Projector basis and spherical harmonics

[zekunlou]

In deepks/utils.py:L17, variable _coef composes _table and then DEFAULT_BASIS. I couldn't find out how _coef works for basis.

proj_basis = [[0,  # l=0 azimuthal quantum number. Is it?
  [4.0, 1.0, -1.0, 0.0, 0.0, 0.0],  # 4.0 for radial length. Is it?
  [2.0, 0.0, 1.0, -1.0, 0.0, 0.0],  # I have no idea on the 5x5 diag block
  [1.0, 0.0, 0.0, 1.0, -1.0, 0.0],
  [0.5, 0.0, 0.0, 0.0, 1.0, -1.0],
  [0.25, 0.0, 0.0, 0.0, 0.0, 1.0]],
 [1,
  [4.0, 1.0, -1.0, 0.0, 0.0, 0.0],
  [2.0, 0.0, 1.0, -1.0, 0.0, 0.0],
  [1.0, 0.0, 0.0, 1.0, -1.0, 0.0],
  [0.5, 0.0, 0.0, 0.0, 1.0, -1.0],
  [0.25, 0.0, 0.0, 0.0, 0.0, 1.0]],
 [2,
  [4.0, 1.0, -1.0, 0.0, 0.0, 0.0],
  [2.0, 0.0, 1.0, -1.0, 0.0, 0.0],
  [1.0, 0.0, 0.0, 1.0, -1.0, 0.0],
  [0.5, 0.0, 0.0, 0.0, 1.0, -1.0],
  [0.25, 0.0, 0.0, 0.0, 0.0, 1.0]],
]

The furthest code block I arrived at is pyscf/gto/mole/format_basis, and I think that [(l, ((-exp, c_1, c_2, ..), in the function comments might be related to the _coef above.

What are the rules/conventions for this format? And if you know, could you please provide me with more references for such a convention? Thanks!

[y1xiaoc]

Thanks for the question! I have converted this issue into a discussion. You are mostly correct about the basis format. It follows the pyscf internal format which is explained here, except that kappa is omitted. The meaning of the matrix follows the basis set exchange convention. Basically the first column corresponds to exponents of the gaussians and the following columns are the contraction coefficients.

[zekunlou]

Thank you very much! I'll check the corresponding links.