Breaking the plane: B₅H₅ is a three-dimensional structure

Abstract

In this study, we delved into the structure of B₅H₅ and questioned some of its accepted assumptions. By exploring the potential energy surface, we found a new three-dimensional structure as the global minimum. This finding is in contrast with the previously hypothesized planar and cage-like models. Our exploration extends to the kinetic stability of various B₅H₅ isomers, offering insights into the dynamic behavior of these molecules.

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Introduction

Even though B₅H₅²⁻ has not yet been synthetized, it is expected to assume a D_3h form, a conjecture first formulated by Lipscomb and coworkers in 1961,^1–3 and later rationalized through the Wade-Mingos rules.^4,5 In 2000, Schleyer and coworkers explored the geometric and electronic implications of electron removal from B₅H₅²⁻ to elucidate the structure of the neutral B₅H₅.⁶ Upon optimization, the initial trigonal bipyramidal form with D_3h symmetry transitioned to a C_4v square pyramid, keeping the five B–H units intact in B₅H₅ (Fig. 1). This transformation from trigonal bipyramid to square pyramid was rationalized via the pairing principle of incompletely filled degenerate orbitals.⁶ However, McKee⁷ identified a C_s structure, characterized as a BH₂⁺ and B₄H₃⁻ complex, which is energetically more favorable than the C_4v square pyramidal isomer by 9.8 kcal mol⁻¹ at the B3LYP/6-31G(d) level. This preferred structure is a trapezoid with three B atoms at the base and two above, incorporating two terminal B–H bonds, a B–H–B bridge, a BH₂ group, and a bare boron (see Fig. 1),⁷ mirroring the planar form of B₅⁻ and neutral B₅.^8,9

Fig. 1 The structures proposed for B₅H₅²⁻ (D_3h) and B₅H₅ (C_4v and C_s).

In our quest to understand the structural transformations induced by the removal of two electrons from the dianions of borohydrides, denoted by the formula B_nH_n²⁻, we explored the potential energy surfaces (PESs) of all borohydrides in the series from n = 5 to 12. Our preliminary screening revealed that for nearly all these dianions, the removal of two electrons result in insignificant structural changes. Nonetheless, two exceptions were identified: B₁₂H₁₂ and B₅H₅. While the former case has been previously reported by us,¹⁰ our focus now shifts to B₅H₅. Contrary to prior assumptions, our results show that the global minimum structure of B₅H₅ is not quasi-planar but rather an asymmetrical three-dimensional form.

Computational details

The systematic exploration of the PES of B₅H₅ in both its singlet and triplet states was carried out through a modified genetic algorithm as implemented in GLOMOS.¹¹ Details on GLOMOS are documented elsewhere.¹² An initial screening was performed at the PBE0/def2-SVP level.^13,14 Isomers within a 50 kcal mol⁻¹ range were re-minimized and characterized at the TPSS-D3/def2-TZVP level.^14,15 The stationary points were further characterized by harmonic vibrational frequency analysis at the same level. The interconversion pathways for lower-energy minima were elucidated and the corresponding transition states (TS) connecting the local minima were confirmed by intrinsic reaction coordinate (IRC) computations. Relative Gibbs free energies, including entropic and thermal corrections at 298.15 K, were computed at the CCSD(T)¹⁶/aug-cc-pVTZ//TPSS-D3/def2-TZVP level. Additionally, the stability of the wave function and the T₁ diagnostic for each isomer were evaluated, indicating stable wave functions across all localized minima with T₁ values below 0.02 for the singlet systems and less than 0.023 for the triplets (see Table S1, ESI†). This suggests that monodeterminantal approaches, such as DFT and CCSD(T), reliably represent the structure and energetics of these isomers. All these computations were performed using Gaussian 16.¹⁷

Chemical bonding was examined using Wiberg bond indices (WBIs) and natural population analysis (NPA) via the NBO 6.0¹⁸ partitioning scheme. Furthermore, the adaptive natural density partitioning (AdNDP) approach,¹⁹ as implemented in Multiwfn,²⁰ provided further insights into the chemical bonding, describing electronic structures in terms of n-center, two-electron (nc-2e) bonds, recovering Lewis concepts such as lone pairs, 2c-2e bonds, and delocalized bonds.

The dynamic behavior was studied using Born–Oppenheimer molecular dynamics (BO–MD)²¹ at 900 K for 30 ps, employing a 1 fs time step and a Nosé–Hoover chain thermostat for temperature control,^22–24 using deMon-2k²⁵ at the PBE0/DZVP²⁶ level. The chosen temperature, while is not real in the macroscopic sense, was selected to regulate the total kinetic energy of the atoms, ensuring they possess enough energy to overcome energy barriers and allow for isomer interconversions at realistic simulation times.

Results

The lowest energy structures of B₅H₅ in both singlet and triplet states are shown in Fig. 2. We identified two structures, 1 and 2, that are energetically more favorable than McKee's proposed structure, 3.⁷ The global minimum, 1, is a three-dimensional entity with C₁ symmetry, characterized by four terminal B–H bonds, a B–H–B bridge, and a bare boron atom. Structure 2, which is only 0.7 kcal mol⁻¹ higher than 1 in Gibbs free energy (computed at CCSD(T)/aug-cc-pVTZ//TPSS-D3/def2-TZVP), adopts a trapezoidal boron skeleton with three B–H units and a –BH₂ group located at one vertex of the larger base, adopting a C_s symmetry. McKee's structure (3), less favorable by 1.7 kcal mol⁻¹ compared to 1, shares a trapezoidal shape with 2 but includes a hydrogen atom bridging the central boron and the –BH₂ group. Structure 4, which is 3.0 kcal mol⁻¹ higher in energy than 3, possesses a distinctive trapezoidal shape with an out-of-plane BH unit. Structures 5, 7, 8, 13, and 14, characterized by pyramidal boron skeletons, are between 6.7 to 38.9 kcal mol⁻¹ higher in Gibbs free energy than 1, with 7 corresponding to Schleyer's C_4v structure. Three C_s-symmetry structures, 6, 9, and 10, consist of a B₄ skeleton with a –BH₂ unit and a bridging hydrogen on a B–B bond, ranging from 6.8 to 17.0 kcal mol⁻¹ above 1 in Gibbs free energy. Isomers 11 and 12 adopt a cage-like structure (ΔG > 17.0 kcal mol⁻¹), albeit with one incomplete face. Specifically, structure 12 is a trapezoid with two B–H–B bridges with an out-of-plane hydrogen atom in one bridge. The lowest-energy triplets, 13 and 14, have ΔG values more than 20 kcal mol⁻¹ above 1. So, the putative global minimum for B₅H₅ is not planar but a three-dimensional structure.

Fig. 2 TPSS-D3/def2-TZVP low-lying energy structures of B₅H₅. Relative Gibbs free energies at the CCSD(T)/aug-cc-pVTZ//TPSS-D3/def2-TZVP level are in kcal mol⁻¹.

WBI analysis identifies two distinct ranges for B–H bond distances, as summarized in Table 1. Isomers 2, 5, and 7, each containing five B–H units, display high average WBI_B–H of around 0.95 and show the shortest average B–H bond lengths, approximately 1.19 Å. In contrast, the presence of 3c-2e B–H–B interactions increases average B–H bond distances and lowers the average WBI_B–H values. An extreme case is structure 12, which features two B–H–B bonds, leading to a WBI of 0.66. Regarding B–B bonds, planar structures 6, 9, and 10 show the highest average WBI_B–B values (nearly 1.0), contrasting with Schleyer's isomer, which has the lowest (WBI_B–B = 0.74). 6, 9, and 10 each contain a 2c-2e B–B bond connecting a BH₂ unit to the B₄H₃ fragment. The formation of the BH₂ unit induces electronic redistribution within the B₄ rhombus, shortening several B–B distances to almost 1.55 Å. In contrast, an increase in the number of multicenter boron bonds correlates with elongated B–B bond lengths and higher WBI_B–B, the C_4v form being the extreme case (vide infra).

Table 1 Average Wiberg bond indices and average bond lengths r_B–B and r_B–H in Å computed at the TPSS-D3/def2-TZVP level

Isomer	r B–H	r B–B	WBIBH	WBIBB
1	1.22	1.67	0.79	0.85
2	1.19	1.69	0.94	0.80
3	1.24	1.67	0.78	0.89
4	1.23	1.66	0.78	0.87
5	1.19	1.72	0.95	0.77
6	1.24	1.62	0.79	1.00
7	1.19	1.71	0.95	0.74
8	1.23	1.71	0.79	0.78
9	1.24	1.63	0.79	0.99
10	1.24	1.65	0.78	1.01
11	1.23	1.71	0.78	0.84
12	1.28	1.65	0.66	0.93

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Let us analyze the bonding properties of 1, 3, and 7 (the global minimum, McKee's isomer, and Schleyer's cage-pyramidal structure, respectively). As depicted in Fig. 3, each has five 2c-2e σ-bonds. Isomers 1 and 3 are composed of four 2c-2e B–H bonds and one B–B bond, while in 7, all are B–H bonds. Isomer 1 features three 3c-2e bonds (one in a B₂H ring and two in a B₃ ring), in contrast to 3 and 7, which have four 3c-2e bonds. Specifically, isomer 3 includes a 3c-2e B₂H bond and another in a B₃ ring. In isomer 7, 3c-2e σ-bonds are found within the B₃ rings of the pyramid's four triangular faces. Each isomer also contains a delocalized 4c-2e bond in a B₄ unit. Distinctly, the B₅ skeleton in 1 is stabilized by a 5c-2e bond, absent in 3 and 7, contributing to its enhanced stability.

Fig. 3 AdNDP analysis for 1, 3, and 7 at the TPSS/def2-TZVP level. Occupation numbers (ON) in |e|.

The stabilization of 1 is further clarified when examining the chemical bonding in the dianion B₅H₅²⁻, which has 22 electrons.²⁷ Ten of these electrons are in the five 2c-2e B–H σ-bonds, leaving twelve for B–B bonding, including three 3c-2e and three delocalized 4c-2e σ-bonds.²⁷ In contrast, neutral B₅H₅ requires different bonding configurations. 7 has five 2c-2e σ-bonds exclusively for B–H bonds, one more than isomers 1 and 3. This leaves ten electrons for B–B bonds in 7, while 1 and 3 each allocate twelve electrons to B–B bonds, similar to the dianion. Therefore, 1 and 3 are capable to maintain twelve electrons for keeping the boron skeleton in B₅H₅, resulting in higher relative stability.

The kinetic stability of isomers 3 and 7, in their isomerization to 1, is detailed in Fig. 4. Isomer 3 converts to 1 through a one-step pathway (Fig. 4a), with a high activation barrier (ΔG^‡ = 26.3 kcal mol⁻¹), indicating that 3 is kinetically stable. In contrast, the transformation of 7 to 1 follows a stepwise mechanism with low barriers via intermediates 4 and 2 (Fig. 4b). Initially, a hydrogen atom migrates from the pyramid's apex to its base, forming a B2–H–B3 bridge and leading to the cleavage of the B1–B2 bond. This results in the quasi-planar structure of 4, crossing a small energy barrier (TS_7-4, ΔG^‡ = 1.3 kcal mol⁻¹). The subsequent conversion of 4 to 2 involves a hydrogen atom shift towards B2, forming a terminal BH₂ group (TS_4-2, ΔG^‡ = 4.9 kcal mol⁻¹). The final step from 2 (a quasi-planar structure) to 1 (a three-dimensional structure) implies the formation of the B2–H–B4 bridge and the B2–B5 bond, involving a barrier of 6.9 kcal mol⁻¹ (TS_2-1). Given that 7 isomerizes to 1via a stepwise mechanism with achievable energy barriers, 7 is considered kinetically unstable.

Fig. 4 Gibbs free energy profile for the conversions of (a) 3 to 1, and (b) 7 to 1 computed at the CCSD(T)/aug-cc-pVTZ//TPSS/def2-TZVP level.

Two alternative mechanisms for the isomerization of 3 to 1 were explored. Both mechanisms involve a stepwise process, with higher activation barriers than the concerted pathway (Fig. S1 and S2, ESI†). The first pathway begins with converting 3 into 2via a 1,2-H migration from B2 to B4, before transitioning to 1 (Fig. S1, ESI†). However, the initial step has a free energy barrier of 31.8 kcal mol⁻¹ (TS_3-2), which is 7.2 kcal mol⁻¹ higher than the barrier of the concerted pathway (TS_3-1, Fig. 4a).

The second pathway initiates with the cleavage of the B2–B3 bond and the formation of a B4–H–B5 bond, leading to 9 (Fig. S2, ESI†). The activation barrier for this initial step (TS_3-9) is 14.9 kcal mol⁻¹. Next, 9 is converted to 6 through a double hydrogen rearrangement viaTS_9-6. This step involves breaking the B4–H–B5 bond and forming the B1–H–B2 bond with a low energy barrier (ΔG^‡ = 5.6 kcal mol⁻¹) and can be viewed as a type II-dyotropic migration.²⁸ The conversion from 6 to 2 (TS_6-2) has an activation barrier of 27.5 kcal mol⁻¹. As in the previous stepwise pathway, this process concludes with converting 2 to 1. Note that the barrier of TS_6-2, acting as the rate-determining step, is 2.9 kcal mol⁻¹ higher than that of TS_3-1, indicating that these alternative routes are energetically less favorable.

To gain deeper insight into the isomerization processes from 3 to 1 and 7 to 1, Born–Oppenheimer molecular dynamics simulations were conducted at 900 K for 30 ps, beginning with structures 3 and 7 (see the Movie S1 and S2 in the ESI†). Isomer 3 displayed minor distortions while preserving its planar structure throughout the simulation, confirming its kinetic stability in line with its high activation barrier (Fig. 4a and Movie S1, ESI†). In the case of isomer 7, a transformation occurs at 9 ps (Movie S2, ESI†), where its pyramidal cage transitions into a trapezoidal shape reminiscent of isomer 4. This stage is characterized by the heightened mobility of hydrogen atoms around the boron-based trapezoid, leading to several structural interconversions between isomers 4 and 2 until 20 ps. When structure 2 forms, it briefly shifts to 1 but reverts to 2. Around 23 ps, 2 undergoes bending and transitions into the stable structure of 1 with minimal distortions for the rest of the simulation. This series of events confirms the kinetic stability of both isomers 1 and 3, as they maintain their structural integrity throughout the simulation.

Conclusion

By exploring the B₅H₅ potential energy surface, we found a three-dimensional structure that challenges the previously accepted planar model as the global minimum for this neutral borohydride. The analysis of the kinetic stability of the B₅H₅ isomers indicates that isomer 3, suggested by Mckee, is a kinetically stable system that could potentially be experimentally detected, but it is not the global minimum. In contrast, isomer 7 (Schleyer's proposal) is likely to transform into isomer 1, making its experimental detection in the gas phase challenging, if not impossible. Through molecular dynamics simulations, we provided detailed insights into the dynamic behavior of these molecules, enhancing our understanding of their stability under various conditions.

These findings open new avenues for re-examining the bonding and structure of boron hydrides, extending beyond theoretical interest, and possibly influencing future experimental endeavors and applications in related chemical areas.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

G. H.-J. and F. M. thank Conacyt for their PhD and postdoc fellowships, respectively. The work in Chile was supported by the National Agency for Research and Development (ANID) via the Fondecyt projects N° 1211128 (W. T.) and 1221019 (A. V.-E.).

References

1. W. N. Lipscomb, Extensions of the Valence Theory of Boron Compounds, Proc. Natl. Acad. Sci. U. S. A., 1961, 47(11), 1791–1795.
2. E. B. Moore, L. L. Lohr and W. N. Lipscomb, Molecular Orbitals in Some Boron Compounds, J. Chem. Phys., 1961, 35(4), 1329–1334.
3. R. Hoffmann and W. N. Lipscomb, Theory of Polyhedral Molecules. I. Physical Factorizations of the Secular Equation, J. Chem. Phys., 1962, 36(8), 2179–2189.
4. K. Wade, Structural and Bonding Patterns in Cluster Chemistry, in Advances in Inorganic Chemistry and Radiochemistry, Elsevier, 1976, pp. 1–66.
5. D. M. P. Mingos, A General Theory for Cluster and Ring Compounds of the Main Group and Transition Elements, Nat. Phys. Sci., 1972, 236(68), 99–102.
6. M. L. McKee, Z.-X. Wang and P. v R. Schleyer, Ab Initio Study of the Hypercloso Boron Hydrides B_nH_n and B_nH_n⁻. Exceptional Stability of Neutral B₁₃H₁₃, J. Am. Chem. Soc., 2000, 122(19), 4781–4793.
7. M. L. McKee, Ab Initio Study of B_nH_n and B_n(NH₂)_n (n = 3–6) Species. A Comparison of Classical and Nonclassical Structures, Inorg. Chem., 1999, 38(2), 321–330.
8. H.-J. Zhai, L.-S. Wang, A. N. Alexandrova and A. I. Boldyrev, Electronic Structure and Chemical Bonding of B₅⁻ and B₅ by Photoelectron Spectroscopy and Ab Initio Calculations, J. Chem. Phys., 2002, 117(17), 7917–7924.
9. J. Barroso, S. Pan and G. Merino, Structural Transformations in Boron Clusters Induced by Metal Doping, Chem. Soc. Rev., 2022, 51(3), 1098–1123.
10. G. Hernández-Juárez, A. Vásquez-Espinal, F. Murillo, A. Quintal, F. Ortíz-Chi, X. Zarate, J. Barroso and G. Merino, Unveiling the Electronic and Structural Consequences of Removing Two Electrons from B₁₂H₁₂²⁻, Dalton Trans., 2023, 52(46), 17398–17406.
11. F. Ortiz-Chi and G. Merino, GLOMOS, Mérida, México, 2020.
12. R. Grande-Aztatzi, P. R. Martínez-Alanis, J. L. Cabellos, E. Osorio, A. Martínez and G. Merino, Structural Evolution of Small Gold Clusters Doped by One and Two Boron Atoms, J. Comput. Chem., 2014, 35(32), 2288–2296.
13. C. Adamo and V. Barone, Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model, J. Chem. Phys., 1999, 110(13), 6158–6170.
14. F. Weigend and R. Ahlrichs, Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy, Phys. Chem. Chem. Phys., 2005, 7(18), 3297–3305.
15. J. Tao, J. P. Perdew, V. N. Staroverov and G. E. Scuseria, Climbing the Density Functional Ladder: Nonempirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids, Phys. Rev. Lett., 2003, 91(14), 146401.
16. J. D. Watts, J. Gauss and R. J. Bartlett, Coupled-Cluster Methods with Noniterative Triple Excitations for Restricted Open-Shell Hartree–Fock and Other General Single Determinant Reference Functions. Energies and Analytical Gradients, J. Chem. Phys., 1993, 98(11), 8718–8733.
17. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. V. Marenich, J. Bloino, B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D. Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V. G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery Jr., J. E. Peralta, F. Ogliaro, M. J. Bearpark, J. J. Heyd, E. N. Brothers, K. N. Kudin, V. N. Staroverov, T. A. Keith, R. Kobayashi, J. Normand, K. Raghavachari, A. P. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene, C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman and D. J. Fox, Gaussian 16, Revision C.01, Gaussian, Inc., Wallingford CT, 2016.
18. E. D. Glendening, C. R. Landis and F. Weinhold, NBO 6.0: Natural Bond Orbital Analysis Program, J. Comput. Chem., 2013, 34(16), 1429–1437.
19. D. Y. Zubarev and A. I. Boldyrev, Developing Paradigms of Chemical Bonding: Adaptive Natural Density Partitioning, Phys. Chem. Chem. Phys., 2008, 10(34), 5207–5217.
20. T. Lu and F. Chen, Multiwfn: A Multifunctional Wavefunction Analyzer, J. Comput. Chem., 2012, 33(5), 580–592.
21. J. M. Millam, V. Bakken, W. Chen, W. L. Hase and H. B. Schlegel, Ab Initio Classical Trajectories on the Born–Oppenheimer Surface: Hessian-Based Integrators Using Fifth-Order Polynomial and Rational Function Fits, J. Chem. Phys., 1999, 111(9), 3800–3805.
22. S. Nosé, A Unified Formulation of the Constant Temperature Molecular Dynamics Methods, J. Chem. Phys., 1984, 81(1), 511–519.
23. G. J. Martyna, M. L. Klein and M. Tuckerman, Nosé–Hoover Chains: The Canonical Ensemble via Continuous Dynamics, J. Chem. Phys., 1992, 97(4), 2635–2643.
24. W. G. Hoover, Canonical Dynamics: Equilibrium Phase-Space Distributions, Phys. Rev. A: At., Mol., Opt. Phys., 1985, 31(3), 1695.
25. A. M. Koster, G. Geudtner, A. Alvarez-Ibarra, P. Calaminici, M. E. Casida, J. Carmona-Espindola, V. D. Dominguez, R. Flores-Moreno, G. U. Gamboa, A. Goursot, T. Heine, A. Ipatov, A. de la Lande, F. Janetzko, J. M. del Campo, D. Mejia-Rodriguez, J. U. Reveles, J. Vasquez-Perez, A. Vela, B. Zuniga-Gutierrez and D. R. Salahub, deMon2k, Version 5, The deMon Developers, Cinvestav, Mexico City, 2018.
26. S. Chiodo, N. Russo and E. Sicilia, Newly Developed Basis Sets for Density Functional Calculations, J. Comput. Chem., 2005, 26(2), 175–184.
27. Y.-F. Shen, C. Xu and L.-J. Cheng, Deciphering Chemical Bonding in B_nH_n²⁻ (n = 2–17): Flexible Multicenter Bonding, RSC Adv., 2017, 7(58), 36755–36764.
28. I. Fernández, F. Cossío and M. A. Sierra, Dyotropic Reactions: Mechanisms and Synthetic Applications, Chem. Rev., 2009, 109, 6687–6711.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4cp00029c

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