title: Response to "Comment on 'Rethinking first-principles electron transport theories with projection operators: the problems caused by partitioning the basis set'" [J. Chem. Phys. 140, 177103 (2014)].
abstract: The thesis of Brandbyge's comment [J. Chem. Phys. 140, 177103 (2014)] is that our operator decoupling condition is immaterial to transport theories, and it appeals to discussions of nonorthogonal basis sets in transport calculations in its arguments. We maintain that the operator condition is to be preferred over the usual matrix conditions and subsequently detail problems in the existing approaches. From this operator perspective, we conclude that nonorthogonal projectors cannot be used and that the projectors must be selected to satisfy the operator decoupling condition. Because these conclusions pertain to operators, the choice of basis set is not germane.
authors.affiliation: Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA.
authors.forename: Matthew G
authors.initials: MG
authors.lastname: Reuter
authors.affiliation: Institute for Advanced Computational Science and Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794, USA.
authors.forename: Robert J
authors.initials: RJ
authors.lastname: Harrison