Energies for cyclic and acyclic aggregations of adamantane and diamantane units sharing vertices, edges, or six-membered rings

TL;DR

This study computes energies for cyclic and acyclic aggregates of adamantane and diamantane units sharing various structural features, revealing linear energy increases in acyclic chains and minima in cyclic ones, with energies approaching a limit as size grows.

Contribution

It introduces detailed energy calculations for polymer-like aggregates of adamantane and diamantane units sharing vertices, edges, or rings, highlighting differences between cyclic and acyclic structures.

Findings

SWB-tension energies increase linearly with size in acyclic chains.

Cyclic aggregates show a minimum in tension energy at certain sizes.

Both cyclic and acyclic chains approach a common energy per unit as size increases.

Abstract

Diamondoids are hydrocarbons having a carbon scaffold comprised from polymer-like composites of adamantane cages. The present paper describes computed total energies and "SWB-tension" energies (often referred to as "strain" energies) for species having $n$ adamantane or diamantane units sharing pairwise: one carbon atom (spiro-[n]adamantane or spiro-[$n$]diamantane); one C-C bond (one-bond-sharing-[$n$]adamantane or one-bond-sharing-[$n$]diamantane); or one chair-shaped hexagon of carbon atoms (1234-helical-cata-[$n$]diamantanes). Each of the five investigated polymer-like types is considered either as an acyclic or a cyclic chain of adamantane- or diamantane-unit cages. With increasing $n$ values, SWB-tension energies for acyclic aggregates are found to increase linearly, while the net SWB-tension energies of cyclic aggregates often go thru a minimum at a suitable value of $n$. In all five cases, a limiting common energy per unit ($E/n$ ) is found to be approached by both cyclic and acyclic chains as $n\to \infty $, as revealed from plots of $E/n$ versus $1/n$ for acyclic chains and of $E/n$ versus $1/n^2$ for cyclic chains.