The Tolman angle ($\theta$), also known as the Tolman cone angle, is a measure of the steric bulk of a ligand, particularly phosphines and phosphites, when coordinated to a metal center. It is widely recognized as the "par excellence descriptor of the steric measure of a phosphine", as highlighted by its recomputation for a wide range of ligands, including simple phosphanes, phosphites, and complex biaryl species used in catalysis.
Understanding the Tolman Cone Angle
Developed by Chad A. Tolman in the 1970s, this concept provides a standardized way to quantify how much space a ligand occupies around a central metal atom. This is crucial in chemistry, especially in coordination chemistry and catalysis, as the size of a ligand significantly impacts:
- The reactivity of the metal center.
- The stability of the metal complex.
- The approach of other molecules (substrates) to the metal.
- The selectivity of a catalytic reaction.
How it's Defined
The Tolman cone angle is defined as the apex angle of a cone with the following characteristics:
- Its apex is located at the center of the metal atom to which the ligand is bonded.
- It encloses all atoms of the ligand out to their van der Waals radii.
- The bond between the metal and the coordinating atom of the ligand (e.g., the P atom in a phosphine) lies along the cone's axis.
Imagine the ligand is a ball attached to the metal by a stick (the metal-ligand bond). The cone angle is the angle needed to completely contain this ball, with the metal at the cone's tip and the stick along the center line.
Significance and Applications
The Tolman cone angle provides a simple, single number that chemists can use to compare different ligands. A larger cone angle indicates a bulkier ligand that occupies more space around the metal center.
| Ligand | Approximate Tolman Cone Angle ($\theta$) |
|---|---|
| $\text{PH}_3$ (Phosphine) | $87^{\circ}$ |
| $\text{PMe}_3$ | $118^{\circ}$ |
| $\text{P(OMe)}_3$ | $107^{\circ}$ |
| $\text{PPh}_3$ | $145^{\circ}$ |
| $\text{P(Cy)}_3$ | $170^{\circ}$ |
| $\text{P(o-Tolyl)}_3$ | $195^{\circ}$ |
Note: Values can vary slightly based on the computational method used.
Practical Examples:
- Catalysis: In catalytic reactions involving phosphine ligands (like Suzuki coupling or hydrogenation), the Tolman angle helps predict how easily the substrate can approach the metal catalyst, influencing reaction rate and product selectivity. Bulky ligands can create a "pocket" that favors a specific orientation of the substrate.
- Complex Stability: Bulky ligands can sterically hinder other ligands from coordinating, influencing the maximum number of ligands a metal can bind or favoring lower coordination numbers.
While the original Tolman model uses an idealized geometric approach, more sophisticated computational methods are now used to calculate cone angles, providing more accurate measures for complex ligands like the bulky biaryl phosphines often used in modern asymmetric catalysis.
The Tolman cone angle remains an essential tool for ligand design and understanding steric effects in coordination chemistry and catalysis.
