Why Diorganyl Zinc Lewis Acidity Dramatically Increases with Narrowing C-Zn-C Bond Angle

Article abstract of DOI:10.1021/acs.inorgchem.9b02193

The Lewis acidity of a metal center is influenced not only by the electronic properties of the bonded ligands but also by the bond angles, which we suggest to be important for zinc diorganyls. Molecular orbital correlation predicts that a narrower C-Zn-C bond angle of the R₂Zn fragment lowers its lowest unoccupied molecular orbital (LUMO) and increases its Lewis acidity, such that it binds added ligands more strongly. Computations on Me₂Zn(bipy) (bipy = 2,2′-bipyridine) yield that, for every 10° of C-Zn-C narrowing close to tetrahedral geometry, the Zn-N distance shortens by 0.027 ? (0.048 ? per 10° for the range 180-90°) and that the LUMO of the Me₂Zn fragment drops by 0.24 eV. A total of 10 dialkyl zinc complexes of bipy or 4,4′-di-tert-butyl-2,2′-bipyridine are crystallographically characterized here. Structure correlations (published and new data) confirm the link between the C-Zn-C angle and Zn-N distance. Principal component analysis provides a detailed picture of the correlated distortions. Relevance for zinc fingers/zinc enzymes is discussed.

Full text of DOI:10.1021/acs.inorgchem.9b02193

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Why Diorganyl Zinc Lewis Acidity Dramatically Increases with
Narrowing C−Zn−C Bond Angle
Bijan Mirabi,‡ Wei Church Poh,‡ David Armstrong, Alan J. Lough, and Ulrich Fekl*
Cite This: https://dx.doi.org/10.1021/acs.inorgchem.9b02193
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ABSTRACT: The Lewis acidity of a metal center is influenced not only by the electronic properties of the bonded ligands but also
by the bond angles, which we suggest to be important for zinc diorganyls. Molecular orbital correlation predicts that a narrower C−
Zn−C bond angle of the R2Zn fragment lowers its lowest unoccupied molecular orbital (LUMO) and increases its Lewis acidity,
such that it binds added ligands more strongly. Computations on Me2Zn(bipy) (bipy = 2,2′-bipyridine) yield that, for every 10° of
C−Zn−C narrowing close to tetrahedral geometry, the Zn−N distance shortens by 0.027 Å (0.048 Å per 10° for the range 180−
90°) and that the LUMO of the Me2Zn fragment drops by 0.24 eV. A total of 10 dialkyl zinc complexes of bipy or 4,4′-di-tert-butyl-
2,2′-bipyridine are crystallographically characterized here. Structure correlations (published and new data) confirm the link between
the C−Zn−C angle and Zn−N distance. Principal component analysis provides a detailed picture of the correlated distortions.
Relevance for zinc fingers/zinc enzymes is discussed.
ialkylzinc complexes are important chemical intermedi-
D
ates.1 Their reactivity depends on both the carbanionic
nature of the metal-bound alkyl and the Lewis acidity of the
zinc center.2 Would widening or narrowing of the C−Zn−C
angle influence the Lewis acidity of the zinc center? In the
1990s, Westerhausen et al. made the intriguing suggestion that,
in diorganylzinc complexes of the type “C2ZnN2”, a linear
relationship exists such that, for every 10° of C−Zn−C angle
narrowing, the Zn−N distances shrink by 0.12(1) Å.3,4 The
most recent study (1996) involved a correlation involving 18
structures (14 were true “C2ZnN2” and 4 had different donor
atoms).5 The effect was reported as a structural observation
without a quantum-mechanical explanation. We suggest that
the structural consequences of C−Zn−C narrowing in the
four-coordinate zinc complexes are explained and predicted
using a molecular orbital (MO) correlation diagram on the
two-coordinate dialkylzinc fragment. The lowest unoccupied
molecular orbital (LUMO) of the C2Zn unit is drastically
lowered upon angle narrowing, and we suggest that this
enhanced Lewis acidity is the reason why the fragment binds
more strongly to the remaining ligands. The applicability of the
analysis will likely extend to Lewis acidic zinc-based catalysts6
and to zinc enzymes.7
Figure 1. Predicted MO energy changes upon decreasing C−Zn−C
bond angle in a homoleptic dialkylzinc compound, as assessed from
altered bonding/antibonding overlap.
changing the qualitative picture.9 The amount of p-orbital
contribution at zinc is probably often overstated in traditional
treatments.2,10−13 Truly “sp-hybridized zinc” would corre-
spond to a C−Zn bond order of 1.0. Our scheme represents
the other end of the spectrum. A pure 3c-4e interaction (4s
only at zinc) would correspond to a C−Zn bond order of 0.5.
The reality seems to be somewhere between the two simplified
pictures, as can be seen from a computed C−Zn bond order
for Me2Zn that is in between.14
A qualitative MO correlation8 diagram for the frontier
orbitals in a generic R2Zn compound may be derived from the
three-center four-electron (3c-4e) interaction shown in Figure
1, using one donor orbital on each of the two carbanions plus
the 4s orbital on Zn2+. Orbital overlap changes upon bending
(more bonding or more antibonding overlap) predict the
resulting energy changes. We chose a simplified, strictly
hypervalent scheme (no p-orbital involvement at zinc), aiming
to make our argument as simple as possible while still making
qualitatively correct predictions. High-level computations
(below; see also the Supporting Information) show that zinc-
based p orbitals are contributing to varying degrees, without
The most significant prediction from Figure 1 is that the
LUMO is lowered when the C−Zn−C angle is narrowed, such
Received: July 23, 2019
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that R2Zn should become more Lewis acidic, leading to
stronger binding of added ligands, for example, the nitrogen
donors in a “C2ZnN2” complex.
Lewis acidity is typically quantified using adduct formation
thermodynamics, where an acid would be considered more
Lewis acidic if formation of the acid−base adduct (keeping the
base constant) is thermodynamically more favorable.15 The
change in the thermodynamic Lewis acidity resulting from C−
Zn−C bending is demonstrated with density functional theory
(DFT), where we used TPSSTPSS/cc-pVTZ, known to be
excellent for zinc.16 The C−Zn−C angle was fixed, and all
other geometric parameters were relaxed (constrained
geometry optimization) in Me2Zn and its two ammonia
adducts Me2Zn(NH3) and Me2Zn(NH3)2. When the C−Zn−
C angle was narrowed from 180° to 147.9° [computed
equilibrium C−Zn−C bond angle for Me2Zn(NH3)2], the
binding energy of the first NH3 fell from −5.29 to −11.31
kcal/mol, while the binding energy of the second NH3 fell
from −3.87 to −7.22 kcal/mol. The trend continued
consistently for 120° and 90° (Table 1). A constrained
Figure 2. LUMO energy changes for the free Me2Zn fragment (top)
and geometry changes for Me2Zn(bipy) (bottom), upon variation of
an enforced C−Zn−C bond angle (TPSSTPSS/cc-pVTZ).
Table 1. Calculated (TPSSTPSS/cc-PVTZ)
Thermodynamic Parameters for the First and Second
Ammonia Binding Events to a ZnMe2 Fragment (Enforced
C−Zn−C Angle)
Me2Zn fragment. While Zn−N strengthening upon C−Zn−C
narrowing is also predicted from the MO diagram of four-
coordinate zinc,19 we find that analyzing the two-coordinate
Me2Zn fragment provides the simplest explanation. As another
effect, upon narrowing of C−Zn−C, the C−Zn distance
slightly elongates (Figure 2, bottom), also predicted (ψ2
becomes more antibonding).
second binding event
first binding event (kcal/mol)
(kcal/mol)
C−Zn−
C angle
(deg)
ΔE
ΔH
ΔG
3.30
−4.04
−8.24
ΔE
ΔH
ΔG
180
147.9
120
90
−5.29
−11.31
−17.60
−23.86
−5.88
−11.91
−18.19
−24.45
−3.87
−7.22
−8.89
−4.46
−7.81
−9.48
3.30
0.3
−2.48
−4.14
Given the wealth of crystallographic data available now, a
structure correlation study involving experimental structures is
timely. For zinc dialkyls, diaryls, or dialkenyls R2Zn(“N2”) with
“N2” = bipy, several crystal structures are known, namely, the
structures that have R = 1-adamantyl and 2-adamantyl,
reported recently,20 as well as older reports with R = methyl,21
1-methylvinyl and 2,2-dimethylvinyl,22 and bis(trimethylsilyl)-
methyl.3 We are adding the characterization of cyclopentyl2Zn-
(bipy) (1) and phenyl2Zn(bipy) (2). Using a common
derivative of bipy, 4,4′-di-tert-butyl-2,2′-bipyridine (tBu2-
bipy), we are adding the characterization of neophyl2Zn-
(tBu2-bipy) (3; neophyl = 2-methyl-2-phenylpropyl),
cyclohexyl2Zn(tBu2-bipy) (4), nBu2Zn(tBu2-bipy) (5), 1-
adamantyl2Zn(tBu2-bipy) (6), tBu2Zn(tBu2-bipy) (7), and
cyclopentyl2Zn(tBu2-bipy) (8). The ethyl complexes Et2Zn-
(tBu2-bipy)23 (9) and Et2Zn(bipy)24 (10) are already known
and were additionally characterized here with reduced R1
factor (1.8% versus 2.2% and 2.0% versus 6.1%, respectively).
The structures of 1−10 (see the SI) were included (PreQuest,
version 5.34) in a database search that was run using ConQuest
(version 2.0.2) on the CSD (version 5.40, updates up to May
2019).25 The search was open to all “C2ZnN2” structures with
four-coordinate zinc, including examples containing two
monodentate nitrogen ligands (not just chelates) as well as
carbon ligands other than alkyl/aryl/alkenyl. In total, 161
crystal structures were retrieved, each with the bond distances
and angles around zinc shown in Figure 3. All permutations of
labels were included, to remove the arbitrariness of atom
labeling. A linear plot of the Zn−N distance versus C−Zn−C
angle (see the SI; R2 = 0.49) yields that, over the full range
90−180°, for every 10° of C−Zn−C narrowing, the Zn−N
distance shortens by 0.055 Å, in good agreement with the
computational result (0.048 Å). A linear plot using the new
−14.13
−10.93
−11.52
geometry optimization is artificial, but the predictive power is
real: if the C−Zn−C angle can be forced to be narrow, e.g., in
a metallacycle, the zinc center is predicted to bind ligands
more strongly. The existence of this causal link does not
preclude that the opposite also holds (pushing a donor ligand
closer to zinc bends the C−Zn−C bond). The C−Zn−C angle
and Zn−N distance changes are coupled.17
To shift focus toward synthetically more practical ligands
than NH3, another constrained geometry optimization was
performed on Me2Zn(bipy) (bipy = 2,2′-bipyridine), a
“C2ZnN2” complex prototypical for zinc dialkyls with N-
chelates, compounds easily synthesized and structurally
characterized. In the regime of modest distortions around
tetrahedral geometry, for every 10° of C−Zn−C narrowing,
the Zn−N distance shortens by 0.027 Å (Figure 2, bottom).
The slope is steeper at large angles, and for the range 90−180°,
the overall bond length change is 0.434 Å, corresponding to
0.048 Å per 10°. The LUMO energy of the underlying Me2Zn
fragment is also shown in Figure 2 (top). The computed
frontier orbitals (see the Supporting Information, SI) have the
symmetries and qualitative appearances shown in Figure 1 and
respond to bending as predicted. The LUMO is essentially the
antibonding component of a 3c-4e interaction.18 The LUMO
energy (Figure 2, top) falls by an impressive 2.12 eV over the
range 180−90° and, in the vicinity of tetrahedral geometry, by
0.24 eV for every 10° of C−Zn−C narrowing, drastically
enhancing the Lewis acidity of the zinc center and
strengthening the interaction between donor atoms and the
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We wondered whether a similar effect may operate in a
biological context, despite the absence of Zn−C bonds. In a
mixed-ligand environment around zinc, it may be hypothesized
that the angles involving the more covalently bonded “softer”
donors control the Lewis acidity of zinc. Sulfur would have the
controlling influence in a S2ZnN2 environment because of the
high degree of covalency in bonding to sulfur.28 We performed
PCA on all “S2ZnN2” small-molecule structures with four-
coordinate zinc in the CSD (355 records), which could be
considered to be structural models, broadly, for the zinc finger
motif.29 PCA seems to indicate that the effect is weaker but
still present. Not the strongest principal component but the
second strongest one,30 a component linking S−Zn−S angle
narrowing to Zn−S bond stretching and Zn−N bond
contraction (and also to N−Zn−N widening) is found,
describing 30.3% of the variance. A linear plot of Zn−N
versus S−Zn−S (see the SI; R2 = 0.13) yields that, over the
range covered, 75−160°, for every 10° of S−Zn−S narrowing,
the Zn−N distance shortens by 0.015 Å (PCA and a linear plot
in the SI).
We conclude that strong evidence for a correlation between
C−Zn−C bond angles and lengths to donor ligands is
provided by statistical analysis of the experimental structures.
Computations demonstrate that artificially narrowing the C−
Zn−C angle lowers the LUMO of the R2Zn fragment, forcing
zinc to become more Lewis acidic and to bind ligands more
strongly. This may provide a design principle for Lewis acids.
Further, related to bioinorganic chemistry, the question of
what influences the Lewis acidity of zinc is prominent. The
nature and number of donor atoms as well as dipoles in the
proximity of zinc are being considered.31 Bond angles are
currently receiving attention.32 The current analysis suggests
that the following effect may be present in nature: when the
bond angle between two relatively covalently bonded ligands
narrows, the Lewis acidity is boosted.33
Figure 3. Internal coordinates and PCA results for C2ZnN2: pictures
and normalized coefficients (coefficients ≥0.05 shown) for the four
top PCAs. PCA1 is multiplied by (−1) to show effects correlated with
C−Zn−C angle narrowing (the absolute phase is arbitrary).
structures 1−10 only (R2 = 0.51) yields similarly 0.056 Å per
10° of C−Zn−C (see the SI). The range of C−Zn−C angles
covered with these new structures that all have very similar sp2
t
nitrogen ligands bipy or Bu2-bipy is 132.8−141.1°, a span of
8.3°, which helps to elucidate the direction of causality for
most of the variation in the data set. Changing the C−Zn−C
angle could cause the Zn−N distance to shorten, but,
conversely, forcing a nitrogen ligand closer to zinc could lead
to a narrower C−Zn−C angle. The C−Zn−C angle span that
results from different nitrogen donor strengths is very small, as
seen when considering structures with sp3 and sp2 nitrogen
separately (full data set). For sp3 nitrogen complexes, involving
NR3 ligands and the like, which are sterically quite bulky, the
average Zn−N distance is 2.240 Å and the average C−Zn−C
angle (63 unique angles) is 131.4°. In contrast, sp2 nitrogen
donors can get closer to zinc, and the average Zn−N distance
is 2.185 Å. Consistent with expectations, the average C−Zn−C
angle (121 angles) shrinks, but only by 3.4°, to 128.0°. This
very modest effect of changing the hybridization at the
nitrogen donor contrasts with the 8.3° span observed with all
bipy/tBu2-bipy ligands and with the ca. 90° span of C−Zn−C
angles in the full data set, suggesting that most of the variation
in the data set is due to enforced (alkyl geometry/sterics/
crystal packing) C−Zn−C angles and that the Zn−N distance
is then governed by the resulting Lewis acidity of zinc. The
softness of the C−Zn−C scissoring mode makes this very
plausible.17
ASSOCIATED CONTENT
* Supporting Information
The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/acs.inorgchem.9b02193.
■
sı
Anisotropic displacement plots for 1−10, experimental
and computational details, and a summary of the
statistics (PDF)
Accession Codes
CCDC 1930109−1930118 contain the supplementary crys-
tallographic data for this paper. These data can be obtained
free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by
emailing data_request@ccdc.cam.ac.uk, or by contacting The
Cambridge Crystallographic Data Centre, 12 Union Road,
Cambridge CB2 1EZ, UK; fax: +44 1223 336033.
A principal component analysis (PCA)26 was run using the
10 internal (1 redundant) coordinates.27 Effective reduction in
the dimensionality occurs when distortions are correlated. For
C2ZnN2, the first four components alone already describe
82.7% of the variance in the data set (Figure 3). The
components are of the type “scissoring coupled to symmetric
stretching” (PCA1 and PCA4), “twist” (PCA2), and “wagging
coupled to asymmetric stretch” (PCA3). The most important
component (PCA1, 33.8% of variance) describes the effect that
couples17 C−Zn−C narrowing with pronounced Zn−N
shortening and some Zn−C bond lengthening.
AUTHOR INFORMATION
Corresponding Author
■
Ulrich Fekl − Chemical and Physical Sciences, University of
Toronto Mississauga, Mississauga, Ontario L5L 1C6, Canada;
Department of Chemistry, University of Toronto, Toronto,
Ontario M5S 3H6, Canada; orcid.org/0000-0001-7345-
1716; Email: ulrich.fekl@utoronto.ca
Authors
Bijan Mirabi − Chemical and Physical Sciences, University of
Toronto Mississauga, Mississauga, Ontario L5L 1C6, Canada
C
https://dx.doi.org/10.1021/acs.inorgchem.9b02193
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(12) Singh, A. P.; Samuel, P. P.; Roesky, H. W.; Schwarzer, M. C.;
Frenking, G.; Sidhu, N. S.; Dittrich, B. A singlet biradicaloid zinc
compound and its nonradical counterpart. J. Am. Chem. Soc. 2013,
135, 7324−7329.
Wei Church Poh − Department of Chemistry, The University of
Hong Kong, Hong Kong, P.R. China
David Armstrong − Chemical and Physical Sciences, University
of Toronto Mississauga, Mississauga, Ontario L5L 1C6,
Canada; Department of Chemistry, University of Toronto,
Toronto, Ontario M5S 3H6, Canada; orcid.org/0000-
0002-5480-1386
(13) The hybridization at Et2Zn with zero, one, or two pyridine
donors is referred to as “sp”, “sp2”, and “sp3”, respectively, in ref 10. It
is similar for generic linear/trigonal/tetrahedral zinc complexes in ref
2. In contrast, ref 11 makes the point that “the 4p orbital is too high in
energy [···]. Hence textbook based concepts such as [···] 4s4p
hybridization, which can be found in the literature today needs to be
reconsidered”. The situation is complex-specific, and ref 12 is referred
to for a carbene-coordinated zinc complex where Zn p orbital
involvement is very pronounced and rightly given emphasis even in
the qualitative description. We thank Reviewer 2 for sharpening our
awareness of that matter.
(14) A C−Zn bond order of 0.75 would result from a wave function
that is exactly in the middle between the 2 × 2c-2e picture (sp-
hybridized zinc) and the 3c-4e picture. We compute 0.81 (for Me2Zn
at 180°, TPSSTPSS/cc-pVTZ; see the SI for DFT-computed bond
order and also for a comparison between the two limiting pictures).
(15) Laurence, C.; Gal, J.-F. Lewis Basicity and Affinity Scales: Data
and Measurement; Wiley VCH: Chichester, U.K., 2009.
(16) Weaver, M. N.; Merz, K. M., Jr.; Ma, D.; Kim, H. J.; Gagliardi,
L. Calculation of heats of formation for Zn complexes: comparison of
density functional theory, second order perturbation theory, coupled-
cluster and complete active space methods. J. Chem. Theory Comput.
2013, 9, 5277−5285.
(17) Compare the computed C−Zn−C scissoring vibration of
Me2Zn(NH3)2 at 122.7 cm−1, which has some N−Zn stretching
mixed in, with the expected phase: with C−Zn−Z narrowing, N−Zn
shortens; displacements are shown in the SI.
(18) Zinc-based p orbitals add mostly to polarization of the 4s
orbital and do not change much the qualitative appearance of the
frontier orbitals. For 180°, the LUMO has no p character at zinc. For
the bent structures, p character at zinc mixes in, polarizing the mostly
spherical component at zinc and distorting it slightly toward the open
side of the C−Zn−C wedge while still maintaining more s than p
character at zinc. See the SI for graphical renderings of MOs and
computed p character.
(19) See the SI for qualitative and DFT-computed MOs of
Me2Zn(NH3)2. The Zn−ligand bonding MOs are quite well
approximated by constructing a hypervalent 5c-8e interaction under
C2v.
Alan J. Lough − Department of Chemistry, University of
Toronto, Toronto, Ontario M5S 3H6, Canada
Complete contact information is available at:
https://pubs.acs.org/10.1021/acs.inorgchem.9b02193
Author Contributions
‡These authors contributed equally.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
Funding by the NSERC, the ACS-PRF, and the University of
Toronto (to U.F.) is gratefully acknowledged. W.C.P. thanks
the University of Hong Kong for an exchange fellowship
(URFP) enabling a research visit to the University of Toronto
Mississauga to work with U.F. We thank Professor Vivian W.
W. Yam (University of Hong Kong) for her generous
facilitation of this exchange visit. U.F. thanks Professors
Sarah Rauscher and Deborah Zamble (University of Toronto)
for valuable discussions. Fioralba Taullaj (University of
Toronto) is acknowledged for synthesis assistance.
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(32) Linder, D. P.; Baker, B. E.; Rodgers, K. R. [(H2O)Zn-
(imidazole)n]2+: the vital roles of coordination number and geometry
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(33) Reference 32 reports the very important computational finding
that the acidity of bound water in the enzyme model [(H2O)
Zn(imidazole)n]2+ increases when the N−Zn−O angle increases or
the N−Zn−N angle decreases. To express the correlation, either of
the angles (O−Zn−N or N−Zn−N), which are linked and inversely
correlated, can be used. Our data suggest that using the N−Zn−N
angle is part of the explanation.
E
https://dx.doi.org/10.1021/acs.inorgchem.9b02193
Inorg. Chem. XXXX, XXX, XXX−XXX