Superatomic states under high pressure

Summary The study of superatoms has attracted great interest since they apparently go beyond the traditional understanding of the periodic table of elements. In this work, we clearly show that superatoms can be extended from conventional structures to states under pressure condition. By studying the compression process of the CH4@C60 system formed via embedding methane molecules inside fullerene C60, it is found that the system maintains superatomic properties in both static states, and even dynamic rotation situations influenced by quantum tunneling. Remarkably, the simulations reveal the emergence of new superatomic molecular orbitals by decreasing the confined space to approach the van der Waals boundary between CH4 and C60. Our current results not only establish a complete picture of superatoms from ambient condition to high pressure, but also offer a perspective for the discovery and exploration of new properties in superatom systems under extreme conditions.


INTRODUCTION
Superatom has attracted significant attention, since it exhibits novel physical and chemical properties, which should be of fundamental interest in the fields of physics, chemistry, and material science. The characteristic of superatoms is often determined by the atom-like electronic arrangement. [1][2][3][4][5][6][7][8][9][10] Mass spectrometry experiment is a key step to identify superatom 3 and the magic number rule for electrons is gradually summed according to the jellium model. 1,[3][4][5] However, there is a concern about the stability of superatoms under convention conditions in the past, and even more on their isolated structures. [11][12][13][14][15][16][17][18][19] At present, it is well known that extreme conditions, especially high pressure, are the common means to create exotic properties that are not accessible at conventional conditions, by influencing the microscopic structure, the interatomic interactions and so on. [20][21][22][23][24][25] For example, the predicted near-room-temperature superconductivity in LaH 10 is experimentally confirmed under high pressure. [26][27][28][29] The emergence of the remarkable properties under high pressure is often found to violate the traditional understanding from structures to states. 21,22 We propose a supposition as to whether the superatoms, as a special class of molecules, can also achieve the transformation from the structure to the state under extreme conditions. This will open up the exploration of superatom in non-ambient environment to enrich the development of superatomic concept and extend their dimension, which could greatly bring new prospects for the efforts to expand the periodic table of superatomic elements and bottom-up construct materials or devices. 7,[30][31][32] We also hope that the reason for the existence of special properties under high-pressure can be explained at the atomic level from the superatomic perspective to promote the development of interdisciplinary studies.
Regarding this issue, it is necessary to study such systems which are of interest in both superatoms and high-pressure field. Fortunately, there are few systems as suitable as fullerene C 60 and its derivatives. 16,[33][34][35][36][37][38] On the one hand, the molecular configuration of single C 60 has be obtained in low-temperature simple cubic phase under hydrostatic pressure by the pressure-transmitting-fluid, in which its covalent interaction of C-C bond is enhanced and lattice constant hardly change compared to that of face-centered-cubic phase under general conditions. This realizes isotropic compression. [39][40][41][42] On the other hand, the derivatives of C 60 can reveal interesting physical and chemical properties after encapsulating atoms or molecules based on its unique confined environment, so that they have potential applications in molecular switches and expected metallic or even superconducting character. 38,[43][44][45][46][47] The interactions between the confined environments and the embedded group have various ranges from general intermolecular interactions to interactions within van der Waals boundaries, offering the new physical phenomena, such as anomalous enhancement of molecular rotation, pressure-induced change of metallic properties. [48][49][50] Therefore, endohedral fullerenes may offer a suitable platform for the study of static superatom properties, especially, the enhanced connection between the inner guest and the outer cage during the compression process, and their dynamic mean state under high pressure. Since the movement of light nuclear elements contained by methane in a confined environment is also attracting much attention, the CH 4 @C 60 , as a typical experimentally confirmed system, 46,51 providing a unique opportunity to explore the superatom properties of the system under compression.
In this work, we take the CH 4 @C 60 system as a representative example to investigate the role of pressure in dealing with superatoms. Based on first-principles calculations, we found the superatomic properties in the compression process from general intermolecular interactions to interactions within the van der Waals boundaries between CH 4 and C 60 . There are changes in the arrangement of superatomic molecular orbitals (SAMOs) and degree of MOs' delocalization. It includes that the localized MOs contributed by CH 4 are gradually converted into SAMOs, accompanied by the generation of 3P-SAMOs. Obviously, these phenomena cannot stand when the compressive condition is removed. This represents a novel superatom physical state under pressure instead of the traditional picture. Our work provides new insights for future research toward the discovery of the physical properties and application of superatoms.

RESULTS AND DISCUSSION
The compression process of CH 4 @C 60 We began our simulation on the structural optimization of the CH 4 @C 60 , which shows the C 3v symmetry ( Figure 1A, Table S1). Given that these structures have one C3 symmetric axis, four H atoms have two typical iScience Article positions as shown in Figure 1A. The average distance between the C atom on the methane molecule and the C atoms on the C 60 cage of CH 4 @C 60 is called the radius of fullerene (r). The radius of initial fullerene (r 0 ) is 3.554 Å , which is coincided with the previous experimental result. 46 To simulate isotropic hydrostatic compression resulting from pressure-transmitting-fluid of experiment, the equal proportional compression of fullerenes was explored. The volume strain (e V ) is defined as 1-r 3 /r 0 3 , which varies from 0.0 to 0.232 upon compression. To study the physical properties being of concern on fullerene under high pressure, the effective strain energy constant (E 00 ), bulk modulus (B), and bond force constant (k r ) for the CH 4 @C 60 were calculated (the details show in Figures 1A-1C). The results show that compared with C 60 (E 00 = 22.643 eV/atom, B = 850.943 GPa, k r = 806.411 N/m), CH 4 @C 60 have higher E 00 (22.928 eV/atom), B (895.693 GPa) and k r (846.467 N/m). It is consistent with the results summarized that the B and E 00 values of the endohedral fullerene than that of the fullerene and may correlate with higher density corresponding to higher mechanical properties. [52][53][54][55] While the higher k r for endohedral fullerene could be explained by comparing the bond lengths between the carbon atoms. 52 These calculations imply that the embedded methane also tends to increase the pressure resistance and rigidity of the fullerene. 52 As a basis of superatomic state exploration, it is fundamental to discuss the change in the electronic structure of superatoms under pressure. The charge distributions of cage and the embedded molecule by Voronoi deformation density (VDD) 56 method were analyzed. As shown in Figure 1D and Table S2, it can be clearly seen that the amount of negative charge transferred from CH 4 to C 60 increases as the compression continue, which comes mainly from the H atoms. In addition, the dramatic increase in the tendency of H atoms to lose negative charges in CH 4 @C 60 compared to isolated methane and the almost no charge transfer between C atoms for isolated C 60 both suggest that intercalated methane induces charge transfer. To ensure the reliability of the above results, Hirshfeld 57 method was also employed, and the results are qualitatively consistent with VDD (Table S3). To provide detailed insights into the intermolecular interaction between CH 4 and C 60 during compression, energy decomposition analysis (EDA) was carried out. Total interaction (E int ), Pauli repulsion interaction (E Pauli ), three attraction interactions, containing the electrostatic (E elect ), orbital (E orb ), and dispersion (E disp ) interactions as a function of e V are shown in Figure 1E. For the attraction interaction of the equilibrium structures, the E disp is dominant, illustrating that interaction between two components is typical van der Waals. While in the compression process, the E elect becomes more important and exceeds the E disp corresponding with the Dr of about À0.17 Å . That is, from this point onwards, the classical coulomb interaction account for the largest proportion of total attractive interactions, rather than van der Waals interaction. 58 Furthermore, the E int changes from negative to positive value as the Dr is À0.21 Å , which suggests that interaction between the CH 4 and C 60 are within van der Waals boundary.
The Raman spectrum characterization of CH 4 @C 60 during compression Given the importance of vibration-related spectra on experimental observation, the Raman spectrum of CH 4 @C 60 was calculated. For CH 4 @C 60 , as shown in Figures 1F and S1, there are three kinds of Raman active vibrational modes, containing radial breathing, tangential pentagonal pinch modes on the cage (marked as Ag (1) and Ag (2)), and a tensile vibration of C-C covalent bonds (marked as Hg (8)). Interestingly, the Ag(2) and Hg (8) modes are unable to distinguish when the e V is 0.160. This phenomenon also can be seen in the Raman spectrum of isolated C 60 ( Figure S2). Actually, it has been observed in the experimental research of C 60 at a pressure of 26 GPa. 24 The merging phenomenon between the Ag(2) and Hg (8) Figures 2B and 2C. Actually, it begins to be generated when the e V increases ( Figure S4). From analysis on density of state ( Figure S5), the MOs belong to the changed electronic configuration are contributed by both methane and C 60 , which are highlighted in right of Figure 2. More strikingly, for the highlighted MOs, there are some regular MOs (MOs1-6) in non-compressed structure. As the r decreases, MOs1-6 are petered out and replaced by SAMOs gradually. This indicates that MOs become more delocalized upon compression. When the e V is 0.042, these MOs are replaced by new SAMOs of 3P x , 3P y and 3P z . Then, the 2F yð3x 2 À y 2 Þ and 2F xz 2 SAMOs are added when the e V is 0.121. These SAMOs, including 3S, 2P x , 2P y , 2P z , 2D z 2 , 2D xy , 2D x 2 À y 2 , 3P x , 3P y , 3P z , 2F z 3 , 2F yð3x 2 À y 2 Þ , 2F xz 2 , 2F zðx 2 À y 2 Þ and 2F xyz , are existed in subsequent compression of the e V from 0.160 to 0.232. There is the emergence of new superatomic molecular orbitals when the confined space decreases to approach the van der Waals boundary ((Dr is iScience Article about À0.20 Å ). From the geometric and electronic structure of CH 4 @C 60 , the superatoms have the change in the interaction analysis and charge transfer under external conditions of high pressure, but the superatomic properties, the atom-like characteristics of MOs, are maintained, which are described as the superatomic state. The these SAMOs generation is firstly caused by the enhanced electron correlation between methane and cage from the charge transfer and intermolecular interaction analyses. More importantly, there is a crucial factor that the interaction between the two parts enter the van der Waals boundary upon the compression, resulting in a new orbital combination with the two parts. To clarify the composition of the orbitals, the contribution ratio of the cage and methane to the orbitals highlighted in Figure 2 was collected (Table S5), which can also be adapted to the above result.
For exploring the importance of changes in properties brought about by compression, the ultravioletvisible (UV-Vis) absorption spectra were performed as shown in Figure S6 and Table S6. When the ε V is 0.232, new sources of absorption peaks are due to the exchange of energy between the F SAMOs and the regular orbitals, resulting in that the latter can be allowed to excited. Moreover, the spectra exhibit interesting phenomena containing the blue-shifted and hyperchromic effect of peaks, which provides a theoretical basis for experimentally fingerprinting the compression.

The potential energy surface of methane rotation in cage
The experimental measurement of molecular states can characterize not only the electron cloud related to the wave function, but also the average dynamic behavior over time. Therefore, we analyzed the rotational behavior of methane and the influence of its interaction with C 60 on the superatomic state ( Figure 3A). The E int curves show the potential energy surface of methane rotation in Figure 3B and they have a certain symmetry and periodicity ( Figure S7). From decomposed components curves in Figures 3C-3F, the main source of energy surfaces is the E Pauli , while the E orb prevents the formation of energy barrier during rotation. This could explain the reduction of force repulsion caused by the charge transfer during compression. While  Figure 3B). Further compression leads to the appearance of potential well, which is mainly contributed by the completely opposite change trend of E disp in the early and late stages of compression due to the van der Waals boundary. Another reason why the potential well appears only in Z 2 is that the isotropy of the rotation of the three H atoms leads to a superposition effect. It illustrates that the methane will spontaneously rotate under pressure.
The electronic structure analysis of the system during methane rotation For further studying the effects of rotational behaviors on superatomic properties, we selected several structures in the rotation process of the maximum compression and analyzed their electronic structures containing the DOS and SAMOs (Figure 4). Comparing with the initial structure, their electronic configuration, 1S 2 1P 6 1D 10 1F 14 1G 18 1H 22 2S 2 1I 26 1J 7 3S 2 2P 6 2D 10 3P 6 3F 14 2G 18 2H 10 , and the HOMO-LUMO gaps (range of 3.06-3.07 eV) almost have no change. These results reveal the existence of the superatomic state in the rotational process.

The quantum tunneling effect during methane rotation
The confined conditions may lead to strong tunneling effects from previous studies, 48,61,62 which affect the state of the system. Not to mention the methane with light elements in this work. Thus, quantum tunneling (QT) needs to be taken seriously. It is noticed that methane rotation in this system has two distinctive features. On one hand, the energy barrier of this process is less than 0.1 eV, on the other hand, the rotational behavior can be seen as a model that the preservation of the center C atom and the rotation of the smallmass H atoms in space position. To better understand the role of QT effects, we next focus on tunneling analysis for the rotation behaviors around the Z 2 axis due to the presence of potential well for Z 2 . The energy barriers of H atoms rotation around Z 2 as illustrated by E int are 0.014, 0.017, and 0.020 eV. For these three processes, we calculated their QT probability (P tunneling ) under the different provided energy (E p ), as shown in Figure 5A. With the increase of E p , P tunneling increases gradually. The high tunneling probability is iScience Article represented in the rotation process, meaning the process can easily occur through tunneling. Taking E p of 0.12 eV as an example, when the e V is 0.0, 0.121, and 0.232, the P tunneling of methane rotation is as high as 5 3 10 À1 , 3 3 10 À1 , 3 3 10 À2 , respectively. Meanwhile, the thermal disturbance probability (P thermal ) for these processes was also studied ( Figure 5B). It is found that P thermal is already very high at above temperature of 100 K, while through the P thermal is low at low temperature, such as at 20 K, the P thermal for the e V of 0.0 (2.8 3 10 À1 ), 0.121 (6.5 3 10 À1 ), 0.232 (6.0 3 10 À3 ) is smaller than P tunneling at the E p of 0.12 eV. These results are thus concluded that H atoms of methane are freedom in fullerene cage, and free rotation can be achieved through QT in situations where thermodynamics cannot work at low temperature. This also validates the result of the relatively free rotation of methane obtained from the experimental electron density analysis 46 and achieves the quantum barrier-free mechanism in the system of methane under fullerene confinement.

Conclusions
In summary, we have theoretical predicted superatomic properties of CH 4 @C 60 under pressure by in-depth electronic analysis. Under pressure, there is the generation of new SAMOs, especially, the change of the molecular orbitals contributed by methane from regular MOs to SAMOs, when the distance between CH 4 and C 60 decreases within the van der Waals boundary. At this time, the methane can rotate to change the symmetry of system. The results show that the superatomic property, atom-like orbitals, are preserved during compression and dynamic rotation, which realize the extension of superatomic state under high pressure from superatomic structure of ambient condition. Moreover, the rotation of methane is freedom in the fullerene cage, even it can be achieved through QT in situations where thermodynamics play a weak role at low temperature. Our findings may provide a perspective to explain the new physical and chemical properties of superatoms in the compression process, and will stimulate the further expansion of the research on superatomic problems.
And the corresponding bond force constant k rb was calculated by differentiation, evaluating at the corresponding binding energy minimum at L 0 b : 67,68 The k r (=2/3 k r1 +1/3 k r2 ) for CH 4 @C 60 and C 60 were calculated.

The calculations of tunneling probability
The quantum tunneling probability (P tunneling ) and thermal disturbance probability (P thermal ) of methane rotation are analyzed. The P tunneling is obtained by Wenzel-Kramers-Brillouin (WKB) approximation, satisfying: which is only relevant to E p for a certain potential energy surface V(x). The x 1 and x 2 in formula are the abscissas of the two intersection points for E = E p and E = V(x), respectively. The P thermal suits the Boltzmann distribution: 69 varying with E p and temperature T, where DE is the difference from E p to the barrier (E b ).

QUANTIFICATION AND STATISTICAL ANALYSIS
Analyses and plots were performed with Microsoft Excel, PowerPoint and MATLAB.

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