gw_ri_rs_compute_z_lp Module Reference

Computes the RI-RS fitting matrix Z_lP. More...

Functions/Subroutines
subroutine, public	compute_z_lp (qs_env, bs_env, ri_rs_grid_points, mat_phi_mu_l, mat_z_lp)
	Computes Z_lP for (1) a tabulated RI basis set or (2) an on-the-fly generated RI basis set.

Detailed Description

Computes the RI-RS fitting matrix Z_lP.

History

09.2026 created Jan Wilhelm 09.2026 moved code by Ritaj Tyagi from gw_ri_rs_non_periodic.F 09.2026 added routine to compute Z_lP for automatic RI optimization

Function/Subroutine Documentation

compute_z_lp()

subroutine, public gw_ri_rs_compute_z_lp::compute_z_lp	(	type(qs_environment_type), pointer	qs_env,
		type(post_scf_bandstructure_type), pointer	bs_env,
		real(kind=dp), dimension(:, :), intent(inout), allocatable	ri_rs_grid_points,
		type(dbcsr_type), intent(inout)	mat_phi_mu_l,
		type(dbcsr_type), intent(out)	mat_z_lp )

Computes Z_lP for (1) a tabulated RI basis set or (2) an on-the-fly generated RI basis set.

  In both cases, the Z_lP coefficients are computed by solving the linear system

    Σ_l' D_ll' Z_l'P = d_lP,

  with D_ll' and d_lP given by

    D_ll' = [Σ_μ ϕ_μ(r_l) ϕ_μ(r_l')]²,

    d_lP = Σ_μν ϕ_μ(r_l) ϕ_ν(r_l) (μν|P).

  For an on-the-fly generated RI basis set, an RI function φ_P may be a contraction of
  Gaussians on neighboring atoms, which requires special computation of d_lP.

Parameters

qs_env	...
bs_env	Band-structure environment containing GW parameters.
ri_rs_grid_points	...
mat_phi_mu_l	...
mat_Z_lP	...

Definition at line 98 of file gw_ri_rs_compute_Z_lP.F.

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