Hyperhalogen properties of early-transition-metal borates

Abstract

The equilibrium structures, stability and magnetic properties of Sc(BO₂)_n^−/0 (n = 1–4) clusters were investigated on the basis of density functional theory calculations. The BO₂ ligands prefer to stretch out in the most stable Sc(BO₂)_n⁻ anions but tend to come together in the lowest-lying Sc(BO₂)₄ structure. According to the MP2 results, the Sc(BO₂)₄⁻ species could be classified as hyperhalogen anions since they have larger vertical electron detachment energies (VDEs, 5.44–8.85 eV) than that of the superhalogen anion BO₂⁻. With titanium and vanadium playing the role of central atom, the Ti(BO₂)_n^−/0 (n = 1–5) and V(BO₂)_n^−/0 (n = 1–6) clusters were studied in a similar manner. In these cases, the central transition metal atoms are inclined to keep their intrinsic spin. In addition, the hyperhalogen identity of the Ti(BO₂)_n⁻ (n = 4, 5) and V(BO₂)_n⁻ (n = 3–6) species were also confirmed by the calculated VDE values.

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1. Introduction

It is well-known that halogen atoms possess the highest electron affinities (EAs) in the periodic table, and the chlorine atom possesses the maximum value, namely 3.61 eV.¹ Atoms and clusters with high EA usually show remarkable oxidation capacity in chemical reactions. Bartlett and co-workers found that PtF₆ could even oxidize a Xe atom,² and then confirmed that the PtF₆ molecule possesses a very high EA of 6.8 eV.³ Such molecules that have higher EAs than the chlorine atom were termed superhalogen by Boldyrev and Gutsev in 1981.⁴ Besides, they recommended a simple formula MX_k+1 for constructing superhalogens, where M is a main group or transition metal atom, X is a halogen atom, and k is the maximal formal valence of M.⁴ The first experimental evidence of such species, namely MX₂⁻ (M = Li, Na, and X = Cl, Br, I), was obtained by Wang's group in 1999.⁵ Afterwards, an increasing number of superhalogen anions have been theoretically predicted or experimentally detected, such as MX₃⁻ (M = Be, Mg, Ca; X = Cl, Br)^6–8 and MCl₄⁻ (M = Sc, Y, La).⁹ Recently, many kinds of superhalogens that are beyond the MX_k+1 formula have been proposed and characterized. To facilitate extra-electron delocalization, multinuclear superhalogen anions have been designed such as P₂F₁₁⁻ and As₂F₁₁⁻,¹⁰ Mg₂F₅⁻,¹¹ Al₂F₇⁻,¹⁰ and H₁₂F₁₃⁻.¹² As a result, higher vertical electron detachment energy can be achieved. By introducing non-halogen ligands, the scope of superhalogen has been further extended to include the chalcogen-based MnO₄,¹³ CrO₄,¹⁴ BO₂,¹⁵ AlO₂,¹⁶ VO₃,¹⁶ BrO₃,¹⁷ IO₃,¹⁷ IO₄,¹⁷ BS₂,¹⁸ and BSO¹⁸ molecules, and those involving electrophilic substituent,¹⁹ organic group,²⁰ and acidic functional group²¹ as ligands.

Superhalogens are strong electron-acceptors and can be used to oxidize systems with high ionization potential, such as benzene²² and small water clusters.²³ They may combine with superalkalis to form ionic compounds that are predicted to possess excellent nonlinear optical response.²⁴ Recent studies have also shown that MnCl₃, one of the experimentally synthesized superhalogens, could be used to tune the electronic and magnetic properties of silicone,²⁵ and that the AlF₄ superhalogen can initiate a radical-substitution chain reaction as the trigger-compound.²⁶ In 2015, Jena predicted that superhalogens could serve as a bridge between complex metal hydrides and electrolytes in Li-ion battery.²⁷ Soon after, the suitability of superhalogen salt for Mg battery electrolyte was experimentally proved.²⁸ The extensive application prospects of superhalogens make them promising agents in chemistry and material science and attract more and more attention.^29,30

Hyperhalogens, another series of electronegative clusters whose EA values are even higher than those of their superhalogen ligands, were proposed by Jena and coworkers in 2010.³¹ Au(BO₂)₂ was reported as the first member of this type of molecules. Thereafter, the strategy of using superhalogen as ligands was employed to design a great many high EA species, e.g., Cu_n(BO₂)_m (n, m = 1, 2),³² Al(BO₂)_n,³³ Ag(BO₂)₂,³⁴ Na(BF₄)₂,³⁵ Mg(BF₄)₃,³⁶ Al(BF₄)₄,³⁷ Al(BH₄)₄,³⁷ and M(IO₃)₂⁻ (M = H, Li, Na, K).³⁸ Furthermore, Jena et al. proposed the concept of “magnetic hyperhalogens” by studying the Fe(BO₂)_n and Mn(BO₂)_n clusters.³⁹ Recently, two series of hyperhalogen anions involving planar and cage-like superhalogen ligands were reported, respectively, and the concept of aromatic hyperhalogen was brought forward as well.^40,41

In this work, theoretical investigation of borates of the first three subgroup elements, namely scandium, titanium, and vanadium, was presented. On the one hand, these transition metal (TM) elements have unfilled d orbitals, which may render the resulting compounds magnetism. On the other hand, they have multivalent properties, so it is interesting to make clear the minimum number of BO₂ ligands they need to exhibit hyperhalogen character with. Besides, our study also aims to (1) reveal the geometrical feature of the resulting Sc(BO₂)_n^−/0 (n = 1–4), Ti(BO₂)_n^−/0 (n = 1–5), and V(BO₂)_n^−/0 (n = 1–6) clusters; (2) detect their stability through examining their dissociation energies of predetermined dissociation pathways; (3) explore the spin state evolution of central atoms and VDE values of the TM(BO₂)_n⁻ (TM = Sc, Ti, V) anions.

2. Computational details

With different spin multiplicity taken into account, the optimized geometries of the Sc(BO₂)_n^−/0 (n = 1–4), Ti(BO₂)_n^−/0 (n = 1–5), and V(BO₂)_n^−/0 (n = 1–6) species were obtained by using the M06 functional⁴² of density functional theory. Frequency and natural bond orbital (NBO) analyses⁴³ were performed at the same level. Single point energies were computed by using the second-order Møller–Plesset (MP2) method. For all calculations, the 6-311+G(3df) basis set was used for B and O atoms, while the Los Alamos set of the double-zeta type LANL2DZ basis set and effective core potential (ECP) were used for the Sc, Ti, and V atoms.

The vertical detachment energies (VDEs) of the Sc(BO₂)_n⁻ (n = 1–4), Ti(BO₂)_n⁻ (n = 1–5), and V(BO₂)_n⁻ (n = 1–6) anions were obtained by two methods. First, the VDE values were indirectly computed as the energy difference between the neutral and the anion both at the anion's geometry by using the MP2 method. Second, the restricted outer valence Green function (OVGF)^44–46 method was used to estimate the VDE values. For all investigated anions, the pole strengths (PSs) are greater than 0.85, justifying the validity of OVGF approximation.⁴⁷ For comparison, the adiabatic detachment energy (ADE) of each anion was also obtained by using the MP2 method, which was computed as the difference in total energy between the neutral and anion at their respective optimized geometries.

All calculations were performed using the GAUSSIAN 09 program package.⁴⁸ Dimensional plots of the molecular structures were generated with the GaussView program.⁴⁹

3. Results and discussion

3.1 Sc(BO₂)_n⁻ and Sc(BO₂)_n (n = 1–4)

3.1.1 Equilibrium geometries and relative stability. We considered all possible configurations of Sc(BO₂)_n⁻ and Sc(BO₂)_n and show their optimized structures in Fig. 1 and 2, respectively. Their relative energies are listed in Tables 1 and 2, respectively. The nomenclature uses Arabic numeral from 1 to 4 to indicate the number of BO₂ ligands in the Sc(BO₂)_n⁻ clusters, followed by a, b, c… indicating the increasing MP2 single point energy order of different isomers. As for the neutral Sc(BO₂)_n series, their structures are named after corresponding anionic ones.

Fig. 1 Equilibrium structures and critical bond lengths (in Å) of the Sc(BO₂)_n⁻ (n = 1–4) clusters. (Color legend: Sc, grey; O, red; B, light pink. Symmetry in parentheses.)

Fig. 2 Equilibrium structures and critical bond lengths (in Å) of the Sc(BO₂)_n (n = 1–4) clusters. (Color legend: Sc, grey; O, red; B, light pink. Symmetry in parentheses.)

Table 1 Relative energy (E_rel, in kcal mol⁻¹), vertical detachment energies (VDEs, in eV), and adiabatic detachment energies (ADEs, in eV) of the Sc(BO₂)_n⁻ isomers. Pole strengths (PS) in parentheses. Dissociation energies (in kcal mol⁻¹) of the Sc(BO₂)_n⁻ → Sc(BO₂)_n−1 + BO₂⁻ (D₁) and Sc(BO₂)_n⁻ → Sc(BO₂)_n−1⁻ + BO₂ (D₂) reactions

Cluster	Isomer	Erel	VDE^OVGF	VDE^MP2	ADE (MP2)	D1	D2
Sc(BO2)^−	1a	0.0	1.70 (0.888)	1.41	1.23	53.6	163.9
	1b	17.6	1.21 (0.896)	1.28	1.26	31.7	142.0
Sc(BO2)2^−	2a	0.0	2.21 (0.882)	1.94	1.91	82.0	149.7
	2b	15.6	1.68 (0.881)	1.56	1.50	64.6	132.3
	2c	21.7	1.44 (0.852)	1.59	1.27	63.0	130.8
	2d	44.1	0.80 (0.817)	0.82	0.79	43.3	111.1
Sc(BO2)3^−	3a	0.0	2.94 (0.940)	2.59	2.45	94.3	134.8
	3b	9.0	3.87 (0.933)	3.46	2.35	84.7	125.2
	3c	13.2	2.36 (0.946)	2.10	2.03	83.3	123.8
	3d	20.2	3.40 (0.933)	3.02	1.90	73.8	114.3
	3e	27.1	3.19 (0.980)	2.97	2.84	61.5	102.0
	3f	27.3	3.57 (0.934)	3.21	1.75	66.4	106.9
	3g	36.5	2.00 (0.977)	1.84	1.77	53.0	93.5
Sc(BO2)4^−	4a	0.0	9.08 (0.917)	8.69	8.67	103.0	142.7
	4b	6.9	8.40 (0.915)	8.85	7.09	98.6	138.4
	4c	17.5	7.87 (0.913)	7.98	6.63	88.6	128.4
	4d	23.5	5.82 (0.929)	5.44	4.45	79.9	119.7
	4e	30.2	6.93 (0.922)	7.08	5.64	74.3	114.1
	4f	49.2	6.02 (0.921)	6.02	4.91	54.3	94.1

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Table 2 Relative energy (E_rel, in kcal mol⁻¹) of the Sc(BO₂)_n isomers and dissociation energies (in kcal mol⁻¹) of the Sc(BO₂)_n → Sc(BO₂)_n−1 + BO₂ (D′₁) and Sc(BO₂)_n → Sc(BO₂)_n−2 + B₂O₄ (D′₂) reactions

Cluster	Isomer	Erel	D′1	D′2
Sc(BO2)	1a′-t	0.0	112.2	—
	1a′-s	10.2	121.3	—
	1b′-t	19.8	99.4	—
	1b′-s	28.4	108.8	—
Sc(BO2)2	2a′	0.0	122.5	206.8
	2b′	6.1	124.0	208.3
	2c′	6.8	120.4	204.7
	2d′	18.1	111.7	196.1
Sc(BO2)3	3a′	0.0	130.7	207.7
	3b′	6.8	125.3	202.2
	3c′	3.5	132.5	209.4
	3d′	7.5	127.6	204.5
	3e′	35.9	101.3	178.2
	3f′	11.2	122.4	199.3
	3g′	20.8	117.6	194.5
Sc(BO2)4	4a′	73.8	33.7	120.7
	4b′	44.4	44.3	131.3
	4c′	44.3	46.1	133.1
	4d′	0.0	82.1	169.1
	4e′	34.2	50.6	137.6
	4f′	36.4	54.1	141.1

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As shown in Fig. 1, isomer 1a of ScBO₂⁻ is linear and similar to the reported structures of FeBO₂, MnBO₂, and MnBO₂⁻.³⁹ The other isomer 1b has C_2v symmetry, where the BO₂ ligand bends to 156.6° and binds with the Sc atom via two O atoms. Both 1a and 1b have magnetic moment of 1 μ_B. However, the neutral ScBO₂ (see Fig. 2) has variable magnetism. The most stable isomer 1a′ of ScBO₂ has a magnetic moment of 2 μ_B, which is similar to the case of ScCl and ScF.⁵⁰ Isomer 1a′′ also has a linear configuration, only it has a magnetic moment of 0 μ_B and slightly shorter Sc–O bond length of 1.867 Å. As for 1b′ and 1b′′, which share similar structural features with 1b, they possess different Sc–O bond lengths (2.225 Å and 2.114 Å, respectively) and magnetic moments (2 μ_B and 0 μ_B, respectively).

As one more BO₂ ligand is introduced, four isomers have been obtained for both anionic Sc(BO₂)₂⁻ and neutral Sc(BO₂)₂. The spin multiplicities of Sc(BO₂)₂⁻ and Sc(BO₂)₂ are 1 and 2, respectively. 2a, the lowest-energy isomer of Sc(BO₂)₂⁻, has a linear structure, in which each BO₂ ligand is attached to the middle Sc atom through a Sc–O bond. The same case was reported for the ground states of Mn(BO₂)₂⁻ and Fe(BO₂)₂⁻.³⁹ The Sc–O bond length (1.979 Å) of 2a is slightly shorter than that of 1a (2.006 Å). Isomer 2b has a planar structure, where the two BO₂ ligands combine with each other, forming a B₂O₄ unit that shows a similar structure to the recently reported (BO₂)₂⁻ anion.⁵¹ In the next isomer 2c, two BO₂ ligands bind with the Sc atom via one and two Sc–O bonds, respectively. The ∠O1B1O2 angle of 2c is 147.5°, indicating a larger ligand distortion relative to structure 1b. As for the last isomer 2d, it has a D_2d-symmetric structure where each BO₂ unit is linked to the center Sc atom by two Sc–O bonds. The Sc atom is coplanar with each BO₂ ligand in this structure and the two BO₂ planes are perpendicular to each other. The ∠OBO angle in 2d is 148.5°, which is close to that of 2c. From Fig. 2 and Table 2, the neutral Sc(BO₂)₂ isomers share similar structures and the same total energy order with their corresponding anions.

Sc(BO₂)₃⁻ and Sc(BO₂)₃ have magnetic moments of 1 μ_B and 0 μ_B, respectively. Seven structures were obtained for Sc(BO₂)₃⁻, and the D_3h-symmetric structure 3a is the most stable one. In 3a, each BO₂ ligand binds with the center Sc atom via one Sc–O bond of 1.990 Å. In contrast, a ScOBO quadrilateral forms in the rest isomers. The C_2v-symmetric isomer 3b can be viewed as one more BO₂ ligand attaching to structure 2c, which is supported by NBO analysis. Both isomers 3c and 3d can be obtained by adding a BO₂ ligand to structure 2b. The difference is that the additional BO₂ ligand bonds with the Sc atom via one O atom in the former but via two O atoms in the latter. In C_2v-symmetric 3e, three BO₂ ligands get together and form a B₃O₆ unit, which is similar to the structure of (BO₂)₃⁻.⁵¹ In the next isomer 3f, a B₂O₄ unit forms and is linked to Sc through three Sc–O bonds. The least favorable structure of Sc(BO₂)₃⁻ is 3g with C_s symmetry, which contains a different B₃O₆ unit compared with 3e. As for neutral Sc(BO₂)₃, all isomers possess a similar structure to their corresponding anions but their stability follows a different order. The largest structural difference is found between 3c and its neutral counterpart, namely 3c′ where one of the BO₂ ligands deviates 45.7° from the horizontal.

Six optimized configurations (μ_B = 0) were obtained for Sc(BO₂)₄⁻ and all of them can be considered derived from the Sc(BO₂)₃⁻ structures. The T_d-symmetric 4a is the most stable isomer of Sc(BO₂)₄⁻, in which each BO₂ ligand connects to the Sc atom via one O atom, forming four Sc–O bonds of 1.958 Å. The four BO₂ ligands keep away from each other and retain their linear geometry in this isomer. In contrast, two or more BO₂ units are combined together in the higher-lying isomers. Isomer 4b lies 6.9 kcal mol⁻¹ higher in energy than 4a. It can be obtained by attaching one more BO₂ ligand to the vertex boron atom of 3b. With two B₂O₄ units linked to the Sc atom separately, the C₂-symmetric 4c is generated. A trimeric BO₂ (B₃O₆) unit forms in both 4d and 4e isomers, and the energy difference between them is 6.7 kcal mol⁻¹. From Fig. 1, 4d and 4e basically inherit the structures of 3e and 3g, respectively, apart from an additional BO₂ ligand being attached to the Sc atom of their precursors. In the least stable isomer 4f, four BO₂ ligands polymerize to form a tetrameric B₄O₈, which is bound to the Sc atom through five Sc–O bonds. Note that all anionic Sc(BO₂)₄⁻ have corresponding neutral Sc(BO₂)₄ structures (μ_B = 1), only the latter has different total energy order from the former. For instance, the most stable isomer of Sc(BO₂)₄, namely 4d′, has a similar structure to 4d, a low-lying isomer of Sc(BO₂)₄⁻. Meanwhile, the lowest-energy isomer of Sc(BO₂)₄⁻ is corresponding to the least favorable configuration (4a′) of Sc(BO₂)₄. This reflects the fact that the loss of extra electron only slightly affects geometry of the studied anions, but varies their relative stability.

3.1.2 Dissociation energy. To explore the thermodynamic stability of the Sc(BO₂)_n⁻ anions, two fragmentation paths were considered, namely Sc(BO₂)_n⁻ → Sc(BO₂)_n−1 + BO₂⁻ and Sc(BO₂)_n⁻ → Sc(BO₂)_n−1⁻ + BO₂. The zero-point-corrected dissociation energies of the Sc(BO₂)_n⁻ anions are listed in Table 1. From the table, these dissociation reactions are highly endothermic. Hence, all Sc(BO₂)_n⁻ anions are stable when it comes to emission of a BO₂⁻ or BO₂ fragment. Besides, the dissociation of a neutral BO₂ ligand requires more energy than detaching a BO₂⁻ anion from Sc(BO₂)_n⁻. As far as the lowest-energy Sc(BO₂)_n⁻ isomers are concerned, it gets more difficult for them to lose a BO₂⁻ unit as n becomes larger. For neutral Sc(BO₂)_n, we also considered two fragmentation pathways, namely Sc(BO₂)_n → Sc(BO₂)_n−1 + BO₂ and Sc(BO₂)_n → Sc(BO₂)_n−2 + B₂O₄. From Table 2, their corresponding zero-point-corrected dissociation energies vary in the range of 33.7–132.5 kcal mol⁻¹ and 120.7–209.4 kcal mol⁻¹, respectively, indicating the stability of Sc(BO₂)_n. It is also noted that there is not much chance for Sc(BO₂)_n to eliminate a B₂O₄ dimer in view of the high dissociation energies.

3.1.3 Hyperhalogen characteristics. Jena and coworkers have reported that MP2 is a reliable method for estimating the vertical detachment energies (VDEs) of metal borate anion and yields results close to those from the CCSD(T) method.³³ On the other hand, the OVGF method is also very popular in assessing the VDEs of anions.^{5–8,10–12,19,21,33,50} Take the ScCl₄⁻ anion as an example. Its VDE value calculated by the OVGF method is 7.18 eV, which agrees quite well with the experimental result of 7.14 eV.⁹ Hence, the VDEs of the Sc(BO₂)_n⁻ anions were obtained by using the MP2 and OVGF methods, respectively. Besides, the adiabatic detachment energies (ADEs) of Sc(BO₂)_n⁻ were also calculated at the MP2 level. All results are given in Table 1. From the table, the results of MP2 and OVGF calculations are basically consistent. According to the MP2 results, the Sc(BO₂)₄⁻ anions exhibit high VDE values ranging from 5.44 to 8.85 eV, which are larger than the VDE of 4.46 eV for the BO₂⁻ anion. Therefore, the Sc(BO₂)₄⁻ species could be classified as hyperhalogen anions. Among the Sc(BO₂)₄⁻ anions, the first three isomers 4a–c possess larger VDE^MP2 values (7.98–8.85 eV) than the rest ones 4d–f (5.44–7.08 eV). This could be attributed to the polymerization of BO₂ units, which is a disadvantage for Sc(BO₂)₄⁻ to distribute the extra negative charge. Besides, it can be seen from Table 1 that the VDE values show an increasing order of 1a < 2a < 3a < 4a, indicating the VDE dependence of Sc(BO₂)_n⁻ on the number of BO₂ ligands. In particular, the VDEs show a sharp increase from Sc(BO₂)₃⁻ to Sc(BO₂)₄⁻, which can be related to the maximum valence state of +3 of the Sc atom.

For comparison, the previously reported VDE values of Al(BO₂)_n⁻,³³ Sc(BH₄)_n⁻,⁵² and ScF_n⁻ (ref. 50) are shown in ESI.† Given that ScF₄⁻ is a superhalogen anion with halogen as ligands, it is not surprising that it possesses a smaller VDE value of 7.74 eV than that of Sc(BO₂)₄⁻ (8.69 eV in the present work). Note that Sc(BO₂)₄⁻ also outperforms other hyperhalogen anions. From Table S1,† the VDE value of Sc(BO₂)₄⁻ is much larger than that of Sc(BH₄)₄⁻ (6.47 eV), although BO₂⁻ has a smaller VDE value compared with BH₄⁻ (4.57 eV). Likewise, Sc(BO₂)₄⁻ is probably a stronger oxidizing agent than Al(BO₂)₄⁻ (whose VDE = 8.28 eV) where a trivalent main group atom plays the role of central core.

3.2 Ti(BO₂)_n⁻ (n = 1–5) and V(BO₂)_n⁻ (n = 1–6)

Next to Sc, the Ti and V atoms have electron configurations of [Ar]3d²4s² and [Ar]3d³4s² and possess maximum valence of +4 and +5, respectively. To reveal how many BO₂ ligands Ti and V require to qualify their borates for being classified as hyperhalogens, the evolution of VDE values of the Ti(BO₂)_n⁻ (n = 1–5) and V(BO₂)_n⁻ (n = 1–6) systems were also studied in this work. Based on above analysis, all the lowest-lying Sc(BO₂)_n⁻ isomers feature a structure where the BO₂ ligands spread apart and each binds with the central Sc atom through a Sc–O bond. In view of this, only the isomers with separated BO₂ ligands were considered for the Ti(BO₂)_n⁻ (n = 1–5) and V(BO₂)_n⁻ (n = 1–6) anions. These structures, together with their corresponding neutral ones, were optimized by the M06 method. Different spin multiplicities were taken into account during optimizations. Note that the neutral Ti(BO₂)_n (n = 1–5) and V(BO₂)_n (n = 1–6) configurations were obtained on the basis of their corresponding anionic structures instead of a thorough structure searching. They are possibly local, but not global minima on the potential energy surfaces.

3.2.1 Geometry and magnetism. The optimized structures of Ti(BO₂)_n⁻ and their corresponding neutral Ti(BO₂)_n are shown in Fig. 3 and 4, respectively, while those of the anionic V(BO₂)_n⁻ and neutral V(BO₂)_n are presented in Fig. 5 and 6, respectively. The nomenclature uses symbol of element plus Arabic numerals from 1 to 6 to indicate the number of involved BO₂ ligands, followed by s, d, t, q, quintet, and sextet to denote the spin state (singlet, doublet, …). To illuminate electronic structure of the resulting borates, some selected molecular orbitals are shown in Fig. S1 (ESI†).

Fig. 3 Optimized structures of the Ti(BO₂)_n⁻ (n = 1–5) clusters. (Color legend: Ti, blue; O, red; B, light pink; symmetry and magnetic moment in parentheses.)

Fig. 4 Optimized structures of the Ti(BO₂)_n (n = 1–5) clusters. (Color legend: Ti, blue; O, red; B, light pink; symmetry and magnetic moment in parentheses.)

Fig. 5 Optimized structures of the V(BO₂)_n⁻ (n = 1–6) clusters. (Color legend: V, purple; O, red; B, light pink; symmetry and magnetic moment in parentheses.)

Fig. 6 Optimized structures of the V(BO₂)_n (n = 1–6) clusters. (Color legend: V, purple; O, red; B, light pink; symmetry and magnetic moment in parentheses.)

Three structures with different spin states (singlet, triplet, quintet) were found for Ti(BO₂)⁻. The singlet isomer is linear, while the other two are slightly bent. It can be found from Fig. 3 and Table 3 that, the isomer where the Ti atom maintains its spin is the most stable, followed by that in a higher spin state, while the one with a total spin state of zero is the least favorable. For example, the stability order is Ti1-t > Ti1-quintet > Ti1-s. The same is valid for the Ti(BO₂)₂⁻ and Ti(BO₂)₃⁻ isomers. That is, the Ti2-q and Ti3-t isomers with two unpaired d electrons from Ti are 3.0 and 17.3 kcal mol⁻¹ more stable than Ti2-d and Ti3-s, respectively. Due to Jahn–Teller effect, Ti3-t has C_2v instead of D_3h symmetry and the symmetry of Ti4-d is lowered to D_2d compared with the lowest-lying structure of Sc(BO₂)₄⁻. In contrast, Ti3-s and its corresponding neutral Ti3′-d hold D_3h symmetry. Likewise, Ti5-s possesses a trigonal bipyramidal geometry with D_3h symmetry. The structures of neutral Ti(BO₂)_n basically resemble those of their corresponding anions. The only exception here is Ti5′-d, in which two BO₂ ligands are combined together.

Table 3 Relative energy (E_rel, in kcal mol⁻¹), vertical detachment energies (VDEs, in eV), and adiabatic detachment energies (ADEs, in eV) of Ti(BO₂)_n⁻ (n = 1–5) and V(BO₂)_n⁻ (n = 1–6). Pole strengths (PS) in parentheses. Dissociation energies (D_e, in kcal mol⁻¹) of the TM(BO₂)_n⁻ → TM(BO₂)_n−1⁻ + BO₂ (TM = Ti, V) reactions

Species	Erel	VDE^OVGF	VDE^MP2	ADE^MP2	De
Ti1-s	23.5	1.57 (0.885)	1.25	0.66	28.5
Ti1-t	0.0	1.77 (0.864)	1.76	1.68	53.4
Ti1-quintet	9.9	1.26 (0.922)	0.62	0.61	26.3
Ti2-d	3.0	3.08 (0.815)	3.67	3.58	141.6
Ti2-q	0.0	2.06 (0.960)	1.65	1.61	136.1
Ti3-s	17.3	2.95 (0.878)	2.58	2.07	126.9
Ti3-t	0.0	4.20 (0.922)	3.71	2.82	130.1
Ti4-d	—	6.66 (0.889)	4.86	4.11	126.3
Ti5-s	—	9.23 (0.911)	9.30	6.29	94.1
V1-d	71.7	2.01 (0.854)	0.93	0.91	14.6
V1-q	0.0	1.95 (0.858)	3.03	2.98	59.5
V1-sextet	5.8	1.49 (0.983)	0.97	0.86	45.6
V2-s	44.3	2.49 (0.849)	2.54	2.44	107.5
V2-t	24.6	4.46 (0.811)	3.62	3.30	139.5
V2-quintet	0.0	2.38 (0.957)	2.11	2.06	134.2
V3-q	—	5.18 (0.908)	5.10	4.02	127.9
V4-s	49.7	7.38 (0.882)	7.23	3.68	68.1
V4-t	0.0	8.44 (0.906)	8.72	5.84	95.5
V5-d	—	9.09 (0.909)	9.27	5.62	93.6
V6-s	—	9.44 (0.910)	8.23	5.87	46.2

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From Fig. 5 and Table 3, the V atom maintains its spin in the lowest-lying isomer of V(BO₂)⁻, namely V1-q. Consequently, it has a magnetic moment of 3 μ_B. High-spin isomer V1-sextet and low-spin isomer V1-d are 5.8 and 71.7 kcal mol⁻¹ higher in energy than V1-q, respectively. All three structures of V(BO₂)₂⁻ are linear with D_∞h symmetry. The magnetic moment is 4 μ_B for the lowest-energy configuration V2-quintet. The electronic structure characteristics of both Ti(BO₂)_n⁻ and V(BO₂)_n⁻ species indicate that the central transition metal atoms are inclined to keep the intrinsic electronic state in their borates. For V(BO₂)_n⁻ (n = 3–6), the BO₂ ligands are distributed individually in each cluster. Obviously, Jahn–Teller distortion also appears in the V(BO₂)_n⁻ series. The geometry of V3-q is still of D_3h-symmetry. In contrast, both V4-t and V4-s are distorted to D_2d-symmetry as the V atom possesses two d electrons therein. V5-d is lowered to C₂-symmetry because the V atom has one d electron left. Similar to the case of 4a and Ti5-s, V6-s does not have d electron from the central metal atom, so it appears to be a regular octahedron with O_h-symmetry. As for the neutral V(BO₂)_n clusters, the BO₂ ligands are also isolated in every structure except that two BO₂ ligands dimerized in V6′-d.

From Table 3, the zero-point-corrected dissociation energies of Ti(BO₂)_n⁻ and V(BO₂)_n⁻ are in the range of 26.3–141.6 kcal mol⁻¹ and 14.6–139.5 kcal mol⁻¹, respectively, indicating the stability of Ti(BO₂)_n⁻ and V(BO₂)_n⁻ with respect to emission of a BO₂ unit.

3.2.2 Vertical electron detachment energy. The VDE and ADE values of Ti(BO₂)_n⁻ and V(BO₂)_n⁻ calculated at the MP2 level are listed in Table 3, where the VDE values from the OVGF method are also listed for comparison. From the table, Ti3-t, Ti4-d, Ti5-s, V2-t, V3-q, V4-s, V4-t, V5-d, and V6-s can be classified as superhalogen anions, among which the Ti3-t, Ti4-d, V2-t, V3-q, V4-t, V5-d isomers with nonzero magnetic moment can be considered as magnetic superhalogens. Besides, the Ti4-d, Ti5-s, V3-q, V4-s, V4-t, V5-d and V6-s species possess larger VDE values than that of BO₂⁻ and can be termed hyperhalogen anions. In a word, with Sc, Ti, and V as central atoms, it requires at least four, four, and three BO₂ ligands, respectively, to qualify the resulting TM(BO₂)_n⁻ (TM = Sc, Ti, and V) clusters to be considered as hyperhalogens. From Table 3, it is noted that the VDE^MP2 values of Ti(BO₂)_n⁻ show a sharp increase from Ti(BO₂)₄⁻ to Ti(BO₂)₅⁻. Such a sudden rise of VDE value is believed to root in the maximum valence state of +4 of the Ti atom. However, the same increase doesn't appear in the V(BO₂)_n⁻ series. From Table S1,† the VDE values of TMF_n⁻ (TM = Sc, Ti, V) can be more or less enhanced by replacing fluorine with BO₂ ligands.⁵⁰

4. Conclusions

The structural, electronic and magnetic properties of three series of early-transition-metal borates, namely Sc(BO₂)_n^−/0 (n = 1–4), Ti(BO₂)_n^−/0 (n = 1–5), and V(BO₂)_n^−/0 (n = 1–6), were studied by performing density functional theory and ab initio calculations. In view of the positive dissociation energies, all studied anionic clusters are stable against the loss of a BO₂ ligand.

The lowest-lying Sc(BO₂)_n⁻ isomers feature a structure where the BO₂ ligands spread apart, whereas the BO₂ ligands begin to combine into a trimer in the lowest-energy Sc(BO₂)₄ structure. This can be related to the maximum valence state of +3 of the Sc atom. By the same token, there is a sharp increase in VDE value from Sc(BO₂)₃⁻ to Sc(BO₂)₄⁻, and the latter species can be classified as hyperhalogens since they possess larger VDE values than that of its superhalogen ligand BO₂⁻. As for Ti and V atoms, they require four and three BO₂ ligands, respectively, to enable their borates to be termed hyperhalogen. Besides, the Ti4-d, V3-q, V4-t, and V5-d species can be considered as magnetic hyperhalogens owing to their nonzero magnetic moment.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 21603032, 21375017), State Key Development Program for Basic Research of China (Grant No. 2013CB834801), Natural Science Foundation of Fujian Province (Grant No. 2016J05032), and MiaoPu Foundation of Fujian Medical University (Grant No. 2015MP034).

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Footnote

† Electronic supplementary information (ESI) available: Selected molecular orbitals of the studied borate anions, and VDE values of some related cluster anions. See DOI: 10.1039/c7ra10238k

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