Review JOSS

[scemama]

Hi!

Here are a few comments to help improve the paper (https://github.com/openjournals/joss-reviews/issues/5472):

• [x] line32 : varioationally -> variationally
• [x] line43: the $D^{\uparrow}$ and $D^{\downarrow}$ determinants need to be indexed by $n$. You can do:
• [x] $\sum_n c_n D_n^{\uparrow} Dn^{\downarrow}$, but this would imply a non-unique set of up- or down-determinants. Otherwise you can use $\sum{ij} c_{ij} D_i^{\uparrow} D_j^{\downarrow}$, but I am not sure that this is the representation you are using in the code.
• [x] lines44->64 : for vector quantities, I would use bold face. For example, I would do: $\mathbf{q}_i = \mathbf{r}_i + \sum_{i \ne j} K_{BF} (r_{ij})\,(\mathbf{r}_i - \mathbf{r}_j)$.
• [x] line54: You are using $\omega$ in the backflow expression, but you use also $\omega$ in the expression of the Jastrow line 49. You should use different letter to avoid confusion.
• [x] line67: I would use a dot instead of \times for matrix multiplication of AO with $W_{SCF}^T$
• [x] line86: $\rho$ is commonly used for the one-electron density. For the $N$-electron density, some authors use $\Pi$.
• [x] line163: In the citation of Wheeler, there is some html <tt>
• [x] In the documentation, to test the software cd test should be replaced by cd tests

[scemama]

• [x] You might want also to remove the disclaimer from the README to match with the requirements of JOSS ;-)

[AbdAmmar]

Hello ! In addition to Anthony's comments,

It would be helpful to include further references in Line 25

• [x] Choo et al 2020, DOI: 10.1038/s41467-020-15724-9
• [x] Yang et al 2020, DOI: 10.1021/acs.jctc.9b01132
• [x] Han et al 2019, DOI: 10.1016/j.jcp.2019.108929
• [x] Kessler et al 2021, DOI: 10.1002/adts.202000269
• [x] Inui et al 2021, DOI: 10.1103/PhysRevResearch.3.043126
• [x] Schätzle et al 2021, DOI: 10.1063/5.0032836
• [x] Lin et al 2023, DOI: 10.1016/j.jcp.2022.111765

and in the "Backflow Transformation" section, Line 52

• [x] Schmidt et al 1981, "Title of the Paper," DOI: 10.1103/PhysRevLett.47.807

• [ ] Providing some insight into the computational cost difference between using automatic differentiation and analytical expressions for the calculation of the Laplacian of the Slater determinants would be interesting. This could help readers understand the trade-offs involved in the chosen approach.

[NicoRenaud]

@scemama Thanks a lot for all the corrections, I've implemented all of them in #148 For the determinants I've used $\sum_n c_n D_n^\uparrow Dn^\downarrow$ as it is what I have implemented in the code. I could implement $\sum{ij} c_{ij} D_i^\uparrow D_j^\downarrow$. Would you recommend that ?

@AbdAmmar Thanks a lot for all the references. I've added them all. Computing the Laplacian of the Slaters with automatic differentiation is extremely slow as I would have to compute the full Hessian and extract the diagonal. I can make a small benchmark of that approach compared to the Jacobi trace I'm using by default. Automatic differentiation is used to compute all the derivative wrt the wave function parameters. I don't believe that this is faster than using analytic expression, but you don't have to derive those expression. I will make a small benchmark of the computational performance.

Thanks again to both of you for your input and apologies for the time it took me to work on it Best

Nico

[scemama]

@scemama Thanks a lot for all the corrections, I've implemented all of them in #148 For the determinants I've used

as it is what I have implemented in the code. I could implement

. Would you recommend that ?

Yes, if you have large CI expansions! You would only need to compute the unique set of $D_i^\uparrow$ and $Dj^\downarrow$ and their gradients and Laplacians. Then you can recombine everything to get the total wave function. This his how we obtain in QMC=Chem a $\mathcal{O}(\sqrt{N{det}})$ scaling for near-FCI wave functions. You can have a look at this presentation: http://irpf90.ups-tlse.fr/files/pacifichem.pdf or this paper: https://arxiv.org/abs/1510.00730 we can also have a zoom to if you want more detail :-)

[tonnylou44853]

Hi!

In addition to the comments above, here is a list of typos I found in the docs:

• [x] "Jastro Kernel" should be "Jastrow Kernel" in the second line of the first paragraph in https://qmctorch.readthedocs.io/en/latest/rst/qmctorch.html.
• [x] I believe this should be a LaTeX symbol instead of plain text: :math: K_{ee} in the first paragraph of https://qmctorch.readthedocs.io/en/latest/rst/qmctorch.html#two-body-jastrow-factors?
• [x] First line in https://qmctorch.readthedocs.io/en/latest/notebooks/wfopt.html#Running-the-wave-function-optimization should be 50 steps instead of 250 steps, as it does not matches with the code below.
• [x] https://qmctorch.readthedocs.io/en/latest/notebooks/geoopt.html#Geometry-Optimization: First paragraph, second line "firs" -> "first".
• [x] https://qmctorch.readthedocs.io/en/latest/notebooks/geoopt.html: Cell in last line is empty.

[NicoRenaud]

@scemama Thanks a lot for all the corrections, I've implemented all of them in #148 For the determinants I've used as it is what I have implemented in the code. I could implement . Would you recommend that ?

Yes, if you have large CI expansions! You would only need to compute the unique set of Di↑ and Dj↓ and their gradients and Laplacians. Then you can recombine everything to get the total wave function. This his how we obtain in QMC=Chem a O(Ndet) scaling for near-FCI wave functions. You can have a look at this presentation: http://irpf90.ups-tlse.fr/files/pacifichem.pdf or this paper: https://arxiv.org/abs/1510.00730 we can also have a zoom to if you want more detail :-)

Thanks for the explanation @scemama ! That sounds like something I will have to do indeed :) I won't have too much time to develop new features on qmctorch before the end of the year. But I will pick this up in January ! I will come back to you ! Thanks !

[NicoRenaud]

Hi!

In addition to the comments above, here is a list of typos I found in the docs:

• [x] "Jastro Kernel" should be "Jastrow Kernel" in the second line of the first paragraph in https://qmctorch.readthedocs.io/en/latest/rst/qmctorch.html.
• [x] I believe this should be a LaTeX symbol instead of plain text: :math: K_{ee} in the first paragraph of https://qmctorch.readthedocs.io/en/latest/rst/qmctorch.html#two-body-jastrow-factors?
• [x] First line in https://qmctorch.readthedocs.io/en/latest/notebooks/wfopt.html#Running-the-wave-function-optimization should be 50 steps instead of 250 steps, as it does not matches with the code below.
• [x] https://qmctorch.readthedocs.io/en/latest/notebooks/geoopt.html#Geometry-Optimization: First paragraph, second line "firs" -> "first".
• [x] https://qmctorch.readthedocs.io/en/latest/notebooks/geoopt.html: Cell in last line is empty.

Thanks @tonnylou44853 ! I've made all the change and will merge as soon as the test are ok ! :) Thanks for all the input

[NicoRenaud]

Thanks a lot everyone for all the input !! I'm closing that issue now :)