# Reply to "Comment on 'Generalization of the Kohn-Sham system that can represent arbitrary one-electron density matrices'"

## TL;DR

This paper responds to criticisms of a previous work on a novel single determinant wave function form that allows non-idempotent 1-electron density matrices, clarifying misconceptions and defending the original approach.

## Contribution

It provides a detailed rebuttal to critiques of their proposed density matrix form and clarifies misconceptions about their method and its properties.

## Key findings

- The proposed density matrix form is valid and well-defined.
- The energy functional can be expressed in terms of the 1-electron density matrix.
- The criticisms regarding invariance and functional forms are addressed and clarified.

## Abstract

Our paper [Phys. Rev. A 93, 052512 (2016)], proposing a novel form of single determinant wave function that admits non-idempotent 1-electron density matrices, has recently received a Comment [Phys. Rev. A ??, 0????? (2017)] suggesting a number of flaws: The form of the 1-electron density matrix that we proposed is deemed invalid; None of the currently known functionals are given in terms of the 1-electron density matrix but known only in the basis where the density matrix is diagonal; In NOFT the energy is not invariant with respect to unitary transformations of the orbitals; The M\"uller functional we used suffers from serious shortcomings; In NOFT there detachment energies should be obtained from the extended Koopmans theorem. Below we will address these criticisms in sequence.