RI_RS

References: Duchemin2019, Duchemin2021

Real-Space Resolution of Identity (RI-RS) method. This approximation replaces the conventional 3-center RI integrals \((\mu\nu|P)\) by a factorized representation on an atom-centered real-space grid with points \(\mathbf{r}_\ell\): \((\mu\nu|P) \approx \sum_\ell \varphi_\mu(\mathbf{r}_\ell) \varphi_\nu(\mathbf{r}_\ell) Z_{\ell P}\). The coefficients \(Z_{\ell P}\) combine the numerical integration weights and the Coulomb potential of the auxiliary basis function \(P\) evaluated at grid point \(\mathbf{r}_\ell\). To reduce the computational cost, only grid points within the sphere \(B^P\) around atom \(P\) are included, i.e. the points with \(|\mathbf{r}_\ell - \mathbf{R}_P| < R_c + r_P\). Here, \(r_P\) is the effective radius of the most diffuse RI auxiliary Gaussian on atom \(P\), at which the basis function magnitude falls below a threshold \(\delta\) (currently controlled through EPS_FILTER). This locality approximation yields a sparse representation of the 3-center integrals and enables reduced computational cost. See details in [Duchemin2019]. [Edit on GitHub]

Mentions: ⭐GW + Bethe-Salpeter equation

Subsections

• GRID_OPTIMIZATION

Keywords

• SECTION_PARAMETERS

• CUTOFF_RADIUS_RL_AO

• CUTOFF_RADIUS_RL_W

• GRID_SELECT

• TIKHONOV

Keyword descriptions

SECTION_PARAMETERS

Type: logical
Default: F
Lone keyword: T
Usage: &RI_RS .TRUE.

Description: Controls the activation of RI-RS in the GW calculation. An empty section, &RI_RS … &END RI_RS, switches RI-RS on with default parameters. [Edit on GitHub]

CUTOFF_RADIUS_RL_AO

Type: real
Default: -1.00000000E+000 [angstrom]
Usage: CUTOFF_RADIUS_RL_AO 8.0

Description: Real-space cutoff radius (in Angstrom) for evaluating the AO basis functions on the RI-RS grid. Override the default radius derived automatically from the most diffuse AO Gaussian on each atom. [Edit on GitHub]

CUTOFF_RADIUS_RL_W

Type: real
Default: -1.00000000E+000 [angstrom]
Usage: CUTOFF_RADIUS_RL_W 20.0

Description: Real-space truncation radius (Angstrom) for the grid-basis G operators in the RI-RS GW self-energy. Default -1.0 disables the truncation (exact grid-basis operators). [Edit on GitHub]

GRID_SELECT

Type: integer
Default: 1
Usage: GRID_SELECT 1

Description: Selection of the atom-centered grid type used in RI-RS optimized by Duchemin and Blase. (1) def2-TZVPP: Available for elements up to the fourth row of the periodic table (see [Duchemin2021]). (2) cc-pVTZ: Available for H, C, N, and O atoms (see [Duchemin2019]). (3) User-provided grids: per-element grid files supplied by the user, read as ri_rs_grid/ in the same format as the built-in sets, with the suffix _rirs.ion. [Edit on GitHub]

TIKHONOV

Type: real
Default: 1.00000000E-008
Usage: TIKHONOV 1.0E-8

Description: Regularization parameter \(\alpha\) used to stabilize the inversion of the grid-overlap matrix \(D\) in the RI-RS method. See Equation (9) in [Duchemin2019]. [Edit on GitHub]