Integral Keyword
Last Update: 12/31/2000

The Integral keyword modifies the method of computation and use of two-electron integrals and their derivatives.

Grid=grid
Specifies the integration grid to be used for numerical integrations. Note that it is important to use the same grid for all calculations where you intend to compare energies (e.g., computing energy differences, heats of formation, and so on). The parameter to this option is either a grid name keyword or a specific grid specification. If a keyword is chosen, then the option name itself may be optionally omitted (i.e., Integral(Grid=FineGrid) and Integral(FineGrid) are equivalent).

The default grid is a pruned (75,302) grid, having 75 radial shells and 302 angular points per shell, resulting in about 7000 points per atom [417]; the value FineGrid is used to specify this grid. Other grids may be selected by giving an integer value N as the argument to Grid.

Grid=UltraFine
requests a pruned (99,590) grid. It is recommended for molecules containing lots of tetrahedral centers and for computing very low frequency modes of systems.

Other special values for this parameter are CoarseGrid, which requests a pruned version of the (35,110) grid, and SG1Grid, a pruned version of (50,194). Note, however, that the FineGrid has considerably better numerical accuracy and rotational invariance than these grids, and they are not recommended for production calculations [417, 301]. Pass0Grid requests the obsolete pruned (35,110) grid once intended for pass 0 of a tight SCF calculation.

Specific grids may be selected by giving an integer value N as the argument to Grid. N may have one of these forms:

• A large positive integer of the form mmmnnn, which requests a grid with mmm radial shells around each atom, and nnn angular points in each shell. The total number of integration points per atom is thus mmm*nnn. For example, to specify the (99,302) grid, use Int(Grid=99302). The valid numbers of angular points are 38, 50 [243], 72 [244], 86, 110 [243], 146, 194, 302 [245], 434 [246], 590, 770, and 974 [247]. If a larger number of angular points is desired, a spherical product grid can be used.

• A large negative integer of the form -mmmnnn, which requests mmm radial shells around each atom, and a spherical product grid having nnn q points and 2*nnn f points in each shell. The total number of integration points per atom is therefore 2*mmm*nnn². This form is used to specify the (96,32,64) grid commonly cited in benchmark calculations: Int(Grid=–96032).

Note, that any value for nnn is permitted, although small values are silly (values of nnn < 15 produce grids of similar size and inferior performance to the special angular grids requested by the second format above). Large values are expensive. For example, a value of 200100 would use 2*200*100*100 or 4 million points per atom!

Raff
Requests that the Raffenetti format for the two-electron integrals be used. This is the default. NoRaff demands that the regular integral format be used. It also suppresses the use of Raffenetti integrals during direct CPHF. This affects conventional SCF and both conventional and direct frequency calculations.

SSWeights
Use the weighting scheme of Scuseria and Stratman [354] for the numerical integration for DFT calculations. The default is BWeights, which uses the weighting scheme of Becke.

BWeights
Use the weighting scheme of Becke for numerical integration.

NoSComp
Turn off symmetry blocking of MO2-electron integrals. NoSymmComp is a synonym for NoSComp.

DPRISM
Use the PRISM algorithm [26] algorithm for spdf integral derivatives. This is the default algorithm.

Rys1E
Evaluate one-electron integrals using the Rys method [248,249,250], instead of the default method. This is necessary on machines with very limited memory.

Rys2E
If writing two-electron integrals, use Rys method (L314) [107,248,249,250]. This is slower than the default method, but may be needed for small memory machines and is chosen by default if regular (non-Rafenetti) integrals are requested (by the NoRaff option).

Berny
Use Berny sp integral derivative and second derivative code (L702).

Pass
Specifies that the integrals be stored in memory via disk, and NoPass disables this. Synonymous with SCF=[No]Pass, which is the recommended usage.

Symm NoSymm
Disables and Symm enables the use of symmetry in the evaluation and storage of integrals (Symm is the default). Synonymous with keywords Symm=[No]Int, which is the recommended usage.

NoSP
Do not use the special sp integral program (311) when writing integrals to disk.

ReUse
Use an existing integral file. Both the integral file and checkpoint file must have been preserved from a previous calculation. Only allowed for single point calculations and Polar=Restart.

WriteD2E
Forces the integral derivative file to be written in HF frequency calculations. Useful only in debugging new derivative code.

IntBufSize=N
Sets the integral buffer size to N integer words. The default value (which is machine-dependant) is generally adequate.

D2EBufSize=N
Sets the integral derivative buffer size to N words.

SCF

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