Understanding the stability, bonding nature and chemical reactivity of 3d-substituted heterofullerenes C₅₈TM (TM = Sc–Zn) from DFT studies

Abstract

The stabilities, bonding nature and reactivity of C₅₈TM (TM = Sc–Zn) heterofullerenes are investigated using DFT methods. The [6:6] structure is more stable than the [5:6] isomer for all of the studied heterofullerenes. Among the title heterofullerenes, C₅₈Zn has the largest heat of formation, and shows low thermal stability due to a great expansion deformation of the C₅₈ cage. For open-shell heterofullerenes, the spin densities are localized on the TM atoms, except for C₅₈Sc and C₅₈Cu in which the spin densities are delocalized over the C₅₈ cage. The QTAIM analyses indicate that the TM–C bonds show a partial covalent characteristic. The degree of covalence slightly increases from left to right across the 3d-block of the periodic table. The chemical reactivity of the studied heterofullerenes can be tuned by substituted TM atoms, deduced from frontier molecular orbitals and Fukui function analyses. The Fukui function also shows that the earlier TM-substituted species, C₅₈Ti, C₅₈V, C₅₈Cr and C₅₈Mn, are more active than other heterofullerenes. The adsorption of ethylene molecules on heterofullerenes is investigated to probe the chemical reactivity of the studied heterofullerenes; the fact that earlier TM atoms show greater reactivity than later TM atoms is in excellent agreement with Fukui function predictions. Moreover, the adsorption energies (E_ads) of earlier TM-substituted heterofullerenes are comparable to that of the previously reported C₅₈Ir(C₂H₄) complex.

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Introduction

The heterofullerene molecules¹ in which one or more carbon atoms that form the fullerene carbon cage are replaced by a heteroatom are well known, as are endo- and exohedral fullerenes. So far, many heterofullerenes have successfully been proven to exist by experiments or theoretical predictions. The heteroatoms consist of main-group elements, B,² N,³ O,⁴ etc. and metal atoms, Fe, Co, Ni, Pt, Ir⁵ and so on.

The previous reports mainly paid attention to the heterofullerenes with an even-number of carbon and other atoms, probably due to the fact that the surface atoms in fullerenes and heterofullerenes tend to form three bonds with neighboring atoms. For example, Muhr et al.⁶ reported on the preparation of monoborafullerenes C₅₉B, C₆₉B, and higher homologues by arc evaporation of doped graphite rods in a modified fullerene reactor. The density functional theory (DFT) study⁵ of C₅₉Pt and C₅₉Ir had shown that the metal atoms were found in three coordinate sites on the fullerene surface. Computational studies⁷ of the structures of C₆₉M, where M = Co, Rh, and Ir, indicated that substitution sites at the more highly pyramidalized poles of the fullerene were energetically favored. A range of C₅₉M compounds of group 6–8 metals were predicted by DFT studies reported by Jensen's group⁸ to have sufficient stability for experimental observation. Campanera et al.⁹ have performed a systematic search of the regioisomers of the heterofullerenes C₅₇Pt₂ and C₅₆Pt₂ by means of density functional calculations to find the most stable structures. They found that the deformation of the carbon framework was a general factor for governing the relative stabilities of the regioisomers. Many studies have also been performed for heterofullerenes with an odd-number of atoms, to probe their existence. The ions [C₅₈Pt]⁻ and [C₅₆Pt]⁻ were produced from C₆₀/Pt film upon laser ablation.¹⁰ The DFT calculations showed that the isomer with one Pt atom replacing the C₂ unit at a [6:6] ring junction of fullerene was more stable than the low symmetry isomer with the C₂ unit at a [5:6] ring junction replaced by a metal atom. Liu has systematically investigated the structural and electronic properties of C₅₈X (X = O, S, Se)¹¹ and C₅₈Si, C₅₈Ge¹² heterofullerenes using hybrid DFT functionals. It is noteworthy that the C₅₈Fe heterofullerene⁵ was found experimentally from the photoionization mass spectrum of the C₆₀–Fe cluster. It is direct proof for the existence of 3d-substituted species. Unfortunately, no further theoretical investigations have been carried out to probe into the structures and electronic properties of 3d-block (Sc–Zn) heterofullerenes. Therefore, we see a need for systematic theoretical studies on C₅₈TM (TM = Sc–Zn) heterofullerenes.

In this paper, we will utilize DFT methods to investigate the structures, stability, bonding nature and reactivity of C₅₈TM, where TM is a 3d-block transition metal. The nature of the interaction between the TM and neighboring C atoms is discussed with quantum theory of atoms in molecules (QTAIM) analyses. The chemical reactivities of the title heterofullerenes are discussed with frontier molecular orbitals and Fukui function. The adsorption of ethylene molecules on heterofullerenes is investigated to compare the chemical activity of the studied heterofullerenes.

Computational details

The three-parameter hybrid functional B3LYP,¹³ implemented in G09 program,¹⁴ was used in the geometry optimization and property calculations. The valence basis set CEP-121G¹⁵ and all-electron basis set 6-31G* were adopted to describe the transition-metal and carbon atoms, respectively. Quantum theory of atoms in molecules (QTAIM)¹⁶ topological analyses based on the wavefunction calculated at the B3LYP/6-31G*(CEP-121G) level of theory were performed with the multiwfn 2.6 program.¹⁷ For comparison, the revised PBE functional (revPBE) proposed by Hammer et al.¹⁸ in conjunction with the double numerical basis set augmented with polarization p-function (DNP) as implemented in the Dmol³ program¹⁹ was also utilized to optimize the geometry structures of the studied heterofullerenes. The reactivity of the heterofullerenes was determined by analyzing the interactions of ethylene molecules with heterofullerenes. The structures of ethylene-adsorbed heterofullerenes were optimized at the revPBE/DZP level of theory. Unrestricted methods were utilized for computing the open shell systems. All possible spin multiplicities were considered in geometry optimizations to obtain magnetic properties for the studied heterofullerenes. The condensed Fukui function²⁰ was calculated to predict the local reactivity of heterofullerenes. The geometry parameters of a pure C₆₀ molecule were first obtained to test the reliability of both calculation schemes described above. The bond distances of the C₂ unit at a 6:6 ring (6–6 bond) and a 5:6 ring (5–6 bond) junction of fullerene obtained at the B3LYP/6-31G* level of theory are 1.395 and 1.453 Å, respectively, which is in excellent agreement with the results of revPBE/DZP (1.404 and 1.458 Å for 6–6 and 5–6 bonds, respectively). Both calculated values are in reasonable agreement with previous theoretical results¹¹ and experimental values.²¹ Therefore, we believe that the selected methods are appropriate to describe the heterofullerenes.

Results and discussion

Structures and stabilities

The substitution of heteroatoms in a C₂ dimer in fullerene can form two isomers because there are two different ways that substitution can occur, which is depicted in Fig. 1. When the C₂ unit at a [6:6] ring junction is replaced by metal atoms, one C_2v isomer can be formed; on the other hand, the removal of a C₂ unit at a [5:6] ring junction results in one low-symmetry C_s structure. For reasons of simplicity, [6:6] and [5:6] will represent the C_2v and C_s isomers, respectively, throughout the following discussion. Our calculations show that the [6:6] structure is more stable than the [5:6] isomer for all of the studied heterofullerenes. The relative energies between these structures are in the range of 0.389–1.981 eV, as shown in Table 1. Fig. 2 shows the binding energies (E_b) of the [6:6] and [5:6] structures (detailed values can be found in Table 1) vs. substituted metals. The E_b values of the [6:6] isomers are larger than those of the [5:6] isomers for all studied species, again confirming the greater stability of the [6:6] isomers. From Fig. 2, one can see that the binding energies do not show a strong dependence on the substitution-metal, and are observed at around 6.80 eV from Sc to Cu for the [6:6] isomers. A dramatic drop to 6.64 eV is found for C₅₈Zn, which reveals the lower stability of C₅₈Zn relative to the other species.

Fig. 1 A schematic representation of the different substitution patterns.

Table 1 Binding energies (E_b) of the [5:6] and [6:6] isomers and relative energies (ΔE) between these two isomers calculated with B3LYP/6-31G*(CEP-121G)

	C58Sc	C58Ti	C58V	C58Cr	C58Mn	C58Fe	C58Co	C58Ni	C58Cu	C58Zn
Eb (eV) [6:6]	6.833	6.847	6.830	6.806	6.802	6.818	6.814	6.808	6.795	6.641
Eb (eV) [5:6]	6.826	6.834	6.811	6.794	6.790	6.807	6.806	6.801	6.778	6.607
ΔE (eV)	0.429	0.750	1.145	0.656	0.658	0.671	0.505	0.389	0.957	1.981

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Fig. 2 The binding energies of the [5:6] and [6:6] isomers for the studied C₅₈TM (TM = Sc–Zn) heterofullerenes.

For the [6:6] isomers, the total energies of different spin multiplicities are listed in Table S1 in the ESI.† All of the studied heterofullerenes, except C₅₈Ti, C₅₈Ni and C₅₈Zn, favor open-shell ground states. The spin multiplicities, values of Ŝ² and spin populations of the TM atoms are collated in Table 2 for the open-shell species. The calculated Ŝ² values are around the expected eigenvalues, therefore, the spin-contaminant can be neglected in the spin-polarization systems. For the open-shell species, the unpaired electrons in C₅₈Sc and C₅₈Cu are delocalized over the C atoms, whereas the rest of the heterofullerenes, C₅₈V, C₅₈Cr, C₅₈Mn, C₅₈Fe and C₅₈Co, are characterized by spin densities localized on the TM atoms. In particular, the Cr, Mn and Fe atoms have a large contribution for unpaired electrons.

Table 2 Multiplicities, values of Ŝ², spin population, distances between TM and bound C atoms (d_TM–C), molecular volumes and Hirshfeld charge of TM and bonded C atoms (C_B) for the [6:6] isomer, and the sum of the covalent radii of the isolated TM and C atoms (r_TM + r_C)

	C58Sc	C58Ti	C58V	C58Cr	C58Mn	C58Fe	C58Co	C58Ni	C58Cu	C58Zn
a The optimized TM–C distances at the revPBE/DZP level of theory.
Multiplicities	2	1	2	3	4	5	2	1	2	1
Ŝ^2	0.751	0	0.753	2.169	3.888	6.003	0.938	0	0.750	0
Spin population (TM)	0.020	—	1.188	3.176	4.152	3.584	1.870	0	0.008	0
dTM–C (Å)	2.245	2.130	2.090	2.080	2.055	2.020	1.991	1.929	1.953	2.036
dTM–C (Å)^a	2.284	2.155	2.112	2.079	2.056	2.034	1.994	1.951	1.975	2.048
rTM + rC (Å)	2.21	2.13	2.02	2.04	2.16	2.02	2.03	1.98	2.15	2.08
Volume (Å^3)	639	635	634	631	633	631	629	626	627	656
Q (TM)	0.64	0.63	0.50	0.57	0.34	0.34	0.20	0.12	0.35	0.39
Q (CB)	−0.12	−0.13	−0.10	−0.12	−0.09	−0.08	−0.06	−0.06	−0.09	−0.07

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The optimized TM–C bond lengths of the [6:6] structures listed in Table 2 are in the range of 1.929(Ni–C)–2.245 Å (Sc–C) at the B3LYP/6-31G*(CEP-121G) level of theory. These values are in agreement with the results of the revPBE/DZP scheme which range from 1.951(Ni–C) to 2.284 Å (Sc–C). It is noteworthy that the optimized TM–C distances in the studied heterofullerenes are comparable with the values of Pt and Ir-substituted heterofullerenes (C₅₈Pt, C₅₈Ir)¹⁰ reported previously. For comparison, the sum of the covalent radii of C and TM atoms (r_TM + r_C) are also collated in Table 1. One can see that the distances of the TM–C bonds (d_TM–C) in the studied heterofullerenes are all close to the sum of r_TM + r_C, which implies that TM–C interactions in heterofullerenes show somewhat covalent characteristics. The Hirshfeld charges²² of the TM and bonded C atoms listed in Table 2 show that there is little charge transfer from TM to C atoms. This indicates that the ionic interaction is not preferred for the studied TM–C chemical bonds. We note that the Zn–C bond length of 2.036 Å is comparable with other TM–C bond distances, but the molecular volume of C₅₈Zn (shown in Table 2) is much larger than other studied heterofullerenes. Therefore, the low stability of C₅₈Zn mentioned above is the result of a great expansion deformation of the C₅₈ carbon cage and not the expected weak Zn–C interaction. In fact, one can find that the Zn–C bonding strength is not obviously weaker than other TM–C interactions from the following QTAIM analyses.

The energy levels of the studied heterofullerenes are depicted in Fig. 3; for the sake of comparison, the orbital energy level of C₆₀ is also shown. As expected, the energy level of C₆₀ is obviously discrete due to its high symmetry (I_h). The energy levels in the studied C₅₈TM (TM = Sc–Zn) heterofullerenes are split for the reduction of symmetry from I_h to C_2v. From Fig. 3, we also find that the gaps between the highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO) of the title heterofullerenes are observably smaller than that of C₆₀, indicating that the chemical reactivity can be tuned by substituted TM atoms.

Fig. 3 The energy levels of the [6:6] isomers for C₆₀ and the studied C₅₈TM (TM = Sc–Zn) heterofullerenes. For open-shell species, the energy levels are split in spin-up (α) and spin-down (β) channels.

The HOMO and LUMO isosurfaces of the title heterofullerenes are depicted in Fig. 4 to analyze the chemical reactivity. The corresponding orbital compositions are collated in Table 3. The spatial distributions of the HOMO orbitals of the title heterofullerenes, except for C₅₈V, exhibit similar characteristics. More specifically, the HOMOs predominantly consist of 2p orbitals of the surface carbon atoms. As for C₅₈V, the HOMO arises from the 3d orbital of the V atom and 2p orbitals of the neighboring carbon atoms. The LUMO of C₅₈Sc shows a significant C(2p) orbital contribution. For the LUMO of C₅₈Ti, the electron density is predominantly built from the 3d orbital of the Ti atom. The LUMO of C₅₈V is similar to that of C₅₈Cr, and is built from the 3d orbital and 2p orbitals of neighboring carbon atoms. C₅₈Mn shows a similar spatial distribution of the LUMO to C₅₈Co, with the C(2p) orbital contributions predominant. The LUMOs of C₅₈Fe and C₅₈Cu are almost entirely composed of 2p orbitals of the surface C atoms. C₅₈Ni features an unignorable Ni(3d) contribution to the LUMO. The LUMO of C₅₈Zn is composed of Zn(3d) orbitals and 2p orbitals of the neighboring C atoms. In general, the frontier MOs of the studied 3d-block heterofullerenes show some degree of difference, therefore they may exhibit different chemical reactivities.

Fig. 4 The frontier molecular orbitals of the [6:6] isomers for the studied heterofullerenes.

Table 3 The HOMO and LUMO orbitals composition for the studied [6:6] heterofullerenes

Species	Orbitals	Orbital compositions
C58Sc	HOMO	Sc (3d)	2.4%	C (2p)	86.7%
	LUMO	Sc (3d)	3.9%	C (2p)	88.4%
C58Ti	HOMO	Ti (3d)	4.0%	C (2p)	81.2%
	LUMO	Ti (3d)	65.4%	C (2p)	7.9%
C58V	HOMO	V (3d)	19.3%	C (2p)	49.4%
	LUMO	V (3d)	32.4%	C (2p)	43.5%
C58Cr	HOMO	Cr (3d)	2.4%	C (2p)	90.0%
	LUMO	Cr (3d)	32.0%	C (2p)	34.6%
C58Mn	HOMO	Mn (3d)	1.4%	C (2p)	94.6%
	LUMO	Mn (3d)	3.4%	C (2p)	86.1%
C58Fe	HOMO	Fe (3d)	1.0%	C (2p)	90.8%
	LUMO	Fe (3d)	0.6%	C (2p)	93.2%
C58Co	HOMO	Co (3d)	1.0%	C (2p)	92.3%
	LUMO	Co (3d)	1.9%	C (2p)	87.5%
C58Ni	HOMO	Ni (3d)	0.6%	C (2p)	92.4%
	LUMO	Ni (3d)	13.5%	C (2p)	74.4%
C58Cu	HOMO	Cu (3d)	1.3%	C (2p)	86.7%
	LUMO	Cu (3d)	<0.5%	C (2p)	91.1%
C58Zn	HOMO	Zn (3d)	<0.5%	C (2p)	89.5%
	LUMO	Zn (3d)	7.7%	C (2p)	81.5%

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Nature of TM–C bond

The quantum theory of atoms in molecules (QTAIM)¹⁶ is a powerful theory for characterizing chemical bonding in metal complexes and clusters. In the present work, QTAIM analyses are performed to deduce the TM–C bonding nature in the [6:6] isomers of C₅₈TM (TM = Sc–Zn). Within the QTAIM framework, a critical point (CP) where the gradient of electron density vanishes, allows us to classify atoms and chemical bonding. The molecular graph for the [6:6] isomer of C₅₈TM is depicted in Fig. 5. In the studied heterofullerenes, we first locate 58 attractors, i.e., nuclei shown as cyan balls in Fig. 5. There exist 89 (3, −1) bond critical points (BCP) connecting C–C or C–TM in the fullerene. One ring critical point (RCP) is located in every 5-membered ring or 6-membered ring, with a total of 32 RCPs found as shown in Fig. 5. Moreover, one cage critical point is situated in the cages of the studied heterofullerenes.

Fig. 5 Molecular graphs of the [6:6] isomers for the studied heterofullerenes with sideview (a) and topview (b). The colour scheme identifying critical points is as follows: cyan ball for attractors, blue ball for bond critical points (BCP), red ball for ring critical points (RCP), green ball for cage critical points (CCP).

The topological properties collated in Table 4 allow an analysis of TM–C bonding characteristics in the studied heterofullerenes. According to QTAIM theory, two types of interactions, i.e., shared interactions and closed-shell interactions, can be identified by analyzing the values of electronic charge density (ρ) and their Laplacian (∇²ρ) at critical points. Shared interactions generally correspond to high values of density and negative values of Laplacian, which demonstrates a covalent nature. Closed-shell interaction is characterized by low density and positive values of Laplacian, which is typical of ionic and van der Waals bonding. However, this criterion has been proven not to be sufficient to describe the bonding nature of heavy atoms in previous works.²³ Another property, the total energy density H(r) (defined as the sum of the local kinetic energy density G(r) and the local potential energy density V(r)) proposed by Cremer and Krala²⁴ has proven to be very appropriate for characterizing the degree of covalency of a bond. A negative H(r) indicates a covalent bond. The C–C bonds show a strong covalent nature. We now pay our attention to the bonding characteristics of TM–C bonds. As Fig. 5 shows, there are four BCPs connecting the TM and neighboring C atoms in the [6:6] (C_2v) structures, and the corresponding parameters in Table 4 are similar for the four BCPs for a given species, so one TM–C BCP parameter is listed in Table 4. We can see that all of the TM–C bondings have positive values of Laplacian and negative H(r) values. Therefore, the nature of the TM–C bonds in the studied heterofullerenes can be described as closed-shell interactions with a partially covalent character. The covalent character can also be quantitatively described by the −V(r)/G(r) relationship. The −V(r)/G(r) value is greater than 2 for covalent bonds, smaller than 1 for closed-shell interactions and in the range of 1–2 for partially covalent interactions. The −V(r)/G(r) relationship is generally used to measure the degree of covalency of one chemical bond. The calculated −V(r)/G(r) values are all larger than 1, which indicate that all of the TM–C bonds in the studied heterofullerenes show some degree of covalent character. Based on the values of H(r) and −V(r)/G(r), one can infer that the degree of covalency slightly increases from left to right across the 3d-block of the periodic table. It is noteworthy that the Sc–C bond corresponds to smaller H(r) value and lower −V(r)/G(r) relationship relative to other TM–C bonds. This indicates that the Sc–C bond is weaker than other TM–C bonds, which is also reflected by the long Sc–C bond length and large charge transfer between Sc and the bonded C atoms. Therefore, it is suggested that the Sc–C interaction is ionic in nature. Moreover, we can infer that the Zn–C bond shows an obvious partially covalent character by analyzing the values of H(r) and −V(r)/G(r). Therefore, the low stability of C₅₈Zn stems from the high degree of deformation of the C₅₈ cage and not the weak Zn–C interaction as analyzed in the above section.

Table 4 Topological properties of the (3,−1) critical point of various TM–C bonds in the [6:6] isomers of the title heterofullerenes

Species	BCP	ρ	∇^2ρ	H(r)	−V(r)/G(r)	G(r)/ρ(r)
C58Sc	Sc–C	0.066	0.141	−0.011	1.244	0.707
C58Ti	Ti–C	0.099	0.096	−0.032	1.570	0.566
C58V	V–C	0.104	0.123	−0.032	1.511	0.606
C58Cr	Cr–C	0.100	0.148	−0.030	1.444	0.667
C58Mn	Mn–C	0.100	0.184	−0.030	1.396	0.759
C58Fe	Fe–C	0.108	0.143	−0.038	1.519	0.682
C58Co	Co–C	0.108	0.210	−0.035	1.400	0.808
C58Ni	Ni–C	0.119	0.196	−0.054	1.524	0.860
C58Cu	Cu–C	0.112	0.148	−0.054	1.592	0.811
C58Zn	Zn–C	0.091	0.131	−0.036	1.527	0.756

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Thermal properties and infrared spectra

In order to probe the thermal stability of the [6:6] isomer of C₅₈TM (TM = Sc–Zn), the heats of formation ΔH⁰_f are calculated at the B3LYP/6-31G*(CEP-121G) level of theory. The energy change of the following reaction with zero-point energy (ZPE) correction is considered to estimate the enthalpy changes ΔH_r and heats of formation ΔH⁰_f:

C₆₀ + TM = C₅₈TM + C₂ (1)

The enthalpy change ΔH_r of the above reaction is calculated as follows:

ΔH_r = (E + ZPE)_C58TM + (E + ZPE)_C2 − (E + ZPE)_C60 − E_TM,atom (2)

With the enthalpy change and heats of formation of C₆₀,²⁵ the TM atoms²⁶ and the C₂ (ref. 27) molecule from previous experimental reports, the heats of formation of C₅₈TM can be evaluated with the following equation:

The estimated heats of formation collated in Table 5 are in the range of 718–908 kcal mol⁻¹, and are all larger than that of C₆₀ (609.6 kcal mol⁻¹). Therefore, the thermal stabilities of the studied heterofullerenes are lower than C₆₀. The values for the heats of formation are also depicted in Fig. 6, and one can see that C₅₈Zn, corresponding to the largest heat of formation, possesses the lowest thermal stability among all of the studied heterofullerenes, which is in excellent agreement with binding energy results. Like the trends of binding energies, the heats of formation of other heterofullerenes do not show an evident element dependence. Comparing with previous reports for C₅₈Ge,¹² and C₅₈X (X = O, S, Se)¹¹ heterofullerenes, our studied 3d species, except C₅₈Zn, have lower heats of formation and are more stable.

Table 5 The heats of formation for the [6:6] isomer of the studied C₅₈TM heterofullerenes

	C58Sc	C58Ti	C58V	C58Cr	C58Mn	C58Fe	C58Co	C58Ni	C58Cu	C58Zn
ΔH^0f (kcal mol^−1)	718	725	757	762	740	750	757	767	763	908

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Fig. 6 The heat of formation of the [6:6] isomers for the studied C₅₈TM (TM = Sc–Zn) heterofullerenes.

The infrared (IR) spectra of the studied heterofullerenes were simulated for use in further experimental assignment. Fig. 7 shows the unscaled IR spectra of the heterofullerenes and C₆₀. One can see that C₆₀ only presents four peaks due to its high I_h symmetry. On the other hand, all of the title heterofullerenes show complicated absorption peaks due to the reduction of symmetry from I_h to C_2v. There are two dominant absorption bands, corresponding to 400–600 cm⁻¹ and 1200–1600 cm⁻¹ in the IR spectra of the heterofullerenes. For all of the studied heterofullerenes, some weak IR spectroscopic signals can be found in the range of 800–1000 cm⁻¹, which are assigned to TM–C bond stretches.

Fig. 7 IR spectra of the [6:6] isomers for the studied C₅₈TM (TM = Sc–Zn) heterofullerenes.

Local site reactivity

In this section, the local reactivity of the [6:6] isomers of C₅₈TM (TM = Sc–Zn) heterofullerenes is analyzed by means of Fukui indices²⁸ to predict the local reactivity sites. This method relates the reactivity of one chemical species with respect to nucleophilic/electrophilic attack to the charge density, and is a successful way of measuring the reactivity of regions of molecules and clusters.^29–31 Parr and Yang²⁸ define the Fukui function (FF) as the partial derivative of the electron density with respect to the total number of electrons at a constant potential:

Owing to the discontinuity of the derivative of the above equation, two different Fukui functions can be defined by applying the finite difference approximation:

The f⁺(r) and f⁻(r) Fukui functions measure the reactivity towards nucleophilic and electrophilic attack, respectively. The FF for radical attack, f⁰(r), is simply the average of these two. The condensed Fukui function proposed by Yang²⁰ can be obtained with the following expression:

f⁺_k = q_k(N + 1) − q_k(N) (7)

f⁻_k = q_k(N) − q_k(N − 1) (8)

where q_k is the electronic population of atom k in a certain chemical species. The values of q_k can be calculated from a numerical integration procedure such as Hirshfeld charge.²² In the present work, the Hirshfeld partial scheme is utilized.

The calculated Fukui indices (FI) of TM atoms for the studied heterofullerenes are listed in Table 6, from which one can see that the TM atoms in C₅₈Ti, C₅₈V, C₅₈Cr, C₅₈Fe and C₅₈Zn corresponding to the higher f⁺(r) values favor nucleophilic attack by molecules such as CO. The Ni atom in C₅₈Ni heterofullerenes shows the feasibility of electrophilic attack. The TM sites in C₅₈Sc, C₅₈Mn, C₅₈Co and C₅₈Cu have comparable f⁺(r) and f⁻(r) values, and are favorable toward any chemical attacks. All of the bonded carbons in the studied heterofullerenes show “ambiphilic” characteristics. It is important to note that all of the bonded C atoms have lower FI values relative to the TM atoms, which indicates that the TM atoms are more active than carbon toward chemical attack. Moreover, later 3d TM atoms may be less active than earlier TM atoms which is revealed by their low f⁰(r) values. Fig. 8 shows the radial Fukui function mapped onto an isosurface of the total electron density (isovalue = 0.017 au) for the studied heterofullerenes. One can see that a high density accumulation is found on the TM atom sites. Therefore, the TM atoms possess greater chemical activity than all of the C atoms. By comparing the studied 3d series, earlier TM atoms correspond to a high density accumulation and are more active.

Table 6 The calculated Fukui indices of TM and bonded C atoms (C_B) in the studied C₅₈TM heterofullerenes

	C58Sc	C58Ti	C58V	C58Cr	C58Mn	C58Fe	C58Co	C58Ni	C58Cu	C58Zn
f^−(TM)	0.059	0.057	0.063	0.049	0.064	0.036	0.051	0.067	0.027	0.028
f^+(TM)	0.064	0.152	0.115	0.087	0.064	0.056	0.048	0.045	0.028	0.054
f^0(TM)	0.061	0.105	0.089	0.068	0.064	0.050	0.049	0.056	0.028	0.041
f^−(CB)	0.025	0.019	0.018	0.023	0.024	0.023	0.020	0.027	0.025	0.022
f^+(CB)	0.024	0.018	0.020	0.023	0.021	0.018	0.021	0.021	0.019	0.046
f^0(CB)	0.024	0.019	0.019	0.023	0.023	0.021	0.020	0.024	0.022	0.034

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Fig. 8 Radial Fukui function mapped onto an isosurface of the total electron density (isovalue = 0.017 au) for the studied heterofullerenes.

Experimental evidence for the ability of the Ir and Pt atoms in some heterofullerenes to bind added ligands has been obtained by conducting laser ablation studies in the presence of 2-butene.¹⁰ The [C₅₈Ir(2-butene)]⁻ adduct was observed in the mass spectrum obtained by laser ablation of a C₆₀/Ir(CO)₂ film in a butene atmosphere.¹⁰ In order to compare the chemical reactivity of the title heterofullerenes with C₅₈Ir and C₅₈Pt, the binding of ethylene molecules (to simply model the 2-butene ligand) on the TM atoms of the studied heterofullerenes is investigated. The geometries of C₂H₄-adsorbed heterofullerenes were obtained at the revPBE/DZP level of theory. The adsorption energies (E_ads) are obtained by evaluating the difference of energy between C₅₈TM(C₂H₄) and the free C₅₈TM and C₂H₄ units. By comparing with bare heterofullerenes, adsorption of an ethylene molecule induces slight elongation of the distances between the TM and neighboring C atoms of the fullerene in all of the studied species as the values in Table 7 show, whereas the TM–ethylene bond lengths are obviously longer than TM–C (fullerene) distances. The C–C bonds in ethylene are slightly elongated relative to free ethylene. The adsorption energies listed in Table 7 indicate that earlier TM atoms show greater reactivity than later TM atoms. This result is in excellent agreement with Fukui function predictions. It is noteworthy that the E_ads values for earlier TM-substituted heterofullerenes are very close to the value of the previously reported C₅₈Ir(C₂H₄) complex, which was confirmed by the experimental observation of a peak in the mass spectrum that may be associated with [C₅₈Ir(2-butene)]⁻.

Table 7 The geometry parameters and adsorption energies of ethylene-adsorbed 3d-sustituted heterofullerenes

	C58Sc(C2H4)	C58Ti(C2H4)	C58V(C2H4)	C58Cr(C2H4)	C58Mn(C2H4)
a The distances between the TM and neighboring C atoms of the fullerene.b The distances between the TM and neighboring C atoms of the ethylene.c The C–C bonding lengths of the adsorbed ethylene molecule.
dTM–C (Å)^a	2.294	2.161	2.114	2.078	2.053
dTM–C (Å)^b	2.898	2.683	2.280	2.270	2.360
dC–C (Å)^c	1.349	1.353	1.349	1.358	1.374
Eads (eV)	0.580	0.774	0.688	0.318	0.420

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	C58Fe(C2H4)	C58Co(C2H4)	C58Ni(C2H4)	C58Cu(C2H4)	C58Zn(C2H4)
dTM–C (Å)^a	2.045	2.003	2.015	1.988	2.080
dTM–C (Å)^b	2.401	2.297	2.097	2.760	2.613
dC–C (Å)^c	1.366	1.375	1.419	1.350	1.354
Eads (eV)	0.641	0.189	0.176	0.213	0.390

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Conclusion

In this paper, the structures, thermal stability, bonding nature and reactivity of C₅₈TM (TM = Sc–Zn) heterofullerenes are systemically investigated by using DFT methods. Our calculations show that the [6:6] structure is more stable than the [5:6] isomer for all of the studied heterofullerenes. For open-shell heterofullerenes, the spin densities are localized on the TM atoms except for C₅₈Sc and C₅₈Cu in which the spin densities are delocalized over the C₅₈ cage. The heats of formation are calculated to probe the thermal stability of the heterofullerenes. C₅₈Zn has the largest heat of formation among all of the studied 3d series. The low thermal stability of C₅₈Zn can be explained by the great expansion deformation of the C₅₈ carbon cage. Moreover, the studied 3d heterofullerenes show a higher thermal stability relative to the previously reported C₅₈Ge, C₅₈X (X = O, S, Se) heterofullerenes. The HOMO–LUMO gaps of the title heterofullerenes are dramatically smaller than that of C₆₀, which indicates that the chemical reactivity can be tuned by substituted TM atoms. Moreover, the frontier MOs of the studied 3d-block heterofullerenes show some degree of difference, therefore they may exhibit different chemical reactivities. The QTAIM analyses indicate that the TM–C bonds show some degree of covalency. The weak IR spectroscopic signals in the range of 800–1000 cm⁻¹, which are assigned to TM–C bond stretches, can be used to further identify these studied 3d heterofullerenes. The surface reactivity is predicted with Fukui indices for the studied 3d heterofullerenes, and the feasibility of chemical attack at the TM atoms is high. The earlier TM-substituted species, C₅₈Ti, C₅₈V, C₅₈Cr and C₅₈Mn, are more active than other heterofullerenes. The binding of an ethylene molecule on the TM atoms of the studied heterofullerenes is investigated to probe their chemical reactivity. The fact that earlier TM atoms show greater reactivity than later TM atoms is in excellent agreement with Fukui function predictions. The ability of the Fukui function to predict the local reactivity sites is confirmed. Moreover, the E_ads values for earlier TM-substituted heterofullerenes are very close to the value of the previously reported C₅₈Ir(C₂H₄) complex, which was confirmed by the experimental observation of a peak in the mass spectrum that may be associated with [C₅₈Ir(2-butene)]⁻.

Acknowledgements

This work is supported by National Natural Science Foundation of China (no. 11204193). The author G. Jiang acknowledges the funding supporting from National Natural Science Foundation of China (no. 11174213).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra04139a

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