Coordinate Scaling in Time-Independent Excited-State Density Functional Theory for Coulomb Systems
Round 1
Reviewer 1 Report
The manuscript contains an interesting analytical work regarding the coordinate scaling in each individual contribution of time independent functionals to be used for the study of excited states of Coulomb systems (atoms, molecules and solids).
The work is properly discussed and an exhaustive bibliography is provided.
This study could be useful in the design of new functionals for the treatment of excited states of molecules in a time independent density functional theory framework.
I recommend publication in Computation.
I have only one minor point:
1) Equation (14) contains two symbols, namely lambda for occupation numbers and capital K for the HOMO label, that could be redundant with lambda used in the manuscript for the length scaling factor and k (not capital) used for the label of the excited state. I would suggest to change symbols in this equation.
Author Response
I would like to thank the referee for the valuable suggestion. I changed the symbols in Eq. (14).
Reviewer 2 Report
This work results from a continued effort from this author who is well known for her consistent contribution in DFT and beyond. The result is novel and important towards a DFT framework for excite states. I have two minor points for the author to consider. At firstly, from what I know, the technique of coordinating scaling was first proposed by Ghosh and Parr, then Levy and Perdew, and Liu-Parr-Nagy et al. For the comprehensiveness of the literature, I would suggest to add at least one paper for each of these previous groups. Secondly, I understand the correlation energy formula, Eq. (22), is much different from that of the ground-state counterpart, shown by Levy-Perdew. Can the author discuss this result by comparing it with the Levy-Perdew formula for the correlation energy density functional? If one assume Ec is a local functional, using the tricks of the earlier work by Liu and Parr in terms of Taylor expansion, what are the consequences?
Author Response
I would like to thank the referee for the valuable suggestions and changed the manuscript accordingly.
I added 4 papers from the groups recommended by the referee and there is a little change in the Introduction..
Eq. (22) is the definition of the correlation energy. It is the same as it was in the ground-state DFT. One can see it e. g. from Eq. (8) of Ref. 15. I added this to the text above Eq. (22). It is the same as the one Levy and Perdew used earlier. It means that the same “ tricks of the earlier work by Liu and Parr in terms of Taylor expansion” can be applied here. But this should be, of course, carefully checked. This can be the subject of future research. I thank the referee the idea.
