# **GRID¶

The numerical integration scheme uses the Becke partitioning [Becke1988a]
of the molecular volume
into atomic ones, for which the quadrature is performed in spherical
coordinates. Radial integration is carried out using the scheme proposed
by Lindh *et al.* [Lindh2001],
while the angular integration is handled by a set of highly accurate
Lebedev grids. Note that the Becke partitioning scheme generally uses
Slater-Bragg radii for atomic size adjustments. For the heavier
elements, with their more variable oxidation states, this can lead to
errors. If the user invokes the *.ATSIZE* keyword, DIRAC
tries to deduce relative atomic sizes from available densities, if it
can find coefficients.

The **radial integration** employs an exponential grid

and is specified in terms of step size \(h\), the inner point \(r_1\) and the outermost point \(r_k_H\), chosen to provide the required relative precision \(R\) (equal to the discretization error \(R_D\).

## .ANGINT¶

Specify the precision of the Lebedev angular grid. The angular integration of spherical harmonics will be exact to the L-value given by the user. By default the grid will be pruned. The highest implemented value is 64.

*Default:*

```
.ANGINT
41
```

## .NOPRUN¶

Turn off the pruning of the angular grid.

## .ANGMIN¶

Specify the minimum precision of the Lebedev angular grid after pruning.

```
.ANGMIN
LEBMIN
```

Close to the nucleus, the precision of the angular grid will be less
than L-value given by *.ANGINT*, but it will not be less
than the integer LEBMIN. Note that giving a LEBMIN value greater than or
equal to the L-value given by *.ANGINT* is equivalent to
turning the pruning off.

*Default:*

```
.ANGMIN
15
```

## .ATSIZE¶

Generate new estimates for atomic size ratios for use in the Becke partitioning scheme. Relative sizes for a pair of atoms A and B are calculated from their contribution to the large component density along the line connecting A and B.

## .IMPORT¶

```
.IMPORT
numerical_grid
```

Import previously exported numerical grid.

For debugging you can also create your own grid file. The grid file is formatted - in free format. A grid file for three points could look like this:

```
3
0.1 0.1 0.1 1.0
0.01 0.2 0.4 0.9
9.9 9.9 9.0 0.8
-1
```

The first integer is the number of points, then come the x-, y-, and z-coordinate, and the weight for each point. The last line is a negative integer. Works also in parallel.

You can export the DIRAC grid simply by copying back the file “numerical_grid” from the scratch directory.

## .NOZIP¶

DIRAC will try to remove redundant grid points when symmetry is present. Each reflection plane reduces the number of grid points by a factor of two. With this keyword you can turn this default symmetry grid compression off.

## .4CGRID¶

Include the small component basis in the generation of the DFT grid even if you run a 1- or 2-component calculation.

This can be useful if you want to compare to a 4-component calculation using the identical integration grid.

By default the small component is ignored in the grid generation when running 1- or 2-component DFT calculations.

## .INTCHK¶

Test the performance of the grid by computing the overlap matrix numerically and analyzing the errors. In addition, the error matrix can be printed.

*Default (no test):*

```
.INTCHK
0
```

*Error analysis:*

```
.INTCHK
1
```

*Print error matrix:*

```
.INTCHK
2
```