Planar wheel-type M©B_nH_n^2−/−/0 clusters (M = Cr, Mn and Fe for dianion, anion and neutral, respectively; n = 6 and 7)

Abstract

We adopted a new “electronic” strategy that is adding two electrons into the d_z² orbital of the central M atom to form a lone pair, which is in contrast to the Hoffmann’s “electronic” strategy that is delocalizing the lone pair on the center atom, to turn the bowl-type MB_nH_n^0/+ (M = Cr and Mn; n = 6 and 7) clusters into planar wheel-type M©B_nH_n^2−/− clusters. Their isoelectronic neutral clusters, Fe©B₆H₆ and Fe©B₇H₇, also possess planar wheel-type structures. The large binding energy, vertical ionization potential, and vertical electron affinity indicate that the planar wheel-type M©B_nH_n^2−/− clusters are chemically stable. This study may open up a new area in coordination chemistry for planar hexa- and hepta-coordinate transition metal and we expect further experimental explorations of synthesis and potential applications.

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1. Introduction

In the 1970s, Hoffmann et al.¹ pointed out that the electronic structure of planar D_4h CH₄ is unfavorable due to a nonbonding p_z-orbital lone pair on the planar tetracoordinate carbon (ptC). Based on this analysis, they suggested that the ptC arrangements could be achieved by using an “electronic” strategy, that is, delocalizing the lone pair by a π acceptor. Consequently, many ptC clusters, designed using “electronic” strategies, have been characterized theoretically and experimentally.^2–4 Since then, planar tetra-, penta-, hexa-, hepta- and octacoordinate main group elements have been investigated extensively.^5–11 However, these extreme violations of classical bonding principles are by no means limited to the main group elements. Numerous planar wheel-type clusters with a central hypercoordinate transition metal (M) encircled by different ligands, such as planar n-membered metal rings (n = 5 to 7)^12–15 and planar n-membered boron rings (n = 7 to 10),^16–22 have been studied experimentally and computationally. The studies from M©B_n (ref. 16 and 22) (the © sign, proposed by Wang and Boldyrev,¹⁸ designates a planar n-membered boron ring with a central M atom and is distinct from the @ sign used for a 3D cage cluster with an endohedral atom) demonstrate that transition metal atoms are more suitable for the central position in the boron ring, because they prefer to participate in delocalized bonding with the boron ring. To achieve the design of M©B_n^k−, Wang and Boldyrev also developed a chemical bonding model in which to satisfy the peripheral B–B bonding and the delocalized σ and π bonding, the required valence for the central transition-metal atom M, is 12 − n − k.^17–19

Compared to pure boron clusters, hydrogenated small boron clusters favor adopting 3D aromatic structures.^23–26 Thus, it is challenging to obtain planar hypercoordinate elements with BH ligands. In 2009, Yu and co-workers²⁷ reported a planar wheel-type D_5h B©B₅H₅⁺ cluster, which is the global minimum according to their calculation. In 2013, Cheng’s group designed some MB_nH_n^0/+ (M = Cr and Mn; n = 6 and 7) clusters.²⁸ Both Cr and Mn⁺ have six valence electrons which were expected to occupy the empty overlapped p_z orbitals of B atoms to obtain the planar wheel type clusters in their assumption. However, the MB_nH_n^0/+ clusters are bowl-type structures and do not reach the planar wheel-type structures due to participation of the d_z² orbital of the M atoms in the overlap between the d_xz and d_yz orbitals of the M atoms and the p_z orbitals of the B atoms. Here, we adopt a new “electronic” strategy that is adding two electrons into the d_z² orbital to form a lone pair, which is in contrast to the “electronic” strategy of Hoffmann,¹ to achieve planar wheel-type M©B_nH_n^2−/− clusters. Density functional theory (DFT) was applied to investigate the geometrical and electronic structures of the planar wheel-type M©B_nH_n^2−/− clusters as well as their isoelectronic neutral clusters, Fe©B₆H₆ and Fe©B₇H₇. The results show that the planar wheel-type M©B_nH_n^2−/−/0 (M = Cr, Mn and Fe for dianion, anion and neutral respectively; n = 6 and 7) clusters are theoretically validated to be favorable, exhibit chemical stability and strong aromaticity, and they may be targeted in future experiments to open a new area of coordination chemistry.

2. Computational details

The geometries of the planar wheel-type M©B_nH_n^2−/−/0 and the bowl-type MB_nH_n^0/+ (M = Cr, Mn and Fe for wheel-type, M = Cr and Mn for bowl-type; n = 6 and 7) were optimized using TPSSh²⁹/6-311+G(3df,p), PBE³⁰/6-311+G(3df,p) and BP86 (ref. 31–33)/6-311+G(3df,p) levels and imaginary frequencies were checked at the same level. Wiberg bond indices (WBI)³⁴ were computed at BP86/6-311+G(3df,p) level using natural bond orbital (NBO)³⁵ to gain insight into the bonding pattern of them. In order to assess the aromatic character, nucleus-independent chemical shifts (NICS),³⁶ proposed by Schleyer and co-workers, were calculated with the ghost atom lying 1 Å (NICS(1)) above and below the M atom. The NICS(1) values were performed at BP86/6-311+G(3df,p) level with the gauge including atomic orbital (GIAO)³⁷ method. The binding energy (E_b) between the M^2−/−/0 and B_nH_n is defined as E_b = E(M©B_nH_n^2−/−/0) − E(M^2−/−/0) − E(B_nH_n). The vertical electron affinity (VEA) and vertical ionization potential (VIP) of M©B_nH_n^2−/−/0 are defined as the total energy difference between M©B_nH_n^2−/−/0 ± e (+for VEA and − for VIP) and M©B_nH_n^2−/−/0 clusters at the optimized geometry of M©B_nH_n^2−/−/0. The E_b, VEA and VIP of the bowl-type clusters can be made by analogy with those of the wheel-type ones. All calculations were performed using the GAUSSIAN 09 (ref. 38) program packages. The dimensional plots of molecular configurations and orbitals were generated with the GaussView program.³⁹

3. Results and discussion

3.1 Geometry structure and energies

The optimized geometries of singlet M©B_nH_n^2−/−/0 and singlet MB_nH_n^0/+are shown in Fig. 1 and 2. And their geometry parameters are listed in Table 1. Since the geometry parameters obtained at the three computation levels are similar, the results shown in Fig. 1 and 2 and Table 1 are only from BP86/6-311+G(3df,p) level. The structures shown in Fig. 1 and 2 are all identified to be true local minima by frequency check. As can be seen from Fig. 1A, adding 2e to the bowl-type CrB₆H₆ cannot achieve the planar wheel-type D_6h Cr©B₆H₆²⁻ which is a transition state with one imaginary frequency that leads to the C_6v bowl-type CrB₆H₆²⁻. However, it is interesting that the D_6h Cr©B₆H₆²⁻ can be stabilized by two Li⁺ cations coordinated above and below the Cr atom (see Fig. 1C). In order to compare with C_6v bowl-type CrB₆H₆, the D_6h Cr©B₆H₆²⁻ that comes from Li₂Cr©B₆H₆²⁻ will be used in the following studies. Besides CrB₆H₆, MnB₆H₆⁺, CrB₇H₇ and MnB₇H₇⁺ can all attain the planar wheel-type structures with high D_6h and D_7h symmetries by adding 2e into them. And the neutral clusters, Fe©B₆H₆ and Fe©B₇H₇ are all the planar wheel-type structures with high D_6h and D_7h symmetries.

Fig. 1 Optimized geometries of the singlet bowl-type and the singlet planar wheel-type clusters with hexagon boron ring at BP86/6-311+G(3df,p). H atoms are white and B atoms are pink.

Fig. 2 Optimized geometries of the singlet bowl-type and the singlet planar wheel-type clusters with heptagon boron ring at BP86/6-311+G(3d`). H atoms are white and B atoms are pink.

Table 1 Calculated B–M–B bond angle (∠BMB/degree), M–B, B–B and B–H bond distances (R_M–B, R_B–B and R_B–H/Å), Wiberg bond indices of M–B and B–B bonds (WBI_M–B, WBI_B–B), total Wiberg bond indices of M and B atoms (WBI_M, WBI_B) and the NBO charges (Q_M and Q_B/|e|) of the singlet bowl-type and the singlet planar wheel-type clusters at BP86/6-311+G(3df,p) level

	∠BMB	RM–B	RB–B	RB–H	WBIM–B	WBIB–B	WBIM	WBIB	QM	QB
a The average NBO charge for B atom.
Cr©B6H6^2− (D6h)	60.0°	1.887	1.887	1.199	1.01	0.64	6.16	3.57	−1.57	0.26
CrB6H6 (C6v)	56.5°	1.905	1.804	1.196	0.99	0.61	6.03	3.47	−1.33	0.20
Mn©B6H6^− (D6h)	60.0°	1.851	1.851	1.204	0.92	0.65	5.62	3.53	−2.00	0.21
MnB6H6^+ (C6v)	57.2°	1.890	1.809	1.193	0.89	0.57	5.46	3.30	−1.29	0.32
Fe©B6H6 (D6h)	60.0°	1.832	1.832	1.194	0.85	0.61	5.20	3.43	−1.72	0.29
Cr©B7H7^2− (D7h)	51.4°	1.988	1.725	1.212	0.84	0.78	5.97	3.64	−2.18	0.1^a
CrB7H7 (C7v)	50.8°	1.996	1.713	1.197	0.81	0.72	5.78	3.49	−1.05	0.11
Mn©B7H7^− (D7h)	51.4°	1.958	1.699	1.205	0.76	0.78	5.42	3.59	−1.64	0.13^a
MnB7H7^+ (C7v)	50.6°	1.995	1.706	1.196	0.74	0.70	5.31	3.36	−0.95	0.19
Fe©B7H7 (D7h)	51.4°	1.944	1.687	1.198	0.68	0.75	4.97	3.48	−1.56	0.25^a

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From the point of view of geometry parameters, it can be said that in general the B–M–B angles, the bond lengths of B–B and B–H bonds of the planar wheel-type clusters are larger than those of the bowl-type ones. In contrast the variation trend of the bond lengths of M–B bond is just the opposite. These results indicate that the interaction between the M atom and the boron ring in the planar wheel-type clusters is stronger than that in the bowl-type ones. As can be seen from Table 1, all B–B bond lengths are significantly longer than the typical B–B bond distances (1.593 Å) reported in the CB₆²⁻,⁴⁰ but are still in the single-bond range of 1.706 to 1.859 Å (ref. 41), except for the longest bond length (1.887 Å) in Cr©B₆H₆²⁻, which indicates very weak B–B interactions. In contrast the M–B bond distances (R_Cr–B = 1.887–1.996 Å, R_Mn–B = 1.851–1.995 Å and R_Fe–B = 1.832–1.944 Å) are notably shorter than the M–B covalent radii sums⁴² (2.25, 2.23 and 2.16 Å for M = Cr, Mn and Fe, respectively), which suggests the existence of robust interactions between the peripheral boron ring and the central M atom.

To compare the energy relationships of the planar wheel-type M©B_nH_n^2−/−/0 with different spin multiplicity, we calculated the single point energies of the corresponding triplet, quintet and septet frames for these planar wheel-type clusters at BP86/6-311+G(3df,p) level. The relative energies based on the singlet are listed in Table 2. We found that the energy of the singlet is the lowest, except for Cr©B₆H₆²⁻ and Cr©B₇H₇²⁻, as the relative energy increases with an increase of the spin multiplicity. For Cr©B₆H₆²⁻ and Cr©B₇H₇²⁻, the energy of the triplet is the lowest. However, further optimization shows that the triplet Cr©B₆H₆²⁻ is also a transition state as the singlet and the symmetry of the triplet Cr©B₇H₇²⁻ is reduced from D_7h to C_2v. For the sake of comparison, the structures of singlet M©B_nH_n^2−/−/0 will be used in the following studies.

Table 2 Calculated relative single point energies for the triplet, quintet and septet M©B_nH_n^2−/−/0 based on the optimized structures of the singlet M©B_nH_n^2−/−/0 at BP86/6-311+G(3df,p) level. The relative energies (eV) are based on the singlet

Spin multiplicity	Cr©B6H6^2− (D6h)	Mn©B6H6^− (D6h)	Fe©B6H6 (D6h)	Cr©B7H7^2− (D7h)	Mn©B7H7^− (D7h)	Fe©B7H7 (D7h)
1	0	0	0	0	0	0
3	−0.33	0.66	1.14	−0.08	1.11	1.52
5	2.65	3.48	3.48	3.01	3.96	4.34
7	5.72	6.60	6.61	5.96	6.73	6.38

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3.2 WBIs and NBO charges

The WBIs of the M–B and the B–B bonds, total WBIs of M and B atoms and the NBO charges for M and B atoms are also listed in Table 1. The Wiberg bond order analyses are consistent with the feature of the geometries. For example, the WBI_B–B = 0.57–0.78 are about half of WBI_B–B = 1.15 computed for D_2d B₂H₄ at the same level, which indicates the strength of the B–B single bond is weak in our systems. The total WBI_B = 3.30–3.64 is close to 4, which implies that the B atoms follow the octet rule in bonding nature. The WBI_M–B = 0.74–1.01 and total WBI_M = 4.97–6.16 indicate that the M atom interacts strongly with the B atom and the boron ring.

As can be seen from Table 1, the M atoms serve as negatively charged centers while the signs of the (average) charges on B atoms are positive. H atoms in all clusters carry negligible charges are not shown in Table 1. The interesting charge distribution that seems contradictory to the electronegativity indicates that not only does M atom donate electrons to boron atoms, but also the boron atoms donate electrons back to the M atom, which is important for these clusters to achieve stable structures.

3.3 Stability

The total energy differences ΔE(M,n) = E(D_6h M©B_nH_n^2−/−) − E(C_6v MB_nH_n^0/+), where M = Cr and Mn, n = 6 and 7, are tabulated in Table 3. It is obvious that D_6h M©B_nH_n^2−/− is more stable than C_6v MB_nH_n^0/+ at the three different computation levels except for Cr©B₆H₆²⁻ due to electrostatic repulsion. However, concerning the thermodynamic stability of D_6h Li₂Cr©B₆H₆, the energy change of the following process CrB₆H₆ (C_6v ¹A₁) + 2Li → Li₂Cr©B₆H₆^−/0/+ (D_6h ¹A_1g) was calculated. With zero-point correction included, we find that the reaction is highly exothermic (ΔE = −4.33 eV), indicating that the desired product is favored thermodynamically.

Table 3 Calculated total energy differences (ΔE(M,n)/eV) between singlet D_6h M©B_nH_n^2−/− and singlet C_6v MB_nH_n^0/+ (M = Cr and Mn; n = 6 and 7) at BP86, PBE and TPSSh/6-311+G(3df,p) levels

	E(Cr, 6)	E(Mn, 6)	E(Cr, 7)	E(Mn, 7)
BP86	0.420	−10.063	−0.813	−11.571
PBE	0.583	−9.860	−0.634	−11.400
TPSSh	0.903	−9.895	−0.366	−11.423

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The HOMO–LUMO energy gap (ΔH–L), E_b, VIP and VEA of D_6h M©B_nH_n^2−/−/0 and C_6v MB_nH_n^0/+ are listed in Table 4. The results of CrB₆H₆ and CrB₇H₇ are comparable to those obtained at TPSSh/6-311G(d) level.²⁸ We can find that the ΔH–L of M©B_nH_n^2−/− is smaller than that of MB_nH_n^0/+ except for Mn©B₇H₇⁻. Compared with the neutral clusters, the VIP of M©B_nH_n^2−/− is small due to electrostatic repulsion. However, the E_b of M©B_nH_n^2−/− is bigger than that of MB_nH_n^0/+, exhibiting better chemical stability. Moreover, for the isoelectronic neutral clusters Fe©B₆H₆ and Fe©B₇H₇, the indices are all improved, which suggests they are highly stable and may be observed in experiment.

Table 4 Calculated HOMO–LUMO energy gap (ΔH–L/eV), Binding energy (E_b/eV), vertical ionization potential (VIP/eV) and vertical electron affinity (VEA/eV) of the singlet bowl-type and the singlet planar wheel-type clusters at BP86/6-311+G(3df,p) level

	H–L	Eb	VIP	VEA
Cr©B6H6^2− (D6h)	0.24	11.89	2.74	—
CrB6H6 (C6v)	1.86	10.40	8.85	2.30
Mn©B6H6^− (D6h)	0.90	12.33	2.07	—
MnB6H6^+ (C6v)	1.79	9.56	—	7.90
Fe©B6H6 (D6h)	1.36	10.31	8.22	1.69
Cr©B7H7^2− (D7h)	0.14	16.13	2.64	—
CrB7H7 (C7v)	1.42	12.07	9.35	3.27
Mn©B7H7^− (D7h)	1.47	15.62	2.54	—
MnB7H7^+ (C7v)	0.96	10.93	—	8.69
Fe©B7H7 (D7h)	1.77	12.78	8.43	1.68

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3.4 Aromaticity and molecular orbital

According to a perfect planar structure, we can propose that the planar wheel-type M©B_nH_n^2−/−/0 should possess aromaticity. NICS is a simple and efficient criterion to characterize aromatic nature. A large negative NICS above molecular plane implies the presence of diamagnetic ring currents. Fig. 3 plots the NICS(1)s of the planar wheel-type M©B_nH_n^2−/−/0, the bowl-type MB_nH_n^0/+ and D_6h C₆H₆. As shown in Fig. 3, the NICS(1)s above and below the plane of M©B_nH_n^2−/−/0 are equal, and are all negative, which can prove that the diamagnetic ring current effect, characteristic for aromticity, exists in M©B_nH_n^2−/−/0. Moreover, we find that the planar M©B_nH_n^2−/−/0 have very strong aromatic character since their NICS(1)s are more negative than C₆H₆. While the NICS(1)s above and below the plane of the bowl-type MB_nH_n^0/+ are not equal. The NICS(1)s in the bowl are much more negative than the one outside the bowl. Especially, the NICS(1) outside the bowl is positive in CrB₆H₆. The results indicate that the aromaticity outside the bowl is much weaker than that in the bowl, or even does not exist. The difference of the NICS(1) between inside and outside the bowl is attributed to the distribution of a π electron that mainly locates inside the bowl (see HOMO − 2 and HOMO − 1 in Fig. 4A and C).

Fig. 3 NICS(1)s of the singlet bowl-type and the singlet planar wheel-type clusters compared with those of D_6h C₆H₆.

Fig. 4 Molecular orbitals of C_6v MnB₆H₆⁺ (A), D_6h Mn©B₆H₆⁻ (B), C_7v MnB₇H₇⁺ (C) and D_7h Mn©B₇H₇⁻ (D) which are singlet.

In order to better understand the perfectly planar wheel-type structure, we analyzed the molecular orbitals (MOs) of M©B_nH_n^2−/−/0 and MB_nH_n^0/+. The MOs of all isoelectronic clusters are very similar and the slight difference is the MOs order. Therefore, we mainly focus on the MOs of MnB_nH_n⁺ and Mn©B_nH_n⁻ (n = 6 and 7). Density plots of the MOs are shown in Fig. 4. From the MnB₆H₆⁺ MOs shown in Fig. 4A, we can easily see that the degenerate HOMO and HOMO − 2 are the distorted π MOs that are responsible for the bowl-type structure. The reason is that the d_z² orbital of the center Mn atom involves in π MOs consisted of p_z orbitals of boron ring. The strong interaction between them leads to the formation of LUMO and HOMO − 2. Thus, Mn d_xz and d_yz orbitals do not completely delocalize over the p_z orbitals of the B atoms (see the degenerate HOMO), and parts of them participate in the p_x and p_y orbitals of the B atoms (see the degenerate HOMO − 3 and HOMO − 8). The remaining MOs do not include Mn d_z², d_xz and d_yz orbitals. However, as can be seen from Fig. 4B that shows the MOs of Mn©B₆H₆⁻, the additional two electrons more than in MnB₆H₆⁺ occupy the HOMO and form the nonbonding lone pair on the d_z² orbital of Mn atom. As a result, Mn d_z² orbital takes no part in the π MOs of the boron ring (see the HOMO − 1) and the Mn d_xz and d_yz orbitals completely extend to the p_z orbitals of the B atoms (see the degenerate HOMO − 2), which makes the HOMO − 1 and the degenerate HOMO − 2 become fully normal π MOs that exhibit the typical pattern of aromatic molecule, benzene. Therefore, Mn©B₆H₆⁻ with six π electrons is considered to be aromatic, conforming to the (4n + 2) Huckel rule. It is the π aromaticity that is responsible for the perfectly planar wheel-type structure. The important MOs that can determine the structures of MnB₇H₇⁺ and Mn©B₇H₇⁻ are exhibited in Fig. 4C and D, which are similar to the previously mentioned case.

4. Conclusion

In summary, we adopted a new “electronic” strategy that is maintaining the lone pair on the center M atom, which is in contrast to the Hoffmann’s “electronic” strategy that is delocalizing them, to achieve planar wheel-type M©B_nH_n^2−/−/0 clusters (M = Cr, Mn and Fe; n = 6 and 7). The lone pair occupies the d_z² orbital and makes it take no part in the π MOs, which is important for the planar wheel-type structures. The chemical stability of planar wheel-type structures is comparable with that of the bowl-type structures. These planar wheel-type M©B_nH_n^2−/−/0 clusters deserve experimental confirmation because they would open up a new area in coordination chemistry for planar hexa- and hepta-coordinate transition metal.

Acknowledgements

This work has been supported by the National Natural Science Foundation of China (nos 21201022 and 11464035), the Specialized Research Fund for the Doctoral Program of Higher Education (New Teachers, no. 20122216120001), the Natural Science Foundation of Jilin Province, China (no. 20120435, 20130204033GX, 20140101052JC, 20140204017GX and 20140101098JC).

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