Numerical Integration

Many integrals in adf are evaluated by numerical integration: Fock matrix elements, several terms in the (bonding) energy, gradients in geometry optimization, and so on. A sophisticated numerical integration procedure is used [104, 105]. It requires only one input parameter which determines the precision of numerical integrals and derives from that the number of integration points.

INTEGRATION accint

accint

A positive real number: the numerical integration scheme generates points and weights such that a large number of representative test integrals are evaluated with an accuracy of accint significant digits. The default for accint depends on the runtype: 4.0 for Single Point runs and simple Geometry Optimizations, including Linear Transits; 5.0 for Transition State searches; 6.0 for the computation of Frequencies; 10.0 in Create runs.

The number of integration points varies strongly with accint, and this determines to a large extent the computational effort. Decreasing accint from 4.0 to 3.0 for instance roughly halves the number of points (this depends somewhat on the molecule).

The defaults should yield good precision for the very large majority of applications. Lower values (3.0 or even 2.0) can be used if precision is not crucial and the purpose is to get an impression. We recommend that you experiment for yourself to get a feel for how results may vary in quality and computing time.

The default in Create mode is very large: 10.0. This is computationally no problem thanks to the simplicity of the single atom case, in particular due to the high symmetry. There is no reason to override the default integration settings when creating basic atoms.