Intuitive Quantifiers of Charge Flows in Coordinate Bonding

Article abstract of DOI:10.1021/acs.organomet.7b00365

ETS-NOCV charge and bond energy analyses have been carried out for a broad range of transition-metal carbonyl complexes L-[M], comprising different ligand classes, transition metals, and coordination geometries. The resulting electronic redistributions are visually assigned to σ donation, π backbonding, and related interactions. We propose a Hirshfeld partitioning of these electronic redistributions to afford the corresponding charge flow contributions Δq_σ, Δq_π, etc. Taken together, a detailed picture of the dative bonding arises, in terms of both energetics and the extent of σ-electron donation and π-electron backbonding. The charge flows Δq_σ and Δq_π appropriately quantify trends in the ligand σ-donor and π-acceptor abilities and are transferable across the transition-metal complexes studied and thus promise to be suitable descriptors for ligand knowledge bases. As a case in point, the TEP is well reproduced by the calculated ν_CO(A₁) frequencies and is 3 times more strongly affected by Δq_σ than by Δq_π, with an additional modest steric influence. Further, empirical relationships are derived among the charge flows Δq_σ and Δq_π, the (L)W(CO)₅ carbonyl stretching frequencies, and the ligand's steric volume %V_bur, which allow estimating the σ-donor and π-acceptor abilities of phosphines from experimental observables. On the other hand, direct Cl:→L-σ? interactions are identified in several cis-(L)Ir(CO)₂Cl complexes, which compromises the use of these species as experimental probes for ligand parameters.

Full text of DOI:10.1021/acs.organomet.7b00365

Article
pubs.acs.org/Organometallics
Intuitive Quantifiers of Charge Flows in Coordinate Bonding
Erik P. A. Couzijn,†,‡ Yu-Ying Lai,†,§ Armin Limacher, and Peter Chen*
Laboratorium fur Organische Chemie, ETH Zurich, Vladimir-Prelog-Weg 2, CH-8093 Zurich, Switzerland
̈
̈
̈
S
* Supporting Information
ABSTRACT: ETS−NOCV charge and bond energy analyses
have been carried out for a broad range of transition-metal
carbonyl complexes L−[M], comprising different ligand classes,
transition metals, and coordination geometries. The resulting
electronic redistributions are visually assigned to σ donation, π
backbonding, and related interactions. We propose a Hirshfeld
partitioning of these electronic redistributions to afford the
corresponding charge flow contributions Δqσ, Δqπ, etc. Taken
together, a detailed picture of the dative bonding arises, in terms
of both energetics and the extent of σ-electron donation and π-
electron backbonding. The charge flows Δqσ and Δqπ
appropriately quantify trends in the ligand σ-donor and π-
acceptor abilities and are transferable across the transition-metal
complexes studied and thus promise to be suitable descriptors for ligand knowledge bases. As a case in point, the TEP is well
reproduced by the calculated νCO(A1) frequencies and is 3 times more strongly affected by Δqσ than by Δqπ, with an additional
modest steric influence. Further, empirical relationships are derived among the charge flows Δqσ and Δqπ, the (L)W(CO)5
carbonyl stretching frequencies, and the ligand’s steric volume %Vbur, which allow estimating the σ-donor and π-acceptor abilities
of phosphines from experimental observables. On the other hand, direct Cl:→L−σ* interactions are identified in several cis-
(L)Ir(CO)2Cl complexes, which compromises the use of these species as experimental probes for ligand parameters.
coupling between vibrations.5d,e Thus, there is a need for
alternative descriptors to build ligand knowledge bases with
more predictive power.
INTRODUCTION
■
The chemical and physical properties of transition-metal
complexes are primarily determined by the electronic and
steric influence of the ligands. Several models have been
developed to describe these ligand properties,1 of which the
Tolman Electronic Parameter (TEP) is well-established and is
widely used to guide the fine-tuning of organometallic
complexes, e.g. in homogeneous catalysis. The TEP corre-
sponds to the CO Al stretching frequency of complexes
(L)Ni(CO)3 as originally determined for various P-donor
ligands;2 a lower νCO(A1) value indicates a more strongly
electron donating ligand on account of increased metal to
carbonyl π backbonding. The TEP was later used to quantify
the electronic properties of other ligands, including N-
heterocyclic carbenes (NHCs) and divalent carbon(0)
compounds.3 Different metal complexes, such as square-planar
cis-(L)M(CO)2Cl (M = Ir, Rh) that are easier to prepare and
handle, have been studied and their CO stretching frequencies
were correlated to the TEP.4
Tolman ascribed the coordinating power of ligands primarily
to their σ-donor and π-acceptor abilities,2 but the TEP is a
measure only of their net donor strength. Moreover, recent
studies question its reliability for multiple reasons.5 The TEP
performs poorly when different ligand types are compared5a
and fails to describe the bonding trends in linear gold
complexes, which are governed by π backbonding.5b In
addition, the CO stretching frequencies were shown to be
affected by through-space ligand interactions5c and by mode
Several models have been proposed to unravel the TEP and
to offer more suitable ligand electronic parameters.5b−e,6
However, the sophisticated method QALE (quantitative
analysis of ligand effects)6a−c relies intricately on a variety of
experimental data, which prohibits its use in predicting the
coordination properties of novel ligands under design. The
theoretical parameters CEP (computationally derived ligand
electronic parameter, i.e. calculated νCO(A1) for (L)Ni-
(CO)3),6d LTEP (local TEP, i.e. mode-decoupled νCO(A1)),5d
MESP (molecular electrostatic potential minimum at the
ligand’s lone pair region),6e−g and the average local ionization
energy6h do not have this limitation, but in turn they do not
provide a straightforward separation into σ-donor and π-
acceptor contributions. The same is true for the metal−ligand
electronic parameter (MLEP, i.e. local L−Ni(CO)3 bond force
constant), which could be derived from experimental data but
so far has been computed.5e
In a different vein, the ligand−metal bonding has been
described in detail either on the basis of the total electron
density or energetically by various quantum chemical
methods.7−14 In the first category fall the quantum theory of
atoms in molecules (QTAIM),8 which computes properties
Received: May 11, 2017
Published: August 28, 2017
© 2017 American Chemical Society
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cm−1 was included in the spectrum and used as internal reference.
Further details, including NMR characterizations, are contained in the
Supporting Information.
Tetracarbonyl(pyridine)iron(0) was synthesized following a liter-
ature procedure.16a FT-IR (n-hexane + pyridine): 2051.0, 1966.8,
1941.3, 1907.4 cm−1.
Tetracarbonyl(trimethylamine)iron(0) was synthesized following a
literature procedure.16b FT-IR (n-heptane): 2049.9, 1963.7, 1932.9
cm−1.
Tetracarbonyl(tris(tert-butyl)phosphine)iron(0) was synthesized
following a literature procedure.16c FT-IR (n-hexane): 2042.3,
1964.7, 1926.2, 1892.0 cm−1.
over atomic basins and bond paths derived from the topology
of the total density; the natural bond orbital (NBO)9
description as an optimal Lewis structure with second-order
perturbations; and the charge decomposition analysis (CDA)10
in terms of the fractions of electrons shared between orbitals of
both fragments. On the other hand, the bonding energetics can
be dissected by the constrained space orbital variation
(CSOV)11 method of sequentially relaxing and mixing each
of the superposed fragment wave functions or by the extended
transition state (ETS)12 model in terms of fragment
preparation, electrostatic interaction, Pauli repulsion, and
orbital interactions partitioned by symmetry. The recent
natural orbitals for chemical valence (NOCV) model13 extends
ETS by extracting the principal electronic redistributions
occurring upon bonding, which usually can be readily assigned
to e.g. σ and π interactions,13g and the orbital interactions are
partitioned accordingly. While the aforementioned analyses
deliver a wealth of detailed insights, their execution and
interpretation requires considerable expertise and some
methods are impracticable for larger, nonsymmetric complexes.
Furthermore, the obtained ligand bonding parameters are often
not readily transferable to other series of complexes (see also
below).
In this article, we introduce intuitive computational
parameters that quantify and dissect the amount of charge
transfer for each bonding mode in transition-metal complexes.
The chemical bonding of a wide range of ligands in various
metal−carbonyl complexes is investigated with the ETS−
NOCV charge and energy decomposition scheme.12,13 We
apply the Hirshfeld partitioning15 to the resulting NOCV
electronic redistributionswhich are matched to σ, π, and
related bonding contributions by visualization13gto obtain
associated charge flows. These charge flow contributions
quantify how many electrons move from the ligand to the
metal fragment or vice versa through each binding mode, which
is a straightforward definition of the σ-donating and π-accepting
ability of a ligand in a transition-metal complex. We show that
the charge flow contributions reproduce commonly accepted
trends in ligand electronic properties and are well correlated
across complexes of different transition metals and coordination
geometries. A couple of anomalies are attributed to additional
specific interactions that are also apparent from the NOCV
electronic redistributions and from structural features. Next, we
relate the L−Ni(CO)3 charge flows to νCO(A1) frequencies in
order to dissect the TEP into σ-donor, π-acceptor, and steric
influences. Finally, empirical equations are derived for
estimating the charge flow contributions from spectroscopic
data for P-donor W(CO)5 complexes. Thus, the proposed
method builds a bridge between theoretical and experimental
concepts in transition-metal chemistry, highlights some of the
complications in constructing accurate empirical models using
ligand knowledge bases, and offers predictive power in ligand
design.
Tetracarbonyl(triphenylphosphine)iron(0) was synthesized analo-
gously to the tris(tert-butyl)phosphine complex. In a Schlenk tube
under an inert atmosphere, triiron(0) dodecacarbonyl (0.52 g, 1.0
mmol) was dissolved in dry methanol (25 mL) and triphenylphos-
phine (780 mg, 2.97 mmol) was added. The mixture was sonicated at
50 °C for several hours. All volatiles were removed under vacuum, and
the residue was redissolved in n-hexane and extracted with acetonitrile.
The product was recrystallized from the hexane phase. FT-IR (n-
hexane): 2050.0, 1977.4, 1944.3, 1909.1 cm−1.
Computational Methods. Density functional theory (DFT)
calculations were performed with ADF 201017 at the BP86/ZORA/
TZP level of theory;18 see section 2 in the Supporting Information for
details. All structures were optimized and subjected to frequency
analyses to confirm that they are minima and to obtain the CO
stretching frequencies νCO. The ligand steric parameter %Vbur was
determined from the optimized cis-(L)Ir(CO)2Cl structures analo-
gously to the procedure of Cavallo and Nolan (see section 2.2 in the
Supporting Information),19 taking a coordination sphere of 3.50 Å
radius at 2.10 Å from the donor atom; %Vbur(Ni) was determined
accordingly with a 3.50 Å sphere at Ni in the optimized (L)Ni(CO)3
complexes.
The ETS−NOCV scheme (also named EDA−NOCV after the
energy decomposition analysis of ADF that implements the ETS
model) was applied to study the interactions of 34 ligands L with
metal fragments Ni(CO)3, cis-Ir(CO)2Cl, Fe(CO)4, and W(CO)5 as a
ligand to metal dative bond is formed to afford complexes L−
Ni(CO)3, cis-L−Ir(CO)2Cl, ax-L−Fe(CO)4, and L−W(CO)5. The
extended transition state (ETS) method decomposes the net bonding
energy BDE into four contributions:17 the preparation energy ΔEprep
required to bring the separate fragments from their optimum spatial
and electronic structures to those in the total molecule, the
electrostatic attraction (ΔVelstat) and Pauli repulsion (ΔEPauli) between
the fragments, and the total orbital interaction energy ΔEoi, reflecting
the stabilization energy gained by relaxation of the sum-of-fragments
electron density to that of the total molecule:
−BDE = ΔEprep + (ΔV
+ ΔEPauli) + ΔEoi
elstat
(1)
The difference between the sum-of-fragments density ρsumfrag and
that of the total molecule ρmol is called the deformation density Δρ.
Mathematically, NOCV analysis13 represents Δρ as a sum of pairs of
complementary eigenvectors (ψ−i, ψi) with corresponding eigenvalues
(−εi, εi) that are equal in magnitude but opposite in sign. Chemically
speaking, the NOCV pairs (ψ−i, ψi) are donor and acceptor orbitals
and εi denotes the net electron transfer from donor to acceptor orbital.
This brings about an electronic redistribution Δρi with associated
contribution ΔEi to the total orbital interaction energy, which can be
computed according to eqs 2 and 3:
EXPERIMENTAL SECTION
■
Δρ(r) =
Δρ(r) =
ε[−ψ 2(r) + ψ2(r)]
∑
∑
i
(2)
i
−i
i
All experiments were carried out under an argon or CO atmosphere
using standard Schlenk techniques and dried and degassed solvents.
Selected tetracarbonyliron(0) complexes were synthesized to confirm
their carbonyl stretching frequencies in apolar solvent. FT-IR spectra
were recorded on a PerkinElmer Spectrum Two instrument equipped
with ATR (trimethylamine complex) or a PerkinElmer Paragon 1000
apparatus. As most of the substances slowly decompose in solution, a
small amount of sample was dissolved in the specified alkane
immediately prior to analysis. The CO2 absorption band at 667
ΔEoi
=
ΔE =
ε[−FTS−i,−i+FTS
]
i,i
∑
∑
i
i
(3)
where FTS is the Kohn−Sham matrix defined over NOCVs with
respect to the transition state density (being the average of ρsumfrag and
ρmol).17 Typically only few NOCV pairs contribute significantly to the
bonding, and visualization of each electronic redistribution Δρi usually
allows unambiguous assignment as, e.g., σ- or π-type bonding.13g
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Exemplary electronic redistributions for the complexes studied in this
article are depicted in section 2.6 in the Supporting Information.
Preliminary Hirshfeld partitionings15 of the electronic redistrib-
utions (see the main text) were performed with a standalone C
program that numerically integrates density data from the TAPE21 file
using a cubic grid. After this proof of concept, the partitioning was
implemented by SCM in a development version of ADF (build
201302062204), providing superior integration accuracy and workflow
efficiency. The charge flow analysis is now available in the ADF2017
release through the keyword “PRINT NOCVHirshfeld”.
RESULTS AND DISCUSSION
Scheme 1 lists the 34 ligands L and 4 metal carbonyl fragments
[M] studied, encompassing different donor elements, transition
■
Figure 1. Main electronic redistributions for the H3P−Ni(CO)3
bonding. Green and orange contours signify charge density
accumulation and depletion, respectively (σ, 0.004 au; π, 0.002
au, one of two equivalent contributions shown; σ*, 0.001 au); note
that these contours do not represent orbitals with phases.
a
Scheme 1. Complexes Studied
CO π systems, reflecting the increased M→π*CO backbonding
that is responsible for the small TEP observed for strong σ-
donor ligands. Conversely, the L←M π backbonding from the
metal dxz and dyz orbitals features a depletion of charge in the
CO π systems, reflecting the competition with M→π*CO
backbonding that leads to a larger TEP.
ETS-NOCV Descriptors. We first tested whether the
NOCV eigenvalues εσ and επ (as did Mitoraj et al.13g) or the
orbital interaction energies ΔEσ and ΔEπ would be suitable to
quantify the magnitude of the σ-donating and π-backbonding
interactions, respectively. However, both εσ and ΔEσ for L−
Ni(CO)3 are found to correlate poorly with those for the other
three series of complexes (see section 3.3 in the Supporting
Information), and in part separate trends can be recognized for
the different ligand classes. For εσ this is likely due to the fact
that the related electronic redistribution Δρσ also contains
contributions from polarizations within both the ligand and the
metal fragment. ΔEσ, on the other hand, depends intricately on
the energy gaps and overlaps between the ligand’s lone pair
being a variable admixture of the coordinating element’s
valence s and pz orbitalsand the metal’s interacting s, pz, and
a
Abbreviations: Vy = vinyl, HMPT = hexamethylphosphorous
triamide, Mes = 2,4,6-trimethylphenyl.
metals, and coordination geometries. A comprehensive range of
ligand types was considered, including phosphines, arsines,
amines, pyridine, (iso)nitriles, CO, and NHCs. Several of these
complexes have been experimentally synthesized and charac-
terized.
Ligand Bonding Decompositions. The ligand−metal
bonding in the complexes in Scheme 1 is usually described in
analogy to the Dewar−Chatt−Duncanson (DCD) model for
alkene π complexes.21,14d,13b,f That is, both the ligand and the
metal fragment have a singlet electronic ground structure and
engage in synergistic σ donation, from the ligand’s lone electron
2
dz orbitals (Figure 2, left). This affords a set of molecular
2
pair into the metal’s dz orbital, and π backbonding, from the
metal’s dxz and/or dyz orbitals into antibonding π* ligand
orbitals. The L−[M] net bond energies were decomposed
accordingly within the ETS−NOCV framework. For most of
the complexes, only the first four NOCV pairs were found to
contribute significantly to the coordinative bonding. As
reported previously13g and as illustrated for (PH3)Ni(CO)3 in
Figure 1, the associated electronic redistributions Δρi are
readily assigned to L→M σ-donation, L←M π backbonding (in
two orthogonal planes along the L−M bond), and a modest σ
Figure 2. Basic orbital interaction diagrams for L→M σ donation (left;
energy levels not drawn to scale) and L←M π backbonding (right;
analogous interaction in the yz plane not shown).
orbitals (MOs) for which a change in the total σ-bonding
stabilization energy is hard to trace back to individual
perturbations in fragment orbital energy levels and overlaps,
undermining any simple correlation. In addition, the extent and
diffuseness of the L s vs L pz orbital depends differently on the
coordinating element and, as a result, their relative contribu-
tions will differ in the bonding of the various ligand classes.
We note that, for π backbonding, acceptable to good
correlations across the series of complexes are found for ∑επ
and for ∑ΔEπ (summing the two mutually orthogonal L←M
π-backbonding contributions). At least for the complexes
2
back-donation from primarily the metal’s dz orbital into the
lowest-energy A1-symmetric σ* orbital of the ligand;13g see the
Supporting Information for all decomposition results and
further examples.
The depicted electronic redistributions not only illuminate
the primary bonding interactions (e.g., donation of part of the
ligand’s lone electron pair into the bonding region, Figure 1
left) but also feature clear contributions on the carbonyl
moieties. The L→M σ-donating interaction is accompanied by
2
an accumulation of charge from the metal dz orbital into the
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studied here, the basic L π*−M d orbital interaction scheme
(Figure 2, right) is less complicated than that for σ donation.
The coordinating element plays only a minor role because
along with the L π* orbitals also the L s and L pz orbitals
become more extended/compact, leading to a longer/shorter
L−M bond, which in part offsets the effects on the L πx/y*−M
dxz/yz overlaps. Hence, the ligand- and metal-dependent
perturbations to the energy gaps and orbital overlaps appear
to affect the π-bonding stabilization energy ∑ΔEπ in a quite
straightforward, proportional way. However, this is not self-
evident: perturbations that invert the ordering of the L π* and
M d energy levels would break the monotony of the trend.
Further, like εσ, also ∑επ includes intrafragment polarizations,
which for other complexes may be manifested in a less orderly
manner than is apparently the case here.
the bonding axis. The resulting charge-displacement functions
provide a detailed description of the bonding character, and
their applicability appears promising. Then again, we think that
our approach offers the following merits. First and foremost,
proper partitioning is warranted also when one or both
fragments bear groups that protrude toward the other fragment,
as is the case for e.g. ortho-substituted NHC complexes.
Conversely, the charge-displacement functions are contami-
nated by contributions from intrafragment polarizations on
such substituents at positions where the partitioning plane
happens to cut through them. Second, the method presented
here consolidates the spatially dependent charge displacements
into a single number per bonding type, which are more
amenable for use as quantifiers in comparative analyses as
illustrated below, and their interpretation is more accessible to
chemists outside this subfield.
All in all, neither the NOCV eigenvalues εi nor the orbital
interactions ΔEi are suitable as general descriptors of the ligand
electronic properties in coordinate bonding.
Ligand Donor/Acceptor Ability. For all four classes of
complexes, Figure 3 shows scatter plots of the L−[M] charge
flows Δqσ and ∑Δqπ, the latter being the sum of the two
mutually orthogonal π contributions. The plots are quite similar
(but see below), demonstrating the general applicability of the
charge flow contributions Δqi to describe ligand donor/
acceptor abilities. Different ligand classes are readily distin-
guished, e.g. the isonitriles and CO (moderate σ donors but
strong π acceptors), amines and pyridine (weak ligands in both
respects), and the NHCs (strong σ donors but weak π
acceptors). Further, the π-electron-poor pNHC23 features large
values for Δqσ as well as for −∑Δqπ, as expected for this
strongly σ donating and π accepting ligand. Thus, the
computed charge flows bear an intuitive, close connection to
experimental chemists’ parlance for organometallic complexes.
The series PHnF3−n, PHnMe3−n, and PMenPh3−n (n = 0−3)
have been connected by lines to highlight the substitution
trends. Going from PH3 to PMe3, as expected the σ donation
(as quantified by Δqσ) increases monotonically with the
number of methyl groups, while the π backbonding
(−∑Δqπ) decreases only slightly. However, replacement of
methyls by phenyl groups (from PMe3 to PPh3) hardly affects
the charge flow contributions. This suggests that, at least in
their complexes with metal carbonyls, alkyl- and arylphosphines
have similar σ-donor and π-acceptor propertiesthat is, their
differing coordinating strengths must in large part be due to
steric effects.2b This is supported by the similar TEPs of
PMenPh3−n as well as by their ETS bonding energy
decompositions (see section 2.4 in the Supporting Informa-
tion): e.g., the Me3P−Ni(CO)3 total “steric” interactions E0 are
2.8 kcal mol−1 less weakening but the total orbital interactions
Eoi are only 1.5 kcal mol−1 stronger than for the PPh3 analogue.
The fluorine substitution trend shows more interesting
features, which we will first discuss for the Ni, Fe, and W
complexes. Going from PH3 to PF3, we find that the π
backbonding (−∑Δqπ) increases significantly up to PHF2, but
then for PF3 it remains essentially the same while the σ-
donation decreases markedly. This strongly nonmonotonic
behavior is not at all apparent from the TEPs of the
fluorophosphines that follow a closely linear trend (calculated
νCO(A1) for HnF3−nP−Ni(CO)3: 2047.35, 2055.89, 2064.85,
and 2073.71 cm−1 for n = 0−3, respectively). This is because
the TEP expresses only the net donor ability of a ligand: i.e., a
reduction in σ donation has a similar effect on the νCO(A1) as
does an increase in π backbonding. Thus, the TEP is a poor
predictor for coordinating properties and applications in which
σ- versus π-induced effects are quite distinct from those in L−
Charge Flow Contributions Δqσ and Δqπ. As mentioned
above, the electronic redistributions Δρi consist of polarizations
between as well as within the fragments: i.e., they extend over
the whole complex. We realized that the flow of charge from
the ligand to the metal moiety or vice versa, as induced by an
NOCV interaction i, could be quantified by partitioning the
corresponding electronic redistribution Δρi between both
fragments. This should provide a much better description of
the dative bonding character than the eigenvalues εi discussed
above, as the unrelated polarizations within each fragment are
disregarded. A well-established procedure that suits our
purpose is the Hirshfeld partitioning,15 in which the property
of interest is integrated over space, at each point weighted by
the ratio between the chosen fragment and the sum-of-
fragments electron densities. Accordingly, each electronic
redistribution Δρi affords a charge flow contribution Δqifrag as
[M]
expressed by eq 4, with illustrations for Δqσ
Ni(CO)3:
for H3P−
Positive/negative Δqifrag values indicate net charge transfer
from/to the fragment in question. As the electronic
redistributions Δρi sum to the deformation density Δρ (eq
2), by definition the fragment’s formal charge Qfrag (being 0 for
L and [M] here) plus all charge flow contributions Δqifrag
equals its Hirshfeld fragment charge within the total molecule,
frag
qH
:
frag
Qfrag
+
Δq frag = qH
∑
(5)
i
In this work, we chose to calculate Δqi[M] with respect to the
transition-metal fragment [M], as it remains very similar across
all studied ligands, thus keeping any numerical errors more
systematic; these values were then negated to get the ΔqiL with
respect to the ligand (hereafter simply denoted Δqi).
In the course of our research, the group of Tarantelli
published the closely related charge-displacement analysis,5b,22
in which the NOCV electronic redistributions Δρi are
partitioned simply by a plane that is moved (typically) along
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Figure 3. Scatter plots of σ-donor and π-acceptor charge flows in the L−[M] bonding. Marker styles indicate the ligand’s coordinating element
(gray, C; blue, N; green, P; violet, As); lines connect the series PHnF3−n, PHnMe3−n, and PMenPh3−n (n = 0−3).
Ni(CO)3,1c,5b,22a,b as may be the case with e.g. the reactivity of
transition-metal catalysts.
In comparison to the other three classes of complexes, the
substitution trend for cis-(PHnF3−n)Ir(CO)2Cl (n = 0−3)
shows a prominent exception. The cis-H2FP−Ir(CO)2Cl
bonding features much less σ donation and only slightly
more π backbonding than that in cis-H3P−Ir(CO)2Cl.
Inspection of the NOCV electronic redistributions reveals
that this is due to donation from a lone electron pair on
chlorine into the opposite P−F σ* antibond (Figure 4), as also
reflected by the rather acute P−Ir−Cl angle of 71.75° in cis-
(PH2F)Ir(CO)2Cl versus 81.35° in cis-(PH3)Ir(CO)2Cl.
To a lesser extent, similar Cl:→L σ* interactions are found in
the cis-Ir(CO)2Cl complexes of AsF3, PCl3, PHF2, PHnMe3−n (n
= 0−3), and PMe2CF3, whereas those of NH3, pNHC, and
PtBu3 feature a Cl···H−N or Cl···H−CMe ancillary contact.
Indeed, for almost all of these ligands, differences are apparent
between the scatter plots of charge flows for L−Ni(CO)3 and
cis-L−Ir(CO)2Cl (cf. Figure 3A vs Figure 3B). These secondary
interactions compromise the transferability of the charge flows
from the nickel carbonyl complexes to cis-(L)Ir(CO)2Cl, and
more in general they signify the challenge of empirically
Figure 4. (left) Second-largest electronic redistribution for the cis-
H2FP−Ir(CO)2Cl bonding ( 0.002 au contours). (right) Schematic
depiction of the Cl:→P−F σ* interaction.
modeling ligand effects accurately using a knowledge base with
a limited set of generic parameters.
Transferability of Δqσ and Δqπ across Metal Com-
plexes. To assess the transferability of the charge flow
contributions, we performed linear regressions among all four
series of complexes under study, as shown in Figure 5. The
intercepts are all rather small and statistically significant only in
some cases, but for consistency we chose to perform all
regressions with intercept. The Δqσ values for the Ir, Fe, and W
complexes correlate well with those for L−Ni(CO)3, certainly
considering the wide scope of ligands investigated here. In
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Figure 5. Linear regressions for the σ-donor (left) and π-acceptor (right) charge flows in the L−[M] bonding. Marker colors indicate the ligand’s
coordinating element (gray, C; blue, N; green, P; violet, As).
addition, the −∑Δqπ values for the Fe and W complexes
correlate particularly well with those for L−Ni(CO)3, while
those for cis-L−Ir(CO)2Cl show somewhat more scatter due to
the mixed-in secondary interactions discussed above. As long as
one stays alert for such specific interactions with ancillary
ligands, the charge flows Δqσ and −∑Δqπ appear to be well
transferable to other complexes, having different coordination
geometries. This renders them promising candidates for ligand
knowledge bases as quantitative descriptors of the σ-donor and
π-acceptor abilities.
Analogous to Hammett correlations for aryl derivatives that
afford relative reaction constants from the slopes of the
substituent trends,24 the linear regressions in Figure 5 reveal
how the charge flows depend on the electronic properties of the
transition-metal moieties. The slopes signify that the σ-
Figure 6. Regression analysis of experimental versus calculated
carbonyl stretching frequencies. The good correlations justify the use
of the BP86/TZP frequencies so as to include complexes that lack
experimental data (see the main text).
accepting ability of [M] increases in the order W(CO)5 <
Ni(CO)3 ≈ Ir(CO)2Cl < Fe(CO)4 and the π-donating ability
in the order Ir(CO)2Cl < Ni(CO)3 < Fe(CO)4 ≈ W(CO)5.
One may envision that the regression coefficients relate to the
charge on the transition-metal moiety, on the diffuseness,
polarizability, and energy levels of the metal’s valence orbitals,
and on the ease by which electron density is transferred to or
most cases DCM) or apolar media (in most cases hexane) is
used for the regression. This is in line with reports that
postulate a fortuitous cancellation of model errors for BP86
frequencies.20 The found strong congruity supports the use of
from the ancillary ligands. However, a more detailed
investigation of these aspects is beyond the scope of the
the calculated νCO as indicators of the ligand electronic
properties, allowing us to include complexes that have not yet
current study.
Correlation of Δqσ and Δqπ with the TEP. We believe
that the charge flow contributions may earn a broad scope of
applicability as quantifiers of σ donation and π backbonding. As
a prototypical example, we use them here to construct a model
describing the TEP. At the same time, this affords a better
understanding as to what constitutes the TEP.
We first compare our calculated νCO values with available
experimental values (see Figure 6, the Experimental Section
and section 3.1 in the Supporting Information). At the BP86/
TZP level of theory a very good congruity is obtained, in
agreement with previous findings using other DFT levels of
theory.5a,6d,14k Oftentimes a frequency scaling factor is applied
to the calculated νCO, which in this case is near unity
irrespective of whether experimental data for polar media (in
been synthesized or for which the experimental data may be
unreliable (see the remarks in section 3.1 of the Supporting
Information). On the other hand, the complexes bearing
(iso)nitriles as well as Ni(CO)4 had to be left out because their
TEP values are strongly affected by vibrational coupling with
the ligand’s CX stretching mode.
While constructing a suitable multivariate regression model,
we found that there is a dependence on the ligand’s
coordinating element. This dependence may have its origin in
the Hirshfeld partitioning, which is performed using the
densities of the isolated ligand and transition metal moieties.
The resulting bias toward the neutral fragments25 may not
affect the partitioned properties equally in all casesespecially
regarding the nature of the coordinating atoms, in whose
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vicinity the largest changes in charge density occur. Thus, we
decided to scale the ligand’s charge flows Δqσ and −∑Δqπ by
the empirical factor fel (el = C, N, P, As), where fP is taken to be
1, as the TEP is based on the P-donor−Ni(CO)3 complexes.
The other scaling factors were optimized such as to minimize
the sum of squared residuals of the multivariate model.
Furthermore, the inclusion of a steric parameter improves the
model particularly for PtBu3 and the NHCs; the ortho
substituents of the latter are approaching the metal carbonyl
moiety and hence have a stronger steric interaction in
comparison to most substituted phosphines. We chose to use
%Vbur(Ni), the percentage of volume occupied by the ligand
within a sphere of radius 3.50 Å around nickel in the BP86/
ZORA/TZP computed structures of complexes L−Ni(CO)3
(see also ref 19). Thus, the following multivariate regression
model was obtained to fit the calculated νCO(A1):
We wish to stress that, again, the found congruity is
exceptional considering the broad range of ligands included.
Keg
́
l et al.14k recently published a systematic investigation on
12 P-donor Ni(CO)3 complexes, correlating various computa-
tional parameters obtained from QTAIM, NBO, and ETS−
NOCV analyses to the TEP. Most parameters performed
clearly worse: only for the QTAIM delocalization index and the
ETS−NOCV ΔEσ did they find comparable R2 values of 0.946
and 0.931, respectivelybut note that, for our somewhat more
diverse subset of 16 P-donor complexes, ΔEσ performs not that
well. If we model the calculated νCO(A1) of just these 16
complexes using the charge flows Δqσ and −∑Δqπ, we do
again obtain an excellent correlation (R2 = 0.9770) even
without a steric parameter.
Estimation of Δqσ and Δqπ from Experimental
Observables. We also sought expressions for the charge
flows Δqσ and −∑Δqπ in terms of CO stretching frequencies.
Such relationships would allow estimating the σ-donor and π-
acceptor abilities of yet other ligands from experimental
observables. However, the phosphine vs NHC complexes in
our data sets exhibit clearly different trends that could not be
readily merged by including any commonly known ligand
descriptor or by applying the aforementioned electronegativity-
related scaling factors. The NHC complexes feature through-
space interactions between the ligand’s ortho substituents and
nearby CO groups. Unsurprisingly, even the inclusion of a
(nondirectional) steric parameter such as %Vbur into the model
cannot properly account for such specific effects on the νCO
values (see section 2.7 of the Supporting Information). For the
current regression modeling we therefore decided to limit
ourselves to the P-donor ligand series, for which the W(CO)5
complexes afforded the smallest deviations. The regression
variables were checked for significance, leading to the following
optimal models (including a frequency scaling factor of 1.0125,
taken as the average of the slopes in Figure 6):
νmodel (cm−1) = 2134(5) − 0.87(18) × %Vbur(Ni)
− fel × [355(20) × Δqσ − 116(12)
× −∑ Δqπ]
(6)
where f C = 1.278, f N = 1.574, f P ≡ 1, and fAs = 0.986. For the
30 complexes (L)Ni(CO)3 under consideration, this model
affords a good R2 value of 0.9684 (σν = 3.7 cm−1, Figure 7); F
Δqσ,model (e) = 6.8(5) + [3.8(5) × νCO(A1)
− 8.6(9) × νCO(A1′)
+ 1.8(4) × νCO(B1)] × 10−3
(7)
−∑ Δqπ,model(e) = [1.7(5) × %Vbur + 5.4(7) × νCO(E)
+ 6.6(8) × νCO(A1) − 13.6(5) × νCO(A1′)
+ 2.4(8) × νCO(B1)] × 10−3
(8)
For the 16 complexes under consideration, the model for
Δqσ afforded a good R2 value of 0.9561 (σσ = 3.4 × 10−3 e) and
that for −∑Δqπ an even better R2 value of 0.9921 (σπ = 7.0 ×
10−3 e). Equations 7 and 8 both involve the frequency of the
(approximately) B1-symmetric CO stretching mode, which
however is a forbidden transition in infrared absorption
spectroscopy. On the other hand, all four relevant stretching
modes of complexes (L)W(CO)5 are Raman active (but one
should bear in mind that these complexes are prone to
photodecomposition). For the steric contribution in eq 8,
%Vbur could be determined on the basis of the crystal structure
of the ligand or of any complex thereof; several W(CO)5
complexes are stable, crystallizable solids. Thus, the models
described above provide a tool to experimentalists to
disentangle the σ-donor and π-acceptor contributions in the
dative bonding of P-donor ligands using physical observables.
Notably, already before Tolman published his seminal work on
Figure 7. Application of charge flows to model the TEP according to
eq 6. Marker colors indicate the ligand’s coordinating element (gray,
C; blue, N; green, P; violet, As).
tests with reduced models confirmed that all variables are
significant (see section 3.4 of the Supporting Information). The
scaling factors fel appear to parallel the Pauling electro-
negativities χel of the coordinating elements; using fel′ = (χel
/χP)3/2 instead, the R2 values decreases marginally to 0.9660 (σν
= 3.8 cm−1). Further investigation is warranted as to whether
this interesting finding has a more fundamental basis and
whether a similar scaling may apply to other properties
obtained through Hirshfeld partitioning. Equation 6 also
indicates that the TEP is affected about 3 times more by an
increase/decrease in σ donation than by an equivalent
decrease/increase in π backbonding, as quantified by the
charge flows Δqσ and −∑Δqπ, respectively.
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the Ni(CO)3 complexes,2 Cotton and Kraihanzel related the
spectroscopic properties of some (L)nW(CO)6−n complexes to
the ligand’s electronics.26
right has the transition-metal moiety rotated by 30° and
features a mirror plane through the NHC heterocycle, which
facilitates the NOCV decomposition28 into the desired σ and π
contributions, as is directly apparent from the depicted
electronic redistributions. The resulting charge flows are
significantly nonzero at Δqσ = 0.392 e and Δqπ = −0.324 e,
as expected for this strongly π accepting NHC ligand. These
values should still be representative as electronic descriptors for
pNHC in its axial coordination to Fe(CO)4, as the L−Fe
rotamer is a mere 0.26 kcal mol−1 higher in energy than the
global energy minimum (at BP86/ZORA/TZP), and in
solution the complex will undergo rapid L−Fe rotation
regardless.
In summary, the NOCV electronic redistributions Δρi should
always be visually inspected (e.g., through ADFview17a or using
any CUBE file visualization software) to ensure their correct
assignment to specific bonding modes. We note that this caveat
applies not just to the charge flow analysis presented here but
to all analyses based on NOCV decomposition (and, in general,
to any matrix diagonalization with potentially degenerate
solutions).
Note on Separability of Charge Flow Contributions.
As illustrated above, the ETS−NOCV−charge flow analysis
may become a straightforward yet powerful diagnostic tool for
computational chemists. However, as with all computational
analyses, one should be cautious to use it as a black box.
Namely, the NOCV decomposition may yield linear combina-
tions of bonding interactions with (nearly) degenerate
electronic redistributions Δρi, in which case the derived charge
flow contributions Δqi are of course also admixtures. This is
unproblematic as long as the bonding interactions in question
are equivalentfor example, for the two π-backbonding
contributions in the C3v-symmetric H3P−Ni(CO)3 (Figure 1,
middle) any linear combination will afford the same, valid
results. Illustrative, however, is the case of pNHC−Fe(CO)4, in
which the electronic redistributions due to σ donation from the
NHC’s lone pair and to π backbonding into the NHC’s π
system happen to be nearly degenerate. This is indicated by
closely similar NOCV eigenvalues ε (see Figure 8).
CONCLUSIONS
■
A comprehensive range of transition-metal carbonyl complexes
L−[M], comprising different ligand classes, transition metals,
and coordination geometries, was studied by DFT calculations.
ETS−NOCV analysis describes the ligand−metal bonding
interaction in such complexes by a set of characteristic
electronic redistributions, which are readily assigned as e.g. σ-
donating and π-backbonding interactions by visual inspection
and which extend over the whole complex. The charge flow
contributions Δqσ and Δqπ introduced in this article follow
intuitively from Hirshfeld partitioning of these electronic
redistributions between the ligand and the metal fragment.
With its implementation in ADF2017, the charge flow analysis
can now straightforwardly be applied in extension to the ETS−
NOCV bonding decomposition scheme.
While they are rooted in rigorous theoretical procedures, Δqσ
and Δqπ reflect the parlance of inorganic and organometallic
chemists to describe ligand−metal bonding in terms of the
extents of σ-electron donation and π-electron backbonding.
The charge flow contributions reconfirm common perceptions
regarding ligand electronic properties and are well transferable
across the studied complexes, comprising a wide variety of
ligands. As such, they appear promising for ligand knowledge
bases as quantifiers of the ligand’s σ-donor and π-acceptor
abilities, going beyond the TEP, which only reflects the net
donor strength of a ligand. In terms of Δqσ and Δqπ (Table S6
in the Supporting Information) the TEP is affected 3 times
more strongly by σ donation than by π backbondingbut
applications e.g. in homogeneous catalysis may require a
different ratio.
TEP values have recently been derived for several NHCs
from the CO stretching frequencies of their cis-Ir(CO)2Cl
complexes or the rhodium analogues,4 but our analyses of such
species revealed direct Cl:→L σ* interactions for various
ligands, which compromises the transferability of their
descriptors to other types of complexes. Apart from that, the
good correlations of Δqσ and Δqπ across different transition-
metal series suggest that σ-acceptor and π-donor scales can also
be created for the metal fragments. Moreover, the derived
empirical relationships to the CO stretching frequencies of
complexes (L)W(CO)5 and %Vbur allow estimation of the σ-
Figure 8. Primary electronic redistributions for the ax-pNHC−
Fe(CO)4 bonding ( 0.004 au contours) in the two lowest-energy
structures.
For the global energy minimum of ax-pNHC−Fe(CO)4 the
NOCV decomposition affords approximately 1:1 linear
combinations of the two bonding contributions, as shown in
Figure 8 on the left.27 As the admixed bonding modes have
opposing dative character, the resulting charge flows are
erroneously close to zero (Δq1 = 0.019 e, Δq2 = −0.012 e).
The local minimum-energy structure shown in Figure 8 on the
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Kovacevic, A.; Zeglis, B. M.; Faller, J. W.; Crabtree, R. H.
donor and π-acceptor abilities of phosphines on the basis of
experimental data. This further supports the use of the charge
flow contributions in the design of novel ligands and
complexes.
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ASSOCIATED CONTENT
* Supporting Information
■
S
́
H.; Slawin, A. M. Z.; Escudero-Adan, E. C.; Benet-Buchholz, J.; Nolan,
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.organo-
met.7b00365.
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L. Dalton Trans. 2005, 1491−1498. (q) Iwatsuki, S.; Kashiwamura, S.;
Kashiwabara, K.; Suzuki, T.; Takagi, H. D. Dalton Trans. 2003, 2280−
2292.
Experimental and computational details, optimized
energies, frequencies, bonding energy decompositions
and charge flows, contours of selected electronic
redistributions, and regression analyses (PDF)
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R. H. Organometallics 2003, 22, 1663−1667. (b) Kelly, R. A., III;
Clavier, H.; Giudice, S.; Scott, N. M.; Stevens, E. D.; Bordner, J.;
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2008, 27, 202−210. (c) Wolf, S.; Plenio, H. J. Organomet. Chem. 2009,
Cartesian coordinates of the calculated structures (XYZ)
AUTHOR INFORMATION
Corresponding Author
*P.C.: tel, +41-44-632-2898; e-mail, peter.chen@org.chem.ethz.
■
694, 1487−1492. (d) Furstner, A.; Alcarazo, M.; Krause, H.; Lehmann,
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C. W. J. Am. Chem. Soc. 2007, 129, 12676−12677.
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ORCID
Yu-Ying Lai: 0000-0002-1921-6923
Peter Chen: 0000-0002-9280-4369
́
9907−9916. (c) Valyaev, D. A.; Brousses, R.; Lugan, N.; Fernandez, I.;
Sierra, M. A. Chem. - Eur. J. 2011, 17, 6602−6605. (d) Kalescky, R.;
Kraka, E.; Cremer, D. Inorg. Chem. 2014, 53, 478−495. (e) Setiawan,
D.; Kalescky, R.; Kraka, E.; Cremer, D. Inorg. Chem. 2016, 55, 2332−
2344.
Present Addresses
‡Thermo Fisher (Bremen) Scientific, Hanna-Kunath-Straße 11,
D-28199 Bremen, Germany.
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M. R.; Prock, A.; Giering, W. P. Organometallics 1996, 15, 295−301.
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Author Contributions
†E.P.A.C. and Y.-Y.L. contributed equally.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
We acknowledge support of this work by the ETH Zurich and
the Swiss National Science Foundation. We are grateful to
SCM for implementing our method of Hirshfeld partitioning of
the NOCV electronic redistributions into ADF, and we thank
M. Mitoraj for fruitful discussions.
■
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DOI: 10.1021/acs.organomet.7b00365
Organometallics 2017, 36, 3205−3214