Request for References

[rudin-jiang]

Hello, this piece of code has been very helpful to me. However, it involves quite a few formulas. Could you provide me with some relevant reference materials? Thank you very much.

[NingZhang1]

Hi, I'm glad it has been helpful to you. Regarding the formulas involved, I don't have specific reference materials to share. The repo was developed by following the .ipynb file in the repository at https://github.com/sunqm/pbchf and working through the associated problems.
The main difference between solids and molecules is that the former utilize periodic Gaussian functions. To derive the formulas, you can think periodic Gaussians as a sum of Gaussian functions centered at lattice points, and then apply translation symmetry wherever possible to simplify the expressions.

[rudin-jiang]

Thank you for your explanation. I now have a basic understanding of this code. In the code, we consider 2*nimg periodic shifts, both in positive and negative directions, considering that this part of the basis functions will contribute to the current lattice. I understand this correctly, right?

[NingZhang1]

The periodic Gaussian function can be expressed as a lattice sum of Gaussian functions. When considering the values of the periodic Gaussian within a given cell r, due to the locality of the Gaussian function, we don't need to consider the Gaussian functions over the entire lattice, but rather only those functions that are not far from the given cell.
Consequently, if a Gaussian function centered at r+a has a non-vanishing value on r, then the Gaussian function centered at r-a will also have a non-vanishing value. Hope this will explain what you are considering.