Density functional theory study of adamantanediyl 2؉ dications C10H14 and protio-adamantyl 2؉ dications C10H16 Golam Rasul, George A. Olah†, and G. K. Surya Prakash Loker Hydrocarbon Research Institute and Department of Chemistry, University of Southern California, University Park, Los Angeles, CA 90089-1661 Contributed by George A. Olah, June 14, 2004 2؉ Structures of the isomeric adamantanediyl dications C10H14 and 2؉ protio-1- and protio-2-adamantyl dications C10H16 were investi- gated by using the density functional theory (DFT) method at the B3LYP͞6–31G** level. Four structures, 1 b–e, were found to be 2؉ minima on the potential energy surface of C10H14 . The 1,3-adaman- tanediyl dication 1b with two bridgehead tertiary carbocationic centers was found to be the most stable structure. On the potential 2؉ energy surface of C10H16 (protonated adamantly cation), five struc- tures, 2 b–f, were found to be minima. Each of the structure contains a two-electron, three-center bond. The COC protonated 1-adamantyl 13 dication, 2f, was characterized as the most stable structure. C NMR Scheme 2. Protioisopropyl and protio-tert-butyl dications chemical shifts of the structures were also calculated by using gauge- including atomic orbital-density functional theory and gauge-includ- 2ϩ ing atomic orbital-self-consistent field methods. protio-adamantyl dications C10H16 , hitherto not yet observed as persistent long-lived species. Superelectrophilic (6) COHor O damantane, C10H16 i, has been used extensively as a model C C protonation of the adamantyl cation is also possible and Acompound to investigate electrophilic reactions of saturated can lead to extremely reactive protio-adamantyl dications. Pre- hydrocarbons. The unique structural features of adamantane are viously, we have been able to show by hydrogen͞deuterium ideal for a systematic study of its cations, including both their exchange experiments and theoretical calculations that the tert- structure and chemical reactivity. The tight interlocking of butyl (7) as well as isopropyl (8) cations can undergo COH cyclohexane rings into the rigid, relatively strain free-chair protonation in superacids to form the activated highly electron- conformation in adamantane makes it stable against deproto- deficient gitonic carbenium-carbonium dications protio-tert- nation, prohibiting the easy formation of double bonds and butyl and protio-iso-propyl dications, respectively (Scheme 2).‡ back-side (nucleophilic or electrophilic) attack (1). Of particular interest is the bridgehead 1-adamantyl cation, Methods which has been prepared and characterized under long-lived The geometry optimizations were carried out by using the DFT stable ion conditions (2). The bridgehead 1-adamantyl cation method (5) at the B3LYP͞6–31G** level. Vibrational frequen- is stabilized by COC hyperconjugation. X-ray crystal struc- cies at the B3LYP͞6–31G**͞͞B3LYP͞6–31G** level were used tural studies of the 3,5,7-trimethyl-1-adamantyl cation dem- to characterize stationary points as minima (number of imagi- onstrates the COC hyperconjugative effect elegantly (3). A nary frequencies ϭ 0) and to evaluate zero point vibrational series of 2,6-disubstituted 2,6-adamantanediyl dications ii energies (ZPE), which were scaled by a factor of 0.98 (9). Final ϭ (Scheme 1) (R C6H5, c-C3H5) were also prepared in energies were calculated at the B3LYP͞6–31G**͞͞B3LYP͞6– superacid media by Prakash et al. (4). The dications were stable 31G** ϩ ZPE level. All energies are given in Table 1. The only with stabilizing groups such as phenyl and cyclopropyl. B3LYP͞6–31G** geometrical parameters and final energies will Attempts to generate the unsubstituted secondary dication ii be discussed throughout, unless stated otherwise. The 13C NMR ϭ (R H) were unsuccessful (4). The previously attempted chemical shifts were calculated by the gauge-including atomic preparation of the 1,3-adamantanediyl dication in superacid orbital-self-consistent field (GIAO-SCF) and GIAO-DFT solutions were also unsuccessful (3). (B3LYP) methods (10–12) using the 6–311ϩG** basis set. The We now report density functional theory (DFT) studies (5) of 13C NMR chemical shifts were referenced to (CH ) Si [calcu- 2ϩ 4 4 the possible isomeric adamantanediyl dications C10H14 and lated absolute shifts i.e., ␴(C) ϭ 194.1 (GIAO-SCF) and 183.8 (GIAO-DFT)]. The GAUSSIAN 03 program (13) was used for all calculations. Results and Discussion The calculated structures of the isomeric adamantanediyl dica- 2ϩ tions, C10H14 1a—e are depicted in Fig. 1. Interestingly, the 1,2-adamantanediyl dication structure 1a is not a minimum on Abbreviations: DFT, density functional theory; ZPE, zero point vibrational energies; GIAO, gauge-including atomic orbital; SCF, self-consistent field; 2eO3c, two-electron, three- center. †To whom correspondence should be addressed. E-mail: [email protected]. Scheme 1. Adamantane (i) and 2,6-disubstituted 2,6-adamantanediyl ‡This is paper no. 64 in the series ‘‘Chemistry in Superacids.’’ Paper no. 63 is ref. 16. dications (ii) © 2004 by The National Academy of Sciences of the USA 10868–10871 ͉ PNAS ͉ July 27, 2004 ͉ vol. 101 ͉ no. 30 www.pnas.org͞cgi͞doi͞10.1073͞pnas.0404137101 Downloaded by guest on September 25, 2021 Table 1. Total energies (-au), ZPE, and relative minima. The carbocationic centers in structure 1c are separated energies (kcal͞mol) by two carbons. Despite charge separation the structure 1c is less No. of stable than 1b. However, the energy difference is only 0.4 ͞ B3LYP͞6–31G**͞͞ imaginary Rel. energy‡ kcal mol. Thus, the structures 1c and 1b are almost isoenergetic, No. B3LYP͞6–31G** ZPE† frequency (kcal͞mol) because both formally charge-bearing carbons are tertiary in 1b but only one of them is tertiary and the other one is secondary Adamantanediyl dication in 1c. Structure 1d can be considered a nonclassical dication. 1a 388.73700 131.6 1 14.6 Carbocationic centers of the structure 1d involve two-electron, 1b 388.76244 133.0 0 0.0 three-center (2eO3c) bonding as indicated by the two adjacent 1c 388.76203 133.1 0 0.4 long COC bond distances of 2.194 and 1.737 Å. On the other 1d 388.75571 132.5 0 3.7 hand, the structure 1e contains two secondary carbocationic 1e 388.75726 133.0 0 3.3 centers separated by three carbons. Both structures 1d and 1e are Protioadamantyl dication less stable than 1b (by 3.7 and 3.3 kcal͞mol, respectively). The 2b 389.93685 144.8 0 18.5 order of stability for adamantanediyl dications is, therefore, 1b Ͼ 2c 389.94022 145.1 0 16.7 1c Ͼ 1e Ͼ 1d Ͼ 1a at the level of calculations. 2d 389.92916 144.6 0 23.1 The COHorCOC protonation of the adamantyl cation could 2e 389.93621 145.3 0 19.4 lead to superelectrophilic (6) protio-adamantyl dications. Five 2f 389.96668 145.0 0 0.0 structures, 2b–f, corresponding to protio-adamantyl dications Adamantyl cation were found to be minima. Structures 2b–f together with the 2g 389.85927 142.0 0 64.4 calculated structures of 1-adamantyl cation 2g and 2-adamantyl 2h 389.83850 141.5 0 76.9 cation 2h are displayed in Fig. 2. The structure 2b corresponds †At B3LYP͞6–316**͞͞B3LYP͞6–31G** scaled by a factor of 0.98. to the C(3)-H protonated 1-adamantyl dication. The structure ‡At B3LYP͞6–316**͞͞B3LYP͞6–31G**† ϩZPE level. contains a carbonium ion center involving a 2eO3c bond and a trivalent carbenium ion center separated by a methylene group. Energy comparison shows that in fact the carbonium-carbenium the potential energy surface as the vibrational frequencies at the structure 2b is 45.9 kcal͞mol lower in energy than the 1- B3LYP͞6–31G**͞͞B3LYP͞6–31G** level shows that it con- adamantyl cation 2g. This finding indicates that similar to the tains an imaginary frequency (i.e., number of imaginary fre- tert-butyl cation (7), the 1-adamantyl cation 2g could also quencies ϭ 1). The gitonic structure 1a can be considered as a undergo proton-deuterium exchange under superacidic condi- substituted ethylene dication with a tertiary and a secondary tions involving structure 2b.In2b three COC bonds are aligned carbocationic center adjacent to each other. The 1,3- in plane with the empty p-orbital on the tertiary carbocation adamantanediyl dication 1b is a minimum on the potential center. However, one of them (C2OC3) is considerably shorter energy surface. The distonic dication contains two tertiary (1.568 Å) than that of the 2g (1.629 Å). This finding suggests that carbocationic centers separated by a methylene group. Expect- hyperconjugative stabilization in 2g can be partly diminished by edly, 1b is considerably more stable than 1a by 14.6 kcal͞mol. further protonation since only two and not three bonds interact CHEMISTRY Structures 1c, 1d, and 1e representing 1,9-, 2,8-, and 2,6- with the carbocation center. As a result the other two aligned adamantanediyl dications were also calculated to be energy bonds (C5OC10 and C7OC8) are elongated to 1.653 Å. Disso- Fig. 1. B3LYP͞6–31G**-optimized structures of adamantanediyl dictations 1a–e. Rasul et al. PNAS ͉ July 27, 2004 ͉ vol. 101 ͉ no. 30 ͉ 10869 Downloaded by guest on September 25, 2021 Fig. 2. B3LYP͞6–31G**-optimized structures of protio-adamantyl dictations 2b–f and 1- and 2-adamantyl cations 2g and 2h. ciation of 2f into 1,3-adamantanediyl dication 1b and H2, how- The global energy minimum for the protio-adamantyl dication ever, was calculated to be favored by 8.4 kcal͞mol. In a related was found to be 2f, which can be considered as the C(3)-C(9) study, Esteves et al. (14) calculated the structures of protio- protonated 1-adamantyl cation. The structure contains a 2eO3c adamantane cation by an ab initio method.