Angular distortions at benzylic carbons due to intramolecular polarization-induced metal-arene interactions: A case study with open-shell chromium(II) NHC complexes

Article abstract of DOI:10.1021/om3012568

The synthesis and full characterization of the unprecedented open-shell Cr(II) benzyl organometallic complexes [Cr(NHC)₂(benzyl)₂] (2) and [Cr(NHC*)(benzyl)₂] (3) (NHC = N,N′- diisopropylimidazol-2-ylidene; NHC* = N,N′-bis(2,6- diisopropylphenyl)imidazol-2-ylidene) from [Cr(benzyl)₃(THF) ₃] and [CrCl₂(THF)₂]/[Mg(benzyl)₂], respectively, uncovered unusually acute angles (93 in 2 and 76 in 3) at the sp³ benzylic C of the coordinated benzyl ligands. Detailed theoretical analyses (DFT and CASPT2) of the four-and three-coordinate Cr(II) species were performed to elucidate the physical origin of the benzyl bending and led to the recognition of a noncovalent, intramolecular polarization-induced metal-arene (PIMA) interaction as being responsible for it. The energetic contribution from a single PIMA interaction is estimated to be ca. 50 kJ/mol. A comparison with the origin of the angular distortions in the d⁰ [Zr(benzyl)₄] complex will also be presented. Sharing the common origin of an induced-dipole charge density scheme with intermolecular anion-π interactions, the intramolecular PIMA interaction concept involving a transition metal unpaired d electron and arene-π orbitals can be viewed as an extension of intermolecular anion-π interactions and leads to remarkable quantitative prediction of the observed structural distortions. PIMA interactions may manifest themselves in diverse structural and dynamic phenomena and have broad implications in chemical sciences.

Full text of DOI:10.1021/om3012568

Article
pubs.acs.org/Organometallics
Angular Distortions at Benzylic Carbons Due to Intramolecular
Polarization-Induced Metal−Arene Interactions: A Case Study with
Open-Shell Chromium(II) NHC Complexes
Andreas A. Danopoulos,*,† Kirill Yu. Monakhov,† Vincent Robert,*,‡ Pierre Braunstein,*,†
Roberto Pattacini,† Susana Conde-Guadano,§ Martin Hanton,§ and Robert P. Tooze§
̃
†Laboratoire de Chimie de Coordination, Institut de Chimie (UMR 7177 CNRS), Universite
67081 Strasbourg, France
́
de Strasbourg, 4 Rue Blaise Pascal,
‡Laboratoire de Chimie Quantique, Institut de Chimie (UMR 7177 CNRS), Universite
Strasbourg, France
́
de Strasbourg, 1 Rue Blaise Pascal, 67008
§Sasol Technology UK Ltd, Purdie Building, North Haugh, St Andrews, Fife, U.K. KY16 9ST
S
* Supporting Information
ABSTRACT: The synthesis and full characterization of the unprecedented open-shell Cr(II)
benzyl organometallic complexes [Cr(NHC)2(benzyl)2] (2) and [Cr(NHC*)(benzyl)2] (3)
(NHC = N,N′-diisopropylimidazol-2-ylidene; NHC* = N,N′-bis(2,6-diisopropylphenyl)imidazol-
2-ylidene) from [Cr(benzyl)3(THF)3] and [CrCl2(THF)2]/[Mg(benzyl)2], respectively, uncov-
ered unusually acute angles (93° in 2 and 76° in 3) at the sp3 benzylic C of the coordinated benzyl
ligands. Detailed theoretical analyses (DFT and CASPT2) of the four- and three-coordinate Cr(II)
species were performed to elucidate the physical origin of the benzyl bending and led to the
recognition of a noncovalent, intramolecular polarization-induced metal−arene (PIMA) interaction
as being responsible for it. The energetic contribution from a single PIMA interaction is estimated
to be ca. 50 kJ/mol. A comparison with the origin of the angular distortions in the d0 [Zr(benzyl)4]
complex will also be presented. Sharing the common origin of an induced-dipole charge density
scheme with intermolecular anion−π interactions, the intramolecular PIMA interaction concept
involving a transition metal unpaired d electron and arene−π orbitals can be viewed as an extension
of intermolecular anion−π interactions and leads to remarkable quantitative prediction of the observed structural distortions.
PIMA interactions may manifest themselves in diverse structural and dynamic phenomena and have broad implications in
chemical sciences.
dipole in a π system and a negative charge is the origin of these
rather counterintuitive attractive polarization forces.1,4 Model
systems in which specific intramolecular, noncovalent forces
can be singled out and correlated to observed macroscopic
features are highly desirable and could lead to new fundamental
and applied knowledge.
Access to new, well-defined chromium organometallics
relevant to the industrially and academically important
homogeneous and heterogeneous oligomerization and poly-
merization of ethylene5−8 has generated considerable interest,
and in this context, we targeted N-heterocyclic carbene
(NHC)-stabilized complexes in order to take advantage of
the unique and tunable stereoelectronic properties of the NHC
ligand. Importantly, NHC ligands are of increasing interest with
a broad range of applications.9−11 Furthermore, unique
activities and selectivities have been reported for Cr-based
catalysts12,13 and Cr−arene π interactions may play a more
significant role during catalysis than previously thought.14
INTRODUCTION
■
Studies on intermolecular noncovalent interactions and their
role in chemical and biological phenomena are of considerable
current interest, owing to their relevance to molecular
recognition, self-assembly, transport, organocatalysis, sensors,
and crystal engineering. A better understanding of the
intermolecular interactions involving polarizable π networks
has been gained through multidimensional experimental and
theoretical work on model systems, including accurate
structural determinations by crystallography and predictions
by high-level computational methods.1
Noncovalent interactions fall in the range of ca. 1−50 kJ/mol
and extend beyond ca. 3.0 Å, where conventional chemical
bonding is absent.1 At shorter distances, they may still be
present but masked by the much stronger covalent bonding.
Currently, the arene−arene and cation−π noncovalent
interactions are the best understood, the latter being common
in nature due to the favorable interaction of electron-rich
domains with neighboring positive charges. Very recently, rapid
progress has occurred on intermolecular perfluoroarene−π, H-
bond−π, and anion−π interactions, π denoting an aromatic ring
system.2,3 The interaction between the induced instantaneous
Received: December 27, 2012
© XXXX American Chemical Society
A
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Herein, we describe novel open-shell benzyl CrII organo-
metallics in which remarkable angular distortions at the Cr−
CH2−Ph sp3 carbon are observed. Although the benzyl ligand is
well known for its ability to interact with electron-deficient
metal centers through its π-aromatic system,15 possibly leading
to rather acute angles at their sp3 benzylic carbon, it will be
demonstrated here, using high-level computational methods,
that this explanation does not provide sufficient insight in our
case. We will also compare the bending of the benzyl ligands in
the new d4 CrII organometallics [Cr(NHC)2(benzyl)2] (2) and
[Cr(NHC*)(benzyl)2] (3) (NHC = N,N′-diisopropylimidazol-
2-ylidene; NHC* = N,N′-bis(2,6-diisopropylphenyl)imidazol-
2-ylidene) with that in the d0 [Zr(benzyl)4] complex, which
exists in two polymorphic structures with different metrical
data, in particular for the benzyl ligands; this has been recently
revisited using DFT methodologies.16 The involvement of
intramolecular noncovalent interactions in the CrII complexes
and the role of polarization effects will be justified. To the best
of our knowledge, the contribution of the latter to the bonding
of open-shell transition metal arene complexes has previously
not been recognized. We anticipate that the study of their
nature, range, scope, and creative manipulation may comple-
ment established paradigms on structure/bonding relationships
and have unforeseeable implications in open-shell transition
metal chemistry. This also opens the possibility that in other
cases, too, a new insight into the reasons for structural
distortions may be required.
Figure 1. (Left) ORTEP of the CrII benzyl complex 2 in 2·THF.
Ellipsoids are at the 40% probability level; only one disordered benzyl
group trans to atom C4 is shown. Hydrogen atoms are omitted for
clarity. Selected distances (Å) and angles (deg): Cr1−C4 2.1624(15),
Cr1−C1 2.1668(16), Cr1−C19A 2.153(3), Cr1···C20A 2.684(3),
Cr1−C26 2.1849(16), Cr1···C27 2.854(2); C4−Cr1−C1 90.76(6),
C4−Cr1−C26 93.59(6), C1−Cr1−C26 158.70(6), C27−C26−Cr1
100.79(11), C20A−C19A−Cr1 93.11(13) C20B−C19B−Cr1
93.18(19). (Right) Partial space-filling representation of the
experimental structure, involving the arene ring of the benzyl and
the iPr group of the corresponding NHC ligand, indicating the
absence of interligand intramolecular contacts.
majority of the examples, the M−CH2−Cipso angle lies in the
110−120° range, intuitively corresponding to a classical η1
arrangement implying an sp3 hybridization for the metalated
carbon. There is a gradual (apparently not bimodal) shift
toward more acute angles, suggesting a flat energy profile
RESULTS AND DISCUSSION
■
Initial attempts showed that complex 2, a N-heterocyclic
carbene-stabilized 3d4-CrII bis-benzyl complex, is accessible
from the CrIII organometallic complex 1 (for structural details,
see Table S1 and Figure S2 in the Supporting Information
(SI))17 by a redox reaction that is not yet fully elucidated
(Scheme 1).
responsible for the decrease of M−CH2−Cipso
.
Remarkably, structurally characterized Cr benzyl
−
(C6H5CH2 , Bz) complexes are relatively rare (26 hits in the
CSD, including 4 for CrII, 20 for CrIII, and 2 for CrVI), despite
the important role of this ligand in the development of stable
transition metal organometallics18 and, consequently, its
widespread use in group 4 metal model compounds (e.g.,
[MBz4], M = Ti, Zr, Hf) and in catalytic precursors.19,20
Only twice before have angular distortions comparable to
those in 2 been observed in Cr chemistry: (i) in the CrVI
complex [Cr(NtBu)2Bz2] and the related [Cr(κ2-
NCMe2CH2CH2CMe2N)Bz2]21 and (ii) the diamagnetic CrII
nitrosyl complex [Cr(NO)(NiPr2)Bz2].22 However, their origin
has not been investigated in detail. When acute (<109°) critical
angles are observed in group 4 and 5 organometallics, two
widely accepted rationalizations are offered. The first invokes
the role of intermolecular crystal packing forces. However, in
the structure of 2·THF, there are no specific intermolecular
contacts involving the benzyl ligands, neither with the solvent
of crystallization nor with neighboring molecules (Figure 2).
The second rationalization postulates overlap between the
empty metal d orbitals and filled π orbitals of the aromatic ring,
in particular the one mostly localized on the aromatic ipso
carbon (see also further discussion below) and has been applied
to d0 [MBz4] (M = Ti, Zr, Hf) complexes.23 However, in
2·THF the dipso values (Cr−C27 2.854(2) Å, Cr−C20A
2.684(3) Å, and Cr−C20B 2.747(3) Å) are at least 30% larger
than the dbenzyl (Cr−C26 2.185(2) Å, Cr−C19A 2.153(3) Å,
and Cr−C19B 2.232(4) Å) (Scheme 2), so that an explanation
restricted to orbital overlaps appears insufficient and we
suspected that other factors may be at work.
Scheme 1. Synthesis of [Cr(NHC)2(benzyl)2] (2) in 2·THF
Complex 2 has limited thermal stability at room temperature
and was characterized by chemical and X-ray diffraction
methods (Table S1, SI). The metal coordination geometry in
2 is distorted square-planar (Figure 1), with an unusual cis-
arrangement of the benzyl ligands.
Noticeably, all ligands in this 12-valence electron complex are
strong carbon σ-donors. Although bond lengths are in the
expected ranges, the values of the bond angles subtended at the
benzylic carbons (hereafter referred to as critical angles) are
remarkable: 100.79(11)° for Cr1−C26−C27 and 93.11(13)°
and 93.18(19)° for Cr1−C19−C20; the latter two values
correspond to the benzyl ligand that is disordered over two
positions, A and B, respectively.
A statistical analysis of transition metal benzyl angles found
in the CSD is provided in Figure S1 (SI). It shows that in the
The high-level theoretical calculations detailed below show
that electrons localized in d orbitals switch on polarization
B
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Very recently, polarization-induced lone-pair−arene interac-
tions were briefly outlined in main group chemistry for
As(III)−πarene complexes.24 However full elucidation of this
phenomenon was not provided, and the conclusions made were
based only on the data obtained from the use of density
functional theory and Hartree−Fock (HF) calculations that do
not deal with polarization effects. Herein, we combine ab initio
and density functional theory (DFT) methods to delineate the
role and mode of action of the PIMA and its structural
consequences.
Full (nonconstrained) gas-phase geometry optimizations of 2
were carried out for the S = 0, 1, and 2 spin states using
relativistic non- and dispersion-corrected25−29 DFT at ZORA-
UBP86(-D3)/TZP and established a quintet (S = 2) ground-
state structure, referred to as 2comput (see Tables S2 and S3, SI).
The other spin states are too high in energy (ca. 0.7 eV for S =
1) to compete with the S = 2 state. Environment continuum
medium effects modeling the situation in solution were also
considered (see Table S4, SI). For both the gas-phase and the
solvent shell situations, the experimental geometry was
reproduced satisfactorily enough (as detailed below) to suggest
that specific intermolecular crystal packing forces are negligible.
To evaluate the possible impact of London dispersion forces
on the benzylic angles in 2comput, we performed constrained
geometry optimizations of the target complex for its S = 2
ground state, with and without dispersion correction. The
relevant potential energy surfaces (PESs) were obtained and are
illustrated in Figure 4. They show the change in the total
Figure 2. Packing in the crystal structure of 2·THF showing the
absence of specific intermolecular interactions.
Scheme 2. Relevant Geometrical Parameters in Metal Benzyl
Systems
forces, leading to a type of interaction, namely, polarization-
induced metal−arene (PIMA) interaction, that has previously
not been identified in transition metal chemistry (Figure 3).
Figure 4. Potential energy surfaces (PESs) obtained from the critical
angle constrained geometry optimizations of 2comput with and without
Grimme’s dispersion correction of D3 generation to the UBP86
functional. The black rhombuses indicate the energy minima on the
PESs.
energy of the system as a function of one critical angle, the
value of which was varied in the range 70−120°, while the
geometry of the molecule was optimized. By fixing a benzyl
angle at 100.0°, which corresponds to the energy minimum on
the potential energy surface without applying dispersion
corrections (UBP86), we find the optimized angle of the
other benzyl ligand at 102.0°. By fixing now a benzyl angle at
95.0°, which corresponds to an energy minimum for the
constrained geometry of 2comput when taking into account
dispersion corrections (UBP86-D3), we find a value of 93.1°
for the angle of the other benzyl ligand. However, the reasons
for differentiation observed experimentally in 2·THF between
the two benzyl angles (ca. 93° and 101°) remains unclear. This
Figure 3. Schematic representation of intramolecular polarization-
induced metal−arene (PIMA) interactions (purple arcs) between a
single electron in a d orbital and the aromatic benzylic system,
resulting in an acute critical angle at the benzylic C atoms in 2. The
arrow along the Cipso−Cbenzylic and Cbenzylic−Cr bonds indicates
electron-withdrawing effects due to the CrII cation; the arrow across
the aromatic ring represents the instantaneous dipole responsible for
the noncovalent interactions.
C
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feature may be the result of the competition between the PIMA
interaction discussed in this work and the steric repulsion that
would result from the simultaneous bending of two benzyl
ligands, and this is the subject of work in progress. The low-
angle value-regime experimentally observed and supported by
DFT calculations including dispersion forces remains intrigu-
ing.
Thus, we wanted to explore in more detail the possible
physical reasons that may contribute to the bending of these
benzylic critical angles and analyze the relevant intramolecular
interactions in 2, using a wave function-based CASPT2 strategy
that is also more suitable for open-shell electronic structures
and when weak interactions are simultaneously present.30 On
the basis of the additivity of the energy corrections inherent in a
perturbative scheme, we explored the polarization effects
involving the aromatic rings (see SI). A CAS[10,10] active
space was first converged onto the benzyl ring π network (6
electrons, 6 MOs) together with the four relevant d-type
orbitals (4 electrons, 4 MOs). These CAS[10,10]SCF
calculations were performed as a function of the critical angle
to evaluate the contributions arising from (i) the interaction
between the Cr d orbitals and the Cipso orbital and (ii) the
fluctuating induced dipole within the π system depicted by six
MOs (Figure 5). The latter contribution evidently cannot be
accounted for using a classical electrostatic description. We
show below that the dominant contribution to PIMA arises
from a polarization of the benzylic π system induced by the
metal d shell rather than by the cationic nature of the soft metal
center.
A leading open-shell character for all spin states (even for S =
0) was observed, meaning that the mostly d-like MOs are
essentially singly occupied. Quantitatively, the analysis of the
wave functions led to natural 3d-type orbitals with occupancy
numbers in the range 0.999−1.001. Subsequently, the active
space was reduced to a minimal CAS[4,4] consisting of the four
singly occupied d-type orbitals, and a perturbative treatment
(CASPT2) was carried out by (i) freezing the benzyl π
network, (ii) allowing the π back-donation, and (iii) including
all the active and inactive MOs. This was done in order to
capture the PIMA energetic contribution and its role in the
dictation of the observed geometry. The potential energy curve
displays a minimum at ca. 103° in the absence of charge
fluctuations within the benzyl ring (Figure 6, top). A similar
observation is made when π back-donation is switched on.
Thus, the origin of the smaller critical angle values (ca. 93.1°)
found experimentally cannot be solely attributed to the direct
interaction between the Cr d and Cipso orbitals.
Figure 5. CASSCF active MOs of 2 and their occupancies
corresponding to the electronic configuration in the S = 2 spin state.
40 kJ/mol is calculated when the angle is changed from 109.5°
to 90° (see Figure 6, bottom).
Indeed, as soon as the polarization effects of the benzyl ring
are included, the minimum is shifted down to ca. 93°,
supporting the herein proposed role of this polarization-
induced mechanism. Using as reference the total energy
corresponding to a critical angle value of 109.5°, we also
calculated an energy stabilization of ca. 23 kJ/mol, as compared
to 5 kJ/mol in the absence of PIMA interaction (see Figure 6,
top). Not only is the experimental structure well reproduced,
but the calculated critical angle value is in excellent agreement
with the value of the most acute angle extracted from our
reference and most accurate CAS[10,10]PT2 calculations (ca.
93° in Figure 6, bottom).
The scope and relative importance of PIMA in the presence
of other intramolecular interactions (covalent or not) in
organometallics were the next key questions to address. Bearing
in mind that the occurrence of PIMA requires (i) occupancy of
a d orbital suitably oriented with respect to the aromatic ring
(see Figure 5) and (ii) the presence of an electron-withdrawing
moiety (the role fulfilled by Cr(II) in 2), we examined how
depletion of electron density on the metal center may influence
the magnitude of the “critical angle”, first by maintaining the
same 3d orbital occupancy and second by moving to a d0
situation. In the former case, the structural impact of removal of
a NHC ligand from 2, leading to a hypothetical three-
coordinate Cr(NHC)(benzyl)2 complex, 2′comput, was theoret-
ically investigated. DFT full and constrained structure
optimization carried out at the UBP86-D3 level of theory led
to a geometry displaying one critical angle value of 76.3°
The behavior of the energy associated with the fluctuating
induced dipole (see π-like MOs in Figure 5) interacting with
the singly occupied Cr 3d-character MOs is monotonic, and a
significant energy gain arising from the PIMA interaction of ca.
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Figure 6. (Top) Dashed blue and solid red curves represent the
CAS[4,4]PT2 total energies (in eV) with inclusion and exclusion of
the PIMA interaction, respectively. The reference energies are taken
for a critical angle value of 109.5° (i.e., sp3 geometry). (Bottom)
Dashed blue curve represents the CAS[10,10]PT2 potential energy
curve (in eV) of the S = 2 ground state of 2 as a function of the critical
angle (deg). A similar curve holds for S = 0, 1. A minimum occurs for
93°, a value observed in the crystal structure. The solid, green curve
represents the variation of the PIMA interaction as a function of the
critical angle.
(Figure 7; 78.2° at UBP86 and Figure S6 in SI) for a S = 2
ground state, which made the synthesis of such a complex
particularly appealing and worthwhile.
Figure 7. Spatial representation of the four highest singly occupied
DFT-generated α-spin MOs with dominant Cr d-type character of the
CrII benzyl complexes 2comput (left) and 2′comput (right) in their ground
states, S = 2. Hydrogen atoms are omitted for clarity.
Although a three-coordinate complex of the type [Cr-
(NHC)(benzyl)2] is expected to be less stable than a four-
coordinate [Cr(NHC)2(benzyl)2] complex and to exhibit a
smaller ligand field (cf. the energy splitting parameters Δ′ and
Δ, respectively, given in Figure 7), three-coordinate complex 3
was obtained by using a carbene ligand with a larger buried
volume31 (Scheme 3). The latter is a unique example of a three-
coordinate CrII complex with carbon-only donor ligands. This
complex was fully characterized by spectroscopic and diffraction
methods (see Figure 8 and Table S1 in SI).
Scheme 3. Synthesis of Three-Coordinate Complex 3
In remarkable agreement with 2′comput, complex 3 exhibits a
Cr center coordinated by one NHC and two benzyl groups and
shows the predicted geometrical features, i.e., a distorted
trigonal planar environment (sum of the angles at Cr 358.1°)
and critical angles at C28 and C35 of 97.9(2)° and 76.6(2)°,
respectively. The occurrence of such an extreme bending was
inspected following the same energy partitioning as for 2. A
comparative summary of the changes in the critical angle values
for 2 and 3 is given in Table 1.
The operation of an instantaneous dipole in the arene ring is
responsible for a reduction of the critical angle value by ca. 10°
with respect to a static picture, leading ultimately to the
experimental values. The gain of 68 kJ/mol due to the PIMA is
an underlying factor for the stabilization of 3 and may be
responsible for its isolability.
result in larger benzylic critical angles. Indeed, this was
observed when the 4d0 complex [ZrBz4] was subjected to an
analysis similar to those described for 2 and 3. For the same
change of the critical angle from 109.5° to 90°, the PIMA
contributions vary by only ca. 10 kJ/mol (versus 40 and 55 kJ/
mol for 2 and 3, respectively), as anticipated. This establishes
that in general, and in particular with softer metal ions, the
cation-induced polarization of the benzyl π system could at best
be a minor contribution to PIMA. The acute critical angles
As mentioned above, we examined the effect of a complete
depletion of the d electron density in the vicinity of the
aromatic ring. This should reduce the PIMA contributions and
E
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refinement toward the understanding of unusual molecular
properties.
EXPERIMENTAL AND THEORETICAL SECTION
■
1. Synthesis and Characterization. 1.1. General Methods.
Elemental analyses were carried out by the microanalytical laboratory
of London Metropolitan University. All manipulations were performed
under nitrogen or argon in a Braun glovebox or using standard Schlenk
techniques, unless stated otherwise. Solvents were dried using standard
methods and distilled under nitrogen prior to use or passed through
columns of activated alumina and subsequently purged with nitrogen
or argon. The light petroleum used throughout had a bp 40−60 °C.
The starting materials N,N′-diisopropylimidazol-2-ylidene and sol-
utions of [Mg(benzyl)2] and [Mg(benzyl)2(THF)2] were prepared
according to literature procedures.32,33 [CrCl2(THF)2] was prepared
by continuous Soxhlet extraction of commercial anhydrous CrCl2 with
THF for 24−48 h under argon.
1.2. Synthesis of fac-Chromium Tri(benzyl)tris(tetrahydrofuran)
(1). To a stirred solution of [Cr(acac)3] (0.24 g, 0.7 mmol) in THF (5
mL) at −40 °C was added dropwise over a period of 5 min a
precooled solution of freshly prepared [Mg(benzyl)2] in ether (15 mL,
0.07 M, 1.05 mmol). After completion of the addition the purple
suspension was stirred at −40 °C for 4 h. By the end of this period the
reaction mixture was orange-brown. The reaction mixture was stored
at −30 °C for 5−8 days, affording large orange-brown crystals, which
were separated by syringing out the supernatant solution, washed with
cold (−40 °C) petrol (2 × 5 mL), and dried with a stream of nitrogen.
Drying under reduced pressure should be avoided because it leads to
decomposition possibly due to loss of THF. The crystalline 1 is
unstable at room temperature, completely collapsing into a brown oil
over 30−40 min. Solutions of 1 in THF are noticeably unstable above
−10 °C. Manipulations of the solid in the glovebox at room
temperature can be carried out, but as quickly as possible (<5 min),
with minor decomposition noticeable in this case too. Yield: 0.25 g. 1
was characterized by single-crystal X-ray diffraction as described below.
Attempts to scale up the reaction (up to ca. 1.0 g of [Cr(acac)3])
resulted in reduced yields.
1.3. Synthesis of cis-Chromium Dibenzylbis(N,N′-diisopropylimi-
ylimidazol-2-ylidene) (2). To a cold (−78 °C) solution of 1 (0.25 g,
0.5 mmol) in THF (3 mL) was added a solution of N,N′-
diisopropylimidazol-2-ylidene in toluene (4 mL, 0.28 M, 1.1 mmol).
The solution color changed to red immediately. Cooling to −30 °C
overnight gave air-sensitive, thermally unstable (>0 °C) dark orange
crystals, which were characterized crystallographically; in the crystal
the complex crystallized with one molecule of THF. Further efforts for
spectroscopic or analytical characterization of 2 were hampered by the
thermal instability.
Figure 8. ORTEP of the CrII bis-benzyl complex 3. Ellipsoids are at
the 40% probability level. Hydrogen atoms are omitted for clarity.
Selected distances (Å) and angles (deg): C1−Cr1 2.124(3), C28−Cr1
2.154(3); C35−Cr1 2.177(4), C36−Cr1 2.310(4), C37−Cr1
2.406(4), C28−Cr1−C35 153.80(14), C1−Cr1−C35 103.64(12),
C1−Cr1−C28 100.66(12), C29−C28−Cr1 97.9(2), C36−C35−Cr1
76.6(2).
Table 1. Critical Angle Values (deg) in 2 and 3
complex
PIMA excluded
PIMA included
experimental
2
3
103
87
93
75
93
77
[85.20(19)°, 88.85(19)°, 92.24(18)°, 98.6(2)°] observed in the
newly redetermined X-ray structure of [ZrBz4] are also
satisfactorily reproduced in the computed geometries of this
complex in the gas phase and in the solvent shell (see Table S5,
SI). With vanishing PIMA contribution, the deviation from sp3
angle can mostly be attributed to standard and enhanced
cation−π interactions owing to the presence of a +4 formal
point charge. Independent studies published during the
completion of our manuscript concluded on the flexibility of
the benzyl critical angles in various crystallographic forms of
[ZrBz4] but did not comment on its physical origin.16
1.4. Synthesis of Chromium Dibenzyl[N,N′-bis(2,6-
diisopropylphenyl)imidazol-2-ylidene)] (3). [CrCl2(THF)2] (0.25 g,
0.9 mmol) and N,N′-bis(2,6-diisopropyl phenyl)imidazol-2-ylidene)
(0.36 g, 0.9 mmol) were placed in a Schlenk tube in the glovebox. The
tube was attached to the vacuum line and cooled to −78 °C by means
of a dry ice acetone bath. At this temperature precooled THF (30 mL)
and dioxane (2 mL) were added, followed by dropwise addition of a
precooled solution of [Mg(benzyl)2(THF)2] in THF (0.42 g, 1.2
mmol in 10 mL). The light green reaction mixture was allowed to
warm to ca. 10 °C over a period of 16 h, giving a dark olive-green
solution. After removal of the volatiles under reduced pressure, the
residue was extracted with ether and filtered through Celite. Removal
of the ether under reduced pressure gave the product as dark green-
black crystalline material. X-ray quality crystals were obtained by
cooling dilute ether or pentane solutions at 4 °C for 2 days. Yield: 0.42
g, ca. 75%. Anal. Found: C, 78.50; H, 7.95; N, 4.25. Calcd for
C41H50CrN2: C, 79.06; H, 8.09; N, 4.50. The 1H NMR spectrum
(C6D6) shows only broad features of low diagnostic value.
CONCLUSION
■
Prompted by the structures of the novel CrII benzyl complexes
2·THF and 3, theoretical calculations led us to suggest that
their unusual acute benzyl angles cannot solely be explained by
the well-established orbital overlap and cation−π interactions,
but are dictated to a considerable degree by intramolecular
PIMA interactions. These manifest themselves when occupied
metal d orbitals are suitably oriented to polarize the π system of
the benzyl ring. Despite the fact that we are dealing here with
cationic metal centers, the occupancy of their d orbitals is
reminiscent of situations encountered in anion−π interac-
tions.1−3 Whereas with empty metal d orbitals cation−π
interactions are obviously enhanced, as in the 4d0 complex
[ZrBz4], PIMA interactions vanish. Although intermolecular
crystal packing forces and steric effects are commonly invoked
to explain structural distortions, they cannot account for the
remarkable structures of 2·THF and 3. The emerging unifying
view which includes PIMA interactions may have broader scope
and applicability. Considering the energy range of PIMA
interactions, we anticipate that these will provide a further
1.5. X-ray Crystallography. A summary of the crystal data, data
collection, and refinement for complexes 1, 2·THF, 3, and [ZrBz4] is
given in Table S1 of the SI. All data sets were collected on a Enraf-
Nonius Kappa CCD area detector diffractometer with an FR591
rotating anode (Mo Kα radiation, λ = 0.71073 Å) and an Oxford
F
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Cryosystems low-temperature device operating in ω scanning mode
with ψ and ω scans to fill the Ewald sphere, except for 3, which was
collected on a Bruker APEX II DUO Kappa-CCD diffractometer
equipped with an Oxford Cryosystem liquid N2 device, using Mo Kα
radiation. The cell parameters were determined using the APEX2
software.34 The programs used for control and integration were
Collect, Scalepack, and Denzo.35 All solutions and refinements were
performed using the WinGX36 package and all software packages
within. All non-hydrogen atoms were refined using anisotropic thermal
parameters, and hydrogen atoms were added using a riding model.
The crystals were mounted on a glass fiber with silicon grease, from
Fomblin vacuum oil. Crystals of the thermally unstable 1 and 2·THF
were quickly selected under a layer of Fomblin, which was kept at low
temperatures (ca. −100 °C) by a stream of cold nitrogen. In 2·THF, a
disorder involved the cocrystallized THF molecule and one of the
metalated benzyls. The solvent was disordered in three positions with
no atom in common and was refined anisotropically with restrained
geometrical and thermal parameters. The benzyl group was found
disordered in two positions with no atom in common and was refined
anisotropically with restrained geometrical and thermal parameters. A
MULTISCAN absorption correction was applied for all structures.37
CCDC crystallographic data (CCDC 868836 (1), 868837 (2·THF),
884835 (3), and 868838 ([ZrBz4]) contain the supplementary
crystallographic data for this paper, which can be obtained free of
charge from the Cambridge Crystallographic Data Center via www.
ccdc.cam.ac.uk/data_request/cif.
2. Computational Details. 2.1. Density Functional Theory
Calculations. DFT geometry optimizations were conducted for the
different spin multiplicities S = 0, 1, and 2, starting from the X-ray data,
first to track the packing effects. All calculations were performed using
the Amsterdam Density Functional (ADF) program developed by
Baerends and others.38,39 The numerical integration was performed
using the procedure developed by te Velde et al.39g,h The molecular
orbitals (MOs) were expanded in an uncontracted set of Slater-type
orbitals (STOs): TZP (no Gaussian functions are involved).39i The
basis set of triple-ζ quality was used for all atoms and augmented with
one set of polarization functions on each atom, i.e., 2p on H, 3d on C
and N, 4p on Cr, and 5p on Zr. The core shells of C and N (1s), Cr
(up to 2p), and Zr (up to 3d) were treated by the frozen-(small)-core
approximation.39c An auxiliary set of s, p, d, f, and g STOs was used to
fit the molecular density and to represent the Coulomb and exchange
potentials accurately in each self-consistent field cycle.39j
Equilibrium structures were optimized without any symmetry
restrictions using analytical gradient techniques.39k Because the BP86
density functional has been shown to be one of the three best GGA-
DFT functionals (along with PBE and PW91), producing the high
accuracy of optimized geometries using the ADF program package,40
geometries and their relevant energies were calculated at the BP86
level of the generalized gradient approximation (GGA): exchange was
described by Slater’s Xα potential39l with self-consistent nonlocal
corrections due to Becke,39m,n and the electron correlation was treated
in the Vosko−Wilk−Nusair (VWN) parametrization39o with self-
consistent nonlocal corrections due to Perdew39p (BP86).39q For the
open-shell complexes, the spin-unrestricted formalism, U, was used.
Grimme’s dispersion correction to (U)BP86 of D3 generation25,29
(denoted as (U)BP86-D3) was implemented to evaluate the
dependence of the studied complexes on dispersion.25−27,41 The
dispersion-corrected (U)BP86 functional has been used efficiently to
account for the possible London dispersion interactions, as was shown,
for example, in ref 42. Scalar relativistic effects were accounted for
using the zeroth-order regular approximation (ZORA).43 Minimum
energy geometries in the gas phase were verified to be equilibrium
structures (no negative imaginary frequencies) through vibrational
analysis.44 With the goal to demonstrate that the gas-phase structures
are independent of the presence of a homogeneous solvent medium
used during crystallization, ZORA-(U)BP86(-D3)/TZP was combined
with the conductor-like screening model (COSMO) of solvation with
the solvent-excluding surface to define the cavities surrounding these
structures.45 THF (ε = 7.58) was used as the solvent, and the atomic
radii were issued from the ADF program. Statistical thermal analysis
was performed.
2.2. Ab Initio CASSCF/CASPT2 Calculations. It is known that some
care must be taken in the presence of open shells. Indeed, the presence
of quasi-degenerate configurations calls for explicitly correlated
methods.46 In this respect, complete active space self-consistent field
(CASSCF) calculations allow one to generate a zeroth-order wave
function starting from the exact Hamiltonian of the system. At this
stage, all the physically relevant electronic configurations based on
optimal MOs are explicitly taken into account. Subsequent second-
order perturbation (CASPT2) calculations are then performed to
include the important atomic-like contributions, which play a crucial
role in the total energy determination. Let us stress that such
calculations are particularly attractive since one can concentrate the
numerical efforts on some part of the system and split the energy
contribution taking advantage of the additive character of a
perturbative treatment. This is precisely the strategy we used. Due
to the presence of four electrons in the Cr 3d orbitals and six electrons
of the π system, “mirror-glassing” CAS[10,10]SCF (10 electrons in 10
MOs) and subsequent CASPT2 were first carried out within each spin
multiplicity. At this stage, the enlargement of the active space to
2
2
include the mostly strongly antibonding dx −y orbital leaves the latter
almost unoccupied. Such calculations were performed by varying one
of the critical Cr−CH2−Cipso angles (CASPT2 potential energy
curve), while the rest of the geometry was maintained identical to the
X-ray one. Then, the active space was reduced down to a minimal
CAS[4,4], and CAS[4,4]PT2 calculations were performed, (i)
including all the inactive and virtual MOs and (ii) leaving out the 3
π-type and 3 π*-type MOs localized on the aromatic ring. The
difference between these two sets of calculations as a function of the
critical angle corresponds to the contributions we would like to
highlight. Besides, the structural impact of this contribution on the
critical angle value can be followed by turning on this specific
contribution. Physically, our inspection focuses on the instantaneous
charge fluctuations on the aromatic ring responding to the electronic
density localized on the Cr ion.
At the CAS[10,10] level of calculations, a leading open-shell
character for all spin states (S = 0, 1, 2) was observed, meaning that
the mostly d-like MOs are essentially singly occupied, and further
quantitative analysis led to natural 3d-type orbitals with occupancy
numbers in the range 0.999−1.001. The CAS[10,10]PT2 calculations
established a S = 2 ground state, the other spin states being too high in
energy (ca. 0.7 eV for S = 1) to compete with the S = 2 state.
All our calculations were performed using the MOLCAS 7.2 suite of
programs.47 In studies of weakly bound systems, one often encounters
the problem known as basis set superposition error (BSSE). The Boys
and Bernardi’s counterpoise correction is a strategy to eliminate such
an artifactual effect.48 This phenomenon has been recently examined
in detail for single molecules, where the problem lies in the definition
of the fragments to evaluate the counterpoise correction.49 Another
option is to increase the basis set quality since the error vanishes in the
limit of a complete basis set. Therefore, particular care was taken in the
definition of the interacting partners, and calculations were repeated by
growing in a balanced way the atomic basis sets. Since our purpose was
to concentrate the numerical effort on the π−π* charge fluctuations,
various extended ANO-RCC basis sets were used for the aromatic ring,
the ipso carbon, and the chromium ion.50
Calculations for the S = 0, 1, and 2 spin states were performed
successively using (i) double-ζ + polarization (DZP, 3s2p1d and
5s3p2d1f for C and Cr, respectively), (ii) triple-ζ + polarization (TZP,
4s3p2d1f and 6s4p3d2f1g for C and Cr, respectively), and ultimately
(iii) quadruple-ζ + polarization (QZP, 5s4p3d2f and 7s5p4d3f2g for C
and Cr, respectively) along with a 2s1p contraction for the hydrogen
atoms of the aromatic ring. The three other nearest neighbor C atoms
of the Cr coordination sphere hold a DZP basis set, while the rest of
the atoms of 2 and 3 are depicted using a DZ basis set. From this
numerical inspection, the convergence of the calculated CASPT2
energy differences with the basis set improvement is reached at the
TZP level. Indeed, the calculated energy differences vary by less than 2
kJ/mol (e.g., 5% for the PIMA contribution) when the basis set is
G
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Article
changed from TZP to QZP. In addition, the positions of the minima of
the potential energy curves are modified by less than 2°, a value that is
well below the experimentally observed critical angle value variations.
In light of this numerical inspection performed on the CrII complex
2, a TZP basis set quality was used for the ZrIV compound [ZrBz4].
The main difference lies in the empty character of the 4d orbitals of
the formally Zr4+ ion.
(10) Enders, D.; Niemeier, O.; Henseler, A. Chem. Rev. 2007, 107,
5606−5655.
(11) Hahn, F. E.; Jahnke, M. C. Angew. Chem., Int. Ed. 2008, 47,
3122−3172.
(12) Kim, S.-K.; Kim, T.-J.; Chung, J.-H.; Hahn, T.-K.; Chae, S.-S.;
Lee, H.-S.; Cheong, M.; Kang, S. O. Organometallics 2010, 29, 5805−
5811.
(13) Yang, Y.; Liu, Z.; Zhong, L.; Qiu, P.; Dong, Q.; Cheng, R.;
Vanderbilt, J.; Liu, B. Organometallics 2011, 30, 5297−5302.
(14) McDyre, L.; Carter, E.; Cavell, K. J.; Murphy, D. M.; Platts, J. A.;
Sampford, K.; Ward, B. D.; Gabrielli, W. F.; Hanton, M. J.; Smith, D.
M. Organometallics 2011, 30, 4505−4508.
ASSOCIATED CONTENT
* Supporting Information
Experimental details, crystallographic data (CCDC 868836 (1),
868837 (2·THF), 884835 (3), and 868838 ([ZrBz4]), and
details of calculations. This material is available free of charge
via the Internet at http://pubs.acs.org.
■
S
(15) See, for example: (a) Legzdins, P.; Jones, R. H.; Phillips, E. C.;
Yee, V. C.; Trotter, J.; Einstein, F. W. B. Organometallics 1991, 10, 986.
(b) Scholz, J.; Rehbaum, F.; Thiele, K. H.; Goddard, R.; Betz, P.;
Kruger, C. J. Organomet. Chem. 1993, 443, 93. (c) Pellecchia, C.;
Immirzi, A.; Pappalardo, D.; Peluso, A. Organometallics 1994, 13, 3773.
(16) Rong, Y.; Al-Harbi, A.; Parkin, G. Organometallics 2012, 31,
8208−8217
AUTHOR INFORMATION
Corresponding Author
*E-mail: danopoulos@unistra.fr (A.A.D.), vrobert@unistra.fr
(V.R.), braunstein@unistra.fr (P.B.).
■
(17) Kohn, R. D.; Kociok-Kohn, G.; Haufe, M. J. Organomet. Chem.
̈
̈
1995, 501, 303−307.
(18) Schrock, R. R.; Parshall, G. W. Chem. Rev. 1976, 76, 243−268.
(19) Zucchini, U.; Albizzati, E.; Giannini, U. J. Organomet. Chem.
1971, 26, 357−372.
Notes
The authors declare no competing financial interest.
(20) Chen, E. Y. X.; Rodriguez-Delgado, A. In Comprehensive
Organometallic Chemistry III; Vol. 4 (Bochmann, M., Vol. Ed.;
Crabtree, R. H.; Mingos, D. M. P., Chief Eds.), Elsevier, 2007; pp
759−1004.
ACKNOWLEDGMENTS
■
We thank the CNRS, the Universite
́
de Strasbourg (UdS), the
ieur et de la Recherche
Minister
̀
e de l′Enseignement Super
́
(21) (a) Coles, M. P.; Dalby, C. I.; Gibson, V. C.; Clegg, W.;
Elsegood, M. R. J. Chem. Commun. 1995, 1709. (b) Siemeling, U.;
(Paris), the International Center for Frontier Research in
Chemistry, Strasbourg (ucFRC, www.icfrc.fr), and the LabEx
“Chemistry of Complex Systems”. A.A.D. is grateful to the
Kolling, L.; Stammler, A.; Stammler, H.-G.; Kaminski, E.; Fink, G.
̈
Chem. Commun. 2000, 1177−1178.
Reg
́
ion Alsace, the Dep
́
artement du Bas-Rhin, and the
(22) Jandciu, E. W.; Kuzelka, J.; Legzdins, P.; Rettig, S. J.; Smith, K.
M. Organometallics 1999, 18, 1994−2004.
Communaute
́
Urbaine de Strasbourg, for the award of a
Gutenberg Excellence Chair (2010−2011), and to the
University of Strasbourg Institute for Advanced Study for a
Fellowship (2013-2014). K.Y.M. is grateful to the Deutsche
Forschungsgemeinschaft (DFG) and the Gutenberg funding for
postdoctoral fellowships. S.C.-G. thanks Sasol Technology UK
for funding. We thank the UdS High-Performance Computing
Center for the provision of computational facilities and the
Service de Radiocrystallographie (Institut de Chimie, Stras-
bourg) for assistance with the crystallography. We are grateful
to Profs. P. Chen, J. C. Green, S. Grimme, and R. Hoffmann for
(23) (a) Bei, X.; Swenson, D. C.; Jordan, R. F. Organometallics 1997,
16, 3282−3302. (b) Giesbrecht, G. R.; Whitener, G. D.; Arnold, J.
Organometallics 2000, 19, 2809−2812.
(24) Zukerman-Schpector, J.; Otero-de-la-Roza, A.; Luana, V.;
̃
Tiekink, E. R. T. Chem. Commun. 2011, 47, 7608−7610.
(25) Grimme, S. J. Comput. Chem. 2006, 27, 1787−1799.
(26) Grimme, S.; Antony, J.; Schwabe, T.; Muck-Lichtenfeld, C. Org.
̈
Biomol. Chem. 2007, 5, 741.
(27) Grimme, S.; Hunerbein, R.; Ehrlich, S. ChemPhysChem. 2011,
̈
12, 1258.
(28) Grimme, S. Chem.Eur. J. 2012, 18, 9955−9964.
(29) Grimme, S.; Anthony, J.; Ehrlich, S.; Krieg, H. J. Chem. Phys.
2010, 132, 154104.
́
their valuable input and to Dr. G. Pilet, M. Verot, and F. Houis
for producing the artwork.
(30) Kepenekian, M.; Le Guennic, B.; Awaga, K.; Robert, V. Phys.
REFERENCES
Chem. Chem. Phys. 2009, 11, 6066−6071.
■
(31) Viciu, M. S.; Navarro, O.; Germaneau, R. F.; Kelly, R. A., III;
Sommer, W.; Marion, N.; Stevens, E. D.; Cavallo, L.; Nolan, S. P.
Organometallics 2004, 23, 1629−1635.
(1) Salonen, L. M.; Ellermann, M.; Diederich, F. Angew. Chem., Int.
Ed. 2011, 50, 4808−4842.
(2) Beer, P. D.; Gale, P. A. Angew. Chem., Int. Ed. 2001, 40, 486−516.
(3) Schottel, B. L.; Chifotides, H. T.; Dunbar, K. R. Chem. Soc. Rev.
2008, 37, 68−83.
(32) Burling, S.; Paine, B. M.; Nama, D.; Brown, V. S.; Mahon, M. F.;
Prior, T. J.; Pregosin, P. S.; Whittlesey, M. K.; Williams, J. M. J. J. Am.
Chem. Soc. 2007, 129, 1987.
(4) Sinnokrot, M. O.; Sherrill, C. D. J. Phys. Chem. A 2006, 110,
10656−10668.
(33) Wagner, B. O.; Hammond, G. J. Organomet. Chem. 1975, 85, 1.
(34) APEX2; BrukerAXS Inc: Madison, WI, USA, 2006.
(35) Hooft, R. COLLECT; Nonius BV, 1997−2000. Otwinoski, Z.;
Minor, W. SCALEPACK, DENZO. Methods Enzymol. 1997, 276, 307.
(36) Farrugia, L. J. J. Appl. Crystallogr. 1999, 32, 83.
(37) Blessing, R. H. Acta Crystallogr., Sect. A 1995, 51, 33.
(38) Baerends, E. J.; Autschbach, J.; Berces, A.; Bo, C.; Boerrigter, P.
́
M.; Cavallo, L.; Chong, D. P.; Deng, L.; Dickson, R. M.; Ellis, D. E.;
Fan, L. ; Fischer, T. H.; Fonseca Guerra, C.; van Gisbergen, S. J. A.;
(5) Bhandari, G.; Kim, Y.; McFarland, J. M.; Rheingold, A. L.;
Theopold, K. H. Organometallics 1995, 14, 738−745.
(6) Agapie, T.; Day, M. W.; Henling, L. M.; Labinger, J. A.; Bercaw, J.
E. Organometallics 2006, 25, 2733−2742.
́
(7) van Leeuwen, P. W. N. M.; Clement, N. D.; Tschan, M. J. L.
Coord. Chem. Rev. 2011, 255, 1499−1517.
(8) (a) Hogan, J. P.; Banks, R. L. Phillips Petroleum Co., Belg. Pat.
530617, 1955; U.S. Pat. 2825721, 1958. (b) Hogan, J. P. J. Polym. Sci.
1970, 8, 2637−2652. (c) Karapinka, G. L. U.S. Pat. 3709853, 1973.
(d) Karol, F. J.; Karapinka, G. L.; Wu, C.; Dow, A. W.; Johnson, R. N.;
Garrick, W. L. J. Polym. Sci. 1972, 10, 2621−2637.
Groeneveld, J. A.; Gritsenko, O. V.; Gruning, M.; Harris, F. E.; van den
̈
Hoek, P.; Jacobsen, H.; van Kessel, G.; Kootstra, F.; van Lenthe, E.;
McCormack, D. A. ; Osinga, V. P.; Patchkovskii, S.; Philipsen, P. H. T.;
Post, D.; Pye, C. C.; Ravenek, W.; Ros, P.; Schipper, P. R. T.;
(9) Cazin, S. J. C. N-Heterocyclic Carbenes in Transition Metal
Catalysis and Organocatalysis; Springer Verlag, 2010.
̀
Schreckenbach, G.; Snijders, J. G.; Sola, M.; Swart, M.; Swerhone, D.;
H
dx.doi.org/10.1021/om3012568 | Organometallics XXXX, XXX, XXX−XXX

Organometallics
Article
te Velde, G.; Vernooijs, P.; Versluis, L.; Visser, O.; van Wezenbeek, E.;
Wiesenekker, G.; Wolff, S. K. ; Woo, T. K. ; Ziegler, T. ADF2010.01;
2010, SCM, Theoretical Chemistry, Vrije Universiteit: Amsterdam,
The Netherlands, http://www.scm.com.
(39) (a) te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca
Guerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. J.
Comput. Chem. 2001, 22, 931. (b) Fonseca Guerra, C.; Visser, O.;
Snijders, J. G.; te Velde, G.; Baerends, E. J. In Methods and Techniques
for Computational Chemistry; Clementi, E.; Corongiu, G., Eds.; STEF:
Cagliari, 1995; pp 305−395. (c) Baerends, E. J.; Ellis, D. E.; Ros, P.
Chem. Phys. 1973, 2, 41. (d) Baerends, E. J.; Ros, P. Chem. Phys. 1975,
8, 412. (e) Baerends, E. J.; Ros, P. Int. J. Quantum Chem. Symp. 1978,
12, 169. (f) Fonseca Guerra, C.; Snijders, J. G.; te Velde, G.; Baerends,
E. J. Theor. Chem. Acc. 1998, 99, 391. (g) Boerrigter, P. M.; te Velde,
G.; Baerends, E. J. Int. J. Quantum Chem. 1988, 33, 87. (h) te Velde,
G.; Baerends, E. J. J. Comput. Phys. 1992, 99, 84. (i) Snijders, G.;
Vernooijs, P.; Baerends, E. J. At. Nucl. Data Tables 1981, 26, 483.
(j) Krijn, J.; Baerends, E. J. Fit-Functions in the HFS-Method; Internal
Report (in Dutch); Vrije Universiteit: Amsterdam, 1984. (k) Versluis,
L.; Ziegler, T. J. Chem. Phys. 1988, 88, 322. (l) Slater, J. C. Quantum
Theory of Molecules and Solids, Vol. 4; McGraw-Hill: New York, 1974.
(m) Becke, A. D. J. Chem. Phys. 1986, 84, 4524. (n) Becke, A. D. Phys.
Rev. A 1988, 38, 3098. (o) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J.
Phys. 1980, 58, 1200. (p) Perdew, J. P. Phys. Rev. B 1986, 33, 8822;
Erratum Phys. Rev. B 1986, 34, 7406. (q) Fan, L.; Ziegler, T. J. Chem.
Phys. 1991, 94, 6057.
(40) Swart, M.; Snijders, J. G. Theor. Chem. Acc. 2003, 110, 34;
Erratum Theor. Chem. Acc. 2004, 111, 56.
(41) (a) Grimme, S. J. Comput. Chem. 2004, 25, 1463. (b) Siegbahn,
P. E. M.; Blomberg, M. R. A.; Chen, S.-L. J. Chem. Theory Comput.
2010, 6, 2040.
(42) See, for example: (a) Ruiz, J. M.; Fonseca Guerra, C.;
Bickelhaupt, F. M. J. Phys. Chem. A 2011, 115, 8310. (b) Banerjee, A.;
Raad, F. S.; Vankova, N.; Bassil, B. S.; Heine, T.; Kortz, U. Inorg. Chem.
2011, 50, 11667. (c) Ames, W.; Pantazis, D. A.; Krewald, V.; Cox, N.;
Messinger, J.; Lubitz, W.; Neese, F. J. Am. Chem. Soc. 2011, 133,
19743.
(43) van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys.
1994, 101, 9783.
(44) (a) Ber
D.; Ziegler, T. Comput. Phys. Commun. 1997, 100, 247. (b) Jacobsen,
H.; Berces, A.; Swerhone, D.; Ziegler, T. Comput. Phys. Commun. 1997,
100, 263. (c) Wolff, S. K. Int. J. Quantum Chem. 2005, 104, 645.
(45) (a) Klamt, A.; Schuurmann, G. J. Chem. Soc., Perkin Trans. 1993,
́
ces, A.; Dickson, R. M.; Fan, L.; Jacobsen, H.; Swerhone,
́
̈
̈
2, 799. (b) Klamt, A. J. Phys. Chem. 1995, 99, 2224. (c) Klamt, A.;
Jones, V. J. Chem. Phys. 1996, 105, 9972.
(46) (a) Banse, F.; Girerd, J.-J.; Robert, V. Eur. J. Inorg. Chem. 2008,
4786−4791. (b) Kepenekian, M.; Vetere, V.; Calborean, A.; Le
Guennic, B.; Maldivi, P.; Robert, V. Chem.Eur. J. 2011, 17, 12045−
12050. (c) Kepenekian, M.; Vetere, V.; Calborean, A.; Le Guennic, B.;
Maldivi, P.; Robert, V. J. Chem. Theor. Comput. 2011, 7, 3532−3539.
(47) MOLCAS The Next Generation. J. Comput. Chem. 2010, 31,
224−247.
(48) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553.
(49) Asturiol, D.; Duran, M.; Salvador, P. J. Chem. Phys. 2008, 128,
144108.
(50) Roos, B. O.; Lindh, R.; Malmqvist, P.-Å.; Veryazov, V.;
Widmark, P.-O. J. Phys. Chem. A 2005, 108, 2851.
I
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