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On the Fundamental Relation Between Molecular Geometry and Real-Space Topology. Combined AIM, ELI-D and ASF Analysis of Hapticities and IntraMolecular Hydrogen-Hydrogen Bonds in Zincocene Related Compounds Stefan Mebs, Maren Annika Chilleck, Kathrin Meindl, and Christian B. Hübschle J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp503667g • Publication Date (Web): 23 May 2014 Downloaded from http://pubs.acs.org on May 29, 2014

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The Journal of Physical Chemistry

On the Fundamental Relation Between Molecular Geometry and Real-Space Topology. Combined AIM, ELI-D and ASF Analysis of Hapticities and IntraMolecular Hydrogen-Hydrogen Bonds in Zincocene Related Compounds.

Stefan Mebs,*[a] Maren Annika Chilleck,[b] Kathrin Meindl,[c] Christian Bertram Hübschle[d] [a] Department of experimental Physics, Freie Universität Berlin, Arnimalle 14, D-14195 Berlin (Germany). E-mail: [email protected], Tel: +493083856084 [b] Department of Chemistry, Humboldt-Universität zu Berlin, Brook-Taylor-Str. 2, D-12489 Berlin (Germany). [c] Molecular Biology Institute of Barcelona (IBMB) CSIC, Barcelona Science Park c/ Baldiri Reixac 4-8 Torre R, 3era Planta 08028 Barcelona (Spain) [d] Laboratory of Crystallography, BGI-building, Universität Bayreuth, Universitätsstr. 30, D-95447 Bayreuth (Germany)

Abstract Despite numerous advanced and widely distributed bonding theories such as MO, VB, NBO, AIM, and ELF/ELI-D, complex modes of bonding such as M-Cp*(R) interactions (hapticities) in asymmetrical metallocenes or weak intra-molecular interactions (e.g. hydrogen-hydrogen (H...H) bonds) still remain a challenge for these theories in terms of defining whether or not an atomatom interaction line (a “chemical bond”) should be drawn. In this work the intramolecular ZnCCp*(R) (R = Me, –(CH2)2NMe2, and –(CH2)3NMe2) and H...H connectivity of a systematical set of 12 zincocene related compounds is analyzed in terms of AIM and ELI-D topology combined with the recently introduced aspherical stockholder fragment (ASF) surfaces. This computational analysis unravels a distinct dependency of the AIM and ELI-D topology against the molecular

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geometry for both types of interactions, which confirms and extends earlier findings on smaller sets of compounds. According to these results the complete real-space topology including strong, medium, and weak interactions of very large compounds such as proteins may be reliably predicted by sole inspection of accurately determined molecular geometries, which would on the one hand afford new applications (e.g. accurate estimation of numbers, types and strengths of intra- and intermolecular interactions) and on the other hand have deep implications on the significance of the method.

Keywords Atoms-In-Molecules,

Electron-Localizability,

Hirshfeld

Surfaces,

Aspherical

Stockholder

Fragments, Metallocenes

Introduction Structural elucidation both by experiments (e.g. X-ray diffraction) and quantum-chemical computations has seen tremendous progress in the last decades. However, despite the contemporary high standards in determination of geometrical parameters, questions of chemical bonding are still highly controversial. According to the concept of molecular orbitals (MO)1 all n atoms comprising a molecular structure are interacting more or less intensively with all remaining n-1 atoms leading to a delocalized electron distribution across the molecule. However, due to the particular symmetries of the contributing atomic orbitals (AO) and the different atomatom distances, this overall interaction can be energetically fragmented into distinct atom-atom contacts – or “chemical bonds” for most molecular structures. But the interpretation of the bonds by optical inspection of the MO-distribution is often not straight-forward or intuitive. This delocalized approach is contrasted by the valence bond theory (VB)2, the MO-related natural


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bond orbitals (NBO)3 approach and the chemical concept of drawing Lewis structures4, which all assign electrons to distinct atom-pairs (as bonding electrons) or to single atoms (as non-bonding electrons), following a set of rules (e.g. Pauli’s exclusion principle or the octet rule). These approaches of localized atom-atom contacts led to the formulation of the widely applied valence shell electron pair repulsion (VSEPR)5 concept, which in many cases affords quite reliable predictions of molecular geometries. In most cases, these complementary methods of defining a molecular structure based on delocalized or localized bonding schemes lead to self-consistent results so drawing bonds into a given geometrical arrangement of atoms is unambiguous. These “classical” concepts of bonding analysis, however, are seriously challenged in case of multi-center bonded systems (e.g. multi-nuclear metal-organic compounds, borane cages), metal-arene and -cyclopentadienyl (Cp) interactions, guest-host-complexes, and weak intra- or inter-molecular interactions (e.g. homopolar hydrogen-hydrogen bonds, and van-der-Waals forces). Often, it is not really clear whether or not a bond should be drawn between two adjacent atoms. To overcome these problems, topological methods have been developed, which promised to shed light into the complex modes of bonding in the mentioned molecular systems. The most prominent approaches are the Atoms In Molecules (AIM)6,7 theory and the Electron Localization Function (ELF)8,9. By topological analysis of the three-dimensional electron density (ED) and the definition of surfaces of zero electronic flux AIM divides direct space into discrete atomic basins, which provides self-consistent atomic properties such as charges and volumes as well as a topological inter-atomic bond paths motif, which often is assigned to the molecular structure. ELF performs a topological analysis of the same-spin pair probability density and thus generates basins of localized electron pairs. However, the disadvantageous reference of the ELF formalism to the uniform electron gas was overcome with the introduction of the Electron Localizability Indicator (ELI-D)10, which is applied in this study. In ELI-D theory space is divided into small regions with the same amount of same-spin electron pairs. In contrast to ELF, the ELID topology is given on an absolute scale, thus results for different molecular systems can ACS Paragon Plus Environment

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directly be compared. By combined use of these two discrete and space-filling partitioning schemes (AIM and ELF/ELI-D) fine details of electron rearrangements due to atom-atom interactions become visible. Accordingly, they found wide applications in the last two decades.1113

The concept of overlapping ELF valence basins with AIM atoms14 is a very helpful tool for the

estimation of bond polarities (Raub-Jansen-Index, RJI). The electron population within an ELF/ELI-D bonding basin connecting two or more atoms is fragmented into particular contributions of the two or more AIM atomic basins enclosing this bond. For homopolar bonds, the electrons within the interatomic ELF/ELI-D bonding basin are to 50% located within each AIM atom, thus RJI = 50%. With increasing bond polarity, the relative electron populations are shifted to the more electronegative atom. In this work, the RJI is used in terms of AIM/ELI-D overlap. The big advantage of AIM is that the electron density can not only be extracted from the molecular wavefunction but also be obtained by experiments (e.g. single-crystal high-resolution X-ray diffraction and subsequent multipole modeling) so that measured and calculated results can directly be compared with each other. This is not possible for MO, VB, NBO, and ELF/ELI-D. In the last years it was discovered that also AIM topology may show ambiguities in complex bonding scenarios such as multi-nuclear metal-organic compounds and borane cages15,16 and moreover a dependency against the use of different density-functional theory (DFT) functionals in theoretical calculations.17-20 These upcoming problems, however, seem mainly to affect the ED itself, but not the virial field (VF), which is the scalar potential energy density field derived from the ED. Another way to analyze a three-dimensional ED distribution is called stockholder partitioning21, that is, the surface of an atom, functional group or molecule in a crystal is defined as all points around the chosen fragment for which 50% of the total ED at this point stem from the fragment. This type of space-partitioning is also discrete but not space-filling like AIM or ELI-D and yields smoth fragmental shapes instead of hard-edged atomic or electron pair basins. The analysis of these so called Hirshfeld surfaces (HS)22 has been widely applied to molecular crystals in order


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to unravel contact patches between different molecules in a crystal. Typically, the ED for HS analysis is constructed by superposition of spherical atomic electron densities. In order to increase the comparability to AIM, we do not use HS in this study but the recently introduced aspherical stockholder fragments (ASF)23, which are extracted from the corresponding aspherical electron densities. Like AIM-topology, HS and ASF can be obtained both from experimentally and theoretically generated structure factors and like AIM, HS and ASF are best suited to analyze very large systems (e.g. molecules in a crystalline environment). The determination of the hapticity (metal-ligand or M-L connectivity) in asymmetric metallocenes represents an ideal problem to uncover the fundamental differences between delocalized and localized bonding scenarios: how many M-L bonds should be drawn by the chemist?24,25 Zincocene related compounds are ideally suited for such a task as they show the largest structural variations of all metallocenes26-32. It is known that the conventional AIM bond paths analysis fails to provide reliable results in these cases both for experiments and for theory (one of the cases in which ED analysis with AIM gives ambiguous results), because a cone of electron density is generated with the metal atom at the tip and the carbon atoms of the Cp(*) ring at the bottom.33,34 Within this cone the gradient of the ED is very flat at all points, which prevents the reliable formation of bond critical points (ED bcp) in the ED so typically less bcp are found than expected. In a recent study we found that the corresponding virial field is more stable.23 The main finding of this study was that virial field and ELI-D topology could unambiguously be traced back to the molecular geometry.23 In the present work, which extends the number of studied cases, these results are confirmed and the explicit relation geometry vs. topology is improved. Another ideal case which challenges conventional bonding theories is the formation of very weak intra- or inter-molecular interactions such as (un)polar H...H or HSπ contacts.35-50 In many cases already the explicit definition of a conventional hydrogen bond (HB) is not simple because they


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depend on geometric (distances and angles) as well as on electronic (type of Lewis base) parameters.51-53 At least it is clear that these forces are of attractive nature. For H...H contacts it is even more difficult to say whether or not a HSH interaction line should be drawn because in contrast to HB there is still some inconsistency in the literature about the energetically aspects of this interactions.54,55 Are the H...H contacts repelling or attractive forces? Although the heavily distorted molecular geometries of sterically strained molecular systems strictly imply repelling HSH contacts, the AIM atomic energies are lower for H atoms involved in these steric interactions compared to those which are not.38,40 Disregarding these energetically aspects, it cannot be neglected that saddle points are found between interacting H atoms in ED, VF and ELI-D.56 However, for asymmetric molecular structures it can hardly be understood why some particular HSH contacts exhibit a saddle-point in one or more of these fields and other contacts do not, although the HSH distances are similar. In a recent AIM, ELI-D and ASF study of a zincocene related compound we could unravel a strong dependency of the HSH topology against the C1-H1SH2 and H1SH2-C2 angles56. Again, the main finding of this former study was that ELI-D, ED, and VF topology could unambiguously be traced back to the molecular geometry. But in this previous study only one large asymmetric zincocene related compound was analyzed so that the results couldn’t be generalized. In the present work, which significantly extends the number of studied cases, the explicit relation geometry vs. topology is improved and the fundamental interdependency of molecular geometry and topology is confirmed. In the present study, a systematical series of 12 zincocene related compounds is theoretically analyzed in terms of geometrical considerations combined with AIM, ELI-D and ASF spacepartitionings in order to unambiguously determine the relation between molecular geometry and number and kind of Zn-C/N and weak intra-molecular HSH/C contacts, respectively. Such a systematic topological study on a set of asymmetrical compounds has the big advantage that a broad range of statistically and in parts also unexpected atomic arrangements might appear for which a systematic screening of a much larger number of model compounds may even be more ACS Paragon Plus Environment

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consumptive. More importantly, the complex electronic impact of all atoms to a distinct bond can hardly be resembled by sole use of model compounds. The number of ligands comprise ethyl (Et),

pentamethylcyclopentadienyl

(Cp*),

Cp*2N

(C5Me4(CH2)2NMe2),

and

Cp*3N

(C5Me4(CH2)3NMe2) leading to the Zn-complexes ZnEt2 (1), ZnEtCp* (2),57 ZnEtCp*2N (3),58 ZnEtCp*3N (4),59 ZnCp*2 (5),31,60 ZnCp*Cp*2N (6),56,59 ZnCp*Cp*3N (7),59 Zn(Cp*2N)2 (8),58 Zn(Cp*2NCp*3N) (9),59 and Zn(Cp*3N)2 (12).59 6 was already part of the two former studies on hapticities and HSH contacts.23,56 For all models the molecular geometries were optimized by theoretical calculations and compared to experimental results, if available. Since it turned out that due to sterical reasons in 12 only one Cp*3N ligand is attached to the central Zn also via the N atom (bidentate binding mode), whereas the other is monodentate, but in 8 both Cp*2N ligands are bidentately connected to the Zn atom (via C and N atoms), the rather small structural differences between these two ligands are obviously highly relevant. Accordingly, two further models have been considered for the heteroleptic form 9, Zn(Cp*2NCp*3N), with Cp*2N being monodentate and Cp*3N being bidentate (10) and vice versa (11). With the exception of 1, 5, and 8, which show quite symmetrical molecular structures, all models are highly asymmetric, which is desired as it leads to a considerably larger variation of geometrical parameters for each type of atom-atom contact and provides a statistical basis for the empirical interpretation of the AIM and ELI-D topologies, which cannot be provided by sole inspection of highly symmetrical metallocenes or sterically strained systems. As a consequence, 45 Zn-C contacts in the range of 1.97-2.70 Å, 55 HSH contacts in the range of 1.98-2.93 Å , and 19 HSπ contacts in the range of 2.43-3.28 Å could be analyzed.

Theoretical calculations Starting from the X-ray solid-state geometries (if available) the molecular geometries of models 1-12 were fully optimized at the BP86/TZVP61 level of theory applying Gaussian0962. By


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subsequent frequency analysis all final geometries were confirmed to be local minima. The wave functions of these theoretical models were directly analyzed with AIM200063 to obtain molecular graph figures and the bond topological properties of electron density and virial field. AIM atomic charges and volumes and the ELI-D were derived from grids of 0.05 bohr grid step size, which were generated with DGRID-4.6.64 For 2, 5, and 9, theoretical structure factors were generated with the program TONTO65 (pseudo-periodic calculations). With these synthetic data-sets subsequent multipole refinements were performed using XD2006.66 Non-hydrogen atoms were expanded to the hexadecapolar level, whereas solely bond-directed multipoles up to the quadrupole level of expansion were refined for the H atoms. Local atomic symmetries and chemical constraints were not applied due to the asymmetry of these systems. The final multipole model was obtained by stepwise refinement of expansion/contraction parameters κ and κ’. The ED obtained by this procedure was used for generation of the ASF surfaces, on which the ED was mapped. Since there are numerous publications on the influence of computational method, choice of basis-set and multipole model to the ED topology67,68 these aspects are not considered in this work. Molecular structures and superpositions of molecular structures are displayed with SCHAKAL.69 The ELI-D and ASF figures are generated with MOLISO.70

Results and discussion Geometries and Energies: Figure 1a-l displays superpositions of experimental (dark grey) and theoretically optimized (red) molecular geometries of models 3 (1c), 4 (1d), 6-8 (1f-h) and 12 (1l), as well as the optimized geometries of 1 (1a), 2 (1b), 5 (1e), and 9-11 (1j-l), for which reliable Xray structures are not yet available. For the optimized geometries the Cp* part of the Cp*2N and Cp*3N ligands show a tilting which leads to increased Zn-Cg distances (Cg = center of gravity of the five-membered Cp* rings, see models 3, 4, 6-8, and 12). This effect has been found before23


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and may be due to the lack of the crystalline environment. Moreover, there is an interesting observation considering the Zn-Cp*(2/3N) contacts: In the smaller compounds 3, 4, 6, and 7 the Zn atom is connected to the Cp* part via the C atom which carries the –(CH2)2/3NMe2 fragment. This leads to the formation of five- and six-membered CCp*-Zn-N-(CEt)2/3 rings and is obviously the preferred configuration. For 8 and 9, however, the increased sterical interaction between the two Cp*2/3N ligands prevents this type of bonding and leads to a shift along the Cp* ring so that the C atom adjacent to the one carrying the –(CH2)2/3NMe2 fragment is bonded to the Zn atom. The only way for the Zn-complex to exhibit the preferred Zn-C coordination is to break one dative ZnN interaction in order to generate space. The second Zn-N interaction can obviously be retained because in models 10-12 both the monodentate and the bidentate Cp*2/3N ligands are connected to the Zn atom in the preferred coordination. Accordingly, the molecular energy of 10 and 11 are 14.66 and 34.86 kJ/mol lower in energy compared to 9. As expected, breaking the Zn-N bond of the larger Cp*3N ligand leads to the lowest molecular energy. Table 1 lists all relevant geometrical parameters of the optimized geometries (a list including the experimental geometries is given in the supporting information). For the Cp*(2/3N) parts the closest Zn-C contacts range from 2.014 Å for the η1-bonded Cp* ligand in 5 to 2.269 Å for the η5bonded Cp* ligand in 1. Models 3, 4 and 5 show slippage values between 0.1 and 1.0 Å, which makes them interesting for additional analysis of real-space bonding indicators, because the hapticity is not self-evident from inspection of the molecular geometry. For the other Cp* ligand in 5, which is generally considered to be η5-coordinated by the Zn atom, a small ring slippage of 0.124 Å is found. As will be shown below, this relatively small slippage is also reflected in the AIM and ELI-D topology, which makes η5-coordination questionable. In 8 and 9, both the closest Zn-C distances (> 2.15 Å) as well as the ring slippages (> 2.03 Å) are by far the largest for all η1(δ)-bonded systems, which confirms those two structures to be significantly affected by sterical stress. Interestingly, the larger Cp*3N ligand in 9 is tighter bonded to the central Zn atom than the smaller Cp*2N ligand, although the Cp*2N ligand forms a six-membered (CCp*)2-Zn-N-(CEt)2 ring. ACS Paragon Plus Environment

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Regarding models 10-12, which each comprise one monodental and one bidental Cp*2/3N ligand, one finds the Zn-C distances of the monodentate ligand to be 0.01-0.04 Å shorter and the slippage to be 0.4-0.6 Å larger, which points toward increased σ-contributions for the monodentate ligand.

Figure 1.

Theoretically optimized (red) molecular geometries of models 1 (a), 2 (b), 3 (c), 4

(d), 5 (e), 6 (f), 7 (g), 8 (h), 9 (i), 10 (j), 11 (k), and 12 (l). For models 3, 4, 6, 7, 8, and 12 also the experimental (dark grey) geometries are given. For clarity, H atoms are omitted for models 3-12.


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Selected geometrical parameters of the optimized geometries of models 2-12.

Table 1.

no. 2 3 4 5

ligand Cp* 2N

Cp*

3N

Cp*

1

Cp*(η ) 5“

d(Zn-C1) d(Zn-Cg) d(Zn-pl) slippage a(Zn-C1-Cg) a(Cg-C1-R) [Å]

[Å]

[Å]

[Å]

[°]

[°]

2.269

1.938

1.938

0.000

58.63

175.20

2.134

2.198

2.068

0.745

76.35

172.13

2.123

2.214

2.070

0.785

77.55

161.90

2.014

2.627

1.970

1.738

104.76

142.16

5

Cp*(η“ )

2.225

1.939

1.935

0.124

86.13

174.31

6

Cp*

2.045

2.650

1.996

1.743

104.66

144.31

2N

6

Cp*

2.090

2.477

2.096

1.320

92.71

159.59

7

Cp*

2.069

2.798

1.928

2.028

112.63

138.14

3N

2.088

2.511

2.094

1.386

94.40

148.30

2N

2.150

2.892

1.977

2.111

113.97

139.34

2N

2.160

2.950

1.936

2.226

117.17

135.08

3N

2.153

2.868

2.027

2.029

112.24

139.95

2N-mono

2.075

2.781

1.953

1.980

111.09

140.77

3N-bi

2.086

2.526

2.091

1.417

95.33

147.76

2N-bi

11 Cp*

2.089

2.465

2.096

1.297

92.11

159.99

11 Cp*3N-mono

2.046

2.640

2.001

1.722

103.98

145.74

3N-mono

2.074

2.790

1.941

2.004

111.74

139.87

3N-bi

2.086

2.510

2.093

1.385

94.43

148.28

7 8 9 9

Cp* Cp* Cp* Cp*

10 Cp* 10 Cp*

12 Cp* 12 Cp*

(2/3N)

d(Zn-C1): distance between the Zn atom and the closest C atom in the Cp*

part. Cg = center of gravity

within the five-membered rings. pl = plane spanned by the five ring C atoms. R = residual connected to the C1 atom (-CH3 or –(CH2)2/3-NMe2). mono/bi = mono/bidentate.

The quantitative determination of the strength of the respective Zn-C interactions is not possible without comprehensive analysis of the isolated ligands and mono-substituted Zn-complexes. However, a rough estimation becomes feasible by systematic comparison of sets of two pairs of compounds comprising the same number/types of atoms. Table 2 shows all possible combinations. For clarity, also the ligand names (Et, Cp*(2/3N)) are given. Considering the three modifications of ZnCp*2NCp*3N (9-11), the most stable model 11 was chosen for this comparison. However, the pairs which include model 8 seem problematic, as only the modification with two ACS Paragon Plus Environment

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bidentate ligands was initially calculated in this study since it was found as sole product in the crystal

structure.

Accordingly,

for

comparision,

another

modification

comprising

one

monodentate and one bidentate ligand was calculated, which is found to be ca. 10 kJ/mol higher in energy compared to model 8 and is thus not further used. According to Table 2, the heteroleptic compounds comprising the Et-ligand (ZnEtCp*(2/3N)) are energetically favoured over those, which contain solely ethyl (ZnEt2, 1) or Cp*-derived ligands (ZnCp*(2/3N)Cp*(2/3N), 5-8, 11, 12). The energetically differences within the latter group of compounds are much smaller. ZnEtCp*3N is slightly more stable than ZnEtCp*2N. Following these observations, the complex stabilities descend in the order: ZnEtCp* (2) > ZnEtCp*3N (4) > ZnEtCp*2N (3) > ZnCp*Cp*2N (6) ≈ ZnCp*Cp*3N (7) ≈ ZnCp*2NCp*3N (11), ≈ Zn(Cp*2N)2 (8) ≈ Zn(Cp*3N)2 (12) ≈ ZnCp*2 (5) > ZnEt2 (1), which is accordance with experimental findings.71

Table 2.

Pairwise relative molecular energies of models 1-12. Ia

Ib

1 Et2

+

1 Et2

+

1 Et2

+

1 Et2

+

IIa

5 Cp*2

2 EtCp* 2N

6 Cp*Cp* 7 Cp*Cp*

1 Et2

8 (Cp* )2

5 Cp*2 5 Cp*2 5 Cp*2 2N

+ + +

3 EtCp* 4 EtCp*

+

6 Cp*Cp* 3N

+ 11 Cp* Cp*

8 (Cp* )2 + 12 (Cp* )2

+ 2N

8 (Cp* )2

3N

+

2 EtCp*

2N

+ 12 (Cp* )2

+

2 EtCp*

3N

3N

3 EtCp* 4 EtCp*

2N

2N

+

2N 3N

+ 12 (Cp* )2

5 Cp*2

#

3 EtCp* 3N

3N

5 Cp*2

+

2N

+ 11 Cp* Cp*

1 Et2

+

2 EtCp*

2N

2N

+

2 EtCp*

3N

#

IIb

+

2N

6 Cp*Cp*

+

3N

7 Cp*Cp* 2N

+ 3N

11 Cp* Cp*

∆E

2 EtCp*

46.67

2N

37.57

3N

44.62

2N

37.14

3N

34.87

3N

42.45

3 EtCp* 4 EtCp* 3 EtCp* 4 EtCp* 4 EtCp*

2N

9.10

3N

2.05

2N

8.67

3N

-0.65

6 Cp*Cp* 7 Cp*Cp* 6 Cp*Cp* 7 Cp*Cp*

3N

7 Cp*Cp* 2N

-0.11 3N

+ 11 Cp* Cp*

9.85

∆E = (Ia + Ib) – (IIa + IIb)


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Hapticities: In the following, we define the ring C atom, which is closest to the Zn atom as C1 (irrespective if the –(CH2)2/3NMe2 fragment is attached to C1 or not) and the second closest as C2. C2 and C2’ are bonded to C1. C3(‘) is connected to C2(‘). According to the geometrical analysis the determination of the Zn-Cp*2/3N hapticities is especially interesting for models 2-6, because Zn-C2(‘) distances below 2.5 Å are present. For the larger models 7-12, all Zn-C2 distances are above 2.5 Å so that the appearance of Zn-C2 virial paths and V2(Zn,C2) ELI-D basins is not expected according to our former studies in which a Zn-C maximum distance of ca. 2.3 Å was found. Table 3 lists all Zn-Cring distances for models 2-6, a complete list of models 112 is given in the supplementary material. For models 3, 4, and 6 the previous results are fully confirmed.23 Short Zn-C2 distances of 2.361 Å, 2.367 Å, and 2.368 Å are found but a saddle point is not observed in ED, VF and ELI-D.

Table 3.

AIM and ELI-D topology of the Zn-C contacts in the optimized geometries of

models 2-6.

no. 2

3

4

Zn

=

d(Zn-C) [Å]

ED

VF

ELI-D

bcp ? sp ? sp ?

Cp*-C1

2.269

yes

yes

yes

Cp*-C2

2.277

yes

yes

yes

Cp*-C2'

2.295

yes

yes

-

Cp*-C3

2.307

yes

yes

-

Cp*-C3'

2.317

yes

yes

-

Cp*-C1

2.134

yes

yes

yes

Cp*-C2

2.361

-

-

-

Cp*-C2'

2.440

-

-

-

Cp*-C3

2.766

-

-

-

Cp*-C3'

2.808

-

-

-

Cp*-C1

2.123

yes

yes

yes

Cp*-C2

2.367

-

-

-

Cp*-C2'

2.462

-

-

-

Cp*-C3

2.786

-

-

-


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Cp*-C3' 5

2.836

-

-

-

1

2.014

yes

yes

yes

1

2.700

-

-

-

1

2.700

-

-

-

1

3.419

-

-

-

1

3.419

-

-

-

3

2.225

yes

yes

yes

3

2.273

-

yes

-

3

2.276

-

yes

-

3

2.347

-

-

-

3

Cp*(η )-C3'

2.349

-

-

-

Cp*-C1

2.090

yes

yes

yes

Cp*-C2

2.368

-

-

-

Cp*-C2'

2.554

-

-

-

Cp*-C3

3.206

-

-

-

Cp*-C3'

Cp*(η )-C1 Cp*(η )-C2 Cp*(η )-C2' Cp*(η )-C3 Cp*(η )-C3' Cp*(η )-C1 Cp*(η )-C2 Cp*(η )-C2' Cp*(η )-C3

6

Page 14 of 66

3.162

-

-

-

2N

Cp* -C1

2.045

yes

yes

yes

2N

Cp* -C2

2.696

-

-

-

2N

Cp* -C2'

2.734

-

-

-

2N

Cp* -C3

3.431

-

-

-

2N

3.449

-

-

-

Cp* -C3'

Two exceptions, however, are found for the seemingly η5-coordinated Cp* ligands in models 2 and 5. Figures 2 and 3 display Zn-C bond paths (ED), Zn-C virial paths (VF), ELI-D iso-surface representations, the ELI-D distribution mapped on the Zn core basin (C(Zn)), and the ED distribution mapped on the ASF surfaces of the Cp* ligands for the theoretically optimized molecular structures of models 2 and 5. As visible in Figure 2 and Table 3, the η5-coordinated Cp* ligand in model 2 exhibits five Zn-C bcp in the ED (2a) and five Zn-C virial paths in the VF (2b). Moreover, the ELI-D distribution on the C(Zn) basin surface is symmetrical (2d) and a symmetrical disc-shaped ED distribution on the ASF surface is exhibited (2e) although the ZnC3 and Zn-C3’ distances are with 2.307 Å and 2.317 Å slightly larger than the proposed 2.3 Å,23 so it seems appropriate to extend the maximum Zn-C distance to a value of about 2.32 Å.


14

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However, only two V2(Zn,C) basins are generated in the ELI-D, but three further “proto-basins” are clearly visible in Figure 2c. Obviously, the generation of these basins is very sensitive against small structural changes in the molecular geometry for highly symmetrical ligands such as Cp*. A slightly different picture is obtained by inspection of model 5. As visible in Figure 3 and Table 3, the seemingly η5-coordinated Cp* ligand shows one bcp (3a), three virial paths (3b), and one V2(Zn,C) basin (3c), although the Zn-C2 and Zn-C2’ distances are with 2.273 Å and 2.276 Å 0.04-0.05 Å shorter than the proposed value of about 2.32 Å. Again, the number of ELID basins is smaller than the number of virial paths, although four further Zn-C “proto-basins” are already formed. The results are supported by the asymmetrical ELI-D distribution on the Zn atom core basin (Figure 3d) and the distorted ring-shaped ED distribution on the ASF surface (Figure 3e), so that we propose this Cp* ligand to be η3-coordinated. The chemical concept of hapticity is a yes-no-based relation and remains arbitrary to certain extent. For highly delocalized ligands such as Cp* not only the ED topology but also the ELI-D topology may fail in clear prediction. Nevertheless, with the combined analysis of the molecular geometry and a suitable set of realspace bonding indicators (including ELI-D and ASF surfaces) a self-consistent distance-based criterion for hapticity can be developed. The respective values (e.g. for Zn-C = 2.32 Å), however, depend on the type of metal atom and the type of ligand. The quantitative ED derived bond topological parameters of the Zn-C interactions are similar to previous results on zincocenes23 and other metal-organic compounds12 and will thus not be discussed in detail. Figure 4a displays the ED at the bcp (ρ(rbcp)) and the kinetic (G) and total (H) energy density over ρ(rbcp) ratios for the bcp of all Zn-C interactions. These results show the same trends which have been found formerly. G/ρ(rbcp) and H/ρ(rbcp) are slightly decreasing with decreasing Zn-C distance, which is in accordance with a increasing covalency of the Zn-C interaction. For Zn-N interactions (see supplementary material) bcp are observed for Zn-N distances up to ca. 2.45 Å compared to maximum Zn-C distances of ca. 2.32 Å.


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Figure 2.

Page 16 of 66

AIM, ELI-D and ASF of model 2: a) bond paths in the electron density (ED), b)

virial paths in the potential energy density (VF), c) iso-surface representation of the ELI-D at Y = 1.3, d) ELI-D distribution mapped on the Zn atom core ELI-D basin surface, e) ED mapped on the ASF surface of the Cp* ligand.


16

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Figure 3.


AIM, ELI-D and ASF of model 5: a) bond paths in the electron density (ED), b)

virial paths in the potential energy density (VF), c) iso-surface representation of the ELI-D at Y = 1.3, d) ELI-D distribution mapped on the Zn atom core ELI-D basin surface, e) ED mapped on the ASF surface of the η3-coordinated Cp* ligand.


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Figure 4.

Page 18 of 66

a) Bond topological properties of the Zn-C interactions, b) Electron populations

plotted against the corresponding ELI-D basin volumes, c) AIM valence electron populations plotted against AIM valence volumes, d) AIM valence electron densities plotted against AIM valence volumes.

Detailed inspection of the properties of the V2(Zn,C) basins affords insight into the electronic effects of the four different ligand types. Table 4 lists ELI-D derived parameters of the Zn-C basins (including Zn-CEt) sorted along increasing electron populations (N001ELI). In Figure 4b, N001ELI is plotted against the corresponding basin volume (V001ELI), which follows a saturation curve. On the one hand, as expected, all ELI-D parameters unravel that the Zn-CEt bonds are localized polar-covalent interactions with the highest electron populations (> 2.2 e), the highest degree of localizability (> 1.61), the lowest distance of the ELI attractor to the Zn-C axis (< 0.088 ACS Paragon Plus Environment

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Å) and the lowest RJI values (< 63.2 %). The increasing delocalization in the Zn-C interaction is reflected in decreasing N001ELI and Ymax and increseasing ∆ELI values. An inverse trend is visible in that a localized bond becomes even more localized if the other ligand of the same Zn-complex shows a higher degree of delocalization and vice versa. According to this, the Zn-C localization decreases in the order Et > Cp*(σ) > Cp*3N > Cp*2N > Cp*(π). In principle, the electronic effects of the different ligand types and different modes of bonding should also be reflected in the AIM charges of the Zn atoms. However, as was found before, it is hardly possible to correlate them to the chemical expectations due to the influence of different ligands to the central Zn atom.23 Unexpectedly, also the electron populations of the Zn atomic ELI-D core basins (C(Zn)) show a dependency against the ligand types. Accordingly, we combine the AIM and ELI-D space-partitioning schemes in order to define an “AIM valence density” by substraction of the electron population of C(Zn) from the AIM atomic electron populations. As all core electrons are removed, one obtains a much more sensitive measure for electronic effects exerted by the ligands to the metal atom. Figures 4c and 4d display the “AIM valence electron populations” (NvalAIM) and the “average AIM valence electron densities” (ρvalAIM) plotted against the respective “AIM valence volumes” (VvalAIM) for the Zn atoms. For NvalAIM a linear increase is found with increasing AIM valence volume, whereas ρvalAIM shows decay with increasing VvalAIM. For models 8 and 9, the valence electrons of the Zn atom are less in number but they are more “compressed”. For 1, the absolute number of valence electrons is much higher, but they are less “compressed”. These results may be related to the sterical stress in the models, which is expected to be highest for 8 and 9 (the only two compounds with two bidentately coordinated ligands) and lowest for 1.


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Table 4.

Page 20 of 66

ELI-D properties of the Zn-C contacts of the optimized geometries of models 2-12.

no.

N(001)

basin

2 Zn-C(Cp*(η5))

[e] V(001)

ELI

3

[Å ] Ymax ∆ELI [Å] RJI

0.29

1.6

1.32

-

83.8

5

0.32

1.7

1.32

-

83.6

3

0.51

3.9

1.33

0.330

70.6

3 Zn-C(Cp* )

0.68

2.0

1.37

0.187

78.2

4 Zn-C(Cp*3N)

0.97

4.0

1.42

0.264

75.9

1.20

4.5

1.45

0.132

72.2

2 Zn-C(Cp*(η )) 5 Zn-C(Cp*(η )) 2N

2N

6 Zn-C(Cp* ) 2N-bi

)

1.20

4.5

1.45

0.137

72.0

3N-bi

)

1.46

7.0

1.51

0.203

70.2

1.47

7.6

1.50

0.204

69.5

1.52

8.1

1.51

0.197

67.9

11 Zn-C(Cp* 12 Zn-C(Cp*

3N

7 Zn-C(Cp* ) 2N-mono

10 Zn-C(Cp*

)

9 Zn-C(Cp*2N)

1.70

8.6

1.56

0.046

67.7

2N

1.73

8.7

1.56

0.078

68.0

3N

1.82

9.7

1.58

0.069

67.2

1.85

11.8

1.52

0.111

58.4

)

1.87

10.8

1.55

0.083

62.1

6 Zn-C(Cp*(η ))

1.89

12.2

1.52

0.108

58.0

8 Zn-C(Cp* ) 9 Zn-C(Cp* ) 3N-mono

11 Zn-C(Cp*

3N-bi

10 Zn-C(Cp*

)

1

3N-mono

12 Zn-C(Cp*

1.89

11.0

1.55

0.076

61.7

1

1.93

11.3

1.56

0.064

61.1

1

5 Zn-C(Cp*(η ))

1.96

12.8

1.52

0.131

56.1

1 Zn-C(Et)

2.23

67.9

1.65

0.074

63.2

4 Zn-C(Et)

2.27

14.3

1.66

0.079

60.9

3 Zn-C(Et)

2.30

15.6

1.65

0.088

59.4

2 Zn-C(Et)

2.35

18.8

1.61

0.081

55.0

7 Zn-C(Cp*(η ))

For all bonds, N(001)

ELI

ELI

)

is the electron population in the Zn-C basins, V(001)

ELI

is the corresponding volume,

Ymax is the value of the ELI-D attractor, ∆ELI is the perpendicular distance of the attractor to the Zn-C axis, RJI is the Raub-Jansen-Index, which defines the relative electron populations of N(001)

ELI

in the Zn and C

AIM atomic basins. mono/bi = mono/bidentate.

In conclusion, the combined AIM, ELI-D, and ASF analysis provides a distinct relation between molecular geometries and Zn-Cp*(2/3N) hapticities as well as a sensitive measure for the electronic and steric effects exerted by different ligand types and different modes of bonding. ACS Paragon Plus Environment

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Hydrogen-hydrogen contacts: In terms of bond critical points in the electron density, models 3-12 comprise the large number of 65 intra-molecular hydrogen-hydrogen bonds (H-H) as well as a number of HSπ and HSN contacts. The real-space bonding indicator analysis of this work, however, is focused on the H...H contacts as the other two types of weak interactions are well understood. As for the Zn-C interactions a distinct relation between the molecular geometries and the AIM and ELI-D topology is observed. Due to the inclusion of a significantly larger set of analyzed compounds in this work the formerly found results56 could be improved. The topological analysis of the ELI-D, however, is quite consumptive and was only performed for the heteroleptic model 9, which includes both the Cp*2N and Cp*3N ligands. Table 5 lists geometrical parameters of the 65 H...H contacts found in models 3-12 (the atomic labeling scheme is given in the supplementary material). The HSH distances range from 1.978 Å to 2.927 Å, the C-HSH angles from 99.81° to 166.62°. The torsion angles seemingly have no effect on the AIM and ELI-D topology and are not included.

Table 5.

Geometrical and topological properties of the HSH contacts in the optimized

geometries of models 3-12. =

=

d(H H)

H H

3

13-27

2.081

134.73 130.24

24-26

2.176

110.52 122.22 -11.70

24-36

2.279

14-30

4

5

6

[Å]

a1 [°]

a2 [°]

a1-a2

no.

[°] 4.49

=

VF sp ? yes

=

no. H H 9

d(H H) [Å]

a1 [°]

a2 [°]

a1-a2 [°]

VF sp ?

14-36

1.978

143.63 144.52

-0.89

yes

-

15-55

2.105

136.11 124.49

11.62

yes

136.15 158.45 -22.30

yes

16-52

2.354

165.04 140.85

24.19

yes

2.586

143.85 129.54

14.31

yes

17-19

2.135

117.86 120.13

-2.27

-

22-23

2.186

120.60 115.06

5.54

-

24-25

2.136

118.16 117.34

0.82

-

25-28

2.351

133.15 124.89

8.26

-

26-36

2.133

111.53 115.57

-4.04

-

28-35

2.141

117.99 117.01

0.98

-

32-64

2.193

107.41 162.28 -54.87

yes

38-44

2.410

131.17 126.02

5.15

-

32-73

2.111

137.67 146.77

-9.10

yes

17-18

2.153

117.66 120.21

-2.55

-

51-66

2.067

148.46 124.03

24.43

yes

23-25

2.153

120.22 117.70

2.52

-

51-74

2.266

126.58 127.39

-0.81

yes

13-32

2.407

144.54 154.82 -10.28

yes

60-62

2.036

116.44 124.73

-8.29

-


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7

8

Page 22 of 66

14-16

2.190

112.96 120.31

-7.35

-

10 15-28

2.381

102.89 134.74 -31.85

20-49

2.758

120.10 160.29 -40.19

-

15-35

2.571

146.44 145.17

1.27

yes

21-22

2.091

119.62 121.80

-

16-17

2.097

121.62 119.61

2.01

-

23-27

2.313

103.82 131.62 -27.80 C10-27

20-75

2.825

126.29 122.58

3.71

yes

59-61

2.176

120.32 115.81

4.51

-

28-35

2.149

116.91 116.84

0.07

-

53-54

2.181

115.17 120.44

-5.27

-

53-55

2.160

116.57 120.07

-3.50

-

14-28

2.362

104.18 133.76 -29.58

C7-28

64-75

2.162

112.37 116.43

-4.06

-

14-35

2.442

149.05 145.91

3.14

yes

11 14-27

2.336

99.81

16-17

2.092

121.61 119.68

1.93

-

15-16

2.099

121.53 119.21

2.32

-

19-51

2.532

111.47 125.48 -14.01

yes

21-22

2.141

119.17 118.31

0.86

-

21-52

2.455

110.86 146.25 -35.39

-

24-36

2.562

134.76 149.78 -15.02

22-24

2.184

120.34 114.10

6.24

-

51-53

2.253

109.49 119.14

28-35

2.147

117.24 115.79

1.45

-

61-71

2.927

117.56 166.62 -49.06

62-65

2.160

120.17 117.14

3.03

-

65-71

2.168

110.26 115.17

56-57

2.184

114.61 120.26

-5.65

-

12 15-28

2.364

103.47 134.66 -31.19

17-19

2.126

118.63 120.22

-1.59

-

15-35

2.506

147.34 145.91

1.43

yes

24-25

2.142

118.69 116.37

2.32

-

16-17

2.104

121.58 118.87

2.71

-

14-36

2.095

144.00 142.83

1.17

yes

22-23

2.202

120.19 113.16

7.03

-

15-51

2.649

135.22 135.22

0.00

yes

28-35

2.145

116.89 116.77

0.12

-

15-54

2.428

106.69 149.62 -42.93

C5-54

54-56

2.171

115.66 120.04

-4.38

-

26-36

2.133

112.60 115.61

-

64-74

2.705

136.75 166.14 -29.39

68-74

2.172

109.46 114.65

-2.18

-3.01

131.21 -31.40

-9.65

-4.91

-5.19

C7-28

C7-27

yes yes C7-28

yes -

For all bonds d(HSH) is the contact distance, a1 and a2 are the C1-H1SH2 and H1SH2-C2 angles, respectively.

The previous results implied the following order for the generation of saddle points with increasing average C-HSH angle (ØCHH): no saddle point ELI-D sp ED bcp VF sp.56 This order is retained in the present study. With few exceptions all H...H contacts follow the proposed trend. According to our results, no HSH saddle point is observed in ELI-D, ED and VF if ØCHH is smaller than ca. 97° (models 6 and 9). Up to ca. 110° exclusively ELI-D sp are found (models 6 and 9). For larger ØCHH values additional ED bcp are generated, but only those H...H contacts with ØCHH values above ca. 125° also exhibit a VF sp (models 3-12). For some H...H contacts, however, no VF sp is found, although expected. This is typically the case if one of the interacting H atoms is involved in another HSH/C/N contact, which may prevent the formation of ACS Paragon Plus Environment

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an ED bcp or VF sp due to the electronic effect of the second H/C/N atom. In contrast, for model 7 a VF sp is observed for the H19SH51 contact, although ØCHH is ca. 118° and thus too small for the generation of a VF sp. Detailed inspection of all individual C-HSH values uncover that ED bcp are generated for C-HSH values larger than ca. 110° (as mentioned above) and a difference between C1-H1SH2 and H1SH2-C2 (∆CHH) of 0-12°. The H19SH51 contact, however, shows a difference of 14.01°. Obviously, the trends are not only related to the average C-HSH values but also to the difference between both C-HSH angles. Interestingly, some HSH contacts are observed in the narrow range of 2.31 Å to 2.43 Å with ∆CHH values above 27.8°. For these contacts, the VF sp is shifted to the adjacent C2 atom to form a C1-H1SC2 contact.

Figure 5.

a) ED at the bcp plotted against the contact distances for the HSH/C/N

interactions, b) Ratio of the ED at the closest ring critical point (rcp) and the ED at the bcp plotted against the contact distances.

Figure 5a displays the electron density at the HSH/C/N ED bcp plotted against the HSH/C/N distances for models 1-9 and 12. The exponential decay found by Espinosa and co-workers for conventional hydrogen bonds (HBr) is also given.72,73 As expected, the H...H contacts follow the


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exponential relation which has been found before and which lies below the HBr relation.39,48 For the HSπ interactions an exponential function was derived from the 19 HSπ contacts in this study. This type of interaction is stronger than conventional hydrogen bonds. However, the absolute values of the ED at the bcp can not unravel if the interaction under consideration may be close to a topological catastrophe in which critical points in the ED vanish. Accordingly, for all ED bcp also the ratio ρ(rrcp)/ρ(rbcp) is given for the ring critical point which is closest to the ED bcp and plotted against the HSH/C/N distances, see Figure 5b. With increasing atom-atom distances the ratio approaches 1.0 for all types of weak interactions, which is expected, because the contacts become weaker. But for the H...H contacts a number of contacts is found with short HSH distances of 2.0-2.2 Å and a ρ(rrcp)/ρ(rbcp) ratio above 95%. Obviously, these contacts are already topologically unstable, although short. It turns out, that these contacts are almost exclusively intra-ligand H...H contacts, which exhibit no VF sp because they are geometrically unfavored. For model 9, a full topological analysis of ED, VF and ELI-D was performed for the HSH/C contacts. The qualitative results are given in Figure 6. The molecular structure is displayed in Figure 6a together with the corresponding HSH/π ED bcp (red), ED rcp (yellow), ED ccp (green), VF sp (pink), and ELI-D sp (blue). Some HSH contacts solely show an ELI-D sp, whereas others have additional ED bcp and VF sp (see Table 5). In cases when bcp and rcp approach each other (mainly intra-ligand contacts), the HSH contact can be considered as topologically unstable in the ED and thus no VF sp is generated as mentioned above. However, if the ED rcp to ED bcp distance is larger than the ED bcp to ELI-D sp distance a VF sp is formed, which is located close to the ED bcp inside the ring formed by the ED bcp. Interestingly, the ELI-D sp are always located opposite to the ED rcp and VF sp points, which leads to a linear arrangement between these different types of critical points. Figure 6b shows the corresponding ELI-D figure. In Figure 6c the ED is mapped on the ASF surface of the Cp*2N ligand. One finds all inter-ligand ED bcp, VF sp, and ELI-D sp to be located exactly on the ASF surface and in the centers of the ACS Paragon Plus Environment

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ED cavities, which confirms our previous results on model 656. ED rcp and ED ccp connect the different Zn-C/N and HSH/π cavities. These results prove the high reliability of the results obtained by such different methods as AIM, ELI-D and ASF. For strong HSH contacts ED bcp, VF sp, and ELI-D sp almost fall together. As found for sterically strained molecular systems54 the H atoms which are involved in H...H contacts are by average ca. 14 kJ/mol lower in energy compared to those H atoms which are not. However, those H atoms, which are involved in HSπ contacts are 64 kJ/mol higher in energy, which makes the discussion based on relative AIM-atomic energies inconclusive. Since a deeper analysis of these energetical results based on DFT-calculations is out of the scope of this work (which is focused on topology), we refer to the literature74,75. In conclusion, like for the Zn-C/N interactions, the combined AIM, ELI-D, and ASF analysis provides a distinct relation between molecular geometries and hydrogen-hydrogen contacts.


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a) Zn-C/N and HSH/π topology of the optimized geometry of model 9 b)

Corresponding ELI-D iso-surface representation (Y = 1.30), c) ED mapped on the ASF surface of the Cp*2N ligand. Red: ED bcp, yellow: ED rcp, green: ED ccp, pink: VF sp, blue: ELI-D sp.


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Conclusion The idea of a principally distinct relation between molecular geometry and complete real-space bond topology is proposed even though this relation may by quite complex for some types of atom-atom interactions. For “standard” covalent bonds (e.g. R3C-CR3), this relation is trivial, but also for medium-strength Zn-C and weak intramolecular HSH contacts such dependencies are clearly observed in this study. For the Zn-C interactions a distance-based criterion was found (d(Zn-C) < 2.32 Å), which determines whether or not a critical point in ED, VF and ELI-D is generated, respectively. In contrast, a dependency against the absolute and relative C1-H1SH2 and H1SH2-C2 angles was observed for the HSH topology, whereas the HSH distance seems to be of much lower importance. If the average of both angles exceeds values of ca. 97°, 110°, and 125°, saddle points are found first in the ELI-D, then also in the ED and finally also in the VF. With few exceptions, the AIM (ED and VF) and ELI-D topology of all analyzed Zn-C and HSH contacts follows this empirically determined trends. Missing saddle points can be well explained by the electronic influences of adjacent atoms (e.g. an H atom is involved in more than one hydrogen-hydrogen bond), which may prevent the formation of saddle points. These observations make the use of large asymmetrical compounds favourable against small model compounds since electronic effects of adjacent atoms not directly involved in the dHB can hardly be foreseen or even be resembled by small model compounds. The inspection of the yes-no based topological properties is nicely complemented by the use of the ASF surfaces, which show electron density distributions between defined molecular fragments such as the central Zn atom or the Cp*(2/3N) ligands. The results of the topological Zn-C and HSH analysis were fully confirmed by the ASF analysis. By systematical screening of 12 zincocene related compounds also the electronic effects and the steric stress exerted by the four different ligand types could be quantified. Due to energetical reasons, the formation of heteroleptic Zn-complexes of the type ZnEtCp*(2/3N) is favoured against the formation of symmetrical compounds ZnEt2 and Zn(Cp*(2/3N))2. Steric stress in complexes comprising exclusively the large Cp*2N and Cp*3N ACS Paragon Plus Environment

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ligands leads to reduction of the denticity of these ligands. Moreover, the Zn atom is not longer attached to the CCp*(2/3N) atom, which carries the –(CH2)2/3NMe2 fragment, but to the adjacent one, which is energetically unfavoured. In future studies, systematic screening of large numbers of large and asymmetric compounds may result in a high level of predictability of any real-space bond topology by sole inspection of accurate molecular geometries. On the one hand, this may help to accurately estimate all types of intra-molecular interactions. On the other hand, such close relation between molecular geometry and topology would raise the question about the significance of the method itself and the amount of extra-information provided by it. This question also includes quantitative properties such as electron populations within AIM atomic or ELI-D bonding basins.

Acknowledgement Dr. Simon Grabowsky is acknowledged for generation of synthetic structure factors for the compounds. Dr. Miroslav Kohout, Dr. Julian Henn, and Pamela Finke are acknowledged for helpful discussions.

Supporting Information Available: Geometrical parameters of all models; topological and integrated AIM and ELI-D properties of the Zn-C and Zn-N contacts; AIM topology of the H...H contacts; cartesian coordinates, figures (ED, VF, and ELI-D) and labeling schemes of models 1-

12. This material is available free of charge via the Internet at http://pubs.acs.org.


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The combined analysis of electron densitiy and electron localizability uncovers a distinct relation between molecular geometry and real-space topology for hapticities and hydrogen-hydrogen bonds.


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


129x158mm (96 x 96 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

176x224mm (72 x 72 DPI)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


125x107mm (96 x 96 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

153x128mm (96 x 96 DPI)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


127x88mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

127x88mm (72 x 72 DPI)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


127x88mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

127x88mm (72 x 72 DPI)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


278x196mm (96 x 96 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

260x182mm (96 x 96 DPI)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


116x260mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

161x177mm (72 x 72 DPI)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


334x242mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

293x250mm (72 x 72 DPI)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


191x176mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

294x243mm (72 x 72 DPI)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


321x242mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

273x186mm (72 x 72 DPI)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


258x172mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

183x212mm (72 x 72 DPI)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


189x170mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

275x249mm (72 x 72 DPI)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


186x185mm (72 x 72 DPI)


Fundamental Relation between Molecular ... - ACS Publications

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