M@C50 as Higher Intermediates Towards Large Endohedral

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C: Physical Processes in Nanomaterials and Nanostructures 50

M@C as Higher Intermediates Towards Large Endohedral Metallofullerenes: Theoretical Characterization, Aromatic and Bonding Properties From Relativistic DFT Calculations Alan Miralrio, Alvaro Muñoz-Castro, Robert Bruce King, and Luis Enrique Sansores J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b08789 • Publication Date (Web): 26 Dec 2018 Downloaded from http://pubs.acs.org on December 27, 2018

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The Journal of Physical Chemistry

M@C50 as Higher Intermediates Towards Large Endohedral Metallofullerenes: Theoretical Characterization, Aromatic and Bonding Properties from Relativistic DFT Calculations Alan Miralrio,1 Alvaro Muñoz-Castro,2 R. Bruce King,3 Luis Enrique Sansores4* Departamento de Física y Química Teórica, DEPg. Facultad de Química, Universidad Nacional Autónoma de México, UNAM, Del. Coyoacán, Ciudad de México 04510, México. 2 Laboratorio de Química Inorgánica y Materiales Moleculares, Universidad Autónoma de Chile, Llano Subercaseaux 2801, San Miguel 890 0000, Santiago, Chile. 3 Department of Chemistry, University of Georgia, Athens, Georgia 30602, United States. 4 Departamento de Materiales de Baja Dimensionalidad, Instituto de Investigaciones en Materiales, UNAM, Apartado Postal 70-360, Ciudad de México 04510, México. 1

ABSTRACT In recent years, endohedral metallofullerenes involving the C50 cages have been observed experimentally to encapsulate several metal atoms. This is the last step in a bottom-up growing mechanism to produce the most commonly observed large metallofullerenes. Nonetheless, currently there is a lack of theoretical rationalization of such compounds. We now report, for the first time, a comprehensive theoretical study extending the experimentally known M@C50 species to endohedral group 3 and 4 elements using dispersion-corrected density functional theory. For C50 fullerene, isomers Cs (266) and D5h (271) are the most energetically favorable cages to host these metals, despite being far from the ground state of neutral C50 fullerene. Interestingly, properties of these endohedral compounds are highly comparable to those of the tri- and tetra- anions of the correspondent hollow fullerene cages. It is found that metal-cage binding energies larger than –5 eV are directly related to relative abundances experimentally measured for the group 3 endohedral metallofullerenes. In addition, hypothetical group 4 metallofullerenes are also expected to be stable. Our results show that the resulting metal atoms transfer charge to the cage, to partially covalentionic compounds, which is the nature of the metal encapsulation within the C50 cage, where the ionic bond character increases for the heavier elements. In all cases, HOMO-LUMO gaps smaller than 0.4 eV are found, in accord with the high reactivity imposed by the need for further growth. Aromaticity NICS(0)iso indices reveal that some carbon rings close to the enclosed metal M are not fully aromatic and some are even antiaromatic, even though hollow C50 fullerene cages are fully aromatic. Thus, the stabilities of the endohedral M@C50 compounds are not fully ruled by the aromatic character of the carbon cage but instead by the energy characteristics of the metal-cage interactions, which are fully characterized by means of energy decomposition analyses. Such results can be useful to guide further experimental explorative synthetic efforts towards more diverse metal species encapsulated within the higher intermediate C50 cage, which can be extended to other intermediate species already experimentally detected. 1 ACS Paragon Plus Environment

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1. INTRODUCTION Fullerenes exhibit an enhanced versatility owing to their capacity to encapsulate atoms and small molecules,1–3 forming compounds known as endohedral fullerenes (EFs). The encapsulated species can include a wide variety of elements,1–5 as well as small molecules6 and clusters, providing further variety to such carbon nanostructures.7,8 Currently, the most commonly studied endohedral metallofullerenes (EMFs) are those which contain lanthanide atoms.2,3 The novel properties shown by these endohedral compounds, which commonly differ from those found on the hollow fullerenes, suggest several potential fields of application; from photovoltaics9 to biomedicine.4,10–13 There is currently great interest in elucidating the intermediate species of variable sizes in the formation of endohedral compounds,14,15 as well as in predicting the most suitable cage among the many fullerene isomers possible.16 In addition, the study of the most recently synthesized EMFs is another current topic, since the characterization of each single EMF represents a major challenge.17– 19

Also, that capacity to enclose other species is relevant by itself since the encapsulated

atoms are isolated, being of interest for applications where the need to protect some metal atoms20 or to isolate hazardous species from the environment21 are fundamental. Other applications which take advantage of the encapsulation feature are the external manipulation of the EMFs with high spin, as single molecule magnets22 or as qubits.23,24 Their interaction with H2 molecules for hydrogen storage25 and to act as catalyst of the hydrogen evolution reaction26 is being explored as well. To date, most of the theoretical and experimental studies focus on EMFs with cages larger than the C60, excluding a vast variety of experimentally known small EMFs.8,27 However, that lack of information has triggered further theoretical works,5,28–32 providing insight into the properties of these novel EMFs with small carbon cages, following a growing mechanism towards C60 and other higher fullerenes.28 Small EMFs ( 60) EMFs. 2. COMPUTATIONAL DETAILS The theoretical characterization of endohedral metallofullerenes M@C50 encapsulating atomic species of group 3 (Sc, Y, and La) and group 4 (Ti, Zr, and Hf) was performed using spin-unrestricted density functional theory (DFT) methods. The generalized gradient approximation (GGA) functional of Perdew−Burke−Ernzerhof (PBE)63,64 was used together with the triple-ζ valence basis set def2-TZVP.65 In that, 28 and 46 core electrons are replaced by a scalar relativistic effective core potential (ECP) for elements belonging to periods 5 and 6, respectively. A further correction to the total electronic energy owing to dispersion interactions was included using the term ‘D3’, proposed by Grimme, et al., and the damping function of Becke & Johnson, (BJ).66 That methodology, hereinafter labeled PBE-D3(BJ)/def2TZVP, was used as implemented in the quantum chemistry code TURBOMOLE version 6.5.67 Energy was converged up to 10-6 Ha using the finest available integration grid ‘M5’. All structures were fully optimized at the two possible lowest spin multiplicities. In addition, only the lowest energy minima with all real vibrational frequencies were reported and analyzed. This method was validated previously,29 by comparing the results obtained at the PBE-D3(BJ)/def2-TZVP level with experimental measurements of geometric,68 vibrational69 and energetic70,71 properties of the original buckminsterfullerene C60 as well as vibrational frequencies measured69 for the endohedral fullerene Ar@C60. We find that the dispersion-corrected method yields better results, compared with similar non-corrected methods used previously.31 In order to perform the structural analyses of the lowest energy structures of the M@C50 endohedral compounds, the most favorable isomers: 260, 263, 266, 270, and 271; of the hollow C50 fullerene were fully optimized maintaining their symmetries C2, C2, Cs, D3 and D5h, respectively. The potential energy surface (PES) of each endohedral M@C50 (M = group 3 and 4 metals) compound at the two lowest possible spin multiplicities was scanned optimizing the structures of the five isomers with the endohedral species initially displaced 7 ACS Paragon Plus Environment


1 Å off the cage center, along seven nonequivalent directions as well as located at the center of the fullerene. The lowest energy minimum was determined through the comparison of the total energy with the zero-point energy (ZPE) correction of all of the stable structures found. Outputs of single-point calculations carried out with Gaussian 09 D.0172 at the PBED3(BJ)/def2-TZVP level of each system analyzed in its ground state (GS) were used to obtain Hirshfeld charges with the wave function analysis program Multiwfn 3.3.7.73 Furthermore, the Gaussview 5.0 program74 was used to obtain from these data the highest occupied molecular orbitals (HOMOs), lowest unoccupied molecular orbitals (LUMOs), and electrostatic potential (ESP) maps on isosurfaces with 0.01 a.u. of electron density for the ESP and 0.02 for frontier orbitals. Splitting among alpha “α” and beta “β” orbitals was indicated when pertinent. In order to determine the HOMO-LUMO gap for all these spinunrestricted calculations, the HOMO-LUMO gap was calculated as the minimum energy gap among (HOMOα, HOMOβ) and the levels (LUMOα, LUMOβ). In addition, the aromaticity indices NICS(0)iso were calculated at the centroid of five nonequivalent relevant rings on the carbon cage, the five closest to the endohedral atom M, of all M@C50 compounds and the corresponding C50 isomers as neutral species as well as trianions and tetraanions. These indices were calculated using the GIAO/PBE-D3(BJ)/def2-TZVP method as implemented in the Gaussian 09 D.01 code, for obtaining the isotropic component of the NMR shielding tensor. The ZPE-corrected binding energy (BEZPE) of each M@C50 was obtained using the equation BEZPE = EZPE (M@C50) – E (M) – EZPE (C50), where E (M) is the energy of the endohedral species with M in its atomic ground state, EZPE (C50) the ZPE-corrected energy of the corresponding cage in its ground state and EZPE (M@C50) the ZPE-corrected energy of the fully optimized endohedral compound. Moreover, vertical ionization energies (VIEs) and vertical electron affinities (VEAs) were obtained for each M@C50 in its ground state and in the three lowest energy C50 isomers. In order to deepen the understanding of the nature of the metal-cage bond, further bonding analysis was based on the ETS-NOCV extension of the Energy Decomposition Analyses (EDA) on the Morokuma-Ziegler framework,75 which is a combination of both ETS76–78 8 ACS Paragon Plus Environment

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and NOCV schemes.79,80 For our analysis, each system was conveniently divided into two main fragments corresponding to the C50 cage and the respective metal center. The ETSNOCV analyses were performed using scalar relativistic DFT methods employing the ADF code81 with all-electron triple- Slater basis sets including double-polarization functions (STO-TZ2P). The Perdew-Burke-Ernzerhof63,64 was used within the GGA. The pairwise correction of Grimme66 (DFT-D3) was included to incorporate the dispersion effects related to London and van der Waals forces. Relativistic effects were incorporated through the ZORA Hamiltonian.82 In order to elucidate if the selected 5 isomers of fullerene C50 proposed as cages (260, 263, 266, 270, and 271) remain among the lowest energy states for the charged fullerenes C503and C504-, and thus, being representative cages for evaluation of endohedral fullerene species, all 271 isomers for those species were optimized with a smaller basis set def2-SVP, fine integration grid ‘M3’ and energy convergence criterion of 10-6 Hartree. The two lowest possible spin multiplicity states were taken into consideration. According to the relative energies ΔE reported in Table S1, the isomers initially proposed remain as the lowest energy states for trianion C503- as well as tetraanion C504-. The lowest energy states for the 5 neutral cages proposed are found ranging from the ground state, the isomer D3 (270) in singlet state, and the isomer C2 (260) in singlet state, 22.73 kcal/mol higher in energy. In case of the trianion, the ground state is the isomer D5h (271) and the other selected cages are found below 15.78 kcal/mol, calculated for the isomer C2 (260) in doublet state. Similarly, the low-lying states for the tetraanion C504- are attributed to the 5 cages proposed. In this case, the ground state for the tetraanion is the isomer D5h (271) in triplet state and the other cages are found below 8.23 kcal/mol, calculated for isomer C2 (263) in singlet state. All of the above is in agreement with previous studies

48,53–55.

In addition, those

calculations denote how isomers 260, 263, 266, 270, and 271 are suitable to be proposed as cages for EMFs containing group 3 and 4 metals, because they are favorable cage arrangements when extra-electrons are introduced upon metal encapsulation.28 Thus, all the following results were obtained considering only these carbon cages. Also, all the relative energies ΔEZPE were obtained with ZPE-corrections, and the PBE-D3(BJ)/def2-TZVP dispersion-corrected DFT level was used in most calculations. 9 ACS Paragon Plus Environment


3. RESULTS AND DISCUSSION 3.1. The C50 Fullerene. Neutral and Charged Species. Table 1 summarizes the main properties of the four lowest energy isomers of neutral fullerene C50 and three in case of the tri- an tetra- anions C503-,4-, which simulates the charge gained by the inclusion of endohedral group 3 and 4 elements in the hollow structure. In agreement with previous studies,48,53–55 isomer D3 (270) in the singlet spin state is found to be the lowest energy isomer for neutral C50. Next higher in energy is isomer D5h (271), in singlet and triplet states, with energy differences calculated as 3.5 and 6.1 kcal/mol, respectively (Table 1). Next higher in energy at 7.4 kcal/mol, is isomer Cs (266) in the singlet spin state. These relative energies can be rationalized by the type of fused pentagon patterns present in each isomer, since the smallest fullerene following the isolatedpentagon-rule (IPR) is C60. Thus, the most stable C50 isomer, D3 (270), has only DFP units around its equatorial region. The next higher energy isomer, namely D5h (271), in addition to DFPs also has a couple of IP units. Finally, isomer Cs (266), besides having an IP and DFPs, exhibits a TSFP unit. Thus, each new type of violation of the isolated pentagon rule destabilizes the carbon cage. However, all those four low-lying states are within a range of 7.4 kcal/mol (Table 1). The HOMO-LUMO gap for C50 has been measured by XPS experiments,83 obtaining a value around 1 eV. This is in agreement with the predicted HOMO-LUMO gap for the ground state of 1.348 eV at the PBE-D3(BJ)/def2-TZVP level (Table 1). Other isomers show considerably smaller gaps (Table 1). In addition, our calculation agrees better with the experimental measurement than the 2.27 eV calculated by Lu, et al.,48 at the B3LYP/631G(d) level.

Table 1. Properties of the four lowest energy states of neutral C50 isomers and of the three lowest energy levels for the charged C503- and C504- anions: Isomer, symmetry, charge, multiplicity M, ZPE-corrected energy difference ΔEZPE (Relative to the lowest energy system), HOMO-LUMO Gap, vertical ionization energy (VIE) and vertical electron affinity (VEA). Values calculated at the PBE-D3(BJ)/def2-TZVP Level. 10 ACS Paragon Plus Environment

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ΔEZPE

HOMO-LUMO

VIE

VEA

(kcal/mol)

Gap (eV)

(eV)

(eV)

1

0.0

1.348

7.662

-2.885

0

1

3.5

0.447

7.056

-3.336

D5h

0

3

6.1

0.184

-

-

(266)

Cs

0

1

7.4

0.943

7.279

-3.067

(271)

D5h

-3

2

0.0

0.100

(266)

Cs

-3

2

7.2

0.186

(270)

D3

-3

2

12.9

0.123

(271)

D5h

-4

3

0.0

0.196

(266)

Cs

-4

1

2.8

0.528

(271)

D5h

-4

1

6.9

0.580

Isomer

Symm

Q

M

(270)

D3

0

(271)

D5h

(271)

The electron affinity of C50 has been measured as -3.35 eV.83 This disagrees with the VEA calculated for isomer D3 (270) of -2.885 eV, but agrees very well with the calculated value of -3.336 eV for isomer D5h (271) (Table 1). It thus appears possible that both isomers are observed in those experiments, owing to their small energy difference. Similar VEA calculations for isomers D3 (270) and D5h (271) were reported previously at the B3LYP/6-31G(d) level, obtaining -2.97 and -3.40 eV, respectively.48 In addition, the VEA of -3.067 eV for the C50 isomer Cs (266) is higher than that of the ground state (Table 1).The vertical ionization energies exhibit behavior opposite to that of the VEAs. Thus the highest VIE of 7.662 eV is found for isomer D3 (270), followed by that of 7.279 eV for structure Cs (266), and finally by 7.056 eV for isomer D5h (271) (Table 1). Low-energy isomers for the fullerene anions C50q- (q = 3, 4) were analyzed in order to compare their properties with those found for the endohedral metallofullerenes described as Mq+@C50q- (q = 3, 4). For the trianion C503-, the isomer ordering changes dramatically with the doublet spin state isomer D5h (271) as the ground state. The next higher energy isomers for C503- are doublet Cs (266) and doublet D3 (270) with energies of 7.2 and 12.9 kcal/mol, respectively, relative to the ground state (Table 1). In contrast, the HOMO-LUMO gap of

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0.100 eV calculated for the ground state is smaller than those calculated for other low energy states (Table 1). For the tetraanionic C504- species, the previous order in the geometry preference is maintained. Thus isomer D5h (271) in a triplet state is the ground state followed by singlet Cs (266) and singlet D5h (271), with energies of 2.8 and 6.9 kcal/mol, respectively, relative to the ground state. The energy difference between the ground state and isomer C504--Cs (266), of about 1.6 kcal/mol, found by Mulet-Gas and coworkers28 at the BP86/ZORA/TZP level is even smaller than the one found by our calculations. Similarly to the trianion C503-, the calculated HOMO-LUMO gap of 0.196 eV for the ground state of the tetraanion C504- is the smallest among all of the low-energy states reported in Table 1. Thus, only neutral C50– D3 (270) isomer has a HOMO-LUMO gap of about 1 eV, among all low-lying isomers, neutral and charged. Moreover, that relatively large HOMO-LUMO gap can be attributed to the electronic shell-closing achieved by fulfilling the Hirsch’s rule 2(N+1)2 with 50 π electrons (with N = 4).40,60 The trianion C503- as well as the tetraanion C504- do not fulfill the magic numbers given by Hirsch’s rule, having 53 and 54 π electrons, respectively. In consequence, electronic shells are not fully closed and the occupied orbitals cannot be stabilized enough to ensure a sizable frontier orbital energy gap.


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C503--Cs (266)

C504--Cs (266)

Hirshfeld

C50-Cs (266)

0.011

-0.103

-0.037

-0.134

-0.050

0.025

0.080

-0.320

-0.270

-0.432

-0.400

ESP

-0.016

C503--D5h (271)

C504--D5h (271)

Hirshfeld

C50-D5h (271)

-0.006

0.005

-0.102

-0.044

-0.126

-0.066

0.025

0.080

-0.320

-0.270

-0.432

-0.400

ESP

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2. Hirshfeld charge distributions and electrostatic potential maps of C50q- (q = 0, 3 and 4). The ESP, mapped on isosurfaces of 0.01 a.u. of electron density, obtained at the PBE-D3(BJ)/def2-TZVP level.



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Next, we consider the isomers D5h (271) and Cs (266) since both are representative low energy structures found for charged fullerenes C50q- (q = 3, 4), and the most comparable to the endohedral compounds of interest. The Hirshfeld charge distributions show that the most positive atoms in the neutral D5h (271) and Cs (266) isomers are located in the fused pentagonal rings, the DFP and TSFP units (Figure 2). In addition, the calculated ESP maps show (Figure 2) that the electrostatic potential around DFPs and TSFPs is higher than that around other carbon atoms. As proven in other studies, these regions are the most amenable to

accept

incoming

electrons

upon

formation

of

anions

or

endohedral

compounds.28,30,31,31,32,84 In addition, fused pentagons in non-IPR fullerenes have been shown extensively as the most reactive sites as well as probable sites for metal coordination upon formation of endohedral compounds.28,30,31,31,32,84 The first assumption is confirmed by the charge distributions and ESP maps calculated for the tri- and tetra-anions C50q- (q = 3, 4) displayed in Figure 2. The most negative charges as well as the lowest ESP regions are obtained at the DFPs and TSFPs. In addition, that accumulation of charge is larger for the tetra-anion than for the tri-anion (Figure 2).


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Figure 3. Frontier orbitals HOMO, LUMO and LUMO+1 of neutral hollow fullerene C50, isomers (266) and (271), which form the cages of the M@C50 compounds. Isosurfaces, of 0.02 a.u. of electron density, obtained at the PBE-D3(BJ)/def2-TZVP level. The frontier molecular orbitals of neutral isomers Cs (266) and D5h (271), later found to form the cages of the endohedral compounds M@C50 (M = groups 3 and 4), are displayed in Figure 3. The HOMO, LUMO and LUMO + 1 of both isomers mainly have π bonding orbitals on the whole fullerene cage, thereby accounting for their relative stabilities. Moreover, all orbitals analyzed for both isomers, except for the LUMO of isomer D5h (271), have p orbitals involving some DFP and TSFP units. Thus, those orbitals are available to bond to the endohedral metal atom. In accord with these observations fused pentagons are expected to be the most suitable sites to bond with metal atoms. In addition, the frontier orbitals obtained for the anionic species C503- and C504- match perfectly with the filling of the previous orbitals with 3 and 4 electrons, respectively, following Hund’s rules (Figure 4). In addition, the tri- and tetra-anions of isomer Cs (266) have larger HOMOLUMO gaps, calculated as 0.186 and 0.528 eV, than those found for their respective ground states (Table 1). As a result, the tri- and tetra-anions of C50–Cs (266) are expected to be less 15 ACS Paragon Plus Environment


reactive than the most stable isomers despite the higher energies of these structures relative to the corresponding ground states.

Figure 4. Frontier Orbitals HOMO-1, HOMO and LUMO of trianion C503-, isomers (266) and (271), and tetraanion C504--Cs (266), the most comparable to the M@C50 compounds. Alpha and beta orbitals are indicated. Isosurfaces, of 0.02 a.u. of electron density, obtained at the PBE-D3(BJ)/def2-TZVP level. 3.2. Endohedral M@C50 Compounds. 3.2.1. Geometrical, Binding, and Stability Properties. Next, we focus on neutral endohedral compounds of group 3 (Sc, Y and La) and group 4 (Ti, Zr and Hf) metals encapsulated inside C50 fullerene. Structural relaxations account for the five low-lying C50 isomers: 260, 263, 266, 270, and 271, with the M atom located at several positions, as stated previously in the computational details. In addition, the two lowest possible spin multiplicities were evaluated. Table 2 summarizes the four low-energy states obtained for each M@C50 compound and their energies ΔEZPE relative to the ground state.


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Table 2. Properties of the four lowest energy isomers of M@C50 (M = group 3 and 4 metals): Cage, symmetry, multiplicity M, bonding site of M atom, ZPE-corrected energy difference ΔEZPE (Relative to the lowest energy System) and HOMO-LUMO Gap. Values calculated at the PBE-D3(BJ)/def2-TZVP Level. M@C50

Sc@C50

Y@C50

La@C50

Ti@C50

Zr@C50

Hf@C50

Bonding

ΔEZPE

Site

(kcal·mol-1)

2

TSFP

0.0

C2v

2

DFP

0.3

C2 (260)

C1

2

TSFP

7.0

Cs (266)

Cs

4

TSFP

20.5

D5h (271)

C2v

2

DFP

0.0

Cs (266)

Cs

2

TSFP

3.5

Cs (266)

Cs

2

DFP

6.2

D5h (271)

C2v

4

DFP

30.8

D5h (271)

C2v

2

DFP

0.0

D5h (271)

C2v

2

IP

6.5

Cs (266)

Cs

2

DFP

8.5

D5h (271)

C2v

4

DFP

31.4

Cs (266)

Cs

1

TSFP

0.0

Cs (266)

Cs

3

TSFP

3.3

Cs (266)

Cs

1

DFP

5.1

D3 (270)

C1

1

DFP

7.2

Cs (266)

Cs

1

TSFP

0.0

Cs (266)

Cs

1

DFP

0.4

D3 (270)

C1

1

DFP

2.6

Cs (266)

Cs

3

TSFP

3.0

Cs (266)

Cs

1

TSFP

0.0

Cs (266)

Cs

1

DFP

1.9

C2 (260)

C1

1

TSFP

2.1

Cs (266)

Cs

3

TSFP

2.7

Cage

Symm

M

Cs (266)

Cs

D5h (271)



This data clearly indicates that the most energetically favorable cages to form the endohedral compounds M@C50, regardless of the metal encapsulated, are isomers Cs (266) and D5h (271) (Table 2). Ground states of all M@C50 compounds are found to remain in the lowest spin state possible (Table 2), with metal atoms bonded to fused pentagonal rings, the DFP and TSFP units (Table 2), see Figure 5 for two representative structures. Compounds M@C50 (M = Sc and group 4) have the metal atom coordinated to the unique TSFP unit present in the Cs (266) cage. However, in the case of Sc@C50, its ground state is followed very closely by the (271) cage, by only 0.3 kcal/mol of energy difference (Table 2). The other compounds with cage (266), enclosing group 4 metals, are not competing as closely with other cages as the Sc@C50. But the TSFP unit, as the preferential region to bond with the metal, is energetically close to the DFP unit. The extreme case which can be mentioned is found for Zr@C50, where the metal bond to the TSFP is more favorable than the DFP unit only by 0.4 kcal/mol (Table 2). After structural relaxation, the point group Cs is maintained (Table 2). The remaining M@C50 (M = Y, La) compounds, bond the metal species to the DFP units of the (271) cage. For these compounds, the point group is reduced to C2v (Table 2). In a similar way, the structures with cage (266) are closer in energy to their respective ground state than others (Table 2). But, the energy difference is considerably larger than those previously discussed. Calculated as 3.5 and 8.5 kcal/mol for Y@C50 and La@C50, respectively. Regarding structure, due to the lack of experimental information on the structures of small EMFs, the most direct comparison can be done with the EMF derivatives of M@C82─C2v(82) with adamantylidene (Ad) enclosing group 3 atoms (Sc, Y, and La).85–87 However, the structural information, experimentally determined, about EMFs containing group 4 elements is scarce. In this sense, titanium carbide88 and titanium-scandium cluster fullerenes89 could be the most relevant in comparison with the information provided for smaller EMFs.37 For both groups, the metal-carbon bond length is found to increase in relation to the atomic number of the endohedral atom (Table 3). This behavior can be rationalized in terms of the ionic radii of the encapsulated metals M3+,4+, which increases as we go down in a group. As previously shown in smaller EMFs,29–31 the increases of the metal-carbon bond length is related to the increases of its ionic character. In contrast, the most off-center displaced Δr species are expected to interact more covalently than the 18 ACS Paragon Plus Environment

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others. Consequently, for each group the smallest off-center displacements Δr of the M atom are found for La@C50 (0.670 Å) and Hf@C50 (1.212 Å). Similarly, the largest M–C bond lengths are obtained with those atoms, calculated as 2.662 Å and 2.194 Å, for La@C50 and Hf@C50, respectively, (Figure 5) since they have the largest ionic radii. The La-C bond length (2.662 Å, Table 3) is almost equivalent to that measured by single crystal X-ray diffraction in La@C82─C2v(9)(Ad), estimated as 2.658 Å.85 In contrast, the largest off-center displacements were found for the lighter endohedral species, Sc@C50 (1.390 Å) and Ti@C50 (1.566 Å). In consequence, both compounds have the shortest metal-cage bond lengths (Table 3), calculated as 2.219 and 2.086 Å for Sc@C50 and Ti@C50, respectively. Also , the Sc-C bond length obtained for Sc@C50 can be directly compared to the 2.323 Å experimentally determined for Sc@C82─C2v(9)(Ad).87 That similarity among the metalcarbon bond lengths of the small EMFs and the larger species is also found for the Y@C50. In that case, the calculated 2.453 Å matches very well with the Y-C bond length, of about 2.475 Å, measured in Y@C82-C2v(9)(Ad).86

Figure 5. Ground-state structures of La@C50 and Hf@C50, with cages (271) and (266), respectively. Relevant metal-carbon bond lengths are indicated. Geometries optimized at the PBE-D3(BJ)/def2-TZVP level. On the other hand, for each M@C50 compound, the structures energetically closest to the ground state are found in a narrow energy range, e. g. from 0.3 to 6.5 kcal/mol, estimated for Sc@C50–D5h (271) and La@C50–D5h (271), respectively. Relative abundances as a function of the number of carbon atoms of several experimentally obtained small EMFs 19 ACS Paragon Plus Environment


have been recently reported by Dunk et al.28 In particular, endohedral compounds encapsulating Sc, Y and La atoms are most abundant for the C44, C50, and C60 fullerene cages. The abundance follows a clear pattern, with M@C44 compounds being the most abundant, followed by M@C50, and finally M@C60. Binding energies for M@C44 (M= group 3, 4) compounds have been recently calculated at the same level of theory used in the present work.30 In this connection, the binding energy of M@C44 (Sc, Y and La) lies in a narrow range, from -6.293 to -6.447 eV.30 These values are in agreement with their higher abundances. In addition, calculations reported in Table 3 show that M@C50 (Sc, Y and La) have slightly smaller metal–cage binding energies. The BEZPE for Sc@C50 is estimated at 5.506 eV (Table 3). In addition, BEZPE values calculated for Y@C50 and La@C50 are -5.464 and -5.835 eV, respectively (Table 3). This decrease in the binding energy is directly related to the decrease in the experimentally observed abundances. Moreover, the increase in the binding energy from Sc@C50 to La@C50 (Figure S1), is similar to the behavior shown by smaller fullerenes containing group 3 metals,29,30 which can be attributed to the decrease in the ionization energy along group 3 (Figure S2).90 The slight increase in the BEZPE found from Sc@C50 to Y@C50 can be attributed to the different carbon cage stabilized for each compound, namely, isomers (266) and (271), respectively. The endohedral compounds M@C50 (M = group 4) are expected to be obtained in large amounts, since their metal–cage binding energies are comparable to those found for group 3 M@C50 endohedral fullerenes (Table 3). The binding energies for the group 4 M@C50 derivatives exhibit a wider range than those for the group 3 metal derivatives, from Hf@C50 (-5.149 eV) to Zr@C50 (-5.821 eV). The value obtained for Ti@C50 (-5.247 eV) agrees well with the previous estimation of -5.56 eV, obtained by Dunk et al.27 In addition, the BEZPE values calculated for M@C50 (M = group 4) are lower than those reported previously for C44 cages, for which Ti@C44 has the lowest BEZPE of -6.070 eV and Zr@C44 has the largest BEZPE of -7.046 eV.30 Thus, the endohedral M@C50 (M = group 4) compounds are suggested to be available in significant amounts, since their stabilization upon metal encapsulation is similar to that of the experimentally characterized endohedral metallofullerenes derived from the C44 cage. As in the previous group, the BEZPE increasing from Ti@C50 to Zr@C50 and decreasing from Zr@C50 to Hf@C50 (Figure S1) can be


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related to the behavior of the ionization energy of the encapsulated species (Figure S2). Thus, lower ionization energies yield higher metal-cage binding energies. Table 3. Properties of the M@C50 endohedral compounds in the ground state: ZPEcorrected binding energy (BEZPE), vertical ionization energy (VIE), vertical electron affinity (VEA), off-center displacement (Δr) of M, shortest M−C bond length, Hirshfeld charge at M atom, and HOMO–LUMO Gap. Values calculated at the PBED3(BJ)/def2-TZVP level.

M@C50

BEZPE

VIE

VEA

Δr

(eV)

(eV)

(eV)

(Å)

M-C Bond length (Å)

Hirshfeld charge

HOMOLUMO Gap (eV)

Sc@C50

-5.506 6.102 -2.612

1.390

2.219

0.402

0.200

Y@C50

-5.464 5.814 -2.355

0.996

2.453

0.529

0.180

La@C50 -5.835 5.837 -2.393

0.670

2.662

0.634

0.175

Ti@C50

-5.247 6.230 -2.606

1.566

2.086

0.376

0.362

Zr@C50 -5.821 6.147 -2.521

1.324

2.192

0.509

0.360

Hf@C50 -5.149 6.142 -2.521

1.212

2.194

0.621

0.356

Regarding ionization energies, the VIE behaves slightly differently for each group (Table 3). For the group 3 metals, the lowest VIE of 5.814 eV is obtained for Y@C50, closely followed by 5.837 eV for La@C50, and finally 6.102 eV for Sc@C50. The VEAs show a similar pattern (Table 3). Thus the VEA of -2.355 eV for Y@C50 is followed by -2.393 eV for La@C50, and finally -2.612 eV for Sc@C50. Moreover, all VIEs of M@C50 (M = group 3) are below the values obtained for their C44 analogues,30 and their respective VEAs are above those calculated for the corresponding M@C44 compounds.30 In consequence, the larger species can be easily ionized. In contrast, the group 4 M@C50 compounds exhibit a simpler behavior. Their VIEs as well as their VEAs decrease upon increasing atomic number of the encapsulated species. Thus Ti@C50 has the highest vertical ionization potential, calculated as 6.230 eV (Table 3). This result is comparable to the value below 6.40 eV, obtained by Dunk et al.,27 at the 21 ACS Paragon Plus Environment


BP86/TZVP level of theory. The corresponding heavier group 4 metallofullerenes, namely Zr@C50 and Hf@C50, have similar VIEs, calculated as 6.147 and 6.142 eV, respectively. Such a similarity between VIEs of zirconium- and hafnium-containing EMFs has been reported previously for the M@C44 compounds.30 In the same way, the VEA decreases from -2.606 eV for Ti@C50 to -2.521 eV for Zr@C50 and Hf@C50 (Table 3). As in the previous case, the VEAs calculated for M@C44 (M = Zr, Hf) are essentially equal.30 In comparison, the VIEs calculated for the smaller M@C44 (M = group 4) endohedral compounds lie above those obtained for M@C50 (M = group 4) while their VEAs show the opposite behavior.30 Thus, M@C50 appears to be more ionizable in comparison to its M@C44 counterparts. 3.2.2. Charge Distributions and Frontier Orbital Analysis. Figure 6 illustrates Hirshfeld charges calculated on all M@C50 compounds. The charge distributions obtained for the EMFs are easily observed to resemble those obtained for the tri- and tetra- anions of C50, as shown in Figure 2. In particular, the M@C50 (M = Sc, group 4) compounds show that the charge donated from the endohedral metal to the carbon cage is accumulated preferentially in the TSFP and IP units of the Cs (266) fullerene, which are the closest positively charged carbon atoms. Similarly, the charges on the M@C50 (M = Y, La) compounds are comparable to those obtained for the C503-–D5h (271) fullerene (Figure 2) with all DFP units negatively charged and with some of the closest carbon atoms positively charged. Moreover, the ESP maps shown in Figure 6 agree with the charge distributions as well as with those obtained for the charged cages C503-,4- (Figure 2), with the lowest ESP obtained around the fused pentagonal rings. In addition, the resulting ESP values for the M@C50 (M = Sc, group 4) compounds around the TSFP unit where the metal atom is located result from the effective screening of the positively charged core by the negatively charged cage (Figure 6).


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Figure 6. Hirshfeld charge distributions and electrostatic potential maps of M@C50 (M = group 3 and 4 metals). The ESP, mapped on isosurfaces of 0.01 a.u. of electron density, obtained at the PBE-D3(BJ)/def2-TZVP level. 23 ACS Paragon Plus Environment


For the group 3 and 4 EMFs, the charge donated by the encapsulated atom increases from the lightest to heaviest species (Table 3). For the M@C50 (M = group 3) compounds, the endohedral metal M donates from 0.402 e in Sc@C50 to 0.634 e in La@C50. Similarly, for the M@C50 (M = group 4) compounds, titanium donates the lowest charge of 0.376 e while Hf donates the highest charge of 0.621 e (Table 3). This behavior can be easily explained by the decrease in the electronegativity of the encapsulated species along each group. The ESP maps displayed in Figure 6 clearly support the increase on the charge donated to the cage, showing larger regions with lower ESP values upon moving down in the group (Figure 6). Thus, the metal–cage interaction in a group becomes more ionic upon increasing the atomic number of the encaged species. This allows for the formation of the ionic compounds Mq+@C50q- (q = 3, 4) with encapsulated metals M of groups 3 and 4. All of the above is consistent with the oxidation states M3+@C2n3- determined experimentally by XPS for large EMFs (n ≥ 60) containing lanthanum and yttrium.41 The inhomogeneous charge distribution on the carbon cages (Figure 6) can be explained by the different types of IPR violations found in these structures.91 As initially formulated by Slanina and coworkers,92 the fused pentagonal units can be stabilized through gaining charges. That is explained by means of the conventional Hückel rule, since a DFP unit with two additional electrons, counting 10 π electrons, becomes aromatic and more stable.92 That assumption can be applicable to multiply charged non-IPR cages, in which the additional electrons are accumulated in the fused pentagonal units, leaving the carbon atoms of the non pentagonal rings positively charged. Thus, the accumulation of charge in the atoms of the multiple fused pentagonal rings (Figure 6) is a consequence of their need to gain more electrons to enhance their stabilities. Conversely, hexagonal rings tend to remain with positive charges since they do not need additional charges. The frontier orbitals HOMO-1, HOMO and LUMO of M@C50 (M = groups 3 and 4 elements) shown in Figure 7 can be easily compared with those obtained for the charged C50 fullerene (Figure 4). In general, all of them are non-degenerate and show p and π bonding orbitals over the whole cage. Scandium and the group 4 metals share a common C50–Cs (266) cage, exhibiting molecular orbitals fully comparable to those found for triand tetra- anions of that cage (Figure 7), with slight changes around the TSFP unit bonded 24 ACS Paragon Plus Environment

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to the encapsulated metal atom. For all of the group 4 metal M@C50 compounds, the HOMO-1 shows two σ bonding orbitals which emerge from the overlap of p orbitals on the fullerene cage and the dxz orbital of the metal. Similarly, the HOMO and LUMO show multiple σ bonding orbitals owing to the overlap of p carbon orbitals with dz2 and dxy orbitals of the endohedral metal, respectively. For Sc@C50 HOMOα-1 and HOMOβ, resemble the HOMO-1 found in the group 4 compounds. Similarly, whereas LUMOα is fully comparable to LUMO of the previous compounds, HOMOα and LUMOβ match HOMO. HOMOβ-1 shows only π bonding orbitals on the whole fullerene surface, with no contributions from the metal center. Thus, the oxidation states Sc3+@C503- and M3+@C504(M = group 4) can be assigned based on formal transference of electrons from the metal to the cage.

Figure 7. Frontier orbitals HOMO-1, HOMO and of M@C50 (M = Sc, La, Ti and Hf). Alpha and beta orbitals are indicated. Isosurfaces, of 0.02 a.u. of electron density, obtained at the PBE-D3(BJ)/def2-TZVP level. The orbitals for the remaining compounds, Y@C50 and La@C50, with the C50–D5h (271) cage, (Figure 7) match those obtained for the tri-anion C503-–D5h (271) (Figure 4). HOMOα1 and HOMOβ have two σ bonding orbitals owing to the overlap of p orbitals on the DFP units with the dx2-y2 metal orbitals. Similarly, HOMOα and LUMOβ have σ bonding 25 ACS Paragon Plus Environment


orbitals formed by the overlap with the metal dxy orbital. In addition, LUMOα and HOMOβ-1 do not have contributions from the metal center. All of the above suggests the partially ionic and covalent metal–cage interaction in all compounds, owing to the formation of several bonding orbitals and metal electrons transferred to the cage. Finally, the calculated HOMO–LUMO gap decreases (Table 3) upon descending on group 3. Sc@C50 (0.200 eV) has the largest gap of its group, followed by Y@C50 (0.180 eV) and La@C50 (0.175 eV). All group 4 M@C50 compounds have calculated HOMO–LUMO gap quite similar, ranging from 0.362 (Ti@C50) to 0.356 eV (Hf@C50). In addition, the group 3 metal compounds have smaller HOMO–LUMO gaps relative to those of M@C50 with encapsulated group 4 metals. Such behavior is consistent with the one observed for the hollow cages, where the tri-anions C503-–Cs (266) and C503-–D5h (271) have HOMO–LUMO gaps calculated as 0.186 and 0.100 eV, respectively. These gaps for group 4 are smaller than the one calculated for the tetra-anion C504-–Cs (266), with a calculated HOMO–LUMO gap of 0.527 eV. As reported in several previous works on small EMFs, large HOMO-LUMO gaps can be related to closing electronic shells by fulfilling Hirsch’s rule 2(N+1)2 and the magic numbers associated. Thus, EMFs with 3239,93,94 and 5095 π electrons yield towards stable and aromatic species with large HOMO-LUMO gaps. Since the number of electrons transferred from the endohedral atom to the cage, EMFs M@C50 enclosing group 3 and 4 metals have 53 and 54 π electrons, respectively. None of these EMFs match with the number or π electrons needed to close electron shells and the small HOMO-LUMO gaps point to those unbalanced valence electron counts.96 3.2.3. Metal-Cage Bond Analysis. The formation of M@C50 species discussed above (M = Sc, Y, La, Ti, Zr, and Hf), is further evaluated in terms of the strain, or preparation energy ∆Eprep related to the deformation of the cage, as well as the nature of the metal–cage bond after encapsulation, given by ∆Eint. This leads to total interaction energies (ΔEtot), obtained as the negative of the bond dissociation energies (De), according to: ΔEtot = -De = ΔEprep + ΔEint


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In this equation the ΔEtot quantity considers neutral fragments, and is directly related to the BEZPE, showing similar values. The resulting ΔEtot values are -5.30 (Sc), -5.21 (Y), -5.87 (La), -5.55 (Ti), -5.70 (Zr), and -5.14 eV (Hf). Similarly to the BEZPE, the behavior of ΔEtot in each group (Figure S1) can be related to the ionization energy of the encapsulated species (Figure S2) and, for the increasing from Sc@C50 to Y@C50, to the different cages stabilized. The preparation energy (∆Eprep), exhibits values ranging from 0.58 to 0.49 eV, which are similar to those found for group 3 M@C44 species, and lower than those for group 4 metals encapsulated in C44 fullerene. The nature of the metal–cage bonding as a result of the favorable encapsulation of group 3 and 4 metals in the C50 fullerene discussed above, has been further studied using energy decomposition analysis within the Morokuma-Ziegler scheme.74 In this framework, each EMF is divided into two main fragments, defined conveniently by the C50 cage and the endohedral metal center considered to be neutral. This allows evaluation of the resulting interaction energy in terms of three main components given by: Eint = EPauli + Eelstat + Eorb + Edisp The ΔEelstat term refers to the electrostatic character of the interaction, obtained from each defined fragment in its unperturbed electron density as isolated species (ΨAΨB). The ΔEPauli term accounts for the repulsive interaction between occupied orbitals, obtained from the energy difference after antisymmetrization and renormalization of the overlapped fragment densities (Ψ0 = NÂ{ΨAΨB}). Finally, the stabilizing ΔEorb term is obtained when the densities of the constituent fragments relax into the final molecular orbitals (ΨAB). In addition, the pairwise correction of Grimme65 (DFT-D3) allows us to evaluate the dispersion interaction (ΔEdisp) related to London forces. To overcome basis set superposition error (BSSE), which is less than 2 kcal/mol, the counterpoise method was used. Thus, the character of the interaction can be obtained from the relative strength between the stabilizing terms, which can be of electrostatic, covalent, or noncovalent character according to the relative contributions of the various terms to the overall interaction energy (Eint).



Figure 8. Selected deformation densities from the NOCV-EDA analysis, accounting for the π→d bond in Sc@C50 as the representative structure with the charge flow from red to blue isosurfaces. For the M@C50 structures, Eelstat denotes a slightly electrostatic character (53–51%; Table 4), which increases its contribution going down in the group, in agreement with the discussion above. However, the covalent contribution to the overall interaction has a similar magnitude, owing to the relevant metal–cage charge transfer upon metal encapsulation. However, the ΔEdisp term contributes less than 1% for all of the structures.


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Figure 9. Selected deformation densities from the NOCV-EDA analysis, accounting for the π→d and π →f bonds in La@C50 with the charge flow from red to blue isosurfaces. Further analysis of the bonding scheme resulting from the formation of M@C50, can be studied by dissecting the EOrb quantity into individual bonding contributions using the Natural Orbitals for Chemical Valence extension of the EDA method (EDA-NOCV). This leads to different deformation densities accounting for the individual in- and out-flow of charges from each bond type. In Table 3 and Figure 8, five main contributions to the overall EOrb term are found in the formation of group 3 and 4 M@C50 structures, owing to the 29 ACS Paragon Plus Environment


availability of the (n-1)d shells (d, in short) of Sc, Y, Ti, Zr, and Hf. However, twelve main contributions are obtained for La@C50, resulting for the (n-1)d and (n-2)f shells (f, in short) of La. The five -d deformation densities (1-5), account for the individual -dxy, -dxz, -dyz, -dx2-y2 and -dz2, bonding patterns, which contribute from 14.7% to 9.8% each for the Sc and Y species, amounting to 64.7% and 56.5%, respectively, to the overall EOrb quantity (Figure 8). For the group 4 species, the contribution decreases from Ti to Hf, going from 75.6% to 60.5 %, indicating that the sum of the different -d bonding patterns is more significant for lighter species. For La@C50, besides the five similar deformation densities, seven bonding contributions are found for each -f bonding pattern. Interestingly, the sum of the different -d bonding contribution amounts to 44.3% of the EOrb term, and the sum of the seven deformation densities accounting for -f bonds, to 26.0%. This indicates the relative contributions of both d- and f- metal orbitals in the bonding characteristics for the formation of La@C50 (Figure 9), thereby showing the more significant contributions of the metal d orbitals. Thus the bonding stabilization of Sc, Y, Ti, Zr, and Hf in their M@C50 derivatives, is based on -d interactions, whereas for La@C50, both -d and -f bonding patterns of significance are found. Interestingly, the contribution to the EOrb term from the respective bonding pattern is rather similar to the one found previously for the M@C44 structures,29 where -d deformation densities account for 64.9% (Sc), 55.7% (Y), 74.7% (Ti), 65.5% (Zr), and 61.0% (Hf) counterparts. However, for La@C44, both -d and -f deformation densities are significant, amounting to 41.6% and 29.6%, respectively. Thus, the endohedral bonding resulting from the encapsulation of group 3 and group 4 metals in C44 and C50 cages is similar. Comparable endohedral bonding is also expected to occur in larger cages.


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Table 4. Energy decomposition analysis (EDA) for the interaction between the endohedral atom M and the C50 cage for the M@C50 series (M = Sc, Y, La, Ti, Zr, and Hf). Also, contribution from each bond type to ΔEorb obtained by the NOCV-ETS analysis. All values in eV. Energy Decomposition Analysis Sc@C50

Y@C50

La@C50

Ti@C50

Zr@C50

Hf@C50

ΔEprep

0.52

0.48

0.49

0.56

0.57

0.58

ΔEPauli

37.30

37.37

34.47

42.66

48.44

47.58

ΔEOrb

-21.08

48.9%

-20.17

46.8%

-19.66

48.1%

-24.37

50.0%

-26.92

49.2%

-25.91

48.6%

ΔEelstat -21.99

51.0%

-22.87

53.1%

-21.07

51.6%

-24.33

49.9%

-27.74

50.7%

-27.34

51.3%

ΔEdisp

-0.04

0.1%

-0.02

0.1%

-0.10

0.2%

-0.08

0.2%

-0.04

0.1%

-0.05

0.1%

ΔEint

-5.25

-5.19

-5.86

-5.61

-5.77

-5.22

ΔEtot

-5.30

-5.21

-5.87

-5.55

-5.70

-5.14

0.21

0.26

-0.03

0.37

0.12

0.01

Δ1

-3.11

14.7%

-2.63

13.0%

-1.68

8.5%

-5.43

22.3%

-4.37

16.2%

-3.82

14.7%

Δ2

-3.08

14.6%

-2.38

11.8%

-1.83

9.3%

-3.91

16.0%

-3.71

13.8%

-3.25

12.5%

Δ3

-2.60

12.3%

-2.26

11.2%

-1.84

9.4%

-3.07

12.6%

-3.41

12.7%

-2.98

11.5%

Δ4

-2.52

12.0%

-2.15

10.6%

-1.72

8.8%

-3.05

12.5%

-3.15

11.7%

-2.75

10.6%

Δ5

-2.35

11.1%

-1.98

9.8%

-1.63

8.3%

-2.97

12.2%

-3.31

12.3%

-2.89

11.1%

Sum

-13.65

64.7%

-11.40

56.5%

-8.70

44.3%

-18.43

75.6%

-17.95

66.7%

-15.68

60.5%

Δ6

-1.23

6.2%

Δ7

-0.87

4.4%

Δ8

-0.70

3.6%

Δ9

-0.77

3.9%

Δ10

-0.57

2.9%

Δ11

-0.52

2.7%

Δ12

-0.44

2.3%

Sum

-5.11

26.0%



3.2.4. Aromaticity Analysis. Aromaticity in some hollow fullerenes as well as EMFs can be related to the stability of the whole compound in accordance with previous observations.30,38 For small EMFs, the high stability and abundance shown by the M@C28 (M = group 4) compounds are intimately related to electron transfer from the metal center to the carbon cage.30,38 That electron transfer produces ionic compounds with oxidation states M4+@C284- similar to the M@C50 compounds analyzed in the current study.30,31,38 Also, the properties of the endohedral compounds can be related directly to those found in the corresponding charged fullerenes.30,31,38 In particular, according to the aromaticity index NICS (0)iso, the M@C28 (M = group 4) compounds as well as the tetra-anion C284- are fully aromatic. This is consistent with their 32 π electrons following the 2(N+1)2 rule of spherical aromaticity.39,57,59 In contrast, the stability shown by other small EMFs is not related to aromaticity. For instance, the previously analyzed M@C36 (M = group 3 metals)28 as well as the M@C44 compounds (M = groups 3and 4)29 exhibit several positive (paratropic) NICS(0)iso values calculated at the centroid of their carbon rings, thereby suggesting local antiaromatic or non-aromatic character, similar to C60. Here we analyze the effect in the aromaticity of the M@C50 compounds in the carbon rings surrounding the metal atom bonded to the cage. Table 5 lists NICS(0)iso values calculated at the centroid of five relevant rings of neutral, tri- and tetra- anions of the cages exhibited by the M@C50 compounds analyzed in this work, i.e., C50 fullerene isomers Cs (266) and D5h (271). Neutral C50 fullerene in its ground state, isomer D3 (270), is fully aromatic and fulfills the spherical aromaticity rule with 50 π electrons. It is remarkable that, according to the large negative NICS(0)iso values, isomers Cs (266) and D5h (271) also are fully aromatic in their neutral as well as charged states (Table 5). The unique exception is the pentagonal ring labeled as R3 of the tetra-anion C504–Cs (266) with a NICS(0)iso index of only 0.76 ppm, which is borderline between antiaromatic and non-aromatic character. In most cases, NICS(0)iso indices for the charged C50 species are smaller than those calculated for neutral isomers in equivalent carbon rings, with the notable exception found for isomer C503-–D5h (271) which has larger negative indices. That high aromaticity is consistent with the larger energy gap (7.2 kcal/mol) 32 ACS Paragon Plus Environment

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between isomer D5h (271) and isomer Cs (266), for the tri-anion C503- (Table 1). For the tetra-anion C504-, isomers Cs (266) and D5h (271) are closer in energy (2.8 kcal/mol) as well as their NICS(0)iso indices (Table 5). Table 5. Aromaticity indices NICS(0)iso of the fullerenes C50q- (q = 0, 3, and 4), isomers Cs (266) and D5h (271), calculated at the centroid (gray spheres) of five nonequivalent relevant rings. Also, indices obtained for the compounds M@C50 (M = group 3 and 4 metals) at the centroid of the five nonequivalent rings closest to the endohedral metal. Red spheres represent the generic location of the endohedral atom. NICS(0)iso (ppm)

System

R1

C50 – Cs (266)

-18.48

C503- – Cs (266)

R2

R3

R4

-9.15

-11.92

-16.58

-6.30

-9.81

-1.37

-2.51

-6.85

-9.04

C504- – Cs (266)

-7.92

-2.59

0.76

-3.17

-6.84

C50 – D5h (271)

-10.83

-15.71

-4.55

-11.61

-4.66

C503- – D5h (271)

-43.98

-65.13

-99.13

-36.78

-10.18

C504- – D5h (271)

-10.00

-7.68

-7.35

-6.96

-7.37

Sc@C50 / (266)

-13.16

-21.51

-11.78

-6.53

-8.73

Y@C50 / (271)

16.92

29.60

31.74

76.06

14.90

La@C50 / (271)

-30.69

52.05

38.23

19.02

-18.09

Ti@C50 / (266)

-18.94

-54.25

-7.61

-0.80

-5.26

Zr@C50 / (266)

-30.66

12.37

0.21

-23.14

-10.94


R5


Hf@C50 / (266)

-25.13

-48.21

-40.48

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-37.53

-17.90

The NICS(0)iso indices for the endohedral M@C50 (M = group 3 and 4 elements) compounds exhibit significant differences, due to the interaction of the endohedral atom with the carbon rings around it. Only for Sc@C50 and Hf@C50, the surrounding carbon rings remain fully aromatic according to their large negative NICS(0)iso values calculated for those five relevant carbon rings closest to the metal, as seen in Table 5. Similarly, Ti@C50 shows large negative NICS(0)iso values, but with a value calculated as only -0.80 ppm for the hexagonal ring labeled R4 (Table 5). This small value could suggest nonaromatic character. In contrast, Y@C50 shows large positive NICS(0)iso indices at all the carbon rings around the metal attached to the cage. Those indices indicate fully antiaromatic character on those rings. On the other hand, mixed aromatic-antiaromatic character is found for La@C50 and Zr@C50 owing to the different signs in the NICS(0)iso values calculated for different rings. In this connection, it is important to note that, independently of the their aromatic character, all M@C50 (M = group 3) compounds have been detected experimentally in similar relative abundances,26 and also their metal-cage binding energies are favorable. Thus, even though Y@C50 can be considered an antiaromatic compound, at least locally, it has been experimentally detected in relatively large amounts26 and can be considered as a viable species. In addition, even though the enclosed metal could change the aromatic character on the carbon rings surrounding it, similarly to other small EMFs,28,29 aromaticity does not rule to additional stability. Instead, the metal–cage binding energy remains as a more reliable global stability indicator. This is consistent with the original observation of C60, as a stable species despite its lack of aromaticity.98 4. CONCLUSIONS Dispersion-corrected relativistic density functional methods were used to characterize theoretically for the first time small endohedral metallofullerenes M@C50 encapsulating group 3 and 4 metals. In comparison to the relative abundances measured experimentally for group 3 compounds, the metal-cage binding energy serves as the best indicator of stability of the endohedral compound. The currently experimentally unknown metallofullerenes M@C50 encapsulating group 4 metals are also predicted to be stable. The 34 ACS Paragon Plus Environment

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carbon cages predicted for the M@C50 complexes are different from the ground state of the neutral isolated C50 fullerene. Isomers Cs (266) and D5h (271) are the most energetically favorable cages to host the metals chosen. The triple sequentially fused pentagonal units as well as the double fused pentagonal units of the cages Cs (266) and D5h (271) are the preferred sites to bond to the encapsulated metal. Electrons are transferred from the metal core to the cage, producing ionic compounds with oxidation states Mq+@C50q- (q = 3 and 4). In addition, the properties of the metallofullerenes studied are directly comparable to those found for charged fullerenes C503- and C504-. The charge transferred to the cage as well as the bond ionic character increase for the heavier elements. Even though the tri- and tetraanions of C50 fullerene are mostly fully aromatic, the endohedral M@C50 compounds can exhibit aromatic, antiaromatic, or mixed character in the carbon rings surrounding the endohedral metal. Thus, aromaticity does not play a decisive role in the stabilization of the endohedral compounds, being consistent with the originally observed stability of C60, which is a fully-aromatic species. The bonding pattern found for the metal-cage interaction, exhibits rather similar characteristics to the M@C44 structures, suggesting that our interpretation can be extended to larger endohedral fullerene cages. Thus, M@C50, serves as an appropriate model to further explore the nature of endohedral metal encapsulation in medium and larger sized EMFs species. Supporting Information The relative energy is listed for all of the 271 isomers of fullerene C50, for neutral as well as tri- and tetra- anions. These calculations were obtained at the PBE-D3(BJ)/def2-SVP dispersion-corrected DFT level. In addition, the lowest energy structures of isomers 266 and 271, obtained at the PBE-D3(BJ)/def2-TZVP dispersion-corrected density functional theory level, for the neutral, tri- and tetra- anions of fullerene C50 are provided. The BEZPE, ΔEtot and ionization energies as function of the atomic number are illustrated. The ground state structures for the neutral endohedral metallofullerenes M@C50 (M = group 3 and 4 metals) are detailed as well.



Author Information Corresponding Author *Email: [email protected]. ORCID Alan Miralrio: 0000-0002-7992-3718 Alvaro Muñoz-Castro: 0000-0001-5949-9449 Notes The authors declare no competing financial interest 5. ACKNOWLEDGMENTS We acknowledge the financial support from FONDECYT 1140359. Also we thank the Direccion General de Asuntos del Personal Académico (DGAPA) for A. Miralrio postdoctoral fellowship and for funding this research under Project IN102616.


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Figure 1. The five lowest energy isomers of C50 fullerene with the pentagonal rings in blue. Structures rotated to show the fused pentagonal units. Geometries optimized at the PBE-D3(BJ)/def2-TZVP Level. 111x102mm (300 x 300 DPI)

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Figure 2. Hirshfeld charge distributions and electrostatic potential maps of C50q- (q = 0, 3 and 4). The ESP, mapped on isosurfaces of 0.01 a.u. of electron density, obtained at the PBE-D3(BJ)/def2-TZVP level. 194x271mm (300 x 300 DPI)


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Figure 3. Frontier orbitals HOMO, LUMO and LUMO+1 of neutral hollow fullerene C50, isomers (266) and (271), which form the cages of the M@C50 compounds. Isosurfaces, of 0.02 a.u. of electron density, obtained at the PBE-D3(BJ)/def2-TZVP level. 73x65mm (300 x 300 DPI)



Figure 4. Frontier Orbitals HOMO-1, HOMO and LUMO of trianion C503-, isomers (266) and (271), and

tetraanion C504--Cs (266), the most comparable to the M@C50 compounds. Alpha and beta orbitals are indicated. Isosurfaces, of 0.02 a.u. of electron density, obtained at the PBE-D3(BJ)/def2-TZVP level. 76x36mm (300 x 300 DPI)


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Figure 5. Ground-state structures of La@C50 and Hf@C50, with cages (271) and (266), respectively. Relevant metal-carbon bond lengths are indicated. Geometries optimized at the PBE-D3(BJ)/def2-TZVP level. 44x24mm (300 x 300 DPI)



Figure 6. Hirshfeld charge distributions and electrostatic potential maps of M@C50 (M = group 3 and 4 metals). The ESP, mapped on isosurfaces of 0.01 a.u. of electron density, obtained at the PBE-D3(BJ)/def2TZVP level. 200x287mm (300 x 300 DPI)


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Figure 7. Frontier orbitals HOMO-1, HOMO and of M@C50 (M = Sc, La, Ti and Hf). Alpha and beta orbitals are indicated. Isosurfaces, of 0.02 a.u. of electron density, obtained at the PBE-D3(BJ)/def2-TZVP level. 83x43mm (300 x 300 DPI)



Figure 8. Selected deformation densities from the NOCV-EDA analysis, accounting for the π→d bond in Sc@C50 as representative structure with the charge flow from red to blue isosurfaces. 50x31mm (300 x 300 DPI)


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Figure 9. Selected deformation densities from the NOCV-EDA analysis, accounting for the π→d and π →f bonds in La@C50 with the charge flow from red to blue isosurfaces. 132x125mm (300 x 300 DPI)



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M@C50 as Higher Intermediates Towards Large Endohedral

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