Computer Assisted Graph Theoretical Analysis of Complex Mechanistic Problems in Polycyclic Hydrocarbons. The Mechanism of Diamantane Formation from Various Pentacyclotetradecanes

The pentacyclotetradecane rearrangement graph culminating in diamantane (1) has been analyzed. The most probable mechanistic pathways from tetrahydro-Binor-S (2 or 3), hydrogenated Katz [2 + 4] norbornadiene dimers (7 and 8), and [2 + 2] norbornene dimers (9, 10, and) were deduced by graphical analysis guided by empirical force field (strain) calculations. Graphs of isomeric hydrocarbons were generated from a chosen precursor by 1,2-alkyl shifts, employing the simulation and evaluation of chemical synthesis (SECS) computer program. Due to the extremely large number of possible intermediates, it was necessary to simplify graph generation by adopting certain assumptions. From a given hydrocarbon precursor, all possible 1,2-shift isomers were generated and their strain energies calculated. The resulting isomer with lowest energy was processed further. Graph generation proceeded in this manner until diamantane was reached. The most probable mechanism for isomerization of 2 or 3 ⟶ 1 is proposed to involve, in sequence, trans-pentacyclo-[8.2.1.1^2,5.0^3,7.0^8,12]tetradecane (6), a tetrasubstituted intermediate (24), 28, and protodiamantane (29). In the actual reaction, 6 was found to be the last isolable intermediate, as predicted by the strain energy calculations. When structures with tetrasubstituted cations were excluded from the graph, sets of interconverting pentacyclotetradecane isomers were obtained. The sets considered were derived from the [2 + 2] norbnene dimer 11 (6 structures), from the [2 + 4] hydrogenated Katz norbornadiene dimer 7 (10 structures), from tetrahydro-Binor-S (2) (13 structures), from 28 (293 structures, designated family [1,2,4] [3,5,6]), and from diamantane (1) (119 structures, family [1,3,5] [2,4,6]). Experimentally, isomerization to the lowest energy isomer within each family prior to further reaction via tetrasubstituted intermediates appears to take place, and the yield of diamantane decreases with the number of family boundaries which must be crossed.