Open AccessCCS ChemistryRESEARCH ARTICLE11 Jun 2022A Distinctive Pattern for Substituent Effects on Transition Metal Centers: Enhanced Electron-Donating Capacity of Cationic Palladium Species Jun-Yan Wu, Bin-Rui Mo, Jin-Dong Yang and Jin-Pei Cheng Jun-Yan Wu Department of Chemistry, Tsinghua University, Beijing 100084 Google Scholar More articles by this author , Bin-Rui Mo Department of Chemistry, Tsinghua University, Beijing 100084 Google Scholar More articles by this author , Jin-Dong Yang *Corresponding authors: E-mail Address: [email protected] E-mail Address: [email protected] Department of Chemistry, Tsinghua University, Beijing 100084 Google Scholar More articles by this author and Jin-Pei Cheng *Corresponding authors: E-mail Address: [email protected] E-mail Address: [email protected] Department of Chemistry, Tsinghua University, Beijing 100084 College of Chemistry, Nankai University, Tianjin 300071 Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192 Google Scholar More articles by this author https://doi.org/10.31635/ccschem.022.202201990 SectionsSupplemental MaterialAboutAbstractPDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareFacebookTwitterLinked InEmail Electronic and bonding situations at reaction centers are often detected by the remote substituent effect. For nonorganometallic reactions, this effect is conventionally described by the well-known Hammett-type substituent constants. However, for most transition metal (TM)-involved systems, no analogous numeral descriptors reflecting the intrinsic differences between metallic and nonmetallic bonding have been rigorously established till present. Herein, we report a Pd(II)–O bond heterolysis energy ΔGhet(Pd–O) study of the archetypal palladium complexes to represent the thermodynamics of the essential bond-breaking step in Pd-mediated transformations. Meanwhile we furnish the new substituent constants σPd+s and therefrom facilitate linear free-energy relationship (LFER) analysis for Pd-catalyzed reactions. Indeed, this led us to find an unexpected electron-donating ability of Pd(II) cation, which provided a gifted experimental support, with the aid of computation, to attribute the frustrating observation of a much scattered curvature in the ΔGhet(Pd–O)-σ+ correlation to the electron-donating capacity of the cationic palladium through back-donation of its d-electrons. Applications of LFER analysis with σPd+ to predict the redox behavior of the palladium complex and in a kinetics vs. thermodynamics mechanistic study of transmetalation added further credence to their applicability to TM systems. Download figure Download PowerPoint Introduction Quantification of structure–reactivity relationships, a general strategy for rational investigation of reactivity and mechanism, relies on defining numeral molecular/group descriptors. A prominent example is the widespread application of the Hammett substituent constant (σ), which was first derived from the relative pKa values of remotely substituted benzoic acids vs. the parent pKa (arbitrarily set as zero, Scheme 1a)1,2 for analyzing/predicting various properties of remote structural variations. This parameter, together with its most popular extensions (e.g., σ+ and σ− for substituents conjugated with electron-density declining and rising reaction centers, respectively,3–7 Scheme 1b), has now been used routinely for interpretation of organic reactions and their mechanisms.8–12 However, this powerful toolset for the LFER studies is not used without limitation. Its success largely depends on how close the target system resembles that of the model reaction from which the specific σ was initially deduced (Schemes 1a and 1b).3–12 Scheme 1 | Substituent effects on metallic and nonmetallic centers. (a) The original definition of Hammett relationship on the basis of benzoic acid ionization. (b) Extension of Hammett relation to the nonmetallic centers conjugating with substituents. (c) Elusive substituent effects on TM centers. Download figure Download PowerPoint Transition-metal (TM) complexes are synthetically important because of their widespread use as catalysts in chemical and industrial transformations.13–19 In contrast to the significant progress in LFER studies of traditional nonmetallic systems, similar understanding of TM centers remains elusive. Whether and how the electronic effects of substituents conjugate with TM atoms have not been well defined (Scheme 1c). Though various substituent constants, including σ,20–26 σ+,27–32 σ−,33–37 and their combinations,38–41 have been arbitrarily chosen to analyze the behavior of metal complexes (for instance, such physical properties as infrared vibration,42–46 NMR shift,45,47–51 etc.) with diverse outcomes, the cause of those capricious correlations28,41,52–62 have hardly been elucidated on the basis of the original models that the corresponding σ series were deduced from. Diverse observations in LFER studies of various organometallic reaction systems have also been reported.35,63–65 We realize that the Hammett analysis mentioned above was often obtained as an apparent consequence of a whole catalytic cycle,27,28,66–68 and thus the actual effect of substituents may be compromised by complicated steps in or out of the cycle. Therefore, it becomes very desirable to find suitable tools to describe the exact impact of remote substituents on TM centers so as to understand their electronic nature and bonding mode with respect to TM atoms and to gain insight into the governing property of TM complexes and their reaction mechanisms. Among various TMs, the square-planar palladium complexes (L2PdRX) have been recognized as privileged catalysts in organic and electrochemical syntheses.69–71 Formal heterolysis of Pd–X bonds that release ionic Pd(II)+ and X− species is widespread in the fundamental steps of catalytic cycles, like transmetalation, migratory insertion, and reductive elimination.72–76 Our group has recently established a method to determine the bond heterolysis energy ΔGhet(Pd–X) of Pd–X bonds in L2PdRX complexes,77 which may provide a good opportunity to investigate the substituent effect on TM centers. Comparison of this process with the heterolysis of t-cumyl chlorides (Schemes 1b and 1c) shows certain commonalities between them. For example, (a) both the bond dissociation processes develop a net positive charge in their respective reaction centers; and (b) in both cases the para-substituents can conjugate with the reaction centers. Naturally, the σ+ may be considered an appropriate parameter for LFER analysis of metallic reactions too, at least for those bearing π-electron-donating groups (π-EDGs). However, our present thermodynamic study of Pd(II)-O bond heterolysis ΔGhet(Pd–O) shows a clue contrary to this expectation. Differing from the t-cumyl cation, the cationic Pd(II) center was observed as not being effectively stabilized by π-EDGs, but showed an electron repulsion effect looking much like that observed in the anionic phenolate system. Counterintuitively, this cationic species can actually serve as a good electron donor, seeming to significantly delocalize its electron towards π-electron-withdrawing groups (π-EWGs, like NO2 and CN). Here, we report these unexpected results in more detail and a new category of substituent constant σPd+ for Pd-centered systems on the basis of the newly measured ΔGhet(Pd–O)s. Further applications of the σPd+ in predicting redox potentials of palladium complexes and in mechanistic analysis are also described. Experimental Methods NMR spectra were recorded on a Bruker AVANCE III HD 400 (Bruker, United States; 1H at 400 MHz, 13C at 100 MHz, 19F at 376 MHz) nuclear magnetic resonance spectrometer. NMR spectra were calibrated individually against the peak of tetramethylsilane (TMS, 0 ppm for 1H NMR), CDCl3 (77.16 ppm for 13C NMR), and CFCl3(0 ppm for 19F NMR). Chemical shifts were given in ppm. For determination of the bond parameters, [(L2)Pd(R)(OC6H4-4-F)] were prepared in situ in the glove box. The mass of [(L2)Pd(R)I], AgBF4, 4-F-C6H4OH, and the added dimethyl sulfoxide (DMSO) was accurately weighed to calculate the precise initial concentration of Pd complexes. The reaction mixture was kept in the glove box for 10 min to establish the equilibrium before being monitored by 19F NMR to determine the equilibrium constant Keq. Electrochemical studies were carried out by using a CHI660e electrochemical workstation (CH Instruments, Inc., United States) with a three-electrode cell. The working electrode was a glassy carbon disk with a 2.0 mm diameter, and the auxiliary electrode was a platinum wire. The reference electrode was Ag/AgNO3, composed of 0.1 M AgNO3 and 0.1 M [NBu4][PF6] in DMSO. Cyclic voltammetry (CV) and differential pulse voltammetry (DPV) were conducted in DMSO with 0.1 M [NBu4][PF6] as the supporting electrolyte at a scan rate of 100 mV/s. The concentration of the analyte solution was ∼2.0 × 10−3 M. All redox potentials obtained were referenced to the Fc+/Fc redox couple and given in Supporting Information Table S1. The rates of ligand exchanges were determined by UV–vis spectroscopy in DMSO by using a Hitachi U-3900H spectrophotometer (Hitachi, Ltd., Japan). The temperature of the solutions was maintained a 20 ± 0.2 oC by circulating bath thermostats. The kinetic processes were monitored by the absorbance increase of products [(tmeda)Pd(C6H4-4-G)(NHC6H4-4-NO2)] at 480 nm. The initial concentrations of 4-NO2-PhNH2 and Pd complex 1 were about 2 × 10−4 M and 2 × 10−3 M individually to ensure the pseudo-first-order kinetics as well as a final absorbance Afinal of approximately 2. The apparent pseudo first-order rate constants kobs (s−1) were obtained by fitting the monoexponential function At = A1exp(-kobst) + C to the observed time-dependent absorbance At. Experimental relative rate constants and corresponding σPd+ derived from equilibrium constants are summarized in Supporting Information Table S2. Time-dependent plots of absorbance At are shown in Supporting Information Figures S1 and S2. Results and Discussion Pd–O bond heterolysis energy of [(L2)Pd(R)(4-F-C6H4O)] 1 The tetra-coordinate Pd(II) complexes [(L2)Pd(R)(4-F-C6H4O)] 1 (Table 1) were prepared according to a literature procedure77 and were characterized by 1H and 19F NMR (see Supporting Information). The Pd–O bond heterolysis free energies ΔGhet(Pd–O) of the complexes, as expressed in eq 1, were determined in DMSO at 293 K, following the strategy recently established77 by measuring the exchange equilibrium of the substrate [Pd + ]2 cation with a reference [Pd–O]1 complex of known ΔGhet(Pd–O) value (taking solvated Pd(II) as the unified standard; for details, see Supporting Information). In eq 2, the unknown ΔGhet(Pd–O) value was evaluated by relating ΔGhet(Pd–O) of the reference Pd complex (8.1 kcal/mol for 1a77), and the measured logKeq. Other ΔGhet(Pd–O)s were derived similarly and are summarized in Table 1. A self-consistency check using a thermodynamic cycle was performed to ensure the reliability of these bond parameters (see Supporting Information). ((1)) ((2)) Table 1 | Thermodynamic Parameters for [(L2)Pd(R)(4-F-C6H4O)] 1 in DMSO at 293 K Complexes R Indicators Keq pK(Pd–O) ΔGhet(Pd–O)a 4-F-C6H4 1a — — 5.91 8.1b 4-NMe2-C6H4 1b 1a 0.10 ± 0.02 4.93 ± 0.08 6.8 ± 0.1 4-OMe-C6H4 1c 1a 0.34 ± 0.07 5.44 ± 0.08 7.4 ± 0.1 4-H-C6H4 1d 1c 1.50 ± 0.14 5.62 ± 0.04 7.7 ± 0.1 4-Ph-C6H4 1e 1c 3.45 ± 0.28 5.96 ± 0.03c 8.2 ± 0.1 4-Cl-C6H4 1f 1e 2.50 ± 0.14 6.32 ± 0.02c 8.7 ± 0.1 4-CF3-C6H4 1g 1a 2.66 ± 0.02 6.33 ± 0.02 8.6 ± 0.1 4-tBu-C6H4 1h 1e 0.40 ± 0.01 5.57 ± 0.01 7.6 ± 0.1 4-CN-C6H4 1i 1g 5.69 ± 0.07 7.08 ± 0.07 9.7 ± 0.1 4-NO2-C6H4 1j 1i 1.68 ± 0.09 7.31 ± 0.02 10.0 ± 0.1 4-COPh-C6H4 1k 1i 0.37 ± 0.01 6.65 ± 0.01 9.1 ± 0.1 4-COOEt-C6H4 1l 1i 0.32 ± 0.01 6.59 ± 0.02 9.0 ± 0.1 2-NO2-C6H4 1m 1i 1.92 ± 0.07 7.36 ± 0.02 10.1 ± 0.1 3-NO2-C6H4 1n 1i 1.24 ± 0.05 7.17 ± 0.02 9.8 ± 0.1 C6F5 1o 1j 0.035 ± 0.008 8.77 ± 0.10 12.0 ± 0.2 1-Nap 1p 1c 0.30 ± 0.03 5.98 ± 0.04 8.2 ± 0.1 2-Nap 1q 1c 0.33 ± 0.02 5.92 ± 0.02 8.1 ± 0.1 Me 1r 1i 0.036 ± 0.003 5.64 ± 0.04 7.7 ± 0.1 1s 1b 1.38 ± 0.07 4.79 ± 0.02 6.6 ± 0.1 1t 1j 1.80 ± 0.05 7.56 ± 0.01 10.4 ± 0.1 1u 1i 1.31 ± 0.08 7.20 ± 0.03 9.7 ± 0.1 1v 1i 1.44 ± 0.10 7.24 ± 0.03 9.9 ± 0.1 1w 1i 2.20 ± 0.11 7.42 ± 0.02 10.2 ± 0.1 aIn units of kcal/mol. bObtained from ref 16. cAverage values based on two indicators. As shown in Table 1, the ΔGhet(Pd–O)s spanned from 6.1 to 12.0 kcal/mol with variation of the ligands (R and L), comparable with the reported ΔGhet(Pd–O)s of [(tmeda)Pd(4-F-C6H4)(OAr)].77 The electron-deficient σ-bound C6F5 group-bearing 1o gave the largest ΔGhet(Pd–O) of 12.0 kcal/mol, and 1s with the cyclohexenyl group gives rather small ΔGhet(Pd–O) of 6.6 kcal/mol, close to that of the NMe2-bearing 1b. This indicates that the cyclohexenyl group is quite electron-rich, and hence, able to stabilize the positive charge evolved in the Pd(II) center during Pd–O bond heterolysis. Variation of dative ligands (L = N or P) exerted a slight impact on ΔGhet(Pd–O)s, resulting in an energy change from 9.7 to 10.4 kcal/mol. Although the ΔGhet(Pd–O)s were scarcely reported, ΔGhet(M–O) of [(PNP)Ru–OCOH] and [(bpy)(CO)3Mn–OCOH] were recently estimated to be 3.7 and ∼5 kcal/mol by Saouma et al.,78,79 falling in a similar region to our ΔGhet(Pd–O)s. Considering the fact that the bond energy of the phenolic H–O bond (ΔGhet(H–O)) was roughly 25 kcal/mol in DMSO (derived from its pKa of 18 in iBonD80), the relatively small ΔGhet(Pd–O) values indicate a much weaker Pd–O electrostatic interaction than that in the corresponding H–O bonds. This is probably because the bulky volume of the palladium complexes and the good electron-donating capacity of the dative N or P ligands were better able to facilitate positive charge delocalization as compared to the proton. Moreover, the small ΔGhet(Pd–O)s suggested a facile heterolysis of the Pd–O bond in DMSO to release phenolic nucleophiles, offering an energetic backup to the previously proposed ionic insertion of CO into the M–O bonds,81,82 and to the dissociative mechanisms for reductive elimination from palladium-heteroatom complexes.54,72,83–85 Evolution of a new substituent constant σPd+ for palladium centers Considering the similarity between the heterolysis pattern of the Pd–O and C–Cl bonds mentioned in the Introduction section (cf. Schemes 1b and 1c), the use of substituent constant σ+ to justify the electronic effect on the cationic Pd(II) center should have been considered reasonable. However, an attempt to correlate the ΔGhet(Pd–O)s in Table 1 with σ+ gave a plot that remarkably deviated from linearity, presenting a largely scattered pattern with definite curvature (Figure 1). This indicates that remote substituents on the aryl ligand (i.e., R directly attaching Pd) impact the electron density of a Pd center in a distinctive way from a nonmetallic one. A further look at the plot finds that, despite of the large scatters, the ΔGhet(Pd–O) does rise steeply with the increase of σ+, revealing a more profound effect of π-EWGs on Pd–O bond heterolysis. Nevertheless, it leads to a demand for a new metrics should be necessary to reflect the substituent effect on Pd centers more precisely. Figure 1 | Correlation of ΔGhet(Pd–O)s with σ+. The fitted line indicates the increasing tendency. Download figure Download PowerPoint Referring to the way for evaluating σ, we now define a new substituent parameter σPd+ for Pd-centered systems (eq 3), taking advantage of the herein derived bond energies ΔGhet(Pd–O)s as the model describers, which are summarized in Table 2 along with the conventional σ values. We need to point out that the model complex L2PdR(OAr), whose ΔGhet(Pd–OAr) served as a benchmark for deriving the respective σPd+, has the following advantages for representing the general trend of electron density variation at many other Pd centers of comparable electronic and steric environments upon altering their remote substitution: (1) Only the remote substituent para to the Pd-attaching aryl ligand R is varied while the rest of the Pd-ligands (L and OAr) and steric elements are sustained. This feature allows a change of electron density at the Pd center to only be the variable of the substituent, a common situation for other Pd complexes as long as their neighborhood is similarly controlled. (2) The remote substituent on a Pd-linking aryl can transmit its electronic effects, especially through conjugation, most efficiently onto palladium, causing the Pd–O bond to become stronger or weaker. Such a change of bond strength, now defined as σPd+, is capable of detecting how this variation in electron density affects the rate and mechanism of reactions occurring at Pd centers by LFER analysis. (3) Analogous to the definition of σ (Scheme 1a), the σPd+s were also based on deliberately measured equilibrium constants of bond heterolysis (eq 3), which warrants the experimental uncertainty of the measurements to be kept generally at a minimum relative to that of other methodologies. σ Pd + = log ( K G / K H ) (3) Table 2 | Substituent Constants for Metallic and Nonmetallic Centers G σPd+ σ+ Δσ+ σ− Class I: π-EDGs NMe2 −0.69 −1.70 1.01 −0.12 MeO −0.18 −0.78 0.60 −0.26 F 0.29 −0.07 0.36 −0.03 Cl 0.76 0.11 0.65 0.19 Ph 0.36 −0.18 0.54 0.02 Class II: Unconjugated tBu −0.03 −0.26 0.23 −0.13 H 0 0 0 0 CF3 0.71 0.61 0.10 0.65 Class III: π-EWGs CO2Et 0.97 0.48 0.49 0.75 COPh 1.03 0.51 0.52 0.83 CN 1.46 0.66 0.80 1.00 NO2 1.69 0.79 0.90 1.27 aσPd+ is a new substituent constant for Pd centers derived from eq 3; σ+ and σ− are extended Hammett constants; Δ+ is the difference between σPd+ and σ+. Examination of these parameters disclosed some clues for insight into electronic properties as well as the bonding modes of the center metal. Compared with σ+, all the σPd+ values shift positively by a Δσ value of 0.1–1.0, depending on the identity of the substituent itself. The larger σPd+ values suggest an enhanced electron-withdrawing effect of the substituent on the metallic center relative to that on a nonmetal central atom, which implies that the Pd(II) cation is more electron-rich than regular carbocations. More details on the interaction of the cationic Pd(II) center with the substituent will be addressed below. Disparity in impact of substituents on Pd and nonmetallic centers Substituents can be divided into three primary types: (1) π-EDGs with n- or π-electrons (Class I), (2) unconjugated (Class II), and (3) π-EWGs with π-orbitals (Class III). For Class I, π-EDGs should generally have two opposite effects: electron-withdrawing induction and electron-donating conjugation. As we are well aware, in the carbocation system, conjugative effect usually overrides inductive effect, and hence π-EDGs exhibit an overall electron-donating property that effectively stabilizes the carbocation (Figure 2, taking NMe2 as an example). However, a comparison of the σPd+ vs σ+ data in Table 2 demonstrates that the σPd+ values are substantially less negative. This suggests that π-EDGs are not as capable of effectively stabilizing the cationic Pd(II) center. As a consequence, their electron-donating ability looks greatly compromised, and the cationic Pd(II) center seems not as readily accepting of π-electrons as compared to the cases of ordinary carbocations. This may be rationalized by considering the following features associated with Pd centers: (a) The preferential occupation of the vacant orbital in a Pd(II) cation by solvent molecule (DMSO in this work) may reduce the electron deficiency of the metal center. (b) The polarizable Pd–O σ-bond may redistribute its bonding electrons to compensate the electronic shift caused by the substituent. (c) The back-bonding between the palladium’s d-electron and the arene’s π*-orbital is able to release its d-electron to the arene ring (Figure 2) and hence offsets part of their electron-donating effects on the π-EDG substituents. This attenuated electron-donating ability revealed here by σPd+ of π-EDGs appears superficially similar to that observed in ionization of phenol (σ−).3 Figure 2 | Comparison of electronic effects of π-EDGs on t-cumyl cation and cationic palladium systems. The arrow and its length indicate the direction of the electron flow and the relative magnitude of each effect. Download figure Download PowerPoint The data of Class II substituents further show that these groups have a rather conventional inductive effect. Again, they exhibit more profound electron-withdrawing ability in metallic systems, which means they can destabilize the palladium cation more significantly than for carbocation. On the other hand, the data of π-EWGs in Table 2 (Class III) are worthy of special attention as these groups have exceptionally strong electron-withdrawing capacity via both the inductive and conjugative effects. As shown in Table 2, the σPd+ values of π-EWGs are roughly twice as large as that of σ+, even remarkably greater than σ−. The latter has been specially used to reflect an enhanced electron shift from the electron-rich center to π-EWGs in the normal nonmetallic systems such as phenolate. These σPd+s provided a clear experimental ground to reveal an efficient delocalization of electrons from the Pd(II)+ center to π-EWGs, in spite of the fact that the Pd(II) species holds a positive charge. This implies an unexpected electron-donating ability of the cationic palladium center that even overrides that of the phenolate oxyanion. More significantly, if one does not pay attention only to the substituent, but rather, also to the side of the metal center, one may realize that it could also imply a much-enhanced adaptability of the metal towards electronic input/output by ligands. This may explain why the metal is such a good mediator for so many polar or radical metallic reactions by facilitating a better-stabilized transition state. As briefly discussed above, the counterintuitive electron-donating ability of the palladium cation is presumably attributed to the back-bonding interaction. Such a back-bonding provides a way for the metal center to conjugate with the π-EWG (Figure 3, taking NO2 as an example), from which the metal’s d-electrons can be smoothly transferred to the electron-deficient π-EWG. This consequence seems much like the stabilization pattern of phenolate oxyanions by remote π-EWGs via conjugation (Figure 3). Figure 3 | The similarity between back-bonding of palladium cations and conjugation of phenolate oxyanions. Download figure Download PowerPoint Theoretical studies on the back-bonding of palladium complexes Extended transition state-natural orbitals for chemical valence (ETS-NOCV) analysis was widely used to decompose orbital interactions as well as to identify bonding modes between metal centers and their ligands.86–88 By deconstructing orbital deformation density as a result of chemical bonding, the orbital interaction between defined fragments can be separated into contributions of several NOCV pairs (NP). A major advantage of the ETS-NOCV analysis is the visualization of the redistribution of electron density upon bond interaction, which provides evidence for determining the charge transfer direction. To identify the bonding mode between the cationic Pd(II) fragment and the anionic σ-arene ligand, density functional theory (DFT) calculations were performed at TPSSh/[6-311+G(d,p)+sdd(Pd)] levels oftheory.89 For palladium complexes bearing different substituents, similar shapes of the computational NP were obtained, and an energy contribution of more than 5 kcal/mol was selected for discussion (Table 3 and Supporting Information Table S3). Theoretical results disclosed that three NPs mainly contribute to the formation of Pd–Ar bonds (Figure 4), which account for ∼90% of the total orbital interaction energy (ΔEorb). The first pair (NP 1) corresponds to the σ-bonding between the two fragments. It plays a dominative role (average eigenvalue = 0.9982) in the formation of the Pd–Ar bond with the energy contribution E(NP 1) of about 95 kcal/mol. NP 2 and NP 3 were assigned to π-back-donation (average eigenvalue = 0.2901, E = −8.30 kcal/mol) from the d-orbital of Pd to the pπ orbital on Caryl and σ-back-donation (average eigenvalue = 0.1431, E = −8.09 kcal/mol), respectively. Similar bonding patterns of back-donation have previously been reported in the literature.86–88 The π- and σ-back-donation contribute moderately with a total orbital energy of approximately 16 kcal/mol (E(NP 2 + NP 3) in Table 3). The back-donation (% of ΔEorb) is roughly 12.5% of the whole Pd–Ar interaction, which is large enough to perturb the conventional substituent effects normally observed in nonmetallic systems. Table 3 | ETS-NOCV Results of [(tmeda)Pd(4-G-C6H4)(DMSO)]+ (kcal/mol) G Δ E orb E (NP1) E (NP2) E (NP3) E (NP2+3) % of Δ E orb Cl −124.23 −96.16 −7.46 −8.17 −15.63 12.6 NMe2 −129.98 −100.81 −7.27 −8.45 −15.72 12.1 NO2 −122.50 −97.42 −8.30 −8.09 −16.39 13.4 F −125.27 −97.13 −7.26 −8.25 −15.51 12.4 OMe −128.33 −99.59 −7.20 −8.49 −15.69 12.2 CN −123.21 −94.95 −8.13 −8.09 −16.22 13.2 Figure 4 | The orbital analysis of the Pd–Ar bond of [(tmeda)Pd(4-NO2-C6H4)(DMSO)]+ by ETS-NOCV (blue = loss of electron density, green = gain of electron density). Download figure Download PowerPoint The presence of back-bonding can also be detected by the change of C–G bond lengths, which reflect the interaction between cationic centers and substituents G (Figure 5). For π-EDGs, the back-bonding would cause weakening of the conjugation interaction between the substituent G and the cationic center and consequently lengthens the C–G bond. On the other hand, for π-EWGs, the π-back-bonding, a form of resonance, will enhance the conjugation and shorten the C–G bond. To realize the magnitude of such interaction, we calculated the lengths of the C–G bonds in carbocation and palladium systems, respectively, and derived the results in Table 4. As shown by their Δd values, the C–G bonds of the π-EDG palladium complexes are about 0.04 Å longer than those of their carbocation counterparts on average. Therein, the NMe2 group shows a most profound electronic repulsion with its connected carbon atom, lengthening the C–N bond by ∼0.06 Å. As expected, the C–G bonds of the π-EWGs palladium complexes are slightly shortened. These comparative computational analyses provide some insights into the electronic interaction and support the presence of back-bonding. Figure 5 | The impact of back-bonding on C–G bond lengths (G = NMe2 and NO2). Download figure Download PowerPoint Table 4 | C–G Bond Lengths in Cationic Palladium and Carbocation Systems G d(C–G) of Palladium Cations d(C–G) of Carbocations Δd NMe2 1.3898 1.3332 0.0566 MeO 1.3633 1.3213 0.0420 F 1.3639 1.3336 0.0303 Cl 1.7745 1.7409 0.0335 tBu 1.5399 1.5278 0.0122 CF3 1.4968 1.5107 −0.0139 COPh 1.4945 1.5123 −0.0179 CN 1.4272 1.4305 −0.0033 NO2 1.4666 1.4877 −0.0211 Application of σPd+ in prediction of thermodynamic property We further applied these new σPd+ values in analysis of redox properties of palladium complexes. Reduction potentials (Ered(Pd+)) of [(tmeda)Pd(4-G-C6H4)(DMSO)]+BF4− were determined by CV and DPV ( Supporting Information Figures S3–S15), and the values are summarized in Supporting Information Table S1. For palladium complexes bearing π-EWGs, more than one reduction peak was detected in the CV curves, which arose from successive reduction of the metal center or the reducible π-EWG. In this case, the first peak was arbitrarily assigned to the reduction of the metal center. The results range from −2.03 V (vs Fc) for the NMe2-palladium complex to −1.49 V for the NO2-analogue. Correlating these potentials with σPd+ gives a linear plot, except for Ered(Pd+) of the NO2-analogue (Figure 6). The dramatic deviation from linearity implies the presence of other disparate reduction mechanisms. According to the reported Ered value of 4-nitrotoluene (−1.48 V in DMSO)90 and 4-nitrobenzene (−1.43 V in DMF),91 we assumed that the reduction peak at −1.49 V should be responsible for the reduction of the nitro group in the NO2-palladium complex. This process precedes the reduction of the metal center. Therefore, the Ered(Pd+) for direct reduction of the metal center of the NO2-palladium complex cannot be directly determined from a simp