Calculated ¹¹B–¹³C NMR chemical shift relationship in hypercoordinate methonium and boronium ions

Abstract

The boronium-carbonium continuum was extended to include hypercoordinated protonated methanes and their boron analogs. The ¹¹B NMR chemical shifts of the hypercoordinated hydriodo boron compounds and the ¹³C NMR chemical shifts of the corresponding isoelectronic and isostructural carbocations were calculated by using the GIAO-MP2 method. The data show good linear correlation between ¹¹B and ¹³C NMR chemical shifts, which indicates that the same factors that determine the chemical shifts of the boron nuclei also govern the chemical shifts of carbon nuclei of these hypercoordinated hydriodo compounds.

A trivalent carbocation is isoelectronic with the corresponding neutral trivalent boron compounds. Olah et al. (1) in 1971 discussed the relationship between (CH₃)₃C⁺ and B(CH₃)₃ based on infrared and Raman spectroscopy. These studies provided unambiguous evidence that the two species possessed analogous structures and bondings. The close relationship between the ¹³C NMR chemical shifts of the carbons in carbocations and the corresponding ¹¹B NMR chemical shifts of the boron atoms in isoelectronic boron compounds was first shown by Spielvogel and Purser (2, 3) and by Nöth and Wrackmeyer (4). The general correlation equation for trigonal species is shown below.‡

1

In Eq. 1, the δ¹³C is the chemical shift of the cationic carbon of the carbocation with respect to tetramethylsilane and the δ¹¹B is the chemical shift of the corresponding boron atoms with respect to the BF₃:OEt₂. The empirically derived Eq. 1, however, is in good agreement with most of the available data that span some 600 ppm on the ¹³C NMR chemical shift scale. Recently, Prakash et al. (5) reported an extension of the relationship to cage compounds.

Williams et al. (6) derived a similar empirical Eq. 2 for the hypercoordinate (7) carbocations (carbonium ions) and their corresponding hypercoordinate boron compounds.

2

These relationships show that the same factors that determine the chemical shifts of the boron nuclei also govern the chemical shifts of carbon nuclei. We now extend this boronium-carbonium continuum to hypercoordinated hydriodo boron compounds and their isoelectronic and isostructural carbocations, hitherto not yet observed under long-lived superacidic stable ion conditions, based on GIAO-MP2 calculations.

RESULTS AND DISCUSSION

The structures of the hypercoordinate protonated methanes and their boron analogs have been optimized at the MP2/6–31G** level by using the gaussian-94 (8) package of programs. ¹³C and ¹¹B NMR chemical shifts were calculated by the correlated GIAO-MP2 method (9, 10) (tzp/dz basis set; refs. 9 and 10) using the aces ii programs (11). ¹³C NMR chemical shifts are referenced to tetramethylsilane, and ¹¹B NMR chemical shifts are referenced to BF₃:OEt₂.

CH₅⁺ and BH₅.

CH₅⁺ (protonated methane) is considered the parent of nonclassical carbocations containing a five-coordinate carbon atom. The C_s symmetrical structure 1a with a three-center, two-electron (3c-2e) bond is the preferred ground-state structure for the CH₅⁺ (12–16). The isoelectronic boron analog of CH₅⁺ is neutral BH₅ and is also C_s symmetrical 1b based on high-level ab initio calculations (17, 18).

The ¹³C and ¹¹B NMR chemical shifts of 1a and 1b were calculated by using the GIAO-MP2 method (9, 10) (Table 1). Calculation of the ¹³C and ¹¹B NMR chemical shifts by the correlated GIAO-MP2 method was shown to reproduce well experimental values for carbocations and boron compounds, respectively (19, 20). The calculated δ¹³C value of 1a is −11.5, 7.1 ppm more shielded than that of CH₄ (δ¹³C = −4.4) at the same level of calculations. The experimental δ¹³C of methane is −2.3. The shielding effect in 1a, however, is expected for such a hypercoordinate (nonclassical) carbocation (6, 7). Evidence for CH₅⁺ in the condensed phase came from hydrogen-deuterium exchange on methane in deuteriated superacids (21, 22) and ESCA studies (G.A.O., unpublished results). Direct NMR spectroscopic observation of the ion was not yet achieved and is difficult because of its expected low concentration and fast exchange in superacids.

Table 1.

GIAO-MP2/tzp/dz calculated and estimated NMR chemical shifts^*

No.	a, δ13C (GIAO-MP2)	b, δ11B (GIAO-MP2)	b, δ11B (estimated)†
1	−11.5	−28.8	−33.8
2	−25.7	−32.4	−38.5
3	−13.0	−35.6	−34.3
4	332.9	62.4	79.8

^*Calculated ¹³C and ¹¹B NMR chemical shifts were referenced to tetramethylsilane and BF₃:OEt₂, respectively. 

^†Estimated by using Eq. 2. 

The calculated δ¹¹B of 1b is −28.8. We also estimated the δ¹¹B values in 1b by applying Eq. 2 and by using the δ¹³C value of 1a. This yielded a δ¹¹B value of −33.8 for the neutral boron compound 1b. The boron chemical shift of −33.8 is reasonably close to the GIAO-MP2 calculated value of −28.8 and thus reconfirms the close relationship between the ¹¹B and ¹³C chemical shifts of isoelectronic carbon and boron analogs 1a and 1b, respectively.

CH₆²⁺ and BH₆⁺.

The calculated parent six-coordinate carbocation, diprotonated methane (CH₆²⁺), has two two-electron, three-center (2e-3c) bonding interactions in its minimum-energy structure 2a (C_2v) (23, 24). The calculated δ¹³C value of the dication 2a is −25.7, 14.2 ppm more shielded than that of five-coordinate monocation CH₅⁺ 1a.

The structure and energetics of the parent hexacoordinate boronium ion BH₆⁺ 2b, isoelectronic with CH₆²⁺ 2a, recently have been studied (25). The C_2v symmetric form 2b with two three-center, two-electron (3c-2e) bonds was found to be a stable minimum for BH₆⁺. Structure 2b is isostructural with CH₆²⁺ 2a. Recently, DePuy et al. (26) were able to generate the BH₆⁺ in the gas phase. We calculated δ¹¹B of 2b as −32.4, 3.6 ppm more shielded than that of five-coordinate neutral BH₅ 1b. The estimated δ¹¹B of 2b obtained from applying Eq. 2 and using a δ¹³C value of −25.7 for 2a is −38.5 ppm, close to that of the GIAO-MP2 calculated value of −32.4 ppm.

CH₇³⁺ and BH₇²⁺.

The structures of parent heptacoordinate carbocation (27), CH₇³⁺, and its isoelectronic boron analog (26), BH₇²⁺, recently have been reported. The C_3v symmetric forms 3a and 3b were found to be the stable minima for CH₇³⁺ and BH₇²⁺, respectively. The ¹³C and ¹¹B NMR chemical shifts of 3a and 3b were calculated. The calculated δ¹³C of 3a is −13.0, and the δ¹¹B value of 3b is −35.6. δ¹¹B for 3b, estimated by the application of Eq. 2 and by using the δ¹³C value in 3a was assessed to be −34.3 ppm, which shielded by only 1.3 ppm more than the GIAO-MP2 calculated value of −35.6 ppm.

CH₄²⁺ and BH₄⁺.

The planar C_2v symmetrical structures containing a three-center, two-electron (3c-2e) bond are preferred for both CH₄²⁺ 4a (28) and BH₄⁺ 4b (25). The calculated δ¹³C value of 4a is 332.9. The estimated δ¹¹B value in 4b obtained by applying Eq. 2 is 79.8, differing by 17.4 ppm from the GIAO-MP2 values of 62.4.

Correlation of ¹³C and ¹¹B NMR Chemical Shifts.

The calculated ¹³C NMR chemical shifts of studied methonium ions, in general, correlate well with the calculated ¹¹B NMR chemical shifts of the corresponding isoelectronic boron analogs (Fig. 1). This correlation indicates that these small hypercoordinate methonium ions and their boron analogs also follow Eq. 2, which was derived for their nonclassical systems (6). The correlation line derived from Fig. 1 corresponds closely to the correlation line of Eq. 2.

Figure 1.

Calculated ¹³C NMR chemical shifts vs. calculated ¹¹B NMR chemical shifts of structures 1–4.

In conclusion, we have extended the ¹¹B–¹³C NMR chemical shift relationship of boronium-carbonium ions to include the parent hypercoordinated methonium ions and their boron analogs. By using the correlated GIAO-MP2 method the ¹¹B NMR chemical shifts of the hydriodo boron compounds and the ¹³C NMR chemical shifts of their corresponding isoelectronic and isostructural carbonium ions were calculated. The data showed good linear correlation between ¹¹B and ¹³C NMR chemical shifts. This finding indicates that these small parent carbonium and boronium ions also follow Eq. 2, derived for the nonclassical systems (6). It seems that the same factors that determine the chemical shifts of the boron nuclei also govern the chemical shifts of the carbon nuclei within the hypercoordinated hydriodo compounds.