Keywords:

 Enthalpies of amino-demethoxylation of Fischer carbenes measured in PhCl are mostly metal independent  ITC experiments carried out in chlorobenzene give reaction enthalpies consistent with static DFT-D calculations that assume implicit solvation

Table of Content

The thermochemistry of the aminolysis of a series of Cr-, Mo-, and W-Fischer carbenes was determined and confronted to static DFT-D computations.

Introduction

Group VI Fischer type carbene complexes of transition metals [1] bear the general structural formula (CO) 5 M=C(X)R wherein the carbene (alkylidene) ligand is connected to a low-valent transition metal centre. The nature of the metal-carbene bond is generally depicted as σdonating/π-accepting. [START_REF] Dötz | Transition Metal Carbene Complexes[END_REF][START_REF] Wang | [END_REF][4][5] The group X is usually an electron donating group having a stabilizing effect towards the electron deficient carbene carbon atom mostly by mesomeric conjugation of an electron lone pair with the vacant  orbital located at the carbenic carbon.

The R group can be any saturated or unsaturated organic group. In typical Fischer carbene complexes the low valent metal centre is stabilized by π accepting ligands such as carbonyls [1] , which generally provide to the carbene ligand a marked electrophilic character, in complete contrast with Schrock type alkylidenes [6][7][8] that display a marked nucleophilicity.

Fischer carbenes possess a few potential reactive sites that directly stem from the electrophilic character of the carbenic carbon. [9][10][11][12][13][14][15] As a consequence of possessing versatile chemical properties, accompanied with the adjustable electronic characteristics of the substituents (X, R) on the carbene carbon atom, Fischer carbenes were found to be very important precursors in both organic and inorganic synthesis [16][START_REF] Wulff | Comprehensive Organic Synthesis[END_REF][START_REF] Wulff | Comprehensive Organometallic Chemistry II[END_REF][START_REF] De Meijere | [END_REF][20][21][22][23][24][25][26][27][28][29] as well as in the synthesis of biological active compounds [30][31][32][33][34].

Among such reactions the aminolysis reaction [35][36] of the Fischer carbenes has been outlined by Dötz et al. [37] as an important step in the synthesis of biologically relevant gelating molecules; its mechanism [38][39][40][41] and kinetics [13,38,[42][43][44] has long been established as a two-step process of partial second order in amine quite similar to the mechanism of the reaction of carboxylic esters with amines as it implies the nucleophilic attack of the amine to carbene carbon atom with the transient formation of a metal ylide, the subsequent transfer of proton from the amine to the methoxy group with the mediation of an exogenous Lewis base (for instance the amine, the solvent or the cosolvent) followed by the departure of the methanol giving the final aminocarbene. Supposedly, the rate and the reversibility of this step-wise reaction is determined by the nucleophilicity (or pK a values) of the amine in question. Intriguingly, although the mechanism of this reaction has been intensively investigated [29,[45][46][47][48] both experimentally and theoretically alongside other structure-reactivity relationship [49][50][51][52][53][54][55][56][57][58][59] evaluations of Fischer carbenes, little has been reported [48] about the actual thermochemistry of any transformation involving Fischer-type carbenes.

In our endeavour to establish a reference dataset of thermochemical data of simple organometallic reactions, we now disclose the results of the study of the amination of prototypical Fischer methoxy-carbenes (2a-c, see Scheme 1) by a set of amines (3a-c, see Scheme 1) by isothermal titration calorimetry (ITC). Since the reliability of the isothermal titration calorimetry in acquiring valuable thermochemical data has been already confirmed [60][61][62], the thermochemistry of the aminolysis reaction of Fischer carbene complexes [12]

Experimental section

General.

All used compounds were stored and handled in a dry argon-filled glove box or in Schlenk tubes connected to a standard vacuum/argon line. Chlorobenzene was purchased from Sigma Aldrich and distilled over calcium hydride and degassed prior to use. Fischer carbene complexes (2a-c) were prepared using a modified literature procedure. [1] Starting hexacarbonylmetal (Cr, W, Mo) complexes (1a-c) were purchased from Sigma Aldrich, stored into a fridge and used as received. Phenyl-lithium (PhLi) and trimethyloxonium tetrafluoroborate ((MeO) 3 BF 4 ) were purchased from Sigma Aldrich, stored into a fridge and used as received. Amines (3a-c) were purchased from Sigma Aldrich and used as received after checking their purity by NMR. All used solvents in the synthesis and reaction tests (CH 2 Cl 2 , Et 2 O, pentane, hexane) were purchased from Sigma Aldrich and distilled over an appropriate drying agent prior to use. Deuterated chloroform was purchased from Sigma Aldrich and dried through neutral alumina prior to use. Analytical characterizations of the known products were done by NMR and IR spectroscopies. All 1D NMR measurements ( 1 H (300, 400, 500, and 600 MHz) and 13 C (75 and 126 MHz), were performed on Bruker DPX 300 and 400, Avance I 500, and Avance III 600 spectrometers with chloroform-d 1 solutions. NMR spectra were recorded at 25°C and referenced to the residual proton and carbon signals of the deuterated solvent ( 1 H, 13 C). 1 H and 13 C signals are reported relative to SiMe 4 (TMS). Chemical shifts δ and coupling constants are expressed in parts per million (ppm) and hertz (Hz), respectively: multiplicity: s = singlet, m = multiplet.

Relevant NMR spectra are given throughout the main text or in Supplementary Information.

Infra-red spectra of powder amorphous samples were recorded on an ATR spectrometer provided by Bruker optics and analyzed with OPUS software. Relevant IR spectra are given in Supplementary Information.

Isothermal Titration Calorimetry.

Isothermal titration calorimetry (ITC) experiments were carried out with a Waters-SAS nano-ITC device [63] (TA Instruments ®) equipped with two stainless steel Hastelloy cells of 1 mL volume each). Auto-equilibration of the ITC was performed before every experiment to reach an acceptable baseline. The solutions of the reactants (2a-c and 3a-c, see Scheme 1) were prepared by dissolving a mass of substrate in pure, freshly distilled and degassed chlorobenzene. ITC experiments were performed using sequential injection at 25⁰ C with a moderate stirring rate (150-200 rpm) in the presence of an excess of amine. The solution of amine (3a-c) was placed in the ITC sample cell while the solution of the Fischer carbene complex (2a-c) was place in the servo-controlled syringe (100 µL). The reference counter-cell (1.0 mL) was entirely filled with pure PhCl. The concentration of the Fischer carbene complex (2a-c) in pure PhCl was 16-19 mmol/L, while the concentrations of the (3a-c) solutions of amine spanned around 30 mmol/L to 130 mmol/L. The content of the syringe was injected into the sample cell through 10 equivalent injections (6.97 µL per injection) while time delay between two consecutive injections was in the range of 1500 to 3000s, depending on the nature of the amine. For each studied system at least three experiments were performed under the same conditions for the determination of enthalpies of reaction. For other determinations of reaction kinetic parameters the concentration of amines was modified. The heat of dilution of Fischer carbene complexes in neat PhCl was systematically determined under conditions identical to those of the main experiments. Afterwards, the obtained heat of blank experiments was subtracted from all the corresponding titration curves. The enthalpy of reaction (Δ r H) of the considered systems 2a-c/3a-c was obtained by summing up the heat released upon first three injections against a molar content introduced during those three injections. Resulting Δ r H values represent an average value of three corresponding experiments. This methodology of ITC measurements in presence of one of the reactants in excess and the subsequent treatment of the ITC data does not allow the extraction of reaction free energies (Δ r G) and entropies (Δ r S), whereas reaction kinetics parameters may be determined.

Although Hagen et al. reported that the obtained rate of the transformation is not the exact rate, but the product of the exact rate with a constant inherent to the ITC device, to the type and conditions of the experiment, the information contained in the ITC measure of heat flow is exploitable to estimate the initial reaction rate and initial rate constant. [64] In the present work we focussed on the determination of initial rate constants and of partial orders in reactants. The method is based on well-known "flooding method" consisting of carrying out reactions in the presence of a large excess in one of the reactants to make the reaction kinetics directly dependent in the limiting reactant. This situation can be described in the following [START_REF] Espenson | Chemical Kinetics and Reaction Mechanisms; McGraw-Hill series in advanced chemistry[END_REF]:

Imagining a fictitious reaction:

(equation 1), its reaction rate in stoichiometric condition of the reactants can be expressed as: Therefore, all the ITC experiments dealing with the determination kinetic parameters were carried out with a large excess of amine in the sample cell. In general, to figure out the initial rate constants and partial reaction order with respect to reactant in excess the following procedure [61] was employed. Integration of equation 3 gives:

. (equation 5). By plotting ln[A] against time and its linear fitting, the initial rate constant k' is obtained.

Consequently, pseudo-first-order kinetics are reachable as well as the partial first-order reaction with respect to the limiting reactant. According to equation 4, by plotting ln[B] against the obtained k' values of various starting concentrations of reactant B and its linear fitting, partial reaction order with respect to reactant B, i.e. the reactant in excess, is obtained. The same method can be used for the reaction product C as it was for the limiting reactant A. The initial rate constant derived from the limiting reactant herein is denoted by k obs while the initial rate constant derived from the reaction product by k. The difference between their values is due to the fact that k includes concentration contributions of both reactants. As mentioned at the beginning of this section, ITC experiments provide the heat flow that is the heat change per time unit, which can be easily transformed into the rate of transformation of the reactants into the product by employing a direct relation between the change of enthalpy (ΔH) [μcal/mol] and the rate v ITC [μM/s] through the change of compensating power (Δp) [μcal/s] and volume of sample cell (V) [L] (see equation 6). The exact concentrations of the reactants are assumed to be known. [START_REF] Wiseman | [END_REF][67] (equation 6)

Then, by plotting the early changes of concentrations of the limiting reactant ([A]) or the product ([C]) after lag time, i.e the response time that is a characteristic of the ITC device, against time (t), the initial rate constants k obs and k, respectively, can be inferred. Subsequently, by plotting the obtained rate constants (k obs and k) against the starting concentration of the reactant in excess ([B 0 ]) the partial reaction order with respect to reactant B can be deduced.

Static DFT-D computational details.

All computations were performed by density functional theory (DFT) using Amsterdam Density Functional package (ADF2013 version). [68][69][70] All geometry optimizations employed the Perdew-Burke-Ernzerhof (PBE) [71][72] GGA functional augmented with Grimme's D3 [73][74] inclusion of mid-to-long range dispersion force with a Becke-Johnson damping (BJ). [74] All computations performed in ADF used the scalar relativistic Zeroth Order Regular Approximation (ZORA) [75][76][77] and were carried out with single polarized triple-ζ (TZP) [78] basis set.

Geometry optimizations by energy gradient minimization were carried out in all cases with an integration grid accuracy spanned 4 -6.5, an energy gradient convergence criterion of 10 -3 au and tight SCF convergence criterion (10 -7 au). Solvation by chlorobenzene was accounted for using the COSMO procedure with Klamt's values of van der Waals radii for atoms, [79] i.e. epsilon -5.62, radius -3.48 Å. All geometry optimizations were confirmed as yielding true energy minima by calculating vibrational modes. Calculations of vibrational modes (analytical second derivative of vibrational frequencies) [80][81][82] were performed at 298.15 K at the same level of theory as the geometry optimizations calculations (i.e. ZORA-GGAPBE-D3(BJ)/TZP level). The vibrational modes were also used for obtaining the thermodynamic parameters of the systems, namely internal energy and entropy, by statistical thermal analysis. Enthalpies and Gibbs free energies of the systems are deduced from the internal energies and entropies. Reaction enthalpies (Δ r H), Gibbs free energies (Δ r G) and entropies (Δ r S) of pair formation are estimated as a difference between corresponding values of the pair and free reactants. Graphical representations of molecular structures were drawn using ADFview v13 implemented in ADF 13 package [68][69][70] or Mercury v3.9. [83] Starting geometries of the reactants (2a-c and 3a-c, see Scheme 1) and the reaction products (4-6a-c, see Scheme 1) were taken from the CSD or built up from the similar structures and optimized as singlet ground states in the chlorobenzene solution (COSMO) phase. In addition, within the study of the mechanism of the aminolysis reaction, the supposed reaction intermediates (see Figure 8) were built up from the previously optimized geometries of the reactants and subsequently optimized as singlet ground states in a chlorobenzene cavity (COSMO).

Reaction Monitoring by 1 H NMR spectroscopy.

The title reactions has already been reported previously. In order to check for their chemical cleanness, i.e. for the absence of any side products revealing interfering processes that may jeopardize the accurate determination of the targeted reaction enthalpies, test reactions were carried out in CDCl 3 without isolating the reaction product and monitored by 1 H NMR spectroscopy.

The tests were run with various reaction times (ranging from 1 hour -5 days) as well as various molar ratios of reactants (up to four equivalents of amine) in order to check the relative length of the amination process and thus evaluate the most optimal conditions to run ITC measures. As all the reaction tests were carried out with the same general procedure, only a general procedure is given herein. A solution of the amine (3a-c, 0.15 mmol) was added by syringe into the solution of the Fischer carbene complex (2a, 2c, 0.15 mmol) in 1 mL of the deuterated chloroform. The resulting mixture was allowed to stir at ambient temperature. After one hour, a second equivalent of the amine was added in the same manner. The reaction mixture was monitored by 1 H NMR spectroscopy. Worthy to note, the 2a/3b system was monitored by 1 H NMR spectra in presence of excess amine 3b (5 equivalents) after 1 day, 2 days and 5 days of the reaction. Into a solution of dry metal carbonyl complex (M(CO) 6 , M=Cr, Mo, W) (4.5 mmol) in 20 mL freshly distilled diethyl-ether, 3 ml of 1.8M solution of phenyl-lithium in diethyl-ether (0.45g, 5.4 mmol) were slowly added by syringe. After 30 minutes of stirring at ambient temperature, solid trimethyloxonium tetrafluoroborate ((MeO) 3 BF 4 ) (0.86 g, 4.5 mmol) was added to the darkcolored reaction solution. The resulting mixture was allowed to stir over night and the solvent was evaporated under reduced pressure. The crude product was subsequently purified chromatographically through silica with 300 mL of pentane and a mixture of 250 mL pentane/100 mL of dichloromethane as the eluents. The product was characterized by 1 H and 13 C NMR spectra as well as by IR spectroscopy (related spectra are given is Supplementary Information, Figures . Yields: 2a = 0.53 g (38%); 2b = 0.59 g (37%); 2c = 0.7 g (35%). NMR: 2a 1 3. Results and discussion.

Verification of chemical selectivity.

Prior to performing ITC experiments, amination reaction monitoring was carried out to estimate whether the reaction of interest could be satisfactorily used with the ITC so as to confirm that no side reaction occurred like suggested by literature. [35][36] Due to the similarities of the series of the investigated Fischer carbene complexes (2a-c, Scheme 1) the reactions of chromium complex (2a) with all the considered amines (3a-c, Scheme 1) were fully checked by 1 H NMR spectroscopy, while the tungsten complex (2c) was monitored only in its reaction with the amine 3b and the molybdenum complex (2b) basically ignored. The reaction tests considered various molar ratios of the reactants and various reaction times followed by a 1 H NMR analysis of the raw medium's composition (see Figure SI 1-3 in the Supporting Information for details).

Noteworthy, under stoichiometric conditions all reactions led to incomplete conversion, the medium containing ca. from 1:2 to 1:6 mixture of the amination reaction product (4a,c, Scheme 1) and the free reactants (see Figure SI 1 and 3). Expectedly, when two equivalents of the amine were used, the conversion of the reactions involving 2a/3a and 2a/3c increases up to almost full conversion and ca. 30% (see Figure SI 1 and 3), respectively, whereas for the 2a/3b reaction [91], even in large excesses of amine, did not produce any reaction product (see Figure SI 2,[4][5]. Quite expectedly the 2a/3a reaction the expected amination reaction product is more efficient than with 2a/3c, most probably due to lower steric strains inflicted by the primary amine 3a. In spite of the low reactivity of 3b with 2a and having in scope the setup of ITC measures using a reasonable time delay between sequential injections of reagent it was found necessary to estimate the influence of the reaction time over conversion for the 2a/3b reaction. The use of a large excess of amine 3b (more than 5 eq) in a reaction with 2a gave no reaction product even after 5 days (see related 1 H NMR spectra given in Figure SI 4-5) at 20 °C. This lack of reactivity of 3b was also noticed when it was opposed to carbene complex 2c.

Thermochemical determinations by ITC.

Following the observation of the rather slow conversion of the alkoxy carbene complexes into the amino products under stoichiometric conditions, ITC measurements were systematically performed with a large excess of amine (3a-c) with respect to the Fischer carbene complex (2ac) to enhance both the reaction rate and conversion with the time constrains of ITC measures. Therefore, to ensure that a proper baseline was recovered after each injection, relatively long time-delays (1500s-3000s) between two consecutive injections were employed. To confirm the chosen conditions as optimal, ITC measurements were done under stoichiometric conditions as well. From the performed ITC experiments, only the raw Δ r H values are derived as thermodynamic parameters of the reaction from heat responses and not from a conventional curve fitting of a series of heat responses, while the initial rate constant and the partial reaction order of amine are obtained as kinetic parameters of the reaction.

Although the studied reaction was exempt of side-reactions, its equilibrium nature was the major issue for ITC measurements. Considering the mechanism of the reaction, the only way to overcome this issue and obtain a satisfactory fast heat response was by employing an excess of amine accompanied with a relatively long time-delay between consecutive injections. For illustration purpose, the ITC thermogram of the reaction of 2a with 3a in stoichiometric condition is given in Figure SI 6, which shows clearly that a standard fitting procedure is not amenable to reach the key thermodynamic parameters. The raw enthalpies of reaction obtained by ITC (raw Δ r H values) of the studied systems (2a-c/3a-c, see Scheme 1) are summarized in Table 1.

Noticeably, in all the systems when the amine is 3b, no heat response ensues at 298.15 K. It suggests that, even though the ITC experiments were performed with a large excess of 3b, its lack of reactivity towards Fischer carbene complexes is not only related to a poor exothemicity but perhaps has to deal with a high barrier of activation in a kinetic determining step (see ITC thermogram depicted in Figure 2 that essentially shows the heat of dilution of the amine). It is worthy to note that the seminal report of Fischer et al. on the reactivity of aniline 3b towards 2a indicated that boiling the reaction mixture for several hours was necessary to produce reasonable amounts of the expected aminocarbene, suggesting that the reaction could hardly succeed at room temperature [91].

Considering the obtained Δ r H values (that are in range from around -15 kcal/mol to -20 kcal/mol) in general, it was concluded that the amination of the Fischer carbenes is energetically quite favorable. From the comparison of the raw Δ r H values of the reaction of amine 3a with the series of the Fischer carbenes 2a-c (around -16 kcal/mol) one may conclude that the nature of the metal centre has no large influence over the enthalpy of the reaction, which remains in all cases within a 5 kcal/mol interval at a central value of -18 kcal/mol. Regarding the raw Δ r H values of the reaction of amine 3c with the same carbenes (ranging from around -18 kcal/mol to -20.5 kcal/mol) the influence of the nature of the metal seems only slightly more pronounced.

However, it seems that the molybdenum carbene complex exhibits the lowest enthalpy values, while the tungsten carbene produces highest Δ r H values. The examples of the ITC thermograms of the investigated systems are shown in Figure 123, while other systems are given in Supplementary Information (see Figure .

Table 1. ITC results obtained from the sequential addition ITC experiments that considered an excess of the amine 3a-c interacting with the Fischer carbene complex 2a-c.

System

Kinetic study

The employed ITC conditions (excess of the amine) allowed determining the initial rate constant and the partial reaction order in amine. However, the only exploitable thermograms were those of the following systems: 2a-c/3a and 2c/3c. Due to its lack of reactivity amine 3b was excluded from kinetic experiments. The results of the kinetic analysis are reported in Table 2 while the corresponding plots are displayed in Figures 45as well as in Figure The obtained initial rate constant (k) values of the systems 2a-c/3a, which span from 6.6*10 -4 s -1 to 6.8*10 -2 s -1 , suggest a moderately swift amination reaction process. It seems that the transformation is roughly ten times slower with the tungstene carbene complex (2c) than with the other metal carbenes. The transformation of system 2c/3c is approximately ten times faster than the transformation of the system 2c/3a. This observation might be correlated to the difference of the pKa values of the used amines (pKa(3a) = 9.34; pKa(3c) ≈ 11). The obtained partial order in amine lies around 2, which is in perfect agreement with the literature [13,38,[42][43][44].

Table 2. Results of the ITC kinetic study obtained from the sequential addition ITC experiments that considered an excess the amines 3a-c interacting with the Fischer carbenes 2a-c. ) where [3a] is the initial concentrations of 3a for the reaction with 2b carried out in ITC calorimeter. The partial reaction order in 3a is 2.18 ± 0.14. right side --Linear fit of the plot of ln(k obs ) values as a function of ln([3a]) starting concentrations for the reaction of 2b with 3a carried out in ITC calorimeter. The partial reaction order with respect to 3a is 2.24 ± 0.12.

System

Static DFT-D calculations.

Theoretical investigations of the amination of the Fischer carbenes were done on the series of the Fischer carbenes (2a-c, see Scheme 1) and various amines (3a-c, see Scheme 1). All the computations were performed at the ZORA-GGAPBE-D3(BJ)/TZP level of theory in chlorobenzene solution (COSMO) phase. Geometry optimizations were done on both reactants (2a-c and 3a-c) and products (4-6.a-c, see Scheme 1) and were confirmed as true minima by performing calculations of vibrational modes. In addition, the calculation of the intermediates of the aminolysis reaction on the systems 2a-c/3b were performed (at the same level of theory).

The derived thermodynamic parameters (Δ r H, Δ r G, Δ r S) of the aminolysis reaction are shown in Table 3. The corresponding optimized geometries are displayed in Figure 6 while the Cartesian coordinates of all related optimized geometries are given in Supplementary Information (see SI, section S.5). Worthy to note, it may be concluded that experimental (see Table 1) and calculated (see Table 3) reaction enthalpy values are in very good accordance. To illustrate this assertion we calculated the energy profile of the reaction of 2a with 3a and 3b assuming in a first approximation that the formation of the intermediary zwitterionic ylide complex could be followed by an intramolecular N-to-O proton transfer leading to the release of MeOH and the aminocarbenes 4a and 4b. Figure 9a displays the model reaction sequence, the energy profile of which is detailed in Figure 9b for the reactions implying both amines 3a and 3b.

In this scenario however, the second order in amine is not evident and the reaction sequence is used essentially to point the main issues pertaining to the actual translation of kinetic information into consistent DFT modelling. Indeed, a second order in amine implies that in the whole process two different molecules of amine intervene at some stage in a determining step.

As drafted here (Figure 9a) this simplified scenario reveals two important features though.

The first one is that the formation of the intermediate ylide requires an activation barrier by ca.

10 kcal/mol higher with amine 3b than with 3a from the reactive complex; the formation of the ylide appears to be an equilibrium rather well balanced between the reactive complex and the ylide with 3a whereas it is unfavourable to the ylide formation with 3b. If one adds the Gibbs energy payload for the formation of the reactive complex of ca. 7 kcal /mol to the activation energy to pass transition state TS1-Bz or Ph, this brings ylide's formation in a challenging position when using 3b, whilst with 3a its formation is still at hand.

The second information is that the intramolecular transfer of proton is even more demanding in term of activation energy with both amines with activation Gibbs energy around 18 kcal/mol, which is inconsistent with experimental observations (Figure 9c depicting transition states TS2-Bz and -Ph). This reveals nonetheless that the proton transfer is crucial to understand the role of a second amine molecule. At this stage it is difficult to state with certainty how this second amine molecule interacts in the proton transfer. At least, its role should be to facilitate proton migration by lowering its activation barrier energy in a demethoxy-amination reaction that already benefits of an overall negative value of reaction Gibbs energy  r G with both bases ( r G = -9 kcal/mol and -19 kcal/mol with 3b and 3a respectively at the COSMO (PhCl) -ZORA-PBED3(BJ)/all electron level). The direct intramolecular proton transfer from the N centre to the O centre of the OMe moiety by a tunnelling effect seems unlikely according to our findings since it was found that amine's concentration was influential over the rate of the reaction. Therefore two options are possible, that are namely the extra-molecular transfer of ylide's N-borne acidic proton to the bulk solution of amine and its redelivery to the OMe moiety, and/or the intramolecular transfer by means of a cyclic transition state in which the second amine would play the role of a H + transfer relay. Those hypotheses have not been further investigated in this study. They would deserve in our view a complete evaluation that falls out of the scope of the present report.

Conclusion.

The amination of the Fischer carbenes 2a-c (Scheme 1) induced by the series of amine 3a-c (Scheme 1) was investigated experimentally using the reaction tests and Isothermal Titration Calorimetry (ITC) as well as theoretically with the help of static Density Functional Theory with Grimme's dispersion corrected (DFT-D3) functionals. ITC measurements, performed with a large excess of amine, allowed the estimation of reaction enthalpies, initial rate constants and partial reaction order in amine. The thermodynamic parameters of the reaction (Δ r H, Δ r G, Δ r S) as well as the thermodynamic parameters (ΔH, ΔG) of the particular intermediates (see Figure 8) of the amination process were also computed. The ITC determination of reaction enthalpy Δ r H gave values larger than -15 kcal/mol, (Table 1), suggesting an energetically favourable amination process for systems 2a-c/3a and 2a-c/3b, while systems 2a-c/3b were found to be rather inert even when a large excess of the amine 3b was used. In addition, no clear dependence of the reaction enthalpy on the nature of the metal centre could be established. The calculated reaction enthalpies (ranging from around -5.5

kcal/mol up to -20 kcal/mol), similarly to the experimental ones, show that in all the exothermic systems the overall energetics is favourable, with calculated Gibbs free energies (ranged from around -4.5 kcal/mol up to -20 kcal/mol) suggesting spontaneous processes for all the systems.

The experimental and the theoretical reaction enthalpy values are in excellent accordance.

Computations also revealed that the reaction of Fischer carbenes with aniline (3b) is not thermodynamically spontaneous nor favoured at 25⁰ C, as both the enthalpy and the Gibbs free energy of the first reaction step consisting of the formation of the first ylide intermediate are largely positive (ΔH value larger than 2.5 kcal/mol; ΔG value larger than 20 kcal/mol) as well as the Gibbs free energy of the second step (proton transfer and potential release of methanol) (ΔG valued around 8 kcal/mol).

5.

  Scheme 1. Schematic representation of the investigated reactions within the study of amination of the Fischer carbenes 2a-c by amines 3a-c.

(equation 2

 2 ), while if the reaction is carried out in a large excess of reactant B, the rate becomes simplified:

2. 5 .

 5 Scheme 2. Synthesis of Fischer carbenes 2a-c from hexacarbonylmetal complexes of Cr, W, and Mo, i.e 1a-c.

Figure 1 .

 1 Figure 1. left side -ITC thermogram of the reaction between 3a (sample call, c=94.5 mM) and 2a (syringe, c=16.3 mM) in chlorobenzene. The titration was performed at 25⁰ C through 10 sequential additions (of 7 µL each). Time between two consecutive injections was 1500 s. Heat released is expressed in µJ/s versus time in s. right side -ITC integrated heat peaks of the thermogram shown on the left side. Integrated heats are expressed in µcal versus molar ratio of the reactants.

Figure 2 .

 2 Figure 2. left side -ITC thermogram of the reaction between 3b (sample call, c=570.9 mM) and 2c (syringe, c=16.0 mM) in chlorobenzene. The titration was performed at 25⁰ C through 10 sequential additions (of 7 µL each). Time between two consecutive injections was 3000 s. Heat released is expressed in µJ/s versus time in s. right side -ITC integrated heat peaks of the thermogram shown on the left side. Integrated heats are expressed in µcal versus molar ratio of the reactants.

Figure 3 .

 3 Figure 3. left side -ITC thermogram of the reaction between 3c (sample call, c=109.1 mM) and 2c (syringe, c=15.7 mM) in chlorobenzene. The titration was performed at 25⁰ C through 10 sequential additions (of 7 µL each). Time between two consecutive injections was 2000 s. Heat released is expressed in µJ/s versus time in s. right side -ITC integrated heat peaks of the thermogram shown on the left side. Integrated heats are expressed in µcal versus molar ratio of the reactants.

Figure 4 .

 4 Figure 4. left side -Linear fit of the plot of the ITC Rate as a function of time for the reaction of 3a (sample call, c=50.7 mM) with 2b (syringe, c=17.0 mM) carried out in ITC calorimeter. ITC Rate is expressed in µM/s and time in s. Obtained k = 1.5*10 -2 ± 1*10 -3 s -1 as the result of the fitting. right side -Linear fit of the plot of logarithm of 2b concentration as a function of time for the same reaction. Obtained k obs = 1.2*10 -4 ± 9*10 -6 s -1 as the result of the fitting.

Figure 5 .

 5 Figure 5. left side -Linear fit of the plot of ln(k) values as a function of ln([3a]) where [3a] is the initial concentrations of 3a for the reaction with 2b carried out in ITC calorimeter. The partial reaction order in 3a is 2.18 ± 0.14. right side --Linear fit of the plot of ln(k obs ) values as a function of ln([3a]) starting concentrations for the reaction of 2b with 3a carried out in ITC calorimeter. The partial reaction order with respect to 3a is 2.24 ± 0.12.

Figure 6 .

 6 Figure 6. Graphic representations of gas phase singlet ground state optimized geometries of the investigated systems at ZORA-GGAPBE-D3-BJ/TZP level of theory in chlorobenzene solution (COSMO) phase. N: bluish; O: red; Cr: violet; Mo: greenish; W: blue; C: grey; H: white. In order to rationalize the experimental difficulties occurring with systems 2a-c/3b, a round of calculations was performed on the supposed intermediates forming in the course of the amination demethoxylation process. The calculation embraced systems 2a/3a-c as well as systems 2b-c/3b. The resulting values of thermodynamic parameters (ΔH and ΔG) of the intermediaries relative to the reactants are shown graphically in Figure 7 and Figure SI 17, while the graphic representations of the considered intermediates are depicted in Figure 8. The results clearly show the differences between amines. Namely, the payload of the nucleophilic attack of amines 3a and 3c giving rise to intermediary ylide T1 is energetically negligible (ΔH values are 0.2 kcal/mol and -1.5 kcal/mol, respectively) while the attack of the amine 3b is energetically quite unfavorable (ΔH values are +9.4 kcal/mol). The calculated Gibbs free energy values of the first step leading to intermediary ylide T1 is thermodynamically unfavorable in all cases and particularly with amine 3b for which the endoergonicity climbs up to G= +24

Figure 7 .

 7 Figure 7. Graphic representation of the ΔH and ΔG values (given as energy expressed in kcal/mol) for particular states (given through reaction coordinate, see also Figure8) within the course of the amination process of the Fischer carbene complex 2a induced by various amines 3a-c. Calculations were performed at the ZORA-GGAPBE-D3-BJ/TZP level of theory assuming chlorobenzene solvation (COSMO) at 298.15K and 1 atm.

Figure 8 .

 8 Figure 8. Schematic representation of the considered particular intermediates of the amination process of Fischer carbenes 2a-c by various amines 3a-c (see also Figure 7).

  H NMR (300 MHz, chloroform-d, δ, ppm) 7.48 -7.34 (m, 3H), 7.34 -7.20 (m, 2H), 4.70 (s, 3H). 13 C NMR (126 MHz, chloroform-d, δ, ppm) 351.0, 224.1, 216.2, 153.7, 130.4, 128.2, 123.1, 67.2. 2b 1 H NMR (400 MHz, chloroform-d, δ, ppm) 7.61 -7.51 (m, 2H), 7.50 -7.38 (m, 3H), 4.87 (s, 3H). 2c 1 H NMR (500 MHz, chloroform-d, δ, ppm) 7.59 -7.51 (m, 2H), 7.50 -7.39 (m, 3H), 4.77 (s, 3H). 13 C NMR (126 MHz, chloroform-d, δ, ppm) 203.6, 197.3, 155.2, 131.8, 128.1, 126.4, 70.2. IR (solid phasepowder, ν, cm -1 ): 2a2061, 1985, 1959, 1888, 1438, 1428, 1247, 1209, 1140, 1126. 2b 2068, 1988, 1962, 1887, 1438, 1428, 1250, 1222, 1141, 1129. 2c 2068, 1982, 1956, 1881, 1437, 1426, 1246, 1221, 1139, 1127.

Table 3 .

 3 Results of static DFT-D calculations. The calculations were performed at ZORA-GGAPBE-D3-BJ/TZP level of theory in chlorobenzene solution (COSMO) phase.

	System	Δ r H [kcal/mol]	Δ r G [kcal/mol]	Δ r S [cal/Kmol]
	2a/3a	-16.2	-16.8	2.0
	2a/3b	-6.7	-7.0	1.1
	2a/3c	-19.8	-19.7	-0.3
	2b/3a	-17.0	-15.5	-4.8
	2b/3b	-6.1	-4.4	-5.8
	2b/3c	-20.6	-18.6	-6.7
	2c/3a	-16.1	-16.6	1.6
	2c/3b	-5.5	-5.7	0.9
	2c/3c	-20.1	-20.1	-0.2
	Regarding calculated Gibbs free energies of reaction (Δ r G values ranged ca. -4 kcal/mol -20
	kcal/mol) Table 3 shows that even though all considered transformations are spontaneous in
	chlorobenzene solution, all reactions involving 3b have the lowest absolute value of Δ r G. All
	considered systems, i.e. systems 2a-c/3a, 2a-c/3b and 2a-c/3c, display quite similar reaction
	enthalpies. As opposed to the obtained ITC trends (Δ r H values of the 2b/3a-c are lowest among
	all related systems), predicted theoretical Δ r H values suggest the highest exothermicity in the
	case of Fischer carbene 2b. Interestingly, the systems, for which experimental ITC values were
	not obtained (i.e. system that include the amine 3b), theoretically have lowest reaction
	enthalpies (in range from -5.5 to -6.7 kcal/mol) as well Gibbs free energies (in range from -4.4 to
	-7.0 kcal/mol) with decreasing values from chromium (2a) to tungsten (2c) carbene complex.

Acknowledgements.

The CNRS and the University of Strasbourg are thanked for their support. M.M. thanks Campus France and the Fund for young talents -Dositeja for financial support.

Funding: This work was supported by the Agence Nationale de la Recherche through the ANR-DFG grant COCOORDCHEM. This work was supported by the Serbian Ministry of Education, Science and Technological Development (Grant 172065 to SDZ).

These two facts related to the systems 2a-c/3b, i.e. relatively high energy barrier of the first reaction step (herein T1) accompanied with an unfavorable second step (herein T2) can rationally explain the experimental difficulties in the determination of thermodynamic reaction parameters by ITC measurements. In addition, the results of the first step of the systems 2a/3a (ΔH = 0.2 kcal/mol) and 2a/3c (ΔH = -1.5 kcal/mol) might explain, in general, the difference in the rate (obtained by kinetic analysis of the ITC results) of the reaction of amines 3a and 3c with the herein investigated Fischer carbenes (see section ITC experimentskinetic study).


Yann Cornaton

Jean-Pierre Djukic

A Noncovalent Interaction Insight onto the Concerted Metallation Deprotonation Mechanism

The CMD/AMLA mechanisms of cyclopalladation and the parent fictitious but challenging cyclonickelation of N,Ndimethylbenzylamine have been investigated by joint DFT-D and DLPNO-CCSD(T) methods assisted by QTAIM-based nocovalent interaction plots (NCI plots) and interacting quantum atoms (IQA ) analyses, and the local energy decomposition (LED) procedure. Bader charges, NCI plots, IQA and the LED analyses clearly suggest that coulombic interactions play an important role and somewhat govern the whole process that is sensitive to the charge borne by the metal centre. It is found that replacement of acetate by acetamidate used as a ligand and a base significantly lowers the barrier to the formation of the key agostic intermediate. The latter shows a peculiar polarization by its immediate ligand environment where a significant electrostatic CH…O interaction with the neighboring carboxylato ligand competes with the strong propensity of the latter to bind the metal center, which is stronger in the agostic intermediate when the carboxylato ligand is the acetate and when the metal is Ni. It is also shown that the hereby idealized cyclonickelation is disfavored as compared to cyclopalladation owing to enhanced electrostatic repulsion in almost all stages of the CMD mechanism.

Introduction

C-H bond activation and functionalization represent challenging goals in modern homogeneous catalysis. 1,2 The Concerted Metallation Deprotonation (CMD)° mechanism, often assimilated to the Ambiphilic Metal Ligand Activation (AMLA) mechanism [3][4][5] is a flexible way to achieve carbometallation that has been particularly developed in Pd(II)-based catalysis and is being used extensively nowadays to promote a host of sophisticated functionalizations of organic compounds. 1,6 If the intimate nature of the agostic C-H…M bond remains a matter of interest and debate, it has long been stressed that it should not be considered strictly as a 3center/2-electron interaction, neither as a non-covalent interaction. 7,[START_REF] Brookhart | Carbon-Hydrogen-Transition Metal Bonds[END_REF] The concept of "syndetic donation" has been put forward by Nielson, Harrison and co-workers [START_REF] Sajjad | [END_REF]10 to characterize the weak donor-acceptor (charge transfer) "covalent" interactions established between the σ-C-H bonding orbital and Pd vacant d orbital with electron density donation from the neighbouring π-system, with variable back donation occurring from the Pd centre to the σ* orbital of the C-H bond in the agostic intermediate. [START_REF] Weinhold | Encyclopedia of Computational Chemistry[END_REF] A recent DLPNO-CCSD(T) [START_REF] Riplinger | [END_REF] -based investigation by Neese and co-workers 13 outlined the role played by dispersion 14 in the stabilization of known agostic C-H…metal complexes, thus opening a new perspective for the investigation of key agostic intermediates in the CMD/AMLA mechanism that outranks the orbitalbased 15 Dewar 16 -Chatt-Duncanson 17 analysis of bond making/unmaking. 13 One missing factor in most studies of the CMD mechanism is indeed the role of non-covalent interactions. In a complex molecular system were a C-H bond is engaged in agostic interactions of weak covalent character with a metal centre it is tempting to consider the coordination environment of the metal consisting of auxiliary bases and ligands as a local multipole, 18 which might also contribute to the chemical activation of the C-H bond as external electric fields do. 19 This conjecture finds its justification in recent theoretical investigations of electric field induced C-H bond activation in CH 4 in the gas phase. 20 According to these studies, whether C-H bond activation and cleavage may occur following an homolytic or heterolytic regime depends on the nature, orientation and strength of the applied electric field and on how this field will stabilize any of the resonance structures 21,22 associated with the C-H bond. [START_REF] Brookhart | Carbon-Hydrogen-Transition Metal Bonds[END_REF]23 We recently qualitatively demonstrated the dual nature of the agostic interactions in intermediates arising in the stereoselective C-H bond palladation 24 of substituted cyclopropyls by using QTAIM [START_REF] Bader | Atoms in Molecules: A Quantum Theory[END_REF] -based Noncovalent Interaction (NCI) plots [START_REF] Contreras-Garcia | [END_REF] and the DFT-based Extended Transition State -Natural Orbitals for Chemical Valence 27 (ETS-NOCV) orbital interaction decomposition framework.

In this study, we address the CMD/AMLA mechanism of cyclopalladation of N,N-dimethylbenzylamine 28 from the point of view of non-covalent interactions, by resorting not only to a standard GGA DFT-D3(BJ) method 29 to compute the associated stationary geometries, to the quantum theory of atoms in molecule [START_REF] Bader | Atoms in Molecules: A Quantum Theory[END_REF] (QTAIM)-based methods such as the Interacting

Please do not adjust margins Quantum Atoms 30, 31, 32 (IQA) to investigate in an interatomic wise chemical bond structure changes, but also to the DLPNO-CCSD(T) method, which is also used in combination with the Local Energy Decomposition analysis method 33 to break down NCI components in a fragment-wise fashion in the key intermediates and transition states. Furthermore, we address the effect of the assisting base by comparing the acetate to acetamidate. 34,35 We also disclose considerations on the fictitious CMD-based cyclonickelation 36,37 to gauge electrostatic interactions.

Results and discussion

The mechanism of C-H bond activation assisted by an ancillary carboxylate or amidate acting as a base is often invoked in the ortho-palladation of aromatics containing an orienting group.

The so-called CMD (or AMLA) mechanism entails three key steps of lower energy payload than the alternative scenario involving an oxidative-addition step of the C-H bond to the metal center. 3,5,38 The first step entails the coordination of the "directing group", here a N,N-dimethylamino group, acting as a ligand giving rise assumably to a so-called "anagostic" intermediate, noted anag (Scheme 1), where the C-H bond to be activated is generally positioned at ca.

Materials and methods.

For convenience, generic names were given to stationary geometries (Scheme 1). To distinguish each chemical system, a code name is used containing as prefix the metal's chemical symbol Pd or Ni and as suffix the base , i.e OAc for acetate and NHAc for acetamidate. For the sake of conciseness all energy profiles have been referenced against the Gibbs energy G of the anag intermediate. All DFT computations have been performed in the gas phase considering exclusively singlet ground and transition states at the generalized gradient approximation (GGA) ZORA-PBE-D3(BJ)/all electron TZP level, which was chosen for the sake of comparison with the recent report of Nielson, Harrison and co-workers. [START_REF] Sajjad | [END_REF] It is worth noting that recent reports by Iron and Janes 39 and Dohm et al. 40 tend to recommend the use of hybrid functionals for a more accurate reproduction of the energetics of reactions, particularly for those involving metal complexes. It is not the purpose of this report to address this issue that deserves a separate study. Finding emerging trends in the role played by non-covalent interactions using differently grounded theoretical frameworks is the main objective of the present study.

Basis set superposition error (BSSE) with the ZORA-PBE-D3(BJ)/all electron triple ζ polarized (TZP) method was previously estimated to represent about less than 3% of the total bonding energy. 41 For safety, a comparison of the interatomic distances in the critical PdOAc-ag intermediate in geometries optimized with the ZORA-compliant TZP and the QZ4P basis sets showed significant distance shortening with the larger basis set only for the C Ar -Pd (∆d (TZP-QZ4P)= -0.044 Å) and O cis -Pd segments (∆d (TZP-QZ4P)=-0.025 Å), the remaining key distances within the reactive site viz. C Ar -H Ar , H Ar -Pd, N-Pd, O cis -H Ar varying by less than 0.01 Å.

For the main objective of this study was exclusively to map out intramolecular NCIs that are relevant to the CMD mechanism, implicit "solvation" was not accounted for here: in real systems, solvents (mostly protic) and excess protonated base may interfere with the C-H bond activation step via a Grotthuss-like mechanism 42 of proton capture/relay. As a consequence the first step of the mechanism that leads to anag is given for information only in the PdOAc system as basically the dissociation of crown shaped Pd 3 (OAc) 6 by the N,N-dimethylbenzylamine ligand and was not computed in all other cases. In the case of Ni, the anag intermediate was assumed to arise from fictitious square-planar singlet state Ni(OAc) 2 or Ni(NHAc) 2 species. It is indeed known that amidates as ligands favour bridging ligation between two metals or terminal binding through the N atom rather than chelation. 44 It is shown below how this property may play a crucial role. So-called Bader charges, [START_REF] Bader | Atoms in Molecules: A Quantum Theory[END_REF] reduced gradient-based NCI plots 26 and Interaction of Quantum Atoms 30 (IQA) analysis are basisset independent methods making use of the computed electron density. The QTAIM-based IQA energy partitioning method developed by Pendas and co-workers 30,31 is a useful tool for investigating interatomic interactions by decomposition into covalent and ionic energy contributions. Based on real-space partitioning of the molecular space, this method, when extended to the Kohn-Sham DFT framework, gives access to a semi-quantitative partitioning of energy contributions of exchange-correlation, and a series of coulombic interaction terms for two-atom interactions within a molecule. The interatomic interaction energy E int AB is the sum of a covalent E covalent AB and an ionic contribution E ionic AB : The version used in this study that is implemented in ADF 45 v2018, does not consider the semi-empirical dispersion contribution arising from Grimme's Becke-Johnson damped correction 46 accounted for by the PBE-D3(BJ) method.

E int AB = E ionic AB + E covalent AB with E ionic AB = E NN AB +E eN AB [ρ]+E Ne AB [ρ]+E eeCl AB [ρ] and E covalent AB = E eeX AB [{ψ i KS }] .
It is nonetheless a useful energy decomposition method for the analysis of multicentre interactions in a multipolar environment (vide infra) where "ionic" and "covalent" contributions are interwoven and delocalized. Here, the IQA analysis is carried out in an atompair wise fashion on a selected group of atoms located in what is designated as the reactive site at TS-ag, ag and TS-CH, that is the group of atoms comprising C Ar , H Ar , the metal (Pd or Ni) and O cis . A wave-function theory-based study has been carried out for these systems using the Domain-based Local Pair Natural Orbital Coupled-Cluster with Single, Double and perturbative Triple excitations [START_REF] Riplinger | [END_REF] (DLPNO-CCSD(T)), starting from the DFToptimized geometries. The DLPNO-CCSD(T) method combines the high accuracy of the coupled-cluster theory, which is often too computationally demanding for a large system, with a low computational cost, similar to DFT. 47 The reduced computational cost arises from the localisation of the orbitals, constructed at the Hartree-Fock level, and the dichotomy with respect to the inter-orbital distance between "strong" (short distance) and "weak" (long distance) pairs, the latter being treated with a second-order perturbation theory as the pair correlation energy decreases very quickly with the inter-orbital distance. To get a deeper understanding of the role of the different contributions to the energy in the reaction, a Local Energy Decomposition 48 (LED) analysis has been performed. The DLPNO-CCSD(T)/LED method 12 is an efficient, accurate and non-perturbative approach for studying non-covalent interactions, where the localized orbitals are assigned to userdefined fragments, allowing to differentiate between intraand inter-fragment contributions to the interaction energy, which can then be decomposed into different contributions.

Please do not adjust margins

For the LED analysis, localised orbitals obtained from the DLPNO-CCSD(T) calculation are assigned to the different fragments based on Mulliken charges analysis. Thus, in case of a fragmentation where an orbital expands on more than one fragment, it will always be assigned to the fragment with the more electronegative atom involved in this orbital. The counterpoise correction for the BSSE is here inherently included. Such an approach has already proved useful to enlighten on the importance of London dispersion in the structural stability of agostic complexes. 13 The interaction energy is decomposed as follows:

prep geo Y X T C Y X WP C X Y CT SP C Y X CT SP C Y X DISP SP C Y X exch Y X elstat C prep el HF prep el E E E E E E E E E E E - - - → - → - - - - ∆ + + + + + + + + ∆ + ∆ = ∆ ) , ( ) ( ) , ( ) ( ) ( ) , ( ) , ( ) , (
where

HF prep el E - ∆ and C prep el E - ∆
respectively describe the Hartree-Fock (HF) and correlation contribution to the electronic preparation of each of the interacting fragments,

) , ( Y X elstat E and ) , ( Y X exch E
respectively describe the intermolecular electrostatic and exchange interaction obtained from HF,

) , ( Y X DISP SP C E - , ) ( Y X CT SP C E → - and ) ( X Y CT SP C E → -
respectively the dispersion and charge transfer components of the correlation contribution of the strong pairs to the interaction,

) , ( Y X WP C E - and ) , ( ) ( Y X T C E -
respectively the corrections to the interaction energy for weak pairs and triple excitations, and

prep geo E - ∆
the geometric preparation of the system from the complex to the separated fragments.

For the LED analysis, the studied systems have been subdivided into five fragments. A chemically meaningful fragmentation has been opted for wherever fragments are separated by non-covalent interactions, viz the metal centre being fragment 1, the dmba ligand fragment 2 and the two auxiliary basis fragments 3 and 4. The H Ar being transferred during the reaction from the dmba ligand to the auxiliary basis in cis, it would change fragment between the ag and McH steps in the above-mentioned fragmentation. To keep a consistent fragmentation throughout the reaction path, H Ar has been removed from the fragment(2 or 3) it is covalently bound to and has been defined as fragment 5. An illustration of the fragmentation used in this analysis is given in Scheme 2. It has to be noted that, by construction, the results of the calculations do not depend on the choice of the fragmentation. Test calculations have been run comparing whether H Ar is considered part of fragment 2 or its own single fragment 5. It appears that contributions involving fragment 2 in the first fragmentation can be retrieved by adding the same contributions involving fragment 2 and fragment 5 in the second. In other words, "superfragments" can be studied by adding the contributions of their constituting fragments. In the following, "superfragments" considered in the study are referred to as the sum of their constituting fragments, e.g. "2+5" is the fragment consisting in the dmba ligand and H Ar (scheme 2). To follow their evolution along the reaction path, every contribution to the interaction energy is given relatively to their value in the anag state of the studied system. Energy profiles for the CMD mechanisms of cyclopalladation and putative cyclonickelation using acetate and acetamidate as assisting bases. Intermediates and transition states were searched and optimized by standard procedures (Figures 1 and2), and the Intrinsic Reaction Coordinate (IRC) procedure was used to confirm the direct relationship of each transition state with its related reactant and product. Imaginary frequencies of transition states are provided for information in Figures 1b and2b. As can be observed in Figure 1a, the energy profile and particularly the energetic barriers for the PdOAc system fit well the one originally reported by McGregor and Davies, 3, 5 who used the dispersion correction-devoid GGA BP86 functional.

If one considers the PdOAc and PdNHAc systems, the barrier to the formation of ag is lowered by ca. 3 kcal/mol when acetate is replaced by acetamidate. Relaxation from TS-ag to ag is isoergonic in the two systems. There is a slightly higher ag-to-TS-CH barrier in the PdNHAc system. Similarly to what McGregor and co-workers reported, 3,5 Overall, the thermochemistry of the PdOAc systems is more exergonic than for PdNHAc if one considers that significant exergonicity is only achieved by the departure of the O protonated acetamidato ligand that isomerizes into acetamide with the additional release of 7 kcal/mol. The NiOAc energy profile (Figure 2a) shows a much larger barrier of activation of 19 kcal/mol for the formation of ag via TS-ag. This barrier is again lowered down by 3 kcal/mol to 16 kcal/mol in the NiNHAc system closer to the one determined for the PdOAc system. The relaxation from TS-ag to ag is equally exoergonic segment as a symptom of a significant coulombic interaction. Again the values of q(O cis ) and q(H Ar ) support a dominant ionic character for this attractive NCI. Though, one interesting feature is the attractive NCI ring structure observed in PdOAc-ag , PdNHAcag and NiNHAc-ag that is generally symptomatic of the existence of a weak C-H σ-tometal d orbital charge transfer interaction, already reported in a previous study. 34 QTAIM investigations (not shown here) confirm indeed the existence of a bond critical point (3,-1) and a bond path for the metal-C Ar interaction.

In TS-CH, the NCI plots do not reveal major attractive domains. The one located in the H Ar -O cis -metal triangle in PdNHAc (Figure 1b) and NiNHAc (Figure 2b) can seemingly be assigned to the coulombic attraction operating between O cis and the metal centre according to the rather high difference of atomic charge q(O cis ) and q(Pd or Ni) (entries 18 in Tables 1 and2).

Bader charges indicate clearly that the Pd centre is less positively charged than the Ni one in related PdOAc/NiOAc and PdNHAc/NiNHAc systems (Table 1 and2, entry 7). It is also evident that the positive charge of H Ar increases steadily on going from TS-ag and ag to TS-CH, i.e. from a value close to neutrality in the former two states to a value of ca. +0.3 in the latter (Table 1 and2, entry 6). This suggests a rather strong repulsion between the metal center and this hydrogen atom in TS-CH, a stage where, like shown in the Please do not adjust margins Please do not adjust margins following, the C Ar -H interaction contains an enhanced ionic character although not dominant.

Interacting Quantum Atoms analysis. As stated above the IQA investigation focussed essentially on the main atoms of the reactive site that embraces a part of the atoms bonded to the metal centre. Figure 3 gives the details of the pair-wise interatomic interaction energies E int for the reactive site with the respective covalent and ionic contributions expressed as a percentage of E int for the three key situations TS-ag, ag and TS-CH in PdOAc, PdNHAc, NiOAC and NiNHAc systems. Negative percentages apply to the E int value and mean that the contribution in question opposes to the dominant one.

The consistency of the values of E int with the chemical reaction of interest can be confirmed by looking at the decreasing E int values for interatomic interaction undergoing the greatest changes. For example, the C Ar -H Ar interaction energy in PdOAc decreases from a value of -139 kcal/mol in TS-ag to -97 kcal/mol in TS-CH. The same variation is observed for NiNHAc, with a decrease from -135 to -105 kcal/mol. The turning point for the ionic interaction contribution to E int for the C Ar -H Ar interaction is TS-CH where its energy share becomes constructive (same sign as the covalent); from a valence bond theory viewpoint it could be related to an increased "weight" of the C Ar -H Ar + resonance structure.

21

For the H Ar -metal interaction in PdOAc, E int evolves from a slightly "attractive" value of ca. -5 kcal/mol in TS-ag to a value of -17 kcal/mol in ag, and abruptly reverses into a repulsive interaction with a value of +18 kcal/mol in TS-CH. This trend that is observed also in PdNHAc, NiOAc and NiNHAc corresponds to a progressive weakening of the covalent H Armetal component already poised by a strong ionic repulsive contribution in TS-ag and ag that eventually dominates in TS-CH. Quite consistently the C Ar -metal interaction, that is built of two constructive covalent and ionic contributions of the same sign in a ~ 7:3 ratio, is strengthened (increasing absolute value of E int ) along the energy path as this interaction gets closer to an exclusive C Ar -metal bond. This E int (H Ar -M) interaction energy reversal that occurs from ag to TS-CH corresponds to interatomic excursions for the C Ar -H Ar , H Ar -O cis and H Ar -M distances of ca. +0.20, -0.55 and +0.10 Å, which in almost all cases but PdNHAc requires a negligible Gibbs energy payload at this level of theory (GGA DFT-D).

The situation around O cis deserves a special attention. This oxygen atom that was previously bound to the metal in anag still preserves a reasonable attractive ionic interaction with it in TS-ag, ag and TS-CH. The value of E int for the O cis -Pd interaction evolves in PdOAc steadily from -126 to -106 kcal/mol in TS-ag and ag to a value of -99 kcal/mol in TS-CH. This clearly indicates that the acetate ligand is not plainly monodentate in ag, this up to the passing of TS-CH where this partial chelation situation is lifted by the capture of H Ar . The comparison of acetato and acetamidato systems informs that the value of E int for the O cis -metal interaction is by 20 to 30 kcal/mol lower in absolute value in PdNHAc-TS-ag and NiNHAc-TS-ag whereas E int for the H Ar -O cis interaction is nearly identical in all four systems. It can be speculated that the lowering of the barrier of activation for the formation of ag in PdNHAc and NiNHAc is rooted in the lower residual chelation of the metal by the cis acetamidate ligand.

DLPNO-CCSD(T)/LED investigation.

Intermediates and transition states that have been optimized above were studied using the DLPNO-CCSD(T)/LED approach. After a user-defined fragmentation of the system, Hartree-Fock and correlation energies were differentiated between intra-and interfragment contributions to the interaction energy and further decomposed into electronic promotion, electrostatic, exchange, dynamic charge polarization, and dispersion contribution (see supporting information for detailed LED energy terms). Considering the PdOAC and PdNHAc systems, the energy barrier to formation of ag is here slightly lowered when replacing acetate by acetamidate, while the relaxation from TS-ag to ag and the ag-to-TS-CH barrier are slightly lowered. In the case of the Ni analogues, the TS-ag-to-ag step is endoenergetic and is lowered by ca. 2 kcal/mol when replacing acetate by acetamidate, while the ag-to-TS-CH barrier is slightly lowered (by less than 1 kcal/mol). For both the acetate and acetamidate, the anag-to-TS-ag step is less endoenergetic for the Pd analogues than for the Ni one; but the ag-to-TS-CH step is lower in energy for PdOAc than for NiOAc, while it is higher for PdNHAc than for NiNHAc. From the construction of the fragmentation (scheme 2), the interaction energy between fragment 5 and any other fragment is purely electrostatic in nature as no orbital was assigned to fragment 5 in the computation, for H Ar has a lower electron population than the other atom(s) it bound to (C Ar or O cis ) in the orbital it is involved in. For the four considered systems, the population on H Ar in the orbital it is involved in with C Ar decreases from around 40 % at anag to 10-15 % in TS-CH where the electron population is similar to the one in the orbital it is involved with O cis , which increases to around 30 % in McH (or McH* in PdOAc). Also, at ag, the distribution of the population in the orbital involving H Ar is of the order of 60 % Please do not adjust margins on C Ar , 30 % on H Ar and 10 % on the metal, which supports the hypothesis of the agostic bond having some 2 electron-3 center character. So, as no orbital is assigned to fragment 5, all the information about the exchange and correlation around the reactive center is included in the interactions between fragments 1, 2, and 3, while fragment 5 gives a deeper insight on the electrostatic behaviour around the reactive center. The interaction energy between fragments 1 and 5 (Figure 5a) is therefore repulsive all along the reaction path and increases continuously from anag to ag and decreases continuously from ag to McH (or McH*) for the four considered systems (Figure 5a). The repulsion barrier between fragments 1 and 5 is lowered when acetate is replaced by acetamidate (Figure 5a, 8 kcal/mol for Pd, and 10 kcal/mol for Ni). The interaction energy between fragments 2 and 5 is attractive all along the reaction path and decreases continuously (Cf Supporting Information Figure S9), while the interaction energy between fragments 3 and 5 is attractive all along the reaction path and continuously decreases (cf. Supporting Information Figure S9), describing the transfer of the proton H_Ar from the dmba to the base in cis, whith the interaction between H_Ar and both fragments always being stabilizing.. The sum of these two contributions (interaction between H Ar , and C Ar and O cis in their respective fragments, i.e. between fragment 5 and "superfragment" 2+3) continuously decreases from anag to ag then continuously increases from ag to McH (or McH*), defining the agostic intermediate ag as a minimum of the interaction energy of the reactive system base-dmba (Figure 5c). The decrease in this energy for the formation of ag represents between 40% (for PdNHAc) and 47% (for NiOAc) of the barrier height in the interaction energy between 1 and 5, this percentage decreases by 3% when acetate is replaced by acetamidate, for both metals. In both case, this decrease arises from an increase of the barrier height of about 10 kcal/mol and a decrease of the well depth of about 7 kcal/mol. The interaction energy between fragments 1 and 2 is attractive all along the reaction path and decreases continuously along the reaction path (see Figure S3 in the Supporting Information)for each of the considered systems (cf. ESI). The same trend is followed by the electrostatic, exchange, and correlation contributions. The electrostatic contribution represents in average 92 % of the interaction energy for the Ni analogues and 89 % for the Pd analogues, all being maximal at TS-ag and minimal at McH (or McH* for PdOAc). The correlation contribution to the interaction energy ranges between 2 % and 3 % for all systems, around 40 % of which are due to dispersion. On the opposite, the interaction energy between fragments 1 and 3 is attractive all along the reaction path and continuously increases (see Figure S4 in the Supporting Information), except for NiNHAc where it decreases from TS-ag to ag before increasing again and for PdNHAc where it decreases from anag to TS-ag before increasing. The electrostatic (Figure 5b), exchange, and correlation contributions follow the same trends. The interaction energy between fragments 1 and 4 (see Figure S5 in the Supporting Information) is attractive all along the reaction path and decreases from anag to TS-ag to ag then increases from ag to TS-CH to McH, except for NiOAc for which it continuously increases (cf. ESI). The same trends are followed by the electrostatic contribution. Exchange contributions follow the trends in the case of PdNHAc and NiOAc, but in the case of NiNHAc and PdOAc it increases from TS-ag to ag. Correlation contributions decrease from anag to TS-ag then continuously increase for all systems (cf. ESI). Dispersion contributions continuously increase along the reaction path for all systems. The electrostatic contribution represents in Please do not adjust margins Please do not adjust margins average 92 % of the interaction energy for the Ni analogues and 90 % for the Pd analogues, this contribution being lowered by almost 1 % when acetate is replaced by acetamidate. The correlation contribution to the interaction energy ranges between 2 % and 3 % for all systems, around 30 % of which are due to dispersion for the Pd analogues and 25 % of which for the Ni analogues. The interaction energy between fragments 2 and 3 (see Figure S6 in the Supporting Information) is attractive all along the reaction path and increases continuously from anag to ag then decreases from ag to TS-CH before increasing again from TS-CH to McH for the four considered systems, note that the TS-ag-to-ag step is quasiisoenergetic for the Ni analogues. The electrostatic contributions continuously increase from anag to ag then decrease from ag to McH. The exchange and correlation contributions continuously decrease from anag to TS-CH then increase from TS-CH to McH. The dispersion contributions follow the same trend when acetamidate is the auxiliary base, but increase from anag to TS-ag for the acetate analogues. The electrostatic contribution to the interaction energy is also repulsive and represents 110 % to 115 % of the interaction energy from anag to ag then increases to 137 % for PdOAc, 138 % for PdNHAc and 140 % for the Ni analogues at TS-CH then decreases again at McH (or McH* for PdOAc). The exchange and correlation contributions are, on the contrary, attractive. The correlation contribution ranges between -5 % and -8 % of the interaction energy from anag to ag then increases to -14 % for the Pd analogues and -15 % for the Ni analogues. The dispersion contribution decreases from around 50 % of the correlation contribution in anag to 27-28 % at TS-CH then decreases again, for all studied systems. The total interaction energy (sum over all interactions) is attractive all along the reaction path and continuously decreasing all along the reaction path (see Figure S10 in the Supporting Information), except for NiOAc for which a barrier of 29 kcal/mol appears for the formation of the agostic intermediate ag. For both Pd and Ni, the total interaction energy is lower for the acetamidate analogue than for the acetate one until the formation of ag, and becomes higher until the formation of McH (or McH*). The same trends are followed by the total electrostatic interaction and the total exchange interaction contributions. The total correlation interaction contribution is, for all four systems, continuously decreasing from anag to TS-CH and then increases towards McH (or McH*). The total dispersion interaction contribution continuously decreases all along the reaction path for the acetamidate analogues, but presents a barrier for the formation of the agostic intermediate ag for both acetate analogues (0.4 kcal/mol for PdOAc and 0.2 kcal/mol for NiOAc). Contributions of the different inter-fragment interactions to the total interaction energy are given in Table 3. The contribution to the total interaction energy only varies significantly for five fragment-pairs: 1-2, 1-3, 1-4, 2-5 and 3-5. The main contribution is the 1-3 interaction at anag for the acetate analogues and at anag and TS-ag for the acetamidate analogues, and the 1-2 interaction for all other geometries, these two contributions remain the two main ones during the whole reaction for all four systems. The 1-2 interaction contribution increases and the 1-3 interaction contribution decreases through the whole reaction, describing respectively the metal-C Ar bond formation and the metal-O cis bond breakage.. Table 3. Contributions (in percentage) of the different inter-fragment interaction energies to the total interaction energy as generated by the LED method from DLPNO-CCSD(T) computations. system state 12 The contribution of the 1-4 interaction follows the same variation than the 1-3 interaction, meaning that the interaction between the metal and both auxiliary bases varies in the same way but for different reasons: Please do not adjust margins General Discussion. The two methods consistently produce a higher energy payload (defined here as the energy required to pass the highest transition state starting from the initial reference state) for cyclonickelation as compared to cyclopalladation. Overall the total electronic energy payload for the anag-to-McH*/McH at the DLPNO-CCSD(T) level is ca. 30 and 18 kcal/mol for the Ni and Pd systems whereas at the GGA PBE-D3(BJ) level the payload amounts respectively ca. 17 Overall the CMD mechanism applied to the cyclopalladation and cyclonickelation of N,N-dimethylbenzylamine shows a major sensitivity to electrostatic repulsion (Figure 6). The latter is indeed largely rooted in the nature of the metal; the Ni centre displaying overall a larger positive charge than Pd, which results in a larger barrier to formation of the agostic intermediate ag.

Also of importance is the nature of the auxiliary base. In the Ni and Pd systems the acetamidato ligands lower the anag-to-ag and the ag-to-McH*/McH barriers. This effect seems to be essentially due to the inherently lower chelating property of the acetamidato ligand and the lower electrostatic repulsion between the C Ar -H Ar bond and the metal induced by charge density donation to the metal from the two acetamidato N ligands. In other terms, the interaction of the carboxy unit C(O) of the base with H Ar is not exclusive in ag: a significant residual ionic interaction exists between the cis-located base and the metal centre in all four systems, which competes with the proton transfer process that appears now to be rather sensitive to the effective charge lying at O cis . Nonetheless, in the PdNHAc and NiNHAc systems, the residual chelation of the cis acetamido ligand is significantly lower than in the PdOAc and NiOAc systems: it seems that significant improvement of the feasibility of the CMD mechanism with first row metal complexes lies, among other issues, in the judicious choice of the auxiliary base that should be a ligand with the lowest propensity for chelation and the strongest ligand to metal σ-donating properties in its monohapto mode.

The sensible decrease of the charge at the metal upon substitution of AcO -for AcNH -contributes indeed to the decrease of the electrostatic repulsion between the metal and H Ar , which persists nonetheless throughout the process and is particularly acute in the ag-to-TS-CH step involving proton transfer and carbometallation. Finally, it must be pointed out according to DLPNO-CCSD(T) calculations that the interfragment interactions 2-4 corresponding to the dmba-totrans-base interaction is increasingly repulsive (total energy) from anag to ag in the four studied systems (cf. ESI). We speculate that minimizing this repulsive contribution of the non-reactive trans-base (fragment 4, scheme 2) by its replacement by a donating anionic ligand of smaller size than AcO -could improve significantly the cyclometallation process.

Conclusions

In In line with previous reports on the CMD mechanism, 3-5, 9, 10, 52 this study suggests that the formation of an agostic intermediate is not only crucial but must occur within a proper multipolar environment around the C-H bond, to enhance the feasibility of the whole carbometallation deprotonation process. It is found that

Please do not adjust margins Please do not adjust margins substitution of acetate for acetamidate as the auxiliary base and ligand should improve the efficiency of the cyclometallation reaction 34,35 owing to lower propensity of the latter base to maintain a residual chelation with the metal centre. Finally, on a wider scope, the possibility of protonrelay effects operating during the cyclometallation reaction 5,43 advocates the inclusion of both explicit and implicit solvation effects particularly with polar protic solvents or reagents as they may actively influence the whole reaction energy profile and modify the structure of the key intermediates and transition states. This aspect of utmost importance, which was eluded in this work is to be addressed in future studies and will be reported on in due time.

Computational details. Geometry optimizations of reactants, intermediates, transitions states and products were performed with the methods of the density functional theory using the SCM-ADF 45 2018.01 package, considering the molecules in the gas phase at the singlet state. The PBE 53 functional augmented with Grimme's DFT-D3(BJ) implementation of dispersion with a Becke-Johnson (BJ) damping function 46 was used in all geometry optimizations. All computations were carried out using scalar relativistic corrections within the zeroth order regular approximation for relativistic effects with ad hoc allelectron (abbreviated ae) single polarization function triple-ζ Slater type basis sets (TZP). 54 Geometry optimizations by energy gradient minimization were carried out in all cases with integration grid accuracy comprised between 4.5 and 6.5, an energy gradient convergence criterion of 10 -3 au, and a tight to very tight SCF convergence criterion. All transition states were submitted to the Intrinsic Reaction Coordinate (IRC) procedure to verify the connection to their reactive complexes and products. Counterpoise correction for basis set superposition error (BSSE) was neglected throughout this study. Vibrational modes were analytically computed to verify that the optimized geometries were related to energy minima or to transition states. Bader (QTAIM) charges [START_REF] Bader | Atoms in Molecules: A Quantum Theory[END_REF] and Interacting Quantum Atoms analyses 30,31 (IQA) were carried out using the embedded QTAIM functionalities of the ADF package. For technical reasons regular all electron TZP Slater type basis sets for all elements except for Pd, for which a basis set with a frozen core up to 3d was used for IQA. Drawings of molecular structures and isosurfaces were produced with ADFview2018.

For each of the four studied system, DLPNO-CCSD(T) [START_REF] Riplinger | [END_REF] calculations with the TightPNO threshold on the PBE-D3(BJ) optimized geometries for anag, TS-ag, ag, TS-CH and McH were performed using the ORCA program system 55 version 4.1.1. The balanced Karlsruhe 2 nd generation default triple-ζ valence plus polarization (def2-TZVP) basis set 56 was used in these calculations, as well as automatically generated auxiliary basis set. 57 The LED analysis 48 has been performed to quantify the different intra-and inter-fragment contributions to the energy. For this analysis, each system has been subdivided into five fragments : the metal center, the transferred H Ar , each auxiliary base and the dmba ligand from which the H Ar ortho to the N,N-aminomethyl group has been removed.

  2.7-3.2 Å from the metal centre with no interaction of the latter with the carbon of the C-H motif. The second step entails the dechelation of one the Pd-bound carboxylates leading, via transition state TS-ag to the formation of an agostic intermediate ag wherein the C-H bond attractively interacts with the metal centre within a multipolar environment where the positioning of the C-H bond close to the vicinal cis carboxylate prefigures the following C-H bond cleavage. The third step, generally occurring with a low barrier of activation, is the C-H bond activation itself that consists of the concerted metallation of the carbon reactive center and the H-atom transfer to the nearby carboxylate via transition state TS-CH that leads to the O-protonated acetato metallacycle McH* or to McH that may hence release the protonated base. A number of reports 5 have addressed the CMD mechanism applied to the cyclopalladation of aromatics , which concluded that the actual energy barrier of the whole process lies in the transition state TS-ag of formation of the "agostic" intermediate ag, a bottleneck sensitive to steric cluttering. In the present study, our scrutiny has focussed on the states that are most tangibly determining the fate of C-H bond activation, that is TS-ag, ag, and TS-CH for Pd and Ni promoted reactions with the assistance of either acetate AcO - or of acetamidate AcNH -.

Figure 1 .

 1 Figure 1. a) Gibbs energy profiles of the cyclopalladation of N,N-dimethylbenzylamine (dmbaH) in the PdOAc (black coloured lines) and PdNHAc systems (red coloured lines). b) NCI plots from ADFview2013 for TS-ag, ag and TS-CH in PdOAc and PdNHAc systems (ZORA-PBE-D3(BJ)/all electron TZP level); NCIs are materialized by reduced density gradient isosurfaces (cut-off value s= 0.02 a.u., ρ= 0.05 a.u.) coloured according to the sign of the signed density λ 2 ρ, i.e in red and blue for attractive and repulsive (or non bonded) NCI domains respectively (cf Supporting Information for larger drawings).

Scheme 2 .

 2 Scheme 2. Illustration of the fragmentation of the system used in the LED analysis considered in this study, where M= Pd or Ni and acetate and acetamidatecorrespond to Y'=O and Y'=NH respectively.

  in the PdOAc system the proton abstracted from the aromatic ligand in TS-CH finds its way to a bridging position in between the two off-plane O atoms of the acetato ligands in what is depicted by structure McH* (scheme 1), whereas in the PdNHAc system, the energy minimum is reached in the McH structure where the off-plane O atom of the acetamidato ligand cis to the palladated C atom is protonated.

Figure 2

 2 Figure 2. a) Gibbs energy profiles of the cyclonickelation of N,N-dimethylbenzylamine (dmbaH) in the NiOAc (black coloured lines) and NiNHAc (red coloured lines) systems (ZORA-PBE-D3(BJ)/all electron TZP level). b) NCI plots from ADFview2013 for TS-ag, ag and TS-CH in NiOAc and NiNHAc systems (ZORA-PBE-D3(BJ)/all electron TZP level) ; NCIs are materialized by reduced density gradient isosurfaces (cut-off value s= 0.02 a.u., ρ= 0.05 a.u.) coloured according to the sign of the signed density λ 2 ρ, i.e in red and blue for attractive and repulsive (or non bonded) NCI domains respectively (cf Supporting Information for larger drawings).

  and the transition from ag to McH via TS-CH is nearly barrierless in the two systems. The NiOAc energy profile (Figure 2a) shows a much larger barrier of activation of 19 kcal/mol for the formation of ag via TS-ag. This barrier is again lowered down by 3 kcal/mol to 16 kcal/mol in the NiNHAc system closer to the one determined for the PdOAc system. The relaxation from TS-ag to ag is equally exoergonic and the transition from ag to McH via TS-CH is nearly barrier-less in the two systems.

Figure 3 .

 3 Figure 3. IQA analysis of TS-ag, ag and TS-CH in PdOAc, PdNHAc, NiOAc, NiNHAc systems. Histogram of atom-pair interaction energies within the reactive site (black coloured, total E int in kcal/mol) are decomposed into their covalent component (blue coloured bars) and ionic component (red coloured bars) (cf ESI for an alternative presentation).

Figure 4 .

 4 Figure 4. Total potential energy profile computed at the DLPNO-CCSD(T)/def2-TZVP level from the DFT-optimized geometries. Energies are expressed relative to anag.

Figure 5 .

 5 Figure 5. Electrostatic interaction energy plot along the reaction path for interfragment interactions 1-5 (a) and 1-3 (b) and the total interaction energy for the interfragment interaction (2+3)-5, which shows an electrostatic interactions minimum at ag for the four systems.

  the 1-3 interaction contribution decreases because of the cleavage of the metalbase bond, while the 1-4 interaction contribution decreases because of the trans influence of the formation of the metalaryl bond. Contributions from 2-5 and 3-5 vary in opposite: being both rather constant from anag to ag, the contribution of 2-5 decreases while the contribution of 3-5 increases, which illustrates that the cleavage of the C Ar -H Ar bond in favor of the formation of the O cis -H Ar bond only takes place after the ag step.. The sum of the contributions of 2-5 and 3-5 interactions is almost constant throughout the reaction for the acetamidate analogues, while it decreases from ag to McH or McH* for the acetate analogues.

  and 12 kcal/mol in total electronic energy. Compared to the GGA PBE-D3 energy profiles for the four systems, the DLPNO-CCSD(T) ones give higher barriers of activation for the ag-to-McH (or McH*) step. This major difference lies in the more accurate physical description49 of the proton transfer process via TS-CH by the DLPNO-CCSD(T) method. The systematic underestimation by DFT50 of proton transfer barriers stems from the self-interaction51 effect that reportedly tends to stabilize delocalized states such as TS-CH.47,48 Therefore this higher DLPNO-CCSD(T) barrier, which is about less than twice as large for the Ni than for the Pd systems (as compared to the quasi "barrierless" ag-to-McH*/McH process computed at the PBE-D3(BJ) level), is rather critical. It is evident from Figure 5c that all the GGA DFT-D optimized geometries of ag used in this study give rise to a minimum value for the interfragment interaction energy between superfragment (2+3) and 5, thus suggesting that the ag geometries used in the calculations are rather close to a local energy minimum at the DLPNO-CCSD(T) level.

Figure 6 .

 6 Figure 6. Summary of the effects governing the reactivity of the ag intermediate in the CMD mechanism. Colour code for unshaded atoms: blue N, dark grey C, light grey H, red O, magenta metal. Red and blue arrows depict attractive and repulsive electrostatic interactions respectively. Charge density donation from the auxiliary bases is drawn in green. The egg-shaped orange-yellow area depicts the weak exchange C Ar -H Ar -metal interaction.

  this study, the CMD/AMLA mechanism of cyclopalladation and cyclonickelation has been investigated by joint DFT-D and DLPNO-CCSD(T) methods assisted by QTAIM-IQA and LED analytical procedures to map out the role of NCIs in the key stages of the reaction. The study points the crucial role played by electrostatic interactions, which somewhat govern the whole process that is very sensitive to the charge borne by the metal centre. This is expressed by a larger energy payload for the formation of the pivotal Ni-ag transient (as compared to Pd-ag) but also by a larger activation barrier for the final C-H bond carbometalation/deprotonation step (ag to McH/McH*) of the CMD mechanism.

Table 1 .

 1 Selected interatomic distances (expressed in Å) and Bader charges in PdOAc and PdNHAc systems.

	entry	system	parameter TS-ag	ag	TS-CH
	1	PdOAc	C Ar -H Ar	1.113 1.161 1.354
	2		O cis -H Ar	2.066 1.995 1.435
	3		Pd-H Ar	2.207 1.875 1.922
	4		C Ar -Pd	2.642 2.286 2.121
	5		q(C Ar )	-0.07	-0.10	-0.22
	6		q(H Ar )	0.08	0.12	0.32
	7		q(Pd)	0.80	0.78	0.75
	8		q(N)	-0.77	-0.81	-0.76
	9		q(O cis )	-1.08	-1.14	-1.04
	10	PdNHAc	C Ar -H Ar	1.112 1.146 1.323
	11		O cis -H Ar	2.113 2.102 1.430
	12		Pd-H Ar	2.255 1.935 2.021
	13		C Ar -Pd	2.541 2.353 2.161
	14		q(C Ar )	-0.08	-0.09	-0.26
	15		q(H Ar )	0.08	0.09	0.33
	16		q(Pd)	0.70	0.70	0.67
	17		q(N)	-0.79	-0.77	-0.78
	18		q(O cis )	-1.06	-1.09	-1.02

Table 2 .

 2 Selected interatomic distances (expressed in Å) and Bader charges in NiOAc and NiNHAc systems. The way NCI plots are depicted in Figures1b and 2bdistinguishes attractive domains (red coloured isosurfaces) from repulsive or non-bonded ones (blue colored isosurfaces). Quite interestingly, all four NCI plots for the TS-ag transition states in Figures1b and 2bshow a threeleaf clover shaped attractive NCI domain in the reaction site that is consistent with the transformation undergoing on the way towards the metastable ag intermediate: the chelation by the base cis to dmbaH recedes to the establishment of the agostic C-H-metal interaction. The attractive component located in the metal-C Ar H Ar , metal-O cis and H Ar -O cis segments is consistent with the large electrostatic attraction between C Ar and the metal suggested by the values of charges of opposite sign already pointed out in recent[START_REF] Sajjad | [END_REF]10 reports. Table1lists Bader charges 25 q for a selection of atoms and interatomic distances for the key C Ar -H Ar -Pd-O cis motif that comprises the C-H bond to be activated, the palladium centre and the off-plane O atom of the cis acetato or acetamido ligands in TS-ag, ag and TS-CH geometries for the PdOAc and PdNHAc systems. Table2lists Bader charges 25 q for a selection of atoms and interatomic distances for the key C Ar -H Ar -Ni-O cis motif that comprises the C-H bond to be activated, the nickel centre and the off-plane O atom of the cis acetato or acetamido ligands in

	entry	system	parameter TS-ag	ag	TS-CH
	1	NiOAc	C Ar -H Ar	1.117 1.179 1.379
	2		O cis -H Ar	2.044 1.910 1.391
	3		Ni-H Ar	1.985 1.715 1.805
	4		C Ar -Ni	2.353 2.048 1.954
	5		q(C Ar )	-0.10	-0.14	-0.26
	6		q(H Ar )	0.08	0.11	0.32
	7		q(Ni)	0.94	0.91	0.89
	8		q(N)	-0.88	-0.80	-0.80
	9		q(O cis )	-1.09	-1.08	-1.02
	10	NiNHAc	C Ar -H Ar	1.126 1.168 1.331
	11		O cis -H Ar	2.027 1.918 1.405
	12		Ni-H Ar	1.990 1.771 1.892
	13		C Ar -Ni	2.271 2.095 1.991
	14		q(C Ar )	-0.10	-0.15	-0.28
	15		q(H Ar )	0.08	0.12	0.33
	16		q(Ni)	0.85	0.81	0.81
	17		q(N)	-0.82	-0.83	-0.80
	18		q(O cis )	-1.08	-1.07	-1.01

NCI plots and Bader charges. TS-ag, ag and TS-CH geometries for the NiOAc and NiNHAc systems. Note that the H Ar -Ni and C Ar -Ni distances of both NiOAc-ag (Table

2

, entry 3 and 4) and NiNHAc-ag (Table

2

, entry 12 and 13) are consistent, although by ~0.3 Å shorter, with those determined by X-ray diffraction analysis by van der Vlugt and co-workers

37

for a phosphonito pyridylphenyl Ni agostic complex wherein the Ni centre is constrained by chelation to the ditopic phosphinitopyridyl moiety (C Ar -Ni 2.355(

8

) Å, H Ar -Ni 2.02(9) Å). As a matter of fact from the view point of the C-H bond activation TS-ag prefigures the multipolar environment by which the C Ar -H Ar bond is surrounded all the way till TS-CH. In intermediate ag, in all four considered systems, attractive NCI isosurfaces are present in the H Ar -O cis

J. Name.,2013, 00, 1-3 |

Acknowledgements

The authors gratefully acknowledge the support provided by the Centre National de la Recherche Scientifique and the University of Strasbourg. Prof Dr Gerard van Koten and Dr Michel Pfeffer are gratefully acknowledged for fruitful discussions.

Conflicts of interest

There are no conflicts to declare Please do not adjust margins