GRID_OPTIMIZATION

Optimizes RI-RS grid using small local atomic environments. For every atom in the structure, a cluster is formed from all atoms whose distance from the centre atom is smaller than CUTOFF_ATOMIC_CLUSTER. The grid points are optimized such that the corresponding RI-RS three-centre integrals reproduce the analytic integrals: For a cluster \(C_I\), the normalized squared RI-RS error is \(E_I = \frac{1}{N_I} \sum_{P\mu\nu \in C_I} \left|(\mu\nu|P) - \sum_{\mathbf{r}_{A\ell} \in C_I} \phi_\mu(\mathbf{r}_{A\ell}) \phi_\nu(\mathbf{r}_{A\ell}) Z_{A\ell P}\right|^2\). The total objective is the average over all local clusters, \(E_\mathrm{loc} = \frac{1}{N_\mathrm{at}} \sum_{I=1}^{N_\mathrm{at}} E_I\). Starting points are generated on radial-Lebedev grids and selected by diagonal Cholesky decomposition in independent atomic clusters. If the selection reaches numerical rank before the requested grid size, unused points in the central atom’s Voronoi cell are added by geometric maximin distance. Before Voronoi filtering, the candidate grid contains at least max(30, 2 RS_AO_RATIO) times the number of AO functions. RS_AO_RATIO is the sole control of the retained points per atom. The optimization adapts the grid to the chemical environment and composition of the structure and can permit substantially smaller grids. Compact grids often work well for small basis sets, but RS_AO_RATIO should be tuned and converged for the chosen basis sets and chemical system. [Edit on GitHub]

Keywords

• CUTOFF_ATOMIC_CLUSTER

• MAX_ITER

• RS_AO_RATIO

Keyword descriptions

CUTOFF_ATOMIC_CLUSTER

Type: real
Default: 3.00000000E+000 [angstrom]
Usage: CUTOFF_ATOMIC_CLUSTER [angstrom] 3.0

Description: Radius of the atom-centred cluster used to optimize the grid points. All atoms within this distance of the centre atom are included. [Edit on GitHub]

MAX_ITER

Type: integer
Default: 300
Usage: MAX_ITER 300

Description: Maximum number of objective-and-gradient evaluations in the single cooperative Cartesian grid optimization. [Edit on GitHub]

RS_AO_RATIO

Type: real
Default: 7.00000000E+000
Usage: RS_AO_RATIO 7

Description: Number of retained real-space points per atomic-orbital (AO) basis function. For every atom A, the count is \(N_R^A=\lceil\alpha N_{\mathrm{AO}}^A\rceil\), where \(\alpha\) is RS_AO_RATIO and \(N_{\mathrm{AO}}^A\) is that atom’s number of AO functions. [Edit on GitHub]