Electronic structure study of H₃BXH₃ (X═B, N and P) as hydrogen storage materials using calculated NMR and XPS spectra

Major structural differences among the boranes

The primary distinguishing structural feature among DB, AB and PB compounds lies in the types of atoms and groups attached to the central boron atom. DB only has hydrogen atoms bonded to the boron atoms, whereas AB and PB respectively have nitrogen and phosphorus atoms connected to the boron atom.⁹ These distinct bonding arrangements and molecular architectures lead to variations in the physical and chemical characteristics of these compounds, including their hydrogen storage capacity and reactivity. In Fig. 2, the structural differences are evident. Diborane has two boron atoms linked by two bridging hydrogen atoms (H_b), with each boron atom forming bonds with two additional hydrogen atoms. In AB, the boron atom is connected to an amino (NH₃) group and three boron–hydrogen (B–H) bonds. Similarly, in PB, the boron atom is attached to a phosphine (PH₃) group and three B–H bonds. Each of these compounds harbours two categories of hydrogen atoms: bridge (H_b) and terminal (H_t) hydrogens in diborane (DB),⁹ and protic (H_p) hydrogens in AB and PB originating from the N–H and P–H bonds. These hydrogens possess partial positive charges (δ⁺). Additionally, there are hydridic (H_h) hydrogens in AB and PB within B–H bonds, carrying partial negative charges (δ⁻).³ This intricate arrangement of atoms and hydrogen groups forms the foundation for the distinctive properties and behaviours of these compounds.

Fig. 2.

Chemical structures of diborane (DB), ammonia borane (AB) and phosphine borane (PB) and their point group symmetry. In DB, the hydrogens are labelled as bridge hydrogens (H_b) and terminal hydrogens (H_t); in AB and PH, the hydrogens are labelled as protic (N–H and P–H) hydrogens (H_p) and hydridic (B–H) hydrogens (H_h).

The structural differences between DB and both AB and PB are quite pronounced. In DB, two boron atoms are linked through bridge hydrogens, presenting a unique arrangement. By contrast, AB and PB feature a single B–X bond (where X═N or P), which allows rotations around this bond. The energy barriers associated with these rotations are defined as the energy difference between eclipsed and staggered conformers, analogous to the behaviour observed in molecules like ethane.²⁹ Specifically, the calculated rotational energy barriers around the B–X bond for H₃B–NH₃ and H₃B–PH₃ have been reported as 2.48 and 2.62 kcal mol^–1 (1 kcal mol^–1 = 4.186 kJ mol^–1) for AB and 2.47 and 2.55 kcal mol^–1 for PB, calculated using the MP2/6-31++G(d,p) and DFT-based B3LYP/6-31++G(d,p) levels of theory respectively.²⁹ For comparison, the rotational energy barrier of ethane (CH₃–CH₃) is 2.875 kcal mol^–1.³⁰ As a result, the present study focused solely on eclipsed AB and PB for the C_3v point group symmetry. This choice aligns with the low-temperature dynamics study of AB, which also adopted the eclipsed structure.³¹ Importantly, the energy barriers observed for AB and PB are approximately half of the earlier estimated 4–6 kcal mol^–1 barrier that restricts internal rotation in DB.³² This difference underscores the varying rotational dynamics between these compounds.

Table 1 compares properties among the three compounds DB, AB and PB. Notably, the B–X bond lengths shows different values: 1.762 Å for B–B (or B⋯B distance) in DB, 1.655 Å for B–N in AB and 1.949 Å for B–P in PB. This trend in bond lengths aligns with expectations, as the van der Waals radii³³ for B, N, and P are 1.92, 1.55 and 1.80 Å respectively. The reported complexation energy (E_c) reveals that the stability of PB is −21.10 kcal mol^–1, comparatively less stable than AB with an E_c of −25.97 kcal mol^–1.³³ Examining the structural parameters of H₃BXH₃ in Table 1, it is evident that the HBN angle in AB (104.88°) increases to 117.82° for the HBP angle in PB, whereas the bond lengths of hydridic hydrogens (H_h–B) in the boranes remain quite similar (1.188 Å for H–B in DB, 1.210 Å for H–B in AB and 1.207 Å for H–B in PB). The lengths of protic hydrogen bonds (H_p–N and H_p–P) exhibit significant differences. Specifically, the H_p–N bond length in AB is notably shorter at 1.015 Å, whereas the H_p–P bond length in PB is significantly longer at 1.405 Å compared with their corresponding hydridic bonds (H_h–B). The H–X bond lengths in AB and PB closely resemble the bond lengths of H–N in ammonia (NH₃), at 1.017 Å, and H–P in phosphine (PH₃), at 1.421 Å.³⁴ In DB, the bridge H_b–B bond length (1.315 Å) is significantly longer than the terminal H_t–B bond length (1.188 Å), indicating a distinct bonding nature. This set of structural parameters contributes to the unique characteristics and behaviours of these boron compounds.

The nature of the N–B bond in AB and P–B bond in PB is predominantly polar. The interaction between the electron lone pair of phosphines and boranes leads to increased acidity of the P–H bond, whereas the P–B bond decreases electron density on the phosphorus atom. As a result, PB displays a longer P–B bond length of 1.949 Å and exhibits a weaker adjacent P–H bond in comparison with AB. In PB, the bond length of P–H_h is 1.416 Å, considerably longer than the N–H_h bond length of 1.015 Å. Owing to its high symmetry (D_2h), DB is a non-polar compound with no permanent dipole moment. By contrast, the dipole moment of AB is 5.40 D, surpassing PB’s dipole moment of 4.35 D. This divergence in dipole moments can be attributed to the larger dipole moment of the Lewis base NH₃ (1.55 D for NH₃ using MP2/6-311+G(3df,2p)) in comparison with PH₃ (0.58 D).³⁷ Furthermore, the interaction energy within the bond formed by PH₃ must result from the distortion of the PH₃ electron pair due to the positive field of the Lewis acid (BH₃). This intricate interplay of polarities and interactions contributes to the varied characteristics and behaviours observed in these compounds.

NMR chemical shifts of the boranes

Further advances in understanding the structure and reactivity of these borane compounds will not only contribute to tackling challenges in the field of hydrogen storage but also to other domains of boron chemistry.³⁸ NMR spectroscopy is a powerful tool for unravelling molecular structures. The structural information provided by the NMR technique is multifaceted, site‐specific, remarkably stable and reliably reproducible over time.³⁹ Our investigation looked into the role of hydrogen atoms within DB, AB and PB through the lens of ¹H NMR chemical shifts. To accomplish this, the NMR absolute isotropic shielding constants (chemical shifts)⁷ for the boranes were calculated. The absolute isotropic shielding constants (σ, ppm)⁷ were calculated using the gauge-independent atomic orbital (GIAO) method^40–43 in conjunction with the B3PW91 functional. This functional has demonstrated accuracy in predicting NMR shield tensor (chemical shifts) for molecules⁴³ and compounds containing boron.⁴⁴

The chemical shift (δ_A, ppm) of atom A in the boranes is given by:

where σ_A⁰ is the absolute isotropic shielding constant of same atom A in a reference compound. Usually, the reference standards for σ_H⁰ and σ_C⁰ are the shielding constants of ¹H and ¹³C in tetramethylsilane (TMS) respectively, whereas the reference standard for σ_N⁰ is ¹⁵N in NH₃ and for σ_B⁰ is ¹¹B in BF₃·OEt₂ (boron trifluoride diethyl etherate).⁴³ In the G16 computational chemistry package, σ_H⁰ = 31.8821 ppm in TMS, σ_B⁰ = 83.6 ppm in B₂H₆, σ_N⁰ = 258.4 ppm in NH₃, all calculated using B3LYP/6-311+G(2d,p) (GIAO).

Table 2 reports the calculated absolute isotropic shielding constants (σ_B) for DB, AB and PB. The marked differences in these σ_B constants arise from the diverse chemical environments of these compounds. Specifically, boron in DB features the smallest shielding constant (σ_B = 85.40 ppm), whereas boron in PB exhibits the largest shielding constant (σ_B = 151.46 ppm). AB falls between DB and PB, with a shielding constant of σ_B = 126.21 ppm. The shielding constants of hydrogens (σ_H) within DB, AB and PB are reported in Fig. 2. A standardised absolute shielding scale for boron is established with reference to the shielding constant in liquid BF₃·OEt₂, which is 110.9 ppm for ¹¹B.⁴⁵ In the present study, utilising the absolute isotropic shielding constant (σ) directly rather than the chemical shift (δ) serves to minimise discrepancies stemming from different methods. For example, σ_B⁰ = 83.6 ppm of B₂H₆ is calculated using the B3LYP/6-311+G(2d,p) (GIAO) and 85.40 ppm using B3PW91/aug-cc-pVTZ. It is important to acknowledge that, although the accuracy of an atom’s absolute isotropic shielding constant in a specific chemical environment hinges on the chosen level of theory,⁴³ employing the same level of theory across a series of compounds can help mitigate certain systematic errors. NMR techniques have been leveraged to investigate B–N and B–P coupling for AB⁴⁶ and PB.⁷

Table 2.The calculated absolute isotropic shielding constant (σ) of DB, AB and PB.

Molecules	Structure	σ(11B) (δB) (ppm)	σ(X) (δX) (ppm)	σ(Hb (HB)) (δH,h) (ppm)	σ(Ht (HX)) (δH,p) (ppm)	Δδ (ppm)
B2H6 (DB)		85.40 (53.32) A	85.4 A, B	32.32 (−0.44) B	27.01 (4.87) B	5.31
H3BNH3 (AB)		126.21 (94.13) A	231.39 (249.122) A B C	29.47 (2.41) B	29.05 (2.83) B	0.42
H3BPH3 (PB)		151.46 (119.38) A	454.37 A B D	30.59 (1.28) B	27.60 (4.28) B	3.0

The experimental chemical shifts of ¹¹B in BH₃ and H₃BNH₃ are 86 and −16.6 ppm.⁴⁴ Unless results are associated with a reference citation, data are calculated using the method in B3PW91/aug-cc-pVTZ (ppm). No reference – absolute shielding (σ).

^{A 11}B chemical shifts relative to the IUPAC standard BF3·OEt₂(δ = 0 ppm) at 20°C (σ_B = 32.08 ppm).⁴⁷

^B Chemical shift (δ_H) with respect to σ_H = 31.8821 ppm of H in TMS.

^C Experimental σ_N⁰ _N = 264.5 ppm in NH₃⁴⁸ and calculated σ_N⁰ = 261.3 ppm in NH₃ using B3PW91/6-31G*.⁴³

^D Calculated σ_P⁰ = 606.110 ppm in PH₃ in gas phase using CCSD(T)/aug-pVQZ⁴⁹ and σ_p = 357.6 ppm for (CH₃)₃PBH₃. δ(free P) is reported to be 246 ppm.⁷

The calculated chemical shifts δ(¹¹B) of AB and PB are referenced against δ(¹¹B) of DB, which is 85.40 ppm. Experimentally, δ(¹¹B) for AB is observed at −21.6 ppm relative to the IUPAC standard BF₃·OEt₂ (δ = 0 ppm) at 20°C. Calculated δ(¹¹B) values for AB show some variability depending on the methods employed, yielding values of −24.7, −23.7 and −27.1 ppm with respect to the IUPAC standard BF₃·OEt₂.⁵⁰ As reported in Table 2, the distinct chemical environments of boron in DB, AB and PB are clearly apparent, as evidenced by their NMR chemical shifts of δ(¹¹B). The shifts in δ(¹¹B) across the boranes are quite significant. Specifically, δ(¹¹B) for AB and PB shifts by 40.80 and 66.06 ppm respectively, relative to δ(¹¹B) of DB. The trend is δ(¹¹B) (PB) > δ(¹¹B) (AB) > δ(¹¹B) (DB). This order reveals the principle that the stronger the chemical environment of boron, the larger its chemical shift.

The hydrogens within the Lewis acid BH₃ and Lewis base XH₃ (X═N and P) of AB and PB exhibit notable differences from the hydrogens in DB. In the staggered configurations, the chemical shifts of the three-fold degenerate protic hydrogens (H_p–X) are 2.83 ppm in AB and 4.28 ppm in PB. Conversely, the chemical shift of three-fold degenerate hydridic hydrogens (H_h–B) in the BH₃ fragment follows the reverse order: 2.47 ppm in AB and 1.28 ppm in PB. Moving to DB, the chemical shifts of the bridge hydrogens (H_bs) and terminal hydrogens (H_ts) are −0.44 and 4.87 ppm respectively. As a result, the two distinct groups of hydrogens in DB, AB and PB exhibit chemical shifts of 5.31, 0.42 and 3.0 ppm respectively. The most substantial difference is observed in the H_bs and H_ts of DB, followed by the H_hs and H_ps of PB. By contrast, the differences between the H_hs and H_ps of AB are the smallest. However, both AB and PB show the same trend: protic hydrogens have a stronger chemical environment than hydridic hydrogens. Importantly, the calculated chemical shifts align with findings from other NMR studies of AB in diverse mediums, including solutions.⁴⁶ This consensus indicates the robustness and validity of the trends obtained in chemical shifts, which reflect the distinct chemical environments and bonding characteristics within these borane compounds.

Fig. 3 compares the NMR hydrogen shielding constants (σ_H) of the boranes. The boranes studied here feature two distinct groups of hydrogen atoms, each with markedly different roles and bonding characteristics. The hydrogen chemical shifts (δ_H) of the boranes are relatively modest when compared with the reference methyl hydrogens (–CH₃). The σ_H value for TMS is 31.88 ppm, indicating that σ_H(boranes) is generally lower than or comparable with σ_H(TMS). The borane compounds host two distinct types of hydrogen atoms, H_b and H_t in DB, and H_p and H_h in AB and PB. As shown in Fig. 3, the difference between hydrogen groups is most pronounced (δ_H = 5.31 ppm) in DB, whereas the difference is least marked (δ_H = 0.42 ppm) in AB. In PB, the hydrogen shielding constant difference is substantial, with a large splitting of 3.0 ppm.

Fig. 3.

Comparison of the NMR absolute isotropic hydrogen and boron shielding constants σ for DB, AB and PB calculated using B3PW91/aug-cc-pVTZ (ppm). The hydrogen chemical shifts of the boranes are in blue for hydridic hydrogens (H_hs), red for protic hydrogens (H_ps) and green for hydrogens in DB.

A notable point is the nuanced role of the hydrogens in DB. It can be argued that DB may be more appropriately represented as H₂B₂H₄, rather than B₂H₆, as the six hydrogens in DB do not all play identical roles. Specifically, the bridge H_bs in DB, formed through three-centre-two-electron bonds, exhibit stronger chemical characteristics compared with the terminal H_ts in DB.⁹ For both AB and PB, the hydridic hydrogens (H_hs) (represented in blue in Fig. 3) within the hydrogens in the H–B bonds demonstrate larger shielding constants than their protic hydrogen (H_ps) counterparts (in red) within the same compound.

Ionisation potentials of the boranes

To further understand the borane compounds, we calculated their IPs.²³ It is important to note that the IP of a compound includes both the valence IP and core IP, which are measured using photoelectron spectroscopy (PES) and XPS respectively. The complete valence IP of DB is readily available,⁹ whereas the availability of data on the experimental valence IPs for AB and PB are quite limited. The first (valence) IP of AB was measured as 10.58 eV for the VIP and 9.44 eV for the adiabatic ionisation potential (AIP) using mass spectrometry.⁵¹ The AIP value agrees with 9.26 ± 0.03 eV determined by a recent photo-electron–photoion coincidence (PEPICO) spectroscopic measurement.²³ The measured IP value of a compound depends on experimental conditions, spectroscopic techniques, resolution and the spectral analyses, and the measurement process.⁵²

Accurate theoretical calculations are essential for molecular spectroscopy, guiding the interpretation of experimental results and enabling more accurate determination of key properties.^52,53 Table 3 compares the calculated valence IPs for the three borane compounds. The agreement between calculated valence IPs and measurements⁹ for DB suggests that the ΔPBE0(SAOP)/et-pVQZ method in the present study is accurate. Therefore, the same method was used to calculated the valence IPs for both AB²² and PB. The complete valence IPs of AB were confirmed by recent gas-phase measurements at the Elettra synchrotron in Italy (please see ‘In proof’ section at the end of this article). This recent measurement of AB increases our confidence in the calculated valence IPs of PB, although no available IPs for PB exist.

The IPs of DB diverge significantly from those of AB and PB complexes, which can be attributed to DB’s distinct D_2h point group symmetry and different structural characteristics. AB and PB share the C_3v point group symmetry in the form of Lewis acid–Lewis base complexes. This commonality allows AB and PB to share the same character table and irreducible representations with orbitals of a₁ and e₁ symmetries. However, the ground state configurations of AB and PB diverge owing to the variations in the valence electronic structures stemming from the nitrogen and phosphorus atoms within the complexes.

Fig. 4 compares the simulated valence IP spectra of AB and PB in the energy region of 5–35 eV. Four major IP bands in PB (top) but five major bands in AB (bottom) appear in the spectra. Although some similarities exist between the spectra of PB and AB, there are notable differences. The lowest five valence IPs of AB span a wider energy range (~11–30 eV) compared with PB (~11–22 eV). The valence IPs and their assignment exhibit an interesting pattern for the a₁ orbitals and the doubly degenerate e₁ orbitals in both AB and PB. There is a small energy gap (ΔIP  0.22 eV) in PB between the outer valence highest occupied molecular orbital (HOMO), 3e₁, a doubly degenerate orbital and the next HOMO, HOMO-1, 7a₁. As a result, the first IP band at approximately 11 eV, which consists of three closely lying states, leads to a single band so that there are four distinct IP bands in the outer valence IP spectrum of PB. However, the IP energy gap between HOMO and HOMO-1 of AB is larger, measuring 2.01 eV, which is likely sufficient for spectrometer resolution, resulting in five IP bands in the spectrum of AB. The IPs of AB agree with a previous calculation using the B3LYP/6-31++G(d,p)//MP/6-31++G(d,p) method,²⁹ which however, does not include orbital 3a₁ at 29.88 eV.

Fig. 4.

Calculated valence ionisation spectra of AB (bottom) and PB (top). The ionisation energies (degeneracy is considered) in Table 3 are convoluted using a Gaussian broadening function with full width at half maximum (FWHM) at 0.05 eV. The related valence states (orbitals) are also indicated in the spectra. Purple spectrum (top) is for PB and blue spectrum (bottom) is for AB.

Further information using energy decomposition analysis (EDA) reveals that in AB,²⁹ the charge transfer (CT) is largely governed by the π(HOMO) orbital with an N → B CT profile. Mallajosyula et al.²⁹ suggested that in PB, the dominant contribution is from the σ(6a₁) orbital with a marginal contribution from the HOMO (3e₁). However, the present study reveals that the outer valence orbitals, such as π(3e₁, 2e₁) and σ(7a₁), do not exhibit distinct CT character, whereas the σ(6a₁) orbital displays a B ← P CT character, and the σ(5a₁) orbital exhibits a B → P CT character. As a result, the IP spectra of AB and PB exhibit similarities in their σ(a₁) states with CT characteristics, but their π(e₁) orbitals are notably different. The π(e₁) orbitals of AB displays CT character, whereas the π(e₁) orbitals of PB exhibit a more covalent character.

Core electron binding energies provide valuable information about the chemical environments of atoms within compounds.⁵⁷ The comparison of calculated CEBE for boron (B 1s) in the different borane compounds – DB, AB, and PB – can reveal important insights into their local electronic structures. As shown in Fig. 5, B 1s CEBE values for DB, AB and PB are 196.53, 194.01 and 193.93 eV respectively. The B 1s CEBE values for DB and AB agree well with available experimental values of 196.5 eV for DB⁵⁸ and 193.73(4) eV for AB,⁵⁹ whereas no experimental B 1s CEBE for PB is available. The trend of B 1s CEBE values among the compounds is as follows: B 1s (PB) < B 1s (AB) < B 1s (DB). This implies that the core electrons of boron in PB require less energy to be ionised (oxidised) compared with those in AB, whereas the core electrons of boron in DB require more energy to be ionised. Lower CEBE values indicate a more chemically reactive environment, which corresponds to a more active chemical environment. This trend aligns with the larger ¹¹B NMR chemical shifts reported in Fig. 3. It is important to note that whereas XPS and NMR techniques have different mechanisms, they both provide valuable information about the chemical and electronic properties of a compound, local to a specific atom.

Fig. 5.

Comparison of the CEBE of B 1s of DB, AB and PB. The order of CEBE is B 1s (PB) < B 1s (AB) < B 1s (DB).

Confirmation

We are pleased to announce the successful completion of gas-phase synchrotron-sourced photoemission and X-ray absorption measurements for ammonia borane at Elettra Sincrotrone Trieste in Italy. The outcomes of these experiments show exceptional agreement with our valence IP and CEBE calculations. Specifically, we precisely determined the complete valence IP spectrum, which encompasses the calculated band at 29.99 eV (3a₁). The calculated B 1s energy, at 194.01 eV, has been confirmed. We are currently in the final stages of manuscript preparation, describing these compelling findings resulting from a decade collaboration between theoretical and experimental approaches.