Non-equilibrium steady state conductivity in cyclo[18]carbon and its boron nitride analogue

A ring-shaped carbon allotrope was recently synthesized for the first time, reinvigorating theoretical interest in this class of molecules. The dual pi structure of these molecules allows for the possibility of novel electronic properties. In this work we use reduced density matrix theory to study the electronic structure and conductivity of cyclo[18]carbon and its boron nitride analogue, B9N9. The variational 2-RDM method replicates the experimental polyynic geometry of cyclo[18]carbon. We use a current-constrained 1-electron reduced density matrix (1-RDM) theory with Hartree-Fock molecular orbitals and energies to compute the molecular conductance in two cases: (1) conductance in the plane of the molecule and (2) conductance around the molecular ring as potentially driven by a magnetic field through the molecule's center. In-plane conductance is greater than conductance around the ring, but cyclo[18]carbon is slightly more conductive than B9N9 for both in-the-plane and in-the-ring conduction. The computed conductance per molecular orbital provides insight into how the orbitals-their energies and densities-drive the conduction.