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GEOMETRY
Converge {E=TolE} {Grad=tolG} {Rad=TolR} {Angle=tolA}
..
END
Converge
Convergence is monitored for three items: the energy, the
Cartesian gradients and the estimated uncertainty in the (chosen type of
optimization) coordinates. For the latter, lengths (Cartesian coordinates,
bond-lengths) and angles (bond-, dihedral-) are considered separately.
Convergence criteria can be specified separately for each of these items:
TolE
The criterion for changes in the energy, in Hartrees. Default: 1e-3.
TolG
Applies to gradients, in Hartree/angstrom. Default: 1e-3. Note, the default value has been changed in ADF2008.01, before it was 1e-2.
TolR
Refers to changes in the Cartesian coordinates or bond lengths, depending on in what coordinates you optimize, in angstrom. Default: 1e-2.
TolA
Refers to changes in bond- and dihedral angles, in degrees. This
is only meaningful if optimization takes place in Z-matrix coordinates.
Default: 0.5 degree.
If only a numerical value is supplied as argument for converge, rather than a
specification by name, it is considered to apply to the gradients (only). The
other aspects (energy and coordinates) retain their default settings then.
Remarks:
1. Molecules may differ very much in the stiffness around the energy minimum. Application of standard convergence thresholds without second thought is therefore not recommended. Strict criteria may require a large number of steps, a loose threshold may yield geometries that are far from the minimum as regards atom-atom distances, bond-angles etc. even when the total energy of the molecule might be very close to the value at the minimum. It is good practice to consider first what the objectives of the calculation are. The default settings in ADF are intended to be reasonable for most applications but inevitably situations may arise where they are inadequate.
2. The numerical integration precision parameter accint (see the key INTEGRATION)
should match the required level of convergence in gradients. Gradients are computed
as a combination of various integrals that are evaluated by numerical integration
in ADF. The integral values have a limited precision: roughly speaking the accint value is the number of decimal digits
in the value of the integrals that are correct. As soon as the gradients, which
are supposedly zero at the exact energy minimum, are of the order or 10**(-accint) they will, in worst cases,
become arbitrary and any attempt to continue convergence may not really
improve things. You may even find that, due to the numerical-integration noise,
the geometries start moving around in a random fashion, while the gradients
vary more or less arbitrarily. As a general rule: set the integration value
higher (by at least 1.0) than the
convergence level required for the gradients. Example: if gradients are to
be converged to 1e-3, set integration 4.5 (implying: higher by 1.5 than
the gradients convergence level).
3. The convergence threshold for the coordinates (TolL, TolA) is not a reliable
measure for the precision of the final coordinates. Usually it yields a reasonable
estimate (order of magnitude), but to get accurate results one should tighten
the criterion on the gradients, rather than on the steps (coordinates). The
reason for this is that the program-estimated uncertainty in the coordinates is
related to the used Hessian, which is updated during the optimization.
Quite often it stays rather far from an accurate representation of the true
Hessian. This does usually not prevent the program from converging nicely,
but it does imply a possibly incorrect calculation of the uncertainty in the
coordinates.