The Magnetic Behaviour of CoTPP Supported on Coinage Metal Surfaces in the Presence of Small Molecules: A Molecular Cluster Study of the Surface trans-Effect

Density functional theory, combined with the molecular cluster model, has been used to investigate the surface trans-effect induced by the coordination of small molecules L (L = CO, NH3, NO, NO2 and O2) on the cobalt electronic structure of cobalt tetraphenylporphyrinato (CoTPP) surface-supported on coinage metal surfaces (Cu, Ag, and Au). Regardless of whether L has a closed- or an open-shell electronic structure, its coordination to Co takes out the direct interaction between Co and the substrate eventually present. The CO and NH3 bonding to CoTPP does not influence the Co local electronic structure, while the NO (NO2 and O2) coordination induces a Co reduction (oxidation), generating a 3d8 CoI (3d6 CoIII) magnetically silent closed-shell species. Theoretical outcomes herein reported demonstrate that simple and computationally inexpensive models can be used not only to rationalize but also to predict the effects of the Co–L bonding on the magnetic behaviour of CoTPP chemisorbed on coinage metals. The same model may be straightforwardly extended to other transition metals or coordinated molecules.


Introduction
Transition metal porphyrinato (MP) and phthalocyaninato (MPc) complexes hold a prominent position among countless adsorbates because of their unique characteristics. Indeed, their conformational flexibility allows them to adopt different structural arrangements on diverse substrates, which may significantly influence their properties. Moreover, the metal centre occupying either the P 2− or the Pc 2− four-fold coordinative pocket often plays an active role in catalysis and sensors [1][2][3][4][5][6][7], while the M nd m configuration drives the corresponding magnetic behaviour [8][9][10][11]. All these features make surface-supported MP and MPc appealing for technological applications, including chemical sensors [11,12], storage [13], spintronic/magnetic devices [14,15], and heterogenous catalysis [12,16]. With specific reference to spintronic applications, the ability to finely tune the adsorbate/substrate spin interaction is crucial and demands a detailed understanding of the interphase electronic properties. In this context, recent studies [17] have also shown that a chemical stimulus, such as the occupation of a M coordinative vacancy by a small Scheme 1. A schematic representation of the molecular clusters adopted to model the S-CoTPP, the CoTPP-L, and the S-CoTPP-L interactions. Grey, white, blue, light blue, orange, and green spheres represent C, H, N, C, MS, and the whole L molecule, respectively. A schematic sketch of isolated and interacting systems is reported in the inset.

Computational Details
Geometrical parameters of the adopted clusters have been optimized without any constraint by exploiting the Amsterdam Density Functional (ADF) suite of programs [34,35]. Scalar relativistic (SR) spin-restricted/spin-unrestricted calculations have been carried out by adopting the Zeroth Order Regular Approximation (ZORA [36,37]), by using the GGA functional BP86 [38,39], by employing a triple-ζ with one polarization function (TZP) Slater-type basis set [40] for all the atoms, and by freezing throughout the calculations the C, N, and O 1s atomic orbital (AO), the Co and Cu 1s-2p AOs, the Ag 1s-3d AOs, and the Au 1s-4d AOs. Incidentally, the same computational set up has been successfully adopted to investigate the ground state properties of a quite large number of M complexes having either Pc 2− or TPP 2− as ligands [15,17,[41][42][43][44][45]. 3D contour plots (CPs) have also been obtained to acquire information about the localization and the character of the frontier MOs. Finally, bonding energies (BEs) have been analysed by means of Ziegler's extended transition state [46] method. According to this scheme, BEs may be written as (1) where, ∆E es , ∆E Pauli and ∆E orb represent contributions due to the pure electrostatic interaction, the Pauli repulsion (hereafter ∆E es + ∆E Pauli = ∆E sr , the steric repulsion), and the orbital interaction, respectively. The last term ∆E prep provides information about the energy required to relax the geometrical structure of the CoTPP and L fragments to the geometry they assume in the final cluster. In this regard, it is noteworthy that atomic fragments from which a molecule/cluster is built must be spin-restricted [35]. Both MS-CoTPP and MS-CoTPP-L BEs have been then corrected by ∆E MS sp , which corresponds to the −∆BE between a spin-unrestricted and a spin-restricted atomic fragment. Amendments to BEs due to the basis set superposition error have been systematically ignored as their contribution is known to be minute [47].

Results and Discussion
The competition between the S-Co and Co-L interactions, as well as its influence on the CoTPP magnetic properties, has been investigated by adopting the following three models: (i) MS-CoTPP (MS = Cu, Ag, Au), representing the surface-supported CoTPP; (ii) CoTPP-L (L = CO, NH 3 , NO, NO 2 , O 2 ), corresponding to the diverse adducts herein considered; and (iii) MS-CoTPP-L, representing the interphase generated by coordinating L to the surface-supported CoTPP. Optimized Cartesian coordinates of the free L molecules, of the free CoTPP complex, and of the MS-CoTPP, CoTPP-L, and MS-CoTPP-L clusters are reported in Tables S1-S29 of the Supplementary Materials (SM), while BEs and oxidation  states for each molecule/adduct/cluster herein considered are collected in Tables S30-S38 of the SM.

CoTPP on Cu, Ag and Au Substrates
The S-CoTPP interaction has been herein modelled by considering the direct interaction of Co with a single Cu, Ag, or Au atom, labelled MS (see Scheme 1). Even though perfectly aware that (i) CoTPP on Ag(111) occupies the surface hollow sites [48] and (ii) CoP [49] and CuP [50] on Cu(111) sit on the bridge sites, similarly to Hieringer et al. [25], who tested the BE of CoTPP on diverse Ag chemisorption sites finding BE minute variations, we decided to choose the on-top site for the sake of simplicity and to take full advantage of symmetry. As such, it is noteworthy that Buimaga-Iarinca and Morari [51] explored in great detail the effect of translation on the BE for MP adsorbed on Ag(111), finding a tiny energy dispersion (0.1 eV) among the different adsorption sites.
The neutral Cu, Ag, and Au atoms have a 3d 10 4s 1 , 4d 10 5s 1 , and 5d 10 6s 1 electronic configuration, respectively, while the low-spin (LS) Co II species occupying the centre of the TPP 2− coordinative pocket carries a single unpaired electron in the Co 3d z 2 -based molecular orbital (MO) [52]. Thus, the C 4v [53] MS-CoTPP cluster may have either 0 or 2 unpaired electrons. In the absence of any constraint on the MS-Co internuclear distance, the antiferromagnetic coupling between the two unpaired electrons is estimated to be significantly and systematically more stable than the ferromagnetic one by 0.71, 0.87, and 0.56 eV for MS = Cu, Ag, and Au, respectively. Moreover, when relativistic effects are taken into account [54], the MS-Co internuclear distances and the MS-Co BEs corresponding to the spin-paired configuration (see Table S31 of the SM) have the well-known trend within the triad, thus indicating that, among the MS-CoTPP interactions, the Ag-CoTPP one is the weakest and most labile. Incidentally, MS-Co BEs amount to 1.17, 0.91, and 1.11 eV for MS = Cu, Ag, and Au, respectively (see Table S31 of the SM).
Although of some interest to grasp the main features of the MS-CoTPP interaction, BEs and internuclear distances are unable to rationalize the CoTPP "switch on" → "switch off" magnetism upon chemisorption on Cu [26,28,29,33] and Ag [20,25,26,30,31,33], as well as the absence of any CoTPP demagnetization upon chemisorption on Au [18,20,21,32,33]. The thorough analysis of the MS-CoTPP frontier MOs turns out to be a Hobson's choice to obtain a rationale for the experimental trend. The MS-CoTPP interaction may be roughly described by a two-electrons/two-orbitals model involving the Co 3d z 2 -based singly-occupied MO (SOMO) and the MS (n + 1)s AO (n = 4, 5, and 6 for Cu, Ag, and Au, respectively). The analysis of their in-phase and out-of-phase combinations ( MS-Co σ and MS-Co σ* in Figure 1) suggests that, upon chemisorption of CoTPP on Cu and Ag, a Co II + MS 0 → Co I + MS I pseudo redox reaction takes place (see Figure 1D). Consistently with the presence of a pseudo redox reaction involving a net Cu 0 → Co II /Ag 0 → Co II charge transfer, the completely occupied Cu-Co σ and Ag-Co σ combinations are mainly localized on the Co 3d z 2 -based MO, while the empty Cu-Co σ * and Ag-Co σ * ones are strongly localized (>50%) on the Cu 4s-based and the Ag 5s-based MO, respectively. As such, it can be also useful to mention that the Cu and Ag Hirshfeld charges (Q) [55] of the Cu-CoTPP and Ag-CoTPP C 4v clusters amount to 0.19 and 0.24, respectively (see Table S31 of the SM). Incidentally, the LS state foreseen by the molecular cluster model herein adopted and implying the presence of a pseudo 3d 8 Co I species well agrees with DFT periodic calculations modelling the CoTPP chemisorption on Cu and Ag surfaces [20,25,26,[28][29][30][31]33]. A change of scenery takes place when MS = Au; besides the comparable localization percentage of the Au-Co σ * MO on the Co 3d z 2 and Au 6s AOs (37% and 42%, respectively), the Au-CoTPP Au Q is close to zero (0.05). In other words, no Au 0 → Co II charge transfer able to "switch off" the CoTPP magnetization upon chemisorption on Au seems to be present [18,21,32,33]. In summary, the obtained results based on the molecular cluster model provide a rationale of the magnetic behaviour of CoTPP upon chemisorption on coinage metals. Notably, such an approach is undoubtedly simpler and computationally less expensive than periodic DFT calculations.

CoTPP-L Adducts (L = CO, NH 3 , NO, NO 2 , O 2 )
The L selection has been determined by the presence in the literature of experimental and theoretical data pertaining to the CoTPP-L adducts [24,25,33]. The L herein considered may be divided in two groups according to their diamagnetic (CO and NH 3 , hereafter 0 L) or paramagnetic (NO and NO 2 , 1 L; O 2 , 2 L) nature, where the superscripts 0, 1, and 2 simply refer to the number of unpaired electrons carried by L. The valence manifold of the CoTPP-0 L adducts is then unavoidably characterized by the presence of a single unpaired electron [24,33] carried by Co II , while the scenery may be more multifaceted when CoTPP-k L adducts (k = 1 or 2) are considered.
Both CO and NH 3 bind CoTPP vertically, C-and N-down oriented [33]; molecular cluster calculations have been then carried out by assuming a C 4v and a C s symmetry [53] for the CoTPP-CO and CoTPP-NH 3 species, respectively (see Tables S10 and S11 of the SM). CoTPP-CO and CoTPP-NH 3 BEs, estimated according to Equation (1) are 0.33 and 0.28 eV, respectively, and are reported in Table S32 of the SM together with the optimized Co-D bond lengths (BLs, D corresponds to the L donor atom) and the Nalewajski-Mrozek ( NM I Co-D ) bond multiplicity indexes [56][57][58][59][60][61][62]. In this regard, it can be useful to mention that the optimized BL C-O passes from 1.139 to 1.157 Å upon moving from the free molecule to the coordinated one, while both the N-H BLs and the H −N − H bond angles (BA) of the coordinated NH 3 are negligibly affected upon coordination.
As expected and anticipated, the electronic structure analysis reveals that the 0 L coordination to CoTPP does not determine any relevant charge transfer able to modify the Co II oxidation state [24,33]. In addition, the spin population analysis confirms that Co maintains its unpaired electron upon coordination, which remains localized on the Co-based 3d AOs (see Figure 2 and Figure S1 of the SM). Even though only two 0 L have been herein considered, it appears likely that the 0 L bonding to CoP-like and CoPc-like molecules cannot significantly perturb their magnetic properties. Similarly to CoTPP-0 L, the 1 L coordination to CoTPP has been explored by taking advantage of the available experimental evidence [18]. In more detail, ADF calculations have been run by assuming a N-down orientation for both NO and NO 2 and by adopting a C s and a C 2v symmetry [53] for the CoTPP-NO and CoTPP-NO 2 adducts, respectively (NO and NO 2 O atoms point toward the meso C atoms of the macrocycle). Optimized geometries (see Tables S12 and S13 of the SM) and BEs have been evaluated for both LS (no unpaired electron) and high spin (HS, two unpaired electrons) states.
Starting from CoTPP-NO, its diamagnetic state (the LS state is found to be 1.05 eV more stable than the HS state) and the peculiar geometry of the [CoNO] 8 fragment (the superscript 8 indicates the total number of electrons mostly localized on the Co 3d and the NO π * orbitals) closely resemble the spin state and the crystal structure of the [Co(NO)(Salen)] adduct (Salen = N,N'-bis(salicylidene)ethylenediamine) [63]. More specifically, the Co − N − O BA is far from being linear both in CoTPP-NO (122.5 • , see Table S33 Table S33 of the SM, and 1.807 Å in [Co(NO)(salen)] [63]), and the Co II species lies significantly above the plane passing through the donor atoms of the four-fold coordinative pocket (0.19 Å in CoTPP-NO and 0.25 Å in [Co(NO)(salen)] [63]). Incidentally, the CoTPP-NO highest occupied MO (the 76a' HOMO) is strongly localized on the {CoNO} 8 fragment (66%), and it accounts for a bonding interaction, σ in character (see Figure 2 and Figure S2 of the SM), between the NO π * || MO and the Co 3d-based AOs lying in the C s symmetry plane, while the 51a" lowest unoccupied MO (LUMO) is reminiscent of the NO π * ⊥ MO (see Figure S2 of the SM).
Despite all these similarities, the different behaviour of the {CoNO} 8 N-O BL upon moving from the free molecule to the coordinated one must be underlined. Theoretical results herein reported show a slight lengthening upon coordination (from 1.166 to 1.185 Å), while the experimental BL of the free NO (1.15 Å) perfectly matches the [Co(NO)(salen)] one [63]. It is also worth noting that, even though the geometry of the {CoNO} 8 fragment herein optimized fits very well the one obtained by Kim et al. for CoTPP-NO by means of periodic DFT calculations [64], their Co-NO BE (1.67 eV) is higher than what we obtained by exploiting the molecular cluster model (1.32 eV, see Table S33 of the SM). This difference could be due to the different exchange-correlation potentials adopted in periodic (PBE [65]) and molecular cluster (BP86 [38,39]) numerical experiments. As a whole, our data indicate that: (i) the CoTPP-NO bonding is accompanied by the Co II → Co I "reduction"; (ii) the saddle conformation adopted by Kim [64].
Notwithstanding the lack of experimental evidence for the CoTPP-NO 2 adduct, just under thirty years ago Rousseau et al. [66] tackled the electronic and molecular properties of the EPR silent CoPc-NO 2 adduct, pointing out that the Co-N NO2 direct interaction characterized by the Y-shaped coordination of NO 2 to CoPc is accompanied by a Co → NO 2 charge transfer able to affect the electronic density on the pyrrolic N atoms.
Analogously to CoTPP-NO, the CoTPP-NO 2 diamagnetic state (LS) is found to be 0.91 eV more stable than the paramagnetic one; moreover, the optimized geometrical parameters of the C 2v CoTPP-NO 2 adduct (see Table S33 of the SM) are very close to those adopted by  [67]. Considering the electronic properties of CoTPP-NO 2 , a thorough analysis of its frontier MOs (see Figure 2) reveals that, contrary to the Co-NO bonding, the Co-NO 2 one is accompanied by the Co II → Co III oxidation. In more detail, the CoTPP-NO 2 45a 1 HOMO is reminiscent of the NO2 π * || SOMO [68] and it is poorly localized (9%) on the Co 3dbased AOs (see Figure 2D), while the 46a 1 LUMO is strongly concentrated (46%) on the Co 3d z 2 AO. As a whole, even though the coordination to CoTPP of both the 1 L herein considered "switches off" the magnetization of the complex (no unpaired electron is present), the 1 L quenching mechanism is opposite in NO and NO 2 : in the former case, it implies the reduction of the Co II centre through the redox reaction NO + Co II → NO + + Co I , while in the latter, the oxidation of the Co II centre through the redox reaction NO 2 + Co II → NO 2 − + Co III takes place. Numerical experiments herein reported have been limited to the superoxo configuration [18] for which both the HS (three unpaired electrons) and LS (one unpaired electron) states have been explored. Analogously to CoTPP-1 L, the LS state appears more stable than the HS one (0.49 eV); moreover, the optimized Co-(η 1 -O 2 ) BL and Co -Ô -O BA (1.858 Å and 119.7 • , see Table S34 of the SM) perfectly fall in the above reported ranges (the optimized O-O BLs in the free molecule and in the (η 1 -O 2 ) species are 1.235 and 1.286 Å, respectively). A thorough analysis of the CoTPP-(η 1 -O 2 ) electronic structure reveals that, similarly to CoTPP-NO 2 , the Co-(η 1 -O 2 ) bonding is accompanied by the Co II → Co III oxidation with all but one spin orbitals reminiscent of the O 2 π g MOs [67] (antibonding with respect to the O-O interaction) occupied; the fourth, π g -like unoccupied MO (VMO) corresponds to the CoTPP-(η 1 -O 2 ) 51a" LUMO, completely localized (86%) on the spin down (↓) component of the π g spin orbital ⊥ to the symmetry plane (see Figure 2E). Consistently with such a picture, the Co spin density is negligible, and the single unpaired electron is completely localized on O 2 (see Figure S3 of the SM). Interestingly, even though the number of unpaired electrons does not vary upon moving from CoTPP to CoTPP-(η 1 -O 2 ) and no magnetization "switch off" is then expected (see Figure 2F), the spin configuration of the superoxo adduct is completely different from that of the pristine complex [33]. A summary of the oxidation state of the Co and L after the coordination is reported in Table S35 of the SM.

CoTPP-L Adducts on Cu, Ag and Au Substrates: The Trans-Effect
Theoretical results pertinent to the MS-CoTPP clusters and the CoTPP-L adducts confirm that simple, tiny, and computationally inexpensive models may be adopted to acquire information about the magnetic behaviour of CoTPP upon chemisorption on coinage metals as well as on perturbations induced by the coordination of k L (k = 0, 1, and 2) on the CoTPP frontier orbitals. The feasibility testing of the same approach to explore the effects induced at the same time by chemisorption and coordination on the CoTPP electronic structure is then challenging on one hand and appealing in terms of computational costs on the other hand. As a result, it may be useful to remember that, while both experimental and theoretical data are available in the literature, the latter studies have mostly been carried out by adopting periodic calculations [18,19,21,[23][24][25]33,76]. Nature, symmetry, and strength of the surface trans-effect characterizing the different S-CoTPP-L interphases have been herein investigated by adopting the MS-CoTPP-L clusters, representative of the L interaction with CoTPP deposited on S. MS-CoTPP-L theoretical outcomes have been then compared with experimental and/or theoretical data from the literature, when available.
MS-CoTPP-0 L results have several common features for both the 0 L herein considered, the most relevant being: (i) the MS-CoTPP-CO LS state (no unpaired electron) is more stable than the HS one (two unpaired electrons) by 0.58, 0.52, and 0.70 eV for MS = Cu, Ag and Au, respectively; (ii) similarly, the MS-CoTPP-NH 3 LS state is more stable than the HS one by 0.77, 0.61, and 0.82 eV for MS = Cu, Ag and Au, respectively; (iii) both the MS-Co and the Co-D BEs decrease upon moving from MS-CoTPP and CoTPP-0 L to MS-CoTPP-0 L for Cu and Ag (Tables S31, S32, S36, S37 of the SM); (iv) both the MS-Co and the Co-D BLs increase upon moving from MS-CoTPP and CoTPP-0 L to MS-CoTPP-0 L for Cu and Ag (Tables S31, S32, S36, S37 of the SM); and (v) the MS-Co interaction weakening induced by the 0 L coordination is accompanied by the MS I + Co I → MS 0 + Co II redox reaction for MS = Cu and Ag. Moreover, the MS-CoTPP-0 L number of unpaired electrons (disregarding that localized on MS) mirrors the CoTPP-0 L one. Incidentally, the doubly occupied MS-CoTPP-CO 30a 1 HOMO (MS = Cu and Ag) is strongly localized on the MS (n + 1)s/nd z 2 (n = 3 and 4 for MS = Cu and Ag, respectively) AOs and the Co 3d z 2 AO, while the doubly occupied MS-CoTPP-NH 3 74a HOMO (MS = Cu and Ag) is strongly concentrated on the MS (n + 1)s/nd z 2 /nd x 2 −y 2 (n = 3 and 4 for MS = Cu and Ag, respectively) AOs and the Co 3d z 2 /3d x 2 −y 2 AOs. Incidentally, MS-CoTPP-CO theoretical outcomes perfectly agree with experimental [76] and theoretical [33] data in the literature.
Even though Au-CoTPP-0 L ADF results are also consistent with the presence of Co II (3d 7 ) and Au 0 (5d 10 6s 1 ) species, it must be remarked that no Co oxidation state variation takes place upon moving from Au-CoTPP to Au-CoTPP-0 L: a consequence of the absence of any Co II → Co I reduction accompanying the chemisorption of CoTPP on Au. As such, it is noteworthy that the lengthening of the Au-Co and Co-D BLs upon the L coordination is less significant than that estimated for Cu-CoTPP-0 L and Ag-CoTPP-0 L (see Tables S31,  S32 and S38). Molecular cluster results pertinent to Au-CoTPP-NH 3 agree very well with experimental data and periodic calculations [18,21].
As a whole, the magnetization of the MS-CoTPP interphase (MS = Cu and Ag) is "switched on" by the 0 L chemisorption, while no variation is expected on passing from Au-CoTPP to Au-CoTPP-0 L (see Figure 3, third and fourth columns). Theoretical results obtained for the adducts CoTPP-1 L and CoTPP-2 L induce us to foresee that the electron exchange taking place at the S-CoTPP-k L (k = 1 and 2) interphases should not be limited to CoTPP and S, possibly involving 1 L and 2 L too. The inspection of Tables S35-S37 of the SM confirms this expectation and clearly shows that the strongest MS-CoTPP-k L trans-effect is associated to the NO coordination, whose presence: (i) decreases the BE MS-Co (1.17 → 0.41 eV, 0.91 → 0.26 eV, 1.11 → 0.49 eV, for Cu, Ag and Au, respectively); (ii) increases the BL MS-Co (2.27 → 2.36 Å, 2.47 → 2.60 Å, 2.46 → 2.56 Å, for Cu, Ag and Au, respectively). Further insights into the MS-Co and the Co-NO interactions may be gained by referring to Figure 4, where MS-CoTPP-k L (k = 1, 2) simplified energy level diagrams are displayed together with 3D plots of the MOs mainly localized on the MS-based ns AO (n = 4, 5 and 6 for Cu, Ag and Au, respectively), the Co-based 3d AOs, and the k L-based π * fragment MOs. The MO localization percentages reported in the figure testifies to the negligible perturbation induced by the MS presence on the Co-NO bond; moreover, it is noteworthy that the MS (n + 1)s-based 83a' SOMO (MS = Cu, n = 3; MS = Ag, n = 4) has a negligible contribution (≤2%) from the Co 3d-based AOs. In addition, both the NO π * ⊥ -based ↓/↑ 54a" and the NO π * || -based ↑/↓ 85a MOs have a VMO character, and all but one (the ↓/↑ 56a" MO) Co 3d-based MOs are completely occupied. The NO trans-effect is then characterized by the transfer of the 1 L unpaired electron to the MS-CoTPP system, prompting Co and MS to assume a 3d 8 (Co I ) and a nd 10 (n+1)s 1 (Cu 0 /Ag 0 ) electronic configuration and taking out, in agreement with periodic calculations [33], any direct MS-Co interaction. Altogether, theoretical outcomes clearly indicate that, even though both the Co oxidation state and its electronic configuration are nearly identical in MS-CoTPP, CoTPP-NO and MS-CoTPP-NO, the NO coordination to MS-CoTPP reduces MS I to its elemental oxidation state through the NO → NO + oxidation inhibiting at the same time any direct MS-Co bonding (see Tables S36 and S37). The NO coordination does not induce any "switch on" effect on MS-CoTPP because the Co species does not vary its oxidation state and the 1 L unpaired electron is used to reduce MS to its elemental oxidation state. It is noteworthy that both experimental studies and period calculations on S-CoTPP-NO support the molecular cluster outcomes herein reported [19,76].
The comparison of the Au-CoTPP-NO frontier electronic structure with those of the Cu-CoTPP-NO and Ag-CoTPP-NO molecular clusters clearly indicates that the different behavior of Au compared to Cu and Ag has, ultimately, to be traced back to the diverse MS-CoTPP interaction on passing from Cu/Ag to Au (look at the second col-umn of Figure 3). Au preserves its 5d 10 6s 1 electronic configuration along the whole Au → Au-CoTPP → Au-CoTPP-NO path, while the NO → NO + oxidation (both the NO π * ⊥ -based and the NO π * || -based Au-CoTPP-NO MOs are empty) provides the electron needed for the Co II → Co I reduction. As a whole, the NO coordination to CoTPP chemisorbed on Au is expected to have a "switch off" effect due to the generation of a Co I 3d 8 closed shell (see Figure 3).
Although not as strong as that induced by the NO coordination, the NO 2 trans-effect is quite effective too (see Tables S31, S33, S36-S38 of the SM); in particular, upon moving from MS-CoTPP and CoTPP-NO 2 to MS-CoTPP-NO 2, the BE MS-Co and BE Co-D decreasing (see Tables S31, S33 and S36-S38) is accompanied by the BL MS-Co and BL Co-D increasing (see Tables S31, S33 and S36-S38). Common features of the MS-CoTPP-NO 2 bonding scheme are: (i) the strong localization of the SOMO on the MS (n + 1)s AO (see Figure 4), which is consistent with a MS nd 10 (n + 1)s 1 elemental electronic configuration (n = 3, 4, 5 for MS = Cu, Ag, Au, respectively); (ii) the NO 2 "closed-shell" nature after coordination and then its "nitrite" character (see above); and (iii) the local "closed shell" electronic configuration (3d 6 ) of Co oxidized by NO 2 to Co III (only the six t 2g -like Co-based spin orbitals {the ↑/↓ 35b 1 , ↑/↓ 33b 2 , ↑/↓ 46a 1 levels in Cu-CoTPP-NO 2 ; the ↑/↓ 35b 1 , ↑/↓ 33b 2 , ↑/↓ 48a 1 levels in Ag-CoTPP-NO 2 ; the ↑/↓ 35b 1 , ↑/↓ 37b 2 , ↑/↓ 50a 1 levels in Au-CoTPP-NO 2 } are occupied). Even though the MS-CoTPP-NO 2 magnetic behaviour is closely reminiscent of the CoTPP-NO 2 one (no "switch on" effect takes place upon chemisorption of NO 2 ), it must be underlined that, similarly to MS-CoTPP-NO, the Au-CoTPP-NO 2 frontier electronic structure differs from the Cu-CoTPP-NO 2 and Ag-CoTPP-NO 2 ones as a consequence of the diverse MS-CoTPP interaction on passing from Cu/Ag to Au. The NO 2 chemisorption on the Au-CoTPP species has then a "switch off" effect on the CoTPP magnetization. Once again, these results agree with experimental data and periodic calculations on Au-CoTPP-NO 2 [18,21].
Any attempt to optimize the geometry of the MS-CoTPP-(η 1 -O 2 ) cluster with the LS configuration (no unpaired electrons) failed, while the HS (two unpaired electrons) geometry optimization converged rapidly and smoothly along the MS triad. Such a peculiar behaviour has to be traced back to the electron transfer processes involving at the same time the Co, MS, and O 2 species (see below).

Conclusions
A series of shared features binds the coordination of k L to CoTPP molecule supported on coinage metal surfaces: (i) both BE MS-Co and BE Co-D (BL MS-Co and BL Co-D ) decrease (increase) upon moving from MS-CoTPP and CoTPP-L to MS-CoTPP-L; (ii) the MS oxidation state in the MS-CoTPP-L cluster is systematically found equal to 0; (iii) the local electronic structure of the CoTPP-L fragment in the MS-CoTPP-L cluster is very similar to that of the CoTPP-L adducts; and (iv) the different MS-CoTPP-L BE Co-D values are scarcely affected by MS, thus confirming the leading role played by the trans-coordinate ligand in the weakening of the direct MS-Co bonding. As a whole, the results presented and discussed herein demonstrate that small and computationally inexpensive molecular clusters can be used to confidently predict the influence of different ligands on the surface chemical bonds of adsorbed metalloporphyrins on diverse coinage metals and then be exploited to drive experiments towards the desired outcomes.