,/U Newell[(NN 3 et)2 Ual.2 (DEB)][107] reported and trinuclear in 2010 on [(NN the 3para)3U3 and(TEB)] meta complex dinuclear (NN tetravalent3 = [N(CH U2IVCH/UIV2 NSitBuMe ) ]) (Figure9) containing aromatic arylacetylide ligands i.e., diethynylbenzene (DEB) and [(NN′3)2U2(DEB)]2 3 and trinuclear [(NN′3)3U3(TEB)] complex (NN′3 = [N(CH2CH2NSitBuMe2)3]) (Figure 9) 2 2 2 2 2 triethynylbenzenecontaining aromatic (TEB) arylacetylide ligands as ligands bridging-spacers i.e., diethynylbenzene for two or three (DEB) metallic and triethynylbenzene 5f /5f and 5f /5f (TEB)/5f spinligands centers. as bridging-spacers for two or three metallic 5f2/5f2 and 5f2/5f2/5f2 spin centers.

~~NR NR RN N U U N~~

~~NR RN RN~~

~~(a)~~

~~R NR N RN U U N RN NR N RN~~

~~(b)~~

~~0 FigureFigure 9. 9. MolecularMolecular structures structures of of the the parapara- ( (aa)) and and meta-diuranium(IV) meta-diuranium(IV) ( (bb)) [(NN [(NN′33)2)U2U2(DEB)]2(DEB)] [107]. [107].~~

As reportedreported by thethe authors,authors, thethe experimentalexperimental investigationsinvestigations of their magnetic properties show thatthat thethe di-di- andand tri-nucleartri-nuclear compoundscompounds appearappear toto displaydisplay weakweak magneticmagnetic communicationcommunication betweenbetween thethe uraniumuranium centers.centers. This This communication communication is is modele modeledd by fitting ﬁtting the direct current (DC)(DC) magneticmagnetic ˆ ˆ ˆ susceptibility data,data, usingusing thethe spinspin HamiltonianHamiltonianH H = ̂ =− −2J2J SSz1z1̂ ·S·Sz2̂ z2, ,which which leads leads to to a a weak ferromagnetic −1 coupling constantconstant i.e.,i.e., JJ == 4.76,4.76, 2.75,2.75, and and 1.11 1.11 cm cm−1,, respectivelyrespectively forfor meta-,meta-, para-diuranium(IV)para-diuranium(IV) andand triuranium(IV)triuranium(IV) complexes. complexes. As As report reporteded in inthe the same same study study [107], [107 geomet], geometryry and andnuclearity nuclearity appear appear to have to havean effect an effect on the on thestrength strength of the of thecoupling coupling between between the the U(IV) U(IV) centers. centers. Turning Turning back back to to the theoreticaltheoretical analysis, geometries of of the the considered considered model model comp complexeslexes were were optimized optimized using using B3LYP B3LYP computations. computations. In t 0 Inthese these models, models, the thebulky bulky SitBuMe Si BuMe2 substituting2 substituting groups groups in the in NN the′3 NNligand3 ligand have been have replaced been replaced by H atoms by H atomsand scalar and relativistic scalar relativistic effects only effects included only included in the us ined theuranium used uraniumeffective core effective potential. core potential.For the simplified For the simpliﬁedmodels derived models from derived the meta- from and the para-bridged meta- and para-bridged dinuclear species, dinuclear the species,BS approach the BS led approach to computed led to J −1 computedvalues equal J values to 1.6 and equal −0.1 to cm 1.6−1 andfor the−0.1 meta- cm andfor para-bridged the meta- and complexes, para-bridged respectively, complexes, in fair respectively, agreement inwith fair experimental agreement trends. with experimental As expected, trends.all complexes As expected, show only all small complexes net spin show density only (Figure small 10) net on spin the densityethynylbenzene (Figure 10 ligands.) on the As ethynylbenzene stated by the authors, ligands. the As computed stated by theHS/BS authors, spin densities the computed mapping HS/BS for meta spin densities(a/b) and mappingpara (c/d) forisomers, meta both (a/b) show and parathat th (c/d)e spin isomers, density both is mostly show localized that the spinon the density two UIV is centers, mostly IV localizedwith no contribution on the two from U centers, the bridged-DEB with nocontribution ligand, explaining from the we bridged-DEBak ferromagnetic ligand, and explaining AF character the weakof the ferromagneticmeta and para and species, AF character respectively of the [107]. meta The and authors para species, conclu respectivelyded that despite [107]. the The structural authors concludeddifference with that the despite actual the meta structural and para difference DEB-bridged with thedinuclear actual metasystems, and the para result DEB-bridged shows that dinuclear coupling systems,in the single the wavenumber result shows range that coupling is not unexpected. in the single wavenumber range is not unexpected.

Figure 10. Net spin density plots for HS/BS meta (a,b) and para (c,d) DEB-bridged dinuclear species. (Reprinted with permission from [107], American Chemical Society, 2010). Magnetochemistry 2018, 4, x FOR PEER REVIEW 8 of 31

One year later, Newell et al. [107] reported in 2010 on the para and meta dinuclear tetravalent UIV/UIV [(NN′3)2U2(DEB)] and trinuclear [(NN′3)3U3(TEB)] complex (NN′3 = [N(CH2CH2NSitBuMe2)3]) (Figure 9) containing aromatic arylacetylide ligands i.e., diethynylbenzene (DEB) and triethynylbenzene (TEB) ligands as bridging-spacers for two or three metallic 5f2/5f2 and 5f2/5f2/5f2 spin centers.

~~NR NR RN N U U N~~

~~NR RN RN~~

~~(a)~~

~~R NR N RN U U N RN NR N RN~~

~~(b)~~

~~Figure 9. Molecular structures of the para- (a) and meta-diuranium(IV) (b) [(NN′3)2U2(DEB)] [107].~~

As reported by the authors, the experimental investigations of their magnetic properties show that the di- and tri-nuclear compounds appear to display weak magnetic communication between the uranium centers. This communication is modeled by fitting the direct current (DC) magnetic susceptibility data, using the spin Hamiltonian H ̂ = −2J Sz1̂ ·Sz2̂ , which leads to a weak ferromagnetic coupling constant i.e., J = 4.76, 2.75, and 1.11 cm−1, respectively for meta-, para-diuranium(IV) and triuranium(IV) complexes. As reported in the same study [107], geometry and nuclearity appear to have an effect on the strength of the coupling between the U(IV) centers. Turning back to the theoretical analysis, geometries of the considered model complexes were optimized using B3LYP computations. In these models, the bulky SitBuMe2 substituting groups in the NN′3 ligand have been replaced by H atoms and scalar relativistic effects only included in the used uranium effective core potential. For the simplified models derived from the meta- and para-bridged dinuclear species, the BS approach led to computed J values equal to 1.6 and −0.1 cm−1 for the meta- and para-bridged complexes, respectively, in fair agreement with experimental trends. As expected, all complexes show only small net spin density (Figure 10) on the ethynylbenzene ligands. As stated by the authors, the computed HS/BS spin densities mapping for meta (a/b) and para (c/d) isomers, both show that the spin density is mostly localized on the two UIV centers, with no contribution from the bridged-DEB ligand, explaining the weak ferromagnetic and AF character of the meta and para species, respectively [107]. The authors concluded that despite the structural differenceMagnetochemistry with 2019the ,actual5, 15 meta and para DEB-bridged dinuclear systems, the result shows that coupling9 of 31 in the single wavenumber range is not unexpected.

FigureFigure 10. 10. NetNet spin spin density plots plots for for HS/BS metameta ((a,ba,b) )and and parapara (c,dc,d)) DEB-bridged dinuclear dinuclear species. species. MagnetochemistryMagnetochemistry(Reprinted(Reprinted with20182018 with, , permission44, permission, xx FORFOR PEERPEER from from REVIEWREVIEW [107], [107 American ], American Chemical Chemical Society, Society, 2010). 2010). 9 9 ofof 3131

SubsequentSubsequent DFT/BSDFT/BS investigations investigations werewerewere carried carriedcarried out ououtt in inin 2012 20122012 by byby R. R.R. Arratia-P Arratia-PérezArratia-Pérezérez and andand Coll. Coll.Coll. [105 [105][105]] on 8 η 8 ontheon the magneticthe magneticmagnetic properties propertiesproperties of the ofof bis(dicyclooctatetraenyl) thethe bibis(dicyclooctatetraenyl)s(dicyclooctatetraenyl) diuranium(IV) diuranium(IV)diuranium(IV) [U( -C 8[U([U(H7ηη)28-C]-C2 model88HH77))22]]22 systemmodelmodel system(Figuresystem (Figure(Figure11). The 11).11). authors, TheThe authors,authors, who used whowho scalar usedused relativistic scalarscalar relativisticrelativistic computations computationscomputations with the withwith Zeroth thethe Order ZerothZeroth Regular OrderOrder RegularApproximationRegular ApproximationApproximation (ZORA) and(ZORA)(ZORA) the PBE andand GGA thethe PBEPBE functional GGAGGA functionalfunctional [148,149] in[148,149][148,149] combination inin combinationcombination with the BS withwith approach, thethe BSBS 2 2 approach,foundapproach, a strong foundfound ferromagnetic aa strongstrong ferromagneticferromagnetic coupling betweencouplicouplingng thebetweenbetween uranium thethe centersuraniumuranium bearing centerscenters the bearingbearing 5f -5f thetheorbitals, 5f5f22-5f-5f22 IV IV ··· ⋅⋅⋅ ··· IV⋅⋅⋅ IV orbitals,theorbitals, U U thethe distance UU⋅⋅⋅UU distancedistance in the (COT) inin thethe2U (COT)(COT)U22UU(COT)IV⋅⋅⋅UUIV2(COT)(COT)complex22 complexcomplex being being equalbeing toequalequal 5.320 toto Å. 5.3205.320 Å.Å.

~~° 1.5501.550 AA°~~

~~888 FigureFigureFigure 11. 11.11.Molecular MolecularMolecular model modelmodel for forfor [U( [U([U(ηηη-C-C-C888HH777))22]]]22 withwithwith DD D2h2h2h symmetrysymmetrysymmetry [105].[105]. [105].~~

1 1 ReturningReturning toto to thethe the5f5f11–5f–5f 5f11 bis(imido)bis(imido)–5f bis(imido) diuranium(V)diuranium(V) diuranium(V) systemssystems [9],[9], systems thethe ZORA/B3LYPZORA/B3LYP [9], the computationscomputations ZORA/B3LYP ofof μ thecomputationsthe couplingcoupling constantconstant of the coupling[146][146] properlyproperly constant reprreproduce [oduce146] properly thethe AFAF charactercharacter reproduce ofof the the parapara AF character [({MeC[({MeC55HH of44}}33U)U) the22((μ para-1,4--1,4- μ N[({MeCN22CC66HH445)])]H diuranium(V)diuranium(V)4}3U)2(µ-1,4-N complexcomplex2C6H4)] diuranium(V)andand thethe ferromagneticferromagnetic complex one andone of theof itsits ferromagnetic metameta isomerisomer one[({MeC[({MeC of its55HH meta44}}33U)U)22 isomer((μ-1,3--1,3- N[({MeCN22CC66HH445)])]H (Figure(Figure4}3U)2( µ12).12).-1,3-N 2C6H4)] (Figure 12).

~~((aa)) ((bb))~~

FigureFigure 12. 12. StructuresStructures ofof thethe para para ( (aa)) and and meta meta ( (bb)) imidoimido diuranium(V)diuranium(V) complexes complexes (reprinted (reprinted with with permissionpermission from from [146], [[146],146], Elsevier, Elsevier, 2012).2012).

TheThe spin-density spin-density plots plots of of the the HS/BSHS/BS statesstates states (Figure(Figure (Figure 13)13)13) illustrateillustrate thatthat thethe spinspin polarization effect isis mainly mainly responsible responsible for for thethe observedobserved magneticmamagneticgnetic character.character. Considering the para-U para-U22imidoimidoimido isomer,isomer, isomer, alternationalternation ofof of thethe the signssigns signs ofof of thethe the atomicatomic atomic spinspin spin populationpopulation populationsss alongalong along thethe the pathpath path isis obtainedobtained is obtained forfor forthethe theBSBS statestate BS state andand and notnot forfor thethe HSHS one.one. InIn contrast,contrast, forfor thethe meta-isomer,meta-isomer, altealternationrnation ofof thesethese signssigns isis obtainedobtained forfor thethe HSHS state,state, whichwhich isis lowerlower inin energyenergy thanthan BSBS one,one, ensuringensuring thethe ferromagneticferromagnetic charactercharacter ofof thethe complex.complex.

~~((aa)) ((bb))~~

FigureFigure 13.13. ZORA/B3LYPZORA/B3LYP spin-densityspin-density (difference(difference ofof alphaalpha andand betabeta electronelectron densities)densities) distributiondistribution plotsplots forfor thethe HSHS ((aa)) triplettriplet andand BSBS ((bb)) statesstates ofof para-U2imidopara-U2imido (blue(blue color:color: positivepositive spinspin densitydensity andand redred color:color: negativenegative spinspin density)density) (reprinted(reprinted withwith permissionpermission fromfrom [146],[146], Elsevier,Elsevier, 2012).2012). Magnetochemistry 2018, 4, x FOR PEER REVIEW 9 of 31

Subsequent DFT/BS investigations were carried out in 2012 by R. Arratia-Pérez and Coll. [105] on the magnetic properties of the bis(dicyclooctatetraenyl) diuranium(IV) [U(η8-C8H7)2]2 model system (Figure 11). The authors, who used scalar relativistic computations with the Zeroth Order Regular Approximation (ZORA) and the PBE GGA functional [148,149] in combination with the BS approach, found a strong ferromagnetic coupling between the uranium centers bearing the 5f2-5f2 orbitals, the U⋅⋅⋅U distance in the (COT)2UIV⋅⋅⋅UIV(COT)2 complex being equal to 5.320 Å.

~~1.550 A°~~

~~Figure 11. Molecular model for [U(η8-C8H7)2]2 with D2h symmetry [105].~~

Returning to the 5f1–5f1 bis(imido) diuranium(V) systems [9], the ZORA/B3LYP computations of the coupling constant [146] properly reproduce the AF character of the para [({MeC5H4}3U)2(μ-1,4- N2C6H4)] diuranium(V) complex and the ferromagnetic one of its meta isomer [({MeC5H4}3U)2(μ-1,3- N2C6H4)] (Figure 12).

~~(a) (b)~~

~~Figure 12. Structures of the para (a) and meta (b) imido diuranium(V) complexes (reprinted with permission from [146], Elsevier, 2012).~~

MagnetochemistryThe spin-density2019, 5, 15 plots of the HS/BS states (Figure 13) illustrate that the spin polarization10 effect of 31 is mainly responsible for the observed magnetic character. Considering the para-U2imido isomer, alternation of the signs of the atomic spin populations along the path is obtained for the BS state and not notfor forthe theHS HSone. one. In contrast, In contrast, for the for themeta-isomer, meta-isomer, alternation alternation of these of these signs signs is obtained is obtained for the for HS the state, HS state,which which is lower is lowerin energy in energy than BS than one, BS ensuring one, ensuring the ferromagnetic the ferromagnetic character character of the complex. of the complex.

~~(a) (b)~~

FigureFigure 13.13.ZORA/B3LYP ZORA/B3LYP spin-densityspin-density (difference(difference ofof alphaalpha andand betabeta electronelectron densities)densities) distributiondistribution plotsplots for for the the HS HS ( a(a)) triplet triplet and and BS BS ( (bb)) states states of of para-U2imido para-U2imido (blue (blue color: color: positivepositive spin spin density density and and red red color: negative spin density) (reprinted with permission from [146], Elsevier, 2012). Magnetochemistrycolor: negative 2018,spin 4, x FOR density) PEER (reprinted REVIEW with permission from [146], Elsevier, 2012). 10 of 31

The topology of the path linking the two magnetic of para-U2imido and meta-U2imido complexes The topology of the path linking the two magnetic of para-U2imido and meta-U2imido plays a crucial role for the electronic communication between the U(V) centers. Furthermore, from complexes plays a crucial role for the electronic communication between the U(V) centers. the MO point of view, the AF interaction between the two uranium(V) ions mediated by the aromatic Furthermore, from the MO point of view, the AF interaction between the two uranium(V) ions imido bridge is mainly due to the effective π-overlap between 5f1 orbitals and the nitrogen orbitals of mediated by the aromatic imido bridge is mainly due to the effective π-overlap between 5f1 orbitals the bridging ligand groups. and the nitrogen orbitals of the bridging ligand groups. As mentioned, the Kiplinger’s group [128] reported in 2008 the occurrence of a significant As mentioned, the Kiplinger’s group [128] reported in 2008 the occurrence of a significant electronic communication between the UIV/UIV (5f2/5f2) centers within the bis(ketimide) binuclear electronic communication between the UIV/UIV (5f2/5f2) centers within the bis(ketimide) binuclear IV IV [(C5Me4Et)2(Cl)An]2(µ-{N=CMe-(C6H4)-MeC=N}) An /An (Th, U) complexes. However, the [(C5Me4Et)2(Cl)An]2(µ-{N=CMe-(C6H4)-MeC=N}) AnIV/AnIV (Th, U) complexes. However, the magnetic character of the coupling between the metal centers could not be shown unambiguously. magnetic character of the coupling between the metal centers could not be shown unambiguously. Computationally, the exchange coupling constant has be estimated considering the simplified Computationally, the exchange coupling constant has be estimated considering the simplified IV IV IV IV [(C5H5)2(Cl)An]2(µ-ketimide) model (An/An = U /U and U /Th ), where C5Me4Et is replaced [(C5H5)2(Cl)An]2(μ-ketimide) model (An/An = UIV/UIV and UIV/ThIV), where C5Me4Et is replaced by the by the Cp = C5H5 ring (Figure 14)[147]. Using ZORA/B3LYP computations, the BS ground state of Cp = C5H5 ring (Figure 14) [147]. Using ZORA/B3LYP computations, the BS ground state of these these UIV/UIV 5f2–5f2 complexes has been found of lower energy than the quintet HS state, indicating UIV/UIV 5f2–5f2 complexes has been found of lower energy than the quintet HS state, indicating a weak a weak AF character (estimated coupling constant |J| < 5 cm−1) which has not yet been confirmed AF character (estimated coupling constant |J| < 5 cm−1) which has not yet been confirmed experimentally to our knowledge. experimentally to our knowledge.

FigureFigure 14.14. StructuresStructures of of the the bis(ketimide) bis(ketimide) diuranium(IV) diuranium(IV) complexes complexes (reprinted (reprinted with with permission permission from from[147], [ 147Springer-Verlag,], Springer-Verlag, 2012). 2012).

TheThe magneticmagnetic exchangeexchange couplingcoupling hashas beenbeen rationalizedrationalized consideringconsidering spinspin densitydensity distributionsdistributions (Figure(Figure 1515).). AsAs obtained obtained for for the the previous previous bis(imido) bis(imido) U VU/UV/UVV(5f (5f11/5f/5f1)) system system [146], [146], thethe AFAF couplingcoupling appearsappears through the alternating alternating signs signs of of the the atomic atomic spin spin populations populations along along the thepath path linking linking the two the twomagnetic magnetic metal metal centers centers 5f2–5f 5f22 –5fin the2 in BS the state, BS state, the AF the character AF character being being mainly mainly explained explained by spin by spinpolarization. polarization.

~~(a) (b)~~

~~Figure 15. ZORA/B3LYP spin-density (difference of alpha and beta electron densities) distribution~~

plots for the HS (a) triplet and BS states (b) of U2bis(ketimide) (blue color: positive spin density and red color: negative spin density). (Reprinted with permission from [147], Springer-Verlag, 2012).

The effect of the replacement of one paramagnetic metal U(5f2) by the diamagnetic Th(5f0) one in the UIV−(μ-ketimide)−ThIV hypothetical complex drastically affects the spin polarization effect; the spin densities tend to zero beyond the ﬁrst neighbors of the paramagnetic center. No magnetic exchange interaction occurs in such a system. C. C. Cummins and Coll. [15,16] reported in 2013 on the electronic structure and magnetic properties analyses of the arene-bridged UIII/UIII dimer [U2(N[tBu]Ar)4(µ-toluene)] (Ar = 3,5-C6H3Me2) complex (Figure 16). Magnetochemistry 2018, 4, x FOR PEER REVIEW 10 of 31

The topology of the path linking the two magnetic of para-U2imido and meta-U2imido complexes plays a crucial role for the electronic communication between the U(V) centers. Furthermore, from the MO point of view, the AF interaction between the two uranium(V) ions mediated by the aromatic imido bridge is mainly due to the effective π-overlap between 5f1 orbitals and the nitrogen orbitals of the bridging ligand groups. As mentioned, the Kiplinger’s group [128] reported in 2008 the occurrence of a significant electronic communication between the UIV/UIV (5f2/5f2) centers within the bis(ketimide) binuclear [(C5Me4Et)2(Cl)An]2(µ-{N=CMe-(C6H4)-MeC=N}) AnIV/AnIV (Th, U) complexes. However, the magnetic character of the coupling between the metal centers could not be shown unambiguously. Computationally, the exchange coupling constant has be estimated considering the simplified [(C5H5)2(Cl)An]2(μ-ketimide) model (An/An = UIV/UIV and UIV/ThIV), where C5Me4Et is replaced by the Cp = C5H5 ring (Figure 14) [147]. Using ZORA/B3LYP computations, the BS ground state of these UIV/UIV 5f2–5f2 complexes has been found of lower energy than the quintet HS state, indicating a weak AF character (estimated coupling constant |J| < 5 cm−1) which has not yet been confirmed experimentally to our knowledge.

~~Figure 14. Structures of the bis(ketimide) diuranium(IV) complexes (reprinted with permission from [147], Springer-Verlag, 2012).~~

The magnetic exchange coupling has been rationalized considering spin density distributions (Figure 15). As obtained for the previous bis(imido) UV/UV (5f1/5f1) system [146], the AF coupling appears through the alternating signs of the atomic spin populations along the path linking the two Magnetochemistrymagnetic metal2019 centers, 5, 15 5f2–5f2 in the BS state, the AF character being mainly explained by11 ofspin 31 polarization.

~~(a) (b)~~

FigureFigure 15. 15.ZORA/B3LYP ZORA/B3LYP spin-densityspin-density (difference(difference ofof alphaalpha andand betabeta electron electron densities) densities) distribution distribution plotsplots for for the the HS HS ( a()a) triplet triplet and and BS BS states states ( b()b of) of U U2bis(ketimide)2bis(ketimide) (blue (blue color: color: positive positive spin spin density density and and redred color: color: negative negative spin spin density). density). (Reprinted (Reprinted with with permission permission from from [ 147[147]],, Springer-Verlag, Springer-Verlag, 2012). 2012).

2 0 TheThe effect effect of of the the replacement replacement of of one one paramagnetic paramagnetic metal metal U(5f U(5f)2) by by the the diamagnetic diamagnetic Th(5f Th(5f)0) one one IV IV inin the the U UIV−((μµ-ketimide)-ketimide)−−ThThIV hypotheticalhypothetical complex complex drastically drastically affects affects the the spin spin polarization polarization effect; effect; the thespin spin densities densities tend tend to tozero zero beyond beyond the the ﬁ ﬁrstrst neighbors neighbors of of the paramagneticparamagnetic center.center. NoNo magneticmagnetic exchangeexchange interaction interaction occurs occurs in in such such a a system. system. C.C. C.C. CumminsCummins andand Coll.Coll. [15[15,16],16] reportedreported inin 20132013 onon thethe electronicelectronic structurestructure andand magneticmagnetic III III t propertiesproperties analyses analyses of of the the arene-bridged arene-bridged U U/UIII/UIIIdimer dimer [U [U2(N[2(N[Bu]Ar)tBu]Ar)4(4µ(µ-toluene)]-toluene)] (Ar (Ar = = 3,5-C 3,5-C6H6H3Me3Me22)) Magnetochemistrycomplexcomplex (Figure (Figure 2018 16 ,16). 4)., x FOR PEER REVIEW 11 of 31

~~R N N U U R R R N N~~

~~t FigureFigure 16. 16.Structure Structure of of the the ( µ(µ-toluene)U-toluene)U2(N[2(N[Bu]Ar)tBu]Ar)44 (Ar(Ar == 3,5-C 6HH33MeMe22) )complex complex [16]. [16].~~

Computationally, DFT DFT geometry geometry optimiza optimizationstions were performed were performed using the using Perdew the−Burke Perdew-Burke-−Ernzerhof (PBE)Ernzerhof exchange-correlation (PBE) exchange-correlation functional [148,149] functional and [the148 ,dispersion149] and thecorrected dispersion B-97D corrected functional B-97D [150] consideringfunctional [150 a model] considering where the a model large sized where 1-adamantyl the large sized and 1-adamantyl 3,5-C6H3Me2 andgroups 3,5-C were6H3 Mereplaced2 groups by weretbutyl replaced and phenyl bytbutyl moieties, and respectively. phenyl moieties, With respectively.reference to the With results reference of DFT to theand results CASSCF/CASPT2 of DFT and calculationsCASSCF/CASPT2 relativistic calculations eﬀects relativisticbeing included effects with being the included Douglas with−Kroll the− Douglas-Kroll-HessHess (DKH) Hamiltonian (DKH) (spin-orbitHamiltonian not (spin-orbit included), not all included),possible spin all states possible of the spin model states compounds, of the model including compounds, singlet, including triplet, quintet,singlet, triplet,and septet quintet, spin andstates, septet were spin explored. states, The were DFT explored. electronic The structure DFT electronic analysis structure showed analysisthat the highestshowed thatfour theSOMOs highest are four 5f SOMOsorbitals areof 5fthe orbitals two uranium of the two centers, uranium followed centers, followedenergetically energetically by two covalentby two covalent δ MOs,δ asMOs, presented as presented in Figure in Figure 17. These17. These latt latterer MOs MOs corresponding corresponding to tothe the U U-arene-U−arene−U bonding contain contributions from ur uraniumanium 5f orbitals overlapping with π antibonding orbitals of the tolyl group.

~~(a) (b)~~

Figure 17. Singly occupied δ bonding natural MOs from the (µ-toluene)U2(N[tBu]Ar)4 complex in its quintet state. (a) SOMO−4 and (b) SOMO−5 (reprinted with permission from [16], American Chemical Society, 2013).

The ground state at the CASPT2 level is the singlet; however, the triplet and quintet are respectively 0.7 and 2.5 kcal/mol higher in energy than the singlet state, whereas the septet is much higher, at 34.5 kcal/mol. As reported by the authors [16], solid-state magnetic susceptibility measurements of the dinuclear system showed complicated features. Indeed, although paramagnetic behavior is observed over the temperature intervals 5−300 K, the 1/χ versus T graph showed minimum values between 95 and 125 K, which is characteristic of a transition to AF state. However, the optical and magnetic properties of UIII-(µ-toluene)-UIII were diﬃcult to relate to reported examples of mononuclear uranium organometallic complexes. The authors did not estimate the coupling constants. As indicated above, remarkable classes of diuranium(V) bridged-oxo complexes exhibiting UVO2+···UVO2+ CCIs and strong AF exchange coupling were reported by various authors [23−32,46−51,61,69,114−116], motivating theoretical investigations [7,8,63−65,71,72,74,75,79]. Among them, strongly coupled binuclear complexes [UO2{N(SiR3)2}2(py)2] forming a butterﬂy-shaped Si– OUO2UO–Si uranium(V)-oxo motif (Figure 18) have been synthesized (2012), X-ray characterized and their electronic and magnetic properties investigated with the support of DFT computations [49]. A Magnetochemistry 2018, 4, x FOR PEER REVIEW 11 of 31

~~R N N U U R R R N N~~

~~Figure 16. Structure of the (µ-toluene)U2(N[tBu]Ar)4 (Ar = 3,5-C6H3Me2) complex [16].~~

Computationally, DFT geometry optimizations were performed using the Perdew−Burke−Ernzerhof (PBE) exchange-correlation functional [148,149] and the dispersion corrected B-97D functional [150] considering a model where the large sized 1-adamantyl and 3,5-C6H3Me2 groups were replaced by tbutyl and phenyl moieties, respectively. With reference to the results of DFT and CASSCF/CASPT2 calculations relativistic eﬀects being included with the Douglas−Kroll−Hess (DKH) Hamiltonian (spin-orbit not included), all possible spin states of the model compounds, including singlet, triplet, quintet, and septet spin states, were explored. The DFT electronic structure analysis showed that the highest four SOMOs are 5f orbitals of the two uranium centers, followed energetically by two covalent δ MOs, as presented in Figure 17. These latter MOs corresponding to the U−arene−U bondingMagnetochemistry contain2019 contributions, 5, 15 from uranium 5f orbitals overlapping with π antibonding orbitals12 of of 31 the tolyl group.

~~(a) (b)~~

tt Figure 17. Singly occupied δ bonding natural MOs fromfrom thethe ((µ-toluene)Uµ-toluene)U22(N[(N[ Bu]Ar)4 complexcomplex in in its quintet state. ( a) SOMO −44 and and ( (bb)) SOMO SOMO−−55 (reprinted (reprinted with with permission permission from from [16], [16], American American Chemical Chemical Society, 2013).

The ground state at the CASPT2 level is the singlet; however, the triplet and quintet are respectively 0.7 0.7 and and 2.5 2.5 kcal/mol kcal/mol higher higher in energy in energy than than the singlet the singlet state, state, whereas whereas the septet the septetis much is higher,much higher, at 34.5 at 34.5kcal/mol. kcal/mol. As reported As reported by bythe theauthors authors [16], [16 ],solid-state solid-state magnetic magnetic susceptibility measurements of the dinuclear system showed comp complicatedlicated features. Indeed, although although paramagnetic paramagnetic behavior isis observed observed over over the the temperature temperature intervals intervals 5–300 5 K,−300 the 1/K, χtheversus 1/χ Tversus graph showedT graph minimum showed minimumvalues between values 95 between and 125 K,95 which and 125 is characteristicK, which is characteristic of a transition of to a AF transition state. However, to AF state. the opticalHowever, and III III themagnetic optical properties and magnetic of U -( µproperties-toluene)-U of wereUIII-(µ-toluene)-U difficult to relateIII were to reported difficult examples to relate of mononuclearto reported examplesuranium organometallicof mononuclear complexes. uranium Theorganometallic authors did notcomplexes. estimate The the couplingauthors did constants. not estimate the couplingAs indicated constants. above, remarkable classes of diuranium(V) bridged-oxo complexes exhibiting V + V + U OAs2 ··· indicatedU O2 CCIs above, and strongremarkable AF exchange classes couplingof diuranium(V) were reported bridged-oxo by various complexes authors [23 exhibiting–32,46–51, U61V,O692,+114···U–V116O2+ ],CCIs motivating and theoreticalstrong AF investigations exchange couplin [7,8,63–g65 ,were71,72 ,74reported,75,79]. Amongby various them, stronglyauthors [23coupled−32,46 binuclear−51,61,69,114 complexes−116], motivating [UO2{N(SiR theoretical3)2}2(py) investigations2] forming a butterfly-shaped[7,8,63−65,71,72,74,75,79]. Si–OUO Among2UO–Si Magnetochemistrythem,uranium(V)-oxo strongly 2018 coupled motif, 4, x FOR (Figurebinuclear PEER REVIEW 18 )complexes have been [UO synthesized2{N(SiR3)2}2 (2012),(py)2] forming X-ray characterized a butterfly-shaped and 12 their of Si– 31 OUOelectronic2UO–Si and uranium(V)-oxo magnetic properties motif (Figure investigated 18) have been with synthesized the support (2012), of DFT X-ray computations characterized [and49]. variable-temperaturetheirA variable-temperature electronic and magnetic measurement measurement properties of of susceptibilit susceptibility investigatyed shows showswith thea aclear clear support signature signature of DFT of of AFcomputations AF coupling coupling between between [49]. A 1 1 thethe 5f 5f1−–5f5f1 centers.centers.

~~R3Si O N N N U~~

~~N O O N U N N N O~~

~~R3Si~~

~~Figure 18. Structure of the butterﬂy-shaped diuranium(V) [UO2{N(SiR3)2}2(py)2] complex [49]. Figure 18. Structure of the butterﬂy-shaped diuranium(V) [UO2{N(SiR3)2}2(py)2] complex [49].~~

The geometriesgeometries of of the the 5f1 –5f5f11–5fstructures1 structures were were optimized optimized in the gasin phasethe gas using phase B3LYP using calculations, B3LYP α α α β calculations,considering theconsidering ferromagnetic the ferromagnetic triplet (fαfα), triplet the BS (f (fαf f),β )the and BS the (f spinf ) and restricted the spin singlet restricted (fαβ )singlet states. αβ (fA striking) states. structuralA striking feature structural of the feature U2O2 ofcore the is U its2O C2 core2v-symmetrical is its C2v-symmetrical diamond shape diamond and anshape average and anU–O average distance U–O of distance 2.094 Å, of with2.094 aÅ, very with short a very U short···U separation U⋅⋅⋅U separation of 3.3557(5) of 3.3557(5) Å. As Å. reported As reported by theby theauthors authors using using B3LYP B3LYP calculations calculations [49 [49],], the the BS BS state state was was calculated calculated to to be be more morestable stable thanthan the triplet and restricted singlet states by 1.4 and 42.7 kcal/mol, respectively, respectively, which which is is in in agreement with the observed AF character of the complex. The U⋅⋅⋅U separation was calculated to be equal to 3.366 and 3.379 Å in the BS and triplet states, respectively, within 0.01 Å deviations from the experimental values. NBO analysis of the bonding in the U2O2 core for both states, based on the calculated Mayer and Wiberg bond orders, reveals formally U–O single and partially double-bond character, which is in agreement with the structural features. The MO analysis shows that the two α and β components of HOMO-27 and HOMO-28, obtained with the B3LYP functional for the BS state, are related to the σ and π bonding interactions, respectively, within the U2O2 core. The π-type orbitals, which are dominated by 2p-contributions from the oxo-bridged atoms, appear to stabilize the diamond U2O2 core. The B3LYP calculated spin density in the AF BS state shows the fαfβ configuration with electrons of different spins localized on each uranium atom. As reported in the same study [49], the calculated U⋅⋅⋅U separation of 3.366 Å is much shorter than twice the covalent radius of the uranium atom (3.92 Å), which may indicate some metal−metal bonding interaction, as predicted by theory [145,151−154]. However, the structural analogy with MoV(μ-O)2MoV complexes which exhibit single Mo–Mo bonds was faced to the paramagnetic state of the UV(μ-O)2UV complex, and no reported examples exist of molecular bonds between two f-block ions in such structures. The authors conclude that the extremely short U⋅⋅⋅U separation exhibited by the diuranium(V) oxo-bridged system indicates strong electronic communication between the two 5f1 centers. However, it was postulated that the geometry of the oxo-group interaction within the diamond-shaped U2O2 core, and not the shortened U⋅⋅⋅U separation, was the primary mediator of the super-exchange. Indeed, as reported by the authors,20d the AF coupling due to super-exchange across the two oxo groups, modeled by a spin Hamiltonian, led to a particularly large fitted value Jexp = −33 cm−1, suggesting that the butterﬂy geometry could be of interest for the building more complex magnetic structures. Other diuranium bis(μ-oxo) systems, synthesized by K. Meyer and Coll. [115], (in 2014) exhibit diamond-core shaped [U(µ-O)2U] structural motifs and remarkably diﬀerent magnetic behaviors depending on the uranium oxidation state. Indeed, the magnetic data show for pentavalent [{((nP,MeArO)3tacn)UV}2(µ-O)2] (tacn = triazacyclononane, nP = neopentyl) structure a UV/UV AF coupled system, while its reduced species, the dianionc UIV/UIV K2[{((nP,MeArO)3tacn)UIV}2(µ-O)2] tetravalent complex, revealed itself to be non-magnetic [115]. These two complexes (Figure 19), have Magnetochemistry 2019, 5, 15 13 of 31

observed AF character of the complex. The U···U separation was calculated to be equal to 3.366 and 3.379 Å in the BS and triplet states, respectively, within 0.01 Å deviations from the experimental values. NBO analysis of the bonding in the U2O2 core for both states, based on the calculated Mayer and Wiberg bond orders, reveals formally U–O single and partially double-bond character, which is in agreement with the structural features. The MO analysis shows that the two α and β components of HOMO-27 and HOMO-28, obtained with the B3LYP functional for the BS state, are related to the σ and π bonding interactions, respectively, within the U2O2 core. The π-type orbitals, which are dominated by 2p-contributions from the oxo-bridged atoms, appear to stabilize the diamond U2O2 core. The B3LYP calculated spin density in the AF BS state shows the fαfβ configuration with electrons of different spins localized on each uranium atom. As reported in the same study [49], the calculated U···U separation of 3.366 Å is much shorter than twice the covalent radius of the uranium atom (3.92 Å), which may indicate some metal-metal bonding interaction, as predicted by theory [145,151–154]. However, the structural analogy with V V Mo (µ-O)2Mo complexes which exhibit single Mo–Mo bonds was faced to the paramagnetic state of V V the U (µ-O)2U complex, and no reported examples exist of molecular bonds between two f-block ions in such structures. The authors conclude that the extremely short U···U separation exhibited by the diuranium(V) oxo-bridged system indicates strong electronic communication between the two 5f1 centers. However, it was postulated that the geometry of the oxo-group interaction within the diamond-shaped U2O2 core, and not the shortened U···U separation, was the primary mediator of the super-exchange. Indeed, as reported by the authors,20d the AF coupling due to super-exchange across the two oxo groups, modeled by a spin Hamiltonian, led to a particularly large fitted value −1 Jexp = −33 cm , suggesting that the butterfly geometry could be of interest for the building more complex magnetic structures. Other diuranium bis(µ-oxo) systems, synthesized by K. Meyer and Coll. [115], (in 2014) exhibit diamond-core shaped [U(µ-O)2U] structural motifs and remarkably different magnetic behaviors depending on the uranium oxidation state. Indeed, the magnetic data show for pentavalent nP,Me V V V [{(( ArO)3tacn)U }2(µ-O)2] (tacn = triazacyclononane, nP = neopentyl) structure a U /U AF IV IV nP,Me IV coupled system, while its reduced species, the dianionc U /U K2[{(( ArO)3tacn)U }2(µ-O)2] Magnetochemistrytetravalent 2018 complex,, 4, x FOR revealed PEER REVIEW itself to be non-magnetic [115]. These two complexes (Figure 13 19 of), 31 have been investigated computationally using B3LYP coupled to the BS approach; scalar relativistic effects been investigated computationally using B3LYP coupled to the BS approach; scalar relativistic effects were accounted for by using the ZORA Hamiltonian [155]. were accounted for by using the ZORA Hamiltonian [155].

~~(a) (b)~~

V V V V IV IV IV IV FigureFigure 19. Optimized 19. Optimized molecular molecular structures structures of the (a) of[U the(µ-O) (a)2U [U] and(µ-O) (b2) UK2[U] and(µ-O) (b)K2U 2][U complexes(µ-O)2U ] (reprintedcomplexes with (reprintedpermission with from permission [155], American from [ 155Chemical], American Society, Chemical 2016). Society, 2016).

The computations reveal the BS ground state of the pentavalent [UV(µ-O)2UV] 5f1-5f1 complex lower in energy than the high spin (HS) triplet state, indicating a AF character in agreement with experimental magnetic susceptibility measurements. The non-magnetic character observed for the tetravalent K2[UIV(µ-O)2UIV] 5f2/5f2 species is also predicted by ZORA/B3LYP calculations which led practically to the same energy for the HS and BS states [115]. As previously reported for related dioxo diuranium(V) systems [49], super-exchange is likely to be responsible for the AF coupling through the π-network orbital pathway within the (µ-O)2 bridge, with the dissymmetrical structure of the U2O2 core playing a determining role. Spin densities in HS and BS states were computed for the UV(µ- O)2UV complex in order to understand and rationalize their AF character. The obtained spin density surfaces (Figure 20) showed that both HS and BS states exhibit localized spin densities on the two magnetic diuranium(V) centers, with significant values on their nearest Ooxo and non-negligible ones on the OAr neighbors.

(a) (b) Magnetochemistry 2018, 4, x FOR PEER REVIEW 13 of 31 been investigated computationally using B3LYP coupled to the BS approach; scalar relativistic effects were accounted for by using the ZORA Hamiltonian [155].

~~(a) (b)~~

Magnetochemistry 2019, 5, 15 V V IV IV 14 of 31 Figure 19. Optimized molecular structures of the (a) [U (µ-O)2U ] and (b) K2[U (µ-O)2U ] complexes (reprinted with permission from [155], American Chemical Society, 2016). V V 1 1 The computations reveal the BS ground state of the pentavalent [U (µ-O)2U ] 5f -5f complex The computations reveal the BS ground state of the pentavalent [UV(µ-O)2UV] 5f1-5f1 complex lower in energy than the high spin (HS) triplet state, indicating a AF character in agreement with lower in energy than the high spin (HS) triplet state, indicating a AF character in agreement with experimental magnetic susceptibility measurements. The non-magnetic character observed for the experimental magneticIV susceptibiIV 2 lity2 measurements. The non-magnetic character observed for the tetravalent K2[U (µ-O)2U ] 5f /5f species is also predicted by ZORA/B3LYP calculations which led tetravalent K2[UIV(µ-O)2UIV] 5f2/5f2 species is also predicted by ZORA/B3LYP calculations which led practically to the same energy for the HS and BS states [115]. As previously reported for related dioxo practically to the same energy for the HS and BS states [115]. As previously reported for related dioxo diuranium(V) systems [49], super-exchange is likely to be responsible for the AF coupling through the diuranium(V) systems [49], super-exchange is likely to be responsible for the AF coupling through π-network orbital pathway within the (µ-O)2 bridge, with the dissymmetrical structure of the U2O2 the π-network orbital pathway within the (µ-O)2 bridge, with the dissymmetrical structure of the U2O2 core playing a determining role. Spin densities in HS and BS states were computed for the UV(µ-O) UV core playing a determining role. Spin densities in HS and BS states were computed for the UV2(µ- complex in order to understand and rationalize their AF character. The obtained spin density surfaces O)2UV complex in order to understand and rationalize their AF character. The obtained spin density (Figure 20) showed that both HS and BS states exhibit localized spin densities on the two magnetic surfaces (Figure 20) showed that both HS and BS states exhibit localized spin densities on the two diuranium(V) centers, with signiﬁcant values on their nearest Ooxo and non-negligible ones on the magnetic diuranium(V) centers, with significant values on their nearest Ooxo and non-negligible ones OAr neighbors. on the OAr neighbors.

~~(a) (b)~~

Figure 20. ZORA/B3LYP spin density surfaces for the HS (triplet) in left and BS states in right of V V U (µ-O)2U complex (blue color: positive and red color: negative spin density). The plotted isodensity surfaces (a) HS and (b) BS states corresponds to a value of ±0.0025 e bohr–3. (reprinted with permission from [155], American Chemical Society, 2016).

Interestingly, the spin density maps show that the difference between the HS and BS states is the sign alternation of the spin populations around the dioxo (µ-O)2 path-linking the two magnetic V 1 U (5fxyz ) centers in its BS state. For the HS state, the spin of the bridging (µ-O)2 ligands is symmetrically polarized by the two UV spin carriers. In contrast, for the BS state, the two oxygen atoms are differently polarized with sign alternation of positive and negative spin densities. The magnetic properties of di- and triuranyl(V) [UO2(dbm)2K(18C6)]2 (dbm: dibenzoylmethanate) and [UO2(L)]3 (L = 2(4-Tolyl)-1,3-bis(quinolyl)malondiiminate) complexes (Figure 21), exhibiting 1 1 1 1 1 diamond-shape U2O2 and triangular-shape U3O3 cores with 5f -5f and 5f -5f -5f conﬁgurations, have been studied experimentally [23–25]. The ZORA/B3LYP calculations (unpublished results) which have been carried out conﬁrm the AF character of these complexes. The estimated J values have been respectively found equal to −24.1 and −7.2 cm−1 for the dioxo and the trioxo species, the used geometries of the magnetic cores being those of the X-ray structures. Magnetochemistry 2018, 4, x FOR PEER REVIEW 14 of 31 Magnetochemistry 2018, 4, x FOR PEER REVIEW 14 of 31 Figure 20. ZORA/B3LYP spin density surfaces for the HS (triplet) in left and BS states in right of UV(µ- V O)Figure2UV complex 20. ZORA/B3LYP (blue color: spin positive density andsurfaces red color:for the negative HS (triplet) spin in leftdensity). and BS The states plotted in right isodensity of U (µ- surfacesO)2UV complex (a) HS and (blue (b) color:BS states positive corresponds and red to color:a value negative of ±0.0025 spin e bohr density).–3. (reprinted The plotted with permission isodensity fromsurfaces [155], (a )American HS and (b Ch) BSemical states Society, corresponds 2016). to a value of ±0.0025 e bohr–3. (reprinted with permission from [155], American Chemical Society, 2016). Interestingly, the spin density maps show that the difference between the HS and BS states is the sign alternationInterestingly, of the the spin spin density populations maps show around that the the dioxodifference (µ-O) between2 path-linking the HS andthe twoBS states magnetic is the UsignV(5f xyzalternation1) centers ofin theits spinBS state.populations For the around HS state, the thedioxo spin (µ-O) of 2 thepath-linking bridging the(µ-O) two2 ligands magnetic is symmetricallyUV(5fxyz1) centers polarized in its byBS thestate. two For UV thespin HS carriers. state, Inthe contrast, spin of for the the bridging BS state, (µ-O) the two2 ligands oxygen is atomssymmetrically are differently polarized polarized by the with two sign UV spinalternation carriers. of Inpositive contrast, and for negative the BS spin state, densities. the two oxygen atomsThe are differentlymagnetic polarizedproperties with signof alternationdi- and oftriuranyl(V) positive and negative[UO2(dbm) spin2K(18C6)] densities.2 (dbm: dibenzoylmethanate)The magnetic andproperties [UO2(L)] 3 of(L =di- 2(4-Tolyl)-1,3-bis(quinolyl)malondiiminate) and triuranyl(V) [UO2(dbm)2K(18C6)] complexes2 (dbm: (Figuredibenzoylmethanate) 21), exhibiting diamond-shapeand [UO2(L)]3 (LU 2O=2 and2(4-Tolyl)-1,3-bis(quinolyl)malondiiminate) triangular-shape U3O3 cores with 5f1-5f1 andcomplexes 5f1-5f1- 5f(Figure1 configurations, 21), exhibiting have diamond-shape been studied U 2experimentallyO2 and triangular-shape [23−25]. UThe3O3 coresZORA/B3LYP with 5f1-5f calculations1 and 5f1-5f1- 1 − (unpublished5f configurations, results) have which been have studied been carried experimentally out confirm [23 the 25].AF characterThe ZORA/B3LYP of these complexes. calculations The Magnetochemistryestimated(unpublished J values2019 results), 5 have, 15 which been have respectively been carried found out equal confirm to − 24.1the AF and character −7.2 cm −of1 for these the complexes. dioxo and15 of Thethe 31 trioxoestimated species, J values the used have geometries been respectively of the magn foundetic equal cores to being −24.1 those and of−7.2 the cm X-ray−1 for structures. the dioxo and the trioxo species, the used geometries of the magnetic cores being those of the X-ray structures.

(a) (b) (a) (b) Figure 21. Optimized molecular structures of dioxo (a) [UO2(dbm)2K(18C6)]2 and trioxo (b). [UO2(L)]3 Figure 21. Optimized molecular structures of dioxo (a) [UO2(dbm)2K(18C6)]2 and trioxo (b). [UO2(L)]3 (L(LFigure == 2(4-Tolyl)-1,3-bis(quinolyl)malondiiminate)2(4-Tolyl)-1,3-bis(quinolyl)malondiiminate) 21. Optimized molecular structures of dioxo Sticks (a) [UOused 2(dbm) to depict2K(18C6)] C, NN2 andand trioxo KK atoms;atoms; (b). H[UOH atomsatoms2(L)]3 havehave(L = 2(4-Tolyl)-1,3-bis(quinolyl)malondiiminate) beenbeen omittedomitted forfor clarity.clarity. Pink and red colorscolo Sticksrs respectively used to depict for uraniumuran C, Nium and and K atoms; oxygen H atoms. atoms (Unpublished(Unpublishedhave been omitted results).results). for clarity. Pink and red colors respectively for uranium and oxygen atoms. (Unpublished results). TheThe obtainedobtained spinspin density density maps maps (difference (difference between between the theα and α andβ electron β electron densities) densities) of the of HSthe and HS BSand states BSThe states ofobtained the of diuranyl the spin diuranyl density species spec maps areiesdisplayed are (difference displayed in between Figure in Figure 22 the. They22. α andThey are β rather areelectron rather similar densities) similar to those to of those the of the HSof V V V V Utheand( µU BS-O)(µ-O) states2U 2Ucomplex of complex the diuranyl (Figure (Figure 20 spec). 20).ies are displayed in Figure 22. They are rather similar to those of the UV(µ-O)2UV complex (Figure 20).

(a) (b) (a) (b) Figure 22. ZORA/B3LYP spin density distributions for the HS (triplet) and BS states of the dioxo Figure[UOFigure2(dbm) 22.22. ZORA/B3LYP2ZORA/B3LYPK(18C6)]2 system spin (blue density color: distributions positive and red for color: thethe HSHS negative (triplet)(triplet) spin andand density). BSBS statesstates The ofof isodensity thethe dioxodioxo [UOsurface[UO22(dbm)(dbm) corresponds22K(18C6)]K(18C6)] 2to2 system a value (blue of 0.0025 color: e positive bohr–3. (Unpublished and redred color:color: negativenegativeresults). (spinspina) (HS); density).density). (b) (BS). TheThe isodensityisodensity surfacesurface corresponds corresponds to to a a value value of of 0.0025 0.0025 e e bohr bohr–3–3.. (Unpublished(Unpublished results).results). ((aa)) (HS);(HS); ((bb)) (BS).(BS).

More recently (2017), the ﬁrst benzoquinonoid-bridged dinuclear actinide complexes were reported by S. Hohloch et al. [156] The target dinuclear systems with different structures, Dipp OMe OMe i.e., UI(L)]2, [Th(L)]2Q , [Th(THF)(L)]2Q and [U(L)]2Q associated with the tripodal tris[2-amido(2-pyridyl)ethyl]amine ligand L, have been synthesized from the dianionic 2,5-bis [2,6-(diisopropyl)anilide]-1,4-benzoquinone (QDipp) and 2,5-bis[2-(methoxy)anilide]-1,4-benzoquinone (QOMe) ligands, as depicted for the quinoid-bridged UIV/UIV diuranium system in Figure 23. Magnetochemistry 2018, 4, x FOR PEER REVIEW 15 of 31

More recently (2017), the first benzoquinonoid-bridged dinuclear actinide complexes were reported by S. Hohloch et al. [156] The target dinuclear systems with different structures, i.e., UI(L)]2, Dipp OMe OMe [Th(L)]2QDipp, [Th(THF)(L)]2QOMe and [U(L)]2QOMe associated with the tripodal tris[2-amido(2- pyridyl)ethyl]amine ligand L, have been synthesized from the dianionic 2,5-bis[2,6- Magnetochemistry(diisopropyl)anilide]-1,4-benzoquinone2019, 5, 15 (QDipp) and 2,5-bis[2-(methoxy)anilide]-1,4-benzoquinone16 of 31 (QOMe) ligands, as depicted for the quinoid-bridged UIV/UIV diuranium system in Figure 23.

~~Ar O N~~

~~(L)M M(L)~~

~~N O Ar~~

~~(a) (b)~~

FigureFigure 23.23. SchematicSchematic depiction depiction ( a)) and molecularmolecular structurestructure ((bb)) ofof thethe imino-alkoxyimino-alkoxy quinoidquinoid OMeOMe diuranium(IV)diuranium(IV) [U(L)][U(L)]22QQOMe system.system. (reprinted (reprinted with with permission permission from from [156], [156], thethe RoyalRoyal SocietySociety ofof Chemistry,Chemistry, 2017). 2017).

AsAs reportedreported byby thethe authors, authors, magnetic magnetic measurements measurements of of the the duranium(IV) duranium(IV) iodide iodide [UI(L)] [UI(L)]2 2and and OMe IV IVIV IV quinoidquinoid [U(L)][U(L)]22QOMe bridgedbridged species, species, which which exhibit exhibit long long intermetallic intermetallic UIV…U U IV... distancesU distances i.e., 5.125(1) i.e., 5.125(1)Å and Å8.904(1) and 8.904(1) Å respectively, Å respectively, indicate indicate that thatthere there is weak is weak magnetic magnetic exchange exchange between between the twotwo uranium(IV)uranium(IV) ionsions whichwhich waswas notnot quantiﬁedquantified fromfrom thethe DCDC susceptibilitysusceptibility measurements.measurements. Furthermore,Furthermore, asas reportedreported inin thethe study,study, the the low-temperature low-temperature susceptibilitysusceptibility datadata indicateindicate thatthat thethe groundground statesstates forfor IV IV thethe twotwo U UIV/U/UIV dimerdimer should should be be non-magnetic non-magnetic singlets. singlets. With With the support of DFTDFT calculations,calculations, usingusing aa hybridhybrid B3PW91B3PW91 functionalfunctional [[157]157] andand aa corecore pseudopotentialpseudopotential forfor uranium,uranium, thethe electronicelectronic structurestructure IVIV IVIV OMe analysisanalysis ofof thethe U UIV/U/UIV diuranium [U(L)]2QOMe systemsystem shows shows that that the fourfour unpairedunpaired electronselectrons occupyingoccupying SOMOs,SOMOs, areare mainlymainly ofof mixed mixed uranium/quinoid uranium/quinoid charactercharacter asas illustratedillustrated byby thethe SOMO-2SOMO-2 (Figure(Figure 24 24),), except except the the SOMO SOMO−−1, which is purely metal-based.metal-based.

OMe FigureFigure 24.24. SOMO-2SOMO-2 ofof thethe [U(L)][U(L)]22QOMe quintetquintet state state system. system. Plot Plot surfaces surfaces displayed displayed with with an an iso-value iso-value of of0.02 0.02 au au (reprinted (reprinted with with permission permission from from [156], [156 the], Royal the Royal Society Society of Chemistry, of Chemistry, 2017). 2017).

TheThe unpairedunpaired spin-density spin-density plot plot (Figure (Figure 25 )25) shows shows that that there there is signiﬁcant is significant spin-delocalisation spin-delocalisation from uraniumfrom uranium to the to quinoid the quinoid bridge. bridge. OMe Importantly, the quinoid ligand of the diuranium(IV) [U(L)]2Q complex could undergo a reversible reduction to form a radical anion. However, the chemical redox reaction leads to an unstable and sensitive anionic complex, despite the fact that X-ray crystallography indicates that the product contains a radical bridge. However, the magnetometry of the anionic species has not been investigated, and the impact of the radical bridge on the intermetallic exchange interaction could not be evaluated. Magnetochemistry 2018, 4, x FOR PEER REVIEW 16 of 31 Magnetochemistry 2018, 4, x FOR PEER REVIEW 16 of 31

~~Magnetochemistry 2019, 5, 15 17 of 31 Magnetochemistry 2018, 4, x FOR PEER REVIEW 16 of 31~~

Figure 25. spin-density plot of the [U(L)]2QOMe. Plot surfaces displayed with an iso-value of 0.02 au Figure 25. spin-density plot of the [U(L)]2QOMe. Plot surfaces displayed with an iso-value of 0.02 au

~~(reprinted(reprinted withwith permissionpermission fromfrom [156],[156], thethe RoyalRoyal SocietySociety ofof Chemistry,Chemistry, 2017).2017).~~

Importantly, the quinoid ligand of the diuranium(IV) [U(L)]2QOMe complex could undergo a Importantly, the quinoid ligand of the diuranium(IV) [U(L)]2QOMe complex could undergo a reversiblereversible reductionreduction toto formform aa radicalradical anion.anion. HoHowever, the chemical redox reaction leads to an unstable and sensitive anionic complex, despite the factfact thatthat X-rayX-ray crystallographycrystallography indicatesindicates thatthat thethe product contains a radical bridge. However, the magnetometry of the anionic species has not been investigated, and the impact of the radical bridgeOMe on the intermetallic exchange interaction could not investigated,FigureFigure 25.25. andspin-density spin-density the impact plotplot of of of the the the radical [U(L)] [U(L)]2 Q2bridgeQOMe.. Plot Plot on surfacesthe intermetallic displayed exchange with anan iso-valueiso-value interaction ofof 0.020.02 could auau not be evaluated.(reprinted(reprinted withwith permission from from [156], [156], the the Royal Royal Society Society of of Chemistry, Chemistry, 2017). 2017).

3.3. Mononuclear Actinide Complexes OMe 3.3. MononuclearImportantly, Actinide the quinoid Complexes ligand of the diuranium(IV) [U(L)]2Q complex could undergo a reversible reduction to form a radical anion. However, the chemical redox reaction leads to an Several uranium-radical systems emerged in thethe mid-2000smid-2000s asas mononuclearmononuclear complexescomplexes exhibitingunstableSeveral and magnetic sensitiveuranium-radical properties anionic complex,systems [62,66,74 ,despiteemerged129–131 the,158 in fact– 170the that]. mid-2000s Structural, X-ray crystallography as spectroscopic mononuclear indicates and complexes magnetic that the exhibiting magnetic properties [62,66,74,129−131,158−170]. Structural, spectroscopic and magnetic exhibitingproduct contains magnetic a radical properties bridge. [62,66,74,129 However, the131,158 magnetometry170]. Structural, of the anionicspectroscopic species and has magneticnot been propertiesproperties ofof variousvarious mononuclearmononuclear uranium(IV)-benzophenoneuranium(IV)-benzophenone radicalradical complexes;complexes; e.g.,e.g. the ketylketyl propertiestBu of variousIV mononucleatBu r uranium(IV)-benzophenone radical complexes; e.g. the ketyl [((investigated,tBu ArO)3tacn)U andIV the(OC impact⋅tBu· Ph of2 )]the complex radical bridge (2) (Figure on the 26 intermetallic), were investigated exchange interaction by O.P. Lam could et not al. [(( tBuArO)3tacn)U IV(OC⋅tBuPh2)] complex (2) (Figure 26), were investigated by O.P. Lam et al. (2008) [((be evaluated.ArO)3tacn)U (OC Ph2)] complex (2) (Figure 26), were investigated by O.P. Lam et al. (2008) (2008)[164] with [164] withthe support the support of DFT of DFT calculations. calculations. The The temperature temperature dependence dependence of of the the magneticmagnetic susceptibility[164] with the data support for this of ketyl DFT radical calculations. complex The shows temperature a similar trend dependence to that of of a previousthe magnetic CO susceptibility data for this ketyl radical complex shows a similar trend to that of a previous CO2 η12- susceptibility data for this ketyl radical complex•− shows a similar trend to that of a previous CO2 η1- η3.3.1-bound Mononuclear uranium Actinide [((AdArO) Complexestacn)U IV(CO )] complex [165]. bound uranium [((AdArO)3tacn)U3 IV(CO2•-)] complex2 [165]. bound uranium [((AdArO)3tacn)UIV(CO2•-)] complex [165]. Several uranium-radical systems emerged in the mid-2000s as mononuclear complexes exhibiting magnetic properties [62,66,74,129−131,158−170]. Structural, spectroscopic and magnetic properties of various mononuclear uranium(IV)-benzophenone radical complexes; e.g. the ketyl [((tBuArO)3tacn)UIV(OC⋅tBuPh2)] complex (2) (Figure 26), were investigated by O.P. Lam et al. (2008) O H N O hexane O [164] with Othe Nsupport of DFT calculations.O The temperature dependence of OtheH magnetic O III O hexane O N O U III O N O N U N O IV O N 1 susceptibility dataN N for this ketyl radical complexN UshowsIV O a similar trend to that of a previousIVN CO2 η - N U O N U IV O N N U O O Ad 3 IV 2•- N N bound uraniumO [(( ArO) tacn)U (CO )] complexO [165]. N O O O

1 2 3 1 2 3 red-brown purple green red-brown purple green O N H FigureFigure 26.26.O Formation FormationO of of U(IV) hexaneU(IV) benzophenone benzophenone ketylO ketyl radical radical complex complex2 through 22 throughthrough a one-electron aa one-electronone-electronO reduction UIII O N O reduction0 ofN 4,4N′-Di-tert-butylbenzophenone by U(III)IV precursor complex [((t-BuArO)III 3tacn)UN III] (1) of 4,4 -Di-tert-butylbenzophenone by U(III) precursorN U complexO [((t-BuArO)3tacn)U ](1)3 followedIII by reduction of 4,4′-Di-tert-butylbenzophenone by U(III) precursor complex [((t-BuArO) tacn)UUIV O] (1) N N Hfollowed abstraction by HO to abstraction form a U(IV) to form diphenyl a U(IV) methoxide diphenyl complex methoxide3 [164 complex]. 3 [164]. N followed by H abstraction to form a U(IV) diphenylO methoxide complex 3 [164]. O TheThe ketylketyl radicalradical complexcomplex 22 waswas modeledmodeledmodeled toto havehavehave threethreethree unpairedunpairedunpaired electrons,electrons, computingcomputing itit asas aa U(III) complex. However, the resu resultinglting orbitals and spin density plots (Figure 2727)) suggest a more U(III) complex.1 However, the resu lting orbitals 2 and spin density plots (Figure 3 27) suggest a more complexcomplex representation.representation.representation.red-brown purple green Figure 26. Formation of U(IV) benzophenone ketyl radical complex 2 through a one-electron reduction of 4,4′-Di-tert-butylbenzophenone by U(III) precursor complex [((t-BuArO)3tacn)UIII] (1) followed by H abstraction to form a U(IV) diphenyl methoxide complex 3 [164].

~~The ketyl radical complex 2 was modeled to have three unpaired electrons, computing it as a U(III) complex. However, the resulting orbitals and spin density plots (Figure 27) suggest a more~~

~~complex representation. ((a)) ((b)) ((cc)) ((d))~~

Figure 27. DFT isosurface contour plots featuring frontier SOMOs and spin density of the ketyl tBu IV tBu [(( ArO)3tacn)U (OC· Ph2)] complex (2). (a) SOMO; (b) SOMO-1; (c) SOMO-2; (d) Spin density. (Reprinted with permission from [164], American Chemical Society, 2008.)

(a) (b) (c) (d) Magnetochemistry 2018, 4, x FOR PEER REVIEW 17 of 31 Magnetochemistry 2019, 5, 15 18 of 31 Figure 27. DFT isosurface contour plots featuring frontier SOMOs and spin density of the ketyl [((tBuArO)3tacn)UIV(OC⋅tBuPh2)] complex (2). (a) SOMO; (b) SOMO-1; (c) SOMO-2; (d) Spin density. Magnetochemistry 2018, 4, x FOR PEER REVIEW 17 of 31 As reported(Reprinted by with the permission authors, from while [164 SOMO-2], American and Chemical SOMO-1 Society, (Figure 2008.) 27) are of δ-type fxyz and fz(x2-y2) pure uraniumFigure 5f orbitals,27. DFT isosurface the highest contour energy plots featuring SOMO fron exhibitstier SOMOs a metal/ligand and spin density character. of the ketyl The resulting As reportedtBu by theIV authors,⋅2tBu while SOMO-2 and SOMO-1 (Figure 27) are of δ-type fxyz and fz(x2-y2) spin density[(( ofArO) the3tacn)U U(IV)(OC 5f complexPh2)] complex (2 )(2 confirms). (a) SOMO; that (b) theSOMO-1; fxyz and(c) SOMO-2; fz(x2-y2) (dorbitals) Spin density. carry the main part ofpure the uranium(Reprinted spin, with 5f with orbitals,a permission small the spin highestfrom [164 polarization ],energy American SOMO Chemical on exhibits the Society, coordinated a 2008.)metal/ligand ligand. character. Variable The resulting temperature spin density of the U(IV) 5f2 complex (2) confirms that the fxyz and fz(x2-y2) orbitals carry the main part magnetization data were measured for two independently synthesized samples. The data of complex of the Asspin, reported with bya thesmall authors, spin whilepolarization SOMO-2 onand theSOMO-1 coordinated (Figure 27)ligand. are of δVariable-type fxyz andtemperature fz(x2-y2) (2) show a steady drop in µ as the temperature is lowered, decreasing from 3.48 µ at 300 K to 1.61 µB magnetizationpure uranium data 5f orbitals, wereeff measured the highest for energy two independ SOMO exhibitsently synthesized a metal/ligand samples. character. The BdataThe resultingof complex 2 2 at 5 K(2 which)spin show density a is steady unusual of the drop U(IV) compared in μ5feff complexas the to temperature common (2) confirms U(IV) is that lowered, (5fthe f)xyz complexesdecreasing and fz(x2-y2) orbitals from and 3.48 is carry likely μB the at due300main K to partto magnetic 1.61 contributionsµBof at the5 K fromwhichspin, thewith is unusual unpaired a small compared electronspin polarization to residing common on on U(IV) the disubstitutedcoordinated(5f2) complexes ligand. benzophenone and isVariable likely due temperature fragment, to magnetic as well as fromcontributionsmagnetization the U(III) from resonance data the were unpaired measured structure electron for (Figure two residing independ 28, 2d).onently the This synthesizeddisubstituted is consistent samples. benzophenone with The thedata DFTof fragment, complex calculations, as in whichwell(2 ) oneasshow from third a steady the of theU(III)drop single in resonanc μeff as radical thee temperaturestructure electron (Figure is is lowered, localized 28, decreasing2d). on This the uranium,fromis consistent 3.48 μB hence, at 300with K increasing tothe 1.61 DFT the µB at 5 K which is unusual compared to common U(IV) (5f2) complexes and is likely due to magnetic magneticcalculations, moment. in which one third of the single radical electron is localized on the uranium, hence, contributions from the unpaired electron residing on the disubstituted benzophenone fragment, as increasing the magnetic moment. well as from the U(III) resonance structure (Figure 28, 2d). This is consistent with the DFT calculations, in which one third of the single radical electron is localized on the uranium, hence, increasing the magnetic moment.

~~O O O O O O O O N N N N IV IV IV IV N U O N U O N U O N U O N NO O O N O N OO OO O O O O N N N N IV IV IV IV N U O N U O N U O N U O 2a N 2bN 2cN N2d O O O O~~

~~Figure 28. Resonance structures of complex 2 (labelled 2a–2d) [164 ]. 2aFigure 28. Resonance2b structures of complex 2c 2 (labelled 2a–2d) [164].2d~~

The authorsThe authors concluded concludedFigurethat 28. that Resonance regarding regarding structures thethe magneticmagnetic of complex data2 data (labelled of of complex complex2a–2d) [164]. (2) ( revealing2) revealing an unusual an unusual 2 •− 3 U(IV)U(IV) 5f complex 5f2 complex which which should should be be considered considered as as a a charge-separated charge-separated U(III)−−LL ↔↔ U(IV)U(IV)−L−•− L(5f3) (5f↔ ) ↔ − •− (5f2) species.(5f2) species.The DFT authors DFT calculations calculations concluded suggest thatsugge regardingst that that coupling coupling the magnetic betweenbetween data the theof complexU UIVIV centercenter (2 )and revealing and the the ketyl an ketyl unusualradical radical L• L 2 − ↔ − •− 3 ↔ ligandligand isU(IV) at leastis 5f at complex physicallyleast physically which reasonable should reasonable be becauseconsid becauseered the as computed athe charge computed-separated frontier frontier U(III) SOMO LSOMO of U(IV) the of molecule theL (5fmolecule) possesses (5f2) species. DFT calculations suggest that coupling between the UIV center and the ketyl radical L•− both metalpossesses and both ligand metal contribution. and ligand contribution. ligand is at least physically reasonable because the computed frontier SOMO of the molecule possesses both metal and ligand contribution. 3.4. Mixed3.4. Mixed Actinide/Transition Actinide/Transition Metal Metal (5f-3d) (5f-3d) and and Actinide/Lanthanide Actinide/Lanthanide (5f (5f-4f)−4f) Complexes Complexes To3.4. date,To Mixed date, only Actinide/Transition only scarce scarce examples examples Metal of (5f-3d)of mixed mixed and (5f-3d) (5f-3d)Actinide/Lanthanide actinide/transitionactinide/transition (5f−4f) Complexes metal metal complexes complexes exhibiting exhibiting − − magneticmagnetic exchangeTo date,exchange only interactions scarceinteractions examples are are foundof found mixed in in(5f-3d) thethe literatureactinide/transitionliterature [1,43 [1,43–45,114,115,11845 metal,114 complexes,115,118121].– 121exhibitingModerate]. Moderate ferromagneticferromagneticmagnetic exchangeexchange exchange interactions coupling coupling waswasare foundmeasured measured in the by by literatureJ. D. J. Rinehart D. Rinehart[1,43 −et45,114,115,118 al. (2007) et al. [1,122] (2007)−121]. for Moderate [ 1the,122 linear] for the IV II IV chloride-bridgedferromagnetic exchange 5f−3d− couplingheterometallic was measured mixed by J. trinuclearD. Rinehart etU al.IV/M (2007)/UII [1,122]IVdimethylpyrazolate for the linear linear chloride-bridgedII μ IV 5f 3d heterometallicII mixed trinuclear U /M /U dimethylpyrazolate (cyclam)Mchloride-bridgedII [( -Cl)UIV 5f(Me−3d2Pz) heterometallic4]2 (MII = Ni, Cu, mixed Co, Zn) trinuclearcluster shown UIV in/M FigureII/UIV 29.dimethylpyrazolate (cyclam)M [(µ-Cl)U (Me2Pz)4]2 (M = Ni, Cu, Co, Zn) cluster shown in Figure 29. (cyclam)MII[(μ-Cl)UIV(Me2Pz)4]2 (MII = Ni, Cu, Co, Zn) cluster shown in Figure 29.

~~(a()a ) (b()b )~~

II IV Figure 29. (a) Structure of the linear cluster (cyclam)Co [(µ-Cl)U (Me2Pz)4]2 and (b) Variable- temperature magnetic susceptibility plot. Orange, purple, green, gray, and blue spheres represent U, Co, Cl, C, and N atoms, respectively. H atoms are omitted for clarity (reprinted with permission from [122], American Chemical Society, 2007). Magnetochemistry 2018, 4, x FOR PEER REVIEW 18 of 31 Magnetochemistry 2018, 4, x FOR PEER REVIEW 18 of 31

Figure 29. (a) Structure of the linear cluster (cyclam)CoII[(μ-Cl)UIV(Me2Pz)4]2 and (b) Variable- Figure 29. (a) Structure of the linear cluster (cyclam)CoII[(μ-Cl)UIV(Me2Pz)4]2 and (b) Variable- temperature magnetic susceptibility plot. Orange, purple, green, gray, and blue spheres represent U, temperature magnetic susceptibility plot. Orange, purple, green, gray, and blue spheres represent U, Co, Cl, C, and N atoms, respectively. H atoms are omitted for clarity (reprinted with permission from MagnetochemistryCo, Cl, C, and2019 ,N5, atoms, 15 respectively. H atoms are omitted for clarity (reprinted with permission from19 of 31 [122], American Chemical Society, 2007). [122], American Chemical Society, 2007).

−1 −1 TheThe measured measured exchange exchange consta constantnt J lies J lies in the in therange range 15–48 15–48 cm − cm1for thefor CoU the2 cluster CoU2 clustercore and core 2.8–19 and The measured−1 exchange constant J lies in the range 15–48 cm for the CoU2 cluster core and 2.8–19 cm2.8–19−1 for cmthe NiUfor2 thecongener. NiU2 congener. To understand To understand the origin theof this origin ferromagnetic of this ferromagnetic coupling within coupling the MU within2 core, the cm−1 for the NiU2 congener. To understand the origin of this ferromagnetic coupling within the MU2 core, ˆ ˆ ˆ ˆ theMU authors2 core, theconsidered authors a considered spin Hamiltonian a spin Hamiltonianof the following of the form: following Ĥ = −2J[ form:ŜCo·(ŜU1H + = ŜU2−)].2J[ SCo·(SU1 + SU2)]. the authors considered a spin Hamiltonian of the following form: Ĥ = −2J[ŜCo·(ŜU1 + ŜU2)]. −− DFT/PBEDFT/PBE calculations calculations which which were were performed performed [58] [58] on on a [(Me 2Pz)Pz)44UCl]UCl] −anionicanionic fragment fragment of of the the DFT/PBE calculations which were performedIV [58] on a [(Me2Pz)4UCl] anionic 2fragment2 of the clustercluster revealed revealed the unpaired electronselectrons ofof the the U UIVcenter center to to reside reside in in the the 5f 5fxyzxyzand and 5f 5fz(xz(x2−−y2) )orbitals,orbitals, as as cluster revealed the unpaired electrons of the UIV center to reside in the 5fxyz and 5fz(x2−y2) orbitals, as shown in Figure 30[122]. shownshown in in Figure Figure 30 30 [122]. [122].

Figure 30. DFT frontier energy level diagram and MOs for [(Me2Pz)4UCl]−-. The Me2Pz- ligands are FigureFigure 30.30. DFTDFT frontierfrontier energyenergy level level diagram diagram and and MOs MOs for for [(Me [(Me2Pz)2Pz)4UCl]4UCl]-. The MeMe22Pz- ligands are shown as skeletal representations, and the U-Cl axis is oriented vertically (reprinted with permission shownshown asas skeletalskeletal representations,representations, andand thethe U-ClU-Cl axisaxis isis orientedoriented verticallyvertically (reprinted(reprinted withwith permissionpermission from [122], American Chemical Society, 2007). fromfrom [[122],122], AmericanAmerican ChemicalChemical Society,Society, 2007).2007). δ −− AsAsAs reported, reported,reported, these thesethese orbitals orbitalsorbitals have have δ δ symmetry symmetrysymmetry with withwith respect respectrespect to toto the thethe U UU−ClCl z-axis z-axis bond, bond, such such that thatthat the thethe overlap with σ and π orbitals of the chloride bridge will be zero. Any of the spin from theII Co2 II 3dz2 overlapoverlap with with σ σ and and π π orbitals orbitals of of the the chloride chloride bridge bridge will will be be zero. zero. Any Any of of the the spin spin from from the the Co Co II3dz 3dz 2orbital orbital feedingorbitalfeeding feedingthroughthrough through thethe chloridechloride the chloride bridgibridgingng bridging ligandsligands will ligandswill thereforetherefore will therefore engageengage rigorously engagerigorously rigorously orthogonalorthogonal orthogonal orbitals,orbitals, leadingorbitals,leading to to leading a a ferromagnetic ferromagnetic to a ferromagnetic exchange exchange exchangeinteraction. interaction. interaction. Consistently, Consistently, Consistently, ferromag ferromagneticnetic ferromagnetic exchange exchange is exchangeis also also observed observed is also II forobserved the NiU for2 cluster, the NiU which2 cluster, features which a Ni featuresII (S = 1) a Nicenter(S =with 1) centerunpaired with electrons unpaired in electronsthe 3dz2 and in the 3d 3dx2−y2z2 for the NiU2 cluster, which features a NiII (S = 1) center with unpaired electrons in the 3dz2 and 3dx2−y2 orbitals.and 3d x2However,−y2 orbitals. despite However, the presence despite of thea large presence axial zero-field of a large splitting axial zero-ﬁeld for NiU splitting2, no indication for NiU of2, theno orbitals. However, despite the presence of a large axial zero-field splitting for NiU2, no indication of the indication of the slow magnetic relaxation is reported, as is typically observed for SMM behavior [1]. slowslow magnetic magnetic relaxation relaxation is is reported, reported, as as is is typically typically observed observed for for SMM SMM behavior behavior [1]. [1]. DuringDuringDuring the thethe same same year year (2007) (2007) there there has has been been a areport report suggesting suggesting that that coupling coupling may may occur occur through through directdirect metal-metal metal-metal orbital orbital overlap overlap in inthe the mixe mixed-valenced-valence linear linear trinuclear trinuclear cluster cluster U(fc[NSiMe U(fc[NSiMe3]2)2 (fc3]2 =)2 direct metal-metal orbital overlap in the mixed-valence linear trinuclear cluster U(fc[NSiMe3]2)2 (fc = 0 II IV III t 1,1(fc′-ferrocenylene) = 1,1 -ferrocenylene) and its and[FeIIU itsIVFe [FeIII(CU5HFe4NSi((CtBu)Me5H4NSi(2)4]BPhBu)Me4 cationic2)4]BPh congener4 cationic which congener is depicted which in is 1,1′-ferrocenylene) and its [FeIIUIVFeIII(C5H4NSi(tBu)Me2)4]BPh4 cationic congener which is depicted in FiguresdepictedFigures 31 31 in and and Figures 32. 32. [18] [18]31 andThe The 32latter latter.[18 molecule] molecule The latter exhibits exhibits molecule a a rigid exhibitsrigid coordination coordination a rigid coordination to to ferrocenylamido ferrocenylamido to ferrocenylamido moieties moieties ··· andmoietiesand U···Fe U···Fe and distances distances U Fe of distancesof 2.9556(5) 2.9556(5) of and 2.9556(5)and 2.9686(5) 2.9686(5) and Å. 2.9686(5)Å. Å.

SiMe2(t-Bu) SiMe (t-Bu) SiMe2(t-Bu) 2 SiMe2(t-Bu) SiMe2(t-Bu) SiMe (t-Bu) SiMe2(t-Bu) 2 N SiMe2(t-Bu) N a. I , Et O, 81% N N a. 2I , E2t O, 81% N N Fe N 2 2 N Fe U Fe b. NaBPh , THF, 51% Fe U Fe U Fe b. NaBP4h , THF, 51% Fe Fe [BPh4] 4 U [BPh ] N 4 N N N N N N N SiMe (t-Bu) SiMe2 (t-Bu) SiMe2(t-Bu) 2 SiMe2(t-Bu) (t-Bu)Me2Si (t-Bu)Me Si (t-Bu)Me2Si 1 (t-Bu)Me2 Si 1 2 1-BPh4 1-BPh4 Figure 31. The transformation reaction of 1 U(fc[NSiMe3]2)2 into [FeIIUIVFeIII(CII5H4IVNSi(IIItBu)Me2)4]BPht 4: FigureFigure 31. 31. TheThe transformation transformation reaction reaction of 1 U(fc[NSiMe of 1 U(fc[NSiMe3]2)2 into3] 2[Fe)2 IIintoUIVFe [FeIII(CU5H4NSi(Fe t(CBu)Me5H4NSi(2)4]BPhBu)4: 1-BPh4 [18]. Me1-BPh42)4]BPh [18].4: 1-BPh4 [18]. Magnetochemistry 2019, 5, 15 20 of 31 MagnetochemistryMagnetochemistry 2018 2018, 4, x4 ,FOR x FOR PEER PEER REVIEW REVIEW 19 19of of31 31

~~(a()a ) (b()b )~~

II IIIV IV IIIII IIIIV III t t t + + + FigureFigureFigure 32. 32. (a )( a 32.X-ray) X-ray(a) Structure X-ray Structure Structure of of[Fe [Fe ofUU [FeFeFeU (C (C5FeH54HNSi(4NSi((C5Bu)MeHBu)Me4NSi(2)4Bu)Me2]) cation4] cation2 )(14] (1 cation) complex.) complex. (1 ) complex.H Hatoms atoms are H are atomsomitted omitted are II II II II IIIV IV III III II IV III forfor clarity. clarity.omitted (b ()b Variable-temperature for) Variable-temperature clarity. (b) Variable-temperature magnetic magnetic data data magnetic for for UFe UFe data2 (1,2 (1, black for black UFe squares) squares)2 (1, black and and squares)Fe FeUUFe andFe (1-BPh Fe(1-BPhU4, red4Fe, red circles).circles).(1-BPh (Reprinted (Reprinted4, red circles). with with (Reprintedpermission permission with from from permission [18], [18], American American from [18 Chemical], Chemical American Society, ChemicalSociety, 2007). 2007). Society, 2007).

ThisThisThis mixed-valent mixed-valentmixed-valent bisferrocenyl bisferrocenylbisferrocenyl complexes complexescomplexes have havehave been beenbeen studied studiedstudied in inin order orderorder to toto understand understandunderstand the thethe dependencedependencedependence of ofof the thethe electronic electronicelectronic coupling couplingcoupling between betweenbetween the thethe tw twotwo irono ironiron centers centerscenters relative relativerelative to toto the thethe linker linkerlinker connecting connectingconnecting them.them.them. When WhenWhen uranium uraniumuranium is isisused usedused as asas a aalinker, linker,linker, 5f 5f5f orbita orbitalsorbitals lsmake makemake this thisthis actinide actinideactinide a aabetter betterbetter mediator mediatormediator than thanthan the thethe zirconiumzirconiumzirconium d-transition d-transition d-transition metal metal metal for for for the the the electronic electronic electronic communication communication communication between between between iron iron iron centers. centers. centers. Indeed, Indeed, Indeed, asas as noted notednoted bybyby the the the authors authors [1[1,18], ,18[1,18],], the the the observed observed observed behavior behavior behavior is indicative is isindicative indicative of an of extremely of an an extremely extremely strong ferromagneticstrong strong ferromagnetic ferromagnetic exchange IV III exchangeUexchange−Fe U interaction,IVU−IVFe−FeIII IIIinteraction, interaction, mediated mediated bymediated direct by orbital by direct direct overlap orbita orbital between overlapl overlap the between between metals the orbitals. the metals metals DFT orbitals. orbitals. calculations DFT DFT calculationswerecalculations performed were were onperformed performed the thorium on on andthe the thorium zirconium thorium and and bisferrocene zirconium zirconium trinuclearbisferrocene bisferrocene Th(fc[NH] trinuclear trinuclear2)2 cationTh(fc[NH] Th(fc[NH] models2)22 )2 cationrelatedcation models models to the related actual related U(fc[NSiMeto to the the actual actual3 ]U(fc[NSiMe2 )U(fc[NSiMe2 system.3 For]23)]22 system.) the2 system. thorium For For the bisferrocene the thorium thorium bisferrocene cation bisferrocene model, cation cation additionally, model, model, additionally,theadditionally, HOMO andthe the HOMO-5HOMO HOMO and (Figureand HOMO-5 HOMO-5 33) consist (Figure (Figure of 33) a 33) uranium co consistnsist 5fof of orbitala auranium uranium interacting 5f 5f orbital orbital with interacting interacting orbitals of with bothwith orbitalsironorbitals atoms of of both atboth the iron iron same atoms atoms time, at at whichthe the same same might time, time, explain which which the might might occurrence explain explain ofthe strongthe occurrence occurrence electronic of of strong communicationstrong electronic electronic communicationmediatedcommunication by actinide-transition mediated mediated by by actinide-transition actinide-transition metal orbital metal overlap. metal orbital orbital overlap. overlap.

FigureFigureFigure 33. 33.33. HOMO-5HOMO-5 HOMO-5 of of ofthe thethe Th(fc[NH] Th(fc[NH]Th(fc[NH]2)222 )model)22 model cation. cation. Green Green and andand magenta magentamagenta color colorcolor for forfor Th ThTh and andand Zr ZrZr metals, metals,metals, respectivelyrespectivelyrespectively (reprinted(reprinted (reprinted with with with permission permission permission from fr om [fr18om], [18], American [18], American American Chemical Chemical Chemical Society, Society, 2007). Society, 2007). 2007).

Finally,Finally,Finally, magnetic magneticmagnetic coupling couplingcoupling was waswas also alsoalso reported reportedreported in inin 2006 20062006 for forfor 5f-4f 5f-4f5f-4f trinuclear trinucleartrinuclear UYb UYbUYb22 cluster2 clustercluster Cp*Cp*Cp*2U[(NC(CH22U[(NC(CHU[(NC(CH2C226CH66H5)tpy)YbCp*5)tpy)YbCp*)tpy)YbCp*2]22 2](tpy]22 (tpy(tpy = terpyridyl)= = terpyridyl) terpyridyl) [108]. [108]. [108 ].

3.5. Magnetic Susceptibility and EPR/NMR Spectra of Actinide Complexes 3.5.3.5. Magnetic Magnetic Susceptibility Susceptibility and and EPR/N EPR/NMRMR Spectra Spectra of ofActinide Actinide Complexes Complexes New developments in the computational transuranium chemistry were surveyed recently (2018) NewNew developments developments in in the the computational computational transurani transuraniumum chemistry chemistry were were surveyed surveyed recently recently (2018) (2018) by N. Katsoyannis [8], with emphasis on the assessment of the magnetic properties of transuranic byby N. N. Katsoyannis Katsoyannis [8], [8], with with emphasis emphasis on on the the asse assessmentssment of of the the magnetic magnetic properties properties of of transuranic transuranic elements. As reported in this review, the magnetic susceptibility and the electronic structure of borate elements.elements. As As reported reported in in this this review, review, the the magnetic magnetic susceptibility susceptibility and and the the electronic electronic structure structure of of borate borate materials, in particular those of Californium (Cf) and Berkelium (Bk) metals, e.g., An[B6O8(OH)5 materials,materials, in in particular particular those those of of Californium Californium (Cf) (Cf) and and Berkelium Berkelium (Bk) (Bk) metals, metals, e.g. e.g. An[B An[B6O68O(OH)8(OH)5 (An5 (An = Cf= Cf III IIIand and Bk BkIII)III [171,172],) [171,172], have have been been studied studied using using both both GGA GGA and and hybrid hybrid functionals functionals in in conjunction conjunction withwith NBO NBO analysis analysis [8]. [8]. Magnetochemistry 2019, 5, 15 21 of 31

(An = Cf III and BkIII)[171,172], have been studied using both GGA and hybrid functionals in Magnetochemistry 2018, 4, x FOR PEER REVIEW 20 of 31 conjunction with NBO analysis [8]. IV − The electronic structures and magnetic properties of Ar3U IV−L complexes, with Ar = C5(CH3)4H − The −electronic structures and magnetic properties of Ar3U −L complexes, with Ar = C5(CH3)4H or C5H5 and L = CH3, NO, and Cl have been investigated recently (2014) [67]. The study or C5H5− and L = CH3, NO, and Cl have been investigated recently (2014) [67]. The study aimed to aimed to provide ab initio data for the magnetic susceptibilities, assignments of the low-energy provide ab initio data for the magnetic susceptibilities, assignments of the low-energy parts of the parts of the electronic spectra, as well as characterizations of selected states based on natural electronic spectra, as well as characterizations of selected states based on natural orbitals and their orbitals and their occupations. For the ground states, relativistic CASSCF and CASPT2 calculations occupations. For the ground states, relativistic CASSCF and CASPT2 calculations were compared to were compared to scalar relativistic DFT using the ZORA Hamiltonian. As concluded by the scalar relativistic DFT using the ZORA Hamiltonian. As concluded by the authors, for the nitrosyl authors, for the nitrosyl complex, the ground state is a closed-shell spin-singlet i.e., a nonmagnetic complex, the ground state is a closed-shell spin-singlet i.e., a nonmagnetic ground state. For the other ground state. For the other L = Cl and CH3 complexes, the ground states are triplets, with no L = Cl and CH3 complexes, the ground states are triplets, with no orbital degeneracy for the chloride orbital degeneracy for the chloride complexes and an orbital-doublet for the methyl complex. complexes and an orbital-doublet for the methyl complex. Furthermore, the nature of the electronic Furthermore, the nature of the electronic ground state and low-energy excited states is evidenced ground state and low-energy excited states is evidenced by the susceptibility curves displaying linear by the susceptibility curves displaying linear χT[67]. The computed susceptibilities from ab initio χT [67]. The computed susceptibilities from ab initio calculations agree well with available calculations agree well with available experimental data; e.g., for the (C5Me4H)3UCl complex, the ab experimental data; e.g. for the (C5Me4H)3UCl complex, the ab initio calculated temperature- initio calculated temperature-independent paramagnetism (TIP) susceptibility χTIP is 8.52 and 10.44 independent paramagnetism (TIP) susceptibility χTIP is 8.52 and 10.44 (units of 103 cm3mol−1) for the (units of 103 cm3mol−1) for the experimental and optimized structure, respectively. experimental and optimized structure, respectively. DFT-based calculations have also been reported [168] and proved to correctly reproduce chemical DFT-based calculations have also been reported [168] and proved to correctly reproduce shifts of diamagnetic uranium(VI) compounds. DFT benchmarking calculations of 1H and 13C NMR chemical shifts of diamagnetic uranium(VI) compounds. DFT benchmarking calculations of 1H and chemical shifts of closed shell U(VI) systems for which experimental data are available (Figure 34), 13C NMR chemical shifts of closed shell U(VI) systems for which experimental data are available were reported [79]. Different levels of GGA and hybrid functionals were employed, i.e., B3LYP [86,87], (Figure 34), were reported [79]. Different levels of GGA and hybrid functionals were employed, i.e., PBE [148], PBE0 [149], LC-ωPBE [173,174], TPSS and TPSSh [175,176] and also including the Grimme’s B3LYP [86,87], PBE [148], PBE0 [149], LC-ωPBE [173,174], TPSS and TPSSh [175,176] and also D3 dispersion corrections [150,157]. Overall, it was found that the most robust methodology for including the Grimme's D3 dispersion corrections [150,157]. Overall, it was found that the most obtaining accurate geometries is the PBE functional with Grimme’s D3 dispersion corrections, whereas robust methodology for obtaining accurate geometries is the PBE functional with Grimme's D3 for 1H and 13C NMR chemical shifts, no special recommendation emerges regarding the best choice of dispersion corrections, whereas for 1H and 13C NMR chemical shifts, no special recommendation density functional, although for spin-spin couplings, the LC-ωPBE functional with solvent corrections emerges regarding the best choice of density functional, although for spin-spin couplings, the LC- ωisPBE a good functional approach. with solvent corrections is a good approach.

~~Cl THF~~

~~O U Ph t-Bu Mes O Mes O Ph N O N N HC CH U P O N P Ph Ph Ph Ph O Ph t-Bu Ph (a) (b)~~

~~FigureFigure 34. 34. StructuresStructures of of Uranyl(VI) Uranyl(VI) monomers monomers ( (aa)) ββ-Ketoiminate-Ketoiminate and and ( (bb)) Carbenes Carbenes Complexes Complexes [79]. [79].~~

TheThe authors authors concluded concluded that that among the invest investigatedigated approaches, the the disagreement disagreement with with 1 13 experimentexperiment of of the the averaged 1HH and and 13CC chemical chemical shifts shifts rarely rarely exceeds exceeds 15% 15% deviation deviation for for the the studied studied 1 13 U(VI)U(VI) compounds. compounds. The The geometry geometry employed employed has has relatively relatively little little effect effect on the 1H and 13CC chemical shifts,shifts, and and increasing increasing the the quality quality of of the the basis basis set set to include triple and quadruple polarizations does does notnot bring bring any any improvement. improvement. For For spin-spin spin-spin couplings, couplings, the the inclusion inclusion of of relativistic relativistic effects effects with with ZORA ZORA 13 includingincluding spin-orbit spin-orbit coupling (SOC) led to a a less less dispersed dispersed set set of of results results for for 13CC NMR NMR signals signals relatively relatively toto scalar scalar ZORA ZORA calculations. calculations. AutschbachAutschbach and and Coll. Coll. [169,170] [169,170] have have recently recently (2016) (2016) investigated investigated theoretically theoretically using using DFT DFT calculationscalculations combined combined with with two-component two-component ZO ZORARA and and four-component four-component Dirac–Kohn–Sham Dirac–Kohn–Sham (DKS) (DKS) relativisticrelativistic frameworks, frameworks, the the SOC SOC effects effects in in a a ur uranium(VI)anium(VI) complex complex regarding regarding NMR NMR chemical chemical shifts. shifts. Gas-phaseGas-phase structures werewere optimizedoptimized using using def2-TZVP def2-TZVP basis basis sets sets and and the the PBE PBE functional functional [148 [148],], as well as wellas with as twowith hybrid two hybrid PBE0 [PBE0149] and [149] B3LYP and functionalsB3LYP functionals [86,87]. Bulk[86,87]. solvent Bulk effects solvent on e theﬀects optimized on the optimizedstructures structures and on the and computed on the computed NMR shieldings NMR sh wereieldings simulated were simulated via the conductor-like via the conductor-like screening screening model (COSMO) [169]. Their study aimed to reassess the giant spin–orbit effects on NMR shifts observed for closed shell uranium(VI) complexes, investigating the role of the exchange– correlation response kernel. As reported by the authors [169], the considered exchange–correlation kernel in two-component ZORA/DFT calculations is crucial to properly predict the giant 1H NMR Magnetochemistry 2019, 5, 15 22 of 31 model (COSMO) [169]. Their study aimed to reassess the giant spin–orbit effects on NMR shifts observed for closed shell uranium(VI) complexes, investigating the role of the exchange–correlation response kernel. As reported by the authors [169], the considered exchange–correlation kernel in two-component ZORA/DFT calculations is crucial to properly predict the giant 1H NMR shifts in closed-shell uranium(VI) hydride complexes, and also of the extremely large SOC induced 13C shifts for uranium(VI)-bound carbon atoms. The range for unknown shifts with the revised approach was successfully predicted, and further predictions have been made for complexes that are synthetically known. Finally, the magnetic susceptibility of actinide(III) cations has been intensively investigated by synergetic experimental and theoretical study, as reported by H. Bolvin and Coll. [177]. Through DFT and SO-CASPT2 calculations, the authors aimed to rationalize the experimental magnetic susceptibilities of [An(H2O)9](CF3SO3) actinide(III) aqua complexes (An = Pu, Am and Cm). The geometry optimizations were performed using the B3LYP functional and an implicit solvation model. Once magnetic susceptibility measurements of An(III) cations were corrected from radioactivity effects, SOC-CASPT2 calculations have been used on free ions and aquo complexes to calculate the electronic structure explaining the magnetic properties of Pu(III), Am(III) and Cm(III). EPR is a useful tool to probe molecular magnetic properties. This tool was used to study U(V) nitride complexes [178]. The relative importance of the investigated spin–orbit and crystal ﬁeld interactions explains the different ground states of the nitride complexes relative to oxo isoelectronic species. In addition, U(V)-U(V) super-exchange coupling in dimers of these complexes has been studied in relation with EPR experiments [178]. Through EPR and magnetic susceptibility measurements, another U(V)-U(V) Ar Ar system, namely U[ OSeO ]2(THF)}2(µ2-OC6H4O), which is found to exhibit unusual magnetic properties, also deserves to be highlighted [179].

4. Conclusions The DFT computation of magnetic coupling constants of polynuclear actinide complexes, mainly of uranium, is now well documented. Several magnetic dinuclear or trinuclear uranium complexes have been successfully investigated; the tried and tested methodology makes use of the broken symmetry approach and a hybrid DFT functional, mainly the B3LYP one. A variety of bridging ligands between the uranium centers have been considered either experimentally or theoretically; among them, imido or ketimide phenyl and benzoquinonoide-based conjugated bridges, but also oxo, nitrido and chalcogeno bridges. Bis- and tris-uranyl-based complexes have also been investigated, as well as inverted-sandwich uranium species. Complexes containing uranium in different oxidation states, U(V), U(IV) and U(III) leading to magnetic electron configurations, 5f1-5f1, 5f2-5f2 and 5f3-5f3 have been studied; the ferromagnetic or antiferromagnetic character of the coupling is generally correctly predicted by DFT computations. The magnetic properties of such complexes arise from spin polarization and super-exchange, which are rationalized thanks to frontier MO and spin density analyses. DFT studies regarding mononuclear uranium complexes, SMMs and mixed 5f-3d or 5f-4f actinide-transition metal and actinide-lanthanide species, are very scarce in the literature. Encouraging results have been obtained over recent decades by applying DFT calculations to investigate and rationalize magnetic exchange coupling within actinide polynuclear systems. The generally good agreement between DFT results and the experimental findings gives us confidence that this computationally-cheap approach will remain useful, even if more sophisticated and accurate post-Hartree-Fock treatments will be more developed in the future, thanks to the increasing power of computers.

Author Contributions: Conceptualization, A.B. and L.B.; Methodology, A.B. and L.B.; Writing—Original Draft Preparation, L.B.; Writing—Review & Editing, L.B., B.L.G. and A.B.; Project Administration, A.B.; Funding Acquisition, L.B., B.L.G. and A.B. Magnetochemistry 2019, 5, 15 23 of 31

Funding: Programme Recherche-Formation Universitaire (PRFU) Grant number: B00L01UN250120180015 from Direction Générale Recherche Scientifique et Développement Technologique (DGRSDT) and Université des frères Mentouri of Constantine 1 (Algeria). Acknowledgments: We acknowledge the High Performance Computing (HPC) resources of Centre Informatique National de l’Enseignement Supérieur (CINES) and of Institut du Développement et des Ressources en Informatique Scientifique (IDRIS) under the allocations 2017 and 2018-[x2016080649] made by the Grand Equipement National de Calcul Intensif (GENCI). Conflicts of Interest: The authors declare no conflict of interest.

~~References~~

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