Electronic structure analysis of electrochemical CO2 reduction by iron-porphyrins reveals basic requirements for design of catalysts bearing non-innocent ligands

Electrocatalytic CO2 reduction is a possible solution to the increasing CO2 concentration in the earth’s atmosphere, because it enables storage of energy while using the harmful CO2 feedstock as a starting material. Notably, iron(ii) tetraphenylporphyrin, [FeII(TPP)]0 (TPP2− = tetraphenylporphyrin tetra-anion diradical), and its derivatives have been established as one of the most promising families of homogeneous catalysts for CO2 reduction into CO. Our earlier work has demonstrated that [Fe(TPP)]2−, a catalytically active species, is best described as an Fe(ii) center antiferromagnetically coupled with a TPP4− diradical. In fact, [Fe(TPP)]2− represents a prototypical example of a diverse array of highly efficient molecular catalysts that feature non-innocent ligands. To obtain valuable insights for future catalyst design, their outstanding catalytic performance warrants an investigation aimed at elucidating the role played by the ligand non-innocence in the reaction. To this end, the reactivity of [Fe(TPP)]2− was first investigated in detail by using density functional theory calculations, and the theoretical results were then validated by reproducing available experimental kinetic and thermodynamic data. Further in-depth analyses pinpointed the electronic-structure feature of the non-innocent TPP ligand that is responsible for the high efficiency of the reaction. Finally, we analyzed the electronic-structure evolution found for the reactions catalyzed by ten related representative non-innocent systems. Our results revealed that for the reactions under consideration, the reducing equivalents are stored on the non-innocent ligand, while CO2 functionalization takes place at the metal center. Therefore, all of the transformations invariably entail two synchronized electron-transfer events: (1) a metal-to-CO2 transfer and (2) a ligand-to-metal electron transfer. The former is affected by σ-donation from the metal dz2 orbital to the CO2 orbital, and the latter is facilitated by orbital coupling between the ligand and the metal center. Our results suggested that ligand non-innocence plays a fundamental role in stabilizing highly active intermediates while realizing high product selectivity for CO2 reduction and that the metal–ligand cooperativity is essential to the high reaction kinetics. On the basis of these findings, we proposed fundamental requirements for design of catalysts with non-innocent ligands.


Introduction
Over the course of the last 30 years, the mean atmospheric CO 2 concentration has increased by 20% and reached a new record of 411 ppm in 2020. 1 On one hand, CO 2 is a major greenhouse gas and largely contributes to global warming. On the other hand, CO 2 is a ubiquitous C1 feedstock that can be used to produce value-added chemicals and biofuels, thereby closing the hydrocarbon cycle. 2 However, due to its high thermodynamic stability and kinetic inertness, CO 2 functionalization typically requires not only an external energy input, but also, more importantly, appropriate catalysts.
[Fe II (TPPcc 4À )] 2À . 16 As such, the two electrons used to reduce CO 2 are stored in the non-innocent TPP ligand rather than the Fe center. However, the earlier mechanistic investigations 10 did not clarify the role of TPP in the CO 2 transformation by 1 2À . Furthermore, a range of homogeneous CO 2 activation catalysts reported thus far are supported by well-known redox active noninnocent ligands, such as porphyrins, 8 corroles, 17 pyridine-diimines 13,14,18 polypyridines, 4b,15,19,20 and N-heterocyclic carbenes 21 to name a few. The reactions with such a diverse array of systems thus give rise to an intriguing question about how the non-innocent ligand interacts with the metal center to trigger the two-electron CO 2 reduction to CO, because apparently not all coordination-unsaturated transition metal complexes bearing non-innocent ligands are capable of activating CO 2 . In fact, although ligand non-innocence has been intensely discussed in general catalysis, [22][23][24][25] its implication with respect to CO 2 functionalization has received relatively little attention.
The present work serves a dual purpose. We rst present a detailed analysis of the electronic-structure evolution in the course of CO 2 -to-CO conversion catalyzed by 1 2À , which shows that the non-innocent nature of TPP is at the core of the high catalytic activity. Then, we analyze the electronic structure changes of the same reaction mediated by ten related catalysts, which also exhibit excellent catalytic performances (Table S1 †). They include eight metal-polypyridine systems and two metalpyridine-diimine derivatives, all containing well-known noninnocent ligands (Scheme 1). Comparison of all systems under consideration enables us to identify the crucial role of noninnocent ligands in CO 2 activation. On the basis of this, we propose fundamental electronic structure requirements for CO 2 reduction with non-innocent systems, which can be used as a guideline for future design of similar catalytic systems.

Computational details
All calculations were performed using the ORCA 4.2 program package. 29 For geometry optimizations and frequency calculations, the hybrid B3LYP density functional 30 was used in combination with the Def2-TZVP basis set for iron and the rst coordination sphere, and the Def2-SVP basis set for all remaining atoms, 31 referred to as the B3LYP/Def2-TZVP/Def2-SVP level of theory hereaer. Tight geometry convergence settings and default SCF convergence settings were used for all geometry optimizations. The nal electronic energies were computed with the B3LYP functional in combination with the Def2-TZVPP basis set for all atoms (referred to as the B3LYP/ Def2-TZVPP level of theory hereaer). Default SCF convergence settings were employed. To account for solvation effects and non-covalent dispersion interactions, the solvation model C-PCM 32 for DMF and the Grimme's D3BJ dispersion corrections were employed, respectively, for all calculations. 33,34 Grid level 5 was used for all the calculations. All calculations were accelerated by using the RIJCOSX approximation. 35 The initial guesses of transition state geometries were obtained at the B3LYP/Def2-TZVP/Def2-SVP level of theory by running relaxed surface scans in the sensible normal modes and/or by calculating using the nudged elastic band method, 36 particularly for delicate transition states. The approximate transition state geometries were then optimized by maximizing the energy in a given normal mode and minimizing the energy in all other normal modes. Subsequent frequency analyses showed that local minima have no imaginary frequency, and transition states have only one imaginary frequency, occasionally besides an additional imaginary frequency of less than 16 cm À1 (see the ESI †). Despite our repeated attempts, this residual frequency could not be removed but is attributed to numerical noise owing to its magnitude.
Enthalpies were calculated by adding the zero-point energy (E ZPE ) and the thermal energy at 298 K (E th ) calculated at the aforementioned level of theory to the electronic energy (E el ) calculated at the B3LYP/Def2-TZVPP level of theory. A k B T term was also added to account for the PV term in an ideal gas approximation. To estimate more accurate energies of intermediates featuring antiferromagnetic spin coupling between the ligand and the metal center, an electronic energy correction (DE el ) calculated by using the method proposed by Malrieu and Trinquier 37 was added to the energy of the broken-symmetry solution (eqn (1a)). Free energies at 298 K were calculated by adding the electronic, translational, vibrational and rotational entropy contributions multiplied by the temperature to the enthalpy. 38 In the case of bimolecular reactions in the gas phase, translational entropic contributions typically account for +10 to +15 kcal mol À1 to Gibbs free energy changes, 9 as suggested by our earlier work on O 2 and CO 2 association with transition metal centers. 39d,40 Apparently, the gas-phase approximation overestimates the condensed-phase free energy signicantly for two reasons. First, translational freedom is largely quenched in the condensed phase, because the volume is occupied by the solvent. 41 Consequently, the translation entropy, which is directly dependent on the volume accessible to the solute, is affected by the passage from the gas to condensed phase. The subsequent loss of entropy can be estimated by calculating the loss of accessible volume (DS AV ). 41 Second, gas-phase free energy does not account for the cavitation free energy (DG cav-disp ). The latter corresponds to the free energy affording the formation of the solvent cage around the solutes. Typically, both effects induce negative Gibbs free energy variations for bimolecular reactions, which partially compensate the large entropic gains calculated in the gas phase. To account for them, we added two correction terms ÀTDS AV and DG cav-disp to the free energy computed in the gas phase (eqn (1b)). The former was calculated following a procedure described elsewhere with the van der Waals radii of the solutes and solvent. 41 The latter was estimated using a linear regression of the cavity surface using the van der Waals radii of the solute. 42 All redox potentials against the SCE electrode in DMF were calculated from the Gibbs free energies of the species of the redox couple, according to the formula: where n is the number of electrons in the reduction, F the Faraday constant (F ¼ 23.061 kcal V À1 mol À1 ), 43 and E 0DMF SCE , the absolute potential of the SCE electrode in DMF, is taken as 4.350 V. 44 The calculated redox potentials associated with the couples 3 1 0 / 2 1 À and 2 1 À / 1 1 2À (where the le and right superscripts denote the multiplicity and charge, respectively) are À1.17 and À1.76 V, respectively. These values are in reasonable agreement with the experimental values of À1.07 and À1.64 V vs. SCE. 7,[45][46][47] These results thus lend credence to the reliability of our present computational setup.
For orbital visualization analysis, the unrestricted corresponding orbitals (UCO) 48 with an overlap between the alpha and beta ones greater than 0.95 were localized using the Pipek-Mezey algorithm. 49 The alpha and beta sets in this subspace were approximated to be identical, and the orbitals thus obtained from the localized subspace were considered as doubly occupied. The singly-occupied UCO and the magnetic orbitals (overlap ranging from 0 to 0.95) were not localized. Among the resulting orbitals, the d orbitals were identied by their predominant Fe character (>70%) according to the molecular orbital (MO) Löwdin population analysis.

Potential energy surfaces
Experimental evidence points out that CO 2 reduction to CO mediated by 1 2À is initiated by CO 2 association with catalytically active 1 2À , leading to an h 1 -CO 2 adduct (A in Fig. 1). Accordingly, in the following section, only pathways involving 1 2À as the catalytically active species are considered.
The CO 2 adduct A then undergoes proton-assisted C-O bond cleavage to produce CO and H 2 O in acidic media. As discussed above, the mechanistic details of the C-O bond breaking have not reached a consensus yet. 8b, 10 To address this question, we initially tested the mechanistic proposition due to Costentin and coworkers, pathway I schematized in Scheme 2. 8b In this mechanistic scenario, the interactions of the leaving O atom of A with two phenol (PhOH) molecules (the proton donor employed in the experiments 8b ) furnish complex C that features two hydrogen bonds between the CO 2 moiety and PhOH. The following C-O bond cleavage is concomitant with the transfer of only one proton, thereby generating an OH À and the product metal-carbonyl complex [Fe(CO)(TPP)] (F) in the end. The relaxed surface scans (Fig. S2 †) in which the C-O distance was systematically varied showed that such a process cannot occur for reasons discussed below. We thus envisioned two more feasible mechanistic scenarios referred to as pathways I 0 and II in Fig. 1. In pathway I 0 , the C-O bond rupture is realized by simultaneous two proton transfer from each PhOH to CO 2 in C, leading to F and H 2 O. In pathway II, A rst reacts with one PhOH molecule (rather than two in pathway I 0 ) to form complex B with only one hydrogen bond. Aer releasing a phenoxide, B transforms into metallacarboxylic acid [Fe(COOH)(TPP)] À (D). Subsequently, D forms a hydrogen bond of its COOH group with an incoming PhOH to convert into complex E, and this intermediate undergoes C-O bond scission assisted by a second proton transfer from PhOH, thereby resulting in F and H 2 O.
Although 1 2À was irrefutably identied to feature a singlet ground state, 16 we investigated the reaction mechanisms on singlet, triplet and quintet potential energy surfaces in order to explore the possibility of the multi-state reactivity. 8g However, our theoretical results predicted that all aforementioned intermediates in the S ¼ 1 and 2 states lie at substantially higher energies than the corresponding diamagnetic ones (Table S2 †). Hence, they are very unlikely to participate in the actual reaction (for details, see the ESI †). Therefore, in the present section, we focus on the singlet reaction mechanism. To avoid confusion, hereaer we add a superscript to each species to denote its spin multiplicity.
The two steps leading to the formation of 1 B are the same for both pathways I 0 and II. For the CO 2 adduct 1 A, we tested two different CO 2 binding modes with the Fe center, namely, h 1 -CO 2 and h 1 -OCO. However, during the geometry optimizations, the h 1 -OCO complex spontaneously decomposes into 1 1 2À and CO 2 . Therefore, the h 1 -CO 2 adduct is the most appropriate model for 1 A. DFT calculations predicted that formation of 1 A traverses a transition state ( 1 TS1) with a moderate barrier of DG ‡ ¼ +9.0 kcal mol À1 and is slightly endergonic with DG ¼ 2.5 kcal mol À1 . This positive DG value originates from the unfavorable entropic term and the limited exothermicity of the CO 2 association (DH ¼ À5.4 kcal mol À1 ). The latter nding can be readily traced back to the fact that typically CO 2 is a weak ligand and the metal-CO 2 interaction is quite weak. 14c,15d,39d In line with this reasoning, the entropy contribution accounts for more than 80% of the barrier. Formation of 1 B from 1 A is appreciably exergonic (DG ¼ À6.8 kcal mol À1 ) and has no detectable barrier (Fig. S2 †). In fact, the step is strongly exothermic due to the formation of a hydrogen bond between the CO 2 molecule and the incoming PhOH (DH ¼ À14.6 kcal mol À1 ), but this exothermicity is partially balanced by the entropic cost of associating two fragments ( 1 A and a PhOH).
In pathway I 0 , formation of 1 C from 1 B was computed to be signicantly endergonic (DG ¼ +6.9 kcal mol À1 ) and barrierless ( Fig. S2 †). Unlike for the formation of 1 B, the enthalpy gain relative to the formation of an additional hydrogen bond between the oxygen of the CO 2 and a PhOH is only moderate (DH ¼ À4.5 kcal mol À1 ) and does not compensate for the unfavorable entropic cost relative to the association of 1 B and PhOH. The subsequent step that consists of the C-O bond cleavage in 1 C followed by the dissociation of the weakly bound H 2 O and PhO À yielding 1 F was estimated to be moderately exergonic (DG ¼ À5.9 kcal mol À1 ). The exergonicity arises from the tremendous entropic contribution due to the dissociation of 1 C into four fragments, i.e. 1 F, H 2 O and two phenolates (PhO À ), even if this step involves a large positive enthalpy change (DH ¼ +22.2 kcal mol À1 ). The conversion of 1 C to 1 F has to overcome a high barrier of DG ‡ ¼ +10.4 kcal mol À1 ( 1 TS2), which can be attributed to lack of enough driving force for the C-O bond cleavage in 1 C as suggested by the estimated enthalpy change (DH ¼ +9.4 kcal mol À1 , Table S10 †). Interestingly, the free energy of the nal product 1 F is on par with that of intermediate 1 B. Despite this, it should be noted that the reaction still proceeds, because the reduction of 1 F to regenerate the catalyst is driven by the potential applied at the electrode.
In pathway II, the transformation of 1 B into 1 D consists of a proton transfer in 1 B followed by the dissociation of the PhO À from the metallacarboxylic acid. The step is moderately endergonic (DG ¼ +7.9 kcal mol À1 ), which originates from an unfavorable enthalpy contribution, although 1 D is stabilized by an intramolecular hydrogen bond between the COOH group and one nitrogen of the porphyrin ligand as indicated by a short N- H interatomic distance of 2.02Å. This step needs to overcome a sizeable barrier ( 1 TS3, DG ‡ ¼ +9.4 kcal mol À1 ) that mostly arises from the need of sufficient driving force associated with the proton transfer in 1 B (DH ¼ +7.3 kcal mol À1 , Table S10 †). Subsequently, the formation of complex 1 E from 1 D is exergonic (DG ¼ À4.2 kcal mol À1 ), wherein a strong enthalpic contribution is balanced by an unfavorable entropic term, owing to the association of two fragments ( 1 D and PhOH). No detectable kinetic barrier could be found for this step (Fig. S2 †). The next step that is composed of the C-O bond scission in 1 E and dissociation of the weakly bound H 2 O and PhO À is slightly exergonic by DG ¼ À2.7 kcal mol À1 . The tremendous entropy contribution arising from the dissociation of 1 E into three fragments ( 1 F, PhO À and H 2 O) offsets the positive enthalpy change, DH ¼ +13.8 kcal mol À1 , similar to the formation of 1 F in pathway I 0 . This transformation needs to pass through a barrier of +8.0 kcal mol À1 ( 1 TS4) that is on par with that of 1 TS2 in pathway I 0 . In analogy to the formation of 1 F in pathway I 0 , this barrier can be attributed to the signicant endothermicity of the cleavage of the C-O bond in 1 E (DH ¼ +6.5 kcal mol À1 , Table S10 †). However, although for both pathways, the barriers leading to 1 F are commensurate, the energy of 1 TS2 is +5.6 kcal mol À1 above that of 1 TS4. This difference largely arises from the prohibitive entropic term resulting from the association of 1 A with two PhOH molecules, because the enthalpy term of 1 TS2 is 4.4 kcal mol À1 lower than that of 1 TS4.
To investigate whether the second proton transfer is essential to the reaction, we examined another reaction channel, in which the C-O bond cleavage takes place at intermediate 1 D to release 1 F and a hydroxide ion (pathway III, Fig. S3 †) rather than a water molecule. The C-O bond cleavage is signicantly uphill (DG ¼ +15.2 kcal mol À1 ) due to a prohibitive positive enthalpic change (DH ¼ +23.6 kcal mol À1 ) and, more importantly, has to cross an unconquerable barrier of DG ‡ ¼ +43.3 kcal mol À1 ( 1 TS5 in Fig. S3 †). In comparison with pathways I 0 and II, the high enthalpic cost of the bond cleavage in the present case apparently stems from the absence of protons to trap the resulting OH À to produce H 2 O, a thermodynamic sink. As a consequence, the C-O bond breaking involves an exceedingly high kinetic barrier. Our nding thus revealed that the C-O bond cleavage is necessarily concurrent with the formation of a water molecule. Following this reasoning, pathway I advocated by Costentin and co-workers 8b in which 1 C directly dissociates into 1 F, PhO À , PhOH and OH À should involve a much higher barrier than that of 1 TS2 in pathway I 0 and can be safely ruled out as being a plausible mechanism.
As shown in Fig. 1, our theoretical results showed that the highest barrier in pathway I ( 1 TS2) is 7.9 kcal mol À1 higher than that in pathway II ( 1 TS3). Hence, the CO 2 reduction process is most likely to proceed along pathway II. To further strengthen this conclusion, we carried out calculations using the doublehybrid w-B2PLYP functional in conjunction with the Def2-QZVPP basis set (Table S10 †). The results indicate that 1 TS2 is 12.0 kcal mol À1 lower in energy than 1 TS3. The energy differences estimated by both density functionals considerably exceeds the typical error range of density functional theory computations. 50 This conrms that pathway II is indeed energetically more favorable, congruent with an earlier computational study. 10 However, the cited work did not investigate the singlet reaction, but only considered the reaction occurring on the triplet and quintet surfaces. Because the estimated barrier differences between the formation of the CO 2 adduct 1 A (DG ‡ ¼ +9.0 kcal mol À1 ), the rst proton transfer (DG ‡ ¼ +9.4 kcal mol À1 ) and the C-O bond cleavage in pathway II (DG ‡ ¼ +7.9 kcal mol À1 ) fall within the typical uncertainty range of computations with hybrid DFT functionals, 51 we cannot unequivocally determine which one is the rate-determining step of the entire catalytic process. Despite this uncertainty, our calculations strongly suggest that the C-O bond breaking involves a sizeable barrier and has to be concerted with a proton transfer, both notions consistent with earlier experimental studies. 7,8 To investigate whether our computational model is consistent with the observed kinetics of the reaction, we computed the turnover frequency of the reaction that requires a complete and precise energy landscape of all intermediates and transition states connecting them. 52 For pathways I 0 and II, the maximum turnover frequency estimated for three different phenol concentrations, [PhOH] ¼ 0.1, 0.75 and 3 M using the method of Costentin and co-workers 53 is summarized in Table 1 (see the ESI † for details). The turnover frequencies calculated for pathway II are in reasonable agreement with the experimental values, while those for pathway I 0 show substantial deviations. More importantly, pathway II is a rst-order reaction with respect to [PhOH], consistent with the experiment, whereas pathway I 0 is a second-order reaction. Therefore, pathway II qualitatively and quantitatively reproduces the experimental ndings, which thus further lends credence to the reliability of our theoretical results, a necessary premise for the following analyses aiming at obtaining qualitative insights into the reaction mechanism.
We also computationally investigated side reactions that lead to H 2 and formic acid (for details, see the ESI †). Typically, these reactions start with formation of a metal-hydride species rather than a CO 2 adduct. 54 However, the former transformation was observed to suffer from a prohibitive kinetic barrier, compared to the generation of 1 A. Furthermore, a previous study has pointed out that h 1 -OCO adducts can also be the precursors for producing formic acid. 39d As specied above, our calculations suggested that such an h 1 -OCO adduct probably cannot exist in the present case. Both ndings likely account for the observed high product selectivity of the CO 2 reduction catalyzed by 1 2À . Table 1 Calculated maximum turnover frequencies for pathways I 0 and II at three different phenol concentrations, following the method described by Costentin and coworkers. The experimental value obtained from foot-of-the-wave analyses by the same authors is also displayed for comparison 2.4 Â 10 2 s À1 3.9 Â 10 3 s À1 Pathway II 3.6 Â 10 4 s À1 2.8 Â 10 4 s À1 1.1 Â 10 6 s À1 Experiment 1.8 Â 10 3 s À1 1.5 Â 10 4 s À1 1 Â 10 5 s À1 Electronic structure analysis of the reaction In the following, the electronic-structure evolution of pathway II was scrutinized. The purpose is to correlate the electronic structure of 1 1 2À with its exceedingly high activity toward CO 2 functionalization, in particular, to pinpoint the role played by the non-innocent TPP ligand. As elaborated in our previous work, 16 the bonding of 1 1 2À is best described as an intermediate spin Fe II center (S Fe ¼ 1) antiferromagnetically coupled with a triplet TPPcc 4À diradical (S TPP ¼ 1), thereby yielding an overall singlet ground state (Fig. 2b). Specically, the Fe center features an electronic conguration of (d xy ) 2 (d z 2 ) 2 (d xz ) 1 (d yz ) 1 , and there are two electrons occupying the low lying TPP centered p* e g orbitals labelled as 1e g (x) and 1e g (y) (in the D 4h point group representation). The Fe d xz/yz and TPP 1e g magnetic orbitals form two spin-coupled pairs that represent two antiferromagnetic exchange coupling pathways. It should be noted that the fragment orbitals of Fe d xz/yz and TPP e g belong to the same representation (e g ) of the effective D 4h point group of 1 1 2À ; therefore, their interactions are symmetry-allowed as indicated by the computed considerable overlap of the two spin coupled pairs (0.33). If both fragment orbital sets transformed as different irreducible representations of the effective D 4h point group, their exchange interaction would feature ferromagnetic coupling on the grounds of the Goodenough-Kanamori rule 55 rather than antiferromagnetic coupling as determined experimentally. 16, 47 In line with this reasoning, the corresponding quintet state ( 5 1 2À ), which features ferromagnetic coupling of these two fragments, was estimated to lie 12.1 kcal mol À1 higher in energy than the singlet state.
As depicted in Fig. 2c, the driving force to generate 1 A largely stems from the s donation from the doubly occupied Fe d z 2 orbital to the vacant CO 2 in-plane p* ðp * ip Þ orbital. The electron acceptor is one of the lowest unoccupied molecular orbitals (LUMOs) of free CO 2 formed by an out-of-phase combination of the 2p z orbitals of the central C atom and the two terminal O atoms and has a larger lobe at the central C atom than those at the two terminal O atoms. Upon CO 2 binding, it gets considerably bent with an O-C-O angle of 130 compared to 180 for uncoordinated CO 2 molecules. As elaborated earlier, 39d such a geometric distortion not only signicantly decreases the energy of the CO 2 p * ip orbital, but also increases the C-p character in it. Thus, the energy difference between the CO 2 p * ip and Fe d z 2 orbitals drops, and their overlap becomes more favored. Consequently, both factors work in synergy to enhance the Fe-CO 2 interactions. Despite this, the resulting bonding MO, hereaer referred to as s Fe-C , contains only 32% CO 2 p* parentage; hence, the bonding remains quite weak, consistent with a moderate enthalpy change of À5.4 kcal mol À1 estimated for the formation of 1 A (vide supra). Nevertheless, this essentially dative interaction can be viewed as partial electron transfer from the Fe center to the CO 2 moiety. Interestingly, the MO analyses revealed that the formation of 1 A is accompanied by an intramolecular b electron transfer from TPP 1e g (y) to Fe d yz , whereas the other spin-coupled pair consisting of the Fe d xz and TPP 1e g (x) MOs remains intact. Different from 1 1 2À , the Fe d xz and d yz orbitals in 1 A are not energetically degenerate anymore, because the former is destabilized by the repulsion with the doubly occupied s orbitals of the two C-O bonds; while the latter is stabilized by its back-donation to the CO 2 out-ofplane p* orbital, the other LUMO of free CO 2 . Consequently, the electronic structure of 1 A is best formulated as having a low spin Fe I center (S Fe ¼ 1/2) that is bound to an approximately chargeneutral CO 2 and is antiferromagnetically coupled with a TPPc 3À radical (S TPP ¼ 1/2), thus giving an overall singlet ground state. More importantly, the TPP-to-Fe electron transfer mitigates the depletion of the electron density of the Fe center resulting from the Fe-to-CO 2 s donation. Therefore, the CO 2 association process does not engender substantial variation of the electron density of the Fe center.
Compared to uncoordinated CO 2 , the bent CO 2 moiety is primed for protonation to afford 1 D. Besides the inuence on its LUMO discussed above, the CO 2 bending also increases the energy of its highest occupied molecular orbital (HOMO), an antisymmetric combination of the two O lone pairs. 39d The interaction of the O lone pairs with a proton is therefore favored by the geometric distortion of the CO 2 moiety. Our theoretical results revealed that the protonation causes an increase of the CO 2 p * ip parentage in the doubly occupied s Fe-C MO from 32% in 1 A to 56% in 1 D (Fig. 2d), thereby indicating substantial covalent character for the Fe-CO 2 H interaction. Consequently, upon going from 1 A to 1 D, the calculated Fe-C CO 2 bond distance shortens from 2.02Å to 1.89Å. This bonding description suggests that, on average, the CO 2 ligand is reduced by one electron at the stage of 1 D. As such, the conversion of 1 A to 1 D is best described as a concerted proton-electron transfer (CPET) to the CO 2 ligand. 56 Moreover, the TPP ligand in 1 D returns to its usual state of a closed-shell dianion, because the protonation is companied by a b electron transfer from TPP 1e g (x) to Fe d xz . Due to the high covalency of the Fe-CO 2 H bond, 1 D has to be described as a resonance hybrid of a low spin Fe II ion (S Fe ¼ 0) bound to a À C(O)OH ligand and a low spin Fe 0 center (S Fe ¼ 0) coordinated by a + C(O)OH ligand. In analogy to the preceding step, the TPP-to-Fe electron transfer balances the Fe-to-CO 2 electron transfer, and the electron density of the Fe center remains largely unchanged. The MO diagram of 1 TS4 (Fig. S8 †) suggests that, over the course of the heterolytic C-O bond breaking, the C-O s bonding orbital evolves into a lone pair of the O atom in the H 2 O product. Accordingly, the resulting C atom formally becomes a carbocation center, and due to its exceedingly high electron-accepting capability, the s Fe-C MO of 1 F acquires more C character (61%) as the expense of the weight of the Fe d z 2 atomic orbital dropping to 35% (Fig. 2e). Hence, at this stage, the two-electron transfer from the Fe d z 2 orbital to the CO 2 p * ip orbital is largely completed. Of note, 1 F also features strong back-donation from the doublyoccupied Fe d xz and d yz orbitals to the C-O p* orbitals. Thus, 1 F is best described as containing a low spin ferrous center bound to a CO ligand and a closed-shell porphyrin dianion.

The role of the non-innocent TPP ligand in the reaction
In the present case, the active species 1 1 2À is formed by a TPP centered two-electron reduction of 3 1 at a mild potential.
Because the electron acceptors are the highly delocalized TPP centered 1e g orbitals, the additional electron density is distributed to the twenty-four atoms of the porphyrin ligand. Therefore, the reduction does not signicantly escalate the interelectronic repulsion of all delocalized p electrons of the reduced TPP 4À ligand. For the same reason, this electron transfer is subjected to a low degree of geometric distortions and hence a reduced reorganization energy. This contrasts with metal centered redox processes for which much more compact and localized d orbitals function as redox active orbitals; consequently, reduction typically causes a much higher gain in interelectronic repulsion. Likewise, a greater reorganization energy is anticipated because of the more signicant distortions of the rst coordination sphere of the metal center. Typically, two-electron reduction processes of 3d transition metal ions cannot readily occur, because the required reduction potentials are oen exceedingly negative. The resulting complexes are likely to be highly reactive and may involve various facile sidereactions or deactivation pathways for electron-richer metal centers, such as H 2 or HCOOH generation (see the ESI †), instead of participating in the target reaction. Therefore, the non-innocent nature of TPP explains why 1 1 2À can be generated at a mild potential and its catalyzed reaction exhibits high faradaic efficiency for CO production.
Although the reducing equivalents are stored on the TPP ligand, CO 2 must associate with the metal center for further activation. This is due to the completely delocalized nature of the p-electrons; because none of the C atoms of TPP possesses sufficient electron density allowing for facile CO 2 binding. In this regard, the Fe center is superior, because its high-lying doubly populated d z 2 orbital has an appropriate shape and can efficiently overlap with the CO 2 p * ip orbital. 39d Hence, the Fe center should be the active site for CO 2 functionalization. However, the required reducing equivalents are stored at the ligand.
The above described situation gives rise to an intriguing question of how the metal center communicates with the ligand in order to efficiently transfer the reducing equivalents to the CO 2 moiety. As elaborated above, the TPP to CO 2 two-electron transfer required for conversion of CO 2 to CO is achieved by two simultaneous electron transfer events. One is the two-electron transfer from Fe d z 2 to CO 2 p * ip , and the other is the two-electron transfer from TPP 1e g to Fe d xz/yz . Both electron-transfer events are coupled in such a way that the electron density of the Fe center does not vary signicantly throughout the reaction. This reduces the energy resulting from the adjustments in the rst coordination sphere of the Fe center, while maintaining the electron donating abilities of the Fe center, thereby preventing the formation of highly energetic intermediates or transition states. This analysis underscores the fundamental importance of the non-innocence of the TPP ligand and its cooperativity with the Fe center to the reactivity, which, at least in part, rationalizes why 1 1 2À exhibits the exceedingly high catalytic activity towards CO 2 reduction.
What happens if the TPP-to-Fe electron transfer cannot take place? As detailed in the ESI, † the triplet state of [Fe(TPP)] 2À ( 3 1 2À ) was computed to lie 5.7 kcal mol À1 above 1 1 2À . It also contains an intermediate spin ferrous center but interacts with an open-shell singlet TPPcc 4À diradical with one a electron and one b electron occupying its 1e g (x) and 1e g (y) orbitals, respectively (Fig. S5 †). In analogy to the electronic structure changes found for the singlet reaction, CO 2 binding to 3 1 2À is also driven by a weak s donation from Fe d z 2 to CO 2 p * ip , concomitant with a spin-allowed electron transfer of a b electron from TPP 1e g (y) to Fe d yz . Consequently, the triplet Fe-CO 2 adduct ( 3 A) is best described as having a low spin Fe I center ferromagnetically coupled with a TPPc 3À radical, and its formation was estimated to be thermodynamically equally probable (DG ¼ À0.2 kcal mol À1 ) with that of 1 A (DG ¼ +2.5 kcal mol À1 ) within the error range of DFT computations. Subsequently, protonation of 3 A to yield 3 D indeed induces further electron transfer from Fe to CO 2 , but unlike on the singlet surface, the electron transfer from TPP 1e g (x) to Fe d xz cannot occur because this process is spin-forbidden. Hence, upon going from 3 A to 3 D, the electron density at the Fe center is signicantly depleted. Congruent with this reasoning, generation of 3 D was calculated to be uphill to DG ¼ +10.0 kcal mol À1 , whereas that of 1 D is only DG ¼ +1.1 kcal mol À1 . In fact, the cost for the formation of 3 D is even greater than the highest barrier in the singlet pathway. As such, these ndings demonstrate that synchronization of the TPP-to-Fe electron transfer with the Fe-to-CO 2 electron transfer is fundamentally crucial to the reaction kinetics. How does the system synchronize the TPP-to-Fe electron transfer with the Fe-to-CO 2 electron transfer? First, the TPP e g and Fe d xz,yz fragment orbitals have comparable energy, otherwise the electron transfer would not be thermodynamically feasible. Most importantly, both sets transform as the same irreducible representation of the effective D 4h point group of 1 1 2À . Consequently, they form two spin-coupled pairs with considerable overlaps. The antiferromagnetic coupling between the ligand and the metal center lowers the energy of the singlet energy surface compared to that of higher spin multiplicities and ensures that the electron transfer does not incur an energetically unfavorable spin crossover. 57 As seen in Fig. 3, along the reaction coordinates of the formation of 1 A, the sum of Fe and CO 2 populations of the b-1e g (x) magnetic orbital slowly increases from about 6% in 1 1 2À to 20% in 1 TS1 and then increases drastically and nally reaches 98% in 1 A. Such a continuous electron transfer minimizes the variation of electron density of the metal center along the reaction coordinates. Consequently, the loss of Fe electron density due to the Fe to CO 2 transfer is immediately compensated by an increasing TPP to Fe electron delocalization in the magnetic orbitals, which likely lowers the activation barrier by increasing the donating abilities of the metal center, even when the complete ligand-tometal electron transfer lacks signicant thermodynamic driving forces. Hence, the antiferromagnetic coupling is pivotal in synchronizing the two electron-transfer events.
The above analyses correlate the electronic structure of 1 1 2À with its high activity. In fact, non-innocent ligands were found for a range of CO 2 reduction catalysts. Besides 1 1 2À , we have analyzed the electronic-structure evolution in the course of the CO 2 -to-CO reactions mediated by at least ten related catalysts (Scheme 2) that are also supported by non-innocent ligand platforms (for details, see the ESI †). For all these systems, the metal center acts as the active site for CO 2 functionalization, but the non-innocent ligand acts as the electron reservoir. Like 1 1 2À , this requires the metal-to-CO 2 electron transfer to be coupled with the ligand-to-metal electron transfer. Our results demonstrated that the main differences among them lie in the nature of the chemical steps accomplishing the ligand-to-metal electron transfer, according to which these catalysts are divided into three categories.
Category I catalysts include 1 1 2À (Fig. 2), 2 2 + (Fig. S9 †) 12 and 3 3 0 (Fig. S10 †). 19 The active species consists of a metal center in its usual oxidation state that is antiferromagnetically coupled with a one-( 2 2 + ) or two-electron reduced ligand diradical ( 1 1 2À and 3 3 0 ). This category is distinguished by the ligand-to-metal electron transfer being achieved by two separate one-electron transfer events; one takes place during the CO 2 adduct formation step, and the other during the rst protonation step.
Category II catalysts consist of 2 4 0 , 2 5 0 and 2 6 0 , 12-14 which either feature a metal center antiferromagnetically coupled with a two-electron reduced ligand in a triplet state ( 2 4 0 , 2 5 0 ), or a metal center coupled with a doubly reduced ligand in a singlet state ( 2 6 0 ). Irrespective of the electronic structures, the electron transfer pathways are identical for these three catalysts. The characteristics of category II catalysts are that, for two separate ligand-to-metal electron transfer events, one occurs during the CO 2 adduct formation step, and the other during the nal C-O bond cleavage step. Here we take the reaction with 2 4 0 as an example to discuss the electronic-structure evolution along the reaction coordinate, and summarize those for 2 5 0 and 2 6 0 in the ESI (Fig. S11 and S12 †).
The reaction mechanism of selective CO 2 to CO conversion catalyzed by 2 4 0 under wet conditions has been subjected to extensive computational and experimental studies. 14 It was found that 2 4 0 rst binds CO 2 to form a h 1 -CO 2 adduct 2 G, which then undergoes protonation to yield metallacarboxylic acid 2 H, and the C-O bond is cleaved concomitant with the second proton transfer, furnishing metal-carbonyl intermediate 2 I and releasing a water molecule.
According to the reported reaction pathway 14 shown in Fig. 4a, we analyzed the electronic structure changes during the reaction. Our present investigation supports the notion that the pyridine-diimine ligand in 2 4 0 is non-innocent, consistent with earlier studies. 14c,18,58,59 As shown in Fig. 4b, 2 4 0 was found to be composed of a low spin Co II (S Co ¼ 1/2) antiferromagnetically coupled with a N 4 Hcc 2À diradical (S N 4 H ¼ 1). This bonding description indicates that, similar to TPP 2À , the N 4 H 0 ligand can harbor additional two electrons in its conjugated p system. Our MO analysis (Fig. 4b) suggests that 2 4 0 contains a Co II center featuring an electron conguration of (d xy ) 2 (d z 2) 2 (d xz ) 2 (d yz ) 1 and two delocalized unpaired electrons populating the N 4 H p* based 1a 0 and 1a 00 MOs, labelled according to their symmetry representation of Cs point group. Of note, besides the N 4 H p * 1a 00 fragment orbital (71%), the Co d yz atomic orbital (29%) makes a sizeable contribution to the 1a 00 MO, because both transform as the A 00 representation of Cs point group. Consequently, the magnetic orbitals of N 4 H p * 1a 00 and Co d yz overlap signicantly, hence leading to strong antiferromagnetic coupling between the ligand and the metal center.
Upon formation of 2 G from 2 4 0 , the doubly-occupied Co d z 2 orbital slightly mixes with the unoccupied CO 2 p * ip orbital. The resulting Co-CO 2 bond is thus essentially dative, as suggested by the estimated dominant Co percentage in the s Co-C MO (77% Co, 23% CO 2 , Fig. 4c). This step is coupled with an electron transfer from N 4 H p * 1a 00 to Co d yz such that the resulting intermediate ( 2 G) is best described as a low-spin (S Co ¼ 0) Co I center weakly bound to a CO 2 0 ligand and to an N 4 Hc À radical (S N4H ¼ 1/2). The subsequent conversion of 2 G into 2 H substantially increases the covalency of the Co-C CO 2 H interaction, as suggested by s Co-C containing nearly identical percentages of Co and CO 2 H (43% Co and 51% CO 2 H, Fig. 4d). Hence, this step can be viewed as the rst Co-to-CO 2 electron transfer. Because s * CoÀC and N 4 H p * 1a 0 belong to the A 0 representation of Cs point group, both fragment orbitals can interact with each other, and the resulting 1a 0 MO acquires sizeable character of s * CoÀC (Co d z 2 44% and CO 2 H 10%). This orbital mixing can be interpreted as a partial electron transfer from the N 4 H ligand to the Co center. The nal C-O bond heterolytic cleavage to afford 2 I and H 2 O further increases the CO character in s Co-C (26% Co and 70% CO, Fig. 4e). Therefore, it is reasonable to consider this step as the second Coto-CO 2 electron transfer, accompanied by completion of the N 4 H p * 1a 0 -to-s * CoÀC electron transfer. Consequently, this results in a Co II center bound to a carbonyl ligand in 2 I.
The reaction entails two intramolecular electron transfer events: a metal-to-CO 2 transfer that is affected by s donation from the doubly-occupied Co d z 2 to the unoccupied CO 2 p * ip orbital, and a N 4 H-to-Co electron transfer that makes up for the loss of electron density on the metal center. Both events are coupled efficiently via the mixing of the ligand-centered electron donating orbitals (N 4 H p * 1a 00 and p * 1a 0 ) and the metal-based electron accepting orbitals (Co d yz and d z 2) of the appropriate symmetry and comparable energies. This orbital mixing gives rise to a spin-coupled orbital pair involving Co d yz and N 4 H p * 1a 00 and a singly-occupied delocalized MO composed of N 4 H p * 1a 0 and s * CoÀC . The rst electron transfer route involving the spincoupled pair is the same as that found for the reaction with 1 1 2À . On the other hand, the second pathway chooses s * CoÀC instead of Co d xz , because Co d xz is doubly populated in 2 4 0 , and s * CoÀC is the lowest-lying vacant Co d orbital besides Co d yz . However, due to the high energy of s * CoÀC , a signicant depletion of the electron density on the metal center is required to give this electron transfer a sufficient thermodynamic driving force. Hence, unlike in 1 1 2À , the transfer is not yet complete in 2 H.
It was found in the 1980s that 1 7 À and its derivatives can catalyze selective CO 2 -to-CO reduction, and the reaction exhibits one of the highest turnover frequencies reported for homogeneous catalysis (Table S1 †). 15h The mechanism of CO 2 reduction by 1 7 À has been extensively studied, particularly in the work published by  In their original study, it was shown that the inclusion of a K + counterion in the vicinity of 1 7 À drastically improved the description of the redox Fig. 4 The proposed catalytic cycle of CO 2 -to-CO conversion catalyzed by 2 4 0 (a), 14e and the electronic structures of the intermediates 2 4 0 (b), 2 G (c), 2 H (d) and 2 I (e). Dashed straight lines between atoms represent hydrogen bonds. Electrons involved in the ligand-to-metal intramolecular transfer are shown by red arrows. Electrons involved in the metal-to-CO 2 electron transfer are shown by green arrows. The weight of Co and CO 2 /CO 2 H/CO in the s Co-C molecular orbital is displayed in green boxes. In 2 H, the weight of Co and N 4 H in the singly-occupied 1a 0 molecular orbital is displayed in red boxes. For clarity, all hydrogens are omitted except the hydrogen of the CO 2 H moiety and that involved in the intramolecular hydrogen bond between the CO 2 H moiety and the amine of the N 4 H ligand.
potentials associated with the formation of the active species. 15d Hence, the active species was proposed to be the ion pair 1 7 À -K + (Fig. 5a), rather than anionic complex 1 7 À . 15d The reduction of CO 2 is initiated by binding of CO 2 to 1 7 À -K + to form an h 1 -CO 2 adduct 1 J, which is then protonated to afford carboxylic acid 1 K. Subsequently, 1 K undergoes a second reduction at the electrode, and the C-O bond breaking is concomitant with a second Fig. 5 The proposed catalytic cycle of CO 2 -to-CO conversion catalyzed by 1 7 À (a), 15d and the electronic structure of the intermediates 1 7 À -K + (b), 1 J (c), 1 K (d) and 2 L (e). Electrons involved in the ligand-to-metal and metal-to-CO 2 intramolecular transfer are shown by green arrows. The weight of Re and bpy in the 1p* molecular orbital (in 1 7 À -K + ) and the weight of Re, bpy and CO 2 /CO 2 H/CO in the s Re-C bonding orbital (in all other intermediates) are displayed in green boxes. For clarity, all hydrogens are omitted except the hydrogen of the CO 2 H moiety. proton transfer, ultimately yielding 2 L and releasing a water molecule and the K + counterion.
As the electronic structure changes of the proposed reaction pathway have been elaborated previously, 15d here we recapitulate only important features in order to compare them with the aforementioned cases. Earlier experimental and computational studies 15e,60 revealed that the diamagnetic ground state of 1 7 À is best formulated as a low spin Re I center (S Re ¼ 0) ligated by a singlet bpy 2À ligand. Binding of K + to 1 7 À does not discernibly change the electronic structure. Specically, the Re center of 1 7 À -K + features an electronic conguration of (d xy ) 2 (d xz ) 2 (d yz ) 2 , and its HOMO (1p*), albeit with dominant bpy p* parentage (74%), contains nonnegligible Re d z 2 character (16%) (Fig. 5b). The mixing of these two fragment orbitals is symmetry-allowed, because both belong to the 1A 0 representation of Cs point group. Furthermore, the Re center moves out of the bipyridine plane, allowing a stronger overlap between the two fragments.
As CO 2 approaches the Re center of 1 7 À -K + to form 1 J, twoelectron transfer from bpy p* to the formally empty Re d z 2 orbital takes place, and simultaneously the latter orbital donates the electron density to the CO 2 p * ip orbital (Fig. 5c). The resulting bonding s Re-C MO of 1 J has a 59% contribution from the CO 2 p * ip orbital. Thus, during this elementary step, on average, approximately one electron is transferred from the ligand to CO 2 via the metal center. Due to the substantial covalent character of the Re-CO 2 interaction, the electronic structure of 1 J is thus best described as a resonance hybrid between a Re I center (S Re ¼ 0) bound to a CO 2 2À ligand and a Re ÀI ion (S Re ¼ 0) interacting with a CO 2 0 moiety. As shown in Fig. 5d, the subsequent protonation further polarizes the Re-C bond in 1 K as indicated by the increased -CO 2 H weight in the s Re-C orbital (Re d z 2 26% and CO 2 H 66%). Finally, an outersphere electron transfer from the electrode to the bpy p* orbital occurs, along with the C-O bond cleavage, thereby yielding intermediate 2 L and releasing a water molecule. Again, the reaction with 1 7 À also involves two coupled metalto-CO 2 and ligand-to-metal electron transfer events, which shi the two electrons stored on bpy directly to the CO 2 ligand while leaving the Re oxidation state essentially unchanged. The coupling of the two electron transfer events is accomplished by mixing of the bpy p* (electron donor) and Re d z 2 (electron acceptor) fragment orbitals, because of their appropriate symmetry and considerable overlap. Different from 1 1 2À , in the present case, the orbital mixing leads to a doubly occupied delocalized MO formed by Re d z 2 and bpy p* rather than two spin-coupled pairs. Because the Re-CO 2 interaction lowers the energy of the Re d z 2 orbital, CO 2 association triggers the direct bpy-to-Re two-electron transfer. This contrasts with the two categories discussed above, whose ligand-to-metal electron transfer proceeds via two separate events.

Basic electronic structure requirements for catalysts with noninnocent ligands
All the CO 2 -to-CO catalytic reactions studied above involve two synchronized electron transfer events: (1) a metal-to-CO 2 two-electron transfer, and (2) a ligand-to-metal one-or two-electron transfer. The former is always effected mainly via s-donation of two electrons from the doubly-occupied metal-centered d z 2 orbital to the empty CO 2 p* orbital. The latter transfer connects highly delocalized occupied ligand p* orbitals with formally unoccupied metal d orbitals. The ligand-metal cooperativity is at the core of the reactivity for all these complexes, thereby ensuring that the electrons stored on the ligand are transferred to CO 2 via the metal center. How does the system ensure the synchronization of the two electron transfer events? All of the investigated catalysts feature strong interactions between the ligand-based electron-donating p* orbital and the metal-based electron-accepting d-orbital, which give rise to molecular orbitals delocalized over the ligand platform and the metal center. In 1 1 2À , the strong antiferromagnetic coupling of the TPP e g orbitals with the d xz,yz atomic orbitals yields the delocalized 1e g MOs. In 2 4 0 , the N 4 H p * 1a 00 fragment orbital mixes with the Co d yz atomic orbital, and at the later stage, the N 4 H p * 1a 0 fragment orbital interacts with the s * CoÀC fragment orbital to give the orbitals 1a 00 and 1a 0 , respectively. In 1 7 À , the bpy p* fragment orbital mixes with the Re d z 2 orbital to generate the 1p* molecular orbital. Irrespective of different interaction modes, the coupling of ligand-and metalbased orbitals is pivotal in ensuring that even marginal losses of the electron density on the metal center is compensated by a continuous ligand-to-metal electron delocalization, as found for the case of 1 2À . This is because the aforementioned orbitals have the same symmetries and similar energies; otherwise, such coupling could not happen.
This work is perfectly in line with the earlier studies on the role of ligand non-innocence in general catalysis. [22][23][24][25] In terms of reactivity, although ligand-centered mechanisms have been occasionally reported, 61,62 in the vast majority of cases, the reactions completely occur at the metal center. In the latter situations, the ligands serve as an "electron reservoir", thus enabling the metal center to maintain its common oxidation state as the reaction progresses, 63,64,68 and the electrons stored on the ligand are transferred to the metal center during the reaction. 22,[63][64][65] Again, such catalysts also feature signicant mixing between the ligand-based redox-active orbitals and unoccupied metal dorbitals, 66 in analogy to our present analysis.
Taken together, for all systems under investigation, noninnocent ligands endorse the following properties to CO 2 -to-CO electrocatalysts. First and foremost, ligand-centered reductions enhance the stability of the active species by providing low-lying redox-active orbitals. By contrast, metal-centered reduction would involve the formation of highly reactive species which are likely deactivated by side reactions or initiate unwanted reactions at electron-rich metal centers, like H 2 or HCOOH production. Furthermore, the ligand-metal cooperativity is essential to the kinetics of the reaction. Owing to the synchronization of both electron transfer events, the metal oxidation state remains unchanged throughout the reaction. In the absence of such synchronization, the reaction would necessarily generate high-energy intermediates as exemplied by the triplet reaction of 3 1 2À .
General molecular structure requirements for catalysts with non-innocent ligands So, how can one design catalytic systems that take the best advantage of the aforementioned properties? First of all, systems with open coordination sites are preferred, which facilitates the s-bonding with CO 2 . This step oen lacks suitable driving force, 10,15d,20 and, in particular, ligand substitution by CO 2 can hardly occur. In this regard, four-coordinated planar or vecoordinate square-pyramidal complexes are excellent candidates.
The synchronization of the ligand-to-metal and metal-to-CO 2 electronic transfer is also dependent on the coupling between the ligand and the metal center, which requires orbitals of similar energies and the same symmetry. Typically, highly conjugated p-systems have a wide range of available MOs, and their varying energies are more likely to match those of the metal d-orbitals. These set orbitals also feature various symmetries, which ensures that such coupling is symmetry allowed. For these two reasons, highly conjugated ligand platforms are clearly excellent candidates. Furthermore, in order to maximize overlap between the lobes of the interacting ligandand metal-based fragment orbitals, the atoms of the ligand interacting with the metal center should employ their p z orbitals in the p-system. For instance, conjugated sp 2 nitrogen donors or carbenes are excellent candidates.
Lastly, the choice of the metal center inuences the metalligand cooperativity. The second or third row transition metals have larger, less compact d orbitals than rst-row congeners and are likely to delocalize more electron density to the ligand. For instance, the molecular orbital of [Mn(bpy)(CO) 3 ] À is much more centered at the metal (24%, Fig. S13 †) than its rhenium counterpart, [Re(bpy)(CO) 3 ] À (16%, Fig. 5). For the same reason, 4d and 5d metals are also expected to donate more electron density to the CO 2 ligand, thus facilitating CO 2 reduction. This, at least in part, explains why rhenium-bipyridine catalysts typically exhibit higher catalytic performances than their manganese counterparts.
In a given row of the periodic table, metals on the le tend to be less electronegative than those on the right. Consequently, the latter are expected to donate less electron density to the CO 2 molecules than the former. Besides this, the number of valence d-electrons also plays a signicant role in the reactivity. The number differs among metals of the same oxidation state; therefore, the available intramolecular electron transfer pathways also change, leading to drastic differences in mechanisms and catalytic performances. For instance, [Fe(qpy)] belongs to category I, while [Co(qpy)] belongs to category II. Because the d xz orbital is doubly-occupied in the latter, one of the electron transfer pathways available in the former case is inactivated in the latter, which results in the shi from category I to category II. Furthermore, relative to [Fe(qpy)], [Co(qpy)] exhibits a better catalytic performance (Table S1 †). In sharp contrast, [Fe(TPP)] by far outperforms [Co(TPP)], although both Fe compounds feature an analogous electronic conguration and so do the Co compounds. 67 Clearly, more detailed investigations are required to pinpoint the exact relationship between the type of metalligand cooperativity and the catalytic performance.

Conclusion
Our computational investigation of the CO 2 -to-CO reduction reaction catalyzed by 1 1 2À proposes the following mechanism: (1) Formation of the adduct, (2) protonation of the adduct, (3) cleavage of the C-O bond, and (4) reduction of the metalcarbonyl and release of a CO molecule. We found a satisfying agreement between the predicted mechanism and the available thermodynamic and kinetic data. In particular, we found that the highest barrier was indeed compatible with the observed turnover frequency of this catalytic reaction.
Most importantly, our present investigation provides a profound understanding of the structure-activity relationship of 1 1 2À . Indeed, the reaction involves two electron transfer events: (1) a metal-to-CO 2 transfer and (2) a ligand-to-metal electron transfer. These two electron transfer events are synchronized in such a way that the electron density of the metal center hardly varies along the reaction coordinates. It was shown that the synchronization of the two electron transfer events is fundamental to the reactivity, because it circumvents the formation of intermediates having highly electron-rich or -decient metal centers. Optimal synchronization is realized by the antiferromagnetic spin coupling between the porphyrin ligand and the metal center, which serves as a conduit between them; consequently, the variation of electron density on the metal center is minimized.
Comparison of the reactivity of 1 2À with those of ten related catalysts with non-innocent ligand platforms enables the generalization of the feature of ligand non-innocence in CO 2 reduction observed for 1 2À . On the basis of these ndings, we propose that ligand non-innocence in CO 2 reduction plays a central role in ensuring a high selectivity and stability, while maintaining fast kinetics through ligand-metal cooperativity. Finally, fundamental requirements to design catalysts with noninnocent ligands are proposed.

Author contributions
S. Y. and F. N. conceived and supervised the project; M. T. carried out theoretical computations. All authors wrote the manuscript.

Conflicts of interest
The authors declare no conict of interest.