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Relativistic densityfunctional theory based on effective quantum electrodynamics
by Julien Toulouse
Submission summary
As Contributors:  Julien Toulouse 
Preprint link:  scipost_202102_00027v1 
Date submitted:  20210218 22:23 
Submitted by:  Toulouse, Julien 
Submitted to:  SciPost Chemistry 
Academic field:  Chemistry 
Specialties: 

Approach:  Theoretical 
Abstract
A relativistic densityfunctional theory based a Fockspace effective quantumelectrodynamics (QED) Hamiltonian using the Coulomb or CoulombBreit twoparticle interaction is developed. This effective QED theory properly includes the effects of vacuum polarization through the creation of electronpositron pairs but does not include explicitly the photon degrees of freedom. It is thus a more tractable alternative to full QED for atomic and molecular calculations. Using the constrainedsearch formalism, a KohnSham scheme is formulated in a quite similar way to nonrelativistic densityfunctional theory, and some exact properties of the involved density functionals are studied, namely chargeconjugation symmetry and uniform coordinate scaling. The usual nopair KohnSham scheme is obtained as a welldefined approximation to this relativistic densityfunctional theory.
Current status:
Submission & Refereeing History
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Reports on this Submission
Anonymous Report 1 on 202141 Invited Report
Strengths
1  I very much appreciate that the author in appendices A and B successively demonstrate that the effective QED Hamiltonian (7) possess the correct chargeconjugation symmetry and is equivalent to an alternative Hamiltonian that has been promoted in recent literature.
2  Focus of the paper is on a relativistic formulation of densityfunctional theory, but foundations for wave function (or more correctly Fock space)based theory is given as well.
3  The DFT section provides foundations as well as important relations for relativistic DFT based on the effective QED Hamiltonian (7).
4  The author points issues that need further study.
5  The authors provides a rich bibliography and appears to me fair in his appreciation of these.
Weaknesses
Some points need possibly further sharpening:
1  First of all, this is not relativistic theory, in the sense of being Lorentz covariant, but rather adheres the pragmatic spirit in which relativistic molecular calculations are carried out presently. This could perhaps be stressed further.
2  A practical realization of the present work will require the development for the practical realization of regularisation/renormalization procedures.
3  The authors refers to (opposite) charge for several quantities. This could perhaps be discussed briefly.
4This is a single author paper. The author adheres to the use of "we", following common practice, but on pages 2, 22 and 25 refers to "my knowledge". I advice being consisten.
Report
This is an absolutely outstanding paper, a veritable treasure trove of important results, which should have very significant impact on the domain of relativistic molecular applications.
Requested changes
The paper can be published as it, but the author should consider the polish suggested above.