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. 2024 Aug 2;9(32):35197–35208. doi: 10.1021/acsomega.4c05912

Electronic Structure, Aromaticity, and Magnetism of Minimum-Sized Regular Dodecahedral Endohedral Metallofullerenes Encapsulating Rare Earth Atoms

Jia-Ming Zhang †, Huai-Qian Wang †,‡,*, Hui-Fang Li ‡,*, Xun-Jie Mei ‡, Yong-Hang Zhang †, Hao Zheng †
PMCID: PMC11325400  PMID: 39157101

Abstract

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A series of minimally sized regular dodecahedron-embedded metallofullerene REC20 clusters (RE = Sc, Y, La, Ce, Pr, Nd, Pm, Sm, Eu, and Gd) as basic units of nanoassembled materials with tunable magnetism and UV sensitivity have been explored using density functional theory (DFT). The contribution of the 4f orbital of the rare earth atom at the center of the C20 cage to the frontier molecular orbital of REC20 gives the REC20 cluster additional stability. The AdNDP orbitals of the four REC20 superatoms that conform to the spherical jellium model indicate that through natural population analysis and spin density diagrams, we observe a monotonic increase in the magnetic moment from Ce to Gd. This is attributed to the increased number of unpaired electrons in the 4f orbitals of lanthanide rare earth atoms. The UV–visible spectrum of REC20 clusters shows strong absorption in the mid-UV and near-UV bands. REC20 clusters encapsulating lanthanide rare earth atoms stand out for their tunable magnetism, UV sensitivity, and stability, making them potential new self-assembly materials.

1. Introduction

Since embedded metallofullerene has metal atoms embedded inside the fullerene cavity, its growth and stabilization mechanism are more complex and are still an unsolved mystery. Fullerene superatoms can serve as special building blocks for constructing nanomaterials due to their ability to encapsulate atoms or molecules.1−5 In 1985, Heath et al. discovered the first stable embedded metal complex, LaC60, which was named metallofullerene.6 Since then, a rich variety of endohedral metallofullerenes (EMFs) with different cage sizes and embedded atoms have been extensively studied.7−19 Compared to larger-sized fullerenes, small fullerenes are relatively unstable due to increased curvature, causing strain within the cage and weakening π-conjugation.20−22 Especially for the smallest fullerene C20, which has all pentagonal faces, the bonds tend to be sp3 bonds rather than the sp2 bonds that are dominant in large fullerenes.16 Through metal doping, it is possible to increase the stability of smaller fullerenes and change their electronic properties.23−35 T. Guo et al.23 reported in 1992 that the experiment of MC28 confirmed that the 5f feature of U in the photoemission spectra of UC28 existing in sublimed films is consistent with the formal 4+ valence state of U. Later, Dunk et al.28 used FT-ICR (Fourier transform ion cyclotron resonance) mass spectrometry and found relatively high abundance of MC28 cations encapsulating group 4 metal atoms and U. The success of the experiment inspired a large number of ab initio reports on small-sized EMFs. A series of EMFs MC28 (M = Ti, Zr, Hf, U),34,35 UC26,29 and PuC2431 of various sizes with large HOMO–LUMO gaps that meet the characteristics of 32-electron systems have been widely reported.

Among all small-sized embedded metallofullerenes, MC20 has also attracted a great deal of attention as the smallest-sized encapsulation material. Many ab initio calculations have been performed for the smallest sized EMFs using a variety of doping atoms that significantly change their stability, electronic structure, and magnetic properties.36−47 Manna and Ghanty reported M@C20 (M = Pr–, Pa–, Nd, U, Pm+, Np+, Sm2+, Pu2+, Eu3+, Am3+, Gd4+, and Cm4+), which exhibit special stability with 26 electrons (HOMO–LUMO energy gap in the range of 2.5–4.9 eV).42 These valence electrons correspond to the fully occupied spd-type energy levels of the cage and the partially occupied f-type molecular orbitals of the cage. In addition, F. Meng et al. designed a series of 32-electron systems consistent with shell closing and obtained MC20 with a larger HOMO–LUMO energy gap (2.22–5.39 eV), where M = Eu3–, Am3–, Gd2–, Cm2–, Tb–, Bk–, Dy, Cf, Ho+, Es+, Er2+, Fm2+, Tm3+, Md3+, Yb4+, No4+, Lu5+, and Lr5+.44

Previous reports on EMFs have tended to incorporate metal atoms that enable them to meet a specific number of valence electrons to exhibit special stability. This article focuses on rare earth (RE) elements, trying to find EMFs with special stability outside of these rules and exploring the effects of encapsulating different RE atoms on the structure, electronic properties, magnetism, and aromaticity of REC20 (RE = Sc, Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd). The main purposes of this study are (1) to obtain the geometric structure and energy properties of a series of REC20 clusters and (2) to explore the effects of encapsulating different rare earth elements on the electronic distribution and magnetism of REC20 clusters. (3) The analysis of the electronic structure of REC20 clusters provides valuable theoretical guidance for researchers to develop cluster-assembled nanomaterials with special magnetic properties.

2. Theoretical Method and Computational Details

The structures of a series of minimally EMFs encapsulating rare earth atom REC20 clusters (RE = Sc, Y, La, Ce, Pr, Nd, Pm, Sm, Eu, and Gd) have been optimized using density functional theory (DFT). DFT calculations use the PBE048 functional, which has successfully predicted the structure of silicon-based and germanium-based clusters doped with lanthanide rare earth atoms of various sizes.49−51 The optimization of the structures of REC20 clusters has been divided into two steps. The larger scalar Stuttgart relativistic effective core potential basis set (ECP10MDF52 for Sc; ECP28MWB53 for Y; ECP46MWB54,55 for La; ECP48MWB for Ce and Pr; ECP50MWB for Nd and Pm; ECP52MWB for Sm and Eu; ECP54MWB for Gd) is chosen for rare earth atoms, and the 6-31g(d,p)56,57 basis set was selected for C during the first optimized process. The cluster structure obtained in the first step is then optimized again at the higher computational level PBE0/RE/SDD//C/cc-pVTZ52,53,58,59 to obtain more accurate structural and energy information. To ensure that the energy minimum was achieved, various probable spin multiplicities were considered, and the harmonic vibrational frequencies were also calculated to guarantee that the optimized structures represented local minima. All optimization calculations were performed by the Gaussian09 program.60

All kinds of wave function analyses, including atomic dipole corrected Hirshfeld atomic charge (ADCH), the spin density (ρalpha – ρbeta) isosurface, and iso-chemical shielding surfaces (ICSS),61−63 were conducted by the multifunctional wave function (Multiwfn) analyzer program,64 visualized by VMD65 and ParaView66 software. Gauge-including magnetically induced current (GIMIC) is generated by the GIMIC2.067 and Gaussian09 programs.60

3. Results and Discussion

3.1. Geometric Structure and HOMO–LUMO Gap

The schematic representation of the structures of REC20 clusters (RE = Sc, Y, La, Ce, Pr, Nd, Pm, Sm, Eu, and Gd) optimized at the PBE0/RE/SDD//C/cc-pVTZ level is portrayed in Figure 1. Specific structural details are listed in Figure S1. To ensure consistency of the results, we optimized the structure of the C20 cluster under the PBE0/C/cc-pVTZ computational model. The energy of caged C20 with C2h symmetry is consistent with the results previously reported by Zeng68 at the same computational level. Table S1 gives the atomic coordinates of the C20 and REC20 clusters. The RE atoms of the REC20 cluster are all located in the center of REC20. The C–C bond length in all REC20 clusters is between 1.44 and 1.55 Å. It can be seen that the encapsulated RE atoms have little impact on the original structure of C20. Among them, EuC20 has the highest Th symmetry, CeC20 and PmC20 clusters show D3d symmetry, LaC20 has D2h symmetry, and the other REC20 clusters (RE = Sc, Y, Pr, Nd, Sm, and Gd) show the symmetry of Ci. It can be seen that embedding different RE atoms can change the symmetry of the C20 cage.

Figure 1.

Figure 1

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Structure images from three different viewing angles of REC20 clusters (RE = Sc, Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd) optimized at the PBE0/RE/SDD//C/cc-pVTZ level and the structure of the C20 cluster at the PBE0/C/cc-pVTZ level. The orange balls and gray balls represent RE atoms and C atoms, respectively.

The HOMO–LUMO gaps and molecular orbital compositions of REC20 (RE = Pr, Nd, Pm, and Sm) clusters obtained by NAO analysis are plotted in Figure 2. Simultaneously, we calculated the ionization potential (IP), electron affinity (EA), and the chemical hardness (η) of the REC20 clusters using the following formula as a more accurate measure of their chemical stability,69 with the results presented in Table 1.

3.1. 1

Figure 2.

Figure 2

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HOMO–LUMO gaps (indicated in black) in conjunction with corresponding orbitals (isosurfaces = 0.002) of REC20 (RE = Pr, Nd, Pm, and Sm) are obtained at the PBE0/RE/SDD//C/cc-pVTZ level, and C20 is obtained at the C/cc-pVTZ level.

Table 1. Ionization Potential (IP), Electron Affinity (EA), and Chemical Hardness (η) of REC20 and C20 Clusters at the PBE0/RE/SDD//C/cc-pVTZ Level.

Cluster IP (eV) EA (eV) η (eV)
C20 7.06 1.79 2.63
ScC20 7.35 2.53 2.41
YC20 7.85 2.92 2.46
LaC20 8.05 3.47 2.29
CeC20 8.56 3.81 2.38
PrC20 8.79 2.48 3.15
NdC20 8.75 2.97 2.89
PmC20 8.54 3.52 2.51
SmC20 9.27 3.82 2.73
EuC20 7.22 2.23 2.50
GdC20 7.31 2.52 2.40
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The molecular orbital compositions of all REC20 clusters are plotted in Figure S2 and Figure S3. For ScC20 and YC20 clusters encapsulating Sc atoms in the fourth period and Y atoms in the fifth period, their central atoms make little contribution to the frontier orbital. This implies that the electronic structures of Sc and Y atoms may not directly affect the reactivity of ScC20 and YC20 clusters. For the REC20 clusters encapsulating lanthanide atoms, the contribution of RE atoms to the frontier orbitals mainly comes from the 4f orbital. Interestingly, for several of the REC20 clusters (RE = Pr, Nd, Pm, Sm), the RE atoms make a significant contribution to the 4f electrons of the α-HOMO orbital, among which Pr, Nd, Pm, and Sm contribute significantly to the α-HOMO orbital. The contribution values are 42%, 40%, 47%, and 52%, respectively. At the same time, these REC20 clusters have large HOMO–LUMO gaps exceeding 3.5 eV, which means that these clusters can be regarded as stable superatoms.12,16 The HOMO–LUMO gaps and η reflect the ability of electrons to jump from occupied orbitals to unoccupied orbitals, which means they have higher chemical stability.40,70,71 Overall, the greater the contribution of the 4f orbital of the RE atom located in the center of the C20 cage to the α-HOMO orbital, the larger the corresponding HOMO–LUMO gap, which means that the 4f orbital of the RE atom has an important contribution to the chemical stability of REC20.

3.2. Spherical Jellium Model

Four REC20 (RE = Pr, Nd, Pm, Sm) clusters with larger η that exhibit special chemical stability are potentially stable superatoms. Their electronic arrangement analysis results show that the electronic arrangement of REC20 is fully consistent with the spherical jellium model (SJM). In the SJM model, when the number of valence electrons in the cluster is 2, 8, 18, 20, 34, ..., each shell can be filled, and it can be written as 1S2, 2P6, 1D10, 1F14, 2S2, ....72 The valence molecular orbital of the REC20 cluster is shown in Figure 3. In addition, the complete molecular orbital of the REC20 cluster is shown in Supporting Information Figure S4.

Figure 3.

Figure 3

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Valence molecular orbitals of REC20 (RE = Pr, Nd, Pm, Sm) clusters. The blue lines represent single electron occupied orbitals, and the red lines represent LUMO orbitals.

Each carbon atom is bonded to the adjacent carbon atom through sp2 hybridization, and the pz electrons of the C atom are left to provide valence electrons for the superatom. In Figure 3, except for the 1H shell orbital, the remaining superatomic orbitals are formed by hybridization of the pz electrons of the carbon atom and the RE atom. The 1H18 orbitals with higher angular momentum of all REC20 superatoms are split into two parts, the preferentially occupied 1H10 orbitals and the LUMO orbital. As shown in Figure 3, encapsulating different RE atoms will affect the energy distributions of the 1P shell and the 1F shell. For PmC20 and SmC20 with higher spins, their 1F shells are clearly split into two parts, single electron occupied (blue line) orbitals and fully occupied orbitals with lower energy than 1P shell electrons. SmC20, which has the highest spin multiplicity, has energy degeneracy in its fully occupied 1F shell orbitals and lower energy 1D shell orbitals. Except for the 1F shell, the electron distribution of all superatomic orbitals in which pz electrons of carbon atoms participate in hybridization can be written as 1S2, 1D10, and 1P6. It satisfies the 2(N + 1)2 rule proposed by Hirsch et al. (N = 2).73

For the four REC20 (RE = Pr, Nd, Pm, and Sm) clusters, their HOMO orbitals and LUMO orbitals belong to different shells. Since the energy difference between electron orbitals with different angular momentum is large, they exhibit a large HOMO–LUMO gap.

3.3. Magnetic Moment and Electron Spin Density

In order to further investigate the influence of RE atoms on C20, the natural population analysis (NPA)74 and ADCH atomic charge75 of REC20 clusters were calculated to explore the charge transfer and charge distribution characteristics of REC20 clusters. The natural electron configuration (NEC), natural charge population (NCP), Hirshfeld charge, and ADCH charges of RE atoms are shown in Table 2.

Table 2. Natural Electron Configuration (NEC), Natural Charge Population (NCP), and ADCH Charge of RE (RE = Sc, Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd) Atoms in REC20 Clusters.

  NPA
  
Cluster NEC NCP of RE (e) ADCH charges of RE (e)
ScC20 [core]4s0.303d3.534p1.004d0.37 –2.19 –0.61
YC20 [core]5s0.334d1.055p0.716s0.015d0.42 0.51 –0.63
LaC20 [core]6s0.304f4.255d2.096p0.865f0.076d0.287p0.01 –4.70 –0.67
CeC20 [core]6s0.314f4.505d2.476p0.895f0.166d0.357p0.02 –4.66 –0.59
PrC20 [core]6s0.324f5.175d2.406p0.895f0.236d0.397p0.02 –4.39 –0.46
NdC20 [core]6s0.334f5.695d2.496p0.895f0.476d0.387p0.02 –4.23 –0.49
PmC20 [core]6s0.334f6.155d2.586p0.915f0.606d0.357p0.02 –3.90 –0.50
SmC20 [core]6s0.344f7.015d2.596p0.915f0.566d0.347p0.01 –3.73 –0.53
EuC20 [core]6s0.344f7.485d2.446p0.925f0.436d0.347p0.01 –2.93 –0.51
GdC20 [core]6s0.364f7.785d2.406p0.927s0.125f0.366d0.36 –2.24 –0.65
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NPA indicates that the charge of the inner orbital (4s, 5s, and 6s) of all RE atoms is transferred to the outer orbital. For the Sc atom, charges are mainly transferred to the outer 3d and 4p orbital. The difference is that the Y atom charges are mainly transferred to the 5p and 5d orbitals with higher energy. For lanthanide atoms (La, Ce, Pr, Nd, Pm, and Sm) whose 4f orbital is not half full, the charge is more likely to be transferred to the 4f orbital, and the charge distribution of the 5d orbital is always around 2.5. As the 4f electron layer gradually reaches half full, the NCP of the lanthanide atoms gradually increases, and the charge transferred from the C20 cage to the RE atom gradually decreases. Except for the Y atom, the NCP and ADCH charges of the other RE atoms are negative and behave as charge acceptors. This is because the RE atom is located at the central charge accumulation position within C20. The completely opposite charge transfer properties shown by NCP and ADCH charges about the Y atom may be due to the vagueness of the minimum set/Rydberg set division criteria of these elements when calculating the NPA charges of transition metal elements, and different divisions will affect the occupancy number as a weighted symmetry orthogonalization (OWSO) process, which in turn affects the charge value.76 Compared with NEC, ADCH charges of RE atoms show better consistency.

Table 3 lists the calculated local magnetic moments of the 6s, 4f, 5d, 5f, and 6d orbitals of RE (RE = La, Pr, Nd, Pm, Sm, Eu) atoms and the total magnetic moments of the REC20 clusters. As shown in Table 3, the magnetic moments of REC20 mainly come from the contribution of unpaired electrons in the 4f orbital of RE atoms. Transferred to the 6p orbital, the electrons in the orbital do not contribute to the magnetic moment, and the contributions of the 5d, 6d, and 7s orbitals are very small and almost negligible. The GdC20 cluster has the largest total magnetic moment (6 μB) among the REC20 clusters. This also shows that the 5d orbital electrons of RE atoms participate in bonding with the C20 cage. In addition, since the La atom has very few unpaired electrons in the 4f orbital, it does not exhibit an obvious magnetic moment. It is worth noting that the magnetic moments on RE (RE = Pm, Sm, and Eu) atoms are even larger than total magnetic moments, indicating that the contribution of C to the total magnetic moment is very limited.

Table 3. Magnetic Moments (μB) of the 6s, 4f, 5d, 5f, 7s, and 6d Orbitals of RE Atoms (RE = La, Pr, Nd, Pm, Sm, Eu, Gd), the Total Magnetic Moments of the RE Atoms, and the Total Magnetic Moments of the Most Stable Isomers.

  Magnetic moments of RE atoms (μB)
Cluster 6s 4f 5d 7s 5f 6d RE Total
LaC20 0.00 0.03 –0.01 0.00 0.13 0.00 0.15 1
PrC20 0.00 0.45 0.00 0.00 0.03 0.00 0.48 1
NdC20 0.00 1.25 0.00 0.00 0.14 0.01 1.40 2
PmC20 0.00 2.83 0.02 0.00 0.30 0.03 3.18 3
SmC20 0.00 3.87 0.02 0.00 0.19 0.02 4.1 4
EuC20 0.00 5.20 0.02 0.00 0.17 0.04 5.43 5
GdC20 0.07 5.80 0.02 –0.17 0.10 0.04 5.86 6
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In order to visualize the distribution of single electrons in three-dimensional space, the spin density (ρalpha – ρbeta) isosurface of REC20 (RE = Sc, Y, La, Pr, Nd, Pm, Sm, Eu) is shown in Figure 4. In the closed-shell system of CeC20, there is no spin density. The Figure 4 clearly shows that in the three systems of ScC20, YC20, and LaC20 clusters, which have almost no magnetic moments, the unpaired electrons are mainly distributed on the outer C20 cage. There is no spin electron distribution around the SC and Y atoms in the cage, and only a very small amount of spin electrons is distributed on the La atom in the C20 cage. Although the spin density isosurface of the C20 cage surface expands as the incorporated Sc, Y, and La atomic numbers increase, the increase in spin electrons on the C20 cage does not contribute to the total magnetic moments of the system. Starting from PrC20, the green area gathers from the C20 cage to the central atom, showing two sets of intersecting cross shapes. Among them, PmC20 is special. Spin electrons are densely distributed around the Pm atom in the cage (green area), and the number of spin electrons distributed on the C20 cage is very small. This can also explain the phenomenon that the magnetic moment on the Pm atom is greater than the total magnetic moment. As the RE doping element changes, we can observe that the green isosurfaces inside and outside the cage gradually expand. Based on the above phenomenon, the magnetic moments of the REC20 clusters mainly come from the contribution of unpaired electrons around the RE atoms in the C20 cage, and the spin electrons on the C20 cage have a limited contribution to the total magnetic moment. When the number of spin electrons in the C20 cage is greater than the number of spin electrons on the C20 cage, the total magnetic moment on the RE atom exceeds the total magnetic moment of the system.

Figure 4.

Figure 4

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Spin-density (ρalpha–ρbeta) isosurfaces of REC20 (RE = Sc, Y, La, Ce, Pr, Nd, Pm, Sm, Eu, and Gd). The isosurface is set to ±0.005. The green and blue isosurfaces show that the spin density has positive and negative values, respectively. Orange and gray balls represent RE atoms and carbon atoms, respectively.

Based on the above conclusion, REC20 clusters doped with lanthanide RE atoms are mainly bonded through the 5d orbital of RE, while the 4f electrons hardly participate in bonding. Combined with magnetic moment analysis, most 4f electrons are not bonded between RE atoms and C20 cages, which means that almost all unpaired electrons remain in this orbital, resulting in an adjustable magnetic spin magnetic moment. It is the tunable magnetic moment exhibited by REC20 clusters that gives them the potential to become the basic structure of new magnetic nanoassembly materials.

3.4. AdNDP

To further investigate the electronic properties of the four REC20 (RE = Pr, Nd, Pm, and Sm) clusters that exhibited higher stability, the electronic interactions between neighboring atoms within the REC20 clusters were studied by adaptive natural density partitioning (AdNDP).77

Taking PrC20 as an example, its AdNDP orbital is shown in Figure 5, and the AdNDP orbitals of the other three clusters are shown in Figure S5. In all four REC20 clusters, excluding the electrons that contribute to the magnetic moment, there are 42 pairs of electrons that can be divided into three types. First, there are 30 2c-2e localized σ C–C bonds on the surface of the C20 cage, and their occupation numbers (ON) are between 1.79 and 1.88|e|. Second, there are 6 delocalized 3c-2e σ bonds with ON between 1.78 and 1.80 in its cage, which form a triangular area on the inside of the cage. This indicates that the encapsulation of Pr atoms enhances the stability of the C20 cage. The shapes of all 2c-2e and 3c-2e orbitals are similar to those shown in Figure 5. Finally, the 6 fully delocalized 21c-2e orbitals present the four configurations shown in Figure 5, which roughly present shapes similar to those of the P shell and D shell electron orbitals. The six 21c-2e pi bonds with ON = 2.00|e| indicate that the delocalized electrons are not only present on the surface of the C20 cage but also distributed inside it. The delocalized electrons distributed inside the cage of the REC20 cluster indicate that it has a certain degree of aromaticity.

Figure 5.

Figure 5

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Bonding analyses of the AdNDP orbitals of PrC20. The occupation numbers (ONs) are indicated.

3.5. Aromaticity

It can be seen from the spin density isosurface that there are delocalized electrons between RE atoms and the C20 cage, which make the REC20 cluster have a certain degree of aromaticity. The impact of encapsulating different RE atoms on the aromaticity of REC20 clusters was further explored by calculating the ICSS of REC20 clusters.62,78 ICSS corresponds to the original definition of nucleus-independent chemical shift (NICS), which embodies isotropic shielding against external magnetic fields.61,62 Based on NICS, ICSS not only considers the shielding value of a specific point but considers the magnetic shielding value as a real space function and studies it by drawing curve diagrams, plane diagrams, and isosurface diagrams to obtain more comprehensive information. The symbol definitions of ICSS and NICS are exactly the opposite. NICS takes the negative value of the magnetic shielding value, while ICSS directly displays the magnetic shielding value at different locations without taking the negative sign. In other words, the more positive the ICSS is, the greater the degree of shielding from the external magnetic field at this point. The more negative the ICSS is, the stronger the degree of deshielding at this location. We calculated the isosurface of the ZZ component of the cluster ICSS (ICSSzz63,79) of REC20 clusters, where the Z direction is perpendicular to the five-atom ring in C20. Figure 6 shows the color-filled maps of ICSSzz at the plane of the RE atom in REC20. The three-dimensional cluster magnetic shielding isosurface of ICSSzz was also plotted for a comparison of color-filled maps. In addition, the ICSSzz of benzene and C20 are shown in Figure 6 for comparison.

Figure 6.

Figure 6

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ICSSzz of benzene, C20, and REC20 (RE = Sc, Y, La, Ce) The color-filled maps are the ICSSzz distribution at the plane of the RE atom. Each contour shows the corresponding shielding surface separately, cyan at 4 ppm, green at 8 ppm, yellow at 16 ppm, orange at 32 ppm, red at 64 ppm, and blue at −4 ppm, respectively.

The ICSSzz value at the center of C20 in Figure 6 is negative, which means that there is a deshielding region at the center of C20, which is consistent with the positive NICS value at the center of C20 in previous reports.80 The ICSSzz isosurface distribution of REC20 clusters shown in Figure 6 and Figure 7 reveals that the aromaticity of C20 cages encapsulating different RE atoms is very different. For non-lanthanide elements, the REC20 clusters encapsulated by Sc atoms and Y atoms show antiaromatic properties as a whole (blue area). This is due to the limited number of electrons in the Sc atoms and Y atoms themselves and their inability to provide delocalized electrons in the cage. In the LaC20 cluster encapsulating La, the first element of the lanthanide series, the ICSSzz value around the central atom is almost 0. The interior of the LaC20 cage can be considered as a deshielding region. As the atomic number increases, a ring-shaped strong magnetic shielding region appears in the central plane of the REC20 cluster. The overall isosurface is distributed in a spindle shape, showing an extremely strong magnetic shielding region (red area) in the central plane inside the cage, while a huge deshielding region appears along the z-axis outside the C20 cage. This reveals that the limited delocalized distribution of free electrons in the 4f orbital of lanthanide atoms of the REC20 cluster forms a ring-shaped magnetic shielding region. However, for the EuC20 and GdC20 clusters that exhibit the highest magnetic moments, the aromaticity at the central plane does not continue to strengthen but weakens, which is likely due to the delocalization of free electrons in a larger area within the cage. The antiaromatic areas on the outside of the EuC20 and GdC20 cages are significantly suppressed, and the aromatic ring width increases significantly, almost covering the entire side of the C20 cage. This may also reflect that the magnetic shielding region of the cluster is no longer highly concentrated near the central atom but is strengthened overall. This all implies that the delocalized electrons are distributed over a larger area within the cage.

Figure 7.

Figure 7

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ICSSzz of REC20 (RE = Pr, Nd, Pm, Sm, Eu, or Gd). The color-filled maps are the ICSSzz distribution in the plane of the RE atom. Each contour shows the corresponding shielding surface separately, cyan at 4 ppm, green at 8 ppm, yellow at 16 ppm, orange at 32 ppm, red at 64 ppm, and blue at −4 ppm, respectively.

From the above discussion, it can be concluded that the aromaticity of REC20 clusters encapsulating different RE atoms is affected by the distribution of delocalized electrons within the cage. When there are fewer delocalized electrons, the REC20 cluster cage is a deshielding region. As the RE atomic number increases, the number of delocalized electrons further increases. The transformation of the ICSSzz isosurface from a local narrow ring to a hemispherical shape wrapping the sides of the C20 cage implies that the delocalized electron distribution trend in the cage is from concentrated distribution in the central part to uniform distribution within the cage.

3.6. Molecular Magnetically Induced Current

In order to more intuitively observe the effect of encapsulating different RE atoms on the aromaticity of REC20 clusters, the molecular magnetically induced current of REC20 clusters was calculated using the GIMIC program package.67 The GIMIC program implements the gauge-including magnetically induced current method. The GIMIC method is based on gauge-including/invariant atomic orbitals (GIAO) and relies on the density matrix produced by the magnetic properties calculation process and the derivative matrix of the density matrix with respect to the magnetic field to calculate the induced current density.67,81 Several representative REC20 clusters (RE = Sc, La, Sm, Gd) were selected, and the plane-shaded streamline diagrams and arrow diagrams of the modes of the magnetically induced current at their central plane are shown in Figure 8. A three-dimensional dynamic visual representation of the magnetically induced current is provided in the Supporting Information, and Figure 9 shows some screenshots.

Figure 8.

Figure 8

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GIMIC maps of REC20 (RE = Sc, La, Sm, and Gd) clusters on the central plane with the magnetic field direction forward along the z-axis (the perpendicular plane facing outward).

Figure 9.

Figure 9

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Screenshots of the GIMIC for REC20 (RE = Sc, La, Sm, and Gd) clusters.

In Figure 8, the ScC20 clusters have obvious paramagnetic currents in the regions around the Sc atoms due to the presence of deshielding regions inside the ScC20 clusters. In contrast, in SmC20 clusters with a strong magnetic shielding region in the central plane, the strong diamagnetic current formed within the SmC20 cage appears as a large circular white area bright near the Sm atoms. Compared with SmC20, although diamagnetic current is also generated near the central atom of LaC20, due to the deshielding area inside it, the diamagnetic current intensity is very weak, and the distribution is unevenly elliptical. It is worth noting that the diamagnetic current within the cage of the GdC20 cluster is obviously distributed over a larger area, which is obviously caused by the distribution of delocalized electrons in a larger area. Although both the paramagnetic current and diamagnetic current appear near the central atom simultaneously, overall the GdC20 cluster still shows strong aromaticity.

3.7. UV–Vis Spectra

In order to further understand the optical properties of the four REC20 (RE = Pr, Nd, Pm, and Sm) clusters with high stability, UV–vis spectra were simulated by calculating the time-dependent density functional theory (TD-DFT) at the PBE0/RE/SDD//C/cc-pVTZ level. In order to ensure the accuracy of the calculation, it is necessary to consider enough energy bands, and 200 excited states were found in the REC20 clusters.

The four REC20 clusters all show five absorption bands, one of which is located in the visible light part and the other four are located in the near-ultraviolet region and the mid-ultraviolet region. The highest peak position of each absorption band is marked in Figure 10. The UV–vis spectra of the four REC20 clusters show that their main absorption regions are all located in the mid-ultraviolet band, accounting for 87.54% (PrC20), 90.47% (NdC20), 91.92% (PmC20), and 79.56% (SmC20) of the total, respectively. The encapsulation of different RE atoms mainly affects the intensity of the first absorption band, among which the first absorption band of the PmC20 cluster is the strongest. The second absorption band located in the mid-ultraviolet region is almost unaffected by the RE atoms, which is mainly due to its characteristics of the C20 cage π → π* electronic transition. The ADCH charge of the RE atom indicates that the embedded RE atom causes electron transfer from the C20 cage to the RE atom, resulting in a blue shift in the UV–vis spectrum of the REC20 cluster with an increasing atomic number of the encapsulated RE. In summary, the UV–visible spectrum emphasizes the extensive mid-UV and near-UV absorption exhibited by the REC20 cluster, especially the excellent performance exhibited by the PmC20 cluster. These findings suggest that their absorption properties in the UV and visible spectrum can be exploited for promising applications in solar energy converters or ultra-high-sensitivity near-UV photodetectors.

Figure 10.

Figure 10

Open in a new tab

Calculated UV–vis spectra of REC20 (RE = Pr, Nd, Pm, Sm) clusters. Curves and vertical lines represent the absorption spectra and oscillator strength, respectively. (a) PrC20, (b) NdC20, (c) PmC20, and (d) SmC20..

4. Conclusion

The structures of a series of minimally EMFs encapsulating rare earth atoms REC20 clusters (RE = Sc, Y, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd) have been optimized using DFT. RE atoms are always located in the center of the C20 cage. The high-stability superatoms of REC20 clusters (RE = Pr, Nd, Pm, Sm) originate from the widening of the HOMO–LUMO gap caused by the larger contribution of the RE atom’s 4f electron orbital to the cluster frontier orbital. NPA and spin density analyses indicate that the 4f orbital of RE atoms contributes significantly to the total magnetic moment. The tunable magnetic moment of REC20 clusters increases monotonically from 0 to 6 μB. ICSSzz isosurfaces and GIMIC show that the aromaticity of the REC20 clusters gradually strengthens with the increase in 4f electrons in RE atoms. The diamagnetic current area in the cage expands from the central atom to the C20 cage, indicating that the delocalized electron distribution area in the cage becomes larger. The UV–vis spectrum of REC20 clusters shows strong absorption in the mid-UV and near-UV bands. In summary, REC20 clusters encapsulating lanthanide metal atoms show potential as stable, highly magnetic assembly materials and as ultrahighly sensitive near-UV photodetection materials.

Acknowledgments

The project was supported by the Natural Science Foundation of Fujian Province of China (Grant No. 2023J01141), the Natural Science Foundation of Xiamen (Grant No. 3502Z202373051), the Science and Technology Plan of Quanzhou (Grant Nos. 2018C077R and 2018C078R), and the New Century Excellent Talents in Fujian Province University (Grant No. 2014FJ-NCET-ZR07).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.4c05912.

  • Tables of Cartesian coordinates for REC20 clusters optimized at the PBE0/RE/SDD//C/cc-pVTZ level; relative energies of REC20 clusters with different spin multiplicities at the PBE0/RE/SDD//C/cc-pVTZ level; Figures of structures of REC20 clusters optimized at the PBE0/RE/SDD//C/cc-pVTZ level; HOMO–LUMO gaps in conjunction with corresponding orbitals of REC20 obtained at the PBE0/RE/SDD//C/cc-pVTZ level; HOMO–LUMO gaps in conjunction with corresponding orbitals of REC20 obtained at the PBE0/RE/SDD//C/cc-pVTZ level; molecular orbitals of REC20 clusters; bonding analyses of AdNDP orbitals of REC20 (PDF)

  • Three-dimensional dynamic visual representation of the magnetically induced current (MP4)

  • Three-dimensional dynamic visual representation of the magnetically induced current (MP4)

  • Three-dimensional dynamic visual representation of the magnetically induced current (MP4)

  • Three-dimensional dynamic visual representation of the magnetically induced current (MP4)

The authors declare no competing financial interest.

Supplementary Material

ao4c05912_si_001.pdf (1.9MB, pdf)
ao4c05912_si_002.mp4 (80.5KB, mp4)
ao4c05912_si_003.mp4 (79.9KB, mp4)
ao4c05912_si_004.mp4 (81.8KB, mp4)
ao4c05912_si_005.mp4 (78KB, mp4)

References

  1. Taninaka A.; Ochiai T.; Kanazawa K.; Takeuchi O.; Shigekawa H. Probing of electronic structures of La@C82 superatoms upon clustering realized using glycine nanocavities. Appl. Phys. Express 2015, 8 (12), 125503. 10.7567/APEX.8.125503. [DOI] [Google Scholar]
  2. Xie W. Y.; Zhu Y.; Wang J. P.; Cheng A. H.; Wang Z. G. Magnetic coupling induced self-assembly at atomic level*. Chin. Phys. Lett. 2019, 36 (11), 116401. 10.1088/0256-307X/36/11/116401. [DOI] [Google Scholar]
  3. Xie W. Y.; Yu F. M.; Wu X. C.; Liu Z. H.; Yan Q.; Wang Z. G. Constructing the bonding interactions between endohedral metallofullerene superatoms by embedded atomic regulation. Phys. Chem. Chem. Phys. 2021, 23 (30), 15899–15903. 10.1039/D1CP02070F. [DOI] [PubMed] [Google Scholar]
  4. Shen Y. B.; Cui M. X.; Takaishi S.; Kawasoko H.; Sugimoto K.; Tsumuraya T.; Otsuka A.; Kwon E.; Yoshida T.; Hoshino N.; Kawachi K.; Kasama Y.; Akutagawa T.; Fukumura T.; Yamashita M. Heterospin frustration in a metal-fullerene-bonded semiconductive antiferromagnet. Nat. Commun. 2022, 13 (1), 495. 10.1038/s41467-022-28134-w. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Wang R.; Yang X. R.; Huang W. R.; Liu Z. H.; Zhu Y.; Liu H. Y.; Wang Z. G. Superatomic states under high pressure. iScience 2023, 26 (4), 106281. 10.1016/j.isci.2023.106281. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Heath J. R.; O’Brien S. C.; Zhang Q.; Liu Y.; Curl R. F.; Tittel F. K.; Smalley R. E. Lanthanum complexes of spheroidal carbon shells. J. Am. Chem. Soc. 1985, 107 (25), 7779–7780. 10.1021/ja00311a102. [DOI] [Google Scholar]
  7. Ito Y.; Fujita W.; Okazaki T.; Sugai T.; Awaga K.; Nishibori E.; Takata M.; Sakata M.; Shinohara H. Magnetic properties and crystal structure of solvent-free Sc@C82 metallofullerene microcrystals. ChemPhysChem 2007, 8 (7), 1019–1024. 10.1002/cphc.200700097. [DOI] [PubMed] [Google Scholar]
  8. Zuo T. M.; Olmstead M. M.; Beavers C. M.; Balch A. L.; Wang G. B.; Yee G. T.; Shu C. Y.; Xu L. S.; Elliott B.; Echegoyen L.; Duchamp J. C.; Dorn H. C. Preparation and structural characterization of the Ih and the D5h isomers of the endohedral fullerenes Tm3N@C80: icosahedral C80 Cage encapsulation of a trimetallic nitride magnetic cluster with three uncoupled Tm3+ ions. Inorg. Chem. 2008, 47 (12), 5234–5244. 10.1021/ic800227x. [DOI] [PubMed] [Google Scholar]
  9. Aoyagi S.; Nishibori E.; Sawa H.; Sugimoto K.; Takata M.; Miyata Y.; Kitaura R.; Shinohara H.; Okada H.; Sakai T.; Ono Y.; Kawachi K.; Yokoo K.; Ono S.; Omote K.; Kasama Y.; Ishikawa S.; Komuro T.; Tobita H. A layered ionic crystal of polar Li@C60 superatoms. Nat. Chem. 2010, 2 (8), 678–683. 10.1038/nchem.698. [DOI] [PubMed] [Google Scholar]
  10. Popov A. A.; Chen C.; Yang S.; Lipps F.; Dunsch L. Spin-flow vibrational spectroscopy of molecules with flexible spin density: electrochemistry, ESR, cluster and spin dynamics, and bonding in TiSc2N@C80. ACS Nano 2010, 4 (8), 4857–4871. 10.1021/nn101115d. [DOI] [PubMed] [Google Scholar]
  11. Zaka M.; Warner J. H.; Ito Y.; Morton J. J. L.; Rümmeli M. H.; Pichler T.; Ardavan A.; Shinohara H.; Briggs G. A. D. Exchange interactions of spin-active metallofullerenes in solid-state carbon networks. Phys. Rev. B 2010, 81 (7), 075424. 10.1103/PhysRevB.81.075424. [DOI] [Google Scholar]
  12. Zhao J. J.; Huang X. M.; Jin P.; Chen Z. F. Magnetic properties of atomic clusters and endohedral metallofullerenes. Coord. Chem. Rev. 2015, 289–290, 315–340. 10.1016/j.ccr.2014.12.013. [DOI] [Google Scholar]
  13. Yang S. F.; Wei T.; Jin F. When metal clusters meet carbon cages: endohedral clusterfullerenes. Chem. Soc. Rev. 2017, 46 (16), 5005–5058. 10.1039/C6CS00498A. [DOI] [PubMed] [Google Scholar]
  14. Bologna F.; Mattioli E. J.; Bottoni A.; Zerbetto F.; Calvaresi M. Interactions between endohedral metallofullerenes and proteins: The Gd@C60-Lysozyme model. ACS Omega 2018, 3 (10), 13782–13789. 10.1021/acsomega.8b01888. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Mwakisege J. G.; Schweitzer G.; Mirzadeh S. Synthesis and stability of actinium-225 endohedral fullerenes, 225Ac@C60. ACS Omega 2020, 5 (42), 27016–27025. 10.1021/acsomega.0c01659. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Zhao J. J.; Du Q. Y.; Zhou S.; Kumar V. Endohedrally doped cage clusters. Chem. Rev. 2020, 120 (17), 9021–9163. 10.1021/acs.chemrev.9b00651. [DOI] [PubMed] [Google Scholar]
  17. Zhang W. X.; Li M. Y.; He J.; Zhao X. Theoretical Insights into the Metal-Nonmetal Interaction Inside M2O@C2V(31922)-C80 (M = Sc or Gd). ACS Omega 2022, 7 (47), 42883–42889. 10.1021/acsomega.2c04978. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Ismael A. K. 20-State molecular switch in a Li@C60 complex. ACS Omega 2023, 8 (22), 19767–19771. 10.1021/acsomega.3c01455. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Sarfaraz S.; Yar M.; Hussain A.; Lakhani A.; Gulzar A.; Ans M.; Rashid U.; Hussain M.; Muhammad S.; Bayach I.; Sheikh N. S.; Ayub K. Metallofullerenes as robust single-atom catalysts for adsorption and dissociation of hydrogen molecules: A density functional study. ACS Omega 2023, 8 (39), 36493–36505. 10.1021/acsomega.3c05477. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Lu X.; Chen Z. F. Curved Pi-conjugation, aromaticity, and the related chemistry of small fullerenes (<C60) and single-walled carbon nanotubes. Chem. Rev. 2005, 105 (10), 3643–3696. 10.1021/cr030093d. [DOI] [PubMed] [Google Scholar]
  21. Handschuh H.; Ganteför G.; Kessler B.; Bechthold P. S.; Eberhardt W. Stable configurations of carbon clusters: chains, rings, and fullerenes. Phys. Rev. Lett. 1995, 74 (7), 1095–1098. 10.1103/PhysRevLett.74.1095. [DOI] [PubMed] [Google Scholar]
  22. Martin J. M. L. C28: the smallest stable fullerene?. Chem. Phys. Lett. 1996, 255 (1), 1–6. 10.1016/0009-2614(96)00354-5. [DOI] [Google Scholar]
  23. Guo T.; Diener M. D.; Chai Y.; Alford M. J.; Haufler R. E.; McClure S. M.; Ohno T.; Weaver J. H.; Scuseria G. E.; Smalley R. E. Uranium stabilization of C28: a tetravalent fullerene. Science 1992, 257 (5077), 1661–1664. 10.1126/science.257.5077.1661. [DOI] [PubMed] [Google Scholar]
  24. Zhao K.; Pitzer R. M. Electronic structure of C28, Pa@C28, and U@C28. J. Phys. Chem. 1996, 100 (12), 4798–4802. 10.1021/jp9525649. [DOI] [Google Scholar]
  25. Makurin Y. N.; Sofronov A. A.; Gusev A. I.; Ivanovsky A. L. Electronic structure and chemical stabilization of C28 fullerene. Chem. Phys. 2001, 270 (2), 293–308. 10.1016/S0301-0104(01)00342-1. [DOI] [Google Scholar]
  26. Peng S.; Zhang Y.; Li X. J.; Ren Y.; Zhang D. X. DFT calculations on the structural stability and infrared spectroscopy of endohedral metallofullerenes. Spectrochim. Acta, Part A 2009, 74 (2), 553–557. 10.1016/j.saa.2009.06.051. [DOI] [PubMed] [Google Scholar]
  27. Zhang Y.; Peng S.; Li X. J.; Zhang D. X. Structural stability, electronegativity and electronic property of endohedral TM@C24 and exohedral TMC24 (TM = Sc, Y and La) metallofullerene complexes: Density-functional theory investigations. J. Mol. Struct. THEOCHEM 2010, 947 (1), 16–21. 10.1016/j.theochem.2010.01.030. [DOI] [Google Scholar]
  28. Dunk P. W.; Kaiser N. K.; Mulet-Gas M.; Rodríguez-Fortea A.; Poblet J. M.; Shinohara H.; Hendrickson C. L.; Marshall A. G.; Kroto H. W. The smallest stable fullerene, M@C28 (M = Ti, Zr, U): stabilization and growth from carbon vapor. J. Am. Chem. Soc. 2012, 134 (22), 9380–9389. 10.1021/ja302398h. [DOI] [PubMed] [Google Scholar]
  29. Manna D.; Ghanty T. K. Prediction of a new series of thermodynamically stable actinide encapsulated fullerene systems fulfilling the 32-electron Pprinciple. J. Phys. Chem. C 2012, 116 (48), 25630–25641. 10.1021/jp308820z. [DOI] [Google Scholar]
  30. Ryzhkov M. V.; Ivanovskii A. L.; Delley B. Electronic structure of endohedral fullerenes An@C28 (An = Th - Md). Comput. Theor. Chem. 2012, 985, 46–52. 10.1016/j.comptc.2012.01.037. [DOI] [Google Scholar]
  31. Manna D.; Sirohiwal A.; Ghanty T. K. Pu@C24: a new example satisfying the 32-electron principle. J. Phys. Chem. C 2014, 118 (13), 7211–7221. 10.1021/jp500453v. [DOI] [Google Scholar]
  32. Miralrio A.; Sansores L. E. On the search of stable, aromatic and ionic endohedral compounds of C28: A theoretical study. Comput. Theor. Chem. 2016, 1083, 53–63. 10.1016/j.comptc.2016.03.010. [DOI] [Google Scholar]
  33. Muñoz-Castro A.; Bruce King R. Evaluation of bonding, electron affinity, and optical properties of M@C28 (M = Zr, Hf, Th, and U): Role of d- and f-orbitals in endohedral fullerenes from relativistic DFT calculations. J. Comput. Chem. 2017, 38 (1), 44–50. 10.1002/jcc.24518. [DOI] [PubMed] [Google Scholar]
  34. Dai X.; Gao Y.; Jiang W.; Lei Y.; Wang Z. U@C28: the electronic structure induced by the 32-electron principle. Phys. Chem. Chem. Phys. 2015, 17 (36), 23308–23311. 10.1039/C5CP04127A. [DOI] [PubMed] [Google Scholar]
  35. Dognon J.-P.; Clavaguéra C.; Pyykkö P. A Predicted Organometallic Series Following a 32-Electron Principle: An@C28 (An = Th, Pa+, U2+, Pu4+). J. Am. Chem. Soc. 2009, 131 (1), 238–243. 10.1021/ja806811p. [DOI] [PubMed] [Google Scholar]
  36. ErkoÇ Ş. Metal atom endohedrally doped C20 cage structure: (X@C20; X = Ni, Fe, Co). Int. J. Mod. Phys. C 2005, 16 (10), 1553–1560. 10.1142/S0129183105008138. [DOI] [Google Scholar]
  37. An Y. P.; Yang C. L.; Wang M. S.; Ma X. G.; Wang D. H. Ab initio investigations of the charge transport properties of endohedral M@C20 (M = Na and K) metallofullerenes. Chin. Phys. B 2010, 19 (11), 113402. 10.1088/1674-1056/19/11/113402. [DOI] [Google Scholar]
  38. Nikolai A. P.; Eugene F. K.; Sergey A. V.; Nguyen Ngoc H.; Oleg N. B.; Andrei I. S.; Irina V. L.; Andrey A. K.; Andrey M. P.; Yurii E. L. Magnetically operated nanorelay based on two single-walled carbon nanotubes filled with endofullerenes Fe@C20. J. Nanophotonics 2010, 4 (1), 041675. 10.1117/1.3417104. [DOI] [Google Scholar]
  39. Samah M.; Boughiden B. Structures, electronic and magnetic properties of C20 fullerenes doped transition metal atoms M@C20 (M = Fe, Co, Ti, V). Int. J. Mod. Phys. C 2010, 21 (12), 1469–1477. 10.1142/S0129183110015968. [DOI] [Google Scholar]
  40. An Y. P.; Yang C. L.; Wang M. S.; Ma X. G.; Wang D. H. Geometrical and electronic properties of the clusters of C20 cage doped with alkali metal atoms. J. Cluster Sci. 2011, 22 (1), 31–39. 10.1007/s10876-011-0354-x. [DOI] [Google Scholar]
  41. Wu J. L.; Sun Z. C.; Li X. J.; Ma B.; Tian M. S.; Li S. R. Theoretical study on the smallest endohedral metallofullerenes: TM@C20 (TM = Ce and Gd). Int. J. Quantum Chem. 2011, 111 (14), 3786–3792. 10.1002/qua.22908. [DOI] [Google Scholar]
  42. Manna D.; Ghanty T. K. Theoretical prediction of icosahedral U@C20 and analogous systems with high HOMO-LUMO Gap. J. Phys. Chem. C 2012, 116 (31), 16716–16725. 10.1021/jp302138p. [DOI] [Google Scholar]
  43. Baei M. T.; Soltani A.; Torabi P.; Hosseini F. Formation and electronic structure of C20 fullerene transition metal clusters. Monatsh. Chem. 2014, 145 (9), 1401–1405. 10.1007/s00706-014-1218-5. [DOI] [Google Scholar]
  44. Meng F. C.; Zhou Z. W.; Zhang P. L.; Jiang M.; Xu X. L.; Wang Y.; Gou J. H.; Hui D.; Die D. Encapsulation of an f-block metal atom/ion to enhance the stability of C20 with the Ih symmetry. Phys. Chem. Chem. Phys. 2015, 17 (6), 4328–4336. 10.1039/C4CP03159H. [DOI] [PubMed] [Google Scholar]
  45. Gonzalez M.; Lujan S.; Beran K. A. Investigation into the molecular structure, electronic properties, and energetic stability of endohedral (TM@C20) and exohedral (TM-C20) metallofullerene derivatives of C20: TM = Group 11 and 12 transition metal atoms/ions. Comput. Theor. Chem. 2017, 1119, 32–44. 10.1016/j.comptc.2017.09.013. [DOI] [Google Scholar]
  46. Muñoz-Castro A.; King R. B. On the formation of smaller p-block endohedral fullerenes: Bonding analysis in the E@C20 (E = Si, Ge, Sn, Pb) series from relativistic DFT calculations. J. Comput. Chem. 2017, 38 (19), 1661–1667. 10.1002/jcc.24809. [DOI] [PubMed] [Google Scholar]
  47. Li J. R.; Wang R.; Huang W. R.; Zhu Y.; Teo B. K.; Wang Z. G. Smallest Endohedral Metallofullerenes [Mg@C20]n (n = 4, 2, 0, −2, and −4): Endo-Ionic Interaction in Superatoms. J. Phys. Chem. Lett. 2023, 14 (11), 2862–2868. 10.1021/acs.jpclett.3c00445. [DOI] [PubMed] [Google Scholar]
  48. Adamo C.; Barone V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. J. Chem. Phys. 1999, 110 (13), 6158–6170. 10.1063/1.478522. [DOI] [Google Scholar]
  49. Xie B.; Wang H. Q.; Li H. F.; Zhang J. M.; Zeng J. K.; Qin L. X.; Mei X. J. Structural and electronic properties of bimetallic Eu2 doped silicon-based clusters. J. Cluster Sci. 2024, 35 (1), 115–127. 10.1007/s10876-023-02466-z. [DOI] [Google Scholar]
  50. Xie B.; Wang H. Q.; Li H.-F.; Zhang J. M.; Zeng J. K.; Mei X. J.; Zhang Y. H.; Zheng H.; Qin L. X. Making sense of the growth behavior of ultra-high magnetic Gd2-doped silicon clusters. Molecules 2023, 28 (13), 5071. 10.3390/molecules28135071. [DOI] [PMC free article] [PubMed] [Google Scholar]
  51. Zeng J. K.; Wang H. Q.; Li H. F.; Zheng H.; Zhang J. M.; Mei X. J.; Zhang Y. H.; Ding X. L. Exploring the stability and aromaticity of rare earth doped tin cluster MSn16– (M = Sc, Y, La). Phys. Chem. Chem. Phys. 2024, 26 (4), 2986–2994. 10.1039/D3CP04803A. [DOI] [PubMed] [Google Scholar]
  52. Dolg M.; Wedig U.; Stoll H.; Preuss H. Energy-adjusted ab initio pseudopotentials for the first row transition elements. J. Chem. Phys. 1987, 86 (2), 866–872. 10.1063/1.452288. [DOI] [Google Scholar]
  53. Andrae D.; Häußermann U.; Dolg M.; Stoll H.; Preuß H. Energy-adjustedab initio pseudopotentials for the second and third row transition elements. Theor. Chim. Acta 1990, 77 (2), 123–141. 10.1007/BF01114537. [DOI] [Google Scholar]
  54. Dolg M.; Stoll H.; Savin A.; Preuss H. Energy-adjusted pseudopotentials for the rare earth elements. Theor. Chim. Acta 1989, 75 (3), 173–194. 10.1007/BF00528565. [DOI] [Google Scholar]
  55. Dolg M.; Stoll H.; Preuss H. A combination of quasirelativistic pseudopotential and ligand field calculations for lanthanoid compounds. Theor. Chim. Acta 1993, 85 (6), 441–450. 10.1007/BF01112983. [DOI] [Google Scholar]
  56. Hehre W. J.; Ditchfield R.; Pople J. A. Self-consistent molecular orbital methods. XII. Further extensions of Gaussian-type basis sets for use in molecular orbital studies of organic molecules. J. Chem. Phys. 1972, 56 (5), 2257–2261. 10.1063/1.1677527. [DOI] [Google Scholar]
  57. Hariharan P. C.; Pople J. A. The influence of polarization functions on molecular orbital hydrogenation energies. Theor. Chim. Acta 1973, 28 (3), 213–222. 10.1007/BF00533485. [DOI] [Google Scholar]
  58. Dunning T. H. Jr Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 1989, 90 (2), 1007–1023. 10.1063/1.456153. [DOI] [Google Scholar]
  59. Dolg M.; Stoll H.; Preuss H. Energy-adjusted ab initio pseudopotentials for the rare earth elements. J. Chem. Phys. 1989, 90 (3), 1730–1734. 10.1063/1.456066. [DOI] [Google Scholar]
  60. Frisch M. J.; Trucks G. W.; Schlegel H. B.; Scuseria G. E.; Robb M. A.; Cheeseman J. R.; Scalmani G.; Barone V.; Mennucci B.; Petersson G. A.; Nakatsuji H.; Caricato M.; Li X.; Hratchian H. P.; Izmaylov A. F.; Bloino J.; Zheng G.; Sonnenberg J. L.; Hada M.; Ehara M.; Toyota K.; Fukuda R.; Hasegawa J.; Ishida M.; Nakajima T.; Honda Y.; Kitao O.; Nakai H.; Vreven T.; Montgomery J. A. Jr; Peralta J. E.; Ogliaro F.; Bearpark M.; Heyd J. J.; Brothers E.; Kudin K. N.; Staroverov V. N.; Keith T.; Kobayashi R.; Normand J.; Raghavachari K.; Rendell A.; Burant J. C.; Iyengar S. S.; Tomasi J.; Cossi M.; Rega N.; et al. Gaussian09; Gaussian Inc.: Wallingford, CT, USA, 2010.
  61. Schleyer P. v. R.; Maerker C.; Dransfeld A.; Jiao H.; van Eikema Hommes N. J. R. Nucleus-independent chemical shifts: a simple and efficient aromaticity probe. J. Am. Chem. Soc. 1996, 118 (26), 6317–6318. 10.1021/ja960582d. [DOI] [PubMed] [Google Scholar]
  62. Klod S.; Kleinpeter E. Ab initio calculation of the anisotropy effect of multiple bonds and the ring current effect of arenes—application in conformational and configurational analysis. J. Chem. Soc., Perkin Trans. 2 2001, (10), 1893–1898. [Google Scholar]
  63. Wang X.; Liu Z. Y.; Yan X. F.; Lu T.; Zheng W. L.; Xiong W. W. Bonding character, electron delocalization, and aromaticity of cyclo[18]carbon (C18) precursors, C18-(CO)n (n = 6, 4, and 2): focusing on the effect of carbonyl (-CO) groups. Chem.—Eur. J. 2022, 28 (7), e202103815 10.1002/chem.202103815. [DOI] [PubMed] [Google Scholar]
  64. Lu T.; Chen F. Multiwfn: A multifunctional wavefunction analyzer. J. Comput. Chem. 2012, 33 (5), 580–592. 10.1002/jcc.22885. [DOI] [PubMed] [Google Scholar]
  65. Humphrey W.; Dalke A.; Schulten K. VMD: Visual molecular dynamics. J. Mol. Graphics 1996, 14 (1), 33–38. 10.1016/0263-7855(96)00018-5. [DOI] [PubMed] [Google Scholar]
  66. Breneman C. M.; Wiberg K. B. Determining atom-centered monopoles from molecular electrostatic potentials. The need for high sampling density in formamide conformational analysis. J. Comput. Chem. 1990, 11 (3), 361–373. 10.1002/jcc.540110311. [DOI] [Google Scholar]
  67. Jusélius J.; Sundholm D.; Gauss J. Calculation of current densities using gauge-including atomic orbitals. J. Chem. Phys. 2004, 121 (9), 3952–3963. 10.1063/1.1773136. [DOI] [PubMed] [Google Scholar]
  68. An W.; Gao Y.; Bulusu S.; Zeng X. C. Ab initio calculation of bowl, cage, and ring isomers of C20 and C20–. J. Chem. Phys. 2005, 122 (20), 204109. 10.1063/1.1903946. [DOI] [PubMed] [Google Scholar]
  69. Parr R. G.; Pearson R. G. Absolute hardness: companion parameter to absolute electronegativity. J. Am. Chem. Soc. 1983, 105 (26), 7512–7516. 10.1021/ja00364a005. [DOI] [Google Scholar]
  70. Manolopoulos D. E.; May J. C.; Down S. E. Theoretical studies of the fullerenes: C34 to C70. Chem. Phys. Lett. 1991, 181 (2), 105–111. 10.1016/0009-2614(91)90340-F. [DOI] [Google Scholar]
  71. Parr R. G.; Zhou Z. Absolute hardness: unifying concept for identifying shells and subshells in nuclei, atoms, molecules, and metallic clusters. Acc. Chem. Res. 1993, 26 (5), 256–258. 10.1021/ar00029a005. [DOI] [Google Scholar]
  72. de Heer W. A. The physics of simple metal clusters: experimental aspects and simple models. Rev. Mod. Phys. 1993, 65 (3), 611–676. 10.1103/RevModPhys.65.611. [DOI] [Google Scholar]
  73. Hirsch A.; Chen Z.; Jiao H. Spherical aromaticity in Ih symmetrical fullerenes: the 2(N+1)2 rule. Angew. Chem., Int. Ed. 2000, 39 (21), 3915–3917. . [DOI] [PubMed] [Google Scholar]
  74. Reed A. E.; Weinstock R. B.; Weinhold F. Natural population analysis. J. Chem. Phys. 1985, 83 (2), 735–746. 10.1063/1.449486. [DOI] [Google Scholar]
  75. Lu T.; Chen F. W. Atomic dipole moment corrected Hirshfeld population method. J. Theor. Comput. Chem. 2012, 11 (01), 163–183. 10.1142/S0219633612500113. [DOI] [Google Scholar]
  76. Lu T.; Chen F. W. Comparison of computational methods for atomic charges. Acta Phys. Chim. Sin. 2012, 28 (01), 1–18. 10.3866/PKU.WHXB2012281. [DOI] [Google Scholar]
  77. Zubarev D. Y.; Boldyrev A. I. ”Developing paradigms of chemical bonding: adaptive natural density partitioning. Phys. Chem. Chem. Phys. 2008, 10 (34), 5207–5217. 10.1039/b804083d. [DOI] [PubMed] [Google Scholar]
  78. Zdetsis A. D. Open-shell magnetic states in alternant and non-alternant nanographenes: Conceptions and misconceptions. Carbon Trends 2024, 14, 100330. 10.1016/j.cartre.2024.100330. [DOI] [Google Scholar]
  79. Wang X.; Liu Z. Y.; Wang J. J.; Lu T.; Xiong W. W.; Yan X. F.; Zhao M. D.; Orozco-Ic M. Electronic structure and aromaticity of an unusual cyclo[18]carbon precursor, C18Br6. Chem.—Eur. J. 2023, 29 (31), e202300348 10.1002/chem.202300348. [DOI] [PubMed] [Google Scholar]
  80. Zdetsis A. D. Structural, cohesive, electronic, and aromatic properties of selected fully and partially hydrogenated carbon fullerenes. J. Phys. Chem. C 2011, 115 (30), 14507–14516. 10.1021/jp2023007. [DOI] [Google Scholar]
  81. Fliegl H.; Taubert S.; Lehtonen O.; Sundholm D. The gauge including magnetically induced current method. Phys. Chem. Chem. Phys. 2011, 13 (46), 20500–20518. 10.1039/c1cp21812c. [DOI] [PubMed] [Google Scholar]

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Supplementary Materials

ao4c05912_si_001.pdf (1.9MB, pdf)
ao4c05912_si_002.mp4 (80.5KB, mp4)
ao4c05912_si_003.mp4 (79.9KB, mp4)
ao4c05912_si_004.mp4 (81.8KB, mp4)
ao4c05912_si_005.mp4 (78KB, mp4)

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