Ligand descriptor analysis in nickel-catalysed hydrocyanation: A combined experimental and theoretical study

Article abstract of DOI:10.1002/adsc.200404363

The problem of choosing the 'right chelating ligand' for a homogeneously catalysed reaction is outlined. A model is introduced that combines mechanistic information and ligand descriptors. This model is used together with automated synthesis tools to study the structure-activity relationship in a diverse set of forty-two ligands, and extract information on active regions in the catalyst space. The concept is demonstrated on nickel-catalysed hydrocyanation, using bidentate phosphine and phosphite ligands. The charge at the ligating atoms, the rigidity of the molecules, the steric crowding around the Ni atom, and the bite angle are found to be the most important descriptors. A comparison is made with literature hydrocyanation data and approaches for designing new homogeneous catalysts are discussed.

Full text of DOI:10.1002/adsc.200404363

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Ligand Descriptor Analysis in Nickel-Catalysed Hydrocyanation:
A Combined Experimental and Theoretical Study
Enrico Burello,a Philippe Marion,b Jean-Christophe Galland,b Alex Chamard,b
Gadi Rothenberga,*
a
vanꢀt Hoff Institute of Molecular Sciences, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam,
The Netherlands
Fax: (þ31)-20-252-5604, e-mail: gadi@science.uva.nl
b
`
Rhodia, Centre de Recherches de Lyon, 85, Rue des Freres Perret, BP62, 69192 Saint Fons Cedex, France
Received: November 26, 2004; Accepted: March 8, 2005
Abstract: The problem of choosing the ꢀright chelat- charge at the ligating atoms, the rigidity of the mole-
ing ligandꢁ for a homogeneously catalysed reaction cules, the steric crowding around the Ni atom, and the
is outlined. A model is introduced that combines bite angle are found to be the most important descrip-
mechanistic information and ligand descriptors. This tors. A comparison is made with literature hydrocya-
model is used together with automated synthesis tools nation data and approaches for designing new homo-
to study the structure-activity relationship in a diverse geneous catalysts are discussed.
set of forty-two ligands, and extract information on
active regions in the catalyst space. The concept is Keywords: adiponitrile; combinatorial catalysis; data
demonstrated on nickel-catalysed hydrocyanation, us- mining; homogeneous catalysis; molecular descrip-
ing bidentate phosphine and phosphite ligands. The tors; QSAR
Introduction
was used to preselect candidates from large ꢀvirtual li-
brariesꢁ of monodentate ligands.[13] In this paper, we ex-
Social and legislative demands for sustainable develop- tend the work to reactions catalysed by bidentate li-
ment in the 21st century is increasing the incentives for gands, presenting descriptor models for nickel-catalysed
developing ꢀgreenꢁ chemical processes. In many cases, hydrocyanation. We study the structure-activity rela-
this can be achieved by converting existing stoichiomet- tionship in a diverse set of ligands, and validate the mod-
ric protocols into catalytic ones. The Metolachlor proc- el by comparing the results to existing mechanistic find-
ess[1] and the clean synthesis of Ibuprofen[2] are just ings. As this model gives quantitative information, it can
two examples of the possible impact that homogeneous be used to indicate active regions in the catalyst space.
catalysis can have on the fine-chemical industry, provid-
ing that the right ligand/metal combination is found.
Unfortunately, that last proviso is much easier said Results and Discussion
than done. The problem of finding ꢀgoodꢁ ligands is
akin to searching for something in a haystack. It is not
necessarily a needle, but it is small enough to rule out
Choosing Descriptors for Chelating Ligands
an exhaustive search of the catalyst space. This is true
even when synthesis robots are used – it is impossible Chelate-forming bidentate ligands participate in numer-
to synthesise and test all combinations.[3–5] It is possible, ous types of homogeneous catalytic reactions, e.g., hy-
however, to narrow the search space using mechanistic droformylation,[14] hydrocyanation,[15] peroxide decom-
information and structure/activity relationships position,[16] and cross-coupling.[17] In most cases, fine-
(SARs).[6–12] A model can then be used to target these tuning of the ligandsꢁ steric and electronic properties is
regions that contain, hopefully, the best catalysts. Feed- essential.[18] At first, it may seem that the number of var-
back of experimental data into the model can enable an iables that determines the activity of a ligand-metal
iterative search of the catalyst space.
complex is large, but in fact the catalytic properties of
Recently, we showed that by combining mechanistic a bidentate ligand can be adequately described using a
information with molecular descriptors it is possible to few well-chosen molecular descriptors.[19–21] It is impor-
build a model for Heck cross-coupling reactions cata- tant to emphasise that these descriptors should prefera-
lysed by monodentate phosphine ligands.[11] This model bly represent physico-chemical characteristics that per-
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DOI: 10.1002/adsc.200404363
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Enrico Burello et al.
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tain to mechanistic information (i.e., the descriptors
The bite angle varies during the catalytic cycle, as con-
should tally with ꢀchemical intuitionꢁ). For example, firmed by many mechanistic studies – a ꢀgood ligandꢁ is
the complexation reaction of a ligand to a metal centre one that can support the metal throughout the cycle, pre-
leads to the concept of bite angle.
venting the elimination pathways. As ligands can adopt
We will consider bidentate ligands as assemblies of geometries with energies slightly above that of the mini-
two parts: a backbone that connects the ligating atoms, mised structures, we introduce a second variable that
and the R groups attached to these ligating atoms. We measures the range of bite angle accessibility (Figure 1,
then divide the ligand descriptors into three classes:
bottom). This flexibility parameter, a, is calculated by
a) chelating effect-related descriptors that provide in- fixing the bite angle of ligands to standard values (908,
formation about the size, flexibility and conforma- 1008, 1108, 1208 and 1308) and minimising the constrain-
tional changes of the ligand upon complexation ed structures. The result is a parabolic energy potential
with the metal;
that depends on the bite angle. The flexibility a is the sec-
b) steric descriptors that pertain to the shape of the li- ond derivative of this polynomial.
gands and the substrate accessibility to the metal
centre; and
We use two descriptors to account for the changes that
result from the ligand/metal binding: DEbind is the energy
c) electronic descriptors that measure the charge dis- difference between the ꢀfree ligandꢁ and the complex,
tribution and the orbital energies at the ligating and Dd is the difference in the inter-atomic distance be-
atoms.
tween the ligating atoms between the ꢀfree ligandꢁ and
the complex. These two descriptors reveal to what ex-
tent a ligand adopts a chelating conformation before
binding to the metal.
Descriptors Related to the Chelating Effect
The bite angle[22] (a) was one of the first parameters em-
ployed to show a structure-activity correlation of chelat- Steric Descriptors
ing ligands in homogeneous catalysis.[23–26] This descrip-
tor calculates the angle between the metal and the two This class includes descriptors such as the molecular vol-
ligating atoms. Its value is a compromise between the li- ume (V) and surface (S) which are commonly used to
gandsꢁ preferred bite angle and the type and number of d characterise the shape of ligands, as well as the cone an-
orbitals available from the metal (Figure 1, top).
gle (V),[27,28] and the sphere occupation (Socc).[29–31] This
last descriptor gives the free accessible space left by a li-
gand after complexation with a metal centre and esti-
mates the ability of that complex to coordinate an addi-
tional substrate (e.g., during an oxidative addition step).
It is related to the size of the ꢀreaction pocketꢁ.
We also calculated the solid angle, the radius at the li-
gandꢁs maximal solid angle and related properties.[29–31]
These descriptors were calculated both for the backbone
and the ligand structures (a full list of the descriptors is
given in Table 1 in the Experimental Section).
Electronic Descriptors
Several studies were performed to separate the elec-
tronic and the steric effect of ligands.[32] Spectroscopic
values and pKa values of phosphines are examples of fre-
quently employed parameters. Here we used the charg-
es of ligating atoms and the HOMO, LUMO and enthal-
py of formation energies (calculated using PM3 semi-
empirical methods, vide infra) as well as dipole mo-
ments. The Mulliken and the electrostatic charges
were also calculated for both ligating atoms at the
ꢀfree ligandꢁ and at the complex conformations.
Figure 1. (Top): The bite angle (a) is the angle formed when
a bidentate ligand coordinates to a metal centre; (bottom) A
flexibility profile showing the energy change vs. the bite angle
(a second degree polynomial function). In this example,
square planar co-ordination structures (a¼908) are disfav-
oured (10 kcal above the minimum). Tetrahedral and trigonal
bipyramidal structures are closer to the minimum and there-
fore more likely to occur.
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An Experimental Example: Catalytic Hydrocyanation
of 4-Pentenenitrile
In this mechanism, the catalyst precursor 1 binds a bi-
dentate ligand to enter the catalytic cycle. It undergoes
both an oxidative addition with HCN and an olefin in-
The nickel-catalysed hydrocyanation of pentenenitrile sertion with 4PN to yield intermediate 4. Olefin reduc-
[Eqs. (1)–(5)] is one of the best examples of homogene- tion leads to structure 5, which then eliminates the dini-
ous catalysis on an industrial scale.[15,18,33–35] Scheme 1 trile product, generating species 2 (or 3) and completing
shows a simplified mechanism for the hydrocyanation the catalytic cycle. Intermediates are stabilised by
ꢀ
ꢀ
of pentenenitrile using bidentate ligand Ni complexes, P Ni P bite angles of 1208 (in trigonal compounds),
analogous to the one proposed by Freixa and van Leeu- 1098 [in the tetrahedral Ni(0) species], and 908 for the
wen for the case of styrene.[24]
allyl, alkyl or hydrido cyano Ni(II) complexes.
Using a parallel reactor system, we screened 42 biden-
tate ligands in a search for the optimal linear:branched
hydrocyanation product ratio ADN:(MGNþESN). A
selection of these ligand structures is shown below
(structures 6–21). Most of the ligands employed in this
study are commercially available and represent a di-
verse set of structures that include biphosphines, biphos-
phites and {P,N,S} ligands. When one has to start almost
at point zero, it is preferable to include as many ligand
families as possible. This is done both to sample different
catalyst options as well as to obtain a model that is able
to screen a broad range of structural variations. For all
the ligands we calculated a total of 39 chelating, steric,
and electronic descriptors (Table 1). The calculation
yields the model input, a two-dimensional matrix where
each row corresponds to an observable (a ligand) and
each column is a descriptor. From the experimental re-
sults we obtain the figure of merit (in this case, % yield
of the desired product, ADN). Yield values range from a
minimum of 0% to a maximum of 72% conversion. The
Scheme 1. Catalytic cycle for pentenenitrile hydrocyanation.
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Figure 3. Descriptors loadings plot. This plot shows the de-
gree of correlation between descriptors. Charge (q) and steric
descriptors are clustered, while the other descriptors are
more scattered (i.e., uncorrelated).
Figure 2. Score plot of bidentate ligands. Compounds are
plotted in the first two principal components, which retain
61% of the information contained in the original descriptors
(R2 ¼0.61). The ligands cluster into biphosphine and biphos-
phite structures (some N and S ligands are included in the
first group). The clustering reflects different charge and steric
properties between the two classes.
alysed: biphosphines and biphosphites (the biphos-
phines group includes also some N and S ligands). The
standard deviation and the average values in the dataset descriptors that influence most this type of clustering
are 16.3 and 9.6, respectively. Two-thirds of the reactions are the charge at the ligating atoms and the sterics of
resulted in a poor yield (0–10%), and only three ligands the molecules as shown in Figure 3, where a correlation
gave >50% yield.
structure between properties is given by plotting the var-
We then used principle components analysis (PCA) to iable loadings of the first two principal components. We
reduce the rank of the problem. PCA creates an irredu- observe clusters for some descriptors, such as the charge
cible “ligand profile”, a minimal representation of the and the steric ones. Others, e.g., the bite angle, the flex-
structural changes among the set of ligands. Using 2, 4, ibility and the HOMO and LUMO energies are more
and 8 PCs we could explain 61%, 83%, and 99% of the scattered.
variance in the data, respectively. Figure 2 shows the li-
From these correlations we see that bidentate ligands
gand representation using the first two principal compo- can be represented by a reduced set of dimensions, the
nents as axes (cumulative variation R2 ¼61%). Two clus- characterisation of which requires minimal information.
ters are observed, reflecting the type of compounds an- Moreover, the score plot in Figure 2 indicates the com-
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poundꢁs position in the catalyst space and estimates the for highly stable complexes during the catalytic cycle
degree of similarity between them. In other words, each and confirms experimental findings which show that rig-
time you introduce a new ligand, you can see which di- id and large bidentate ligands are effective in catalytic
rection you are taking in the catalyst space.
hydrocyanation.[14] Compounds with rigid backbones,
such as the Xantphos-type ligands 14–16, where the do-
nor atoms are well oriented to form the metal complex,
induce small variations in the bite angle and therefore
adopt the desired binding mode. When phosphites are
Variable Importance (VIP) Studies
The structure-activity correlation determined using PLS used, the additional oxygens increase the flexibility of
regression analysis results in a two-component model. the backbone and with it the chance of “losing” the op-
The gross statistical performances of a PLS model can timal orientation. This effect can be avoided by tuning
be deduced from the parameters R2 (the goodness of the interactions between the R groups and the backbone
fit or explained y-variation) and Q2 (the predicted y-var- and/or by omitting the oxygens that bind the phosphorus
iation). Our model gives R2 ¼0.850, and Q2 ¼0.785. to the backbone structure.
There is evidently a good correlation between some of
The third-ranked variable is the sphere occupation de-
the descriptors and the yield. To identify which descrip- scriptor (Socc), a measure of the steric crowding around
tors (i.e., which properties of the ligands) have a strong the nickel atom. Ligand-metal complexes with Socc val-
effect on the catalytic activity, we plotted the contribu- ues of 70–80% are found to be the most active. These li-
tion of each descriptor to the model (Figure 4).
gands are able to coordinate the other reagents (the pro-
We see that the most important variables are the elec- ton, the cyanide and the olefin) that contribute little to
trostatic and the Mulliken charges at the ligating atoms. the steric crowding. Moreover, Socc is correlated better
These electronic properties are known to influence the with the cone angle V (R2 ¼0.65), than with the bite an-
complexꢁs stability and the elementary steps of the cata- gle a (R2 ¼0.31, see score plot in Figure 3). This differ-
lytic cycle.[14,18,24] Ligands with electron-withdrawing ence reflects the fact that calculations of Socc and V
substituents at the phosphorus atoms are weak bases take into account also the R group steric effect, while
and can easily compensate the high electron density of a is mainly a measure of the backbone structure. The
the d10 zerovalent nickel by back-donation. An elec- R groups affect the accessibility of other substrates to
tron-poor nickel atom will readily coordinate the olefin the metal centre and “push” the reagents together to fa-
substrate. Moreover, kinetic studies[36] indicate that the vour the coupling process during the elimination step.[36]
rate of reductive elimination (the rate-limiting step) is Socc can therefore be considered as an indicator of such R
increased by electron-withdrawing ligands such as phos- group effects. Ligands with ortho substituents on the
phites. The order of activity found in our dataset was: phenyl rings (e.g., 21) increase the steric crowding at
NR3 <SR2 ꢁPR3 <P(OR)3.
the metal centre, with a strong influence on the catalytic
The first steric property found to influence activity is a activity. Such cases would favour a reaction with 4PN
chelating effect-related descriptor: the energy differ- over 3PN, as the former is less hindered and thus has a
ence between the free and the coordinated conforma- better chance to coordinate to the Ni atom. For the
tion of ligands (DEbind). The model selects ligands where same reason, the formation of the linear product ADN
only few structural arrangements are necessary to form is also preferred over that of the bulkier MGN and
a chelate complex. This requirement reflects the need ESN isomers.
The group of steric variables and the bite angle (a)
form the last group of important parameters that affect
the catalytic activity. The bite angle indicates a peak of
activity around 1058–1108, which explains why large bi-
phosphines that stabilise the tetrahedral complexes also
enhance the reductive elimination step.[24] Conversely,
small bite angle ligands (e.g., dppe or dppp), stabilise
square planar geometries, accelerating the deactivation
pathways and thus forming Ni(II) complexes such as
Ni(L)2(CN)2. The remaining descriptors (backbone
structural parameters, HOMO and LUMO energies, di-
pole moments, etc.) are not so relevant to this model.
Although the first homogeneously catalysed hydro-
cyanation of linear alkenes was published in 1954 by Ar-
Figure 4. Variable importance (VIP) plot, showing the impor-
tance of every variable in the model. The solid columns de-
note the descriptors highlighted in Figure 3. VIP values high-
er than 1.0 are attributed to descriptors that contribute most
in the prediction of ligands activity.
thur and co-workers,[37] only a few more examples repre-
senting this class of substrates can be found in the liter-
ature. In the last ten years, the Xantphos ligand and sev-
eral of its structural variations have been extensively
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studied in the hydrocyanation of 1-octene, styrene and that could then be interpreted in terms of mechanistic
w-unsaturated fatty acid esters. A direct comparison be- arguments. The charge at the ligating atoms, the rigidity
tween the catalytic activities of the ligands tested in this of the molecules, the steric crowding around the Ni atom
study and the Xantphos-type compounds presented in and the bite angle are found to be the most important de-
the previous works is not possible, as the starting mate- scriptors. In this way the model provides a rational and
rial used in our study (pentenenitrile) differs from those quantitative way to screen virtual libraries of ligands
used in the literature. To overcome this problem we in- in search of new hydrocyanation catalysts. This combi-
cluded in our library several Xantphos-type ligands nation of synthesis and in silico screening will be the sub-
and modelled them. These ligands showed moderate ac- ject of future work in our laboratory.
tivity (less than 30% conversion) in the hydrocyanation
of pentenenitrile, destabilising the square-planar geom-
etry of the divalent state and stabilising the tetrahedral
geometry of the zerovalent state by means of a wider
bite angle.
Experimental Section
Another approach to design better catalysts is to en-
Materials and Instrumentation
hance the reductive elimination rate. Biphosphites
have proven to be versatile ligands in this case, as the re-
action is facilitated by electron-withdrawing ligands. Bi-
Reactions were performed in a glove box under an inert atmos-
phere using a Gilson 215 automated robot platform equipped
phosphites containing aryl groups and having wide bite with two sampling syringes and modified to enable orbital stir-
ring and temperature control.[39] The temperature homogenei-
angles combine the two effects, and make good catalysts
(the ligands used by Casalnuovo et al.[38] are designed to
combine these two features using glucose backbones
and trifluoromethyl groups at the meta-position in the
PPh moieties). Indeed, in our work, the ligands that
gave the highest conversion (e.g., compound 21) also dis-
played both characteristics: a rather rigid and large
backbone, and electron-withdrawing ligating atoms.
Although the bite angle and electronic effects seem
reasonable, an increasing steric crowding around the
nickel atom might also enforce the reductive elimina-
tion step. Freixa and van Leeuwen evidenced this argu-
ment for the methoxycarbonylation reaction of alkenes
with palladium catalysts, where it was shown that steric
bulk is more important than the bite angle.[24] We also
find that the presence of bulky substituents on the P
atoms enhances the conversion of pentenenitrile by in-
creasing the steric crowding around the nickel atom.
We believe this feature (encoded by the Socc descriptor)
is another way to control the catalytic activity of ligands
in pentenenitrile hydrocyanation.
ty in each well was ꢂ18C. GC analyses were performed using a
Varian CP 7331 gas chromatograph with a 100 mmꢃ10 m capil-
lary column. All chemicals were purchased from commercial
sources (>99% pure) and used as received. All products are
known compounds and were identified by comparison of their
spectral properties and GC retention times to those of com-
mercial samples. Lewis acids were diluted in DMF to 1.5 M
concentration and filtered prior to reaction.
Procedure for Catalytic Hydrocyanation of 4-
Pentenenitrile
The catalyst precursor Ni(COD)2 (10 mmol, 2.7 mg), ligand
(50 mmol for monodentate and 100 mmol for bidentate li-
gands), 3-pentenenitrile (300 mmol, 24.3 mg), Lewis acid stock
solution (10 mmol, 0.67 mL), cyanohydrin (300 mmol, 8.1 mg),
diisopropylbenzene (2 mg, internal standard) and DMF
(2000 mmol, 146.2 mg) were added to 3-mL reaction vials.
These were sonicated for 20 min and subsequently heated to
708C. After 2 h stirring, the vials were cooled to 258C, and
the reaction mixtures were diluted with DMF and analysed
by GC.
Conclusions
Computational Methods
The brute force approach to bidentate ligand optimisa-
tion is hampered by the huge diversity of the multi-di-
A detailed description of the use of the principal component
analysis (PCA) and partial least squares (PLS) analysis meth-
mensional ligand space. A complete search is not possi- ods in the assessment of virtual ligand libraries was recently
published for monodentate palladium-phosphine ligands.[11]
ble, and even a partial search is likely to require the syn-
Here we introduce an additional parameter, the variable im-
thesis and testing of large numbers of compounds with
portance (VIP), to estimate the contribution of each descriptor
hardly any activity. One way to overcome this problem
in the PLS model. PLS modelling is a simultaneous projection
is to use predictive models to preselect ꢀgood regionsꢁ
of the variables matrix X and the figures of merit matrix Y on
of the catalyst space and search there for ligands. Focus-
ing on the catalytic hydrocyanation of pentenenitrile, we
derived a QSAR (multivariate) model that correlates
the ligandsꢁ activities with their structural and electronic
properties. The choice of targeted descriptors (i.e., relat-
lower-dimensional hyper-planes. The coordinates of the points
in these hyper-planes are the elements of the low-rank matrices
T and U. The PLS algorithm uses additional loadings, w, (also
called weights) to express the correlation between U and X.
This analysis has two objectives: (a) to reduce the dimensional-
ed to the reaction) is the first step in order to get a model ity of the problem and still give a good approximation of the X
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and Y spaces; and (b) to maximise the correlation between X
and Y.
Molecular Geometry optimization
Molecular Mechanics and semi-empirical PM3 methods[40]
within the Spartan program[41] were used to optimise the geo-
metries of ligands. The structures obtained were then used as
the starting point for the calculation of all descriptors (see Ta-
ble 1). The Steric programme[42] was employed to calculate the
solid angle of ligands and related properties.
We used cross-validation to determine the model dimen-
sionality (number of principal components). A component n
is considered significant if the value PRESS/SS is smaller
than 1, where PRESS is the sum of square differences between
observed and predicted Y values when observations are kept
out, and SS is the residual sum of squares of component (nꢀ1).
An important issue that drives the selection of descriptors is
the level of theory used in the calculations. In combinatorial
chemistry this choice is mainly influenced by the size and mo-
lecular complexity of the libraries and the computing time
available. When you have to handle large libraries, simple
and efficient rules that enable a rapid selection of structures
are the only applicable solution. Molecular modelling force
fields are a fast and precise tool for obtaining ligand geome-
tries.[43] These programmes give good results and offer the ad-
vantage of performing data analysis on molecules before they
are synthesised. Moreover, to validate our calculations, the bite
angles of known ligands were compared with their crystallo-
graphic data deposited at the Cambridge Crystallographic Da-
tabase and with other molecular modelling results performed
elsewhere.[22] The trends we observed were in good agreement
with both controls.
Assessment of Variable Importance (VIP)
The influence of each descriptor on the figure of merit is calcu-
lated as the VIP parameter. This is the sum over all model di-
mensions of the VIN (variable influence) contributions. For a
given descriptor k and a given PLS dimension a, (VINak)2 is
equal to the squared PLS weight (wak)2 of that term, multiplied
by the SS explained by that PLS dimension. The accumulated
value VIPk [Eq. (6)] is then divided by the total percentage
of explained variance and multiplied by the number of terms
in the model. A descriptor with VIPk >1 is considered as rele-
vant to the model.
ð6Þ
Table 1. Molecular descriptors used to characterize ligand structures.[a]
Entry Symbol Description
Chelating effect descriptors
Min.
74.2
0.012
16.9
0.19
Max.
127.7
0.044
96.0
4.35
Mean
107.3
0.025
42.9
2.06
Std. Dev.
1
2
3
4
5
6
a
a
Bite angle [degrees]
10.7
0.008
18.5
1.13
1.24
1.24
Flexibility [(kcal molꢀ1degreesꢀ2)]
DEbind
Dd
d(P1–P2)
Free-Chelate conformation energy difference [kcal molꢀ1
Free-Chelate conformation distance difference [ꢃ]
Ligating atoms distance, free conformation [ꢃ]
Ligating atoms distance, chelate conformation [ꢃ]
]
[e]
3.10
3.10
8.05
8.05
5.69
5.69
d(P1–P2)c
Steric descriptors
7[b]
Mw
S
V
dPATH
V
Wmax
Socc
Asap
Rmax
Molecular weight [amu]
226
258
242
3.7
4.06
4.8
38.0
14.8
2.75
987
988
1051
12.6
6.93
12.2
87.0
57.9
549
587
584
9.2
5.87
8.0
64.5
37.7
3.97
190
173
188
2.3
0.67
2.3
18.6
12.6
1.14
8[b, c]
9[b, c]
Van der Waals surface [ꢃ2]
Volume enclosed in van der Waals surface [ꢃ3]
Sum of bond distances between ligating atoms[e] [ꢃ]
Tolmanꢁs cone angle [rad]
Maximum numerical solid angle [sr]
Percentage of sphere occupation [%]
Area under numerical solid angle profile [ꢃsr]
Radius at numerical solid angle profile peak [ꢃ]
10
11[b]
12[b]
13[b]
14[b]
15[b]
6.42
Electronic descriptors
16[c]
EHOMO
ELUMO
GAP
m
q1,P
q2,P
HOMO [eV]
LUMO [eV]
ELUMO –EHOMO [eV]
Dipole moment [Debye ]
Electrostatic potential on P atom [kcal molꢀ1
Mulliken charge on P atom [e]
ꢀ8.68
ꢀ1.22
6.54
0.41
0.01
ꢀ6.99
0.94
8.47
8.73
1.28
1.29
ꢀ7.72
ꢀ0.13
7.60
2.56
0.72
0.50
0.42
0.46
2.19
0.38
0.42
17[c]
18[c]
19[c]
20[c, d]
21[c, d]
]
ꢀ0.03
0.67
[a]
Some descriptors were computed more than once, e.g., the volume was computed both for the complete ligand and for the
backbone.
Calculated also for the backbone structure.
Calculated for both the free and the chelating conformations. The statistics refer to the chelating conformation only.
Averaged charge values between the two ligating atoms were also computed.
The distance was calculated considering the minimum bonding path distance between P1 and P2 ligating atoms.
[b]
[c]
[d]
[e]
Adv. Synth. Catal. 2005, 347, 803–810
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ꢂ 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
809

Enrico Burello et al.
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Adv. Synth. Catal. 2005, 347, 803–810