Rethinking first-principles electron transport theories with projection operators: The problems caused by partitioning the basis set

We revisit the derivation of electron transport theories with a focus on the projection operators chosen to partition the system. The prevailing choice of assigning each computational basis function to a region causes two problems. First, this choice generally results in oblique projection operators, which are non-Hermitian and violate implicit assumptions in the derivation. Second, these operators are defined with the physically insignificant basis set and, as such, preclude a well-defined basis set limit. We thus advocate for the selection of physically motivated, orthogonal projection operators (which are Hermitian) and present an operator-based derivation of electron transport theories. Unlike the conventional, matrix-based approaches, this derivation requires no knowledge of the computational basis set. In this process, we also find that common transport formalisms for nonorthogonal basis sets improperly decouple the exterior regions, leading to a short circuit through the system. We finally discuss the implications of these results for first-principles calculations of electron transport.