On modeling the induced charge in density-functional calculations for field emitters

The default assumption of many density-functional theory codes that the simulation cell is spatially periodic implies any unbalanced charge in will cause solution to diverge, unless imbalance removed some unphysical way. Periodic thus makes it difficult model accurately and field are induced at apex a single carbon nanotube (CNT) when background electric applied. We describe how containing 1.8 nm capped end (5,5) CNT can be calculated from macroscopic with an external acting on whole CNT. With this method, tip has been analyzed using program ONETEP, linear-scaling code iterates density kernel localized orbitals self-consistently minimize Helmholtz free energy. results shown include (1) sheath mobile outside framework nuclei; (2) Kohn–Sham (KS) including states occupied applied; (3) total effective potential distribution as function applied field; (4) field-enhancement factor 50 deduced change field. computation also shows (5) zero extends into barrier over distance least 0.12 beyond Fermi equipotential, consistent KS for boundary between emitter barrier.