English

• 1. INTRODUCTION

  As a typical electron deficient element (two electrons in four valence orbitals), beryllium (Be) prefers the multicenter bonding to have the number of its valence shell electrons as much as possible. Such a bonding preference is particularly useful for designing the species with non-classical planar hypercoordinate carbon (phC). In 2008, Wang group first designed a series of planar tetracoordinate carbon (ptC) species involving beryllium^[1]. In 2010 and 2016, Wu and Wang groups designed BeH-based ptC species with the carbon skeletons of monocyclic arenes and ethylene, whose structural models were also extended to various types of nanomolecules^{[2, 3]}. In 2018 and 2019, Guo et al. reported a series of global minima ptC species, including CBe₄Au₄, CBe₄Li₄, and CBe₃X₃⁺ (X = H, Li, Na, Cu, Ag)^[4–6].

  In comparison with the being employed for designing ptC species, beryllium was more frequently and successfully employed in designing species with planar pentacoordinate carbon (ppC) previously. In 2010 and 2012, Wang, Wu, and Merino joint groups reported the global energy minima (GEM) ppC species CAl₄Be, CAl₃Be₂^–, CAl₂Be₃^2–, and CAl₂Be₃Li^– by substituting the aluminum atom(s) in milestone CAl₅⁺ with beryllium atom(s)^{[7, 8]}. In 2018, Wu group further found that these GEM ppC species can be further stabilized by introducing H atom on the peripheral edges involving beryllium atom^[9]. In 2012, Merino group designed the GEM CBe₅E^– (E = Al, Ga, In, Tl) with a CBe₄E ppC core moiety^[10]. In 2008, Luo et al. reported the hexatomic species CBe₅ and CBe₅^4– with a ppC^[11]. Remarkably, though highly negatively charged CBe₅^4– was unstable, it was employed subsequently as a core moiety to design dozens of σ and π double aromatic GEM species with a ppC CBe₅E_n^n–4 (n = 1~5) by introducing various kinds and numbers of monovalent elements (including H, Li, Na, K, F, Cl, Br, Au) to the bridging positions of Be–Be edges^[12–15].

  Beryllium has also been applied to design the species with planar hexacoordinate carbon or boron (p6C^[16] or p6B^[17]) as well as the planar heptacoordinate transition metals. Beryllium was utilized to design the monolayer sheets with perfect ptC^[18], the zig-zag double chain nanoribbon with ppC and ribbon aromaticity^[19], the quasi-ppC-containing monolayer sheet featuring the half metallic property and negative Poisson ratio^[20], and the semi-conductive monolayer sheet with quasi-p6C^[21].

  In the application of beryllium to design phC species, the most exciting part by far should be the design of ppC, because beryllium was involved in more than half of GEM ppC species. In particular, the ppC-containing CBe₅^4– derivatives were the paragon of such non-classical molecule design. Dozens of species can be designed by stepwise introduction of various mon-valent elements onto the Be-Be edges of CBe₅^4– and the majority of these species were turned out to the GEM. Is there a similar paragon that can be employed in the design of ptC? The answer is positive. We will show in the following that CBe₄^2– species can play the parallel role in designing ptC species to that played by CBe₅^4– in designing ppC species.

  2. COMPUTATIONAL METHODS

  The geometries of designed species were optimized and the subsequent harmonic vibrational frequencies were analyzed at both B3LYP/BS1 and B2PLYP-D/BS1 levels. Herein, BS1 is a mixed basis set used in this work with aug-cc-pVTZ for elements lighter than Cu and aug-cc-pVTZ-PP for Cu and heavier elements; while B2PLYP-D is a double hybrid B2PLYP functional considering the empirical dispersion. The geometries and frequencies obtained using B3LYP functional were not different in essential from those obtained using B2PLYP-D, so the B3LYP functional was employed for further studies, including electronic structure analyses and stability explorations. The chemical bonding in the designed species was interpreted using adaptive natural density partitioning (AdNDP) analyses at the B3LYP/BS2 level, where BS2 denotes a mixed basis sets with 6-31G(d) for elements lighter than Br and LANL2DZ for heavier elements. The potential energy surfaces of the concerned components were explored using the stochastic search algorithm. Both the singlet and triplet surfaces were considered. The generated random structures were initially optimized at the B3LYP/BS2 level, and then ten lowest isomers were optimized and harmonic vibrational frequencies were analyzed at the B3LYP/BS1 level. The energies of these isomer were further improved at the CCSD(T)/BS1 level and the relative energies were compared using the CCSD(T)/BS1 single point energy in combination with the zero-point energy corrections obtained at the B3LYP/BS1 level (abbreviated as CCSD(T)//B3LYP). The dynamic stability of designed species was studied using Born-Oppenheimer molecular dynamic (BOMD)^{[22, 23]} simulations at the B3LYP/BS2 level at 298 K. The structural evolution during simulation was described by the root-mean-square derivation (RMSD, in Å) relative to the B3LYP/BS2-optimized structures. The nucleus-independent chemical shifts (NICS)^[24-26] were calculated at the centers of the three-membered rings and the points located 2 Å above the centers of the three-membered rings and above ptCs to assess the aromatic nature of these ptC species. The AdNDP analyses were performed using AdNDP program^{[27, 28]}, the stochastic search algorithm^{[29, 30]} was realized using GXYZ 2.0 program^{[31, 32]}, the CCSD(T) calculations were carried out using MolPro 2012.1 package^[33], and all other calculations were performed using Gaussian 16 package^[34].

  3. RESULTS AND DISCUSSION

  We had recently reported the ptC species CBe₄M_n^n–2 (M = Li, Au, n = 1~3)^[35]. In that work, we focused on achieving the 14 valence electrons species with ptC rather than the systematic design of ptC species based on a good template structure. Nevertheless, we found that the similar structural model might be extended to the congeners of Li and Au, including Na, Cu, and Ag, though the potential energy surfaces of corresponding species were not explored. Therefore, consulting the previous excellent works on designing ppC species based on CBe₅ core moiety, we speculated that CBe₄ might be another excellent core moiety for systematically designing new ptC species by attaching the monovalent atoms on the Be–Be edges. First, we verify the molecular charges of CBe₄ cluster, which can be deduced from our previously reported species having the formula of CBe₄M_n^n–2 (n = 1~3). If the value of n is extended to zero, a dianionic cluster with the formula of CBe₄^2– (0, see Fig. 1) can be obtained. At both B3LYP/BS1 and B2PLYP-D/BS1 levels, such a cluster adopts the planar structure in C_2v symmetry and encloses a ptC. As a comparison, neutral CBe₄ and the highly negatively charged CBe₄^4– adopt the non-planar structures in D₂ and D_2d symmetries, respectively, and thus they are disregarded in the following. The C–Be interatomic distances in 0 are 1.60 and 1.68 Å, short enough for each beryllium atom to be counted as a coordination to center carbon, so 0 is an eligible ptC species.

  Figure 1

  

  Figure 1.  Optimized structure of CBe₄^4–, CBe₄^2– (0), and CBe₄ at the B3LYP/aug-cc-pVTZ level (A) and the AdNDP view of chemical bonding in 0 (B)

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  The AdNDP analysis revealed that 0 had seven pairs of valence electrons, in which three of them were highly diffused Be–Be two-center two electron (2c-2e) σ bonds with occupation number of 1.97 |e|. The diffusion character of such σ bonds, possibly attributed to the high negative charges of the molecule and the metallic nature of beryllium, is unbeneficial to the stabilization of 0 because the electrons at the position far from the nuclei will be reactive. Therefore, the elimination of such diffused σ bonds is highly desired. In contrast, though the remained four pairs of electrons involve all five atoms, they are less diffused than the Be–Be 2c-2e bonds. Note that such four 5c-2e bonds (ON = 2.00 |e|) supported eight electrons to valence shell of the central carbon, which stabilizes the molecule by making the carbon meet the octet rule. In addition, four pairs of electrons consist of three 5c-2e σ and one 5c-2e π bonds, matching the famous 4n+2 rule with n = 1 and 0, respectively, so the preference of ptC structure in 0 may stem from the novel σ and π double aromaticity. Therefore, retaining such 5c-2e bonds is also highly desired. Remarkably, according to our extensive exploration of CBe₄^2– potential energy surface, 0 is GEM and locates 4.17 kcal·mol^–1 lower in energy than the second lowest isomer (0a, see Fig. S4) at the CCSD(T)//B3LYP level. As a comparison, CBe₅^4– ppC structure is a high energy local minimum. The lower molecular charge and the GEM nature of 0 suggest its higher plausibility as a core moiety than CBe₅^4– species for the subsequent design of phC species.

  The systematic design of the ptC species was realized by attaching the monovalent element on the bridging positions of 0, similar to the design of ppC species based on CBe₅^4–. The literature survey had revealed the feasible bridging atoms (E) that had been employed for the ppC design based on CBe₅^4–, including group 1 elements H, Li, Na, group 11 elements Cu, Ag, Au, and group 17 elements F, Cl, Br, I. In this work, the design of ptC species involves the stepwise introduction of these monovalent E elements onto the Be–Be edge(s). As shown in Scheme 1, for the species with one or two E atoms, i.e. CBe₄E^– and CBe₄E₂, we considered two possible structural models, which are labelled as M1/M1′ and M2/M2′, respectively. Note that a new model can be found for both CBe₄E^– and CBe₄E₂ species (M1″ and M2″, see Scheme 1) during the isomer search.

  Scheme 1

  

  Scheme 1.  Stepwise introduction of E atom(s) on the Be–Be of CBe₄^2–

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  We have computed the isomers in various model structures. Fig. 2 shows those with lower energies. If E is an alkali or group 11 metal, it tends to bind CBe₄ moiety on the top Be–Be edge (M1 model) of CBe₄^2– structure (see CBe₄E^– (E = Li (1), Na (4), Cu (7), Ag (10), and Au (13)) in the first column of Fig. 2) rather than on the side Be–Be edge (M1′ model). If E is H or a halogen, it prefers neither top nor the side Be–Be edges, but prefers the terminal position on a bottom Be atom (M1″ model) (see CBe₄E^– (E = H (16), F (19), Cl (22), Br (25), and I (28)) in the fourth column of Fig. 2). Note that the ground electronic state for 19 is triplet (E = F) and that for other CBe₄E^– species is closed-shell singlet.

  Figure 2

  

  Figure 2.  Optimized structures of ptC species designed based on 0. The necessary bond lengths regarding molecular symmetries are given in Å

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  When two E atoms are anchored on the CBe₄ moiety to give CBe₄E₂ species, the situation is similar in structural preference to CBe₄E^–: If E is an alkali or group 11 metal, two E atoms tend to bind CBe₄ moiety with one E atom on top and the other on the side Be–Be edges (M2 model), respectively (see CBe₄E₂ (E = Li (2), Na (5), Cu (8), Ag (11), and Au (13)) in the second column of Fig. 2) rather than both on the side Be–Be edges (M2′ model). As a comparison, if E is H or a halogen, corresponding CBe₄E₂ species prefer the M2″ model (see CBe₄E₂ (E = H (17), F (20), Cl (23), Br (26), and I (29) in the fifth column of Fig. 2) with one E atom on side Be–Be edge and the other E atom on the terminal position of a bottom Be atom. The ground electronic state of all CBe₄E₂^– species is closed-shell singlet.

  Nevertheless, when three E atoms bind the CBe₄ moiety, corresponding CBe₄E₃⁺ species always prefer the M3 model structure (Scheme 1) despite the type of E atom. The third and sixth columns of Fig. 2 show the structures of these 10 species, i.e. CBe₄E₃⁺ (E = Li (3), Na (6), Cu (9), Ag (12), Au (15), H (18), F (21), Cl (24), Br (27), and I (30)).

  As Fig. 2 shows, all these thirty species adopt planar structures with carbon atom surrounded by four Be atoms. The C–Be distances in 1~30 range from 1.568 to 1.736 Å, shorter than the sum of covalent radii of C and Be (1.790 Å), so the carbon atoms in 1~30 are the well-defined ptCs. The Be–Be distances in 1~30 range from 1.869 to 2.208 Å, covering the typical lengths of Be–Be single^[36], double, and pseudo-triple bonds^{[37, 38]}. Remarkably, there are three very short Be–Be distances in CBe₄H₂ (2) and CBe₄H₃⁺ (3) (1.893/1.893, 1.891 and 1.869 Å, respectively), within the range of ultrashort metal-metal distances (USMMDs, defined as d_M–M < 1.900 Å)^[39] and suggesting the strong Be– Be interactions. We further re-optimized the geometries of CBe₄H₂ (2) and CBe₄H₃⁺ (3) to verify the USMMDs at the CCSD(T) level and corresponding geometric parameters are given in Fig. 2 in the parenthesis and red font. As Fig. 2 shows, the above ultrashort Be–Be distances were elongated slightly to 1.935/1.910, 1.911, and 1.888 Å, respectively after the optimization at the CCSD(T) level and only a Be– Be distance (1.888 Å) in 3 was still shorter than 1.900 Å and can be regarded as the USMMD. The USMMD of 1.888 Å can be rationalized by electronic analysis.

  The chemical bonding in these ptC species can be described by the AdNDP analysis. The AdNDP results for CBe₄Cu_n^n–2 and CBe₄H_n^n–2 (n = 1~3) are shown representatively in Fig. 3, while those for other species are similar to E = Cu or E = H, thus they are given in the Supporting Information. As Fig. 3 shows, in CBe₄Cu_n^n–2 (n = 1~3) species, a diffused Be–Be 2c-2e σ bond with ON of 1.93 or 1.87 |e| can be found for the Be–Be edges without bridging Cu atom (see the first column in upper part), while a less diffused Be–Cu– Be 3c-2e σ bond with ON of 1.84~1.98 |e| can be found for the Be–Be edges with a Cu atom (see the second column in upper part). As a comparison, the peripheral bonding in CBe₄H_n^n–2 (n = 1~3) is a little different in that there is a Be–H 2c-2e σ bond with ON of 2.00 |e| covering the terminal Be–H group of CBe₄H^– and CBe₄H₂. Other peripheral bonding patterns are similar to that in CBe₄Cu_n^n–2 (n = 1~3) species, including a diffused Be–Be 2c-2e σ bond (ON = 1.84 or 1.93 |e|) on Be–Be edges without H atom and a less diffused Be–H–Be 3c-2e σ bond (ON = 1.98 or 1.99 |e|) on Be–Be edges with an H atom. Remarkably, the bonding patterns concerning the core CBe₄ moieties in CBe₄Cu_n^n–2 and CBe₄H_n^n–2 (n = 1~3) species are similar as they possess three CBe₄ 5c-2e σ bonds (ON = 1.97~1.99 |e|) and one 5c-2e π bond (ON = 1.97~1.99 |e|). These four orbitals are also similar to that in CBe₄^2– template molecule and provide the basis for adopting the ptC structures. By meeting our initial expectation on the electronic structures of derived species (stepwise eliminating the diffused Be–Be σ bonds but retaining four central 5c-2e bond), the designed species would possess the better and better stability when number of E atoms (n) increases. In addition, the AdNDP results can rationalize the existence of USMMD in 18. As shown in Fig. 3, there are five orbitals contributed positively to shorten the concerned Be–Be distance, including one Be–H–Be 3c-2e σ bond, three CBe₄ 5c-2e σ bonds and one CBe₄ 5c-2e π bond. Please note that this does not mean that there is a pseudo-quintuple bond between two beryllium atoms because each of the four 5c-2e bonds only contributes partially for such Be–Be bonding.

  Figure 3

  

  Figure 3.  AdNDP view of chemical bonding in CBe₄Cu^– (7), CBe₄Cu₂ (8), and CBe₄Cu₃⁺ (9) as well as CBe₄H^– (16), CBe₄H₂ (17), and CBe₄H₃⁺ (18)

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  As mentioned above, both the CBe₄^2– template molecule and its derivatives retain three 5c-2e σ bonds and one 5c-2e π bond. Such an electronic structure not only leads to the planarity, but also corresponds to six delocalized σ electrons and two delocalized π electrons, meeting the Huckel's 4n + 2 rule for n = 1 and 0, respectively and suggesting the novel 6σ + 2π double aromaticity. To corroborate the existence of aromaticity, the NICS calculations were performed by using the highly stable CBe₄E₃ species as the examples. The results for CBe₄Cu₃⁺ (9) and CBe₄H₃⁺ (18) are shown representatively in Fig. 4, while those for other species are given in Supporting Information. As shown in Fig. 4, the centers of Be–C–Be triangles in 9 possessed the NICS values of –25.5 and –18.8 ppm, while those in 18 showed the values of –24.7 and –21.6 ppm, suggesting the existence of σ aromaticity in both 9 and 18. Simultaneously, the points located 1.0 Å above the molecular plane all possessed the negative NICS values, ranging from –10.1 to –22.4 ppm and suggesting the existence of π aromaticity.

  Figure 4

  

  Figure 4.  NICS values of CBe₄Cu₃⁺ (A) and CBe₄H₃⁺ (B). Along the vertical line, the NICS points (red balls) are 0.5 Å apart from their neighbors

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  The stabilization effect of bridging E atoms can be verified by the variation of HOMO-LUMO gaps (Gap). The value for CBe₄^2– is only 0.53 eV at the B3LYP/BS1 level. As shown in Fig. 5, the CBe₄E^– and CBe₄E₂ species possess the obviously enlarged Gaps of 1.37~1.88 eV and 1.30~2.42 eV, respectively. Moreover, when the diffused Be–Be 2c-2e bonds are completely eliminated in CBe₄E₃⁺ species, the Gaps increased dramatically to 2.38 to 4.59 eV. Except that E is an alkali metal (Li and Na), other CBe₄E₃⁺ species possess the Gaps higher than 3.47 eV. Especially for E = H and halogens, the Gaps are all wider than 4.21 eV, revealing their well-defined electronic structures. The difference between H/ halogens and alkali/group 11 metals mainly lies in their electronegativity. From electronic structure point of view, H can be considered as a halogen because it needs only one electron to have its valence shell occupied fully. When the Be–Be edges of CBe₄ core were surrounded by H and halogens (the typical non-metals), the resulted species should possess better electronic structures than the species whose Be–Be edges of CBe₄ core were surrounded by the alkali and group 11 metals. Consistently, the HOMO-LUMO gaps of the former are wider than those of the latter.

  Figure 5

  

  Figure 5.  Variation of HOMO-LUMO gaps (Gap, in eV) with the increasing number of E atom

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  To assess the possibility to realize the ptC species designed in this work, the systematic exploration of potential energy surfaces (PESs) was carried out using the stochastic search algorithm. According to the relative energy determination at the final CCSD(T)//B3LYP level, only the GEMs of CBe₄E₂ (E = H, F, Cl, Br, I) components did not adopt the ptC structure, while those of all other CBe₄E_n^n–2 (E = H, Li, Na, Cu, Ag, Au, F, Cl, Br, I; n = 1~3) components adopted one of the ptC models shown in Scheme 1. As shown in Fig. S4, S5, and S6 in the Supporting Information, these GEMs located 0.6 to 21.8 kcal·mol^–1 below their second lowest isomers at the CCSD(T)//B3LYP level, suggesting their good thermodynamic stability.

  The dynamic stability is equally important for the experimental viability of computationally designed species. In this work, the dynamic stability was studied using 100 picoseconds BOMD simulations for 26 GEM ptC species (including 0) at the B3LYP/BS2 level. The results for CBe₄^2– (0), CBe₄Cu₃⁺ (9), CBe₄F₃⁺ (21), and CBe₄H₃⁺ (18) are shown representatively in Fig. 6, while those for other GEMs are given in Figs. S7, S8, and S9 in the Supporting Information. We found that the RMSD plots for many of GEM ptC species showed upward jumps, suggesting the significant changes in the position of atoms. The detailed structural examination revealed that the geometry of CBe₄^2– shows the reversible isomerization to a structure (0c) we located during the PES exploration. As Fig. 6 shows, 0c took up for the larger proportion during the simulation than 0, but the reversible transformation still suggested the high viability of 0 and indicated the high flexibility of Be atoms in 0.

  Figure 6

  

  Figure 6.  RMSD versus simulation time for the BOMD simulation of CBe₄^2–, CBe₄Cu₃⁺, CBe₄F₃⁺, and CBe₄H₃⁺, respectively at the B3LYP/BS2 level and 298 K

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  The RMSD plot for the simulation of CBe₄Ag₂ (11) shows the irreversible upward jump, which corresponds to the structural evolution to an isomer having a tetrahedral carbon (see 11a in Fig. S5), so it is dynamically unviable. That of CBe₄Cu₃⁺ (9) shows some reversible and fleeting upward jumps. However, the detailed structural sampling revealed that the upward jumps corresponded to the flexibility of the molecule as a whole rather than the isomerization. The RMSD plot for CBe₄F₃⁺ (21) does not show the upward jump and the fluctuation of RMSD values is small, suggesting the rather rigid structure of 21. Interestingly, the RMSD plot for CBe₄H₃⁺ (18) shows two stepwise upward jumps, which correspond to two times of isomerization. In the first isomerization, the structure of 18 is converted to its second lowest isomer (see 18a in Fig. S6), while in the second isomerization, 18a is converted to 18 again. As shown in Fig. 6, if the labels (numbering of the atoms) are considered, we can see a Be–H group rotate around the central ptC during two times of isomerization. In the majority of simulation time, the structure of 18 is adopted, so 18 is also dynamically viable. The plots for CBe₄Li₂ (2), CBe₄Na₂ (3), CBe₄Cu₂ (8), and CBe₄I₃⁺ (30) are similar to that of 18, thus though they are not dynamically stable, they are still dynamically viable. The RMSD plots of other ptC GEMs are similar to 9 or 21, thus they are dynamically stable and viable.

  4. CONCLUSION

  In summary, we had proved that the strategy for designing ppC species based on CBe₅^4– can be transferred to design the ptC species based on CBe₄^2–. The monovalent atoms including group 1 elements H, Li, Na, group 11 elements Cu, Ag, Au, and group 17 elements F, Cl, Br, I are all suitable for further stabilizing CBe₄^2– by anchoring the monovalent atoms on its Be–Be edges to stepwise eliminate the highly diffused Be–Be 2c-2e bonds. In thirty-one designed ptC species (including CBe₄^2– itself), twenty-five of them are dynamically viable global energy minima, which are potentially possible for experimental realization in experiments. Remarkably, the dynamic simulations suggest that the Be and E atoms in some ptC species are highly flexible but the basic ptC geometry can be maintained during the changes of atom positions, thus suggesting the stable but flexible bonding nature.

  
  
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  Figure 1  Optimized structure of CBe₄^4–, CBe₄^2– (0), and CBe₄ at the B3LYP/aug-cc-pVTZ level (A) and the AdNDP view of chemical bonding in 0 (B)

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  Scheme 1  Stepwise introduction of E atom(s) on the Be–Be of CBe₄^2–

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  Figure 2  Optimized structures of ptC species designed based on 0. The necessary bond lengths regarding molecular symmetries are given in Å

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  Figure 3  AdNDP view of chemical bonding in CBe₄Cu^– (7), CBe₄Cu₂ (8), and CBe₄Cu₃⁺ (9) as well as CBe₄H^– (16), CBe₄H₂ (17), and CBe₄H₃⁺ (18)

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  Figure 4  NICS values of CBe₄Cu₃⁺ (A) and CBe₄H₃⁺ (B). Along the vertical line, the NICS points (red balls) are 0.5 Å apart from their neighbors

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  Figure 5  Variation of HOMO-LUMO gaps (Gap, in eV) with the increasing number of E atom

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  Figure 6  RMSD versus simulation time for the BOMD simulation of CBe₄^2–, CBe₄Cu₃⁺, CBe₄F₃⁺, and CBe₄H₃⁺, respectively at the B3LYP/BS2 level and 298 K

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