Ab initio insights into the face, edge, and vertex interactions of BH₄¹⁻ with electron-accepting molecules

Abstract

The ab initio calculations at the MP2/aug-cc-pvdz computational level were used to analyze the interactions of FCN, ClCN, BrCN, CF₃H, CF₃Cl, CH₃OH, HF, HCl, HCN, SH₂, SHF, SF₂, H₂O, HOCl, HOBr, CO, N_2, and H₂ molecules with BH₄¹⁻. On BH₄¹⁻, three sites were accessible for interactions with L molecules to form BH₄(L)¹⁻ aggregates. The faces, edges, and vertices of BH₄¹⁻ as electron donors, could interact with electron acceptor species. In addition, the BH₄¹⁻ anion, through its σ-holes, could obtain electrons from interacting molecules. The significant preference of some molecules was interaction along the triangular faces, BH₄(L)_f¹⁻ (where L = ClCN, BrCN, FCN, CF₃Cl, CF₃H) whereas, for others, the vertices, BH₄(L)_v¹⁻ (where L = HOCl, HOBr, PF₃) or edges, BH₄(L)_e¹⁻ (where L = H₂O, HF, HCl) of BH₄¹⁻ might be more suitable for interaction. Some molecules, such as CH₄ and H₂, despite their preferred facial interactions, could interplay with the vertex counterpart through an edge intermediate. It seems that accepting electrons (triel bonding) by BH₄¹⁻ σ-holes had important roles in the face interactions for BH₄(L)_f¹⁻ adducts. Bader's Quantum Theory of Atoms in Molecules (QTAIM) and Natural Bond Orbital (NBO) calculations were used to analyze optimized complexes. Noncovalent interaction (NCI) analysis was used for further determination of interactions in BH₄(L)¹⁻ adducts.

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Introduction

Boron hydrides and borane clusters are important classes of metal hydrides that have been the subject of many studies.^1–5

Boron hydrides and borane clusters exhibit unusual bonding behavior and diverse structures, which have led to their use as ligands in inorganic chemistry and building blocks in materials science. In addition, these compounds have diverse applications stemming from their unique structures and bonding properties. These include applications in energy, materials science, and medicine. They can be used as fuels, in neutron-capture therapy for cancer treatment, and as components in polymers for heat resistance and other functional properties.⁶

Much attention has been paid to boron hydrides, thanks to their hydrogen-storage capacity, with a special emphasis on boron tetrahydride (BH₄¹⁻).^7–15 The latter is a building block of various hydrogen-storing compounds, such as Al₃Li₄(BH₄)₁₃,⁷ Mg(BH₄)₂,⁸ Ti(BH₄)₃,⁹ KSc(BH₄)₄,¹⁰ Al(BH₄)₃,¹¹ Zr(BH₄)₄,¹² Hf(BH₄)₄,¹² Th(BH₄)₄,¹³ and U(BH₄)₄,¹³ which can be liquid or solid-phase materials. Therefore, more detailed studies on the properties of BH₄¹⁻, especially with regard to Lewis acids and Lewis bases, are in demand. The nature and accessibility of BH₄¹⁻ as a bidentate ligand^8–13 in various BH₄⁻¹-containing clusters can be explained by investigating its intermolecular interactions with different electron donors and electron acceptors by theoretical methods. We focused on BH₄¹⁻ as a compound that could form hydrogen-rich clusters and might be used as a hydrogen-storage system.

Previously, we studied the interaction of B₆H₆²⁻ with HF¹⁴ and H₂.¹⁵ On the negatively charged surface of B₆H₆²⁻, the centers of the B₃ triangular faces on the B₆H₆²⁻ octahedral structure, built by B–B bonds, exhibit minimal electrostatic potential. These triangular faces were electron-rich basic centers for the adsorption of H₂ and HF molecules. In addition, other negative regions of electrostatic potentials were located on the H vertices of B₆H₆²⁻, but their charge densities were lower than those of the B₃ triangles. Thus, the most significant action of H₂ and HF molecules was interaction with the center of B₃ triangles, which had greater charge densities.^14,15 Similar studies using borane and carborane clusters have shown that B–B and B–C bonds could contribute as electron donors in intermolecular interactions.^16–20

In line with those projects, the tetrahedral BH₄¹⁻ as an electron source or Lewis base, could contribute to the interactions with different kinds of electron acceptors or Lewis acids. In accordance with this idea, various types of intermolecular interactions might be considered. For this purpose, BH₄¹⁻ could be implemented in different types of interactions, including dihydrogen bonding (DHB),²¹ halogen bonding (XB),^22,23 chalcogen bonding (ChB),^24,25 pnictogen bonding (PnB),^26,27 tetrel bonding (TtB),^28,29 and triel bonding (TrB).³⁰

The tetrahedral structure of BH₄¹⁻, through its B–H vertices, H–H edges, and H₃ triangular faces, could act as an electron donor to do three types of interactions with electron-acceptor molecules. Due to the different characteristics of the electron acceptors, one would expect them to have different preferences for interaction with each one of these sites on BH₄¹⁻ (as an electron donor). Our results could aid selectivity of the interaction of several electron acceptors with an electron donor.

Computational methods

Calculations were done using the Gaussian 09 system of codes.³¹ The geometries of the isolated BH₄¹⁻, L (where L = ClCN, BrCN, CF₃Cl, FCN, CO, N_2, H₂O, CF₃H, CH₃OH, HCl, HCN, HF, SH₂, SHF, SF₂, H₂O, CH₃OH, HF, HCl, HCN, CF₃H, H₂, HOCl, HOBr) and BH₄(L)¹⁻ complexes were fully optimized at the MP2 computational level³² with the aug-cc-pVDZ basis set.³³ Harmonic vibrational frequency calculation confirmed the structures as minima, and enabled the evaluation of the zero-point energy (ZPE). The XYZ coordinates (Z-matrices) for gas-phase-optimized structures are given in Table S1 in the SI. A counterpoise procedure was used to correct the interaction energy for the basis set superposition error.³⁴ AIMAll^35,36 packages were used to obtain bond properties and molecular graphs. The NBO analysis³⁷ was done employing the same method and basis set using the NBO program provided with Gaussian 09.

Result and discussion

Three zones were available on BH₄¹⁻ for interactions with other molecules: H₃ triangular faces, H₂ edges, and BH vertices of BH₄¹⁻ (Fig. 1). The H₃ triangular faces were present as electron acceptors for TrB and electron-donor sites for various trifurcated interactions. TrB returns to a type of interaction containing a group 13 (B, Al, Ga, etc.) element as an electron acceptor, forming a bond with an electron-rich region such as a lone pair, π-electron, or σ-electron.³⁰ Conversely, the H₂ edges have good conditions for contributing as electron-donor sites for some interactions like bifurcated DHB. Finally, the BH vertices of BH₄¹⁻ may contribute to conventional DHB, XB, ChB, PnB and TtB. For this purpose, BH₄¹⁻ was employed in a set of various types of interactions discussed below.

Fig. 1 Face, vertex, and edge positions of BH₄¹⁻ complexes (schematic).

Triel bond complexes BH₄(L)_f¹⁻

In BH₄(FCN)_f¹⁻, BH₄(ClCN)_f¹⁻, BH₄(BrCN)_f¹⁻, BH₄(ClCF₃)_f¹⁻, BH₄(N₂)_f¹⁻ and BH₄(CO)_f¹⁻ adducts, many intermolecular interactions were due to XB, PnB or TtB along with considerable L → BH₄ charge transfers (TrB) (Fig. 2). A significant part of the interactions in these adducts returned to charge transfers from guest molecules to the σ-hole (σ*) of the B–H bonds of BH₄¹⁻, so it was termed TrB. The stabilization energies of these adducts showed the following stability (Tables 1 and S2):

BH₄(BrCN)_f¹⁻ > BH₄(ClCN)_f¹⁻ > BH₄(ClCF₃)_f¹⁻ > BH₄(FCN)_f¹⁻ > BH₄(CO)_f¹⁻ > BH₄(N₂)_f¹⁻

Fig. 2 BH₄(L)¹⁻ complexes at the MP2/aug-cc-pVDZ level (schematic).

Table 1 The SE^ZPE+BSSE, ΔH, and ΔG in kcal mol⁻¹ calculated at MP2/aug-cc-pVDZ^a

Adduct	SE^ZPE+BSSE	ΔH	ΔG	Adduct	SE^ZPE+BSSE	ΔH	ΔG
a BH4(CH4)e^1−* (v1 = −48(1)) and BH4(H2)e^1−* (v1 = −29(1)) are optimized nonlocal structures. SE^ZPE+BSSE denotes zero point- and counterpoise-corrected stabilization energies.
BH4(ClCN)v^1−	−12.74	−13.52	−8.78	BH4(HOBr)v^1−	−20.82	−23.64	−18.65
BH4(BrCN)v^1−	−16.28	−18.49	−12.10	BH4(HOCl)v^1−	−16.61	−19.29	−11.15
BH4(CF3Cl)v^1−	−7.13	−8.03	−2.02	BH4(SF2)v^1−	−21.58	−24.58	−16.98
BH4(FCN)v^1−	−5.96	−6.34	−2.74	BH4(SFH)v^1−	−23.87	−26.82	−19.52
BH4(CO)v^1−	−1.87	−2.31	2.10	BH4(SH2)v^1−	−8.43	−9.79	−3.71
BH4(N2)v^1−	−1.39	−1.90	1.35	BH4(PH3)v^1−	−3.88	−4.59	0.86
BH4(H2O)v^1−	−10.23	−11.65	−6.02	BH4(PH2F)v^1−	−16.36	−18.67	−10.79
BH4(CH3OH)v^1−	−11.68	−12.93	−6.89	BH4(PHF2)v^1−	−15.4	−17.85	−9.65
BH4(HCl)e^1−	−15.88	−18.19	−11.64	BH4(PF3)v^1−	−12.41	−14.92	−7.46
BH4(HCN)f^1−	−17.1	−18.38	−12.77	BH4(H2)f^1−	−0.27	1.12	−4.86
BH4(HF)e^1−	−16.07	−17.94	−12.07	BH4(H2)v^1−	0.32	1.79	−5.44
BH4(CH4)f^1−	−1.7	−1.94	1.94	BH4(H2)e^1−*	−0.09	0.78	−4.01
BH4(CH4)e^1−*	−1.48	−2.16	2.11	BH4(CCl3H)f^1−	−14.15	−16.88	−9.81
BH4(CH4)v^1−	−0.94	−0.90	−1.08	BH4(CF3H)f^1−	−13	−14.35	−7.67

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For BH₄(FCN)_f¹⁻, in which the F atom seldom contributes as a halogen-bond donor, which results in halogen-bond interactions, NBO analysis indicated a partial charge of +0.0015 for the FCN molecule resulting from an NCF → BH₄ charge transfer. More detailed analysis showed interactions of lone pairs on the F atom with the σ*_(B–H3) orbital (or a σ hole) of BH₄¹⁻ as TrB interactions. Therefore, the tendency to have TrB led to a face–center interaction between FCN and BH₄¹⁻. The vibrational stretching frequencies (ν) and lengths of B–H bonds (r) are given in Tables 2–4. In free BH₄¹⁻, the amount of ν_(B–H) and r_(B–H) was 2291 cm⁻¹ and 1.2490 Å, respectively. These interactions caused contraction (0.0139 Å) along with a blue shift (28 cm⁻¹) of the C–F bond and contraction (0.0039 Å) along with a blue shift of B–H3 (28 cm⁻¹, the B–H trans to the FCN molecule) due to the greater contribution of B–H in adduct formation. BH₄(FCN)_f¹⁻ showed a blue shift (3–28 cm⁻¹), besides 0.0003 and 0.0039 Å reductions for its B–H bonds.

Table 2 Unscaled vibrational frequencies (ν, cm⁻¹) with corresponding intensities (values given in parentheses, km mol⁻¹) and bond distances (r, Å) for the selected bonds of free molecules

Compound	R	ν	Compound	r	ν
H2	0.7548	4465	SH2(S–H)	1.3496	2754(1)
PF3(P–F)	1.6294	825(203)	SHF(S–F)	1.6776	782(68)
PHF2(P–F)	1.6494	806(178)	SF2(S–F)	1.6498	798(141)
PH2F(P–F)	1.6727	780(120)	H2O(O–H)	0.9659	3804(4)
PH3(P–H)	1.4266	2452(34)	CH3OH(O–H)	0.9657	3843(44)
HOCl(Cl–O)	1.7326	740(10)	HF(H–F)	0.9248	4082(116)
HOBr(Br–O)	1.8596	645(14)	HCl(H–Cl)	1.2878	3025(43)
FCN(F–C)	1.2846	1026(63)	HCN(H–C)	1.0779	3456(74)
ClCN(Cl–CN)	1.6502	742(10)	CF3H(C–H)	1.0955	3226(21)
BrCN(Br–C)	1.7974	596(2)	CCl3H	1.0935	3202(1)
CF3Cl(C–Cl)	1.7568	480(1)	N2	1.1318	2157(0)
BH4^1−	1.2490	2291(615)	CO(C–O)	1.1502	2072(34)
CH4	1.0980	3207(19)

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Table 3 Unscaled vibrational frequencies (cm⁻¹) with corresponding intensities (values given in parenthesis, km mol⁻¹) for complexes

Adduct	ν	Δν	ν(B–H)	Δν(B–H)	ν(B–H)	Δν(B–H)	ν(B–H)	Δν(B–H)	ν(B–H)	Δν(B–H)
BH4(H2)f^1−	4353(131)(H–H)	−112	2297(556)	6	2297(556)	6	2301(424)	9	2306(201)	15
BH4(H2)v^1−	4365(126)(H–H)	−100	2297(598)	6	2297(598)	6	2300(330)	8	2313(366)	22
BH4(CF3Cl)v^1−	485(15)(C–Cl)	5	2309(369)	18	2309(177)	18	2309(465)	17	2333(528)	33
BH4(CF3CH)v^1−	3202()114(C–H)	−24	2307(449)	16	2307(449)	16	2310(82)	18	2367(480)	67
BH4(CO)v^1−	2067(28)(C–O)	−5	2296(515)	5	2296(530)	5	2301(135)	9	2309(500)	9
BH4(N2)f^1−	2152(1)(N–N)	−5	2299(504)	8	2299(550)	10	2301(61)	9	2306(587)	6
BH4(HCN)f^1−	3161(755)(H–C)	−295	2316(429)	25	2316(75)	25	2316(427)	24	2383(486)	83
BH4(ClCN)f^1−	732(156)(Cl–N)	−10	2307(446)	16	2307(446)	16	2309(102)	17	2357(510)	57
BH4(FCN)f^1−	1054(56)(F–C)	28	2294(562)	3	2294(562)	3	2300(125)	9	2319(493)	28
BH4(CH3OH)e^1−	3494(682)(O–H)	−349	2280(388)	−11	2328(123)	37	2334(430)	42	2357(507)	57
BH4(HCl)e^1−	1388(3875)(H–Cl)	−1611	2228(238)	−46	2383(91)	92	2421(424)	119	2434(323)	137
BH4(HF)e^1−	3271(1466)(H–F)	−811	2295(432)	4	2353(164)	62	2373(447)	81	2373(451)	73
BH4(HOBr)v^1−	385(652)(O–Br)	−260	1978(5326)	−313	2434(103)	143	2503(289)	211	2511(288)	211
BH4(HOCl)v^1−	422(238)(O–Cl)	−318	1932(5488)	−359	2442(124)	151	2522(285)	230	2523(283)	223
BH4(H2O)v^1−	3543(520)(H–O)	−261	2270(486)	−21	2309(319)	18	2341(298)	49	2351(503)	51
BH4(SH2)v^1−	2433(657)(S–H)	−321	2256(747)	−35	2320(111)	29	2338(461)	46	2350(492)	50
BH4(SHF)f^1−	358(881)(S–F)	−424	1959(3167)	−332	2442(98)	151	2509(247)	217	2532(266)	232
BH4(SF2)f^1−	466(981)(S–F)	−332	1957(2320)	−334	2430(50)	139	2494(275)	202	2508(293)	208
BH4(PH3)f^1−	2391(169)(P–H)	−61	2288(436)	−3	2294(339)	3	2305(259)	13	2321(564)	21
BH4(PH2F)f^1−	540(303)(P–F)	−240	2061(2206)	−230	2386(119)	95	2422(347)	130	2433(282)	133
BH4(PHF2)f^1−	601(354)(P–F)	−205	2147(1186)	−144	2365(81)	74	2404(384)	112	2423(358)	123
BH4(PF3)f^1−	648(442)(P–F)	−177	2225(871)	−66	2362(69)	71	2389(355)	97	2399(436)	99
BH4(BrCN)f^1−	545(9)(Br–C)	−51	2242(769)	−49	2347(102)	56	2362(411)	70	2373(472)	73
BH4(CH4)f^1−	3194(12)(C–H)	−13	2297(528)	5	2297(528)	5	2303(248)	3	2311(392)	20
BH4(CH4)v^1−	3191	−16	2298(583)	6	2298(583)	6	2301(332)	9	2315(416)	15
BH4(CCl3H)f^1−	3066	−136	2310(345)	18	2310(345)	18	2311(71)	19	2379(523)	79

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Table 4 Selected bond lengths (Å) of BH₄(L)¹⁻ aggregates at MP2/aug-cc-pVDZ

Adduct	r	Δr	r(B–H)1	Δr(B–H)1	r(B–H)2	Δr(B–H)2	r(B–H)3	Δr(B–H)3	r(B–H)4	Δr(B–H)4
BH4(H2)f^1−	0.7608(H–H)	0.0060	1.2485	−0.0005	1.2486	−0.0005	1.2485	−0.0005	1.2472	−0.0018
BH4(H2)v^1−	0.7601(H–H)	0.0053	1.24846	−0.0007	1.2484	−0.0007	1.2484	−0.0007	1.2470	−0.0020
BH4(CF3Cl)f^1−	1.2482(C–Cl)	−0.5086	1.2479	−0.0011	1.2471	−0.0020	1.2471	−0.0020	1.2430	−0.0060
BH4(CF3CH)f^1−	1.0977(C–H)	0.0022	1.2477	−0.0013	1.2476	−0.0014	1.2477	−0.0014	1.2386	−0.0104
BH4(CH3OH)e^1−	0.9843(O–H)	0.0186	1.2402	−0.0088	1.2440	−0.0051	1.2440	−0.0051	1.2522	0.0032
BH4(CO)f^1−	1.1510(C–O)	0.0008	1.2483	−0.0007	1.2486	−0.0004	1.2486	−0.0005	1.2466	−0.0024
BH4(HCl)e^1−	1.4221(H–Cl)	0.3442	1.2350	−0.0140	1.2351	−0.0140	1.2308	−0.0182	1.2704	0.0214
BH4(HCN)f^1−	1.1001(H–C)	0.0222	1.2469	−0.0022	1.2469	−0.0022	1.2468	−0.0022	1.2365	−0.0125
BH4(HF)e^1−	0.9633(H–F)	0.0385	1.2399	−0.0092	1.2389	−0.0101	1.2391	−0.0100	1.2527	0.0037
BH4(HOBr)v^1−	2.0761(O–Br)	0.2165	1.2235	−0.0255	1.2238	−0.0252	1.2254	−0.0236	1.3583	0.1093
BH4(HOCl)v^1−	2.0381(O–Cl)	0.3055	1.2227	−0.0264	1.2227	−0.0263	1.2227	−0.0264	1.3956	0.1466
BH4(N2)f^1−	1.1320(N–N)	0.0002	1.2481	−0.0007	1.2483	−0.0007	1.2482	−0.0008	1.2472	−0.0019
BH4(ClCN)f^1−	1.6496(C–Cl)	−0.0006	1.2475	−0.0015	1.2475	−0.0015	1.2475	−0.0015	1.2398	−0.0092
BH4(H2O)v^1−	0.9832(H–O)	0.0173	1.2469	−0.0021	1.2423	−0.0067	1.2415	−0.0075	1.2533	0.0043
BH4(FCN)f^1−	1.2707(F–C)	−0.0139	1.2487	−0.0003	1.2487	−0.0003	1.2487	−0.0003	1.2451	−0.0039
BH4(SH2)e^1−	1.3778(H–S)	0.0282	1.2452	−0.0038	1.2428	−0.0062	1.2428	−0.0062	1.2536	0.0046
BH4(SHF)f^1−	1.9294(S–F)	0.2518	1.2209	−0.0283	1.2261	−0.0229	1.2208	−0.0282	1.3672	0.1182
BH4(SF2)f^1−	1.8328(S–F)	0.1830	1.2241	−0.0249	1.2267	−0.0223	1.2241	−0.0249	1.3326	0.0836
BH4(PH3)f^1−	1.4365(P–H)	0.0099	1.2450	−0.0040	1.2474	−0.0016	1.2490	−0.0001	1.2494	0.0004
BH4(PH2F)f^1−	1.7946(P–F)	0.1219	1.2342	−0.0148	1.2314	−0.0176	1.2331	−0.0160	1.2903	0.0413
BH4(PHF2)f^1−	1.7458(P–F)	0.0964	1.2385	−0.0106	1.2340	−0.0152	1.2333	−0.0157	1.2748	0.0258
BH4(PF3)f^1−	1.70768(P–F)	0.0782	1.2361	−0.0130	1.2379	−0.0111	1.2379	−0.0111	1.2635	0.0145
BH4(BrCN)f^1−	1.8251(Br–CN)	0.0277	1.2388	−0.0102	1.2407	−0.0083	1.2408	−0.0082	1.25833	0.0093
BH4(CH4)f^1−	1.0996(C–H)	0.0015	1.2463	0.0027	1.2485	−0.0005	1.2485	−0.0005	1.2485	−0.0005
BH4(CH4)v^1−	1.0997(C–H)	0.0016	1.2469	−0.0021	1.2481	−0.0009	1.2481	−0.0009	1.2481	−0.0009
BH4(CCl3H)v^1−	1.1044(C–H)	0.0064	1.2370	−0.0121	1.2473	−0.0017	1.2473	−0.0017	1.2473	−0.0017

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In the BH₄(ClCF₃)_f¹⁻ complex, a greater proportion of intermolecular interactions could be classified as TrB. A partial charge of +0.0013 resulted from charge transfers from CF₃Cl to BH₄¹⁻. In addition, some XB interactions appeared between BH₄¹⁻ and ClCF₃ species. The most intense charge transfers between BH₄¹⁻ and ClCF₃ returned to lp(Cl) → σ*_(B–H4). Due to this charge transfer, we saw the most variations in the bond length and frequencies for bonds directly involved in these interactions. The data given in Tables 2–4 show that B–H stretching frequencies for BH₄(CF₃Cl)_f¹⁻ had a blue shift (17–33 cm⁻¹) along with 0.0011 to 0.0060 Å reductions in their bond distances. The greatest variations (33 cm⁻¹, 0.0060 Å) were seen for B–H trans to the CF₃Cl molecule. In addition, for CF₃–Cl, a contraction of ∼0.5086 Å and a blue shift of 5 cm⁻¹ were obtained.

For BH₄(CO)_f¹⁻, the interaction of CO as a sigma donor π-acceptor molecule with BH₄¹⁻ elicited some information about the nature of intermolecular contacts. BH₄¹⁻, through its B–H bonds as electron donors, interacted with the CO molecule. In contrast, the CO molecule interacted with the σ holes of BH₄¹⁻ through its π-bonds and lone pairs, particularly the σ hole related to the B–H3 bond of BH₄¹⁻. The sum of these intermolecular interactions directed the CO molecule to align with a triangular face of BH₄¹⁻. The presence of a partial charge of +0.0007 for the CO molecule suggested the preference of TrB in the optimized structure of BH₄(CO)_f¹⁻.

In BH₄(N₂)_f¹⁻, the N₂ molecule, to some extent, had the characteristics of CO, but it was a weaker σ-donor and had weaker π-acceptor properties than CO. Therefore, its interactions mainly occurred as an electron donor molecule with σ*_(B–H3) or σ-hole prolongation to the B–H3 bond. Electron donation by the N₂ molecule could be provided from lone pairs or N–N bonding electrons. The data given for the NBO (Table 5) show the presence of a 0.0030 partial charge for the N₂ molecule, which indicates N₂ → BH₄ charge transfer. Also, for BH₄(CO)_f¹⁻ and BH₄(N₂)_f¹⁻, we can see B–H bond contraction of 0.0004–0.0024 and 0.007–0.0019 Å along with blue shift for B–H vibrational frequencies of 5–9 and 6–10 cm⁻¹. On the other hand, a red shift of 5 cm⁻¹ and bond elongation of 0.0008 and 0.0002 Å were seen for CO and N₂ molecules, respectively.

Table 5 NBO charge transfer (Q) of the BH₄(L)¹⁻ complexes at the MP2/aug-cc-pVDZ level of theory

Complex	Donor	Acceptor	E^2	Q(L)	Complex	Donor	Acceptor	E^2	Q(L)
BH4(ClCF3)f^1−	BD(B–H2)	BD*(C–Cl)	0.23	0.0013	BH4(ClCN)f^1−	BD(B–H2)	BD*(C–Cl)	0.59	−0.0021
	BD(B–H3)	BD*(C–Cl)	0.27			BD(B–H3)	BD*(C–Cl)	0.27
	BD(B–H4)	BD*(C–Cl)	0.20			BD(B–H4)	BD*(C–Cl)	0.59
	BD(B–H5)	BD*(C–Cl)	0.53			BD(B–H5)	BD*(C–Cl)	0.59
	LP(Cl)	BD*(B–H2)	0.56			LP(Cl)	BD*(B–H2)	0.69
	LP(Cl)	BD*(B–H3)	0.57			LP(Cl)	BD*(B–H3)	3.5
	LP(Cl)	BD*(B–H4)	2.97			LP(Cl)	BD*(B–H4)	0.69
	LP(Cl)	BD*(B–H5)	0.57			LP(Cl)	BD*(B–H5)	0.69
BH4(FCN)f^1−	LP(F)	BD*(B–H2)	0.34	0.0015	BH4(HCF3)f^1−	BD(B–H2)	BD*(C–H10)	4.00	−0.0151
	LP(F)	BD*(B–H3)	1.58			BD(B–H4)	BD*(C–H10)	3.92
	LP(F)	BD*(B–H4)	0.34			BD(B–H5)	BD*(C–H10)	3.96
	LP(F)	BD*(B–H5)	0.34
BH4(BrCN)f^1−	BD(B–H2)	BD*(C–Cl)	9.67	−0.0388		LP(Br)	BD*(B–H2)	1.10	−0.0388
	BD(B–H3)	BD*(C–Cl)	0.44			LP(Br)	BD*(B–H3)	2.91
	BD(B–H4)	BD*(C–Cl)	0.13			LP(Br)	BD*(B–H4)	0.5
	BD(B–H5)	BD*(C–Cl)	0.13			LP(Br)	BD*(B–H5)	0.5
BH4(HCl)e^1−	BD(B–H4)	BD*(H–Cl)	94.45	−0.1702	BH4(HF)e^1−	BD(B–H4)	BD*(H–F)	22.39	−0.0452
	BD(B–H5)	BD*(H–Cl)	1.35			BD(B–H3)	BD*(H–F)	0.41
	BD(B–H2)	BD*(H–Cl)	0.35			BD(B–H2)	BD*(H–F)	2.91
	BD(B–H5)	BD*(H–Cl)	0.35
BH4(HCN)f^1−	BD(B–H2)	0.25	BD*(N–C)	−0.0214	BH4(HOCl)v^1−	BD(B–H3)	BD*(H–Cl)	7.65	−0.5059
	BD(B–H2)	4.06	BD*(C–H)			BD(B–H4)	BD*(H–Cl)	7.21
	BD(B–H3)	0.69	BD*(C–H)			BD(B–H5)	BD*(H–Cl)	7.44
	BD(B–H4)	0.17	BD*(N–C)			BD(H–Cl)	σ*(B)
BH4(HOBr)v^1−	BD(B–H3)	σ*(Br)	213.11	−0.3757	BH4(N2)f^1−	BD(B–H2)	BD*(N–N)	0.11	0.0030
	LP(BR)	BD*(B–H3)	13.40			BD(N–N)	BD*(B–H3)	0.43
						LP(N6)	BD*(B–H3)	0.39
						LP(N7)	BD*(B–H3)	0.34
BH4(CH3OH)v^1−	BD(B–H5)	BD*(O–H)	11.23	−0.0188	BH4(H2O)v^1−	BD(B–H5)	BD*(O–H)	8.13	−0.0138
	BD(B–H4)	BD*(O–H)	0.49
	BD(B–H3)	BD*(O–H)	0.27
	BD(B–H2)	BD*(O–H)	0.27
BH4(SFH)v^1−	BD(B–H2)	BD*(S–H)	2.26	−0.4264	BH4(SF2)v^1−	BD(B–H2)	BD*(F–S)	1.51	−0.3847
	BD(B–H3)	BD*(S–H)	9.62			BD(B–H3)	LP(S)	0.78
	BD(B–H4)	BD*(S–H)	4.30			BD(B–H4)	LP(S)	0.99
	BD(B–H5)	BD*(S–F)	286.14			BD(B–H5)	BD*(S)	220.27
	BD(S–H)	BD*(B–H2)	1.61			BD(B–H5)	BD*(F–S)	9.46
	BD(S–H)	BD*(B–H3)	2.66			LP(S)	BD*(B–H2)	0.53
	BD(S–H)	BD*(B–H4)	1.67			LP(S)	BD*(B–H3)	0.62
	LP(S)	BD*(B–H2)	1.03			LP(S)	BD*(B–H4)	0.63
	LP(S)	BD*(B–H3)	0.22			LP(S)	BD*(B–H5)	3.10
	LP(S)	BD*(B–H4)	1.23			LP(S)	BD*(B–H3)	1.20
	LP(S)	BD*(B–H5)	0.45			LP(S)	BD*(B–H4)	1.20
	LP(S)	BD*(B–H3)	0.76
BH4(SH2)v^1−	BD(B–H2)	BD*(S–H)	0.06	−0.0295	BH4(CO)f^1−	BD(B–H4)	BD*(C–O)	0.23	0.0007
	BD(B–H3)	BD*(S–H)	0.79			BD(B–H5)	BD*(C–O)	0.24
	BD(B–H4)	BD*(S–H)	0.79			BD(C–O)	BD*(B–H3)	0.45
	BD(B–H5)	BD*(S–H)	13.14			LP(C)	BD*(B–H3)	0.72
	BD(S–H8)	BD*(B–H2)	0.07			LP(C)	BD*(B–H4)	0.18
	BD(S–H8)	BD*(B–H3)	0.65			LP(C)	BD*(B–H5)	0.18
	BD(S–H8)	BD*(B–H4)	0.22			LP(O)	BD*(B–H3)	0.17
	LP(S)	BD*(B–H5)	0.08
	LP(S)	BD*(B–H3)	0.07
	LP(S)	BD*(B–H5)	0.06
	LP(S)	BD*(B–H2)	0.15
BH4(PH3)v^1−	BD(B–H2)	BD*(P–H8)	0.12	−0.0039	BH4(PH2F)v^1−	BD(B–H2)	BD*(P–F7)	0.46	−0.1773
	BD(B–H4)	BD*(P–H8)	0.61			BD(B–H5)	BD*(P–F7)	47.07
	BD(B–H5)	BD*(P–H7)	0.12			BD(B–H5)	BD*(P–H8)	4.83
	BD(B–H5)	BD*(P–H9)	0.84			BD(B–H5)	BD*(P–H9)	4.96
	BD(P–H7)	BD*(B–H2)	0.57			BD(P–H8)	BD*(B–H2)	1.06
	BD(P–H8)	BD*(B–H4)	0.12			BD(P–H9)	BD*(B–H5)	0.64
	BD(P–H8)	BD*(B–H4)	0.12			lp(P)	BD*(B–H5)	9.09
BH4(PHF2)v^1−	BD(B–H5)	BD*(P–H7)	7.94	−0.1469	BH4(PF3)v^1−	BD(B–H5)	BD*(P–F7)	5.24	−0.0974
	BD(B–H5)	BD*(P–H8)	29.10			BD(B–H5)	BD*(P–F8)	18.37
	BD(B–H5)	BD*(P–H9)	3.49			BD(B–H5)	BD*(P–H9)	5.25
	BD(P–H9)	BD*(B–H2)	1.59			lp(P)	BD*(B–H4)	6.38
	lp(P)	BD*(B–H4)	1.27
	lp(P)	BD*(B–H5)	1.24
BH4(H2)f^1−	BD(B–H2)	BD*(H–H)	0.37	−0.0013	BH4(H2)v^1−	BD(B–H4)	BD*(H–H)	1.83	−0.0034
	BD(B–H4)	BD*(H–H)	0.37			BD(H–H)	BD*(B–H4)	0.12
	BD(B–H5)	BD*(H–H)	0.37
BH4(CH4)f^1−	BD(B–H2)	BD*(C–H7)	0.36	−0.0027	BH4(CCl3H)v^1−	BD(H1–B)	BD*(C–H)	6.49	−0.0244
	BD(B–H3)	BD*(C–H7)	0.30			BD(H1–B)	BD*(C–Cl8)	0.26
	BD(B–H4)	BD*(C–H7)	0.36			BD(H2–B)	BD*(C–H)	6.47
	BD(B–H5)	BD*(C–H7)	0.36 0.06			BD(H2–B)	BD*(C–Cl9)	0.26
	BD(C–H7)	BD*(B–H2)	0.38			BD(H3–B)	BD*(C–H)	6.56
	BD(C–H7)	BD*(B–H3)	0.06			BD(H3–B)	BD*(C–Cl7)	0.27
	BD(C–H7)	BD*(B–H4)	0.06			BD(H4–B)	BD*(C–H)	0.63
	BD(C–H7)	BD*(B–H5)
BH4(CH4)v^1−	BD(H1–B)	BD*(C–H9)	1.59	−0.0025
	BD(H2–B)	BD*(C–H9)	0.11
	BD(H3–B)	BD*(C–H9)	0.11
	BD(H4–B)	BD*(C–H9)	0.11

---

For the BH₄(BrCN)_f¹⁻ adduct, in addition to XB, we could have BrCN → BH₄ charge transfer (TrB) as part of the interaction between fragments. Hence, in this case, a net partial charge of −0.0388 for BrCN could be considered to be a result of an XB interaction. Comparison of interaction energies obtained by NBO (Table 5) analyses indicated that the contribution of the halogen bond was more significant than that of the triel bond between BrCN and BH₄¹⁻. In BH₄(BrCN)_f¹⁻, we had a 49 cm⁻¹ red shift and 0.0093 Å elongation for B–H trans to the BrCN molecule, and a blue shift of 56–73 cm⁻¹ besides a 0.0082-to-0.0102 Å reduction for other B–H bond distances. In contrast, for the Br–C distance of the BrCN molecule, a bond elongation of 0.0277 and red shift of 51 cm⁻¹ were seen.

For the BH₄(ClCN)_f¹⁻ aggregate, in addition to the L → BH₄ charge transfer (TrB), XB as another important interaction between BH₄¹⁻ and ClCN could be possible. Hence, in this case, the net partial charge −0.0021 of ClCN could be considered to be a result of an XB interaction. Comparison of the interaction energies obtained by NBO analysis indicated that the contribution of the triel bond was a significant part of interactions between ClCN and BH₄⁻¹ and it provided a stronger stabilization effect compared with the halogen bond. In BH₄(ClCN)_f¹⁻, we had a 16–57 cm⁻¹ blue shift besides a 0.0015-to-0.0092 Å reduction in B–H bond distances. The greatest changes (57 cm⁻¹, 0.0092 Å) were observed in the B–H trans to the ClCN molecule. In contrast, in the ClCN molecule, a bond contraction of 0.0006 and a red shift of 10 cm⁻¹ were observed for the Cl–CN bond.

As a result, the nature of the intermolecular interactions had a crucial role in determining the stability and properties of the BH₄(L)_v¹⁻ adducts. Therefore, as a common principle, the triel bond played a significant part in shaping adducts between BH₄⁻¹ and N₂, CO, FCN, ClCN, and ClCF₃ molecules.

In these adducts, for TrB intermolecular interactions, L must be in the appropriate orientation to a σ hole of BH₄¹⁻. Hence, it can be seen from the optimized structures of BH_f(FCN)_v¹⁻, BH₄(ClCN)_f¹⁻, BH₄(BrCN)_f¹⁻, BH₄(ClCF₃)_f¹⁻, BH₄(N₂)_f¹⁻ and BH₄(CO)_f¹⁻ aggregates that the L molecule is often coaxing with a σ hole of BH₄¹⁻. In other words, the preferred location for L is situated on a triangular face of the BH₄¹⁻ anion.

XB complexes BH₄(L)_v¹⁻

The tetrahidroborate anion formed halogen-bonded BH₄(ClOH)_v¹⁻ and BH₄(BrOH)_v¹⁻ aggregates with HOCl and HOBr molecules (Fig. 2). The stability of these adducts was −18.69 and −23.76 kcal mol⁻¹, respectively, which were more stable than the previously discussed complexes. Partial charges of −0.5059 for HOCl and −0.3757 for HOBr suggested more charge transfers from BH₄¹⁻ to L for these adducts. For BH₄(ClOH)_v¹⁻ and BH₄(BrOH)_v¹⁻, for a strong halogen bond, one hydride atom moved away from BH₄¹⁻ and approached the halogen atom of hypohalid acid. Therefore, because of the strong halogen bond interaction, HOBr and HOCl preferred to interact with a vertex B–H rather than the triangular faces of BH₄¹⁻. Thus, more stable halogen bond formation might be the primary driving force for the directionality and structural preference for these adducts.

For the XB complexes BH₄(HOCl)_v¹⁻ and BH₄(HOBr)_v¹⁻, elongations of 0.3055 and 0.2165 Å along with red shifts of 318 and 260 cm⁻¹ were observed for O–X bonds. For the BH₄¹⁻ moiety, elongations of 0.1466 and 0.1093 Å and red shifts of 359 and 313 cm⁻¹ for B–H involved in the interaction were observed, along with a bond contraction of 0.0264 and 0.0236–0.0255 Å and blue shifts of 151, 223, 230 and 143, 211 cm⁻¹ were observed for other B–H bonds when X = Cl and Br, respectively.

DHB aggregates

BH₄(HCl)_e¹⁻, BH₄(HF)_e¹⁻, BH₄(HCN)_f¹⁻, BH₄(HCF₃)_f¹⁻, BH₄(HCCl₃)_f¹⁻, BH₄(HOCH₃)_v¹⁻, BH₄(H₂O)_v¹⁻, BH₄(H₂)_f¹⁻, BH₄(H₂)_v¹⁻, BH₄(CH₄)_f¹⁻, BH₄(CH₄)_v¹⁻ and BH₄(H₂S)_v¹⁻ were the next categories of aggregates optimized as dihydrogen-bonded adducts (Fig. 2). It seems that the driving force behind the formation of these complexes was the dihydrogen bond interaction between BH₄¹⁻ (dihydrogen bond acceptor) and the counterpart molecule (dihydrogen bond donor). The data in Tables 1 and S2 show that the stabilities of these adducts were in the order:

BH₄(HCN)_f¹⁻ > BH₄(HCl)_e¹⁻ > BH₄(HF)_e¹⁻ > BH₄(HCCl₃)_v¹⁻ > BH₄(HCF₃)_v¹⁻ > BH₄(HOCH₃)_v¹⁻ > BH₄(H₂O)_v¹⁻ > BH₄(H₂S)_v¹⁻ > BH₄(CH₄)_f¹⁻ > BH₄(CH₄)_v¹⁻ > BH₄(H₂)_f¹⁻ > BH₄(H₂)_v¹⁻

Interaction of CH₃OH, H₂O, or H₂S molecules with BH₄¹⁻ gave simple dihydrogen bond complexes in which the former molecules acted as dihydrogen bond donors and BH₄¹⁻ acted as a dihydrogen bond acceptor. The results of these interactions were BH₄(HOCH₃)_v¹⁻, BH₄(H₂O)_v¹⁻ and BH₄(H₂S)_v¹⁻ dihydrogen bonded adducts, respectively. These structures showed distortion from the vertex towards edge interactions, and L was very close to a B–H apex with respect to the other one. Therefore, we classified them as BH₄(L)_v¹⁻ aggregates. In the case of BH₄(CH₃OH)_v¹⁻, the O–H bonds exhibited an elongation of 0.0186 Å and a red shift of 349 cm⁻¹. On the other hand, 0.0032 Å lengthening and 11 red shifts for B–H involved in DHB (B–H⋯H–O), but 0.0051-to-0.0088 contractions and blue shifts of 37, 42, 57 cm⁻¹ for other B–H bonds were observed.

For the DHB adduct BH₄(H₂O)_v¹⁻, 0.0173 Å elongations along with a red shift of 261 cm⁻¹ for the H–O bond involved in DHB were observed. For the BH₄¹⁻ moiety, an elongation of 0.0043 Å and red shift of 21 cm⁻¹ for B–H in DHB, and bond contractions of 0.0021, 0.0067, and 0.0075 Å and blue shifts of 92, 119, and 137 cm⁻¹ for the remainder of the B–H bonds were observed.

In the DHB complex BH₄(H₂S)_v¹⁻, an elongation of 0.0282 Å along with a red shift of 321 cm⁻¹ for the H–S bond involved in DHB was observed. For the BH₄¹⁻ moiety, an elongation of 0.0046 Å and red shift of 35 cm⁻¹ for the B–H encountered in DHB, and bond contractions of 0.0038 and 0.0062 Å and blue shifts of 29, 46, and 50 cm⁻¹ for the remainder of the B–H bonds were observed.

HCl and HF, as dihydrogen bond donors, formed the DHB complexes BH₄(HCl)_e¹⁻ and BH₄(HF)_e¹⁻, respectively, with BH₄¹⁻ as a dihydrogen bond acceptor. As seen from Fig. 2, in these adducts, HCl and HF chose an unsymmetrical bifurcated dihydrogen bond interaction with BH₄¹⁻. Hence, the preferred direction for these molecules was an unsymmetrical bifurcated dihydrogen bond interaction in which, along an edge, they interacted with BH₄¹⁻.

In these adducts, elongations of 0.3442 and 0.0385 Å along with red shifts of 1611 and 811 cm⁻¹ were observed for the H–X bonds in BH₄(HCl)_e¹⁻ and BH₄(HF)_e¹⁻ complexes. For the BH₄¹⁻ moiety, elongation of 0.0214 and 0.0037 Å, a red shift of 46 cm⁻¹ and blue shift of 4 cm⁻¹ for B–H involved in the DHB interaction were observed. Also, for the remaining B–H bonds, bond contraction of 0.0140, 0.0182 and 0.0101, 0.0100, and 0.0092 Å and blue shifts of 92, 119, 137, and 62, 73, and 81 cm⁻¹ were observed when X = Cl and F, respectively.

In addition to DHB, another type of intermolecular interaction helped to increase the stabilization of some of these adducts. For example, in BH₄(HCN)_f¹⁻ with stabilization energy of −18.28, in addition to DHB interaction, HCN can have TtB with BH₄¹⁻, a type of noncovalent bond in which a group-14 element (C, Si, Ge, Sn, Pb) as a Lewis acid interacts with a Lewis base. The TtB leads to greater stability of BH₄(HCN)_f¹⁻ relative to BH₄(HCl)¹⁻ and BH₄(HF)¹⁻ aggregates. Therefore, these two interactions make it more stable than the other ones. In both interactions, BH₄¹⁻ has the role of electron donor and HCN is the electron acceptor. The B–H bonds of BH₄(HCN)_f¹⁻ showed a 5–83 cm⁻¹ blue shift of their vibrational frequency and a 0.0022–0.0125 Å decrease in their bond lengths with adduct formation. Most blue shifts (83 cm⁻¹) and bond contraction (0.0022) were seen for the B–H bond, which was trans to the intermolecular interaction. These intermolecular interactions reduced the σ(B–H) to σ*(B–H) charge transfers, resulting in stronger B–H bonds. In the case of the HCN molecule, a 0.0222 Å increase in the H–C bond distance and red shift of 295 cm⁻¹ were found with adduct formation.

In BH₄(HCF₃)_v¹⁻, HCF₃, as a hydrogen bond donor, stayed coaxial with BH₄¹⁻, and most of the charge transfers occurred for σ_(B–H) to the σ*_(H–CF3) orbitals in a trifurcated dihydrogen bond interaction. With a stabilization energy of −14.55, it had moderate stability between the studied adducts. For the BH₄(HCF₃)_v¹⁻ adduct, a blue shift of 67 cm⁻¹ with a 0.0104 Å decrease in the B–H bond trans to HCF₃, as well as a contraction of 16 and 18 Å with a blue shift of 16 and 18 cm⁻¹ for other B–H bonds, was found. Conversely, in the CF₃H molecule, for the C–H bond, a red shift of 24 cm⁻¹ and bond elongation of 0.0022 Å were obtained.

In BH₄(CHCl₃)_v¹⁻, the CHCl₃ (as a HBD) remained on the face of the BH₄¹⁻ (as a DHA), and by trifurcated DHB interacted with the tetrahydroborate anion. Charge transfers occurred from σ_(B–H) orbitals to σ*_(H–CCl3). A stabilization energy of −17.05 kcal mol⁻¹ indicated relatively strong DHB in this aggregate. For the BH₄(HCCl₃)_v¹⁻ adduct, a 79 cm⁻¹ blue shift along with a 0.0121 Å decrease for B–H bond prolongation to HCCl₃, as well as a 17 Å contraction with 18 and 19 cm⁻¹ blue shifts for other B–H bonds, were observed. On the other hand, for the C–H bond of the CCl₃H molecule, a red shift of 136 cm⁻¹ and bond elongation of 0.0110 Å were obtained.

In contrast to the SH₂ formed by DHB, the interaction between HSF and SF₂ with BH₄¹⁻ could be considered to be a combination of ChB and TrB that resulted in BH₄(HSF)_v¹⁻ and BH₄(SF₂)_v¹⁻ complexes. The stabilization energies of these aggregates were −26.57 and −24.28 kcal mol⁻¹, so they were more stable than other studied systems. More significant interactions in these adducts were seen for σ_(B–H5) as a ChB acceptor with σ*_(S–F) as a ChB donor. In addition, the contribution of ChB increased from BH₄(HSF)_v¹⁻ to BH₄(SF₂)_v¹⁻, and comparison of their structures showed a greater vertex characteristic in BH₄(HSF)_v¹⁻ with respect to BH₄(SF₂)_v¹⁻. A more detailed analysis of NBO data indicated some additional σ_(B–H) to σ*_(S–H) charge transfers in BH₄(HSF)_v¹⁻, which led to greater stability of this adduct with respect to the BH₄(SF₂)_v¹⁻ complex.

For the ChB adducts BH₄(SHF)_v¹⁻ and BH₄(SF₂)_v¹⁻, elongations of 0.2518 and 0.1830 Å along with red shifts of 424 and 332 cm⁻¹ were observed for S–F bonds trans to S⋯H interactions. For the BH₄¹⁻ moiety, elongations of 0.1182 and 0.0836 Å and red shifts of 332 and 334 cm⁻¹ for B–H involved in B–H⋯S interactions were noted; bond contractions of 0.0229, 0.0282, 0.0283 and 0.0223, and 0.0249 Å and blue shifts of 151, 217, 232 and 139, 202, and 208 cm⁻¹ for other B–H bonds, were observed for BH₄(SHF)_v¹⁻ and BH₄(SF₂)_v¹⁻, respectively.

To investigate the interplay between the PnB and TrB, interactions of BH₄¹⁻ with PH₃, PH₂F, PHF₂, and PF₃ molecules were considered. The stabilities of related adducts were in the order:

BH₄(PH₂F)_v¹⁻ > BH₄(PHF₂)_v¹⁻ > BH₄(PF₃)_v¹⁻ > BH₄(PH₃)_v¹⁻

A combination of weak DHB and PnB interactions led to a BH₄(PH₃)_v¹⁻ adduct with a stabilization energy of −4.41 kcal mol⁻¹. The nature of interactions moved to PnB in more fluorinated phosphines. In BH₄(PH₃)_v¹⁻, a PnB interaction appeared between σ_(B–H5) as an electron donor and σ*_(P–H9) as an electron acceptor; simultaneously, a DHB interaction occurred between σ_(B–H4) as an electron donor and σ*_(P–H8) as an electron acceptor. The presence of both interactions in this adduct required a specific orientation of components to cause effective contact between overlapping orbitals. Also, a partial charge of −0.0039 indicated charge transfers from BH₄¹⁻ to PH₃.

BH₄(PH₂F)_v¹⁻ contained a PnB interaction between σ_(B–H5) as an electron donor and σ*_(P–F7) and σ hole P–F7, as an electron acceptor, as well as TrB by LP(P) to σ*_(B–H5) charge transfers. BH₄(PH₂F)_v¹⁻, with SE of −18.36 kcal mol⁻¹, was the most stable complex in this series. The BHP bond angle of 143° enhanced weak interactions, contributing to adduct formation and greater stabilization of the corresponding aggregate.

BH₄(PHF₂)_v¹⁻ was mainly obtained through a PnB interaction between σ_(B–H5) as an electron donor and the σ hole of P–F8, σ*_(P–F8) as an electron acceptor, besides a weak TrB resulting from LP(P) to σ*_(B–H) interactions. BH₄(PHF₂)_v¹⁻, with SE of −17.57 kcal mol⁻¹ and BHP bond angle of 125°, was in the next level of stability from phosphine adducts. This angle was reached due to weak TrB interactions that included adduct formation, and made the complex more stable.

Similarly, BH₄(PF₃)_v¹⁻ was primarily obtained by a PnB interaction between σ_(B–H5) as an electron donor and σ*_(P–F8) as an electron acceptor. Also, a weak TrB was found for LP(P) to σ*_(B–H4) and other σ*_(B–H) orbitals charge transfers. BH₄(PF₃)_v¹⁻, with SE of −14.81 kcal mol⁻¹ and BHP angle 117°, was in the third order of stability between phosphine complexes. This angle was observed due to some weaker interactions that helped the greater stabilization of complexes. The HPF and HPH bond angles were 167, 167, 170, and 149° for BH₄(PF₃)_v¹⁻, BH₄(PHF₂)_v¹⁻, BH₄(PH₂F)_v¹⁻, BH₄(PH₃)_v¹⁻, respectively. These data indicated that, especially in the case of fluorinated phosphines, this angle was less affected by a change in the number of F atoms on the phosphine molecule. On the other hand, results for fluorinated phosphines indicated that increasing the number of F atoms in phosphine molecules led to banishment of TrB and, therefore, a reduction in the stability of the related adducts.

For the PnB adducts BH₄(PH₃)_v¹⁻, BH₄(PH₂F)_v¹⁻, BH₄(PHF₂)_v¹⁻ and BH₄(PF₃)_v¹⁻, elongations of 0.0099, 0.1219, 0.0964 and 0.0782 Å along with red shifts of 61, 240, 205, and 177 cm⁻¹ were observed for P–H and P–F bonds trans to P⋯H interactions. For the BH₄¹⁻ moiety, elongations of 0.0004, 0.0413, 0.0258 and 0.0145 Å and red shifts of 3, 230, 144, and 66 cm⁻¹ for B–H trans to the B–H⋯P interaction were observed. Also, bond contractions of 0.0001, 0.0016, 0.0040 and 0.0106, 0.0152, 0.0157 and 0.0111, 0.0130 Å, as well as blue shifts of 3, 13, 21 and 95, 130, 133 and 74, 112, 123, and 71, 97, 99 cm⁻¹, were observed for other B–H bonds of adducts, respectively.

From the interaction of BH₄¹⁻ with the H₂ molecule, BH₄(H₂)_f¹⁻ and BH₄(H₂)_v¹⁻, as local minima adducts, and BH₄(H₂)_e¹⁻, as an nonlocal structure, were optimized. The stabilities of these adducts were −0.57, −0.01 and −0.39 kcal mol⁻¹, respectively. Hence, face-centered interactions aided adduct formation relative to head-to-head counterparts. The partial charge of components indicated that, in both adducts, the electron acceptor ability of H₂ was preferred. In BH₄(H₂)_f¹⁻, trifurcated DHB and TrB could be seen between interacting components. However, for BH₄(H₂)_v¹⁻, an orbital overlap between σ_(B–H4) as an electron donor and σ*(H–H) as an electron acceptor led to a conventional dihydrogen-bonded adduct. In comparison, H₂ molecules preferred to interact through a triangular face rather than a vertex or edge interaction.

Interaction of BH₄¹⁻ with the CH₄ molecule led to BH₄(CH₄)_f¹⁻ and BH₄(CH₄)_v¹⁻ as local minima and BH₄(CH₄)_e¹⁻ as a nonlocal structure, which stabilities of −2.35, −1.52 and −2.07 kcal mol⁻¹, respectively. Results show that facial adduct is more stable than the adduct that formed by vertex-to-vertex interaction. The partial charge of components indicates that in both adducts, the electron acceptor ability of CH₄ is preferred. In the BH₄(H₂)_f¹⁻, a trifurcated DHB a TrB bond can be seen between interacting components. But for BH₄(H₂)_v¹⁻ an orbital overlap between σ_(B–H4) as an electron donor and σ*(H–H) as an electron acceptor leads to a conventional dihydrogen bond adduct. In comparison, CH₄ molecules prefer to interact through a triangular face rather than a vertex or edge interaction.

The vibrational stretching frequencies of B–H bonds (Table 2) in free BH₄¹⁻ appeared at 2291 cm⁻¹. The results given in Table 3 show that interactions between BH₄¹⁻ and counterpart H₂ molecules resulted in a blue shift of B–H stretching vibrations. Hence, the B–H stretching vibrations in BH₄(H₂)¹⁻ aggregates led to a 6–22 cm⁻¹ blue shift due to adduct formation. Moreover, the blue shift in BH₄(H₂)_v¹⁻ (22 cm⁻¹) belonged to a B–H bond that interacted directly with the H₂ molecule. Also, for BH₄(H₂)_f¹⁻, a 15 cm⁻¹ blue shift belonged to a B–H bond in the trans direction relative to the interaction center. These blue shifts led to a 0.0005-to-0.0020 Å decrease in B–H bond lengths (Table 4). Most contractions returned to those B–H bonds that showed the greatest blue shift in their stretching frequencies. For example, a 0.0020 Å decrease was observed for the B–H bond involved in the interaction for BH₄(H₂)_v¹⁻ and, similarly, 0.0018 Å was ascribed to the B–H in the trans position relative to the center of the interaction. In contrast, for H₂ molecules, we observed red shifts of −100 and −112 cm⁻¹ in BH₄(H₂)_v¹⁻ and BH₄(H₂)_f¹⁻ aggregates, respectively. These red shifts were in agreement with the 0.0053 and 0.0060 Å increases in the H₂ bond distances for BH₄(H₂)_v¹⁻ and BH₄(H₂)_f¹⁻ aggregates. These changes occurred due to the BH₄¹⁻ to H₂ charge transfers that led to the strengthening of B–H bonds and weakening of H₂ bonds.

Atoms in molecules (AIM) analysis

The AIM theory^35,36 was used to study the nature of BH₄(L)¹⁻ interactions. Table 6 and Fig. 3 show the results and molecular graphs of AIM calculations, in which p is electron density at intermolecular bond critical points (BCP), ∇² is the Laplacian, and the −G/V is the ratio between the kinetic and potential electron energy density at BCP in BH₄(L)¹⁻ complexes. If the gravitational G overshadows the potential V, then the positive profile of ∇² indicates a reduction in charge density along the intermolecular bond path. In this case, the bond is known as a “closed-shell interaction”, such as hydrogen bonds or other intermolecular weak bonds.

Table 6 Topological parameters for fully optimized BH₄(L)¹⁻ adducts

	p	Δp	G	V	−G/V	H
BH4(H2)f^1−	0.0055	−0.0045	−0.0037	0.0009	4.2064	−0.0028
BH4(H2)v^1−	0.0068	−0.0044	0.0039	−0.0005	7.7423	0.0034
BH4(CF3Cl)f^1−	0.0093	−0.0086	0.0069	−0.0018	3.8655	0.0051
BH4(CF3H)f^1−	0.0168	−0.0124	0.0119	−0.0004	27.4113	0.0115
BH4(CH3OH)v^1−	0.0246	−0.0149	0.0147	−0.0002	97.6208	0.0146
BH4(CO)e^1−	0.0056	−0.0049	0.0036	−0.0013	2.6724	0.0022
BH4(HCl)e^1−	0.0748	−0.0008	0.0303	0.0297	1.0259	0.0660
BH4(HCN)f^1−	0.0179	−0.0129	0.0123	−0.0006	21.1163	0.0117
BH4(HF)e^1−	0.0357	−0.0189	0.0219	0.0031	7.1625	0.0250
BH4(HOBr)v^1−	0.0963	−0.0054	0.0465	0.0411	1.1309	0.0876
BH4(HOCl)v^1−	0.1213	0.0087	0.0554	0.0641	0.8643	−0.0087
BH4(N2)f^1−	0.0044	−0.0039	0.0031	−0.0008	3.9787	0.0023
BH4(ClCN)f^1−	0.0110	−0.0102	0.0085	−0.0018	4.7774	0.0067
BH4(H2O)v^1−	0.0224	−0.0137	0.0133	−0.0004	33.9675	0.0129
BH4(FCN)f^1−	0.0062	−0.0077	0.0062	−0.0015	4.2360	0.0047
BH4(SH2)v^1−	0.0248	−0.0125	0.0135	0.0010	13.1511	0.0145
BH4(SHF)v^1−	0.1166	0.0190	0.0501	0.0691	0.7255	0.1191
BH4(SF2)v^1−	0.1072	0.01286	0.0438	0.0567	0.7732	0.1007
BH4(PH3)v^1−	0.0077	−0.0064	0.0051	−0.0013	3.9258	0.0038
BH4(PH2F)v^1−	0.0633	−0.0005	0.0273	0.0268	1.0187	0.0541
BH4(PHF2)v^1−	0.0538	−0.0045	0.0229	0.0184	1.2449	0.0414
BH4(PF3)v^1−	0.0454	−0.0075	0.0192	0.011702	1.6454	0.0310
BH4(BrCN)f^1−	0.0253	−0.0160	0.0161	0.0001	149.0463	0.0162
BH4(CH4)f^1−	0.0072	−0.0060	0.0050	−0.00095	5.26316	0.0040
BH4(CH4)v^1−	0.0082	−0.0053	0.0048	−0.0004	11.1081	0.0044
BH4(CCl3H)v^1−	0.0227	−0.0152	0.0157	0.0004	35.7	0.0161

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Fig. 3 Molecular graphs of BH₄(L)¹⁻ complexes at the MP2/aug-cc-pVDZ level.

The positive values of ∇² in Table 4 indicate that all interactions in BH₄(L)¹⁻ complexes were closed-shell. In addition, −G/V > 1 indicated the non-covalent character of these interactions.

NBO analysis

NBO³⁷ calculations were done on BH₄(L)¹⁻ complexes, and showed that these complexes were the products of orbital overlaps between BH₄¹⁻ and L molecules. In the case of boron tetrahydride, several positions might act as electron donors simultaneously, it could also act as an electron acceptor through the σ-holes on its B–H bonds. Table 5 lists the quantity of charges transferred from the donor to the acceptor (Q_ct) for BH₄(L)¹⁻ adducts. According to data given in Table 5, the Q_ct for L molecules was negative, which indicated that the electron donation of BH₄¹⁻ was preferred to its electron acceptor properties in BH₄(L)¹⁻ adducts.

Non-covalent interactions (NCI) analysis

NCIs within and between molecules are important in all branches of chemistry. The NCI method provides valuable results to deepen insights about the NCIs present in molecular adducts.^38,39 The NCI method visualizes noncovalent interactions, including hydrogen bonding (attractive interactions), steric repulsions, and van der Waals forces within structures involving NCIs. Therefore, to distinguish the repulsive van der Waals interactions and electrostatic forces present in the BH₄(L)¹⁻ adducts, NCI calculations were conducted.

The findings from the NCI analysis are presented in 2D RDG plots and 3D topological representations. We determined the types of interactions happening in the system using the NCI reduced density gradient approach.^38,39 Fig. 4 and S1 are NCI scatter plots, which represent the relationship between the sign of the second Hessian eigenvalue (signλ₂ρ) and RDG. This plot indicated that weak attractive interactions were present between BH₄¹⁻ and L within BH₄(L)¹⁻ adducts.

Fig. 4 Correlation between Q(L) (transferred charges, NBO) and ρ (electron density, AIM) for BH₄(L)¹⁻ adducts.

The parameter sign(λ₂) ρ > 0 illustrates repulsive forces, whereas the parameter sign(λ₂) ρ < 0 illustrates attractive interactions, between interacting components. If parameter sign(λ₂) ρ = 0, then van der Waals interactions are in adducts.^38,39

Notably, different types of NCIs, including weak van der Waals forces, attractive interactions, and steric repulsion forces, were observed in BH₄(L)¹⁻ complexes (Fig. 5 and S1). The 3D color-filled RDG isosurfaces shown in Fig. 6 and S2 also illustrate the steric repulsions, noncovalent bonds, and weak van der Waals forces between BH₄¹⁻ and L molecules. In NCI 3D images, the λ₂ sign has been used to distinguish between attractive and repulsive interactions based on a particular color. In the context of NCI plots, blue surfaces represent strong attractive interactions, weak attractive interactions (weak van der Waals forces) are typically shown in green, while repulsive interactions are depicted in red, as shown in Fig. 6 and S2. The density and area of green areas between BH₄¹⁻ and L molecules were not identical, which indicated that the interactions of BH₄¹⁻ with various molecules occurred at different energies.

Fig. 5 NCI analysis of BH₄(L)¹⁻ adducts.

Fig. 6 3D iso-surface of BH₄(L)¹⁻ adducts.

Conclusions

The interaction between BH₄¹⁻ with 25 small molecules (L) was investigated. Our results provided several interesting insights into the characteristics of BH₄¹⁻ in BH₄(L)⁻¹ adducts. In addition to its vertices, edges, and faces, BH₄¹⁻ can act as an electron donor toward electron acceptor species. Its σ-holes may serve as electron acceptors for electron donor species to form BH₄(L)¹⁻ aggregates. For face-centered interactions (which arise from the contribution of the σ-holes in B–H bonds), most variations were observed for the bond length and stretching vibrational frequency of the B–H bond involved in intermolecular interactions with counterpart molecules. These variations occurred as a contraction along with a blue shift for this bond. For vertex and edge interactions, most variations were elongation and a red shift for B–H bonds during intermolecular interactions.

Conflicts of interest

There is no conflict of interest.

Data availability

The data supporting the conclusions reached from our study are included in the article.

Supplementary information: Table S1, the XYZ coordinates for the gas phase of optimized structures; Table S2, the SE^un, ΔZPE, SE^ZPE, BSSE, SE^ZPE+BSSE, ΔH, and ΔG of adducts; Fig. S1, the NCI analysis and Fig. S2, 3D iso-surface of BH₄(L)¹⁻ adducts. See DOI: https://doi.org/10.1039/d5ra05000f.

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