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 sloppy 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 by far not 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 a preliminary for a Frequencies run).
Numerical integration accuracy
The key INTEGRATION determines
the numerical precision of integrals that are evaluated in ADF by numerical
integrals, 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 NumInt precision value of 6.0 may be required. We recommend at least 5.0 in
TS searches and in tricky optimizations, and 4.0 in normal optimizations. For
optimizations with user-set convergence criteria we recommend to set the integration precision
at least 1.5 higher than the requested level of convergence for the
gradient. For examples, a convergence threshold of 1e-3, should be combined
with integration=(3+1.5)=4.5
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).
However, in optimizations and TS searches, the program will internally reduce
the integration settings
as long as the geometry is far from convergence, so the costs in
intermediate geometry steps may not so large. See the key INTEGRATION.
