Quantum Chemical Insight into La2C96: Metal Carbide Fullerene

Article pubs.acs.org/IC

Quantum Chemical Insight into La2C96: Metal Carbide Fullerene La2C2@C94 versus Dimetallofullerene La2@C96 Ruisheng Zhao,†,‡ Kun Yuan,† Shengdun Zhao,† Xiang Zhao,*,†,‡ and Masahiro Ehara*,‡ †

Institute for Chemical Physics, School of Science & School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China ‡ Institute for Molecular Science, Okazaki 444-8585, Japan

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S Supporting Information *

ABSTRACT: A family of dilanthanum-containing endohedral metallofullerene La2C2n (n = 46−51) was synthesized recently. In the present work, a systematical investigation on La2C96 series including the carbide clusterfullerene form La2C2@C94 and the conventional dimetallofullerene form La2@C96 was implemented by density functional theory, combined with statistical mechanics. Three isomers, i.e., La2@ D2(191838)-C96, La2C2@Cs(153479)-C94, and La2C2@C1(153491)-C94 were disclosed to be thermodynamically stable at the temperature region of endohedral metallofullerene formation. La2@D2(191838)-C96 is the prevailing isomer at low temperature, while La2C2@Cs(153479)-C94 and La2C2@C1(153491)-C94 are the most and second-most abundant isomers at high temperature. Interestingly, the highest occupied molecular orbital (HOMO) of La2C2@C1(153491)-C94 is distributed on one pole of the cage, and the lowest unoccupied molecular orbital (LUMO) of this isomer is mainly located on the equator of the cage, which can facilitate synthesis of regioselective derivatives. This work will provide useful information for further experimental identification and application of La2C96.

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INTRODUCTION Fullerene, the structure of which consists of carbon atoms arranged in a closed sphere, is a unique allotrope of carbon and was discovered by Kroto et al. in 1985.1 The species of pure fullerene are limited to C60,1 C70,2,3 C76,4 C78,5−7 C80,8 C82,6 C84,9 and C90,7 but can be greatly enlarged by derivation. Generally, there are three strategies to derive fullerene, namely, (i) encapsulate atom(s), cluster or small molecule into the hollow cavity, (ii) attach atom(s) or functional group(s) to the outer sphere, and (iii) replace carbon atom(s) with other atom(s), resulting in three types of derivatives (i.e., endohedral,10 exoheral,11−15 and doping fullerenes;16−18 the carbon cage framework is preserved best in the endohedral derivatives). Although noble gases,19−21 small neutral molecules,22,23 metal atoms, and metal clusters all can be encapsulated in fullerene cages, endohedral metallofullenes (EMFs) (i.e., the latter two cases) have attracted the most attention, because of the exclusive and significant electron transfer from the metal moieties to the fullerene cage, which bestows some unprecedented features on fullerenes.10 EMFs can be generally divided into two groups, namely, classical EMFs (Mx@C2n, where M = metals) and clusterfullerenes (such as nitrides (M3N@C2n or M′xM″3−nN@C2n), carbides (M2C2@C2n−2 or M3C2@C2n−2), oxides (MxOy@C2n), sulfides (MxSy@C2n), and methano (M3CH@C2n) and cyano (M3NC@ C2n) clusterfullerenes. The classical dimetallofullerene (M2@ C2n) and trimetallofullerene (M3@C2n) share the same © 2017 American Chemical Society

molecular formulas, i.e., M2C2n and M3C2n, with carbide clusterfullerenes, M2C2@C2n−2 and M3C2@C2n−2, and structure elucidation of these EMFs is a challenge for both experimental and theoretical investigations.10 With regard to the experiment, some carbide clusterfullernes were erroneously elucidated as classical EMFs, because it is difficult to distinguish the two types of EMF for mass spectrometry, UV-vis-NIR absorption spectroscopy, and so on; theoretically, the density functional theory (DFT) methods without long-range corrections had a tendency to underestimate the stabilities of some isomers of these EMFs, which may result in incorrect conclusions.10,24,25 Especially, it is relatively difficult to obtain EMF crystals with large carbon cages (C2n, 2n ≥ 90) for single-crystal X-ray measurement, because of the low availability and rotation of inner moiety. (Note that, currently, single-crystal X-ray diffraction is the only method that can unambiguously elucidate the structure of EMF).24 Recently, a series of crystals of lanthanum carbide fullerene were obtained, including La2C2@ C90, La2C2@C92, La2C2@C94, La2C2@C96, La2C2@C98, La2C2@ C100, La2C2@C102, and [email protected]−28 These lanthanum carbide fullerenes exhibit some unique features. For instance, compared with La2@D5(450)-C100, La2C2@D5(450)-C100 exhibits a 5% axial compression.27 Received: July 23, 2017 Published: September 21, 2017 11883

DOI: 10.1021/acs.inorgchem.7b01833 Inorg. Chem. 2017, 56, 11883−11890

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Inorganic Chemistry

Table 1. Relative Energies (ΔE) and HOMO−LUMO (for Closed Shell) or SOMO−LUMO (for Open Shell) Gaps of La2@C96 and La2C2@C94 Series at the M06-2X/6-31G* ∼ LanL2DZ Level La2@D2(191838)-C96 La2@D2(191835)-C96 La2@C2(191809)-C96 La2@C2(191810)-C96 La2@C1(191811)-C96 La2@C2(191819)-C96 La2@C1(191753)-C96 La2@D2d(191815)-C96 La2@Cs(191822)-C96 La2@D6d(191839)-C96 La2C2@Cs(153479)-C94 La2C2@C2(153476)-C94 La2C2@Cs(152345)-C94 La2C2@C1(153413)-C94 La2C2@C1(153477)-C94 La2C2@C1(153491)-C94

number of adjacent pentagon pairs, PA

multiplicity

ΔE (kcal/mol)

gap (eV)

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

triplet triplet triplet triplet triplet triplet triplet triplet triplet triplet singlet singlet singlet singlet singlet singlet

0.0 4.8 6.2 8.4 12.2 12.6 14.5 17.6 18.2 19.9 32.3 32.6 38.8 39.4 40.3 40.5

1.83 2.54 2.13 2.02 2.46 2.58 2.83 2.02 2.56 2.95 2.88 2.65 2.86 2.64 2.65 2.59

semiempirical AM1 and DFT B3LYP methods are collected in Tables S1−S4 in the Supporting Information, and the stable isomers of both C944− and C966− all satisfy the well-known isolated pentagon rule (IPR). Both the semiempirical AM1 and DFT B3LYP results indicate that Cs(153479)-C944− and D2(191838)-C966− are the most stable ones of C944− and C966− anions, respectively. The relative energies of La2@C96 and La2C2@C94 are collected in Table 1. La2@D2(191838)-C96 with a triplet ground state is the most stable isomer of La2@C96 and La2C2@ C94 series, and La2C2@Cs(153479)-C94, which is less stable than La2@D2(191838)-C96 (by 32.3 kcal/mol), is the most stable isomer of La2C2@C94 series. La2C2@C1(153491)-C94 (i.e., La2C2@C1(132)-C94, which was isolated and unambiguously characterized recently) is not the most stable isomer of La2C2@C94 series, and its energy is 8.5 kcal/mol higher than that of La2C2@Cs(153479)-C94. Since the potential energies cannot reflect the thermodynamic stabilities of EMFs at elevated temperature, the abundances of La2@C96 and La2C2@C94 isomers at a wide temperature range were calculated (see Figure 1). At absolute zero, La2@D2(191838)-C96 is the most abundant isomer, and its abundance decreases as the temperature increases. In sharp

In the present work, we investigated one of these lanthanum carbide fullerenes, La2C2@C94. Since the classical metallofullerene and metal carbide fullerene, which share the same molecular formula, can coexist, the La2@C96 series were also investigated. For instance, La2@D5(450)-C100 was isolated and its structure was unambiguously elucidated by single-crystal Xray diffraction in 2011,29 and La2C2@C1(175)-C98 was isolated and definitely characterized recently; the theoretical investigation indicates that La2@D5(450)-C100 is thermodynamically stable at low temperature (∼0−1500 K) while La2C2@ C1(175)-C98 possesses good stability at elevated temperature (>1000 K).26

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COMPUTATION SECTION

Since the La2C2 cluster and each of the La atoms donate four and three electrons to C94 and C96 cages, respectively, 8986 C944− and 12 840 C966− anions with less than two adjacent pentagon pairs (PA = 0−2, where PA denotes the number of adjacent pentagon pairs) were first screened at the semiempirical AM1 level.30 The relative stable cage anions (within 30.0 kcal/mol) were extracted and reoptimized at the B3LYP/6-31G* level,31 and the cage anions with low relative energies ( 2, suggesting that the metal-cage bonds of the three isomers possess covalent characteristics, which can also be demonstrated by the overlaps of occupied orbitals between La atoms and carbon cages, as shown in Figure S2 in the Supporting Information. The bond ellipticity (ε) values for all of the bonds in Table 3 is greater than zero, indicating that these bonds are

Table 2. Populations of FMOs, and Energy Barriers and Reaction Energies of add-1 and add-2 bond

population of FMOs (%)

energy barrier, E⧧ (eV)

reaction energy, ΔE (kcal/mol)

C14− C73 C17− C29 C3−C43 C44− C45 C30− C51 C10− C11 C56− C57

(2.31, 2.72)

add-1 15.5

−32.7

(2.55, 2.13)

18.6

−22.6

(1.87, 1.68) (0.40, 0.40)

21.3 26.7

−18.9 −14.1

(1.36, 1.32)

25.1

−11.1

(0.19, 0.19)

29.1

−3.0

(0.13, 0.05)

32.3

−0.7

C12− C13 C56− C57 C36− C37 C17− C18 C19− C20 C40− C41 C79− C80

(2.33, 2.01)

add-2 11.6

−37.6

(3.94, 4.07)

12.1

−27.0

(3.80, 3.22)

14.9

−24.4

(0.25, 0.11)

17.6

−17.9

(0.82, 0.59)

22.4

−12.8

(1.52, 1.19)

25.0

−9.3

(0.04, 0.09)

24.2

−4.4

more negative reaction energies than the counterparts with low populations, such C10−C11 for 1 and C79−C80 for 2. There are a few exceptions in which the thermodynamic and kinetic stabilities are not consistent with the populations of the corresponding FMOs. For instance, the sites of C12−C13 are more thermodynamically and kinetically favorable than those of C56−C57 for the addition of 2, but the former sites possess a low HOMO population. The inconsistency should be due to the fact that, besides the population of FMOs, other factors, such as charge population and local strain energies, may also influence the regioselectivity.39 These results suggest that different regioselective derivatives of La2C2@C1(153491)-C94 can be formed via addition reaction with reagents possessing

Figure 4. Bond critical points (BCPs) of (a) La2@D2(191838)-C96, (b) La2C2@C1(153491)-C94, and (c) La2C2@Cs(153479)-C94 (BCPs are highlighted by blue circles). 11886

DOI: 10.1021/acs.inorgchem.7b01833 Inorg. Chem. 2017, 56, 11883−11890

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Inorganic Chemistry Table 3. Bond Critical Point (BCP) Indicators of La2@ D2(191838)-C96, La2C2@C1(153491)-C94, and La2C2@ Cs(153479)-C94

bond La97− C34 La97− C23 La98− C10 La98− C63 La97− C38 La97− C57 La97− C56 La98− C25 La98− C26 La97− C36 La98− C25 La98− C26 La98− C48

electronic density, ρBCP (a.u.)

Laplacian of the density, ∇2ρBCP (a.u.)

total energy density, HBCP (a.u.)

ratio of the absolute value of the potential energy density to the kinetic energy density, |VBCP|/ GBCP (a.u.)

0.046

La2@D2(191838)-C96 0.130 −0.004

0.046

0.130

0.046

Table 4. Bond Distance, Mayer Bond Orders, and Delocalization Indices of La2@D2(191838)-C96, La2C2@C1(153491)-C94, and La2C2@Cs(153479)-C94 bond distance, d (Å)

bond ellipticity, ε (a.u.)

10.003

0.746

−0.004

9.846

0.743

0.130

−0.004

9.803

0.735

0.046

0.129

−0.004

10.097

0.755

0.043

La2C2@C1(153491)-C94 0.138 −0.002 16.675

2.404

0.045

0.151

−0.003

14.654

1.294

0.045

0.142

−0.003

12.939

1.151

0.046

0.157

−0.003

13.339

0.383

0.044

0.141

−0.002

16.522

2.542

0.045

La2C2@Cs(153479)-C94 0.139 −0.004

11.401

0.276

0.044

0.154

−0.003

17.136

0.743

0.044

0.139

−0.003

14.822

0.998

0.041

0.135

−0.001

27.742

5.123

La97−C34 La97−C23 La98−C10 La98−C63 La97−C38 La97−C57 La97−C56 La98−C25 La98−C26 La97−C36 La98−C25 La98−C26 La98−C48

Mayer bond order

La2@D2(191838)-C96 2.633 0.202 2.630 0.203 2.630 0.204 2.635 0.202 La2C2@C1(153491)-C94 2.660 0.164 2.634 0.124 2.642 0.152 2.596 0.139 2.656 0.144 La2C2@Cs(153479)-C94 2.642 0.138 2.610 0.136 2.655 0.147 2.768 0.111

delocalization indices, δ 0.299, 0.300, 0.300, 0.299,

0.298a 0.299a 0.300a 0.298a

0.561 0.552 0.567 0.561 0.547 0.553 0.549 0.548 0.477

a

Delocalization indices for both alpha and beta spin were given for the La2@D2(191838)-C96 isomer.

were simulated and depicted in Figure 5, since these spectra are very useful to distinguish different isomers with the same molecular formula. It is reported that the UV-vis-NIR spectra are sensitive to the structures of carbon cages.10,53 There are three absorption peaks at 416, 666, and 1130 nm for La2@ D2(191838)-C96. Four and three absorption peaks can be observed for La2C2@C1(153491)-C94 and La2C2@Cs(153479)C94, respectively. For the former one, the four absorption peaks are located at 315, 460, 944, 1454 nm, and for the latter one, the three absorption peaks are located at 324, 634, 1030 nm. The weak absorption peak at 1454 nm for La2C2@C1(153491)C94 may help to distinguish this isomer from La2C2@ Cs(153479)-C94, because there is no absorption peak in vicinity of 1454 nm for the latter isomer. Meanwhile, compared with the cases of the two La2C2@C94 isomers, the wavelengths of absorption peaks of La2@D2(191838)-C96 are larger, which may be useful to tell it from the two La2C2@C94 isomers. Note that the peaks at 416 nm in Figure 5a, 315 nm in Figure 5b, and 324 nm in Figure 5c may be inauthentic peaks of TD-DFT calculations and cannot be observed in experiment, because TD-DFT calculations usually produce a fixed number of excited states and the high-energy states sometimes are not real states. The simulated IR spectra of the three isomers are illustrated in Figures 5d−5f. The IR spectrum of La2@D2(191838)-C96 can be divided into three regions. The first region at 0−200 cm−1 stems from translating and rocking vibrations of the two inner La atoms, and such low frequencies of these signals should be due to the large mass of the La atoms. The second region is observed at 200−900 cm−1, and the peaks at this region are attributed to the breathing vibration of the carbon cage. The third region, which is located at 900−1750 cm−1 originates from the C−C stretching mode of the carbon cage, and the strongest peak is observed at 1387.58 cm−1. Different from the case of La2@D2(191838)-C96, the IR spectra of La2C2@C1(153491)-C94 and La2C2@Cs(153479)-C94 can be divided into four regions, and the former three regions are similar to those observed for La2@D2(191838)-C94. Analogous to La2@D2(191838)-C96, the signals of the first regions are

of π character, especially for the bonds with large ε, such as La97−C38 and La98−C26 of La2C2@C1(153491)-C94, and La98−C48 of La2C2@Cs(153479)-C94. The Mayer bond order and the delocalization index,49−52 which is a quantitative measure of the number of electron pairs shared between two atomic spaces, were calculated to gain more insight into the bond interactions between La atoms and carbon cages, as collected in Table 4. The bond distances of La and vicinal carbon atoms of cages are ∼2.65 Å for all three isomers, and the Mayer bond orders of La2@D2(191838)-C96 are slightly larger than those of the other two isomers, corresponding to more significant covalent characters of La2@ D2(191838)-C96. The delocalization indices also demonstrate the covalent character of the interactions between La atoms and carbon cages (note that the delocalization index of an ideal ionic bond is zero). Based on the HBCP, Mayer bond orders, and delocalization indices, the interactions between La atoms and cage C atoms of La2@D2(191838)-C96, La2C2@C1(153491)-C94, and La2C2@ Cs(153479)-C94 are mainly ionic but possess covalent characteristics. The values of HBCP is negative, but very near to zero; although the Mayer bond orders are not zero, they are far away from 1, which corresponds to a single bond; and the delocalization indices of bonds between La atoms and cage C atoms are much smaller than those of typical covalent La−C bonds of La2C2 moieties (ca. 0.9). Simulated Infrared and UV-vis-NIR Spectra. The infrared (IR) and UV-vis-NIR spectra of La2@D2(191838)C96, La2C2@C1(153491)-C94, and La2C2@Cs(153479)-C94 11887

DOI: 10.1021/acs.inorgchem.7b01833 Inorg. Chem. 2017, 56, 11883−11890

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Inorganic Chemistry

Figure 5. (a−c) Simulated UV-vis-NIR and (d−f) infrared (IR) spectra of La2@D2(191838)-C96, La2C2@C1(153491)-C94, and La2C2@Cs(153479)C94.

fullerene (La2C2@C94), was performed. In the low-temperature region, La2@D2(191838)-C96 is the overwhelming isomer, whereas in the elevated temperature region, La2@Cs(153479)C94 and the recent isolated isomer, La2@C1(153491)-C94, are the most and second-most abundant isomers, respectively. The frontier molecular orbitals of La2@C1(153491)-C94 are unique, and in particular, the highest occupied molecular orbital (HOMO) is mainly distributed on one pole of the cage, whereas the lowest unoccupied molecular orbital (LUMO) is located on the equator of the cage. This feature provides the ability to synthesize regioselective endohedral metallofullerene derivatives. The metal-cage interaction was demonstrated to be mainly ionic but possess covalent characteristics, using bond critical point indicators and Mayer bond order analysis. UV-visNIR and IR spectra of the three La2C94 isomers were simulated, which can provide useful information for further identification of La2C96.

related to stretching and rocking vibrations of the inner La2C2 clusters, and the ranges of this region are 0−200 and 0−220 cm−1 for La2C2@C1(153491)-C94 and La2C2@Cs(153479)-C94, respectively. The signals of the second (200−900 cm−1 for La2C2@C1(153491)-C94, and 220−940 cm−1 for La2C2@ Cs(153479)-C94) and third regions (900−1800 cm−1 for La2C2@C1(153491)-C94, and 940−1800 cm−1 for La2C2@ Cs(153479)-C94) are also ascribed to the breathing vibrations of fullerene cages and stretching vibrations of C−C bonds of the carbon cages, respectively. In contrast to La2@D2(191838)-C96, there is a peak over 1800 cm−1 for each of the two La2C2@C94 isomers (1898.42 cm−1 for La2C2@C1(153491)-C94 and 1904.68 cm−1 for La2C2@Cs(153479)-C94) attributed to the stretching vibration of the C−C bonds of La2C2 clusters, but these peaks may not be useful to distinguish La2C2@C94 and La2@C96 isomers, because the signals are too weak to be observed. The intensities of signals at the second regions can help to discriminate between the La2C2@C94 and La2@C96 isomers. Intensities of these signals of the two La2C2@C94 isomers are generally stronger than those of La2@D2(191838)C96. Moreover, the signals at the third regions are useful to distinguish the two La2 C 2 @C 94 isomers. For La2 C 2 @ Cs(153479)-C94, the intensities of the strongest (at 1302.32 cm−1) and the second-strongest (at 1392.41 cm−1) signals are quite similar, whereas for La2C2@C1(153491)-C94, the intensities of the two strongest peaks (at 1458.31 and 1376.39 cm−1) vary significantly.

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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.7b01833. Relative energies of C944− and C966−, electron affinities and ionization potential, molecular orbitals, and Cartesian coordinates (PDF)

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CONCLUSIONS A systematically theoretical investigation combining density functional theory with statistical mechanics on a dilanthanumcontaining endohedral metallofullerene La2C96, covering both convential dimetallofullerene (La2@C96) and carbide cluster-

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (X. Zhao). *E-mail: [email protected] (M. Ehara). 11888

DOI: 10.1021/acs.inorgchem.7b01833 Inorg. Chem. 2017, 56, 11883−11890

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Inorganic Chemistry ORCID

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Xiang Zhao: 0000-0003-3982-4763 Masahiro Ehara: 0000-0002-2185-0077 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been financially supported by the National Natural Science Foundation of China (Nos. 21573172, 21773181, and 21663024) and China Postdoctoral Science Foundation (No. 2017M613125). One of the authors (X.Z.) appreciates JSPS for an Invitational Fellowship (No. S17037) for Research in Japan. The financial support from the Nanotechnology Platform Program (Molecule and Material Synthesis) of the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan is also acknowledged.

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