Structures and stabilities of higher coordinate onium-boronium dications (X⁺BH₃⁺ and X⁺BH₅⁺; X = NH₃, PH₃, H₂O, and H₂S)

Abstract

Structures of higher coordinate onium-boronium dications (X⁺BH₃⁺ 1–4a and X⁺BH₅⁺ 1–4d; X = NH₃, PH₃, H₂O, and H₂S) were calculated by using the ab initio method at the MP2/6-311+G** level. All of the dications 1–4a contain a four-coordinate boron atom with a three-center two-electron bond involving boron and two hydrogens. On the other hand, all the dications 1–4d contain a six-coordinate boron atom with two three-center two-electron bonds. The thermodynamics of the complexations of 1–4a and H₂ to form 1–4d were computed. Deprotonations of 1–4d were found to be substantially endothermic.

Higher coordinate compounds involving a main group element are of both theoretical (1–4) and experimental (5) interest. Schmidbaur and coworkers have prepared a variety of higher coordinate boron (6), carbon (7, 8), nitrogen (9), oxygen (10), phosphorus (11), and sulfur (12) complexes with gold and determined their x-ray crystal structures. They have prepared trigonal bipyramidal (7) {[(C₆H₅)₃PAu]₅C}⁺ and octahedral (8) {[(C₆H₅)₃PAu]₆C}²⁺ complexes involving five- and six-coordinate carbon, respectively, representing the isolobal (5) analogs of CH₅⁺ and CH₆²⁺. Lithiated five- and six-coordinate carbocations, CLi₅⁺ and CLi₆²⁺, respectively, were also calculated to be stable minima (13–15).

We previously reported (16) computed structures of the four-coordinate boronium ion BH₄⁺ and the six-coordinate boronium ion BH₆⁺. The structure of BH₄⁺ is planar with a three-center two-electron (3c-2e) bond (16). The structure of BH₆⁺ contains two 3c-2e bonds (16). The structures of BH₄⁺ and BH₆⁺ were found to be isostructural with their isoelectronic carbon analogs CH₄²⁺ (17) and CH₆²⁺ (18, 19), respectively. DePuy et al. were able to prepare and observe the BH₄⁺ and BH₆⁺ ions experimentally in the gas phase by reacting BH₂⁺ and H₂ and BH₄⁺ and H₂, respectively (see Scheme S1; refs. 20 and 21).

Scheme 1.

Structures of BH₄⁺ and BH₆⁺.

Recently we reported (22) ab initio-calculated structures of protonated BXH₂ and BX₂H (BXH₃⁺ and BX₂H₂⁺; X = F and Cl) as well as their dihydrogen complexes BXH₅⁺ and BX₂H₄⁺. In continuation of our study we now have extended our investigations to the higher coordinate onium-boronium dications (X⁺BH₃⁺ and X⁺BH₅⁺; X = NH₃, PH₃, OH₂, and SH₂).‡

Results and Discussion

Calculations were carried out with the GAUSSIAN 98 program system (23). The geometry optimizations were performed at the MP2/6-311+G** level. Vibrational frequencies at the MP2/6-311+G**/MP2/6-311+G** level were used to characterize stationary points as minima (number of imaginary frequency = 0) and evaluate zero-point vibrational energies that were scaled by a factor of 0.96 (24). For improved energy, single-point energies at MP4(SDTQ)6-311+G** on MP2/6-311+G** optimized geometries were computed. Final energies were calculated at the MP4(SDTQ)/6-311+G**/MP2/6-311+G** + zero-point vibrational energy level. Thermodynamics of the selected complexation and protonation processes are given in Table 1. The calculated energies are given in Table 2. MP2/6-311+G** geometrical parameters and final energies will be discussed throughout unless stated otherwise.

Table 1.

Dissociation energy ΔE₀ at 298 K for the selected processes

Process	ΔE0†, kcal/mol
H3N+BH5+1d → H3N+BH3+1a + H2	+23.9
H3P+BH5+2d → H3P+BH3+2a + H2	+26.2
H2O+BH5+3d → H2O+BH3+3a + H2	+21.0
H2S+BH5+4d → H2S+BH3+4a + H2	+23.0
H3N+BH5+1d → H3N+BH5+1e + H+	+18.3
H3P+BH5+2d → H3P+BH5+2e + H+	+29.0
H2O+BH5+3d → H2O+BH5+3e + H+	+7.9
H2S+BH5+4d → H2S+BH5+4e + H+	+17.7

^† At MP4(SDTQ)/6-311+G**/MP2/6-311+G** + zero-point vibrational energies level. 

Table 2.

Total energies (arbitrary units), zero-point vibrational energies and relative energies (kcal/mol)

	MP2/6-311+G**// MP2/6-311+G**	ZPE†	MP4(SDTQ)/6-311+G**//MP2/6-311+G**	Rel. energy‡, kcal/mol
H3N+BH3+1a	82.10296	40.7	82.13927	2.8
H3N+BH21b	82.10172	36.7	82.13731	0.0
H2NBH21c	81.80118	29.1	81.83471	182.3
H3N+BH5+1d	83.31232	53.7	83.35587	0.0
H3N+BH41e	83.27616	48.8	83.31895	18.3
H3P+BH3+2a	368.29369	34.2	368.34047	0.0
H3P+BH22b	368.26971	29.4	368.31531	11.0
H2PBH22c	367.95513	23.3	367.99940	203.1
H3P+BH5+2d	369.50727	46.8	369.56016	0.0
H3P+BH42e	369.45327	41.3	369.50513	29.0
H2O+BH3+3a	101.91317	32.4	101.94288	15.1
H2O+BH23b	101.93220	28.7	101.96102	0.0
HOBH23c	101.65843	21.6	101.68629	165.3
H2O+BH5+3d	103.11643	44.5	103.15340	0.0
H2O+BH43e	103.09736	40.0	103.13371	7.9
H2S+BH3+4a	424.49422	28.7	424.53832	1.2
H2S+BH24b	424.49084	24.3	424.53320	0.0
HSBH24c	424.21875	18.7	424.25812	167.0
H2S+BH5+4d	425.70157	40.9	425.75229	0.0
H2S+BH44e	425.66677	35.7	425.71583	17.7

^† Zero-point vibrational energies (ZPE) at MP2/6-311+G**//MP2/6-311+G** scaled by a factor of 0.96. 

^‡ Relative energies at MP4(SDTQ)/6-311+G**//MP2/6-311+G** + ZPE level. 

X⁺BH₃⁺ Dications; X = NH₃, PH₃, H₂O, and H₂S.

The ammonium-boronium dication H₃N⁺BH₃⁺ 1a (Fig. 1) was found to be a minimum on the potential energy surface. The structure 1a can also be considered as ammonium-substituted BH₄⁺. The structure is characterized with a four-coordinate boron atom having a 3c-2e bond involving boron and two hydrogens. In dication 1a the boronium ion (–BH₃⁺) unit and the ammonium ion (–NH₃⁺) unit are separated by a distance of 1.505 Å. The structures of phosphonium-boronium H₃P⁺BH₃⁺ 2a, oxonium-boronium H₂O⁺BH₃⁺ 3a, and sulfonium-boronium H₂S⁺BH₃⁺ 4a dications (Fig. 1) were also calculated and found to be minima on the potential energy surface. Similar to 1a, each of the 2–4a structures also contains a 3c-2e bond involving boron and two hydrogens.

Figure 1.

MP2/6-311+G** structures of 1–4.

Deprotonation energies of 1–4a were computed and are listed in Table 1. Deprotonation of 1a to give monocation H₃N⁺BH₂ 1b was calculated to be slightly exothermic by 2.8 kcal/mol. The structure 1b can be considered as an ammonium-substituted borane. However, deprotonation of 2a to give H₃P⁺BH₂ 2b was found to be endothermic by 11.0 kcal/mol. On the other hand, deprotonation of 3a and 4a were computed to be exothermic by 15.1 and 1.2 kcal/mol, respectively. We also calculated the deprotonation energies for 1–4b. Deprotonation of 1–4b into neutral 1–4c, however, were calculated to be highly endothermic (by 165–203 kcal/mol; see Table 2).

X⁺BH₅⁺ Dications; X = NH₅, PH₃, H₂O, and H₂S.

Complexation of 1a with H₂ leads to H₃N⁺BH₅⁺ 1d, which was found to be a stable minimum on the potential energy surface (Fig. 2). The structure 1a can be considered as an ammonium-substituted BH₆⁺ (16). The ammonium-boronium dication 1d contains a six-coordinate boron with two 3c-2e bonds. In dication 1a the boronium ion (–BH₅⁺) unit and the ammonium ion (–NH₃⁺) unit are separated by a distance of 1.544 Å. The formation of 1d from complexation of 1a and H₂ is an exothermic (by 23.9 kcal/mol) process (Table 1). In comparison, the formation of BH₆⁺ from BH₄⁺ and H₂ was calculated to be exothermic by 17.7 kcal/mol (16). The calculated structure of the six-coordinate parent BH₆⁺ was reported first by Rasul and Olah in 1997 (16). In the same year the ion was prepared by DePuy et al. in the gas phase by complexing BH₄⁺ with H₂ (20, 21). The structures of phosphonium-boronium H₃P⁺BH₅⁺ 2d, oxonium-boronium H₂O⁺BH₅⁺ 3d, and sulfonium-boronium H₂S⁺BH₅⁺ 4d dications (Fig. 2) were also calculated and found to be minima on the potential energy surface. Similar to 1d, each of the 2–4d structures also contains two 3c-2e bonds involving boron and two hydrogens. Formation of 2d, 3d, and 4d from complexations of 2a, 3a, and 4a, respectively, and H₂ were also found to be exothermic (by 26.2, 21.0, and 23.0 kcal/mol) processes (Table 1).

Figure 2.

MP2/6-311+G** structures of 1–4d and 1–4e.

Deprotonation energies of dications 1–4d were calculated and are displayed in Table 1. Deprotonation of 1d to give monocation H₃N⁺BH₄ 1e was found to be endothermic by 18.3 kcal/mol. The structure 1e contains a 3c-2e bond and can be considered an ammonium-substituted BH₅. We previously calculated (25) the structure 1e at the MP2/6-31G** level. Thus deprotonation of 1d is a unfavorable process.

Deprotonation of 2d, 3d, and 4d to give 2e, 3e, and 4e were also computed to be endothermic by 29.0, 7.9, and 17.7 kcal/mol, respectively (Table 2).

As expected, the calculated deprotonation energies (ΔE₀) of the dications X⁺BH₃⁺ 1–4a and X⁺BH₅⁺ 1–4d (Tables 1 and 2) indicate an increase in the stability of the dications toward deprotonation with the increase in the size of the X atoms. The instabilities of the small multicharged cations are due mainly to the charge–charge repulsion. A significant implication of the study of multicharged onium-boronium dications is the relationship of their bonding nature to carbon analogues, i.e., carbon superelectrophiles (26) involved in superacid media. Better stabilization of some of these dications by Schmidbaur-type auration (5) with (C₆H₅)₃PAu, an isolobal analogue of H⁺, however, should be possible.

In conclusion, present ab initio calculations at the MP2/6-311+G** level indicate that the onium-boronium dications (X⁺BH₃⁺ 1–4a and X⁺BH₅⁺ 1–4d; X = NH₃, PH₃, H₂O, and H₂S) are stable minima. The optimized structures show that 1–4a all contain a four-coordinate boron atom having a 3c-2e bond involving boron and two hydrogens. Calculated structures show that 1–4d all contain a six-coordinate boron atom having two 3c-2e bonds. Thermodynamics of the complexations of 1–4a and H₂ to form 1–4d were computed. Deprotonations of 1–4d to form 1–4e were found to be substantially endothermic.

Abbreviation

3c-2e

three-center two-electron