Precision
*********

The quality of the calculation, *given* the selected model Hamiltonian
(density-functional, relativistic features, spin-
restricted/unrestricted, ...) is determined to a large extent by
several technical precision parameters.

The most significant ones are:

"Basis set"
   Obviously, the quality of the basis set may have a large impact on
   the results. As a general rule, minimum and almost-minimum basis
   sets (types SZ and DZ) may be used for pilot calculations, but
   polarization functions should be included (DZP, TZP) for more
   reliable results.

"SCF convergence"
   The self-consistent-field (SCF) and geometry optimization
   procedures terminate when convergence criteria are satisfied. If
   these are set too loosely, the results may carry large *error
   bars*. The default SCF convergence tolerance is tight enough to
   trust the results from that aspect. However, when the SCF procedure
   encounters severe problems an earlier abort may occur, namely if a
   secondary (less stringent) criterion has been satisfied (see the
   key SCF). Although this still implies a reasonable convergence, one
   should be aware that, for instance, the energy may be off by a few
   milli-Hartree (order of magnitude; may depend quite a bit on the
   molecule). It is recommended that in such cases you try to overcome
   the SCF problems in a secondary calculation, by whatever methods
   and tricks you can come up with, rather than simply accept the
   first outcomes. Note: In a geometry optimization the SCF
   convergence criteria are relaxed as long as the geometry
   optimization has not yet converged. This should generally not
   affect the final results: the SCF density and hence the energy
   gradients may be somewhat inaccurate at the intermediate
   geometries, but since these are not a goal in themselves the only
   concern is whether this might inhibit convergence to the correct
   final geometry. Our experiences so far indicate that the
   implemented procedure is reliable in this aspect.

"Geometry convergence"
   This is a far more troublesome issue. Three different types of
   convergence criteria are monitored: energy, gradients and
   coordinates. The energy does not play a critical role. Usually the
   energy has converged well in advance of the other items. The
   coordinates are usually what one is interested in. However, the
   program-estimated uncertainty in the coordinates depends on the
   Hessian, which is not computed exactly but estimated from the
   gradients that are computed in the various trial geometries.
   Although this estimated Hessian is usually good enough to guide the
   optimization to the minimum - or transition state, as the case may
   be - it is far from accurate enough to give a reasonable estimate
   of force constants, frequencies, and as a consequence, neither of
   the uncertainties in the coordinates. An aspect adding to the
   discrepancy between the Hessian-derived coordinate errors and the
   true deviations of the coordinates from the minimum-energy geometry
   is that the true energy surface is not purely quadratic and using
   the Hessian neglects all higher-order terms. The gradients provide
   a better criterion for convergence of the minimizer and therefore
   it is recommended to tighten the criterion on the gradients, rather
   than anything else, when stricter convergence than the default is
   required. The default convergence criteria, in particular for the
   gradients, are usually more than adequate to get a fair estimate of
   the minimum energy. Tighter convergence should only be demanded to
   get more reliable coordinate values (and in particular, when the
   equilibrium geometry needs to be determined as is normally required
   for a frequency run).

"Numerical integration accuracy"
   The BeckeGrid key block (or alternatively the old INTEGRATION key
   block) determines the numerical precision of integrals that are
   evaluated in ADF by numerical integration, primarily the Fock
   matrix elements and most of the terms in the gradients. In
   addition, the integration settings also determine several other
   computational parameters. The demands on numerical integration
   precision depend quite a bit on the type of application. The SCF
   convergence seems to suffer hardly from limited integration
   precision, but geometry convergence does, especially when tight
   convergence is required and also in transition state searches,
   which are generally more sensitive to the quality of the computed
   energy gradients. An extreme case is the computation of
   frequencies, since they depend on differences in gradients of
   almost-equal geometries. Frequency calculations on molecules with
   sloppy modes suggest that a BeckeGrid of "good" quality may be
   required. Note: A large integration value implies that a lot more
   points will be used in the numerical integrals, thereby increasing
   the computational effort (roughly linear in the number of points).
