Geometry Optimization

No convergence

First of all one should look 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 geometry optimization converged. 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. Here’s 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.

In the next two sections we’ve collected some troubleshooting tips that apply only to the new or only to the old branch. In the last section, we also address a very rare issue with very short bonds that may appear independently of the optimization branch.

New Branch

Are there constraints imposed on the optimization? If yes, then check that the constraints do not break the symmetry. ADF automatically preserves symmetry when the starting structure is symmetric and no Symmetry NOSYM has been specified. This symmetry preservation may conflict with constraints if the constraints are not specified according to symmetry. For example, if two inter-atomic distances are symmetry-equivalent and you freeze one of them, then you should also freeze the other explicitly.

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-degrees 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.

Old Branch

Spurious jumps

Problem: During geometry optimization in Z-Matrix coordinates, the atomic configuration makes a large unrealistic jump.

Possible cause 1: the triplet of atoms to which the current atom is related by the Z-matrix is (almost) co-linear. When, in a geometry step, the triplet passes through co-linearity, the dihedral angle for the current atom should make a discontinuous jump of 180 degrees. This is not checked in the program and the dihedral angle may not get corrected, resulting in a geometric jump of the atom (and hence of all atoms related to it by the Z-matrix).

Cure: Check the triplets of atoms, used in your Z-matrix to define the dihedral angles. If one of them is almost colinear, then redefine the Z-matrix or use Cartesian optimization.

Possible cause 2: the connectivity of the Z-matrix does not reflect some important bonds. Especially when the molecule contains (a large number of) rings, this badly affects the stability of the geometry update step. The reason is basically that computed Cartesian forces are transformed into changes of the curvilinear internal coordinates. The transformation between the two systems of coordinates is non-linear, but mathematically assumed to be linear. This is only a good approximation for small steps.

Cure: Redefine the Z-matrix and/or (if the geometry steps are very large) set a smaller upper bound on the maximum step (key GEOMETRY, subkey step).

Constraints are violated

Problem: constraints are violated: coordinates that were specified as frozen turn out to change during the optimization or coordinates that should remain the same start to differ after a few geometry update cycles.

Possible cause: there is an internal conflict between different demands, usually: symmetry versus constraints. The problem arises easily when a constrained optimization is requested for a molecule with some symmetry while the coordinates were defined with a Z-matrix structure that does not properly reflect the symmetry. Usually the deviations from the requested constraints are small. If they are really large, there might be a bug and you should contact ADF support.

Cure: redefine the Z-matrix and/or use Cartesian optimization (if the constraints are expressible in Cartesians).

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 relativity).