Prominent Ligand Types in Modern Cross-Coupling Reactions - New Trends in Cross-Coupling: Theory and Applications - page 22

Cone Angle ( q )

R 2

R 1 R 3

P

2.28 Å

M

Figure 2.1 Definition of cone angle.

palladium intermediate (L 1 Pd), which is generally proposed to be the
catalytically active species in most modern cross-coupling processes, with
some exceptions. 8 Steric properties of ligands are often described in terms of
''cone angle'' (y), a parameter introduced by Tolman to measure the physical
space that a ligand occupies (Figure 2.1). 9 The value of y for symmetrically
substituted ligands (cases where for PR 3 all R groups are equivalent) is de-
fined by the angle that is created by a cylindrical cone extending 2.28 Å
(typical Ni- P bond length) from the metal (or other atom center) to the
outermost atoms of the R groups on the ligand using CPK models (space-
filling models, named after the scientists who pioneered the use: Robert
Corey, Linus Pauling and Walter Koltun). For unsymmetrically substituted
ligands, Tolman also described a model for the determination of y by the
summation of the partial cone angles. 9b Thus, an individual partial cone
angle (y i ) is determined for each of the R n substituents (n ¼ 1-3) and the total
cone angle is calculated according to eqn (2.1). Even today, this method is
still widely used for the estimation of ligand bulkiness (Table 2.1).

3 X

3

y ¼ 2

y i
2

(2 : 1)

i ¼ 1

As a representative example of a calculation of y for an unsymmetrical
ligand, the cone angle y of PPh 2 (t-Bu) is calculated as (2/3)(1451/2 þ 1451/
2 þ 1821/2) ¼ 1571.
However, the CPK-based cone angle parameter to quantify the steric
demand imposed by a supporting ligand is not without limitations. Most
ligands do not actually form perfect cones. In addition, when multiple lig-
ands are coordinated to a single metal center, there can be inter-ligand
meshing, resulting in decreased steric demand relative to what one would
predict based on the sum of the individual partial cone angles. Tolman's
model uses several rough approximations: the 2.28 Å M-L bond length
assumption is not necessarily accurate for non-phosphine ligands and
different metal centers, and an idealized tetrahedral geometry (R-P-R bond