We thank you for your handling of our manuscript entitled "DCore: Integrated DMFT software for correlated electrons" and the referee for his/her very careful reading and a lot of feedback. The referee accepts the usefulness/greatness of the DFT+DMFT program (DCore) presented in the manuscript and is satisfied with the quality of the manuscript. The referee explicitly says ``I find the manuscript well written and clear for practitioners in the field''. The referee however provides suggestions/comments for minor revisions for further improving the readability. We examined each suggestion/comment very carefully and made minor revisions throughout the manuscript. We provide a summary of major changes below. In addition, we highlight changes in the enclosed copy of the revised manuscript.

Best regards, Hiroshi Shinaoka, Junya Otsuki, Mitsuaki Kawamura, Nayuta Takemori, Kazuyoshi Yoshimi

List of changes

• Section 2: We have added Figure 1 and explained more technical details of DFT+DMFT calculations. We have added Sec. 2.3 on MPI parallelization and have removed the last subsection in Sec. 2.
• Section 3: We have updated Figure 3 and added a description of the program dcore_pre following the suggestions.
• Section 4: We have made minor updates for Figure 4 and updated the text following the suggestions.
• Section 6.1: We have added more descriptions especially on technical details following the suggestions.
• We have made minor revisions through the manuscript to improve the readability following the suggestions and comments.
• We have updated DCore to version 3.0.0, which supports TRIQS 3.0.x and Python3.

Comment #1-#2

Thank you for pointing out the mistakes. We have updated the manuscript following the comments.

Comment #3-#4

Thank you for pointing out the misleading expression on the charge self-consistent calculations. We have reformulated these sentences as follows.

DCore does not support charge self-consistent calculations [9], which are supported by other programs such as eDMFT and DMFTwDFT. In a charge self-consistent calculation, the DFT effective potential is updated using the density matrix obtained by DMFT calculations. This is essential especially in performing lattice optimization. DCore specializes in the analysis of multi-orbital Hubbard models.

Comment #5

I recommend the authors to spend a paragraph on formulating the problem of the electron structure in a periodic system. Defining notions such as the unit-cell, spin-orbital indices, correlated and non-correlated shells, real space unit-cell coordinates, momentum space k-vectors, etc. before defining he Hamiltonian in the Model section Eqs. (1-2). I think this would make the manuscript more accessible for non-experts.

Thank you for the suggestion. We have added one paragraph at the beginning of Sec. 2.2 to define a lattice, primitive vectors, and Fourier transform.

Comment #6

After Eq. (3) the local interaction is limited to intra-shell interaction, I think it would be in place to stress that it is also assumed to be limited to local interaction in each unit-cell.

Thank you for the suggestion. We have modified the sentence as follows.

... is limited to intra-shell interactions and local interactions in each unit cell.

Comment #7

For the uninitiated condensed matter theorist I think the statement
"All non-interacting orbitals (e.g., deep oxygen orbitals) belong to the non-interacting shell." can be misleading. These electrons in the deep oxygen orbitals are -- in fact -- interacting with the Coulomb interaction, however the interaction is treated on a DFT level rather than DMFT. I recommend the authors to explain the different levels of approximations for the electron-electron interaction used in the correlated and (the in the DMFT treatment) non-interacting shells.

Thank you for pointing out the insufficient explanation of the concept of "non-interacting shell". In Sec. 2.1 of the revised manuscript, we explain the procedure of one-shot DFT+DMFT calculations and the meaning of ``intereacting'' at the DMFT level.

Comment #8--#9

8. Please consider name/define all quantities introduced in Eqs. (4-7) preferably before the equations. 9. Please consider defining in what space the Green's functions and self-energies are matrices in before Eq. (8).

Thank you for the suggestion. We have revised the first sentence of Sec. 2.3 to name all quantities in the equation and to explicitly state that they are defined in the spin-orbital space.

Comment #10

The $\Sigma^\mathrm{imp}$ self-energy is defined in Eq. (7) but not used in Eq. (8-9) please clarify the connection between impurity and lattice self energy.

Thank you for pointing out the unclear point. We have added one more equation to relate the two self-energies as Eq. (10) in the revised manuscript.

Comment #11

I find the statement "The Green’s functions and the self-energies are assumed to be either spin-diagonal or spin-off-diagonal." potentially confusing. It can be interpreted as G and Sigma can only be either purely diagonal or purely off-diagonal. Please consider clarifying the second case with probably? a dense matrix representation in spin-space with both diagonal and off-diagonal components.

Thank you for pointing out the misleading statement. We rephrased this sentence as follows.

The Green's functions and the self-energies are assumed to be either spin-diagonal or dense matrices in the spin space with both diagonal and off-diagonal components.

Comment #12

Since the mixing factor is called $\sigma_\mathrm{mix}$ while $w$ is used in the manuscript in e.q. Eq. (11), please consider changing the manuscript as to agree with the DCore syntax and use $\sigma$ instead.

Thank you for the suggestion. In the revised manuscript, we use $\sigma_\mathrm{mix}$ for the mixing parameter.

Comment #13

In the list of double counting approaches, the "dressed" Green's function is mentioned. Unfortunately I can not find this Green's function defined in the manuscript. Please consider naming the quantities in Eq. (4-7) to increase clarity.

Thank you for the suggestion. We have added a reference to Eq. (7) where this quantity is defined, and have renamed "dressed" to "local" in line with this equation.

Comment #14

I find the spin_orbit flag confusing and potentially misleading. Is its function equivalent to the DFT notion of "collinear" and "non-collinear" calculations? If yes, I recommend the authors to change the flag in DCore to adhere to the DFT community lingo.

Thank you for the suggestion and we appreciate it very much. However, the non-collinear option would be bit ambiguous because this flag could be used for non-magnetic calculations with spin-offdiagonal hoppings. Thus, we would like to consider introducing a new flag name in a future release based on feedback from the user.

Comment #15

On page 8 the DFTTools project is mentioned but not cited, please consider adding a citation there.

Thank you for pointing out the missing reference. We have added references to the paper of TRIQS/DFTTools wherever the DFTTools project is mentioned.

Comment #16

Please note that the indices $\alpha$ and $\beta$ are defined as spin-orbital indices in Eqs. (1-2). I think the definition of the interaction 4-rank tensor on page 8 for the Kanamori interaction breaks this, using the same indices for orbital only indices. Please consider clarifying this.

Think you for pointing out the inconsistency in our notations. On page 8 of the revised manuscript, we explicitly show the form of the kanamori interaction in the two notations to clarify the meaning of the indices.

Comment #17

References for interactions: Please add (original) references for the tree types of interactions, Kanamori, Slater-F and Slater-UJ interactions. In particular I think Table 2 deserves explanation/referencing.

Thank you for the suggestions. We have added references to an original paper and a review article in the caption of Table 2 and in the main text.

Comment #18

Please consider moving the http links, now embedded in the text, to the list of references.

Thank you for the suggestion. Following the suggestion, we have moved all the http links in the main text to the references.

Comment #19

The current http links are pointing at the master-branch documentation. I.e. their content will change as the master-branch evolve. I recommend the authors to use a release branch/tag when linking to the documentation in order for the content to agree with the manuscript also in the future.

Thank you for the suggestion. In the revised manuscript, the tag name, i.e. "v3.0.0", is used when linking to the online documentation.

Comment #20

Technical question: Why is DCore, being a pure python project, using CMake for installation? In my opinion using the Python ecosystem module installation approach would be a little more user-friendly.

Thank you for the technical suggestion on the build system. We have removed CMake from DCore. DCore v3.0.0 is now "pip-installable" as a pure Python package.

Comment #21

On page 13 the pomerol ED solver is mentioned, please consider adding a reference there.

Thank you for pointing out the missing reference. We have added a reference to pomerol where it is mentioned.

Comment #22

In Eq. (20-21) new second-quantized notation is introduced with $d$ operators and $\alpha$, $\beta$ as orbital-only indices, not in line with Eq. (1-2). Please consider making the notation coherent.

Thank you for pointing out the inconsistent notations. We have updated these two equations in line with Eqs. (1-2).

* Section 2: We have added Figure 1 and explained more technical details of DFT+DMFT calculations. We have added Sec. 2.3 on MPI parallelization and have removed the last subsection in Sec. 2.
* Section 3: We have updated Figure 3 and added a description of the program **dcore_pre** following the suggestions.
* Section 4: We have made minor updates for Figure 4 and updated the text following the suggestions.
* Section 6.1: We have added more descriptions especially on technical details following the suggestions.
* We have made minor revisions through the manuscript to improve the readability following the suggestions and comments.
* We have updated DCore to version 3.0.0, which supports TRIQS 3.0.x and Python3.