Linear MgCp?2 vs Bent CaCp?2: London Dispersion, Ligand-Induced Charge Localizations, and Pseudo-Pregostic C-H?Ca Interactions

Article abstract of DOI:10.1021/acs.inorgchem.7b03079

In the family of metallocenes, MgCp?₂ (Cp? = pentamethylcyclopentadienyl) exhibits a regular linear sandwich structure, whereas CaCp?₂ is bent in both the gas phase and solid state. Bending is typically observed for metal ions which possess a lone pair. Here, we investigate which electronic differences cause the bending in complexes lacking lone pairs at the metal atoms. The bent gas-phase geometry of CaCp?₂ suggests that the bending must have an intramolecular origin. Geometry optimizations with and without dispersion effects/d-type polarization functions on MCp₂ and MCp?₂ gas-phase complexes (M = Ca, Mg) establish that attractive methyl?methyl London dispersion interactions play a decisive role in the bending in CaCp?₂. A sufficient polarizability of the metal to produce a shallow bending potential energy curve is a prerequisite but is not the reason for the bending. Concomitant ligand-induced charge concentrations and localizations at the metal atoms are studied in further detail, for which real-space bonding and orbital-based descriptors are used. Low-temperature crystal structures of MgCp?₂ and CaCp?₂ were determined which facilitated the identification and characterization of intermolecular pseudo-pregostic interactions, C-H?Ca, in the CaCp?₂ crystal structure.

Full text of DOI:10.1021/acs.inorgchem.7b03079

Article
pubs.acs.org/IC
Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX
Linear MgCp*2 vs Bent CaCp*2: London Dispersion, Ligand-Induced
Charge Localizations, and Pseudo-Pregostic C−H···Ca Interactions
Rumpa Pal,† Stefan Mebs,‡ Ming W. Shi,§ Dylan Jayatilaka,§ Joanna M. Krzeszczakowska,∥
Lorraine A. Malaspina,† Michal Wiecko,⊥,∇ Peter Luger,⊥ Malte Hesse,† Yu-Sheng Chen,#
Jens Beckmann,† and Simon Grabowsky*,†
†Universitat Bremen, Institut fur Anorganische Chemie und Kristallographie, Leobener Straße 3 and 7, 28359 Bremen, Germany
̈
̈
‡Freie Universitat Berlin, Institut fur Experimentalphysik, Arnimallee 14, 14195 Berlin, Germany
̈
̈
§The University of Western Australia, School of Molecular Sciences, 35 Stirling Highway, Perth Western Australia 6009, Australia
∥University of Warsaw, Biological and Chemical Research Centre, Chemistry Department, Zwirki i Wigury 101, 02-089 Warsaw,
Poland
⊥Freie Universitat Berlin, Institut fur Chemie und Biochemie, Anorganische Chemie, Fabeckstraße 36a, 14195 Berlin, Germany
̈
̈
#ChemMatCARS, Center for Advanced Radiation Sources, c/o Advanced Photon Source/ANL, The University of Chicago, 9700
South Cass Avenue, Building 434D, Argonne, Illinois 60439, United States
S
* Supporting Information
ABSTRACT: In the family of metallocenes, MgCp*2 (Cp* = pentamethylcyclopentadienyl)
exhibits a regular linear sandwich structure, whereas CaCp*2 is bent in both the gas phase and
solid state. Bending is typically observed for metal ions which possess a lone pair. Here, we
investigate which electronic differences cause the bending in complexes lacking lone pairs at
the metal atoms. The bent gas-phase geometry of CaCp*2 suggests that the bending must
have an intramolecular origin. Geometry optimizations with and without dispersion effects/d-
type polarization functions on MCp2 and MCp*2 gas-phase complexes (M = Ca, Mg)
establish that attractive methyl···methyl London dispersion interactions play a decisive role in
the bending in CaCp*2. A sufficient polarizability of the metal to produce a shallow bending
potential energy curve is a prerequisite but is not the reason for the bending. Concomitant
ligand-induced charge concentrations and localizations at the metal atoms are studied in
further detail, for which real-space bonding and orbital-based descriptors are used. Low-
temperature crystal structures of MgCp*2 and CaCp*2 were determined which facilitated the
identification and characterization of intermolecular pseudo-pregostic interactions, C−H···Ca, in the CaCp*2 crystal structure.
20
Therefore, it was a surprise when SmCp*2 and other
subsequently discovered Cp* complexes with lanthanoids or
alkaline-earth metals that do not bear a lone pair (e.g.,
CaCp*2,21,22 SrCp*2,23 BaCp*2,23 and EuCp*224) turned out to
be bent as well: i.e., they do not follow VSEPR model
predictions.25,26 Hence, they are called non-VSEPR struc-
tures.27 In case of alkaline-earth-metal Cp* complexes, MgCp*2
is linear in both the gas phase22 and solid state,28 whereas
CaCp*2 is bent in both the gas phase21,22 and solid state29 (see
Figure 1). The Cg−Ca−Cg angle is 154° from gas-phase
electron diffraction (GED)22 and 147.7/146.3° for the two
independent molecules in the asymmetric unit of the crystal
structure.29 A crystallographic study on various Cp* complexes
of alkaline-earth-metal and lanthanide ions indicates a linear
relationship between the bending angle (Cg−M−Cg) and the
corresponding metal radii.29 Here, we present a low-temper-
ature (12 and 100 K) crystallographic study in conjunction with
INTRODUCTION
■
Metallocenes belong to the fundamental knowledge base of
organometallic chemistry,1−3 that have fascinated researchers
due to their curious structural and bonding properties.4−7 Since
the discovery of ferrocene, bis(cyclopentadienyl)iron(II)
(FeCp2), in 1951 and the related Nobel Prize award,8
spectacular advances involving metallocenes are still being
made today. Very recently, the protonation of ferrocene was
described,9 and the double oxidation of bis-
(pentamethylcyclopentadienyl)iron(II) (FeCp*2) was reported,
yielding salts of the stable Fe(IV) dication [FeCp*2]2+.10 In
transition-metal complexes, metal−ligand M−Cp or M−Cp*
bonding has been studied on the basis of experimental and
theoretical electron density analyses.11−15
Classic ferrocene related Cp and Cp* sandwich complexes
with spherical central cations are linear: i.e., the two rings are
parallel to each other and the Cg−M−Cg angle (Cg = centroid
of the ring) is around 180°. Initially, the existence of bent-
sandwich structures was thought to be restricted to metal atoms
Received: December 11, 2017
that bear a lone pair (e.g., SnCp*2 and PbCp*217).18,19
16
© XXXX American Chemical Society
A
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complexes were considered separately as model systems
(Figure 2) to include all probable effects as discussed below.
Three different reasons have been put forward in the
literature to explain the bending in CaCp*2. The structure of
this article is composed to cover the three following points.
London Dispersion and Analysis of Methyl···Methyl
Interactions. The usual notion of methyl−methyl or hydro-
gen−hydrogen contacts is that they are repulsive. Conforma-
tions and reactivity in organic chemistry are often explained by
steric hindrance between alkyl groups: e.g. transannular strain
in medium-sized rings42 or allylic 1,3-strain.43 Although the
claim of the discovery of hydrogen−hydrogen bonding as a
stabilizing interaction in molecules and crystals44 was discussed
controversially,45 it has been shown that “dihydrogen contacts
in alkanes are subtle but not faint”, so that methyl−methyl
interactions become stabilizing and result in higher melting
points in n-alkanes with increasing alkane chain lengths.46 The
attractive term of the van der Waals equation (London
dispersion) is the reason for the stability of many well-known
and unusual compounds.47−51 Attractive forces due to London
dispersion are ascribed to nondirectional instantaneous dipole-
induced dipole interactions; hence, they are a class of
noncovalent interactions (NCIs).52−54 The importance of
London dispersion interactions to reactivity is more and
more recognized: e.g., in the case of skeletal rearrangement
reactions.55
It has been suggested that ring−ring distances in MCp*2
complexes are such that there may be attractive London
dispersion interactions between methyl groups on different
rings.35 This is corroborated by the fact that several MCp*2
complexes (M = Sm, Eu, Yb) are bent in the solid state, but
with larger alkyl substituents on the cyclopentadienyl rings the
bent angle opens up to maintain the same range of H···H
distances.27,56 It has been shown using molecular mechanics
that a force field which accounts for London dispersion forces
between the methylated cyclopentadienyl rings can explain the
bending.57,58 However, it is questionable how reliable such
estimates are, and furthermore molecular mechanics cannot
account for core deformation effects or induced charge
concentrations. Bent triple-decker Eu and Yb metallocenes
without alkyl substituents at the central C8H8 ring have been
taken as evidence against the importance of London
dispersion.59 Even if weak attractive interactions are important,
other factors such as covalent bonding, core polarization,
Figure 1. Molecular structures of MgCp*2 (left) and CaCp*2 (right)
obtained from their crystal structures at 100 K (MgCp*2) and 12 K
(CaCp*2, major disorder component).
electron-density- and orbital-derived criteria to investigate the
effects that cause bending. We use MgCp*2 and CaCp*2 as
model compounds because they present the two borderline
cases. Both MgCp*2 and CaCp*2 are highly reactive species
that extend their coordination sphere by reaction with σ-donor
ligands of different strengths such as N-heterocyclic carbenes,30
Cp*Ga(I),31 and CO.32,33 This means that there is no
structure−reactivity correlation that would allow conclusions
about the differences in the electronic situations of MgCp*2
and CaCp*2.
All ab initio calculations in the literature,34,35 addressing
linear vs bent geometries in MgCp*2 vs CaCp*2, respectively,
have considered MgCp2 and CaCp2 as model systems, instead
of Cp* complexes, which can lead to erroneous conclusions.
Although MgCp2 is monomeric and linear in both the gas
phase36 and crystal form,37 there is no experimental evidence
for a monomeric CaCp2 structure. In the crystal form, CaCp2 is
a coordination polymer with four Cp ligands in the
coordination sphere of the Ca2+ ion in a η5:η5:η3:η1 fashion,38
and the gas-phase structure does not exist due to low vapor
pressure. It has been argued19,39 that monomeric CaCp2 must
be bent because calcium halides, e.g. CaF2,40 and CaCp*2 are
also bent. To address the distortion at the metal atom, a basis
set was constructed with the aim of obtaining bent CaCp2.39
Other ab initio calculations show that CaCp2 is a linear
molecule and ∼3−5 kJ mol−1 is needed to bend it to 160°.35,41
In the present study, for the first time both Cp and Cp*
Figure 2. All model systems considered in this study.
B
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induced valence population, and ligand repulsion act together
to provide a very shallow bending potential curve35 as a
prerequisite to allow bending.
(first row in Figure 2) as model compounds in this study to
investigate the differences in LICCs at Mg2+ and Ca2+ ions.
Intermolecular Interactions and Agostic Interactions.
One of the most interesting structure and bonding properties of
organometallic compounds is the interaction of so-called
chemically inert C−H bonds of ligands with the transition
metals. Soon after the observation of unusually short C−H···M
contacts, Brookhart and Green recognized the importance of
these interactions for fundamental organometallic trans-
formations and named them “agostic”.77,78 A possible
classification of agostic interactions involves the chain lengths
between the interaction partners (e.g., α- and β-agostic
interactions).79 In the stringent definition, the nature of the
agostic interaction is described as a hydrogen atom being
covalently bonded to both a C atom and a transition-metal
atom, forming a three-center−two-electron bond.77 However,
C−H···M contacts span such a broad range of geometric
parameters and electronic features that it became necessary to
introduce other terminologies to distinguish “agostic” bonds
from noncovalent C−H···M contacts, which are called
“anagostic”.80,81 It has been difficult to characterize these C−
H···M interactions of varying strength, and hence a
combination of different techniques such as X-ray and neutron
diffraction, spectroscopic techniques (NMR, EPR, vibrational
spectra), topological analysis of charge density, molecular
orbital descriptions, and NBO analysis82 have been used to
explore them.77,83−88
Nature of the Metal Ion and the Metal···Cp* Bonding.
Concerning the electronic distribution around the metal atom,
two different explanations have been put forward to understand
the bent geometries in alkaline earth metal dihalides and related
compounds.
(a) Within the framework of the polarized ion model,60 large
cations may be polarized by anions. This is referred to as
“inverse polarization”, as opposed to the more common
polarization of anions by cations. In the case of MX2
compounds, only a bent structure can possess a permanent
dipole moment and is thus stabilized due to charge−dipole/
dipole−dipole interactions.61−63
(b) An alternative covalent bonding model64−66 explains that
while lighter atoms such as Be and Mg have only valence ns and
np orbitals for σ-bond formation with the ligands, the heavier
metals Ca, Sr, and Ba may involve their inner (n − 1)d orbitals,
which, due to symmetry restrictions, leads to a bent structure.
In terms of σ- and π-bonding character, simpler σ-bonded MX2
systems (e.g., CaF2) are predominantly bent,35 whereas π-
bonding sometimes favors VSEPR geometry and sometimes
prefers distortions.67 Cylindrical π-donor cyclopentadienyl
ligands appear to disfavor bending, and thus alkaline-earth-
metal and lanthanide(II) metallocenes (MCp2) are quasi-
linear,35 whereas hitherto unknown isoelectronic cations
[LaCp2]+ and [ScCp2]+ have been computed to be bent.34
However, the extent of metal−ligand covalency and of σ- and
π-bonding aspects are under debate.41,68
Agostic Interactions. The nature of agostic interactions is
governed by a distortion of an organometallic moiety which
brings an appended C−H bond into close proximity with the
metal center to form an intramolecular C−H···M interaction,
the metal atom having locally enhanced Lewis acidic sites and
the hydrogen atom of the C−H moiety developing a degree of
hydride character.83 Agostic C−H···M interactions are
characterized by relatively short M−H distances (∼1.8−2.3
Å), small M−H−C bond angles (∼90−140°), C−H bond
activation (elongation), a topological pattern indicating the
presence of a M−H bond (electron density at the bond critical
point in the range 0.04−0.05 au, Laplacian 0.15−0.25 au),88
Although initially these two models ((a) polarized ion model
and b) covalent bonding model) were discussed controversially,
detailed ab initio calculations show that the cation polarization
and d-orbital participation arguments are “two sides of the same
coin”.27,69 The radial density maxima of the outermost semicore
3p orbital of Ca and the inner 3d orbital of Ca are found in
similar regions.66 This means that, in spite of significant energy
differences between the two orbitals, a clear geometric
separation is not possible. Similarly, for d0 transition-metal
compounds, [MCH3]2+ (M = Sc, Y, La), it has been shown that
the radial nodal structure of 3d, 4d, and 5d orbitals involved in
M−C bond formation results in a significant polarization of
electron density in the inner electronic shells of the M atoms.70
The “extended VSEPR model”,71 based on the Laplacian of
the electron density, shows a nonspherical shape of the metal
core in bent alkaline-earth MX2 compounds.39,72,73 The local
maxima in the Laplacian maps are manifestations of bonding
and nonbonding electron pairs of Lewis theory. In the presence
of ligands, charge distributions in accessible n − 1 quantum
shells of metal atoms get distorted and produce local ligand-
induced charge concentrations (LICCs) around the metal
atoms spatially opposite to the attached ligands.74 Con-
sequently, these charge concentrations force the ligands to
find orientations as remote as possible from these local maxima
around the metal atom, resulting in a bent geometry. It is well
documented that the charge concentrations in the n − 1 outer
core shell of d-block elements arise from polarization of (n −
1)d and ns valence electrons. These (n − 1)d electrons can
actually be considered as valence electrons in the case of
transition metals and their chemistry, which even holds true for
d0 elements such as Ca.74−76 The LICCs produce local Lewis
acidity at the metal atom and thus intricate further interesting
bonding features. We have added the mono-Cp/Cp* cations
1
and a decreased NMR JC−H coupling constant.
Anagostic Interactions. Anagostic interactions are similar to
hydrogen bonds, with greater M−H distances (∼2.3−2.9 Å)
and wider M−H−C bond angles (∼110−170°) in comparison
to agostic interactions. The bonding situation is mostly
governed by electrostatics and three-center−four-electron
bonds.80
Pregostic Interactions. Weaker agostic bonds that still show
the signature of agostic interactions were termed pregostic by
Venanzi et al.89 The criteria are the same as for agostic
interactions (see above), but at a lower range of values.
Pseudo-Agostic Interactions. Intermolecular pseudo-agostic
interactions (IPA)82,90 are those in which the C−H bond can
donate electron density to an electron-deficient metal atom in
the same manner as in conventional intramolecular agostic
bonds. The same criteria as for agostic interactions hold (see
above).
Pseudo-Pregostic Interactions. Pseudo-pregostic interac-
tions are intermolecular pregostic interactions as defined in this
work (see the third section in the Results and Discussion).
To distinguish these interactions (agostic, anagostic,
pregostic, pseudo-agostic, pseudo-pregostic), the nature of the
metal atom, whether electron deficient or electron rich, plays a
crucial role. Local Lewis acidity at the metal center controls
C
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Table 1. Comparison of Experimental and Theoretical (B3LYP-D3/6-311++G(2d,2p)) Geometrical Parameters of CaCp*2 and
a
MgCp*2 and Computed Model Systems (Figure 2)
b
M−Cr
M−Cg
CMe···CMe
HMe···HMe
α
β
γ
CaCp*2, bent
2.617
2.320
min: 3.865
max: 6.111
min: 3.455(1)
max: 6.323(1)
5.207
min: 2.446
max: 5.201
min: 2.282
max: 6.196
4.010
155.1
32.6
1.7
c
CaCp*2, expt
2.633(8)
2.341(4)
147.6(1)
19.3(1)
2.5(1)
2.5
CaCp*2, linear
CaCp2
2.642
2.348
179.9
36.0
2.639
2.349
179.9
35.9
MgCp*2
2.312
1.968
4.370
3.060
3.160
3.151
180.0
36.0
1.1
MgCp*2, expt, eclipsed
MgCp*2, expt, staggered
MgCp2
2.308(6)
2.304(6)
2.336
1.963(1)
1.959(1)
2.001
4.019(2)
4.339(2)
177.6(1)
8.1(1)
36.0(1)
36.0
0.8(1)
0.9(1)
d
180.0
179.9
CaCp*+
2.499
2.185
2.2
3.8
CaCp+
2.520
2.213
MgCp*+
2.214
1.844
MgCp+
2.221
1.859
a
Definitions: Cr, ring carbon atom; CMe, methyl carbon atom; Cg, ring center of gravity. Except for the angle α and those entries where minimum
and maximum values are given, all entries refer to average values. In nearly all cases, the sample standard deviations are smaller than the number of
b
digits given in this table, so that we did not add them. The definitions of the angles α, β, and γ are given in ref 28 and in the header to the table. This
c
scheme was reprinted with permission from ref 28. Copyright 2003 American Chemical Society. There are two symmetry-independent molecules in
the asymmetric unit of CaCp*2. Only the molecule with no disorder in the five-membered ring and only the major disorder components for the
d
methyl groups were considered in this table. There is no standard deviation for this angle, because only half of the molecule is symmetry
independent and the other half is generated by crystallographic mirror symmetry.
agostic interactions.83,91 It has been shown that LICCs can be
12 K for CaCp*2 at the synchrotron Advanced Photon Source,
ChemMatCARS, Beamline 15ID-B, with an Apex 2 CCD detector.
found opposite to the hydrogen atom, which always points
toward a charge depletion zone at the central atom.74 Agostic
The software CrysAlisPro was used for data integration, processing,
absorption correction, scaling, and merging of the MgCp*2 data set.
bonding displayed by Lewis acidic d0 transition metals (such as
For CaCp*2, the APEX2 software suite was used for data integration.
Absorption correction and scaling was performed in SADABS, and the
unmerged data were used in the refinement. Further crystallographic
information and details about data collection and structure refinement
Ca) should be different from that of their later dn (n ≥ 2)
electron-rich transition-metal counterparts, which are able to
back-donate electrons and thus support a nascent alkene ligand.
In d0 compounds, a significant C−H activation is often absent
and delocalization of the C−H−M linkage over the metal−alkyl
moiety has been observed, as described by Scherer and
McGrady.83 The presence of close C−H···M contacts was
already noted in CaCp*2, BaCp*2, and related organo-
lanthanide species,29 but they were not investigated in detail
and not classified, which we will do in this study.
according to the Independent Atom model in the software SHELXL92
are given in Table S4. In CaCp*2, one of the five-membered Cp* rings
and several methyl groups are disordered over two positions. The
occupancies are nearly equal; however, for calculations of properties or
visualization purposes, only the major disorder component is used. In
MgCp*2 and CaCp*2, hydrogen atoms were found from the Fourier
difference map and then fixed geometrically on the basis of the residual
density peaks (AFIX 137). C and Ca atom anisotropic displacement
parameters (ADPs) were refined freely, whereas the H atom Uiso
values were determined using the SHELX riding model. After the
refinement, all C−H bond distances were elongated to 1.077 Å
according to averaged distances from neutron diffraction experiments
as reported in ref 93 to ensure the accurate calculation of energies and
interligand or intermolecular distances. Crystallographic information
files (CIFs) of the refined models are deposited with the Cambridge
Stuctural Database under deposition numbers CCDC 1532482 and
1532483. CIFs of the geometries with elongated C−H bonds as used
in this paper were additionally deposited in the Supporting
Information of this paper.
EXPERIMENTAL AND THEORETICAL SECTION
■
Synthesis, Crystallization, and Measurement. CaCp*2 crystals
were prepared under inert conditions according to previously reported
methods.29 MgCp*2 is a known compound28 and was obtained here
from a salt metathesis reaction of MgCl2 with LiCp* in Et2O and
subsequently recrystallized from toluene. Both compounds are highly
moisture sensitive, so that crystals were picked and prepared under a
constant flow of cold nitrogen gas. Crystals of both compounds are
soft and have weak scattering power, so that data sets could only be
collected up to a maximum resolution of 0.7 Å with a conventional X-
ray source at 100 K for MgCp*2 (Center for Microscopy,
Characterization and Analysis, University of Western Australia,
Excalibur Diffractometer, Oxford Diffraction CCD detector) and at
Computational Details. Molecular geometries for all compounds
shown in Figure 2 were fully optimized using B3LYP and B3LYP-D3/
6-311++G(2d,2p) levels of theory within the Gaussian09 package in
D
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the isolated state.94 The D3 version of Grimme’s dispersion correction
was applied.95 For the sandwich compounds, MCp*2 and MCp2, the
calculations were started separately from both linear and bent
structures at both levels of theory. The absence of imaginary
frequencies confirmed that the final optimized geometries were in
their local minima. In the case of MgCp*2, at the B3LYP-D3 level,
even very tight optimization conditions could not get rid of one low
negative frequency (−1.12 cm−1), which is in the noise of the method,
so that the resulting geometry was used for further analysis.
For CaCp*2, alternatively other dispersion-corrected functionals
were used (B97D and M06XD) as well as the B3LYP-D3BJ version of
the dispersion correction. All yielded qualitatively the same bent
geometries as B3LYP-D3. Other basis sets with lower degrees of
polarization functions or no polarization functions at all (6-311+
+G(d), 6-311++G, 6-31G(d)) were also used to study the influence of
polarization. SCF calculations at the fixed linear and bent geometries
obtained at B3LYP-D3/6-311++G(2d,2p) and B3LYP/6-311++G-
(2d,2p) levels were carried out with HF and MP2 functionals using the
same basis set to derive method-dependent energy differences. Relaxed
potential energy surface (PES) scans were carried out for the four
compounds MgCp2, CaCp2, MgCp*2, and CaCp*2 at the B3LYP-D3/
6-31G(d) and B3LYP-D3/6-311++G(2d,2p) levels with varying Cg−
M−Cg angle ranging from 140 to 180° in 5° intervals. For each angle,
all the other parameters were fully relaxed, with the Cg−M−Cg angle
kept fixed.
Single-point calculations of two different dimers of CaCp*2 at their
experimental geometries from the crystal structure were performed at
the B3LYP/6-311++g (2d,2p) level of theory. The interaction energies
of these dimer motifs were calculated using B3LYP/6-31G(d) in
conjunction with the model energy assumptions96 used within the
program Crystal Explorer (CE).97 Hirshfeld surfaces combined with an
electrostatic complementarity analysis98 as implemented in the CE
program97 were used to analyze the crystal packing.
The resulting wave functions were analyzed using various bonding
descriptors: topological analysis and calculation of integrated AIM
properties (charges and volumes) were carried out within the
framework of the quantum theory of atoms in molecules
(QTAIM)71,99 in the AIM2000 package;100 natural bond orbital
(NBO) and natural population analyses (NPA) were carried out using
the NBO6.0 program101 interfaced to Gaussian 09; electron
localizability indicator (ELI-D) basins102,103 and Laplacian grids were
generated using DGrid-4.6;104 the reduced density gradient (RDG)
based noncovalent interactions (NCI) descriptor105,106 was obtained
using NCI-MILANO.105 ELI-D, Laplacian, and NCI isosurfaces were
visualized with MolIso107 and the VMD package.108
Figure 3. Relaxed PES scans at the B3LYP-D3/6-311++G(2d,2p)
level of theory. The energies given are relative to the linear geometries.
Note that the bending potentials for the Mg compounds are much
steeper (left ordinate) and those for the Ca compounds much flatter
(right ordinate).
level. The result was a linear geometry. This finding supports
the argument that London dispersion interactions are
responsible and, more specifically, that dispersion interactions
between the methyl groups of the Cp* rings must be the
structurally directing motif for the bending. Table 1 shows that
upon bending the Ca−Cp* interactions become stronger, as
indicated by shortened M−C and M−Cg distances.
To quantify stabilization of the bent geometry over the linear
geometry, single-point calculations were performed at the
benchmark fully correlated MP2 level. HF, B3LYP, and B3LYP-
D3 results are also presented for comparison in Table 2. In all
Table 2. Stabilization Energy of CaCp*2, Bent over Linear
Geometry, Calculated with Various Methods of Theory with
and without Dispersion Correction
ECaCp* ,bent − ECaCp* ,linear (kJ mol−1
)
2
2
12.0
−4.3
2.0
HF (no disp)
MP2 (disp)
B3LYP (no disp)
B3LYP-D3 (disp)
RESULTS AND DISCUSSION
−4.8
■
London Dispersion and Analysis of Methyl···Methyl
Interactions. In Table 1, relevant geometric parameters of
experimental and optimized structures are shown for all model
systems (Figure 2). CaCp*2, CaCp2, MgCp*2, and MgCp2 exist
in the staggered conformation (β angle around 36°, see
definition of angles in the header of Table 1), except for one of
the two independent molecules in the asymmetric unit of the
crystal structure of MgCp*2. The Cg−M−Cg angle α shows
linear or quasi-linear minimum geometries for CaCp2, MgCp*2,
and MgCp2, but a bent minimum geometry for CaCp*2
computed to be 155°, which is in line with the PES scans
(Figure 3). In contrast, for CaCp*2, the optimization results in
a linear structure if dispersion correction was not included
(B3LYP level with the same basis set), even if the starting
geometry is bent, whereas the B3LYP-D3 optimized structure is
bent, even if the starting geometry is linear. Hence, the
dispersion term causes the bending. To test whether dispersion
interactions specifically between the methyl groups cause the
bent structure, we performed an optimization of the CaCp2
structure, which lacks the methyl groups, at the B3LYP-D3
the cases, the single-point input geometry for the bent structure
was taken from the B3LYP-D3 optimization, whereas the linear
geometry was taken from the B3LYP optimization. Both
methods that include dispersion effects (MP2 and B3LYP-D3)
confirm the bent structure to be 4−5 kJ/mol more stable than
the linear structure, whereas both methods without dispersion
effects or corrections (HF and B3LYP) favor a linear geometry.
To get an estimation of the dispersion interaction energy
between the two rings (disregarding the ring−metal inter-
actions), Grimme’s dispersion correction95 was calculated using
Crystal Explorer at the B3LYP/6-31g(d,p) (Fit = D2) level for
linear MgCp*2 and linear as well as bent CaCp*2. This method
was parametrized to basis set superposition error corrected
MP2 interaction energies and is known to be accurate to 2 kJ
mol−1 relative to CCSD(T) energies.96 The dispersion energy
is indicated in Figure 4, together with the minimum and
maximum HMe···HMe distances and the H···H bond paths in the
electron density. Roughly, the shorter the H···H distances, the
greater the dispersion energy. In linear MgCp*2 (Figure 4a),
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Figure 4. Molecular graphs from a QTAIM analysis of (a) MgCp*2, (b) CaCp*2, bent, (c) CaCp*2, linear, (d) MgCp2, and (e) CaCp2. Bond paths
are shown by light brown lines. Bond critical points (bcps), ring critical points (rcps) and cage critical points (ccps) are marked with red, yellow, and
green dots, respectively. Estimation of Grimme dispersion energies between the two Cp* rings (disregarding the ring−metal interactions) using
Crystal Explorer show the relationship between HMe···HMe distance and dispersion energy.
the average HMe···HMe distance between two Cp* rings is at a
minimum, 3.060 Å, and it produces the largest stabilizing
dispersion energy. Consequently, MgCp*2 is linear because, to
increase the attractive London-type H···H contact on one side,
it has to decrease it on the other side. This means that the
linear geometry is partially caused by the attempt to maximize
average London interactions, and not only by steric stress, weak
polarizability of Mg2+, or unfavorable C−H···H contact angles.
In linear CaCp*2 (Figure 4c), the average HMe···HMe distance,
4.010 Å, is much higher than in MgCp*2 because of Ca2+
having a larger radius than Mg2+; thus, no bond paths in the
electron density are found. Hence, for CaCp*2 (Figure 4b) to
maximize average London interactions the molecule must bend
to bring two to three methyl groups into close contact with
each other (here visualized as bond paths), leading to the
shortest HMe···HMe contact of 2.446 Å. In MgCp2 and CaCp2,
attractive London-type H···H contacts are not realized.
We have seen that the dispersion interaction energies play
the decisive role in determining the geometry of the system.
This dispersion energy term in B3LYP-D3 is an ad hoc energy
offset to the final molecular energy. Therefore, the correction is
applied after the density matrix has been calculated. In other
words, at any given geometry, B3LYP and B3LYP-D3 electron
densities are identical. This means that the electron correlation,
as included in the DFT-hybrid functional B3LYP, is not
sufficient to bend the molecule: it is the extra empirical
dispersion energy term that bends the CaCp*2 molecule, and
this is not reflected at all in the B3LYP-D3 electron density.
Remarkably, this means that the topological bond paths shown
in Figure 4 as well as all features related to the electron density
such as the NCI plots in Figure 5 are identical between the
B3LYP and B3LYP-D3 calculations. In turn, this means that
these features (bond paths and NCI regions) are not a
quantum-chemical representation of London dispersion and
hence do not visualize the reason why CaCp*2 bends. Indeed,
one can go further and say that any features in these plots are
precisely not the reason for bending because they also occur in
B3LYP (and in HF for that matter): i.e., they are maps showing
the non-dispersion features in the electron density of the
methyl−methyl interactions. It is known that the connection
between the dispersion energy and the electron density is the
perturbation and deformation of the electron cloud of the core
(Figure 6).109−113
Here we show that the NCI descriptor does not at all (DFT)
or only to a negligible extent (MP2) reflect London dispersion
forces (see Figures S2−S6 and related discussion in the
Supporting Information). This has been implied already by
Johnson et al. in ref 106 and recently shown explicitly by
Contreras-Garcia et al.: “...both dispersion-corrected and non-
dispersion-corrected functionals give quantitatively the same
image provided the geometry is kept fixed.”.114 This is even true
for a comparison of NCI integrated volumes obtained after
highly correlated CCSD and promolecular calculations.114
Hence, the information about dispersion is nearly entirely
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Figure 5. Isosurface representations of the noncovalent interaction (NCI) index. sign(λ2)ρ in au (see color scale) is mapped onto the reduced
density gradient isosurface (s(r) = 0.5): (a) MgCp*2; (b) CaCp*2, bent; (c) CaCp*2, linear; (d) MgCp2; (e) CaCp2. Blue surface parts refer to
attractive forces and red to repulsive forces. Green indicates weak interactions.
carried by the geometry, and the NCI regions (such as those in
Figure 5 between the methyl groups) can be understood as a
qualitative fingerprinting empirically correlated to dispersion
interactions but not as a quantum-chemical representation of
dispersion. The same holds for QTAIM bond paths. Previously,
the NCI descriptor has been used successfully and convincingly
in this qualitative fashion to unravel contributions of London
dispersion to noncovalent interactions, even at the DFT
level.106,115−117 Relevant to this study (compare Intermolecular
Interactions and Agostic Interactions), it was concluded on the
basis of NCI plots that “dispersion is the major contribution to
stabilize a metallocene dimer”.118
Nature of the Metal Ion and the Metal···Cp* Bonding.
Polarization of the Ca2+ core cannot be the reason for the bent
CaCp*2 geometry because CaCp2 is always linear. However, so
far we have not investigated the contribution of polarization at
the metal atoms and the degree of covalent bonding in M−C
interactions. In order to test the effect of polarization in the
CaCp*2 molecule, we have performed B3LYP-D3 calculations
with smaller basis sets, where fewer polarization basis functions
are used on the metal and the carbon atoms, 6-31G(d) and 6-
311++G(d), and a corresponding basis set without any
polarization functions, 6-311++G. If no polarization functions
are used, structure optimizations do not converge. In the case
of the two basis sets with only a single d-type polarization
Figure 6. Estimation of the effect of London dispersion on the
electron density in the form of a difference of the MP2 and B3LYP
electron densities for CaCp*2 at a contour level of 0.009 au: blue,
positive; red, negative. For a MP2-HF difference plot, see Figure S2c.
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Figure 7. ELI-D localization-domain representation of (a) MgCp*+ and (b) CaCp*+ at an isovalue of 1.578. H atom domains are depicted in
transparent mode. Black dots denote attractors of ELI basins. (c, d) Corresponding Laplacian plots with an isovalue of −3.78 au. (e, f) ELI-D basin
representations (one representative basin per core or valence basin type) delineated with their zero-flux surfaces or truncated at an electron density
isovalue of 0.001 au. The basin populations are also cut at the same isovalue and averaged over all five basins per core or valence basin type. Core
basins (C(M)) are given in turquoise/green, disynaptic valence basins (V(M,Cring)) in dark blue, and trisynaptic valence basins (V(M,Cring,Cring)) in
red. Values in parentheses are the population standard deviations upon averaging.
function for non-hydrogen atoms, both linear and bent
geometries occur for CaCp*2 but are energetically indistin-
guishable (Figure S1 in the Supporting Information). This
means that polarization at the metal atom in CaCp*2 plays a
facilitating role in that it produces a shallow bending potential
curve without which the attractive London dispersion energy
terms between the methyl groups would not be sufficiently high
to keep the molecule in a bent conformation.119
To characterize, visualize, and quantify the effects of the
polarization on the metal atoms and the M−Cp* bonding, in
this section linear and bent CaCp*2, CaCp*+, MgCp*2, and
MgCp*+ model systems and the free Cp*− anion (Figure 2)
have been analyzed. The cations have been chosen to study the
effect of polarization in the density induced by one ligand.
Results for CaCp2, CaCp+, MgCp2, MgCp+, and Cp− pertaining
to the research question in this chapter are similar to those for
their Cp* counterparts and are therefore deposited in the
Supporting Information. Topological and integrated ELI-D
bond descriptors for all the model systems are given in Table
S2.
Figure 7 shows the ELI-D in two representation types:
namely, localization-domain (first row) and basin representa-
tions (third row) of MgCp*+ and CaCp*+ in comparison to
Laplacian isosurfaces (second row). Structured ligand-induced
charge localizations (LICLs, a term introduced in this study)
are visible in the ELI-D around Mg2+ (Figure 7a), although they
are less pronounced than in the Ca analogue (Figure 7b) and
the appearance is different as expected, as it involves only p-
type orbitals. Ligand-induced charge concentrations (LICCs)
cannot be seen in the Laplacian, which is spherical in the case of
Mg (Figure 7c). In CaCp*+, there are five C(Ca) ELI-D basins
opposite to five Ca−C bonds (Figure 7b), similar to the case
for well-known trans-LICCs74 from Laplacian plots (Figure
7d). It seems that the ligand-induced signatures in the ELI-D
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are more detailed than in the Laplacian, which means that
LICLs and LICCs are complementary without contradicting
each other. The LICLs and LICCs are retained upon
complexation with a second Cp* ring (see Figure S7 in the
Supporting Information). For the bent CaCp*2 structure
localization and concentration of electrons toward the open
side are observed (Figure 8c,d).
II. Six V2(Ca,Cr) σ basins exist in the bent structure (Figure
S7) with lower average electron population, 0.177(24) e,
in comparison to ten disynaptic basins with 0.205(1) e in
the linear structure (Figure S7), although the extents of
localization of electrons in these basins are similar.
III. The average electron population in the V3(M,Cr,Cr) π
basins in the bent geometry is higher in comparison to
the linear geometry, indicating stronger π bonding M−C
interactions in the bent case.
II and III do not support the increase in σ-type covalent
bonding upon bending found previously using, e.g., NBO
analyses.34 To gain insights about this inconsistency, in the next
paragraph NBO analyses similar to those in previous studies are
described.
The charges on the metal atoms given in Table 3 are
significantly below 2, with the QTAIM charges being on
Table 3. Natural Population Analysis (NPA) Metal Charges,
Q(NPA), QTAIM Metal Charges, Q(AIM), and Natural
Atomic Orbital (NAO) Valence s, p, d Populations for Ca2+
and Mg2+ (4s, 4p, 3d Orbitals for Ca and 3s, 3p Orbitals for
a
Mg)
Q(NPA)
Q(AIM)
s
p
d
CaCp*2, bent
CaCp*2, linear
CaCp2
1.78
1.79
1.78
1.75
1.78
1.83
1.81
1.79
1.81
1.46
1.51
1.52
1.53
1.59
1.67
1.68
1.68
1.72
0.066
0.064
0.063
0.035
0.038
0.112
0.138
0.141
0.122
0.015
0.018
0.029
0.003
0.006
0.022
0.035
0.058
0.063
0.144
0.132
0.129
0.218
0.183
CaCp*+
CaCp+
MgCp*2
MgCp2
MgCp*+
MgCp+
Figure 8. CaCp*2, bent: (a) lowest unoccupied molecular orbital
(LUMO); (b) lone valency orbital, LV, from NBO analysis. The
contour level is 0.0265. Color code: blue, positive isosurface; red,
negative isosurface. (c, d) ELI localization domains around the Ca2+
ion (isovalue ELI = 1.598) from a calculation of dimer 1 as extracted
from the crystal structures. In (c), the Ca2+ ion is involved in C−H···
Ca intermolecular interactions, whereas the Ca2+ ion in (d) is not. In
Figure S18 in the Supporting Information, dimer 2 is shown, where
Ca2 is involved in a similar interaction and Ca1 is not.
a
All charges are given in e. All AIM-based charges are values cut at an
outer electron density contour of 0.001 au.
average lower by almost 0.2 e than the NPA charges. Deviations
from a charge of 2 are a measure of the degree of involvement
in covalent bonding. Ca is less positively charged than Mg,
especially in the AIM charges. This is in contrast to Ca being
more electropositive than Mg, which might lead to the
expectation of Ca being more positively charged. However,
the results confirm that the Ca ion is involved in more covalent
bonding. The slight decrease of charges upon bending in
comparison to the linear structure of CaCp*2 similarly indicates
more covalent bonding with the ligands.
Natural atomic orbital populations (NAO) are also given in
Table 3. NAO valence populations indicate participation of
these formally empty orbitals in the bonding. Weak Mg 3p
orbital valence population is responsible for the small LICLs in
Figure 7a. The contributions of Ca 3d orbitals are higher than
those of Ca 4s orbitals, with minor 4p orbital participation. The
3d orbital participation in all Ca compounds is similar to the 3s
orbital participation in the Mg compounds, which is reflected in
the more enhanced LICL/LICC features in the Ca compounds
in comparison to the Mg compounds (Figure 7 and Figure S7).
The 3d orbital population is highest in CaCp*+, probably
because the Ca−Cp* distance is shortest and thus the ligand-
induced effect is highest.
In a topological analysis of the ELI-D of the MCp*+
compounds (Figure 7e,f), the sum of electron populations of
the Ca core basins, C(Ca), is about 18 e, and for C(Mg) it is
about 8 e (Table S2), corresponding to Mg2+ and Ca2+. For Ca
there are two types of core basins which represent the LICLs,
and for Mg there is only one type. A disynaptic V2(M,Cr) basin
represents the σ-bonding part of the M−C interaction (shown
in blue in Figure 7e,f), whereas a trisynaptic V3(M,Cr,Cr) basin
(shown in red) represents M−C π bonding.
In the case of bent CaCp*2, the electron distribution is more
asymmetrical in comparison to the linear CaCp*2 structure
(Figure S7). Some noticeable differences between linear and
bent structures are as follows.
I. Four distinct C(Ca) basins in the bent geometry are
present with an average electron population of 2.06(10)
e with more localized electrons (dmax = 0.26(5), ELI-Dmax
= 1.609), in comparison to ten C(Ca) basins with a
population of 0.82(8) e and less localized electrons (dmax
= 0.35(1), ELI-Dmax = 1.610) in the linear structure
(Figure S7). dmax is the distance of the attractor
perpendicular to the straight bond axis.
In case of linear vs bent CaCp*2, there is a slight increase in
the total 3d orbital population toward the bent geometry. This
is consistent with the fact that adding d polarization functions is
essential to allow bending. Individual d orbital populations (dxy,
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Figure 9. Intermolecular C−H···Ca and CH3···H3C interactions in the CaCp*2 crystal structure forming the two different dimers: (a) dimer 1; (b)
dimer 2. RDG-based NCI isosurfaces for (c) dimer 1 and (d) dimer 2. sign(λ2)ρ in au (see color scale) is mapped onto the reduced density gradient
isosurface (s(r) = 0.5).
dyz, dxz; see Table S3 in the Supporting Information) show that
Intermolecular Interactions and Agostic Interactions.
MgCp*2 crystallizes in the monoclinic space group P21/c with
Z′ = 1.5 (Figure S8). In an earlier reported structure of
MgCp*2 at 200 K,28 one Cp* group was disordered over two
sites with occupancies 0.80:0.20. The two disordered species
were described as nearly staggered, β = 23.6°, and between
eclipsed and staggered, β = 11.9°. (For the definition of β, see
Table 1.) However, in the current data set collected at 100 K
the disorder has disappeared. The formerly disordered
molecule exists in the eclipsed conformation (β = 8.1(1)°),
and the second molecule in the asymmetric unit is in the
staggered conformation, with the Mg2+ ion being in an
inversion center. Both MgCp*2 molecules are linear with
∠Cg···Mg···Cg being 177.6(1)° (eclipsed) and 180° (stag-
gered). In the crystal packing, one staggered conformer does
not directly connect to another staggered conformer; instead, it
is surrounded by six eclipsed molecules with C−H···π and
CH3···H3C intermolecular contacts (Figure S10).
relative contributions from π bonding are slightly higher than
2
2
2
those from σ populations (s, dz , dx −y ), suggesting that π
bonding dominates the covalent bonding, as expected from the
ELI-D analysis. However, σ populations are not negligible and,
more importantly, they increase upon bending, whereas π
populations change only slightly with bending. Thus, in
agreement with previous studies,34 σ bonding contributions
increase for the bent metallocene structures, although they
represent a minor fraction of the total covalent bonding. The
average Ca−C Wiberg bond order increases from 0.338 to
0.356 upon bending. Although our findings in the framework of
the NBO analysis are consistent with previous findings for
MCp2 (M = Sc, La),34 in contrast to those studies we
+
emphasize that increased covalent σ bonding is not the reason
for CaCp*2 to remain/exist in the bent conformation, but it is a
concomitant effect. Attractive Me···Me London dispersion
interactions are the reason for CaCp*2 to be bent.
In bent CaCp*2, the ELI-D isosurface plot around Ca2+
(Figure 8c,d and Figure S18) is similar to the lone valence (LV)
type of orbitals from the NBO analysis (Figure 8b). The LV
population is small, 0.099 e, and the ELI-D basin in the region
also has a small electron population (Table S2). Hence, it is not
clear if the region really depicts local Lewis basicity. Another
indication that this may not be the case is the plot of the
LUMO of CaCp*2 in Figure 8a, which has a high probability
density on the same open side and would indicate a local Lewis
acidic character. These observations are important for the
interpretation of the nature of C−H···M interactions to be
studied in the crystal packing.
CaCp*2 crystallizes in the monoclinic space group P21/n
with Z′ = 2. The asymmetric unit is shown in Figures S9 and
S14. One of the two molecules in the asymmetric unit has a
disordered Cp* ring at 12 K, and many of the methyl groups
are also disordered. However, in an earlier paper on the
CaCp*2 crystal structure at 116 K29 the disorder was not
resolved and not modeled, although large ADPs suggested the
disorder to be present. Both molecules are bent and are in the
staggered conformation, with the Cg···Ca···Cg angles equaling
147.6(1) and ∼148.4(1)° (disordered).
In contrast to MgCp*2, the central metal ion in CaCp*2
interacts with symmetry-inequivalent neighboring molecules via
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C−H···Ca contacts, yielding two different types of dimers, 1
and 2, shown in Figure 9. In dimer 1, Ca1 interacts with one
methyl group, and in dimer 2 with two methyl groups. In
addition to the C−H···Ca interactions, further intermolecular
H···H close contacts appear in the dimers (Figure 9a,b) with
distances similar to the interligand H···H distances that are
representative of the attractive dispersion interactions which
cause the bending. In gas-phase calculations of the dimers at the
experimental geometries (major disorder components), bond
paths and corresponding bcps can be identified for both C−
H···Ca and CH3···H3C interactions. The topological values for
the C−H···Ca contacts are comparable to those of CH3···H3C
interactions (Tables S1 and S5). To investigate further the
nature of these C−H···Ca and CH3···H3C interactions, RDG-
based NCI isosurface plots were generated for both dimers
(Figure 9c,d). For both types of interactions, regions with dark
green color can be found, which means that they are slightly
attractive in nature. The Grimme dispersion energies between
the two CaCp*2 units in the dimers were calculated at the
B3LYP/6-31g(d,p) level (Fit = D2), within CrystalExplorer:
−66.8 kJ mol−l for dimer 1 and −105.6 kJ mol−l for dimer 2.
The higher dispersion energy term for dimer 2 is in agreement
with the greater number of C−H···Ca and H···H contacts in
dimer 2 (Figure 9a,b), which is represented by more
pronounced NCI regions between the molecules in dimer 2
(Figure 9c,d).
unlikely that the C−H···Ca interactions are similar to hydrogen
bonds (anagostic): rather, they are agostic or pregostic.
A detailed investigation of the C−H···Ca contacts on the
basis of associated geometrical and topological parameters is
presented in Table S1, with NBO analysis and frontier
molecular orbital diagrams presented in Table S6 and Figure
S17. These data establish that the character of the C−H···Ca
interactions is that of weak agostic interactions, called pregostic
interactions (see the Introduction), based on geometry,
electron, and orbital analyses, as follows.
Geometry and Density Analysis. Structural parameters fall
at the borderline for agostic bonds, as reported in the literature
(see the criteria listed in the Introduction). H···Ca distances are
slightly smaller than C···Ca distances, and ∠C−H···Ca angles
are between 90 and 110° (Table S5), which is in the range of
agostic interactions. Likewise, there is a bond path between Ca
and H, but the ρ(r) and ∇2ρ(r) values of the corresponding C−
H···Ca bond critical points (Table S5) are slightly lower than
those in Popelier’s criteria for agostic bonds.88
Orbital Analysis. The frontier molecular orbital analysis
shows delocalization of electrons between the Ca atom and the
neighboring C−H and C−C bonds of the Cp* ring, similar to
β-agostic interactions in d0 systems.83,91 In particular, the
HOMO-1 and HOMO-2 orbitals in both dimer 1 and dimer 2
depict a significant amount of delocalization between the metal
and ligand orbitals (Figure S17). An NBO analysis confirms the
delocalized nature of the C−H···Ca contacts. It shows
delocalization from σ(C−H) bonds to a low-lying Ca orbital,
a characteristic of agostic bonds formed by dn (n ≥ 2)
transition-metal complexes. In addition, C−C to M electron
donation, a further characteristic of agostic interactions, can be
found. However, the energy terms associated with these
electron delocalizations are very small and point toward
interactions which are weaker than regular agostic interactions.
It is noteworthy that in dimer 1 the low-lying orbital of Ca1
which is involved in the C−H···Ca interaction has a higher
occupancy than the corresponding orbital in the Ca2 atom,
suggesting that this intermolecular interaction affects the
electronic distribution. The same is true for atom Ca2 in
dimer 2.
Figure 10 shows the complementarity of the electrostatic
potential (ESP) mapped onto Hirshfeld surfaces (HSs).98 In
ELI-D Analysis. The two different Ca atoms in the dimeric
arrangement as transferred to the gas phase show nontrivial
differences in the ELI-D isosurface plots (Figure 8c,d). The
ELI-D isosurface disappears at the particular side of the Ca
atom which faces toward the methyl group, a signature of
enhanced local Lewis acidity characteristic of an agostic bond,
whereas the other Ca atom that is not involved in any C−H···
Ca interaction still shows the intact ELI-D surface at the same
isovalue.
In summary, the C−H···Ca contacts in CaCp*2 show a
combination of various features present in the literature for
agostic interactions. A d0 metal center is involved and the
geometric and topological values are in the range of weak
agostic interactions, weak M←L σ donation and delocalization
of metal and ligand orbitals are present, and a weak increase in
the local Lewis aciditiy through the interaction occurs. These
characteristics lead toward a classification as a pregostic bond.
However, since it is an intermolecular weak agostic interaction,
on the basis of the above analysis we propose that it should be
called a pseudo-pregostic interaction.
Figure 10. Electrostatic potential (ESP) mapped onto molecular
Hirshfeld surfaces for MgCp*2 in (a, b) and CaCp*2 (c, d). The color
scale is −0.01 au (red) to 0 au (white) and 0.01 au (blue).
both compounds, the π system of the Cp* rings leads to a
negative ESP (red) and the rim region to a positive ESP (blue).
The pocket generated in the bent CaCp*2 geometry exhibits a
significantly positive ESP and is hence electrophilic (Figure
10c). In other words, the pocket is acidic and there is no sign of
a significant charge accumulation at the metal (compare Figure
8 and the related discussion). Hence, according to the ESP, it is
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CONCLUSIONS
AUTHOR INFORMATION
Corresponding Author
*E-mail for S.G.: simon.grabowsky@uni-bremen.de.
ORCID
Rumpa Pal: 0000-0003-3080-3333
Stefan Mebs: 0000-0003-2877-3577
Jens Beckmann: 0000-0002-8548-1821
Simon Grabowsky: 0000-0002-3377-9474
■
■
The higher polarizability of the Ca2+ ion in comparison to the
Mg2+ ion was shown to be a prerequisite for the bending of
CaCp*2, but not the reason, which is in fact London dispersion
interactions between the methyl groups on the Cp* rings. The
effect of dispersion on the electron density was shown to be
near the atomic cores and is not represented rigidly in the
noncovalent interaction (NCI) index or in the topological
analysis within the quantum theory of atoms in molecules
(QTAIM). Nevertheless, the NCI index and QTAIM bond
paths can be understood as qualitative fingerprints of dispersion
interactions at a fixed geometry.
Present Address
∇Current address for M.W.: Bundesinstitut fur Risikobewer-
̈
tung, Max-Dohrn-Straße 8-10, 10589 Berlin, Germany.
Ligand-induced charge concentrations (LICCs) based on the
Laplacian of the electron density or ligand-induced charge
localizations (LICLs) based on the ELI (the term LICL is
coined in this study) are inherent properties of the d0 alkaline
earth metal ion Ca2+ in interaction with the Cp* rings and
represent its polarizability. However, LICCs/LICLs are effects
concomitant with the bending but are not the reason for the
bending. The LICLs are more sensitive to polarization by
ligands than LICCs in that they detect a structured pattern also
for the MgCp*+ ion, not only the CaCp*+ ion. Although a
significant involvement of Ca d orbitals in the bending of
CaCp*2 and an increase in σ bonding contributions upon
bending are confirmed, the major contribution to the Ca···C
interaction is of π character.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
S.G. thanks the German Research Foundation (DFG) for
funding within the Emmy Noether scheme GR 4451/1-1. All
authors thank Prof. Dr. Wolfgang Scherer (University of
Augsburg, Germany) for valuable suggestions and Dr. Julia
̈
Contreras-Garcia (University Pierre et Marie Curie-Sorbonne
University, Paris, France) for helpful discussions and proof-
reading of the manuscript. We further thank Dr. Gabriele Saleh
(Trinity College Dublin, Ireland) and Prof. Frank A. Weinhold
(University of Wisconsin, Madison, WI, USA) for help with the
NCI-Milano and NBO6.0 programs. The authors acknowledge
the X-ray diffraction facilities as well as the scientific and
technical assistance of the Centre for Microscopy, Character-
isation and Analysis, The University of Western Australia, a
facility funded by the University, State and Commonwealth
Governments. This work was supported by using computer
resources of the High-Performance Computing Service of the
ZEDAT of the Free University of Berlin. ChemMatCARS is
principally supported by the Divisions of Chemistry and
Materials Research, National Science Foundation, under grant
number NSF/CHE-1346572. Use of the Advanced Photon
Source, an Office of Science User Facility operated for the U.S.
Department of Energy (DOE) Office of Science by Argonne
National Laboratory, was supported by the U.S. DOE under
Contract No. DE-AC02-06CH11357.
In the crystal structure of bent CaCp*2, various C−H···Ca
contacts were observed. According to geometric, topological,
NBO, and ELI-D analyses, the interactions were found to be of
pregostic nature. Since these interactions are intermolecular, we
propose to call them pseudo-pregostic interactions.
ASSOCIATED CONTENT
■
S
* Supporting Information
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.inorg-
chem.7b03079.
PES scans, asymmetric units of MgCp*2 and CaCp*2,
crystal packing diagrams, electron density maps,
crystallographic quality indicators, frontier orbital dia-
grams of CaCp*2 dimers, difference electron density
plots, difference NCI plots, Hirshfeld surfaces with
curvedness, crystallographic details, geometry and
electron-density topology, topological and integrated
ELI-D parameters, NAO valence populations, geometry,
topological, and NBO analysis of C−H···Ca interactions,
and coordinates of optimized geometries (PDF)
Coordinates of experimental geometry of MgCp*2 used
in this paper that include elongated C−H bond distances
in contrast to the CIFs deposited with the CSD (CIF)
Coordinates of experimental geometry of CaCp*2 used
in this paper that include elongated C−H bond distances
in contrast to the CIFs deposited with the CSD (CIF)
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DOI: 10.1021/acs.inorgchem.7b03079
Inorg. Chem. XXXX, XXX, XXX−XXX