Pride, Prejudice, and Penury of ab initio Transport Calculations for Single Molecules
This chapter describes several principle approaches to transport calculations based on time-dependent density functional theory (TDDFT). It presents a brief account of the basic principle strategies. The chapter explains in more detail one of them, the standard method of ab initio transport calculations. It discusses an attempt to justify the procedure from the point of view of TDDFT, list loose ends and apparent conceptual difficulties. The chapter discusses some well-known limitations of common density functional approximations, and their implications for transport calculations. Transport can be investigated in several different languages, all of which are equivalent in the regime where their validity overlap. Since transport is often a weak tunneling process, the position of the molecular levels relative to the leads greatly affects the calculated current. If a molecule is weakly coupled to the leads, there is every reason to think that standard functional approximations will make huge errors in the calculation of currents.