What is it about?
For decades, chemists have used the Tolman cone angle to describe the steric demand of phosphine ligands in transition-metal complexes. Originally, these cone angles were derived from idealised molecular models and assumed fixed ligand geometries. In this work, we introduced a practical method for determining Tolman cone angles directly from experimentally determined crystal structures. By analysing more than 4,000 transition-metal complexes from the Cambridge Structural Database, we showed that ligand steric properties are not fixed constants but vary with molecular conformation, the coordinated metal centre and the surrounding chemical environment. Rather than replacing Tolman's concept, this work extended it from an idealised geometric model to an experimentally derived structural descriptor. The statistical analysis revealed that even identical ligands can exhibit a surprisingly broad distribution of cone angles—and may even adopt different cone angles within the same complex. Looking back, the study represents an early example of extracting chemically meaningful descriptors from large experimental datasets. Highlights - Development of a practical method for determining Tolman cone angles directly from crystallographic data. - First large-scale statistical analysis of ligand cone angles based on more than 4,000 experimentally determined transition-metal complexes. - Demonstration that ligand steric demand varies with molecular conformation, coordination environment and metal identity. - Early example of data-driven descriptor development using crystallographic databases. - Improved understanding of steric effects in homogeneous catalysis.
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Why is it important?
Catalysis depends strongly on the steric environment around the metal centre. Reliable steric descriptors are therefore essential for understanding catalyst performance and designing improved ligand systems. This work demonstrated that experimentally observed molecular structures provide a richer and more realistic description of ligand steric effects than idealised models alone. It showed that steric descriptors should be regarded as statistical quantities rather than fixed molecular constants. The study also demonstrated the potential of large crystallographic databases as quantitative research tools—an idea that has since become central to cheminformatics, computational chemistry and data-driven catalyst design. This work, published in 1995, anticipated today's widespread use of large experimental datasets to derive molecular descriptors and establish structure–property relationships.
Perspectives
When this work began, analysing thousands of crystal structures was far from routine. I downloaded crystallographic data during the day and let my first laptop perform the calculations overnight. At the time, this seemed like an ambitious computational exercise. Looking back, it is fascinating to see that the project anticipated many ideas that today fall under the umbrella of data-driven chemistry and materials informatics. It demonstrated that large experimental databases could be mined to derive chemically meaningful molecular descriptors - an approach that has since become an essential strategy in modern chemical research.
Prof. Dr. Thomas Ernst Müller
Ruhr-Universitat Bochum
Read the Original
This page is a summary of: Determination of the Tolman cone angle from crystallographic parameters and a statistical analysis using the crystallographic data base, Transition Metal Chemistry, December 1995, Springer Science + Business Media,
DOI: 10.1007/bf00136415.
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