No convergence

Problem: The SCF procedure does not converge, the errors of successive cycles don't diminish. This may be due to any of a large number of causes. Some of the more frequently occurring:

Possible Cause 1: Electrons are hopping back and forth between two (or more) spatially very different orbitals at successive cycles. The reason that this may happen is that in dft virtual (empty) one-electron orbitals tend to have a too-low orbital energy compared to the occupied ones, so that, if the true HOMO-LUMO gap is small enough, the computed spectrum may produce an empty orbital below an occupied one. Consequently, on the next SCF cycle the program may assign electrons according to the aufbau principle (say) and hence put electrons in orbitals that were empty on the previous cycle, and vice versa. On the next cycle, however, the now-occupied orbital gets a higher energy and the energy ordering is reversed again, resulting in re-adjusting the assignment of electrons. This may lead to strong oscillations and non-convergence.

Cure 1: Add a NewDIIS keyword anywhere in the input file.

NEWDIIS

This keyword will turn on a new (experimental) DIIS procedure during SCF that may help with reaching convergence. If this does not help, try the Cure 2 below.

Cure 2: Apply the feature keeporbitals (key OCCUPATIONS), to let the program try to keep orbitals occupied that are spatially similar over subsequent cycles, rather than assigning electrons according to energy ordering.
Often one can converge a system in which one equally occupies the problematic orbitals in a spin-restricted calculation. One can then use the TAPE21 from this calculation as a starting point for the next calculation with the keeporbitals feature (key OCCUPATIONS).
You may also apply strong damping (option mix, key SCF), and suppress the DIIS procedure (key SCF, option DIIS, specifications ok and cyc): all these tricks may help to let the program operate more carefully (and more slowly) in SCF updating. Note that the default SCF cycle at which the DIIS will start is rather low. This value can be increases with the specification cyc in the option DIIS of the key SCF.
For very problematic cases one can use the option smearq of the key OCCUPATIONS to smear the electrons out over orbitals that lie around the fermi level and that are close in energy. One can then use the TAPE21 from this calculation as a starting point for the next calculation with a lower vale of the smearq parameter, etecetera. Note that this may introduce fractional occupation numbers.

Possible Cause 2: You have put a wrong number of (valence) electrons in the system, so that you are, for example, trying to compute a highly ionized system. Although this should in principle not always give rise to SCF problems, it turns out to happen often in practice.

Cure: Check that the net total charge of the molecule is correct.
If you want to compute a strongly charged system that seems to cause SCF problems, try to use the Keeporbitals feature (key OCCUPATIONS). See also previous cure.

Remark: In case of SCF convergence problems, always check carefully whether it is a technical problem or a physical one. Technical problems may be addressed with various SCF strategy parameters.
More often you'll find it is in fact a physical problem. The system at hand may have two or more configurations that are competitive in energy, so that a one-determinant wave function approach is not suitable anyway, even within DFT. In such a case you should reconsider what you want in fact to be computed.