Atomic and Ionic Radius Characterization in Chemical Systems

Atomic and ionic radii represent fundamental descriptors for the spatial extent of atoms and ions within materials and molecules. Despite their seeming simplicity, precise characterisation of these radii has posed a longstanding challenge owing to the diffuse nature of electron clouds and the variety of definitions employed. Covalent, van der Waals and ionic radii have traditionally been derived from empirical interatomic distances, while quantum-chemical approaches have introduced electron density contours and orbital-based metrics. Recent advances integrate experimental thermodynamic data with high-level computational methods to yield reproducible radius definitions, facilitating consistent comparisons across chemical systems. The resulting characterisations underpin predictions of periodic trends, reactivity patterns, crystal packing and steric effects in catalysis. Furthermore, recognition of anisotropy in ionic shapes and the development of multi-directional steric descriptors have expanded the utility of size metrics in designing functional materials and catalysts. Ongoing efforts aim to unify diverse radius definitions into a coherent framework that bridges empirical observation and theoretical rigour, with significant implications for materials science, inorganic chemistry and molecular engineering.

Research from Nature Portfolio

Recent studies have demonstrated a thermodynamically consistent approach to defining atomic and molecular surfaces via electron density contours. By comparing iso-density surfaces contoured at a cut-off of 0.0016 atomic units with experimental phase-change measurements across a diverse set of molecules, a near-perfect agreement was found, yielding a mean unsigned deviation of 1.6% and a correlation coefficient of 0.995. This work establishes a robust experimental validation for an electron density threshold as a universal descriptor of atomic and ionic boundaries, offering a standardised metric that aligns quantum-chemical evaluations with thermodynamic observables.

Research from all publishers

Theoretical calculations of absolute atomic radii employing Slater orbitals for the principal maximum in the radial distribution function have delivered a consistent set of radii for over 100 elements. These theoretical values reproduce periodic trends, the d-block and f-block contractions, and correlate qualitatively with ionisation potentials, electronegativity, atomic polarizability and chemical hardness. Such orbital-based radii enable prediction of size-dependent physical properties and offer a unified computational framework for atomic size metrics. Additionally, investigations into pyrite-type crystals have revealed that ionic shapes, particularly for p-valence shell chalcogen ions, are better described as anisotropic ellipsoids. By defining parallel and perpendicular radii along high-symmetry axes, accurate interatomic distances in MX₂ compounds can be derived, and the ionic volume emerges as a nearly invariant crystal-chemical constant. In the field of catalysis, a computational workflow utilising electric-field-derived Sterimol parameters has been introduced to assess steric contributions in asymmetric catalysis. By replacing hard-sphere van der Waals radii with an occupied-space metric derived from the molecular electric field, this method retrieves established structure-selectivity relationships and provides a more accurate steric descriptor for highly polarised systems.

Atomic and Ionic Radius Characterization in Chemical Systems publication trend

The graph below shows the total number of articles in atomic and ionic radius characterization in chemical systems across all publications each year (not limited to Nature Index journals).

Technical terms

Atomic radius: A measure of the size of an atom, often defined by covalent or van der Waals boundaries or by electron density contours.

Ionic radius: The effective radius of an ion in a crystal lattice, inferred from interatomic distances and electrostatic considerations.

Iso-density surface: A surface of constant electron density used to delineate atomic or molecular boundaries in computational chemistry.

Thermodynamically effective surface: A representation of atomic or molecular surfaces derived from experimental thermodynamic phase-change data aligned with electron density thresholds.

Sterimol parameters: Multi-directional steric descriptors comprising three distance vectors that quantify the occupied space around a substituent based on size metrics.

Slater orbital: A mathematical approximation of atomic orbitals characterised by exponential decay, used in quantum-chemical calculations of electron distributions.

References

1. Electron iso-density surfaces provide a thermodynamically consistent representation of atomic and molecular surfaces. Nature Communications (2024).
2. Theoretical Calculation of Absolute Radii of Atoms and Ions. Part 1. The Atomic Radii. International Journal of Molecular Sciences (2002).
3. Modeling the Shape of Ions in Pyrite-Type Crystals. Crystals (2014).
4. Computational workflow for steric assessment using the electric field-derived size. Electronic Structure (2023).