:orphan:
 

.. index:: **GRID
.. _**GRID:

========
\*\*GRID
========

The numerical integration scheme uses the Becke partitioning :cite:`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.* :cite:`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 :ref:`GRID_.ATSIZE` keyword, DIRAC
tries to deduce relative atomic sizes from available densities, if it
can find coefficients.

The  **radial integration** employs an exponential grid

.. math::

   r_k=e^{kh};\quad w_k = r_k;\quad S=\sym_{k=-\infty}^{\infty}=w_kf\left(r_k\right)

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

.. index:: .RADINT
.. _GRID_.RADINT:

.RADINT
-------

Specify the maximum error in the radial integration.

*Default:*

::

    .RADINT
     1.0D-13

.. index:: .ANGINT
.. _GRID_.ANGINT:

.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

.. index:: .NOPRUN
.. _GRID_.NOPRUN:

.NOPRUN
-------

Turn off the pruning of the angular grid.

.. index:: .ANGMIN
.. _GRID_.ANGMIN:

.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 :ref:`GRID_.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 :ref:`GRID_.ANGINT` is equivalent to
turning the pruning off.

*Default:*

::

    .ANGMIN
     15

.. index:: .ATSIZE
.. _GRID_.ATSIZE:

.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.

.. index:: .IMPORT
.. _GRID_.IMPORT:

.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.

.. index:: .NOZIP
.. _GRID_.NOZIP:

.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.

.. index:: .4CGRID
.. _GRID_.4CGRID:

.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.

.. index:: .DEBUG
.. _GRID_.DEBUG:

.DEBUG
------

Very poor grid - corresponds to

::

    .RADINT
     1.0D-3
    .ANGINT
     10

.. index:: .COARSE
.. _GRID_.COARSE:

.COARSE
-------

Coarse grid - corresponds to

::

    .RADINT
     1.0D-11
    .ANGINT
     35

.. index:: .ULTRAFINE
.. _GRID_.ULTRAFINE:

.ULTRAFINE
----------

A better grid than default - corresponds to

::

    .RADINT
     2.0D-15
    .ANGINT
     64

.. index:: .INTCHK
.. _GRID_.INTCHK:

.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