| In molecular systems, the high angular momentum f electrons which occupied onthe unfilled valence shells always present more complex electronic structure wheninteracting with other electrons. The low angular momentum p electrons commonlypresent various orbital hybridizations and spin polarization features. Studying theinteractions between f electrons and p electrons is an important challenge of basistheory research and has important significances for designing molecular devices ornanoscale materials. In this work, we studied the electronic structures of a series ofendohedral metallofullerenes (EMFs) encapsulating4f and5f elements based on thefirst-principle density functional theory (DFT) and discussed the relevantmethodologies.It is well known that U@C28in one of the smallest EMFs experimentallyobtained and it forms in high abundance. Hence, theoretically confirming itselectronic structure is of fundamental significance for future studies on theinteractions in complex molecular systems containing f valence electrons. Here weprovide a detailed analysis of the geometric and electronic structure of neutral U@C28by using both scalar and spin-orbital relativistic DFT methods. It is showed thatU@C28has a (cage)2triplet ground state with Tdsymmetry instead of the longbelieved (5f)1(cage)1ground state with D2symmetry. Its34valence electronspreferentially adopt the32-electron principle, forming a stable U-cage covalentinteraction which fulfills the s-, p-, d-, f-type orbitals of U atom. The remaining twovalence electrons cannot break the electronic configuration and thus occupy on thedouble-degenerated highest occupied molecular orbital on the cage. This findingsuggests that the32-electron rule can also apply to the neutral U@C28which containsmore than32valence electrons. We also expect the conclusion and the methodological considerations could provide supports for the future EMF studies.As a representative lanthanide EMF, Gd@C82has attracted widespread attentionsince it was first synthesized. The questions of the most favorable position of Gd stayin the C82cage and the electronic structure of the ground state have been repeatedlydisputed until the recent experiments gave the exact conclusion. However, thesequestions are still not resoved in theoretical studies due to the lack of relevantbenchmark work. In this work，we systematically compared and evaluated thecomputational geometries and electronic state structures of Gd@C82based on thecalculations from10different density functional methods with the scalar relativisticeffects consideration by relativistic effective core potential (RECP) approach. Ourresults show that, the appropriate choice of exchange-correlation functionals is thedecisive factor for predicting the nature of Gd@C82accurately. The electronicstructure of the ground state (septet) and the energy gap between the ground state andthe low-lying exited state (nonet) which was obtained from pure density functionalmethods, such as PBE and PW91, are well agree with recent experimental observation.We find that, choosing appropriate exchange-correlation functionals is more importantthan the selection of basis set for C atoms.4-31G*and6-31G*have been able to givethe most reasonable results. Little obvious improvement could be obtained whencontinue to enlarge the basis set of C atoms. It is interesting that, in contrast to purefunctionals, the popular used hybrid functionals in previous studies, such as B3LYP,could infer the qualitative correct ground state only when employing small basis setfor C atoms. This work will provide important theoretical methodology references forfurther density functional studies on Gd@C82and its derivatives systems in the future.Scientists have found that the size of the cavity of EMFs can influence theproperties of the inner molecule. In this work, the neutral diuranium molecule wasencapsulated into the C90fullerene. The neutral U-U dissociation potential energysurfaces of different electronic states confined in the C90fullerene were scanned andthe quintet and the septet of these states were found to be low-lying. In the fullerenecage, the U2molecule easily disintegrates along the axis of the fullerene, and thenchemically adsorbed on the both ends of the fullerene. The charge distribution and themolecular orbital properties of the complex were also uncovered. This work couldhelp us to understand the geometric conformations and electronic interactions ofdimetallic molecules when encapsulating them into fullerenes which have big enough cavities.The M@C60model which forms by encapsulating a single metal atom into C60fullerene is a typical EMF model. However, the structural and electronic properties ofU@C60are overlooked largely for a long time. In this work, we studied the geometricand electronic structures of U@C60based on relativistic DFT method. It is showedthat the U atom faced to a six-membered ring in C60fullerene and U@C60has a tripletground state. The triplet spin state is mainly dominated by the two5f electrons of theU atom. Interestingly, the nearest U-C distance in U@C60is shorter than that inU2@C60, meanwhile, the U atom possesses more positive charges in U@C60than thatin U2@C60. This can be attributed to that the U atom can be approximately consideredas a trivalent cation, while it is tetravalent in U@C60. Further analysis showed that theinteraction between U and the cage is a mixture of ionic and covalent interactions.The covalent interactions are contributed from the5f electrons and the non-ignorable6p electrons of U. This study indicates that the special5f electrons of U may presentmultifarious behaviors in fullerenes.Previous dimetalloendofullerene research has mostly focused on homonuclearbimetallic cases, in which the two metal atoms/ions possess certain equivalentproperties providing similar metal-cage interactions. However, as of today, to the bestof our knowledge, no experimental or theoretical studies have been carried out on thecoexistence of a lanthanide and an actinide metal in the same EMF cage. Here wedesign a novel heteronuclear EMF (U-Gd)@C60, by using DFT method, which showsan encapsulation energy of about-5.53eV, comparable to that of U2@C60, La2@C80,and Lu2@C76.(U-Gd)@C60is found to have a surprising twofold, single-electronU-Gd bond that results from the strong nanoconfinement of the fullerene, dominatedby uranium’s5f and6d and gadolinium’s5d atomic orbitals. The ground state showsan11-et high spin state, and the net spins distributed on the U-pole carbons arerelatively scattered, while they are highly concentrated on the Gd-pole carbons. Theexceptional electronic characteristics of this novel EMF, containing both uranium andgadolinium atoms encapsulated, might prove useful for future applications in nuclearenergy and biomedicine.The cages in currently studies of EMFs are all ideal fullerenes with simplecharacters. These fullerenes can only provide the roles of spatial confinement andcharge acceptance from the inner metals. Also, these cages are deviated from the actual situation that there often exist defect structures in the natural carbon materials.Herein, we introduce an adatom-type spin polarization defect on the surface of atypical endohedral stable U2@C60to predict the associated structure and electronicproperties of U2@C61based on the density functional theory method. We found thatdefect induces obvious changes in the electronic structure of this metallofullerene.More interestingly, the ground state of U2@C61is nonet spin in contrast to the septetof U2@C60. Electronic structure analysis shows that the inner U atoms and the Cad-atom on the surface of the cage contribute together to this spin state, which isbrought about by a ferromagnetic coupling between the spin of the unpaired electronsof the U atoms and the C ad-atom. This discovery may provide a possible approach toadapt the electronic structure properties of EMFs.C60has [6,6](connecting two hexagons) and [5,6](connecting a pentagon and ahexagon) C–C bonds. This means that only two kinds of adatom-type defects can beformed on its surface. In this study, we introduce a C adatom on the [5,6] C–C bondof the cage surface of the U2@C60and studied the electronic structures of.a defectiveEMF U2@C61-Def[5,6]. It is shown that unlike the U2@C61-Def[6,6] which has anonet ground state, the U2@C61-Def[5,6] has a quintet ground spin state with a lowertotal energy than the U2@C61-Def[6,6]. This is due to the antiferromagnetic couplingof the net spin electrons of the U2unit with the net spin of both the cage and theadatom. Compared with the U2@C60, the [5,6]-type defect demonstrates almost nochange in the HOMO-LUMO gap, while the [6,6]-type defect does show a reduction.The electronic states and energy gaps of EMFs can therefore be engineered in acontrollable manner by introducing different adatom-type defects.The previous U2@C61studies have indicated that the adatom defect is animportant factor of the magnetism of carbon materials. Hence, appropriatelydescribing the electronic behaviors of adatom defect is the precondition oftheoretically studying the spin polarization problems of relevant carbon materials. Theself-consistent charge density functional tight binding (SCC-DFTB) method is awidely well-received quantum computational method with high efficiency incalculating electronic structures. However, this method calculates an unreasonableelectronic structure of C61fullerene which contains a typical spin-polarized adatomdefect. Some suitable corrections by adding the Hubbard U parameters are thenneeded. In this work, with the traditional DFT result as a reference, we calculated the electronic structure of a defective fullerene C61with an adatom defect using DFTB+Umethod. The FLL and pSIC types of corrections were added for both p and sp shells ofcarbon atoms in C61structure. We found that the electronic structure can bereasonably resolved, and the HOMO-LUMO gap can be improved by consideringthese corrections. This work can provide methodological references for the electronicstructure calculations of carbon materials base on DFTB method in the future. |
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