On Chemical Validation of Topological Analyses
There is no unique definition of atomic properties, because atoms-in-molecules are not well defined within the domain of quantum mechanics. This has resulted in proliferation of methods for assigning atomic charges and characterizing atoms in molecules. These approaches can be divided into 1) Partitioning the wave-function in Hilbert space (orbital-based methods), 2) Partitioning a descriptor in real space (density-based methods), and 3) Electrostatic potential fitting methods. In this regard, it is desirable to discuss and establish guidelines for developing and assessing atoms-in-molecules and population analysis.
There is much to do in Quantum Chemical Topology (QCT), a field of research with great promise for the analysis of electronic structure. Many of the general Quantum Theory of Atoms in Molecules (QTAIM)-related approaches are useful in a descriptive sense because they produce quantities that can simplify the analysis of complicated densities. Sometimes the utility of these methods and quantities are obvious to the practicing chemist. For example, the Electron Localization Function (ELF), can be readily used for the identification of electrides in crystalline and molecular systems. QTAIM can be used to calculate atomic charges, and it offers an elegant framework for comparing experimental densities with calculations. Unnecessary controversies and conflict have historically arisen when chemists have encountered what they perceive as overclaims regarding the predictive utility of topological analyses. Such criticism should be taken the right way. Not as calls to arms, but rather as constructive motivation to improve, and as a reminder to always look critically at one’s own work.
To advance this field I think we as a community need to become better at validating various methods against observables. Specifically those observables that are relevant to general chemists. For example, stability, reactivity, and structure. Of course, correlation does not mean causality. However, knowledge of correlation between topological quantities and other physical observables, and the limits of these correlations, are nonetheless essential to allow for predictive use of any topological methodology. To extrapolate insight from a density one needs to know:
- What does the topologically obtained quantity [insert favorite] correlate with?
- When does the correlation break down?
- Why does the correlation work here and not there?
If answered thoroughly, questions such as these may help to improve upon the physical interpretation of different QCT approaches, and provide valuable clues that may guide future development efforts.
So the question I ask is: Do we need more focused chemical validation of QCT methodology? Is there any interest in developing common benchmarks and test sets for cross validation of methods? Such test sets and benchmarks need not be limited to QCT. In fact, I wish for the same in the Energy Decomposition Analysis (EDA) field.
For an example of the approach that I advocate, you may look at one article where I attempt to quantify electron localization using “basin partitioning”. I there ask which kind of partitioning of normal ELF basins allow for quantities that correlate with chemistry, and which do not?
Reading material: A Chemically Meaningful Measure of Electron Localization. (Quiz: There is an obvious mistake in one equation. Can you find it?)
I look forward to a fruitful discussion!