Issue 2: Do I Really Need to Perform Stability Analysis?
The iterative self-consistent field (SCF) procedure is at the core of
each HF or KS-DFT calculation to optimize the coefficients of the atomic
basis set. The final coefficient obtained from a converged SCF
calculation correspond to a stationary point of the HF or KS energy
functional. For molecules containing only main‑group elements, the
coefficients almost always correspond to (usually the lowest) minimum
energy solution, but in principle, there is no formal guarantee that
this behavior is universal.158 In fact, for some
problematic molecules—or for poorly chosen initial guesses—the SCF
procedure can finish on an excited state or on a maximum. In these
scenarios, the final wave function is said to be unstable, since it has
a higher energy than the corresponding stable one. In order to make sure
that the lowest-energy SCF solution is reached, we should check its
stability using a stability analysis algorithm, and eventually make sure
to remove the instability before reporting the final result. While in
principle every calculation—even on simple “high-gap” cases—can
erroneously converge to an unstable SCF solution, it becomes crucial to
perform stability analysis for systems that have several low lying
states, such as transition metals.159,160Unfortunately, some of the most popular quantum chemistry software
packages do not use the stability analysis algorithm as a default
procedure for every completed SCF calculation, while a surprisingly
large minority of software even lack such algorithm altogether. This is
a clear indication of the fact that even experienced users often
overlook the issue of the stability of the final solution. Experiment 10
uses several low gap systems, some of them containing transition metals,
to remind the users of the importance of the stability analysis.