Grid and Dealiasing Function Keywords in the Jaguar Input File

Overview
Examples

The grid and dealiasing function keywords allow you to select from among the various sets of grids and dealiasing functions available in the grid and dealiasing (.grid and .daf) input files, which are described in The Dealiasing Function File and The Grid File for Jaguar Calculations, and from the grids generated within Jaguar. These keywords are used to specify which grid or dealiasing sets correspond to particular descriptions; this correspondence is often indicated by keyword values depending on the order of sets in the grid and dealiasing input files.

Predefined DFT Grids

For DFT calculations, there are various predefined grids available. Grids are used in DFT calculations because analytic evaluation of the integral of the exchange-correlation functional is usually impossible, so the integration is performed with numerical quadrature. As in many SCF codes, Jaguar uses a multi-center numerical integration scheme [277] where numerical integration is performed around each atom using individual radial and angular grids, then integrals on these atomic grids are combined to yield the total integral. As Voronoi volumes are used to partition the space, the integration scheme is independent of the atomic configuration of the system. A typical Jaguar job uses multiple grids during the calculation: for example, to speed up the SCF run, a coarse (or "medium") grid can be used for some of the SCF cycles, while a less coarse (or "fine") grid is used for the SCF cycles near convergence. Likewise, separate grids are also used for the evaluation of gradients and second derivatives. By default these are denser than the "medium" and "fine" grids. Separate grids are also used for CPHF and post-CPHF calculations.

There are two methods for specifying predefined grids:

Method 1

Use the keywords dftgrid, dftgrid_m, dftgrid_f, dftgrid_g, dftgrid_d, dftgrid_p, and dftgrid_c, which accept various forms for the values (seeTable 2). The dftgrid keyword specifies the default to be used for all relevant DFT grids in the calculation. For control over grids in various calculation stages as described above, you can use the dftgrid_x keywords.

Table 1. Description of dftgrid keywords
Keyword	Description
dftgrid	Specifies a single grid that replaces all relevant DFT grids in the calculation. Sets a global default.
dftgrid_m	Grid for initial SCF cycles; default medium
dftgrid_f	Grid for SCF cycles near convergence; default fine
dftgrid_g,	Grid for gradients; default gradient
dftgrid_d	Grid for second derivatives; default der2
dftgrid_p	Grid for CPHF calcuations; default main-cphf
dftgrid_c	Grid for post-CPHF calculations; default post-cphf

All of these keywords can take values as listed in Table 2.

Table 2. Values for dftgrid keywords
Value	Description
N,M	The grid uses N radial shells (Mura distribution) and M Lebedev angular points per shell (minimal pruning)
medium	Predefined grid. See Table 3 for details.
fine	Predefined grid. See Table 3 for details.
gradient	Predefined grid. See Table 3 for details.
ultrafine	Predefined grid. See Table 3 for details.
der2	Predefined grid. See Table 3 for details.
main-cphf	Predefined grid. See Table 3 for details.
post-cphf	Predefined grid. See Table 3 for details.
sg0	SG-0 Grid [309]. 23 radial shells (MultiExp distribution) and 170 Lebedev angular points per shell. Note, for some large atoms, 26 radial shells are used.
sg1	SG-1 Grid [310]. 50 radial shells (Handy distribution) and 194 Lebedev angular points per shell
sg2	SG-2 Grid [311]. 75 radial shells (double exponential distribution) and 302 Lebedev angular points per shell
sg3	SG-3 Grid [311]. 99 radial shells (double exponential distribution) and 590 Lebedev angular points per shell

The SG-X grids use the pruning schemes as they are defined in their related papers. These grids are fairly dense grids (even for SG-0), so Jaguar runs that use them are generally slower than runs that use Jaguar's default grids. The SG-X grids should be used without the pseudospectral approximation (nops=1).

Method 2

Use the grid keywords gdftmed, gdftfine, gdftgrad, gdftder2, and gdftcphf to select predefined grids for the SCF (gdftmed and gdftfine), gradient, second derivative, and CPHF calculations, by setting the value to the grid index. The grids are indexed with negative numbers; the definitions are given in Table 3 with the keyword for which the grid is the default. You can set these keywords to any of the indices listed in the table to change the default grid for a particular calculation stage. These grids are also used for other parts of the calculations, such as the pseudospectral SCF iterations and charge fitting (see Other Grids below).

As an example, to use the −14 grid throughout a geometry optimization, you would set the following keywords:

gdftmed=-14
gdftfine=-14
gdftgrad=-14

Table 3. Jaguar internally defined grids.
Index	Grid Type	Radial Grid	Max Angular Points/Shell	Pruned	Default for Keyword
−8	2nd Derivative	105 points (Mura Dist.)	434 (Lebedev)	Yes	gdftder2
−9	Post CPHF	26 points (Mura Dist.)	Atom Dependent	Yes	gdftcphf
−10	Medium	50 points (Geom. Dist.)	60 (Lebedev)	Yes	gdftmed
−11	Fine	85 points (Geom. Dist.)	194 (Lebedev)	Yes	gdftfine
−12	Gradient	80 points (Geom. Dist.)	590 (Lebedev)	Yes	gdftgrad
−13	Ultrafine	105 points (Mura Dist.)	434 (Lebedev)	Yes
−14	Unpruned	200 points (Mura Dist.)	590 (Lebedev)	Minimal^a
−15	Main CPHF	18 points (Mura Dist.)	Atom Dependent	Yes
−21	Unpruned	200 points (Mura Dist.)	1202 (Lebedev)	Minimal^a
−22	Unpruned	200 points (Mura Dist.)	2702 (Lebedev)	Minimal^a
−23	Unpruned	200 points (Mura Dist.)	5810 (Lebedev)	Minimal^a
^aMinimal pruning means that the number of angular grid points is reduced for radial shells with small radii, to improve numerical stability.

Customized DFT Grids

You can also define your own DFT grids using three keywords, which specify the number of radial shells, the number of angular points per shell, the pruning scheme, and the distribution of the radial shells. The keywords and their settings have the form:

ndfgrdX1=nr
ndfgrdX2=na
idfgrdX=pqq

where:

X is m, f, g, u, d, p, or c, signifying “medium,” “fine,” “gradient,” “ultrafine,” “second derivatives,” “main-CPHF”, and “post-CPHF,” and correspond to grids −10, −11, −12, −13, −8, −15, and −9 (see Table 3 for details)
nr is the number of radial shells
na is the angular grid entry number from Table 1 in The Grid File for Jaguar Calculations
p
- 1—geometric distribution [253], the default for medium, fine, and gradient grids),
- 2—Becke’s Gauss-Chebyshev distribution [254]),
- 3—described in Ref [255])
- 4—the Mura-Knowles distribution [256], the default for the ultrafine, second derivative, CPHF, and grid −14.
qq is a two-digit number denoting the pruning scheme. The values of qq
- 00—the default for the medium grid,
- 11—the default for the fine and gradient grids, and
- 22—turns off pruning.
- 33—the default for the second derivative, CPHF, and ultrafine grids.

The value for ndfgrdX2 is interpreted as an offset, to be added to the angular value for each radial shell that is determined from the pruning scheme. You can get more information about both pseudospectral and DFT grids for a job by setting ip23=2 in the input file.

Other Grids

Table 4 shows the types of grids that can be specified for portions of the calculation that do not involve density functional theory. Generally, these grid types are used for pseudospectral SCF iterations or for charge fitting. The grid definitions correspond to those in Table 3.

The grid-related keywords and their allowed and default values are given in Table 5, where name corresponds to one of the grid types listed in Table 4. As an example, gmedium=2 indicates that the medium grid to be used is the second one listed in the .grid file, while geldens=-3 indicates that an electron density calculation should use a cubic grid.

You can read in your own set of grid points and weights by using gname=-6 in the gen section and the GPTSFILE line at the top of the input file (see Jaguar Input File Format).

Table 4. Pseudospectral, charge-fitting, and electron density grid types
Name^a	Description
coarse	Least expensive, least accurate level
medium	Used for most SCF iterations
fine	Sometimes used for a limited number of iterations
ufine	Ultrafine; most accurate level
grad	Used in gradient computation
lmp2	Grid used for LMP2 energy calculations
lmp2grad	Grid used for LMP2 gradient calculations
charge	Grid used for charge fitting
eldens	Used for electron density calculations
^aThese names are used in the grid-related keywords described in Table 5.

Table 5. Keywords for specification of length scales for sorting of basis functions, grid usage, and dealiasing function usage. name is one of the grid types from Table 4
Keyword	Value	Description	Default for
lname	1	Only one length scale used	lcoarse
	2	Basis functions are sorted into short- and long-range	lmedium, lfine, lufine, lgrad
gname	>0	Specifies which parameter set from `.grid` file should be used for grid (e.g., 2 for second)	gcoarse (1), gmedium (2), gfine (3), gufine (4), ggrad (4), glmp2 (4), glmp2grad (2), geldens (4)
	−1	Use spherical charge fitting grid generated by Jaguar for grid gname	gcharge
	−2	Use cubic charge-fitting grid generated by Jaguar for grid gname	none
	−3	Use cubic electron density grid generated by Jaguar for grid gname	none
	−6	Use grid and weights from file specified by `GPTSFILE` line in input file for grid gname	none
dname	>0	Specifies which dealiasing function from the `.daf` file should be used	dcoarse (1), dmedium (2), dfine (3), dufine (4), dgrad (5)