![ConeAng](https://upload.wikimedia.org/wikipedia/commons/a/a6/ConeAng.png)
In
coordination chemistry
A coordination complex consists of a central atom or ion, which is usually metallic and is called the ''coordination centre'', and a surrounding array of bound molecules or ions, that are in turn known as ''ligands'' or complexing agents. Many ...
, the ligand cone angle (a common example being the Tolman cone angle or ''θ'') is a measure of the
steric bulk of a
ligand
In coordination chemistry, a ligand is an ion or molecule (functional group) that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's electr ...
in a transition metal
coordination complex
A coordination complex consists of a central atom or ion, which is usually metallic and is called the ''coordination centre'', and a surrounding array of bound molecules or ions, that are in turn known as ''ligands'' or complexing agents. Many ...
. It is defined as the
solid angle
In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point.
The poi ...
formed with the metal at the vertex and the outermost edge of the
van der Waals spheres of the ligand atoms at the perimeter of the cone (see figure). Tertiary
phosphine ligands are commonly classified using this parameter, but the method can be applied to any ligand. The term ''cone angle'' was first introduced by
Chadwick A. Tolman, a research chemist at
DuPont
DuPont de Nemours, Inc., commonly shortened to DuPont, is an American multinational chemical company first formed in 1802 by French-American chemist and industrialist Éleuthère Irénée du Pont de Nemours. The company played a major role in ...
. Tolman originally developed the method for phosphine ligands in nickel complexes, determining them from measurements of accurate physical models.
Asymmetric cases
The concept of cone angle is most easily visualized with symmetrical ligands, e.g. PR
3. But the approach has been refined to include less symmetrical ligands of the type PRR′R″ as well as diphosphines. In such asymmetric cases, the substituent angles' half angles, , are averaged and then doubled to find the total cone angle, ''θ''. In the case of diphosphines, the of the backbone is approximated as half the chelate
bite angle
In coordination chemistry the bite angle is the ligand–metal–ligand bond angle of coordination complex containing a bidentate ligand. This geometric parameter is used to classify chelating ligands, including those in organometallic complexes ...
, assuming a bite angle of 74°, 85°, and 90° for diphosphines with methylene, ethylene, and propylene backbones, respectively. The Manz cone angle is often easier to compute than the Tolman cone angle:
:
Variations
The Tolman cone angle method assumes empirical bond data and defines the perimeter as the maximum possible circumscription of an idealized free-spinning substituent. The metal-ligand bond length in the Tolman model was determined empirically from crystal structures of tetrahedral nickel complexes. In contrast, the solid-angle concept derives both bond length and the perimeter from empirical solid state crystal structures. There are advantages to each system.
If the geometry of a ligand is known, either through crystallography or computations, an exact cone angle (''θ'') can be calculated. No assumptions about the geometry are made, unlike the Tolman method.
Application
The concept of cone angle is of practical importance in
homogeneous catalysis
In chemistry, homogeneous catalysis is catalysis by a soluble catalyst in a solution. Homogeneous catalysis refers to reactions where the catalyst is in the same phase as the reactants, principally in solution. In contrast, heterogeneous catalysi ...
because the size of the ligand affects the reactivity of the attached metal center. In an example, the selectivity of
hydroformylation
Hydroformylation, also known as oxo synthesis or oxo process, is an industrial process for the production of aldehydes from alkenes. This chemical reaction entails the net addition of a formyl group (CHO) and a hydrogen atom to a carbon-carbon d ...
catalysts is strongly influenced by the size of the coligands. Despite being
monovalent, some phosphines are large enough to occupy more than half of the
coordination sphere
In coordination chemistry, the first coordination sphere refers to the array of molecules and ions (the ligands) directly attached to the central metal atom. The second coordination sphere consists of molecules and ions that attached in various ...
of a metal center. Recent research has found that other descriptors—such as percent buried volume—are more accurate than cone angle at capturing the relevant steric effects of the phosphine ligand(s) when bound to the metal center.
See also
*
Bite angle
In coordination chemistry the bite angle is the ligand–metal–ligand bond angle of coordination complex containing a bidentate ligand. This geometric parameter is used to classify chelating ligands, including those in organometallic complexes ...
*
Steric effects (versus electronic effects)
*
Tolman electronic parameter
The Tolman electronic parameter (TEP) is a measure of the electron donating or withdrawing ability of a ligand. It is determined by measuring the frequency of the A1 C-O vibrational mode (ν(CO)) of a (pseudo)-C3v symmetric complex, Ni(CO)3by inf ...
References
{{Reflist
Tertiary phosphines
Stereochemistry
Organometallic chemistry
Coordination chemistry