| Citation: |
Xuefeng Zhao, Bo Jin, Chengyong Zhou, Caixia Yuan, Yanbo Wu. Be2H3L2– (L=CH3 and F–I): Hyperhalogen Anions with Ultrashort Beryllium-Beryllium Distances[J]. Chinese Journal of Chemical Physics , 2023, 36(2): 224-230. DOI: 10.1063/1674-0068/cjcp2204058
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The superalkali cations and superhalogen anions commonly have different type of core moieties. Based on the previous reports that Be2H3L′ 2+ (L′=NH3 and noble gases Ne−Xe) are superalkali cations, in the present work, we designed the superhalogen anions Be2H3L2− (L=CH3 and halogens F−I), and both superalkali cations and superhalogen anions can be constructed using Be2H3 as the core moiety. The newly designed Be2H3L2− species are much more stable than their isoelectronic cationic counterparts Be2H3L′ 2+, as can be reflected by the highly exergonic substitution reaction of L′ ligand in Be2H3L′ 2+ with isoelectronic L− to give Be2H3L2−. These anionic species possess the well-defined electronic structure, which can be proven by their large HOMO−LUMO gaps of 4.69 eV to 5.38 eV. It is remarkable that Be2H3L2− can be regarded as the hyperhalogen anions due to the extremely high vertical detachment energies (5.38 eV to 6.06 eV) and the Be−Be distances in these species (1.776 Å to 1.826 Å) are short in ultrashort metal-metal distances (defined as dM−M<1.900 Å) between main group metals. In the designed five small model species, three of them, i.e. Be2H3L2− (L=CH3, Cl, and Br), are kinetical viable global energy minima, which are the promising target for generation and characterization in anion photoelectron spectroscopy. The analogue molecule [t-Bu−Be2H3−t-Bu]− with bulky protecting tert-butyl (t-Bu) groups is designed as a possible target for synthesis and isolation in condensed states.
Superatom, a cluster of atoms that seem to exhibit some of the properties of elemental atoms, is important for our understanding of electronic structures and chemical bonding in discrete molecular systems [1]. In particular, superatoms commonly tend to have a closed shell of electrons, just as elemental atoms do. The most familiar superatoms known in this field are superalkali and superhalogen [2, 3], which are defined to possess the vertical detachment energies (VDEs) lower than 3.89 eV and vertical electron affinities (VEAs) more negative than −3.62 eV, respectively [4, 5]. Hence, such clusters may exhibit the strong trend to lose or gain an electron, very similar to alkali metals or halogens, respectively. A special type of superhalogen is hyperhalogen [6]. It is initially denoted as the species with peripheral halogen atoms being replaced by superhalogen moieties so that their VEAs can be even larger than their superhalogen building blocks. Subsequently, hyperhalogens are generally referred to any cluster with VEA obviously more negative than chlorine (e.g. VEA < −5.00 eV) [7-13].
Due to their low VDEs or VEAs, superalkali metals and superhalogens almost always exist as positive and negative ions, typically as the cationic and anionic portions of salts, respectively. Correspondingly, scientific researchers often study the superalkali metal cations and superhalogen anions rather than corresponding neutrals. In general, the superalkali metal cations can be identified by checking their VEAs, which should be less negative than −3.89 eV, while the superhalogen and hyperhalogen anions can be verified by examining their VDEs, which should be greater than 3.62 and 5.00 eV, respectively.
The previously reported superalkali cations are generally in the forms of X@Mn+, where electronegative X is surrounded by n alkali metal atoms (M) [14-23]; such as XLi3+ (X=CO3, SO3, SO4, O4, and O5) [16], XLi4+ (X=PO4, AsO4, VO4) [17], X3Li3+ (X=C, Si, Ge) [19], E3M3+ (E=C−Pb, M=Li−Cs) [20], etc. In contrast, the superhalogen anions are generally in the forms of Mx@Xy−, where x electropositive M atoms are surrounded by y ligands with high EA [13, 24-34]. This can be exemplified by MX3− (M=Be, Mg, Ca; X=F, Cl, Br) [25, 26], NaxClx+1− (x=1−4) [28], Al13I − [29], BX4− and AlX4− (X=F, Cl, Br) [30], etc. Can we use the same core structure to construct both the superalkali metal cations and superhalogen anions? If the answer is positive, it can be optional to design superalkali metal cations or superhalogen anions through proper selection peripheral groups.
In designing the species with ultrashort metal-metal distances (USMMDs, i.e. dM−M<1.900 Å) [35-41], we accidentally found that the cationic Be2H3L′ 2+ (L′=NH3, PH3, and noble gases Ar−Xe) species possess the VEAs ranging from −2.56 eV to −3.68 eV, which is the concrete evidence for their superalkali metal cation nature. In addition, their HOMO−LUMO gaps are rather large (7.50 eV to 8.65 eV at the B3LYP/aug-cc-pVQZ level), indicating their well-defined electronic structure. Remarkably, the Be−Be distances in these cationic species are shortened to the values around 1.700 Å, which place them in the group of molecules with the shortest metal−metal distance [39].
Be2H3L′ 2+ species were constructed by stabilizing the cationic electron-accepting Be2H3+ core, a local energy minimum with ultrashort Be-Be distance of 1.683 Å, with the neutral electron-donating L′ ligands [39]. It would be natural to quest whether the neutral ligands can be replaced by the mono-anionic ligands to give the mono-anionic superhalogen with USMMDs and the well-defined electronic structure, either? If the answer is “yes”, Be2H3+ would be a feasible core structure for constructing both superalkali cations and superhalogen anions. Simultaneously, because the exotic structures are more commonly realized in negative ion photoelectron spectroscopy (PES) [7, 8, 28, 31, 42-44], if such anionic structures are stable enough, they will be more promising to be realized than their cationic counterparts. In this sense, it would be highly demanded to check the feasibility of Be2H3+ based anionic species with special attention on their VDEs, electronic properties, Be−Be distances, and stability. In this work, it will be demonstrated that the isoelectronic substitution can lead to the expected anionic species with very high VDEs, well-defined electronic structures, ultrashort metal-metal distances, and excellent stability.
For calculations with different accuracies, different basis sets were used: BS1 denotes aug-cc-pVQZ for H, Be, C , F, Cl and Br, while aug-cc-pVQZ-PP for I; BS2 denotes 6-31G(d) for H, Be, C, F, Cl and Br, while SDD for I. The species designed in this work (1−5 in FIG. 1) were confirmed to be energy minima by harmonic frequency analysis at both B3LYP/BS1 and MP2/BS1 levels. Their geometries were reoptimized at the CCSD(T)/BS1 level. Natural bond orbital (NBO) [45] analyses and adaptive natural density partitioning (AdNDP) [46] analyses were performed at the B3LYP/BS1 and B3LYP/BS2 level, respectively. The potential energy surface analyses of 1−5 were performed using a stochastic search algorithm at B3LYP/BS2 level [47, 48]. The 10 lowest-energy isomers were further reoptimized at the B3LYP/BS1 level; then the geometries of five lowest-energy B3LYP/BS1 isomers were finally refined at the high precision CCSD(T)/BS1 level. The relative free energy was the sum of CCSD(T)/BS1 electronic energy and B3LYP/BS1 Gibbs free energy correction. Vertical detachment energies (VDEs) and vertical electron affinities (VEAs) were calculated using outer-valence Green’s functions (OVGF) at the OVGF/BS1 level [49]. At 298 K, 100-ps Born-Oppenheimer molecular dynamic (BOMD) [50, 51] simulations of the species 1−5 were run at the B3LYP/BS2 level. The GXYZ program and the AdNDP program were used to carry out the stochastic search algorithm and the adaptive natural density partitioning (AdNDP) analyses [52, 53], respectively. The CCSD(T) calculations were completed by the MolPro 2012.1 package [54], and all other calculations were performed using the Gaussian 09 package [55].
This study was triggered by the dative nature of ligands-to-Be2H3 bonding in our previously reported cations [L′→Be2H3←L′]+ (L′=NH3, Ne, Ar, Kr, or Xe), whose ligands L′ and Be2H3+ core both can be the equilibrium structures [39]. Hence, we tried to replace two neutral L′ ligands with two isoelectronic “mono-anionic” ligands (L−) like CH3− and halogen anions F−, Cl−, Br−, and I−, etc., leading to the mono-anionic species Be2H3L2− with a Be2H3 core as well. According to our calculation results, Be2H3L2− (L=CH3, F, Cl, Br, or I) in D3h symmetry are confirmed to be true energy minimum (see 1−5 in FIG. 1) at both B3LYP/BS1 and MP2/BS1 levels. The Be−Be distances (dBe−Be) in 1−5, 1.776−1.824 Å optimized at the CCSD(T)/BS1 level, are slightly longer than those of their sister molecules Be2H3L′ 2+ (dBe−Be=1.692−1.735 Å), but they are still well below the threshold of 1.900 Å, so 1−5 possess the ultrashort metal-metal distances between two beryllium atoms. Eq.(1) describes the reactions of replacing neutral L′ ligands NH3 and Ne−Xe in Be2H3L2′+ with L− groups being CH3− and F −, Cl−, Br−, I −, respectively, to give Be2H3L2−.
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Be2H3L′+2+2L−→Be2H3L2−+2L′ |
(1) |
As shown in Table I, for L′=NH3 and Ne, Ar, Kr, Xe versus L−=CH3− and F −, Cl−, Br−, I −, the reactionis exergonic with free energies change ΔG of −211.6, −348.3, −252.3, −226.6, and −200.5 kcal/mol, respectively, suggesting that the affinity between anionic group L− and Be2H3 core is much higher than that between neutral ligand L′ and Be2H3 core. From designing strategy point of view, an obvious reason for such large difference in affinity would be the strong Coulomb attraction between the positively charged Be2H3+ core and the negative charge L− groups.
| L′ | L– | ΔG/(kcal/mol) | ||
| NH3 | CH3– | –211.6 | ||
| Ne | F – | –348.3 | ||
| Ar | Cl – | –252.3 | ||
| Kr | Br– | –226.6 | ||
| Xe | I – | –200.5 |
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We perform AdNDP analyses to better understand the bonding in 1−5. AdNDP is used to describe the electronic structure. It can analyze n-center two-electron (nc-2e) bonds of a molecular system, where n ranges from 1 to the total number of atoms. In this work, two schemes of AdNDP analysis are employed to describe the bonding patterns among atoms in 1−5. The difference between two schemes lies in the manners of bonding between two beryllium atoms. In scheme 1, the n values of the generated AdNDP orbitals are as small as possible. The results for 1 are shown in scheme 1 of FIG. 2. As the figure shows, the interactions between two Be atoms can be partitioned into three 3c-2e σ bonds formed by Be atoms and bridging H atoms (patterns A−C for 1), which are akin to the B−H−B bonds in diborane [56]. In scheme 2, patterns A−C are converted to three Be2H3 5c-2e orbitals (patterns F−H), which can be regarded as a pseudo-triple bond, a non-classical counterpart of classical triple bond. Specifically, pattern H is a σ-shaped orbital without any nodal surface, whereas patterns F and G are degenerate orthogonal π-shaped orbitals with the nodal surface between two beryllium atoms. The formation of these three orbitals should be the key reason to obtain the ultrashort Be−Be distance in 1. Next, our attention is paid to the L−Be bonding. As shown in patterns D and E in FIG. 2, the L−Be (L=CH3 and F−I) bonding in 1 are depicted by two 2c-2e σ bonds. The bonding patterns in 2−5 are similar to those of 1, and they are given in Supplementary material (SM).
The traditional NBO analyses are also performed and the natural charges of 1−5 are given in FIG. 1, while the Wiberg bond indices (WBIs) describing the covalent interactions are shown in Table II. As FIG. 1 shows, the natural charges on H, Be, C, and halogens F−I are negative, positive, and negative, revealing the alternate “−, +, −” charge distribution, which are a kind of favourable Coulomb interactions. As shown in Table II, the WBIBe−H values for 1−5 range from 0.45 to 0.47, while three hydrogen bridge atoms interact with two Be atoms respectively, and there are six Be−H connectivities, the total WBIBe−H values are 2.70−2.82. This corroborates the formation of three Be2H3 5c-2e bonds discussed above. It should be noted that the WBIBe−Be values in 1−5 range from 0.40 to 0.50, which indicates the significant interaction between the two beryllium atoms. The WBIBe−E (L=CH3 or halogens F−I) values for 1−5 range from 0.56 to 0.93, indicating the substantial Be−L covalent interactions.
| Compound | vmin | EHOMO-LUMO | VDE | VEA | WBI | |||||
| Be | H | L | Be−Be | Be−L | Be−H | |||||
| 1 | 94 | 4.69 | 5.38 | 2.25 | 2.65 | 0.97 | 3.56 | 0.50 | 0.69 | 0.47 |
| 5.42a | 2.42a | |||||||||
| 2 | 232 | 4.93 | 5.64 | 2.38 | 2.34 | 0.94 | 0.60 | 0.40 | 0.56 | 0.45 |
| 3 | 150 | 5.38 | 6.06 | 2.38 | 2.75 | 0.97 | 0.90 | 0.48 | 0.83 | 0.47 |
| 4 | 126 | 5.29 | 6.00 | 2.32 | 2.81 | 0.98 | 0.95 | 0.49 | 0.88 | 0.47 |
| 5 | 102 | 4.97 | 5.62 | 2.19 | 2.87 | 0.98 | 0.99 | 0.50 | 0.93 | 0.47 |
| 6 | 20 | 4.16 | 4.49a | 2.27a | ||||||
| a These values are calculated at the OVGF/aug-cc-pVTZ level. | ||||||||||
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The Be2H3L′ 2+ species possess the well-defined electronic structure, and they exhibit very low VEAs, which renders them as the superalkali cations. As the isoelectronic species to Be2H3L′ 2+, the anions 1−5 possess the well-defined electronic structures, too, which can be proven by their large HOMO−LUMO gaps (4.69 eV to 5.38 eV). Therefore, it would be natural to wonder whether species can be superhalogen anions or even hyperhalogen anions. Consequently, we evaluate their VDEs at the OVGF/BS1 level. The VDEs of 1−5 are given in Table II, these values range from 5.38 eV to 6.06 eV, which are much higher than the VDE of chlorine anion (3.62 eV) and also higher than 5.00 eV, so it can be regarded as the hyperhalogen anions.
The above VDE studies suggest that it would be very difficult for 1−5 to lose an electron. Simultaneously, the OVGF/BS1 calculation suggest their positive VEA values (2.19 eV to 2.38 eV) at the OVGF/BS1 level, so there is no tendency for 1−5 to obtain an electron. The VDE and VEA results indicate that 1−5 are stable regarding the electron gaining and losing.
To better understand the thermodynamic stability of 1−5, the potential energy surfaces of these structures are explored using a stochastic search algorithm [42, 43], and the searched isomers are calculated with high precision. The calculation results show that 1−5 are all global energy minima. Compared with their second lowest isomers, the energy differences at the CCSD(T)/BS1 level are 7.4, 0.7, 6.9, 5.7, and 5.2 kcal/mol, respectively. Thus, 1−5 are stable thermodynamically. The isomers of 1−5 and their relative energies are given in the SM.
To be experimentally realized, 1−5 should be kinetically stable as well. Their kinetic stability was examined by 100-ps BOMD simulations at 298 K. Structure evolution of a species during a simulation is described by the root-mean-square derivations (RMSD) relative to its optimized geometry (due to the high rotational freedom, the H atoms on methyl groups of 1 are not considered during the calculation of RMSD). As shown in FIG. 3, the RMSD plots for 2 and 5 display the irreversible jumps, suggesting the occurrence of significant structural changes, so 2 and 5 are kinetically unstable. The RMSD values of 1 are interesting in that there are frequent interconversions between 1 and its nearest isomer 1a, showing the high flexibility for the positioning of H and methyl groups in 1. Nevertheless, during the dynamic simulations, 1 is the major existing form, so it is kinetically feasible at 298 K. In contrast, the RMSD plots for 3 and 4 have no irreversible jumps and a few high fluctuations correspond to the softness of the molecules rather than the tendency of isomerization. Therefore, 3 and 4 should be kinetically stable.
On the whole, the exceptional stability of diberyllium species 1, 3, and 4 suggest their high probability of experimental realization. To further stabilize such a type of structures, the bulky terminal groups would be necessary. Taking 1 as an example, we use the large tert-butyl (t-Bu) groups to replace the methyl groups, leading to the energy minimum [t-Bu−Be2H3−t-Bu]− (see 6 in FIG. 4). The Be−Be distance in 6 (1.806 Å) is even shorter than that (1.826 Å) in 1, which may be the results of dispersion of negative charge that reduces the Coulomb explosion effect in the Be2H3 core. Diberyllium species 6 is computed to have the relatively large HOMO−LUMO gap (4.16 eV) and VDE (4.49 eV), as well as the positive VEA (2.27 eV), which reveal its good stability with regard to electron transition and electron gaining/losing. Given that its parent species 1 is a kinetically feasible global minimum, 6 would be a feasible target for chemical synthesis.
In summary, we have designed anionic cluster Be2H3L2− (L=CH3−, F −, Cl−, Br−, and I −) with the ultrashort beryllium-beryllium distances in Be2H3 core moiety and proven their eligibility as the hyperhalogen anions. Hence, together with our previous prediction that superalkali cations can be designed based on Be2H3 moiety as well, we have demonstrated that the superalkali cations and superhalogen anions can be optionally obtained through attaching the proper type of terminal groups onto Be2H3 moiety. It is remarkable that the newly designed anionic cluster Be2H3L2− are much more stable than their sister cationic species [L′→Be2H3←L′]+, which can be attributed to the more favourable Coulomb interactions and electron-sharing bond nature between L groups and Be2H3 core. These mono-anionic species reveal to possess the large HOMO−LUMO gaps, high VDEs, positive VEAs, as well as the good thermodynamic and kinetic stabilities, which suggest their high possibility for experimental realization and characterization in the negative ion photoelectron spectroscopy. The designed [t-Bu−Be2H3−t-Bu]− with bulky protecting group as a abulky analogue would be more feasible target for chemical synthesis.
Supplementary materials: AdNDP-generated orbitals (two phases shown in blue/white or green/white) related to bonding to beryllium in 2–5 and B3LYP/BS1-optimized structures for 1–5 and their lowest isomers are shown. The relative free energies (kcal/mol) calculated using CCSD(T)/BS1 electronic energies plus B3LYP/BS1 Gibbs free energy corrections are given.
This work was supported by the National Natural Science Foundation of China (No.22073058), the Natural Science Foundation of Shanxi Province (No. 201901D111018 and No.20210302124682), the Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi (No.2020L0618).
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Figures(4) / Tables(2)
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| L′ | L– | ΔG/(kcal/mol) | ||
| NH3 | CH3– | –211.6 | ||
| Ne | F – | –348.3 | ||
| Ar | Cl – | –252.3 | ||
| Kr | Br– | –226.6 | ||
| Xe | I – | –200.5 |
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| Compound | vmin | EHOMO-LUMO | VDE | VEA | WBI | |||||
| Be | H | L | Be−Be | Be−L | Be−H | |||||
| 1 | 94 | 4.69 | 5.38 | 2.25 | 2.65 | 0.97 | 3.56 | 0.50 | 0.69 | 0.47 |
| 5.42a | 2.42a | |||||||||
| 2 | 232 | 4.93 | 5.64 | 2.38 | 2.34 | 0.94 | 0.60 | 0.40 | 0.56 | 0.45 |
| 3 | 150 | 5.38 | 6.06 | 2.38 | 2.75 | 0.97 | 0.90 | 0.48 | 0.83 | 0.47 |
| 4 | 126 | 5.29 | 6.00 | 2.32 | 2.81 | 0.98 | 0.95 | 0.49 | 0.88 | 0.47 |
| 5 | 102 | 4.97 | 5.62 | 2.19 | 2.87 | 0.98 | 0.99 | 0.50 | 0.93 | 0.47 |
| 6 | 20 | 4.16 | 4.49a | 2.27a | ||||||
| a These values are calculated at the OVGF/aug-cc-pVTZ level. | ||||||||||
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