coordination chemistry A coordination complex is a chemical compound consisting of a central atom or ion, which is usually metallic and is called the ''coordination centre'', and a surrounding array of chemical bond, bound molecules or ions, that are in turn known as ' ...

, the ligand cone angle (θ) is a measure of the steric bulk of a

ligand In coordination chemistry, a ligand is an ion or molecule with a 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 el ...

in a transition metal

coordination complex A coordination complex is a chemical compound consisting of a central atom or ion, which is usually metallic and is called the ''coordination centre'', and a surrounding array of chemical bond, bound molecules or ions, that are in turn known as ' ...

. 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 poin ...

formed with the metal at the vertex of a

cone In geometry, a cone is a three-dimensional figure that tapers smoothly from a flat base (typically a circle) to a point not contained in the base, called the '' apex'' or '' vertex''. A cone is formed by a set of line segments, half-lines ...

and the outermost edge of the van der Waals spheres of the ligand atoms at the perimeter of the base of the cone. 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, DuPont, Du Pont, duPont, or du Pont may refer to: People * Dupont (surname) Dupont, also spelled as DuPont, duPont, Du Pont, or du Pont is a French surname meaning "of the bridge", historically indicating that the holder of the surname re ...

. 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. PR₃. 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 angle on a central atom between two bonds to a bidentate ligand. This ligand–metal–ligand geometric parameter is used to classify chelation, chelating ligands, including those in organometallic ...

, 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: :

\theta = \frac \sum_i \frac

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 where the catalyst is in same phase as reactants, principally by a soluble catalyst in a solution. In contrast, heterogeneous catalysis describes processes where the catalysts and substrate are in d ...

because the size of the ligand affects the reactivity of the attached metal center. In an example, the selectivity of

hydroformylation In organic chemistry, 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 () and a hydrogen ...

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.

References

{{Reflist Tertiary phosphines Stereochemistry Organometallic chemistry Coordination chemistry

Asymmetric cases

Variations

Application

See also

References