The number of ideal rings on the diamond lattice; application to crown ethers

Abstract

Three independent computing methods are described for the calculation of the number of different conformations of rings of up to 26 atoms, superimposable on the diamond lattice. Our computations extend results published earlier and show them to be partly incorrect. As an application, the number of different conformations for ‘ideal’ crown ethers has been calculated (6-crown-2, 12-crown-4,18-crown-6, and partly, 24-crown-8) and a comparison has been made with structures determined by X-ray crystallography.