Geometry Optimization troubleshooting
*************************************

See also the section on geometry optimization in the AMS manual.

**No convergence**

First of all, one should look at how the energy changed during the
latest ten or so iterations. If the energy is changing more or less in
one direction (increasing or decreasing), possibly with occasional
jumps, then there is probably nothing wrong with the optimization.
This behavior is typical in the cases when the starting geometry was
far away from the minimum and the optimization has a long way to go.
Just increase the allowed number of iterations, restart from the
latest geometry, and see if the optimization converges.

If the **energy oscillates** around some value and the energy gradient
hardly changes, then you may need to look at the calculation setup. We
give some recommendations below.

The success of geometry optimization depends on the accuracy of the
calculated forces. The default accuracy settings are sufficient in
most cases. There are, however, cases when one has to increase the
accuracy in order to get the geometry optimization to converge. First
of all, this may be necessary if you tighten the optimization
convergence criteria. In some cases it may be necessary to increase
the accuracy also for the default criteria. What you can do to
increase the accuracy of gradients:

* Increase the numerical quality to "good"

* Add an ExactDensity keyword or select "Exact" in the "Density used
  in XC-potential" list in the Details:Accuracy panel. This will make
  the calculation 2 or 3 times slower.

* Tighten the SCF convergence criteria, for example, to 1e-8.

Example input with some of these stricter settings using a TZ2P basis
set. ExactDensity is not included here since it will make the
calculation much slower.

   NumericalQuality Good
   Basis
     Type TZ2P
     Core None
   End
   SCF
    converge 1e-8
   End

**Small HOMO-LUMO gap**: check the HOMO-LUMO gap at the last SCF cycle
at a recent geometry. Is it comparable with the changes in the MO
energies between geometries? If yes, then it is possible that the
electronic structure changes between optimization steps, which may
lead to non-convergence. This may indicate a fundamental problem with
the calculation setup. First of all, check that you obtain a ground
state in a single-point calculation. Is the spin-polarization value
correct? Try calculating some of the high-spin states if possible and
see if they have lower energy. If the MO repopulation that is taking
place is between MOs of different symmetry, then you can try freezing
the number of electrons per symmetry using an OCCUPATIONS block.

Are there **constraints** imposed on the optimization? Note that using
constraints may break the symmetry (by AMS), even if the starting
geometry is symmetric and the constraints do not have to break
symmetry.

**Optimization in Cartesian coordinates** usually needs more steps to
converge compared to delocalized. If you haven't tried delocalized
optimization for the system, then you should do it. **Near 180-degree
angles** with optimization in delocalized coordinates. ADF normally
does not have a problem with a near-180-degree valence angle if the
initial value of the angle was larger than 175 degrees or if it is a
terminal bond angle. If the initial angle was larger than 175 degrees
then it gets a special treatment. For example, any torsion angle that
contains the three atoms is removed or replaced with a torsion angle
involving only the two end atoms of the near-180-degree angle. If the
angle defines a terminal bond then two angles in two coordinate planes
are used to define the bond instead of a valence and a torsion angle.
However, if the initial value of the angle was far from 180 degrees
and has become close to it during optimization then optimization may
become unstable, especially if this is an angle connecting large
fragments. In this case, it may be useful to restart geometry
optimization from the latest geometry. As a last resort, you may want
to constrain the angle to a value close, but not equal, to 180
degrees.


Very short bonds
================

If the computed equilibrium geometry appears to exhibit unlikely
values, typically significantly *too short* bond lengths, you may have
run into a basis set problem, in particular (but not only) if the
Pauli relativistic method is applied.

**Problem**: Optimized bond lengths are clearly too short. The energy
may also look suspicious.

**Possible cause 1**: Basis set trouble: onset of Pauli variational
collapse, if you have applied the Pauli relativistic option. Caused by
small (or absent) frozen cores and/or relatively large basis sets,
applied to heavy elements.

**Possible cause 2**: Basis set trouble also, but quite different from
the previous potential cause: you have used relatively *large* frozen
cores. When the atoms approach each other during the optimization and
the frozen cores start to overlap, the energy computation and the
computed energy gradients become more and more incorrect. This is a
result of the inappropriateness of the frozen core approximation,
which indeed assumes that frozen cores of neighboring atoms do not
significantly overlap. Without going into a detailed explanation here,
the net effect is that certain repulsive terms in the energy
computation are missing and hence a spurious tendency to a "core
collapse" arises, yielding too short bond lengths.

**Cure**: Best is to abandon the Pauli method and use the ZORA
approach instead for any relativistic calculation. If for whatever
reason you insist on using the Pauli formalism, apply bigger frozen
cores and, if that doesn't help, reduce the basis set (not by deleting
polarization functions, but by reducing the flexibility of the
occupied-atomic-orbitals space, in particular *s*- and *p*-functions).
Note, however, that large frozen cores can be a cause for trouble by
themselves, irrespective of any relativistic feature. If you have
reason to believe that your frozen cores might be too *large*, given
the resulting bond lengths in your calculation, you have to pick
smaller cores (and hence be very wary of using the Pauli formalism for
any relativitic calculation).
