Trends in Metallophilic Bonding in Pd-Zn and Pd-Cu Complexes

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Author(s): Paenurk, Eno; Gershoni-Poranne, Renana; Chen, Peter

Publication Date: 2017-12-26

Permanent Link: https://doi.org/10.3929/ethz-b-000234635

Originally published in: Organometallics 36(24), http://doi.org/10.1021/acs.organomet.7b00748

Rights / License: In Copyright - Non-Commercial Use Permitted

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ETH Library Trends in Metallophilic Bonding in Pd- Zn and Pd-Cu Complexes

Eno Paenurk, Renana Gershoni-Poranne, and Peter Chen*

Laboratorium für Organische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich, Switzerland

Abstract

Metallophilic interactions stabilize the bond between closed-shell metal centers, which electrostatically repel one another. Since its introduction, the origin of this interaction has been argued to be either London dispersion forces or dative bonding, but as yet there is no definitive answer. Insight into the nature of metallophilic bonding would provide the key for rational tuning of the stabilizing interaction, for example, in specific transmetalation transition states. We now report on a computational study focused on the metallophilic d8-d10 bond in recently published families of Pd(II)-Cu(I) and Pd(II)-Zn(II) heterobimetallic compexes. We show that dative bonding outweighs dispersion interaction in controlling the metallophilic bonding energy in the studied heterobimetallic complexes, and elucidate the governing orbital interactions.

1. Introduction

The term “metallophilic attraction” was suggested in 1994 by Pyykkö to describe the counterintuitive attraction between two closed-shell cationic metals, which otherwise would be expected to repel each other.1 The nomenclature for this type of interaction specifies the last filled subshell of the interacting metals, for example: d10-d10, d10-d8, d8-d8, d8-s2, d10-s2 or s2-s2 (where d8 is an extension of the closed-shell definition, which applies when crystal-field splitting is large).2 The earliest clear example of such bonding was reported in 1964 in a Co(I)-Hg(II) complex, which contains a d8-d10 bond,3 using the conventional nomenclature.

The nature of this type of bond – whether it is mainly a dative bond or a dispersion interaction – has been disputed for some time. Nowell and Russell, who reported on the Co(I)-Hg(II) complex,

1 suggested that the compound is a Lewis acid-base complex.3 This Lewis acid-base description of the metallophilic bonds gained general popularity and these types of complexes are now often referred to as Metal-Only Lewis Pairs. Moret has reviewed this type of bonding for specific cases in which Pd(II) and Pt(II) are the d8 components,4 and presents the respective square-planar complexes as two-electron donors, with the dz2 orbital available to form dative bonds to Lewis- acidic metals. Dewhurst and coworkers have recently published a broader review on Metal-Only Lewis Pairs and point out that discerning different types of bonding between transition metals is not easy, because the overall bonding interaction may comprise several components, such as ionic, covalent, dative, and closed-shell interactions.5 An alternative description of the metallophilic bonding was proposed by Pyykkö, who, based on his studies on aurophilicity (attraction between Au cations), ascribed the attraction to a dispersion effect, i.e. an effect stemming from the correlated motion of electrons.1,6

In addition to its fundamental value in chemical bonding theory, more detailed knowledge regarding the nature of metallophilic interaction has potential applicability in several fields of chemistry, e.g. supramolecular design7 or catalysis. A relevant example was recently reported by Espinet, with regard to metallophilic interaction in heterobimetallic complexes and transition- metal catalyzed cross-coupling catalysis. In a series of studies on the Pd-catalyzed Negishi cross- coupling, Espinet and coworkers proposed that the bonding interaction between an electron-rich Pd(II) and positively-charged Zn(II) in the transmetalation transition state (TS) is responsible for lowering the reaction barrier, which leads to reversible transmetalation and undesired homocoupling.8–11 Similarly, the favorable metal-metal interaction between Pd(II) and Cu(I) in the transmetalation TS of the Sonogashira cross-coupling has been used to rationalize the low rearrangement barriers.12 Insight into the nature of the intermetallic attraction would provide the foundation for tuning the interaction energy and, in turn, the transmetalation reaction barriers.

This required insight can, in principle, be accessed by quantum mechanical calculations. However, computational investigation of transition-metal compounds is notoriously difficult. Depending on the system, transition-metal compounds can have partially-filled and/or nearly degenerate d orbitals, which lead to significant static electron correlation effects.13 In such cases, the systems are multi-reference in nature, and thus single-reference methods are unlikely to provide correct results, e.g. in transition-metal dimers.14 While Density Functional Theory (DFT) is also a single- reference method, it is nevertheless often the method of choice for computation of transition-metal 2 compounds,13 and has often been employed for studying intermetallic interactions.15 However, due to the paucity of suitable experimental reference data, the accuracy of the results cannot be easily assessed.

Herein, we report on a computational study of substituent effects on the d8-d10 bond in recently reported families of Pd(II)-Cu(I)16 and Pd(II)-Zn(II)17 heterobimetallic complexes, from which we derive trends in bond strength. Furthermore, we evaluate and elucidate the different components contributing to the metallophilic bond.

2. Methods

2.1. Computational methods

DFT was selected as the method of choice for the quantum chemical calculations performed, due to its low computational cost. The size of the systems studied renders use of more computationally expensive methods, such as configuration interaction or coupled cluster, prohibitive and unfeasible. As mentioned, the drawback of DFT is that the level of accuracy for a specific system is not known a priori, a problem which is especially relevant to calculations with transition metals. Various benchmark studies have been conducted to examine the accuracy of DFT for transition metal chemistry in general18 or for narrower applications, e.g. Cu complexes,19 Ni or Pd catalysis,20 or aurophilic interactions.21,22 These studies provide guidance in selecting the density functional most suitable for a given study, but concern has been raised about the transferability of such benchmark studies to any specific case of interest.23 For this reason, a preceding benchmarking process was undertaken for this work, using a pre-selected set of density functionals. This set of functionals was chosen based on the recommendations of the aforementioned reviews and studies, and we further explored their ability to accurately treat our systems. The results of the benchmarking are discussed in the Supporting Information. The following sections detail only the methods relevant to the main narrative of this report.

The notations of the methodology in this work take the general form of (Hamiltonian)-Method- (Additional parameters)/Basis set. The descriptors in brackets are only specified if: a) the Hamiltonian is not the non-relativistic Hamiltonian and/or b) additional parameters are present, such as dispersion correction. If the property described was obtained by complete basis set (CBS) extrapolation, this is specified by replacing the basis set size description by “CBS”, e.g. def2-CBS

3 to denote the extrapolated value from def2-TZVP and def2-QZVPP calculations of the Ahlrichs def2 basis sets.24

2.1.1. Geometry optimizations

The ORCA 3.0.3 program25 was employed for geometry optimizations and energy calculations. Geometry optimizations were performed using the meta-GGA functional M06-L26 with the def2- TZVP basis set24 and the Stuttgart effective core potential (ECP) on Pd (ECP28MWB),27 together with Grimme's D3 dispersion correction.28,29 Resolution of Identity (RI) by Coulomb fitting with the general Weigend J auxiliary basis set30 was used to increase the efficiency of the calculations. SCF (self-consistent field) convergence was set to ΔE ≤ 10-8 au and the “tight optimization” setting available in ORCA was employed together with the “Grid5” DFT integration grid. In all cases, numerical frequencies were calculated to confirm real minima (i.e., Nimag = 0) and to obtain the zero-point energy (ZPE) correction. As discussed and justified in the Supporting Information, “Grid6” was selected to resolve the numerical inaccuracies that resulted in several compounds displaying small imaginary frequencies. The general notation of the geometry optimization is M06L-D3/def2-TZVP(ECP).

2.1.2. Single point calculations

All energies reported were obtained with single-point calculations performed using the meta- hybrid M06 functional31 together with the D3 dispersion correction on the optimized geometries. The calculations employed the scalar relativistic version of the 2nd order Douglas-Kroll-Hess (DKH2) Hamiltonian32,33 and the respectively recontracted all-electron def2-TZVP-DK and def2- QZVPP-DK basis sets as provided in ORCA 3.34,35 The energy change criterion for SCF convergence was set to 10-6 au and all calculations were performed using Grid5.

The Ahlrichs def2 basis sets have been shown to reduce the SCF error when a complete basis set (CBS) extrapolation is performed.36 To perform this extrapolation, properties resulting from triple- ζ and quadruple-ζ calculations are combined by an equation that estimates the value of the property at the complete basis set limit. The extrapolation in this work was done using the following equation:

퐸(푋) 푒−퐵∙푌 − 퐸(푌) 푒−퐵∙푋 퐸∞ = DFT DFT (1) DFT 푒−퐵∙푌 − 푒−퐵∙푋

4 where X = 3 and Y = 4 for the triple/quadruple extrapolation used in this work. For this study, the parameter B was set to be equal to 6, which has been determined to be an optimal value when combined with Jensen’s polarization consistent basis sets.37 The effect of the CBS extrapolation on the results is briefly discussed in the Supporting Information.

All resulting energies were corrected with the respective zero-point energies obtained from M06L- D3/def2-TZVP(ECP) frequency calculations.

2.2. Analysis of computational results

2.2.1. Energy Decomposition and Non-Covalent Interaction analysis

The ADF 2014.0738–40 program package was used for Energy Decomposition Analysis (EDA).41,42 The calculations were performed with the scalar-relativistic ZORA (Zeroth Order Regular Approximation) Hamiltonian43–45 and the GGA functional PBE46 with the relativistically optimized Slater-type QZ4P basis set.47 Dispersion was accounted for with Grimme's D3 correction with Becke-Johnson damping.48 This corresponds to a general notation of ZORA-PBE- D3(BJ)/QZ4P for the calculations. All of the single-point calculations were done on the M06L- D3/def2-TZVP(ECP) optimized geometries.

Energy decomposition analysis was done with the Extended Transition State (ETS) method combined with Natural Orbitals for Chemical Valence (NOCV), as implemented in ADF.49,50 The total binding energy of the fragments, ∆Ebind, was partitioned into five terms:

Ebind = Eelstat + EPauli + Eorb + Edisp + Eprep (2)

The first four terms are calculated by specifying the fragments in the compound and running the

ETS-NOCV analysis. The preparation energy, ∆Eprep, was calculated separately by computing the energy difference between the fragments in their complex geometry and their infinitely separated, relaxed gas-phase geometry. For this, geometries optimized at the M06L-D3/def2-TZVP(ECP) level were used for ZORA-PBE-D3(BJ)/QZ4P single-point calculations and the resulting energy of the “dissociated geometry” was subtracted from the energy of the “fragment-in-complex” geometry.

2.2.2. Substituent Effects

Substituent effects are usually investigated with linear free energy relationships,51–53 which study empirical correlations between the rate or equilibrium constant of a reaction and the respective substituent parameters. The use of substituent parameters is in and of itself an expedient tool for investigating the nature of various interactions. Since the publication of Hammett’s seminal paper,54 many refinements and additional models have been developed, with the aim of affording better correlations, covering a wider range of systems, and offering more extractable information.51,53 In addition to the Hammett σ constant, Swain-Lupton55,56 and Hammett σ+57 constants were selected for studying substituent effects in this work. Because the different constants all provide a qualitatively similar result, only the Hammett σ correlation plots are presented here; the other correlations are discussed in the Supporting Information. The values of all the substituent constants used in this work were extracted from the literature and are provided in the Supporting Information.

2.2.3. Other methods

The Multiwfn 3.3.858 program was employed for partial charge calculation in Atoms in Molecules (AIM)59,60 framework, on a grid with 0.1 Bohr spacing.

Atoms in Molecules (AIM)59,60 analysis, Bond Order analysis (Mayer Bond Order,61 Wiberg Bond Order,62 and Delocalization Indices61,63), Non-Covalent Interaction (NCI)64 analysis, and Natural Bond Orbital (NBO)65 analysis were also executed but proved less diagnostic in the present problem. These results are documented in the Supporting Information.

3. Results

Three types of Pd-containing d8-d10 complexes were chosen for this study, all of which are suspected of having a closed-shell metal-metal interaction. The general form of each type is + represented by compounds [bis-(1,10-benzo[h]quinolinato)Pd(II)·Cu(I)(C3H4N2)] (1a), [bis-

(1,10-benzo[h]quinolinato)Pd(II)·Zn(II)(C6F5)2] (2a) and [bis-(1,10-benzo[h]quinolinato)

Pd(II)·Zn(II)(Ph)2] (3a), respectively, as displayed in Scheme 1. Compounds [bis-(1,10- benzo[h]quinolinato)Pd II  Cu I (IPr)]+ (4) and 2a were previously synthesized, and the crystal structures were solved by X-Ray diffraction and reported.16,17 For the calculations performed in

6 this work, compound 1a was used, which is a modified version of the actual compound which was experimentally prepared, 4. Namely, we truncated of the ligand on Cu in order to to reduce the computational cost without severely altering the system. Benchmarking calculations confirmed that the truncation did not alter the core of the compound, where the metal-metal interaction occurs (further details in the Supporting Information). Compound 3a was constructed by replacing the fluorines in compound 2a with hydrogens.

1a 2a 3a 4

Scheme 1. Structures of parent compounds 1a, 2a, 3a, and 4.

In addition to the parent compounds described above, three distinct families of compounds were studied. Each family comprises several derivatives of the respective parent compound, each bearing different substituents on either the Pd (families 1 and 2) or Zn (family 3) fragments of the complex. The various substituents differ from one another in their electronic effects, encompassing σ- and π-electron donating and withdrawing groups. The entire list of compounds is given in Table 1.

Table 1. Compound identifiers.

Id. X Id. X Id. X 1a H 2a H 3a H 1b Me 2b Me 3b Me 1c tBu 2c tBu 3c F 1d F 2d F 3d Cl

1e Cl 2e Cl 3e Br 1f Br 2f Br 3f I

1g I 2g I 3g NH2

1h NH2 2h NH2 3h NMe2

1i NMe2 2i NMe2 3i NO2

1j OMe 2j OMe 3j CF3

a 1k NO2 2k NO2 3k 2,4,6-F-Ph

a 1l CF3 2l CF3 3l 2,4,6-Me-Ph

a These represent the full ligands on Zn, not the substituent in para position.

3.1. Dissociation energies

Energies of the gas-phase dissociation reactions for the compounds (Scheme 2) were calculated to study the substituent effect on the binding strength between the Pd and the d10 metal fragment. The results obtained at the DKH2-M06-D3/def2-CBS-DK//M06L-D3/def2-TZVP(ECP) level of theory are given in Table 2.

Scheme 2. General scheme of the gas-phase dissociation reactions studied by computations.

Table 2. ZPE-corrected dissociation energies (kcal mol-1, DKH2-M06-D3/def2-CBS//M06L-D3/def2- TZVP(ECP)).

Id. ∆Ediss Id. ∆Ediss Id. ∆Ediss 1a 70.2 2a 32.9 3a 25.9 1b 72.2 2b 36.9 3b 26.5 1c 73.9 2c 38.5 3c 26.3 1d 69.5 2d 32.8 3d 31.0 1e 66.8 2e 32.6 3e 31.8 1f 70.2 2f 34.9 3f 32.9 1g 67.1 2g 32.7 3g 26.7

1h 75.7 2h 35.2 3h 30.1 1i 74.7 2i 33.5 3i 34.8 1j 80.2 2j 40.3 3j 38.7 1k 58.7 2k 29.2 3k 31.8 1l 63.2 2l 31.4 3l 30.9 4 81.6

First and foremost, it is imperative to compare the computationally obtained values with the small amount of available experimental data. The dissociation energy of compound 4 to the respective Pd-centered and Cu-centered fragments has been measured experimentally by T-CID to be 51 kcal mol-1 in the gas phase.16 Computationally, the same energy was found to be between 77 and 82 kcal mol-1 (depending on the method) – a discrepancy of up to 31 kcal mol-1. We deemed it necessary to determine whether the selected computational method (DKH2-M06-D3/def2-CBS- DK) is to blame for this discrepancy. To verify that this level of theory is indeed capable of reproducing experimental values, a second reaction energy was calculated: the dissociation of Cu[IPr]+ from benzene (Scheme 3). This dissociation was also measured experimentally,16 and thus affords an opportunity for further benchmarking. The calculated dissociation energies of 41.4 kcal mol-1 and 45.6 kcal mol-1, for the truncated and the full Cu fragment, respectively, closely match the experimental value of 42 kcal mol-1, measured with the same technique as above, indicating that the discrepancy is not due to an inadequate choice of method, but perhaps due to the complex nature of the metal-metal interaction.

Scheme 3. Gas-phase dissociation reaction of Cu-aryl complex, studied by T-CID.

As mentioned above, a possible source of error with transition metal compounds is the existence of multi-reference character, i.e. strong static correlation, in the systems, in which case no single- reference calculation may be considered reliable.13 However, static correlation in the compounds studied in this work is likely to be low due to their expected closed-shell nature. This was

9 investigated by performing various multi-reference diagnostics, none of which indicated the existence of multi-reference character (further information in the Supporting Information), at least to the extent that these indicators are reliable for very large molecules. With practical limits on the execution of higher-level quantum chemical calculations, and with ongoing validation of the separate experimental results, we believe that the present study may nevertheless provide useful insights if one considers the trends, regularities, and especially anomalies, rather than absolute bond energies.

3.2. Bonding analysis

All the analysis methods employed in this work verified a stabilizing interaction between the metals. The most insightful results come from the study of substituent effects and energy decomposition analysis, which will be discussed separately in the following sections. The results obtained with other methods and the appropriate discussion can be found in the Supporting Information.

3.2.1. Substituent effects

Systematic substitutions in the compounds enable us to study the electronic effects on the binding energies, i.e. the trends, despite the ~30 kcal mol-1 difference between the experimentally obtained value and the computed one. Whether this discrepancy is a constant deviation, or one that scales with size (separate work in our group on other systems seems to indicate this might be the case), any trends discovered through this analysis are expected to be reiterated by experimental values, if and when obtained, because the systems are all of similar size. Thus, insight from these values could be instrumental in designing complexes with a specific dissociation energy. Moreover, any such future experimental values would help assess the accuracy of the computational method used in this work.

As mentioned in the Methods section, we used three different types of constants to investigate the substituent effects: Hammett σ, σ+, and Swain-Lupton. The plots of the correlations of dissociation energies and Hammett σpara constants for the compound families 1, 2, and 3 are given in Figure 1 (the respective plots for σ+ and Swain-Lupton constants appear in the Supporting Information). It appears that the strongly π-donating substituents (NH2 and NMe2) deviate significantly from the

10 linear correlation, indicating that they do not conform to the trend set by other functional groups in these compounds. Further analysis of this phenomenon is given in the Discussion section.

2 Figure 1. Correlations of dissociation energies and Hammett σpara constants of a) family 1 (R = 0.886), b) family 2 (R2 = 0.775), and c) family 3 (R2 = 0.700). Trend lines were computed without the data points of

NMe2 and NH2 substituents, which are denoted in red.

Comparison of the plots and correlation parameters suggests that the compounds of family 1 exhibit the most systematic trend with respect to the electronic properties of the substituents. Families 2 and 3 show weaker correlations, possibly due to the combination of multiple factors, i.e. both metal-metal and ligand-ligand interactions, which exist concurrently in the compounds of families 2 and 3. The fact that the total binding energy is a superposition of separate contributions makes it difficult to isolate the relationship between one single factor and the total energy.

3.2.2. Energy Decomposition Analysis

Energy decomposition analysis (EDA) allows for partitioning of the total binding energy into specific contributions (the energy contributions are listed in the Supporting Information). These provide insight into the relative weight of the different factors that influence the binding strength. The correlations between the interactions and the total binding energy are given in Figure 2. It should be noted that the dispersion interaction energy as calculated with the D3 scheme cannot be expected to show large variations between compounds that are geometrically very similar, because the D3 approach calculates the dispersion interaction based on the geometry of a compound, and not its electron density.28 To assess the validity of the D3-derived dispersion interaction energies, comparative calculations with the density-dependent dDsC method66 and with the Local Energy Decomposition67 were performed. These two method corroborate the trends obtained with the D3-

11 derived dispersion interaction energies, indicating that they are indeed suitable for our analysis (further details regarding the agreement between the three dispersion methods is in the Supporting Information).

Figure 2. Plots of the respective contributions to the total binding energy of the a) family 1, b) family 2, and c) family 3.

In ETS-NOCV, ∆Eorb is further decomposed into pairwise energy contributions for each pair of interacting orbitals. Generally, only a few significant contributions to ∆Eorb exist, enabling identification of dominant interactions. The NOCVs, which describe the deformation density (i.e. the difference between the electron density of the fragments before and after they are allowed to interact), further enable analysis and visualization of the charge donation that is associated with specific orbital contributions. This gives a good basis for both descriptive and quantitative analysis of bonding interactions. The deformation densities of the highest energy contributions to the orbital interaction in compounds 1a and 2a are shown in Figure 3. These are characteristic for all of the compounds in family 1 and families 2 and 3, respectively.

1a 1a 2a

I -1 II -1 I -1 ∆Eorb = -30.1 kcal mol ∆Eorb = -9.4 kcal mol ∆Eorb = -17.6 kcal mol

Figure 3. Deformation densities for compound 1a and 2a. Red: areas of charge depletion, Blue: areas of charge accumulation. Cut-off value ±0.005 au. Carbon-bound hydrogens not displayed for clarity.

We observe a relationship between the electrostatic interaction energy and the partial charges of the carbon coordinated to Pd in compound families 1 and 2. This type of remote effect is reminiscent of the observation made for a different type of complex, where it was shown that the partial charges of Pd(II) and Pt(II) centers are affected by the substituents in the para position of the pincer ligands bound the metal.68,69 In family 3, a similar correlation is observed between the interaction energy and the partial charge of the Zn atom (Figure 4).

Figure 4. Plots of electrostatic interaction energy versus partial charges in respective fragments in their complex geometry for a) family 1, b) family 2, c) family 3 and compound 2a.

4. Discussion

There are two main schools of thought regarding the origin of closed-shell intermetallic interactions. The first argues that metal-metal interactions arise from orbital interactions. This is demonstrated, for example, by Hoffmann’s report that the interaction between the d orbitals on the two metals in homobimetallic d10-d10 complexes is repulsive, unless s and p orbitals are allowed to mix with the d orbitals.70,71 However, this hybridization argument has been called into question following more rigorous calculations.21 For heterobimetallic compounds, it has been proposed that the d8-d10 bond stems mostly from donor-acceptor interactions,4 and the same Lewis acid-base rationalization has been invoked to describe various metal-metal bonds in the so-called Metal-

Only Lewis Pairs.5 In contrast, the second school of thought, led by Pyykkö, claims that closed shell intermetallic interactions are mainly dispersive interactions.1 Theoretical studies based on Pyykkö’s work have estimated the metallophilic attraction to be approximately 10 kcal mol-1, with minor variations depending on the specific compound.2,72–75 It should be noted that a more recent DFT study by Otero-de-la-Roza et al. suggests that dispersion interaction is not as important a component in metallophilic attraction as suggested by Pyykkö, and is of relatively similar magnitude for all metals, with the total interaction energy ranging from 4 to 8 kcal mol-1.21

We have studied our systems using several methods and techniques in order to determine the physical origin of the intermetallic interaction in the studied complexes. Though our investigation afforded a great deal of information, we found the most informative techniques to be EDA and the study of substituent effect, which afford insight that is corroborated by the other methods.

The relative weight of the different interactions can be analyzed by EDA. It can be seen clearly from Figure 2 that the electrostatic interaction is the predominant stabilizing interaction in almost all cases (with the exception of compounds 3h and 3l). In families 2 and 3, the electrostatic contribution and orbital-interaction contribution increase at a similar rate with the increase in total binding energy. However, in family 1 the binding strength increases more rapidly with increasing electrostatic term than the other interactions, indicating a much stronger dependence of the overall binding energy on this contribution. From the perspective of applications, this means that any attempt to tune the interaction energy of the compounds in family 1 would most likely involve tuning the electrostatic interaction. As the electrostatic interaction between two partially positively-charged metal centers is certainly repulsive, this attractive interaction can be attributed to metal-ligand and ligand-ligand interactions. A similar case of strong electrostatic interaction involving the ligands has been computationally characterized in closed-shell Au dimers.76 The strong effect of the ligand can be supported by the relationship observed in family 1 between the magnitude of the negative partial charge on the coordinated carbon of the benzo[h]quinolato (bhq) ligands and the total electrostatic interaction, as visible in Figure 4. A similar correlation exists in family 2, and in family 3 there is a correlation between the electrostatic interaction energy to the partial charge on Zn. The latter illustrates the involvement of the d10 metal in the metal-ligand interaction. With regard to potential applications in modulating the transmetalation TS energy, the electrostatic interaction is likely to play a lesser role, because the reaction takes place in solution. Depending on the dielectric properties of the solvent, the electrostatic interaction would be, to a 14 large extent, screened out. As the dispersion interaction can also be expected to be weakened,77,78 the binding of the fragments in solution phase would likely be mostly due to orbital interactions.

The stabilizing interactions are always counteracted by Pauli repulsion, which increases in strength as the complex become more tightly bound. Effectively, it is the difference between the Pauli repulsion energy and the sum of the stabilizing interaction energies that determines the bond strength. Because these individual components are large in energy compared to the bond strength, relatively small deviations in any of the components result in significant changes in the bond energy. The dissociation energy also includes the preparation energy, i.e. the energy required to deform the free fragment geometry into the bound geometry. For the compounds under study, this contribution does not vary systematically and is below 20 kcal mol-1 in family 2, and below 10 kcal mol-1 in families 1 and 3.

The deformation densities that characterize the highest orbital-interaction energy contribution for 1a (-30.1 kcal mol-1, Figure 3) show depletion of electron density from Pd d-orbitals, the Pd-C bond, and the π-system on the ligand, concomitant with increase of electron density in the region between Cu and the bhq carbon. For all of the members of family 1, this pattern of density shift corresponds mainly to the interaction between the LUMO on the Cu-fragment (largely Cu 4s in character) and the Pd 4dz2 (HOMO, except for 1h and 1i) on the Pd-fragment. In addition, this deformation density can be assigned to a withdrawal of electron density from Pd 4d and 5s orbitals, the Pd-C σ-bond, and the bhq π-system. The second largest contribution for 1a (-9.4 kcal mol-1) corresponds mainly to loss of electron density from the Pd 4d and 5s orbitals concomitant with an increase in density in a Cu 4p orbital.

The strongest orbital interaction for 2a (-17.6 kcal mol-1) also corresponds to donation from the HOMO of the Pd-fragment to the LUMO of the Zn-fragment. As visible from the deformation density, this interaction builds up electron density between the metals and thus largely characterizes the intermetallic attraction. It is thus evident that the HOMO-LUMO interaction between the d8 and d10 metal fragments has a strong energetic effect on the metallophilic interaction energy. From an application perspective, this means that either the HOMO or LUMO energies can be potential targets for manipulating the binding energy.

Having noted the relevance of HOMO-LUMO interactions in our systems, it is interesting to examine the high-lying occupied orbitals of the Pd-fragment. The three highest occupied Kohn-

Sham orbitals (HOMO-2, HOMO-1, HOMO) on the Pd-fragment are depicted in Figure 5. The H- substituted Pd-fragment orbitals are characteristic for most compounds, with the exception of NH2- and NMe2-substituted fragment orbitals, for which NH2-substituted compound is a characteristic representative. Inspecting the HOMO of the H-substituted fragment reveals that the donor orbital is indeed largely made up of the Pd 4dz2, as expected by simple crystal field theory considerations, and as proposed by Moret.4 However, it is further visible that specific substituents change the character of the HOMO, even effecting a different ordering of the highest occupied orbitals in the cases of the NH2- and NMe2-substituted compounds. For these complexes, the energies of the π- symmetric d orbitals (dxz and dyz) are higher than that of the dz2 orbital, due to a stronger interaction with the amine substituents in the 1,4 positions. In other words, the dz2 orbital is less affected by the electron-donating character of the amine substituents. This is because the dz2 orbital has σ- symmetry relative to the square planar coordination plane, but the amine substituents are π-donors and directly interact only with the π-symmetric d orbitals. The twisting out from the square planar geometry of the current complexes reduces the extent of this symmetry constraint, but does not 10 nullify it. Since the interaction with the d metal occurs mainly with the dz2 orbital, this results in the actual binding strength being lower than would be predicted by the Hammett σ constant, which is a descriptor of the overall electronic nature of the substituent. This also explains why these two complexes are outliers in the correlation plots of dissociation energies and substituent constants. The disparate electronic character of amines can also be deduced from the respective Swain- Lupton parameters and the resulting correlations, as is demonstrated and discussed in the Supporting Information.

Subst. HOMO HOMO-1 HOMO-2

(1a)

NH2

(1h)

Figure 5. Examples of the highest occupied Kohn-Sham orbitals of the Pd-fragments in their respective complex-bound geometry from ZORA-PBE-D3(BJ)/QZ4P//M06L-D3/def2-TZVP(ECP) calculations. Isosurface value is 0.07. Carbon-bound hydrogens not displayed for clarity.

Comparing the respective magnitudes of orbital and dispersion interactions in metallophilic attraction is most appropriate for compound family 1, which does not display strong ligand-ligand interactions (unlike the π-systems in families 2 and 3). For these compounds, the total dispersion interaction lies between 7 – 9 kcal mol-1. However, it is important to consider that this value describes the sum of dispersion interactions in the complex, of which the metal-metal interaction is only one component. In other words, the metal-metal dispersion interaction is necessarily smaller than 7 – 9 kcal mol-1.79 From our previous analysis of the individual contributions to the orbital interaction, it can be observed that the total metal-metal orbital interaction is a composite of the second highest contribution (e.g. -9.4 kcal mol-1 for 1a) and a portion of the highest -1 contribution (e.g., -30.1 kcal mol for 1a). Thus, we conclude that |ΔEdisp| < |ΔEorb| for the intermetallic interactions. We believe this result to be true despite two issues: a) the evident tendency of DFT to overbind the fragments, which may indicate overestimation of orbital interactions, and b) the dependence of the dispersion interaction energy on its definition in the method used.

The relative importance of dispersion and Lewis acid-base interaction can be further deduced from the apparently opposite substituent effect in families 2 and 3. Our results show that placing electron-donating groups on the Pd ligands strengthens the binding, whereas placing them on the Zn ligands weakens it. This observation is consistent with donor-acceptor type interactions being the controlling factor of the binding, where Zn is the Lewis acid and Pd is the Lewis base. In other words, if the metallophilic interaction is sensitive mainly, let alone exclusively, to changes in dispersion forces, any electron-donating substituent would be expected to increase the binding energy, regardless of the placement of the substituent. It is useful to keep in mind that this does not necessarily mean that the dispersion interaction is weaker in magnitude, only that it is not

17 sensitive to substituent effects. We note that this analysis is based on results obtained with the Minnesota functionals, which inherently include middle-range correlation effects; the D3 scheme only corrects for long-range behaviour.80 Thus, the potential problem of the D3 dispersion correction not accounting for changes in electron density is circumvented. Consequently, the geometries optimized with the M06L functional and the energies calculated with the M06 functional should, in principle, properly reflect the interplay between dispersive and orbital interactions.

It is interesting to note that the binding of a d10 metal (in our case, Cu(I) or Zn(II)) to the Pd(II) complex is comparable to the binding of a proton – the acceptor orbital of a d10 metal has strong s-orbital character and thus acts as an electrophile with little orientation preference. A similar isolobal analogy81,82 between a proton and a gold phosphine was first recognized by Lauher and Wald in 1981,83 and has attracted considerable attention since.84 Visual comparison of the LUMO of the Au(I) analogue of the Cu-fragment with the LUMO of the Cu-fragment and of the Zn- fragment (Figure 6) suggests that this isolobal analogy should also be valid in our systems. While the analogy between gold and hydrogen has been employed mainly to study hydrides by replacing the hydrogen with gold, we envision that hydrides could be interesting systems for gaining a deeper insight into our complexes. Namely, Pd(II) and Pt(II) complexes have previously been investigated with regards to the preferred site for protonation in the protodemetalation reaction, as the microscopic reverse of C-H activation,85–90 which, by the isolobal analogy, may illuminate some aspects of the d8-d10 complexes. The protonation can occur on either the metal or the metal-carbon bond, in principle. In his review of platinum hydrides, Puddephatt emphasizes that the Pt-Me σ- bond is close in energy to the Pt 5d orbitals, and the site of protonation thus depends on the ancillary ligands that modulate the orbital energies.91 Likewise, the electronic structures of pincer ligands have been shown to influence the outcome of the reaction of the Pt(II) center with alkyl halides – the products of which bear structural similarity to the compounds in Family 1.92 A similar situation exists for Pd(bhq)2 in our systems, with the 4dz2 orbital, the Pd-C σ-bond, and the 4dxz and 4dyz orbitals. Namely, π-donating substituents on the bhq ligands raise the energy of 4dxz and

4dyz orbitals (demonstrated in Figure 5), and σ-donating substituents raise the energy of the Pd-C

σ-bond and 4dz2 orbital. The particular substitution on the bhq ligand can, therefore, determine which orbital on the Pd(bhq)2 complex becomes the HOMO. It is thus possible that the investigation of the d8-d10 interaction in this type of compound can benefit from studies of

18 protonation of d8 complexes. In this extreme case, the proton being an electrophile with (formally) no electrons, the dispersion interaction would effectively be zero, allowing one to examine electrostatic and orbital contributions cleanly.

Au-analogue Cu-fragment in 1a Zn-fragment in 2a

Figure 6. Examples of the lowest unoccupied Kohn-Sham orbitals of d10 metal fragments in the respective complex-bound geometries from ZORA-PBE-D3(BJ)/QZ4P//M06L-D3/def2-TZVP(ECP) calculations. Isosurface value is 0.07.

5. Conclusion

We report on a comprehensive computational investigation aimed at improving our understanding of the nature of the metallophilic interaction between d8 and d10 metals. The target compounds chosen for this study consist of Pd(II) as the d8 metal and either Cu(I) or Zn(II) as the d10 component. Two of these compounds have been experimentally synthesized and characterized16,17 and their structures and thermochemical properties (binding energy) were used to benchmark the computational models, revealing a large numerical discrepancy between the computed and the experimentally obtained binding energy. Nevertheless, our investigation, which utilized various methods for the analysis of the nature of the interaction, has uncovered trends and qualitative comparisons that provide chemically relevant insight.

The results indicate that dispersion plays a lesser role in modulating the binding of the d8 and d10 metal fragments, compared to electrostatic and orbital interactions. This is most clearly demonstrated by the results of the ETS-NOCV analysis, which give relatively low and fixed dispersion interaction energies for most compounds, while the electrostatic and orbital interactions (Figure 2) vary between compounds. The plots of substituent effects on the dissociation energy corroborate this result by displaying opposite trends, depending on the placement of the

19 substituents on either the d8 or the d10 component (Figure 1). The picture that emerges from ETS- NOCV demonstrates that the strongest interaction is with the Pd-fragment HOMO that can be 2 visually identified as the Pd 4dz2 and C sp orbitals. Perturbative NBO analysis also shows that the 10 d electrophile has the strongest interaction with the Pd 4dz2 as well as Pd-C σ-bonds (discussed in the Supporting Information).

In light of these conclusions, we propose that modulation of the interaction energy in the type of d8-d10 complexes studied in this work can be achieved by altering the electrostatic and orbital interactions. The former is responsible for the attraction between the ligands and the metals, as well as for the repulsion between the metals; the latter – referring specifically to the energy of the 10 Pd 4dz2 orbital or the energy of the d metal LUMO – directly influences the metallophilic attraction energy. Extending this knowledge to tuning the transmetalation energy barriers Sonogashira and Negishi coupling reactions requires accounting for solvent effects, which attenuate the electrostatic and dispersion interaction significantly and, consequently, render the orbital interaction as the de facto handle for controlling the transition state energy.

Associated content

Supporting Information

Computational benchmarking results; additional substituent-effect data and discussion; multi- reference character investigation; AIM analysis; NCI analysis, bond order analysis; NBO analysis; ETS-NOCV data; electronic and zero-point energies of all studied compounds (PDF)

Cartesian coordinates of all optimized structures studied (XYZ)

Author information

Corresponding Author [email protected]

ORCID

Eno Paenurk: 0000-0002-6921-757X

Renana Gershoni-Poranne: 0000-0002-2233-6854

Peter Chen: 0000-0002-9280-4369

Notes

The authors declare no competing financial interests.

Acknowledgments

We thank Chen group members Robert Pollice, for help with computations and for constructive discussions, and Marek Bot, for assistance with the ETS-NOCV method. E.P. acknowledges the Archimedes Foundation for financial support. R.G.P. acknowledges a Vatat postdoctoral fellowship. The work was supported financially by the ETH Zürich, the Schweizerischen Nationalfonds, and the Deutsche Forschungsgemeinschaft (SPP1807).

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