Geometries are forgiving, basins are not: a practical guide to optimizing chemical structures

A calculated molecular or materials structure is the input to almost every later number in a computational study, yet the step that produces it is usually reported in one line. Two kinds of failure are distinguished here, and the heuristic that follows is offered with its range of validity. Within a basin of the potential energy surface, and for the stiff modes and well-behaved closed-shell systems covered by the benchmarks reviewed, geometries are forgiving in energy: for well-chosen methods, bond lengths converge to a few tenths of a picometer and rotational constants to a few megahertz, and the coordinate system and Hessian guess mainly change the cost of the optimization; they can also change convergence behavior and, in difficult cases, the stationary point reached. Between basins, the answer can change qualitatively, because a wrong conformer, cluster isomer or polymorph can shift energies and properties by more than a change of functional or basis set in the examples examined. The heuristic fails for properties that depend on the geometry to first order, for very soft modes and weak interactions, and for systems in which the level of theory changes the topology of the surface. Published benchmark data on coordinates and optimizers, local and global search, wave-function and density-functional levels, basis sets and composite methods are replotted in a common graphical style; this does not make them statistically commensurable, and directly comparable results are distinguished from illustrative comparisons across studies. The review covers molecular optimization, conformer and cluster search, transition-structure location and machine-learned potentials, with periodic relaxation treated briefly. Worked examples show where a wrong basin or an unbalanced level changed a conclusion. Universal machine-learned potentials are assessed as pre-optimizers, a reporting standard is proposed, and a decision scheme by system class is given. Where the literature contains no benchmark, this is stated explicitly.