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.