beta

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beta#

Functions for dealing with beta functions.

jrystal.pseudopotential.beta.beta_sbt_grid(r_grid: List[Float[Array, 'r']], nonlocal_beta_grid: List[Float[Array, 'beta r']], nonlocal_angular_momentum: List[List[int]], g_vector_grid: Float[Array, 'x y z 3'], kpts: Float[Array, 'kpt 3'] | None = None) → List[Float[Array, 'kpt beta x y z']][source]#

Calculate the spherical bessel transform of the beta functions for multiple atoms.

\[eta_l(G) = \int_0^\infty eta(r) j_l(Gr) r^2 dr\]

Return the beta function value of angular momentum values \(l\) at the reciprocal vectors \(G\) per atom

Parameters:

  • r_grid (List[Float[Array, "r"]]) – the r grid corresponding to the beta functions.

  • nonlocal_beta_grid (List[Float[Array, "beta r"]]) – beta values.

  • nonlocal_angular_momentum (List[List[int]]) – angular momentum corresponding

  • functions. (to the beta)

  • g_vector_grid (Float[Array, "x y z 3"]) – reciprocal vectors to interpolate.

  • kpts (Optional[Float[Array, "kpt 3"]]) – k-points. Default is None.

Returns:

A List of jax.array of the beta functions evaluated in reciprocal space grid.

Return type:

List[Float[Array, “kpt beta x y z”]]

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