Abstract
Structures of the isomeric adamantanediyl dications C10H142+ and protio-1- and protio-2-adamantyl dications C10H162+ were investigated by using the density functional theory (DFT) method at the B3LYP/6–31G** level. Four structures, 1 b–e, were found to be minima on the potential energy surface of C10H142+. The 1,3-adamantanediyl dication 1b with two bridgehead tertiary carbocationic centers was found to be the most stable structure. On the potential energy surface of C10H162+ (protonated adamantly cation), five structures, 2 b–f, were found to be minima. Each of the structure contains a two-electron, three-center bond. The C—C protonated 1-adamantyl dication, 2f, was characterized as the most stable structure. 13C NMR chemical shifts of the structures were also calculated by using gauge-including atomic orbital-density functional theory and gauge-including atomic orbital-self-consistent field methods.
Adamantane, C10H16 i, has been used extensively as a model compound to investigate electrophilic reactions of saturated hydrocarbons. The unique structural features of adamantane are ideal for a systematic study of its cations, including both their structure and chemical reactivity. The tight interlocking of cyclohexane rings into the rigid, relatively strain free-chair conformation in adamantane makes it stable against deprotonation, prohibiting the easy formation of double bonds and back-side (nucleophilic or electrophilic) attack (1).
Of particular interest is the bridgehead 1-adamantyl cation, which has been prepared and characterized under long-lived stable ion conditions (2). The bridgehead 1-adamantyl cation is stabilized by C—C hyperconjugation. X-ray crystal structural studies of the 3,5,7-trimethyl-1-adamantyl cation demonstrates the C—C hyperconjugative effect elegantly (3). A series of 2,6-disubstituted 2,6-adamantanediyl dications ii (Scheme 1) (R = C6H5, c-C3H5) were also prepared in superacid media by Prakash et al. (4). The dications were stable only with stabilizing groups such as phenyl and cyclopropyl. Attempts to generate the unsubstituted secondary dication ii (R = H) were unsuccessful (4). The previously attempted preparation of the 1,3-adamantanediyl dication in superacid solutions were also unsuccessful (3).
Scheme 1.
Adamantane (i) and 2,6-disubstituted 2,6-adamantanediyl dications (ii)
We now report density functional theory (DFT) studies (5) of the possible isomeric adamantanediyl dications C10H142+ and protio-adamantyl dications C10H162+, hitherto not yet observed as persistent long-lived species. Superelectrophilic (6) C—H or C—C protonation of the adamantyl cation is also possible and can lead to extremely reactive protio-adamantyl dications. Previously, we have been able to show by hydrogen/deuterium exchange experiments and theoretical calculations that the tert-butyl (7) as well as isopropyl (8) cations can undergo C—H protonation in superacids to form the activated highly electron-deficient gitonic carbenium-carbonium dications protio-tert-butyl and protio-iso-propyl dications, respectively (Scheme 2).‡
Scheme 2.
Protioisopropyl and protio-tert-butyl dications
Methods
The geometry optimizations were carried out by using the DFT method (5) at the B3LYP/6–31G** level. Vibrational frequencies at the B3LYP/6–31G**//B3LYP/6–31G** level were used to characterize stationary points as minima (number of imaginary frequencies = 0) and to evaluate zero point vibrational energies (ZPE), which were scaled by a factor of 0.98 (9). Final energies were calculated at the B3LYP/6–31G**//B3LYP/6–31G** + ZPE level. All energies are given in Table 1. The B3LYP/6–31G** geometrical parameters and final energies will be discussed throughout, unless stated otherwise. The 13C NMR chemical shifts were calculated by the gauge-including atomic orbital-self-consistent field (GIAO-SCF) and GIAO-DFT (B3LYP) methods (10–12) using the 6–311+G** basis set. The 13C NMR chemical shifts were referenced to (CH4)4Si [calculated absolute shifts i.e., σ(C) = 194.1 (GIAO-SCF) and 183.8 (GIAO-DFT)]. The gaussian 03 program (13) was used for all calculations.
Table 1. Total energies (-au), ZPE, and relative energies (kcal/mol).
| No. | B3LYP/6-31G**//B3LYP/6-31G** | ZPE† | No. of imaginary frequency | Rel. energy‡ (kcal/mol) |
|---|---|---|---|---|
| Adamantanediyl dication | ||||
| 1a | 388.73700 | 131.6 | 1 | 14.6 |
| 1b | 388.76244 | 133.0 | 0 | 0.0 |
| 1c | 388.76203 | 133.1 | 0 | 0.4 |
| 1d | 388.75571 | 132.5 | 0 | 3.7 |
| 1e | 388.75726 | 133.0 | 0 | 3.3 |
| Protioadamantyl dication | ||||
| 2b | 389.93685 | 144.8 | 0 | 18.5 |
| 2c | 389.94022 | 145.1 | 0 | 16.7 |
| 2d | 389.92916 | 144.6 | 0 | 23.1 |
| 2e | 389.93621 | 145.3 | 0 | 19.4 |
| 2f | 389.96668 | 145.0 | 0 | 0.0 |
| Adamantyl cation | ||||
| 2g | 389.85927 | 142.0 | 0 | 64.4 |
| 2h | 389.83850 | 141.5 | 0 | 76.9 |
At B3LYP/6-316**//B3LYP/6-31G** scaled by a factor of 0.98.
At B3LYP/6-316**//B3LYP/6-31G**† +ZPE level.
Results and Discussion
The calculated structures of the isomeric adamantanediyl dications, C10H142+ 1 a—e are depicted in Fig. 1. Interestingly, the 1,2-adamantanediyl dication structure 1a is not a minimum on the potential energy surface as the vibrational frequencies at the B3LYP/6–31G**//B3LYP/6–31G** level shows that it contains an imaginary frequency (i.e., number of imaginary frequencies = 1). The gitonic structure 1a can be considered as a substituted ethylene dication with a tertiary and a secondary carbocationic center adjacent to each other. The 1,3-adamantanediyl dication 1b is a minimum on the potential energy surface. The distonic dication contains two tertiary carbocationic centers separated by a methylene group. Expectedly, 1b is considerably more stable than 1a by 14.6 kcal/mol.
Fig. 1.
B3LYP/6–31G**-optimized structures of adamantanediyl dictations 1 a–e.
Structures 1c, 1d, and 1e representing 1,9-, 2,8-, and 2,6-adamantanediyl dications were also calculated to be energy minima. The carbocationic centers in structure 1c are separated by two carbons. Despite charge separation the structure 1c is less stable than 1b. However, the energy difference is only 0.4 kcal/mol. Thus, the structures 1c and 1b are almost isoenergetic, because both formally charge-bearing carbons are tertiary in 1b but only one of them is tertiary and the other one is secondary in 1c. Structure 1d can be considered a nonclassical dication. Carbocationic centers of the structure 1d involve two-electron, three-center (2e—3c) bonding as indicated by the two adjacent long C—C bond distances of 2.194 and 1.737 Å. On the other hand, the structure 1e contains two secondary carbocationic centers separated by three carbons. Both structures 1d and 1e are less stable than 1b (by 3.7 and 3.3 kcal/mol, respectively). The order of stability for adamantanediyl dications is, therefore, 1b > 1c > 1e > 1d > 1a at the level of calculations.
The C—HorC—C protonation of the adamantyl cation could lead to superelectrophilic (6) protio-adamantyl dications. Five structures, 2 b–f, corresponding to protio-adamantyl dications were found to be minima. Structures 2 b–f together with the calculated structures of 1-adamantyl cation 2g and 2-adamantyl cation 2h are displayed in Fig. 2. The structure 2b corresponds to the C(3)-H protonated 1-adamantyl dication. The structure contains a carbonium ion center involving a 2e—3c bond and a trivalent carbenium ion center separated by a methylene group. Energy comparison shows that in fact the carbonium-carbenium structure 2b is 45.9 kcal/mol lower in energy than the 1-adamantyl cation 2g. This finding indicates that similar to the tert-butyl cation (7), the 1-adamantyl cation 2g could also undergo proton-deuterium exchange under superacidic conditions involving structure 2b. In 2b three C—C bonds are aligned in plane with the empty p-orbital on the tertiary carbocation center. However, one of them (C2—C3) is considerably shorter (1.568 Å) than that of the 2g (1.629 Å). This finding suggests that hyperconjugative stabilization in 2g can be partly diminished by further protonation since only two and not three bonds interact with the carbocation center. As a result the other two aligned bonds (C5—C10 and C7—C8) are elongated to 1.653 Å. Dissociation of 2f into 1,3-adamantanediyl dication 1b and H2, however, was calculated to be favored by 8.4 kcal/mol. In a related study, Esteves et al. (14) calculated the structures of protio-adamantane cation by an ab initio method. The most stable structure was found to be the van der Waals complex between H2 and 1-adamantyl cation.
Fig. 2.
B3LYP/6–31G**-optimized structures of protio-adamantyl dictations 2 b–f and 1- and 2-adamantyl cations 2g and 2h.
The structure 2c corresponds to the C(9)-H protonated 1-adamantyl cation. Structure 2c is slightly more stable than 2b by 1.8 kcal/mol (Table 1) as the two positive charge-bearing carbons in 2c are now separated by two carbon atoms. Structures 2d and 2e correspond to the C(8)-H and C(6)-H protonated 2-adamantyl dication 2h, respectively. They are less stable than 2b by 4.6 and 1.4 kcal/mol, respectively. Structure 2d was characterized as a nonclassical dication. The carbocationic center of 2d involves a 2e—3c bond with two long C—C distances of 1.978 and 1.837 Å. Structure 2e contains a secondary carbenium ion center and a five coordinated carbonium ion center separated by three carbons.
The global energy minimum for the protio-adamantyl dication was found to be 2f, which can be considered as the C(3)-C(9) protonated 1-adamantyl cation. The structure contains a 2e—3c bond involving two carbons and a hydrogen and a carbenium ion center separated by a methylene group. The structure is substantially more stable than 2b by 18.5 kcal/mol (Table 1). Two different dissociation paths for the dication, deprotonation, and dedihydrogenation were calculated. Deprotonation of 2f into 2g is substantially endothermic by 64.4 kcal/mol. On the other hand, dissociation of 2f into 1,3-adamantanediyl dication 1b and H2 was calculated to be endothermic by 10.4 kcal/mol.
The 13C NMR chemical shifts of the dications 1 a–e and 2 b–f as well as monocations 2g and 2h were calculated by the GIAO-DFT methods using a 6–311+G** basis set (Table 2). For comparison the 13C NMR chemical shifts of the dications were also calculated by the GIAO-SCF method and are listed in Table 2. The experimental 13C NMR spectrum of the 1-adamantyl cation 2g shows an absorption at δ13C 301 (15) [with respect to (CH4)4Si], representing the bridgehead carbocationic center C+. The deshielded peak at δ13C 301, however, is 34 ppm more shielded than that of the tert-butyl cation (335.2 ppm; ref. 15). This finding also reflects the extensive C—C hyperconjugative interactions of the neighboring three C—C bonds with the p orbital of the carbocationic center. The GIAO-DFT calculated δ13C value of the C+ in 2g is 310.2, which can be compared with the experimental value of 301.0 ppm. The calculated δ13C values of the C+ carbon of the 2-adamantyl cation 2h was found to be more deshielded at 346.0. This result indicates that no significant C—C or C—H hyperconjugative interaction of the neighboring bonds with the p orbital of the carbocationic center is possible in cation 2h.
Table 2. GIAO calculated 13C and NMR chemical shifts.
| No. | Atom | GIAO-SCF | GIAO-DFT | Exp. |
|---|---|---|---|---|
| Adamantanediyl dication | ||||
| 1a | C1 | 288.6 | 268.3 | |
| C2 | 303.6 | 276.3 | ||
| 1b | C1, C2 | 304.6 | 283.8 | |
| 1c | C1 | 341.2 | 336.0 | |
| C9 | 298.7 | 283.7 | ||
| 1d | C2, C8 | 298.7 | 283.7 | |
| C3, C7 | 83.6 | 113.1 | ||
| C4, C6 | 56.0 | 86.6 | ||
| 1d | C2, C8 | 56.0 | 86.6 | |
| C3, C7 | 83.6 | 113.1 | ||
| C4, C6 | 298.7 | 283.7 | ||
| 1e | C2, C6 | 297.1 | 289.7 | 277.1† |
| Protioadamantyl dication | ||||
| 2b | C1 | 316.4 | 303.7 | |
| C3 | 71.2 | 90.0 | ||
| 2c | C1 | 322.6 | 315.7 | |
| C9 | 46.0 | 54.2 | ||
| 2d | C2 | 107.7 | 118.4 | |
| C3 | 159.8 | 163.1 | ||
| C4 | 45.5 | 57.4 | ||
| C8 | 51.5 | 59.5 | ||
| 2e | C2 | 318.8 | 313.2 | |
| C6 | 39.8 | 47.8 | ||
| 2f | C1 | 176.3 | 207.2 | |
| C9 | 100.4 | 117.3 | ||
| Adamantyl cation | ||||
| 2g | C1 | 321.8 | 310.2 | 301.0‡ |
| 2h | C2 | 354.7 | 346.0 |
The calculated δ13C value of the bridgehead C+ carbon of the most stable adamantanediyl dication 1b was found to be 283.8, which is in fact ≈26 ppm more shielded than the calculated bridgehead C+ of the monocation 2g. This finding could also be caused by the extensive C—C hyperconjugative interactions. The δ13C values of the carbenium C+ and carbonium C+ of the protio-adamantyl dication 2b were computed to be 303.7 and 90.0, respectively. The δ13C of the carbenium C+ of 2b is ≈20 ppm more shielded than the C+ atom of the dication 1b. However, the calculated δ13C of the carbenium C+ of the most stable protio-adamantyl dication 2f was found to be more deshielded at 322.8.
As shown in previous studies persistent (stable), distonic carbenium dications are observable in superacidic media, generally when the two carbocationic centers are separated by two carbon atoms (1,4-dications). Although highly reactive alkyl dications generated by further protonation [protosolvation (6)] of alkyl cations cannot be observed by slow spectroscopic methods (such as NMR) in superacid media as persistent species, computational data give additional support for their transient existence and involvement in superacid-catalyzed processes. Such dicationic species play an important role in superacidic chemistry. Our previous studies have demonstrated that the tert-butyl (7) and even the 2-propyl (8) cations can be protolytically activated in superacid solutions.
In conclusion, structures of the possible isomeric adamantanediyl dications C10H142+ 1a–e and protioadamantyl dications C10H162+ 2 b–f were calculated at the DFT B3LYP/6–31G** level. The 1,2-adamantanediyl dication structure 1a is not a minimum on the potential energy surface of C10H142+. The 1,3-adamantanediyl dication 1b with two tertiary carbenium centers was found to be the lowest energy isomer of adamantanediyl dications. The structure of 1,9-adamantanediyl dication 1c was calculated to be slightly less stable than 1b by 0.4 kcal/mol. Thus, the structures 1c and 1b are energetically almost identical. Two other isomers of adamantanediyl dications 1d and 1e were also found be slightly less stable than 1b. The stability order for adamantanediyl dications was predicted to be 1b > 1c > 1e > 1d > 1a. Five structures, 2 b–f, corresponding to protio-adamantyl dications were characterized as minima. The structure 2b corresponds to the C(3)-H protonated 1-adamantyl dication. The structure contains a tertiary carbenium ion center and a carbonium ion center involving a 2e—3c bond separated by a methylene group. The lowest energy structure for the protio-adamantyl cation, however, was found to be the C(3)-C(9) protonated 1-adamantyl dication 2f. This structure is substantially more stable than 2b by 18.5 kcal/mol (Table 1). The 13C NMR chemical shifts of the structures were also calculated by using GIAO-DFT and GIAO-SCF methods.
Acknowledgments
Support of our work by the National Science Foundation is gratefully acknowledged.
Abbreviations: DFT, density functional theory; ZPE, zero point vibrational energies; GIAO, gauge-including atomic orbital; SCF, self-consistent field; 2e—3c, two-electron, three-center.
Footnotes
This is paper no. 64 in the series “Chemistry in Superacids.” Paper no. 63 is ref. 16.
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