Ligand cone angle (also known as the Tolman cone angle or θ) is a measure of the size of a ligand. It is defined as the solid angle formed with the metal at the vertex and the hydrogen 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 introduced by Chadwick A. Tolman a research chemist at Dupont.^[1][2][3]

Contents 1 Asymmetric cases 2 Variations 3 Application 4 Cone angle values 5 References

[edit] 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, θ_i/2, are averaged and then doubled to fined the total cone angle, θ. In the case of diphopshines the θ_i/2 of the backbone is approximated as half the chelate bite angle assuming a bite angle of 74, 85, 90 deg. for diphosphines with methylene, ethylene, and propylene back bones respectively.

θ = (2/3) Σθ_i/2

[edit] Variations

The Tolman cone angles assume empirical bond data and defines the perimeter as the maximum possible circumscritption of an idealized free spinning substituent. In contrast the solid-angle concept derives both bond length and the perimeter form empirical solid state crystal structures.^[4][5] There are advantages to each system.

[edit] Application

The concept of cone angle is of practical importance in homogeneous catalysis because the size of the ligand affects the reactivity of the attached metal center. In a famous example, the selectivity of hydroformylation catalysts is strongly influenced by the size of the coligands.

[edit] Cone angle values

Cone angles of common phosphine ligands in degrees:

ligand	angle (deg)
PH3	87
PF3	104
P(OCH3)3	107
dmpe	107
depe	115
P(CH3)3	118
dppm	121
dppe	125
dppp	127
P(CH2CH3)3	132
dcpe	142
P(C6H5)3	145
P(cyclo-C6H11)3	170
P(t-Bu)3	182
P(C6F5)3	184
P(2,4,6-Me3C6H2)3	212

One remarkable features become clear from these data: some ligands occupy more than half of the coordination sphere of a metal center.

[edit] References

1. ^ Tolman, Chadwick A. (1970-05-01). "Phosphorus ligand exchange equilibriums on zerovalent nickel. Dominant role for steric effects". Journal of the American Chemical Society 92 (10): 2956-2965. doi:10.1021/ja00713a007. http://dx.doi.org/10.1021/ja00713a007. Retrieved 2009-12-04. 
2. ^ Tolman, C. A.; W. C. Seidel, L. W. Gosser (1974-01-01). "Formation of three-coordinate nickel(0) complexes by phosphorus ligand dissociation from NiL4". Journal of the American Chemical Society 96 (1): 53-60. doi:10.1021/ja00808a009. http://dx.doi.org/10.1021/ja00808a009. Retrieved 2009-12-04. 
3. ^ Tolman, C. A. (1977). "Steric Effects of Phosphorus Ligands in Organometallic Chemistry and Homogeneous Catalysis". Chem. Rev. 77: 313–48. doi:10.1021/cr60307a002. 
4. ^ Immirzi, A.; A. Musco (1977). "A method to measure the size of phosphorus ligands in coordination complexes". Inorganica Chimica Acta 25: L41-L42. doi:10.1016/S0020-1693(00)95635-4. http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TG5-43B8S8H-KF&_user=10&_coverDate=12%2F31%2F1977&_rdoc=60&_fmt=high&_orig=browse&_srch=doc-info(%23toc%235245%231977%23999749999%23253901%23FLP%23display%23Volume)&_cdi=5245&_sort=d&_docanchor=&_ct=107&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=59cd327789cffac36f7a8627f88eaec5. Retrieved 2009-12-04. 
5. ^ Niksch, Tobias; Helmar Görls, Wolfgang Weigand (2009). "The Extension of the Solid-Angle Concept to Bidentate Ligands". European Journal of Inorganic Chemistry 9999 (9999): NA. doi:10.1002/ejic.200900825. http://dx.doi.org/10.1002/ejic.200900825. Retrieved 2009-12-04.