Er3+ Photoluminescence in Er2@C82 and Er2C2@C82

May 24, 2017 - The charge state of C824− was demonstrated in both Er2@C82 and Er2C2@C82, which was in contrast to the C826− suggested experimental...
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Er3+ Photoluminescence in Er2@C82 and Er2C2@C82 Metallofullerenes Elucidated by Density Functional Theory Jian Wang,†,‡ Yuan-yuan Zhao,§,∥ Po-Heng Lee,*,‡ and Stephan Irle*,† †

Institute for Advanced Research and Department of Chemistry, Nagoya University, Nagoya 464-8602, Japan Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China § Frankfurt Institute for Advanced Studies (FIAS), Goethe-University, Ruth-Moufang-Strasse 1, D-60438 Frankfurt am Main, Germany ‡

S Supporting Information *

ABSTRACT: Metallofullerenes with two erbium atoms encapsulated in IPR C82 cage isomers Cs-6 (I), C2v-9 (II), and C3v-8 (III) were investigated using density functional theory. The calculations suggest that erbium atoms assume a trivalent state with Er (4f11) valence electronic configuration in Er2@C82 and Er2C2@C82, where two electrons (6s2) per Er atom are transferred to the cage carrying four negative charges (C824−), while the third electron is promoted from the 4f to the 5d shell, becoming involved in covalent bonding to near atoms. Experimentally, Er3+-like emission from 4I13/2 to 4I15/2 was observed, and our calculations indicate that the Er−Er covalent metal bond in Er2@C82, and the Er−C/C2 covalent bonds in Er2C2@C82, can account for the observed photoluminescence despite the cage with C824−. Such existence is the reason that the C2 unit was found to be neutral on the basis of MEM-Rietveld X-ray measurements, although formally it should be described as C22−. Our prediction for isomer photoluminescence intensity agrees with the experimentally determined order (III > I > II), where the most pronounced activity of isomer III in Er2C2@C82 stems from its higher charge of formal Er3+ and its largest HOMO−LUMO gap.

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INTRODUCTON Metallofullerenes were discovered in 1985,1 when buckminsterfullerene (C60) was first reported.2 Fullerenes generally possess high electron affinities. For example, C60 has energetically low-lying triply degenerate lowest unoccupied molecular orbitals, making it possible to take up to six negative charges distributed over the cage.3 Counterions can be located outside the cage as in the case of so-called “exohedral” alkali-metalfullerene complexes,4−9 or trapped inside, in which case the complexes are called “endohedral” metallofullerenes. The latter type is the more widely recognized metallofullerene species, partially owing its attractiveness to the fact that the characteristic properties of enclosed metal atoms are protected from environmental influence. This allows the exploitation of their unique atomic spectroscopic or magnetic features in macroscopic quantities, and provides a way for “transporting” the metal atoms of interest, for instance when applied as magnetic resonance imaging (MRI) contrast.10 The most common metallofullerene cage sizes are C80−C86, but smaller species including non-IPR M@C28 (M = Ti, Zr, U),11 IPR Li@C60,12 and larger metallofullerenes such as Sm2@C10413 have been isolated and characterized as well. Depending on the electron affinity of the cage and the electropositivity of the encapsulated metal, charge transfer is expected from metal to cage, which is why metallofullerenes are sometimes called “superatoms”.12,14 It is interesting to note that although a wide range of metals have been successfully encapsulated inside fullerene cages,14,15 iron group metal atoms were excluded. More electropositive © 2017 American Chemical Society

main group elements such as calcium, or d-block transition metals such as scandium and yttrium, readily become entrapped when their oxides are mixed into the graphite used for the hightemperature production of fullerene via laser evaporation or Krätschmer−Huffman synthesis.16 This finding suggests that charge transfer from metal to carbon is an important stabilizing energetic contribution during the metallofullerene cage selfassembly process. During the past decade it was discovered that nonmetallic species can become coencapsulated with the metal atoms. For instance, the compound originally reported as Sc2@C86 was turned out to be actually [email protected],18 Subsequently, many metallocarbide fullerenes were discovered experimentally18−26 and described theoretically,27−31 up to the Sc4C2@C8020,31 compound with four metal ions. Another class of encapsulated species are the trimetallonitride M3N@C2n fullerenes3,32−37 and the recently discovered MnO2@C2n metallo-oxide species.38 One metal atom in the lanthanide family, namely, erbium (Er), has attracted considerable attention. Shinohara et al. synthesized and characterized both Er2@C82 and Er2C2@C82 compounds, proposing that these species with nearly identical cage properties possess a 6-fold negatively charged C826−.25 Their proposal was based on the fact that the characteristic photoluminescence at 1520 nm from Er3+ ions was observed in both species, albeit with higher intensity from the carbide Received: March 16, 2017 Published: May 24, 2017 6576

DOI: 10.1021/acs.inorgchem.7b00695 Inorg. Chem. 2017, 56, 6576−6583

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Inorganic Chemistry containing species. However, in the remainder of this work we report that the charge state of the cages in both Er2@C82 and Er2C2@C82 compounds corresponds to a 4-fold negative charged C824−. The covalent metal−metal bonds in the cases of bimetal endohedral fullerenes M2@C82 (M = Y, Sc) and Lu2@C76 appeared in [email protected] Though many experimental investigations demonstrated emission from characteristic intraconfigurational 4f11 fluorescence of the trivalent erbium 4I13/2 → 4I15/2,25,40−43 theoretical investigations for various fields of Er-bearing metallofullerenes have been scarce so far.44 In the present work we demonstrate the seemingly unresolvable conundrum regarding how the characteristic photoluminescence at 1520 nm from Er3+ ions was observed in both Er2@C82 and Er2C2@C82 even though the cage charge is only 4-fold negative. Additionally, the charged C826− cage in Er3N@C82 and Er2+ or Er3+ in Er@C82 were discussed. The calculations provided clues to understand charge states of various cages and encapsulated units in endohedral metallofullerenes.

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Figure 1. Relative energies (ΔE) of nine neutral C82 isomers and their corresponding species with charge states −2, −3, −4, and −6, respectively.

contamination (⟨S2⟩) values of calculations in quintet and nonet spin states to confirm the septet spin state as the electronic ground state for the investigated species. In the case of isomers I and III we optimized the structures of the Er2@C82 with structures close to Cs symmetry (Figure 2). However, as mentioned above, no symmetry constraint was

COMPUTATIONAL METHODS

All calculations have been carried out using the TURBOMOLE program.45 DFT calculations were performed using Becke’s three parameter functional with the nonlocal Lee−Yang−Parr correlation functional level (B3LYP) and Ahlrich’s def-SVP basis sets for carbon and the Stuttgart−Dresden SRSC97-ECP effective core potential (ecp28-mwb) and basis sets with (14s13p10d8f1g)/[10s8p5d4f1g] for Er, including explicit consideration of Er(f) electrons and without, assuming in the latter case a 6s25d1 valence configuration to emulate the effects of strong electron correlation. In order to avoid problems with the orientation and shape of Er f orbitals, no symmetry constrains were adopted in full geometry optimizations. Mulliken population analysis (MPA) and natural orbital population analysis were performed on the basis of the optimized geometries to estimate partial atomic charges. In addition, single point calculations were performed to calculate bond orders via natural bond orbitals analysis using the B3LYP method with same the basis sets and pseudopotentials for Er atoms as implemented in the Gaussian 03 program package.46

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RESULTS AND DISCUSSION Empty C82 Isomers. The nine empty IPR isomers of C82 were, respectively, optimized with total charges of 0, −2, −3, −4, and −6. For C82 and C824−, our calculations are basically consistent with previous reports by Poblet’s group.30 On the basis of relative isomer stabilities of their optimized structures, the following isomers were selected as favorable candidates to encapsulate Er2, Er2C2, and Er3N units: Cs-6, C2v-9, and C3v-8, where the numbers follow the notation of Fowler and Manolopoulos. These three isomers have the lowest relative energies (ΔE) in the three charge states −3, −4, and −6, as shown in Figure 1. Moreover, due to its relatively low energy in the −2 charge state, the C2-5 cage was also considered for encapsulation of one Er atom. It should be noted that the naked anions are not stable in vacuum without counterions, as indicated by positive orbital energies of their highest occupied molecular orbitals (MOs). We noticed that the three cages for charge states −4 and −6 are identical to the ones proposed earlier by the experimental group for the Er2@C82 and Er2C2@ C82 compounds, where they were named as isomers I (Cs-6), II (C2v-9), and III (C3v-8).25 Dierbium Containing Metallofullerenes Er2@C82. For testing stabilities of encapsulated Er3+ dications in C82 cages, geometry optimizations were performed with the septet spin state due to its formal valence electronic configuration Er (4f11). In addition, we also checked the energies and spin

Figure 2. Molecular structures of Er2@C82 isomers I, II (A, B, and C), and III, optimized in their septet electronic ground state. The green spheres represent erbium atoms.

enforced on the shape of the MOs. For isomer II, three choices for the positions of the two Er ions were investigated, which we label in the remainder of the text as A (C2 symmetry), and B and C (both C1 symmetry). B and C are geometrically enantiomorphous, as can be seen in Figure 2. Totally, the relative isomer energies ΔE increase in the order of III (0.00) < II (B (2.35) ≈ C (2.41) < A (8.82)) < I (9.50), with units of kcal/mol. The difference between enantiomers B and C is a numerical error below the accuracy of the employed convergence thresholds for geometry and wave function optimizations. This sequence is consistent with the order of ΔE in C824− isomers, III (0.00) < II (3.74) < I (9.50), rather than the corresponding order in C826−, II (0.00) < III (13.51) < I (14.95). Moreover, all six unpaired electrons apparently are localized on valence orbitals of the erbium atoms, such that Mulliken charges q on Er are typically showing a spin density around 3. For instance, in isomer III, the number of unpaired spins is 2.99, since the Mulliken charge q(Er) = 21.37α + 18.38β (Table S1). 6577

DOI: 10.1021/acs.inorgchem.7b00695 Inorg. Chem. 2017, 56, 6576−6583

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Figure 3. Schematic frontier molecular orbital correlation (energy in eV) between the empty cage C82 isomers (optimized at singlet spin state) and the corresponding Er2@C82 compounds (α orbital (left) and β orbital (right)). Symbols L and H denote orbitals of LUMO and HOMO. The L + 2 orbitals in empty C82 (III) are 2-fold degenerate orbitals. For clarity, the Er (4f) orbitals are omitted.

corresponding covalent bonds was reflected by shared electron numbers (SENs) of each Er with the other Er and carbon atoms on the cage shown in Figure 4. We roughly considered

In order to understand electron transfer processes, orbital analysis usually provides deeper insight than traditional population analyses. Here we perform an analysis based on the orbital correlation of unoccupied MOs in the empty C82 cage isomers optimized in a closed-shell singlet spin state with the corresponding occupied highest MOs of Er2@C82 in Figure 3, which allows intuitive insight into the electron transfer process in endohedral metallofullerenes. Consequently, we noticed that the first two lowest unoccupied MOs (LUMO and LUMO + 1) in the empty C82 cage isomers become four (two α plus two β) singly occupied orbitals in the corresponding Er2@C82 compounds, such as HOMO − 2 to HOMO − 5 in isomer I; HOMO − 1, HOMO − 2, HOMO − 4, and HOMO − 5 in isomer IIB (as an example for isomer II); and HOMO − 2 to HOMO − 5 in isomer III by about 1 eV energy lower than their corresponding unoccupied MOs. Such a phenomenon demonstrates that the cage possesses C824− rather than the experimentally proposed C826− charge state. The rest two electrons (Er (4f11)) are found to locate in HOMO and HOMO − 1 in isomer I, HOMO and HOMO − 3 in isomer IIB, and HOMO and HOMO − 1 in isomer III, respectively. They appeared as Er−Er covalent metal bonds by somehow mixed sd- (i.e., HOMO − 1 in isomer III) and sf- (i.e., HOMO in isomer III) orbitals. Such bonding was further supported by Er−Er bond order calculations (using Gaussian 09) with 0.20 (I), 0.23 (IIB), and 0.24 (III), respectively. In addition, valence electron configuration provided information to gain an insight into the hybrid Er−Er bond orbital feature. For example, q(Er, sdf) = 4f11.335d1.126s0.90 for isomer III, which agreed with the experimental finding of a peak as “s” from the density of state by Hung et al. However, this differs from their presentations of 4f11.435d0.676s0.00 calculated at both LDA and LSDA + U levels.44 Our results indicated that the valence electrons on the erbium appeared in its 5d6s orbitals besides the expected 4f shell. This has no effect on the reasonable spin numbers (6 unpaired electrons) calculated by total q(Er) and spin contamination exhibited as a normal value (⟨S2⟩ = 12.036). Such a phenomenon was thought to originate somehow from back-donation of electrons from near atoms to the sdf orbitals of the Er due to their orbital overlaps. The existence of the

Figure 4. Shared electron numbers (SENs) of each Er with the rest of the atoms in Er2@C82 isomers I, IIB, and III, respectively.

that it was a process of 6s2 electrons from each Er transferred to be C824− and its 4f promoted to the 5d shell for the formation of covalent bonds. In particular, we supposed that the C826− inferred by Shinohara’s group accounted for the hindrance of the electron back-donation on the exploration of electron transfer from each independent Er to the Er−Er covalent bond. The geometric optimizations in quintet and nonet spin states were tested for favorability of Er2+ with formal valence electron configuration Er (4f12) in the former and C826− charge state in the latter. The full data were presented in the Supporting Information (Table S1). For similarity, isomer III was selected for a description of their representative properties. First, their structural stabilities are less competitive by ΔE, and are 5.25 and 14.98 kcal/mol higher than the calculated values in a septet spin state. Second, the optimization in the quintet spin state indicated three spins from Er (4f) orbitals and one from a singly occupied Er−Er covalent bond (by HOMO − 9 and LUMO + 1 in Figure S1a). Such abnormal occupation results in the calculation with an undesirable high degree of spin contamination (⟨S2⟩ = 7.01) compared to its normal value (⟨S2⟩ = 6.0) because of its 4f11.59 not the expected 4f12 of Er in the valence electron configuration. Third, Mulliken charge q(Er) = 21.58α + 18.11β calculated in the nonet spin state indicates that seven spins are from the erbium atoms, among 6578

DOI: 10.1021/acs.inorgchem.7b00695 Inorg. Chem. 2017, 56, 6576−6583

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was the highest in ΔE (9.05 kcal/mol) in contrast to its sequence in Er2@C82 compounds, which should be by the reason for the Er2C2 restrained in C2 symmetry so as to cause its unstable geometry. The data calculated in quintet and nonet spin states were collected in Table S2 for supporting the calculations in septet as the ground state. The orbital analysis was performed as an effective method to disclose the influence of C2 on the Er2@C82 in the process of electron transfer. Figure 6 exhibited that, similar to the case in the Er2@C82, the frontier unoccupied MOs of LUMO and LUMO + 1 in each C82 empty cage were fully occupied by displaying four singly occupied MOs of HOMO to HOMO − 3 in the corresponding Er2C2@C82. Thus, the C824− rather than C826− charge state was suggested repeatedly in our calculations. Herein, no orbitals of the Er−Er covalent metal bond were found to behave as in Er2@C82, which was further supported by its weak bond order, such as 0.05 in isomer III. The long Er−Er distance (3.670 Å in isomer III) was caused obviously by the addition of C2 into the Er−Er covalent bond (3.551 Å in distance). Alternatively, we found that the LUMO (σg2p) of the C2 molecule becomes two singly occupied MOs in Er2C2@C82, such as HOMO − 24 and HOMO − 25 in isomer I, HOMO − 20 and HOMO − 21 in isomer IIB, and HOMO − 22 and HOMO − 23 in isomer III, respectively. This supported the formation of the C22− charge state (totally by (Er)23+C22−@ C824−) in contrast to its neutral charge proposed by Shinohara et al. Further, the shared electron characteristic of Er−C/C2 was demonstrated to be obviously strong (Figure 7), in

which six are demonstrated from formal Er (4f) orbitals and one is from the singly occupied Er−Er covalent bond (by HOMO − 11 and LUMO + 1 in Figure S1b). Further, the eighth spin is found on the cage with one singly occupied orbital (by HOMO and LUMO + 8 in Figure S1b) relative to LUMO + 2 of the empty C82, indicating of the formation of C825− rather than the expected C826− charge state. Collectively, the Er2+ (4f12) and C826− did not appear in the optimized Er2@ C82, and are favorably replaced by Er2+ (4f11) and C824− calculated in the septet electronic ground state. Instead of the rough presentation of (Er2)4+@C824−, we prefer a more reasonable formation as ((Er3+)26+: (Er−Er)2−)4+ @C824− where Er−Er belongs to the Er2 unit. Dierbium Carbide Metallofullerenes Er2C2@C82. Maintaining the symmetries of the compounds in Figure 2, the C2 unit was encapsulated inside the Er2@C82 by the Er−C2−Er framework. The corresponding Er2C2@C82 isomers were optimized in their septet ground state (Figure 5), showing

Figure 5. Molecular structures of Er2C2@C82 isomers I, II (A, B, and C), and III, optimized in their septet electronic ground state. The green and dark gray spheres represent erbium atoms and the C2 unit, respectively.

Figure 7. Shared electron numbers (SENs) of each Er with the rest of the atoms in Er2C2@C82 isomers I, IIB, and III, respectively.

that ΔE (kcal/mol) values increased in the order III (0.00) < II (B (2.61) ≈ C (1.10)) < I (6.65). Here we note that isomer IIA

Figure 6. Schematic frontier molecular orbital correlation (energy in eV) between the empty cage C82/C2 (optimized at singlet) and the corresponding Er2C2@C82 (α orbital (left) and β orbital (right)). Symbols L and H denote orbitals of LUMO and HOMO. For clarity, the Er (4f) orbitals are omitted. 6579

DOI: 10.1021/acs.inorgchem.7b00695 Inorg. Chem. 2017, 56, 6576−6583

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as in previous theoretical reports on M3N@C2n (M = Sc, Y; 2n = 68−98). This was verified by the orbital analysis shown in Figure 8, indicating that LUMO + 2 together with LUMO + 1 and LUMO on the empty C82 isomers are doubly occupied to be as HOMO to HOMO − 5 in the corresponding Er3N@C82 isomers. Similar to the case in (Er3+)26+C22−@C824−, the formation of (Er3+)39+N3−@C826− was proposed. Here we noticed that ΔE values (in kcal/mol) of the compounds increase in the order isomer II (0.00) < I (1.55) < III (17.66), partially differing in the sequence of C826−: II (0.00) < III (13.51) < I (14.95). This might be coaffected by stabilities of the Er3N encapsulated into the C82, because they deviate from the plane geometry of the bare Er3N molecule by their average dihedral angle of 1.82° (I), 10.90° (II), and 4.32° (III), as listed in Table S3. Further, the stronger shared electron numbers between Er and N are exhibited in all three compounds, while almost no SENs between the Er−C/cage were presented (see Figure S2), which is slightly different from the case in the Er2C2@C82. This further illustrates that geometries of encapsulated units inside the cage have an effect on corresponding compounds in terms of their stabilities and formations of bonding. Thus, in order to further explore probable C826− in M2@C82, M = La was particularly noticed for investigations due to its high electropositivity. Isomer III as an example was optimized in its singlet and triplet spin states with ΔE of 1.37 kcal/mol higher in the former than the latter. Though the result did not show the C826− charge state by orbital analysis, C825− appeared alternatively by presenting a singly occupied La−La covalent bond of HOMO − 1(α) in the triplet and 1-electron 2-center bonds of the HOMO and LUMO in the singlet (Figure S3). This indicated that, compared to C824− in Er2@C82, the cage with higher electronegativity was attained by the encapsulated metal candidate with higher electropositivity. The aforementioned calculations indicated that the Er (4f11) valence electron configuration was responsible for both Ern+ (n = 2, 3) charge states in the compounds. Here, on one hand, we found the formation of Er (4f12) in Er@C82 optimized in its triplet spin ground state (see Table S4). We optimized four compounds based on isomers selected in the section describing the empty isomers, namely, as I (C2v-9), II (Cs-6), III (C2-5), and IV (C3v-8), respectively. Their ΔE (in kcal/mol) values increase in the order I (0.00) < II (1.58) < III (4.78) < IV (12.00), which agrees with that of the corresponding C822− species shown in Figure 1. Thus, another case, Er (4f12) for the Er2+ charge state (Figure S4), was proposed. However, we need to especially point out that electronic properties of Er@C82 (I) were experimentally reported from the Er (4f11) valence electron configuration,47 which differs from the present calculations of Er (4f12) as its ground electronic state due to the 3ΔE with 8.48 kcal/mol lower than the 5ΔE. In addition, we also tested calculations on M@C82 (I) (M = Y, La, and Lu), indicating the M with 3+ in their charge states. This agrees with

particular for isomer III, which should be the origin for missing the detection of the charge in the C2. In order to further confirm C22−, we performed single point calculations on q2C2@ C82. Herein, the symbol q was used to replace the Er atoms for switching off their electrons shared with carbon atoms in the cage and the C2. As a result, the Mulliken charge indicates Δq(C2) = −1.97 in contrast to the value of almost zero calculated in Er2C2@C82, which further testified that the existence of shared electrons creates errors of the charge state found by the calculation and experiment. The aforementioned calculations demonstrated that the appearance of the Er (4f11) valence electron configuration cannot deduce a C826− charge state in both Er2@C82 and Er2C2@C82 compounds (Scheme 1). Only two electrons (6s2) Scheme 1. Electron Transfer Diagram for Er2@C82 and Er2C2@C82 Compounds (Upper) and for Er3N@C82 and Er@C82 Compounds (Lower)

of each Er were found to be transferred to the cage (C824−), while the third one (4f) contributed to the doubly occupied Er−Er covalent metal bonds and the C2 (σg2p) orbitals. For both compounds, their LUMO−HOMO gaps increase in the order of isomer IIB < I < III, corresponding to the values (in eV) of 1.13 < 1.17 < 1.38 in Er2@C82 and 1.29 < 1.67 < 1.92 in Er2C2@C82, which agree with the sequence detected experimentally. This is also in accordance with the LUMO + 2− LUMO + 1 (relative to LUMO−HOMO of C824−) gap of the empty C82 isomers by II (0.44) < I (0.62) < III (1.32) rather than LUMO + 3−LUMO + 2 (relative to LUMO−HOMO gap of C826−) gap by isomers III (0.00) < I (0.45) < II (0.83), as listed in Table 1. The larger HOMO−LUMO gap and higher charge of Er (formal 3+) in Er2C2@C82, in particular for isomers I and III, explained the higher photoluminescence intensity detected by experiment. C82m− and Ern+. The C82m− (m = 6) charge state was sought in Er3N@C82 compounds optimized in their 10-fold spin state

Table 1. Orbital Energy (in eV) Correlation between LUMO + 3−LUMO + 2/LUMO + 2−LUMO + 1 of the Empty C82 and LUMO−HOMO of the Er2C2@C82 and Er2@C82 C82

Er2C2@C82

isomer

LUMO + 3−LUMO + 2

LUMO + 2−LUMO + 1

I IIB III

0.45 0.83 0.00

0.62 0.44 1.32 6580

Er2@C82

LUMO−HOMO 1.67 1.29 1.92

1.17 1.13 1.38 DOI: 10.1021/acs.inorgchem.7b00695 Inorg. Chem. 2017, 56, 6576−6583

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Figure 8. Schematic frontier molecular orbital correlation (energy in eV) between the empty cage C82 and the corresponding Er3N@C82 isomers I, II, and III (α orbital (left) and β orbital (right)) optimized in their 10-fold electronic ground state. Symbols L and H denote orbitals of LUMO and HOMO. The green and blue spheres represent erbium and nitrogen atoms, respectively.

previously reported theoretical and experimental studies. Furthermore, the oxidation state of M with the divalence was previously demonstrated to be more favorable than the trivalence when M = Tm (tested by the same calculation) and Sm in [email protected],49 Thus, we considered that the present computational level was reliable for the optimizations. Such a difference is ready to be explored experimentally. On the other hand, one hypothesis of Er (4f11) for Er3+ in Er2@C80-Ih was proposed, because C80-Ih has only two electrons occupied in its 4-fold degenerate HOMO and can accommodate an additional six electrons to form a stable closed-shell electronic state. As a result, we found only five electrons transferred to the empty cage, leading to a C825− (i.e., ∼Er2.5+) charge state (Figure S5). Further, the Er−Er was found to be singly occupied, with a distance elongated to 3.963 Å compared to 3.551 Å in Er2@C82 (III) with doubly occupied orbitals. Obviously, cases of M−M bonding are related to the M with different charge states. A more specified discussion on the valence state of the metal atoms (M = Lu, Y, and Sc) influenced by their third ionization potentials and ns2(n − 1)d1 → ns1(n − 1)d2 excitation energies in dimetallofullerenes was previously reported.50 Collectively, on the basis of the present calculations, charge configurations of cage (m−) and metal (n+) are influenced by general cofactors (Scheme 2) as follows: (i) electropositivity of metal atoms and electronegativity of cages; (ii) geometries of the encapsulated units, such as M, M2, M2C2, and M3N; and (iii) space limitation of the cage relative to the dimension of the encapsulated unit. The present results provided useful information to understand charge states of the cage and the encapsulated unit in various endohedral metallofullerenes.

Scheme 2. Proposed Influence Factors on Charge Configurations for Endohedral Metallofullerenesa

a

Symbols C, M, and EU denote cage, metal, and encapsulated unit.

and dierbium−carbide endohedral metallofullerenes such as Er2@C82 and Er2C2@C82 with cages of Cs-6 (I), C2v-9 (II), and C3v-8 (III). For each compound, the frontier molecular orbital correlation demonstrates that unoccupied orbitals of LUMO and LUMO + 1 of the empty cages become fully occupied. This indicates that two electrons (6s2) per Er are transferred, resulting in a C824− configuration which is in contrast to the previously proposed C826− configuration. Further, one 4f electron of the erbium is promoted to its 5d shell and then is involved in covalent bonding to the near atoms, such as Er−Er and Er−C in Er2@C82, and Er−C and Er−C/C2 in Er2C2@C82. This explains why Er3+-like emission (4f11) from 4I13/2 to 4I15/2 was detected experimentally although the cage formally carries only four negative charges. In addition, the strong covalent binding of Er−C/C2 also makes MEM-Rietveld X-ray measurements fail to explore C22− in electronic structure. For three isomers, the HOMO−LUMO gap, i.e., LUMO + 2−LUMO + 1 of C82, increases in the order II < I < III, which agrees with the photoluminescent intensity. The encapsulated C2 also enlarges the HOMO−LUMO gap, especially for isomers III

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CONCLUSIONS Density functional theory calculations have been performed to elucidate the molecular and electronic structures of dierbium 6581

DOI: 10.1021/acs.inorgchem.7b00695 Inorg. Chem. 2017, 56, 6576−6583

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Inorganic Chemistry

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and I, compared to values for Er2@C82. In addition to the identification of C824− in Er2@C82 and Er2C2@C82, the 6-fold negatively charged C826− was confirmed in hypothetical Er3N@ C82 compounds with three covalent Er−N bonds. Furthermore, we recommend experimental investigations on the photoluminescent properties of Er2+ (4f12) to distinguish the widely studied Er3+ (4f11).

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b00695. Five figures and four tables of supplementary computational results, and Cartesian coordinates (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Po-Heng Lee: 0000-0003-2962-5162 Stephan Irle: 0000-0003-4995-4991 Present Address ∥

Fuel Cell Cutting-Edge Research Center (FC-Cubic), Technology Research Association, AIST Tokyo Waterfront Main Building, 2-3-26 Aomi, Koto-ku, Tokyo 135-0064, Japan. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.W. and S.I. acknowledge support from the Global Century of Excellence (GCOE) Program in Chemistry at Nagoya University. J.W. and P.-H.L. wish to acknowledge the Research Grants Council (RGC) Early Career Scheme Fund (539213), General Research Fund (15273316), Collaborative Research Fund (C7044-14G), and Theme-Based Fund (T21-711/16-R), as well as the National Rail Transit Electrification and Automation Engineering Technology Research Center (1BBYL) for providing financial support.

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REFERENCES

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Article

Inorganic Chemistry

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