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Electronic and magnetic properties of molecule-metal interfaces: transition metal phthalocyanines adsorbed on Ag(100)

We present a systematic investigation of molecule-metal interactions for transition-metal phthalocyanines (TMPc, with TM = Fe, Co, Ni, Cu) adsorbed on Ag(100). Scanning tunneling spectroscopy and density functional theory provide insight into the charge transfer and hybridization mechanisms of TMPc as a function of increasing occupancy of the 3d metal states. We show that all four TMPc receive approximately one electron from the substrate. Charge transfer occurs from the substrate to the molecules, inducing a charge reorganization in FePc and CoPc, while adding one electron to ligand \pi-orbitals in NiPc and CuPc. This has opposite consequences on the molecular magnetic moment: in FePc and CoPc the interaction with the substrate tends to reduce the TM spin, whereas in NiPc and CuPc an additional spin is induced on the aromatic Pc ligand, leaving the TM spin unperturbed. In CuPc, the presence of both TM and ligand spins leads to a triplet ground state arising from intramolecular exchange coupling between d and \pi electrons. In FePc and CoPc the magnetic moment of C and N atoms is antiparallel to that of the TM. The different character and symmetry of the frontier orbitals in the TMPc series leads to varying degrees of hybridization and correlation effects, ranging from the mixed-valence (FePc, CoPc) to the Kondo regime (NiPc, CuPc). Coherent coupling between Kondo and inelastic excitations induces finite-bias Kondo resonances involving vibrational transitions in both NiPc and CuPc and triplet-singlet transitions in CuPc.


I. INTRODUCTION
The interaction of molecules with solid surfaces governs the self-assembly of supramolecular layers 1,2 as well as the electronic and magnetic properties of metal-organic heterostructures 2,3 and single molecule devices. 4,5 The large variety of organic and metal-organic complexes, combined with the possibility of tuning the chemical reactivity and electronic ground state of different complexes within the same family of molecules, make such systems increasingly attractive for applications. However, electronic interactions at the interface with a metal may induce charge transfer, distort the ligand field, and reduce electron-electron correlation effects via screening and hybridization. The intricate interplay between all these processes is far from being understood.
Transition-metal phthalocyanines (TMPc) represent a well-known class of molecules with organic semiconducting properties in the bulk and a broad spectrum of applications that includes field-effect-transistors, gas sensors, and photovoltaic cells. 6 Due to their relatively simple and robust structure as well as versatile chemistry, TMPc have assumed the role of a model system to study the interaction of metal-organic complexes with metal surfaces. Their flat adsorption geometry facilitates the bonding of both the central TM ion and organic ligands to the substrate, whereas their capability to coordinate many different metal atoms allows for a systematic in-vestigation of their magnetic properties.
The interaction of TMPc with metal surfaces has been studied by many techniques, including scanning tunneling microscopy (STM), 2,7-25 ultraviolet and X-ray photoelectron spectroscopy (UPS-XPS), 9,[26][27][28][29] x-ray absorption spectroscopy (XAS), 3,9,[30][31][32] and density functional theory (DFT). [33][34][35][36] Investigations of the magnetic properties of TMPc have mostly focused on MnPc 24,36 , FePc, 3,14,15,36 and CoPc, 3,[19][20][21][22][23][34][35][36] for which it was shown that adsorption on a metallic surface tends to quench the magnetic moment of the TM ion. A corollary to such investigations is the implicit assumption that the magnetic properties of TMPc at surfaces depend almost exclusively on the ground state of the TM ion. However, a recent investigation by our group has highlighted the possibility of inducing a magnetic moment delocalized over the Pc organic ligand, which affects the spin degeneracy and symmetry of the molecular ground state as well as the electrical conductance measured at different sites within the same molecule. 7 Unpaired spins induced by charge transfer in Pc ligands have also been found to affect the conductance properties of TbPc 2 single molecule magnets adsorbed on Au 37 and their coupling to ferromagnetic surfaces. 38 Indeed, a growing number of experiments indicates that the organic ligand directly affects the magnetism and transport properties of metal-organic 23,39,40 as well as purely organic complexes 41 adsorbed on surfaces.
These results evidence the need to take into account arXiv:1203.2747v1 [cond-mat.mtrl-sci] 13 Mar 2012 the full molecular structure in order to understand and predict the magnetic properties of adsorbed systems.
Here we present a comprehensive study of four different TMPc (TM = Fe, Co, Ni, Cu) deposited on Ag(100) in order to shed light on the mechanisms that lead to changes of both the TM and ligand magnetic moments at the TMPc/metal interface. Scanning tunneling spectroscopy (STS) combined with DFT allows us to elucidate the role of charge transfer, hybridization, and correlation at the molecule-metal interface on the magnetic properties. The paper is organized as follows: after presenting the experimental and theoretical methods (Section II), we first introduce the theoretical electronic structure of TMPc in the gas-phase (Section III), which serves as the starting point of our investigation. We then describe the experimental and theoretical adsorption geometry of the molecules on Ag(100) (Section IV), including a discussion of electronic chirality effects, which were revealed in a previous work on CuPc. 2 The electronic structure of adsorbed TMPc is discussed in Section V, where STS data are compared with the molecular projected density of states (PDOS) derived from ab-initio DFT calculations. The magnetic properties of TMPc are addressed in Section VI using STS to measure the intensity and spatial extension of Kondo anomalies in the differential conductance, including the coupling to vibrational and magnetic degrees of freedom in NiPc and CuPc as well as the theoretical description of triplet-singlet excitations in CuPc using a multi-orbital approach. Further, we calculate the magnetic moments of adsorbed TMPc and compare them to the gas-phase magnetic moments in neutral and negatively charged species in order to understand the effects of charge transfer and intramolecular exchange and their dependence on the TM ion. Finally, Section VII summarizes the more general conclusions of this work.

A. Experiment
TMPc were evaporated in ultra high vacuum (UHV) from a heated quartz crucible onto a sputter-annealed Ag(100) single crystal kept at room temperature, after degassing the 99% pure powder material (Sigma Aldrich) for 24 hours. The deposition rate was ∼ 0.05 monolayers/min; the base pressure during evaporation was below 5 × 10 −10 mbar. Spectroscopic measurements were performed using an STM operating at 5 K. Conductance (dI/dV ) spectra were obtained with the lock-in technique, using a bias voltage modulation of frequency 3 kHz and amplitude 1 mV rms for the low energy spectra (−0.1 < V < 0.1 V), and 3 mV rms for the larger energy range (−2 < V < 1 V). A background spectrum acquired on the bare Ag surface with the same feedback conditions was subtracted to all spectra in order to enhance molecular resonances and minimize features originating from the tip or substrate electronic structure. 42 Hence, only relative dI/dV values are significant in these spectra. dI/dV maps were acquired in the constant current mode, with an amplitude of 3 mV rms . Maps of the Kondo resonance were obtained using the d 2 I/dV 2 signal in order to scan at a finite voltage. 7 Both topographic and conductance images were processed using the WSxM software. 43 Further details on the spectroscopic methods can be found in the Supplementary Information of Ref.7.

B. Theory
The theoretical electronic structure of both gasphase and adsorbed TMPc have been obtained from ab-initio calculations using the VASP implementation of DFT in the projected augmented plane wave scheme. 44,45 Different approximations, namely LDA, 46 GGA, 47 GGA+vdW, 48,49 and GGA+U 50 have been compared in order to obtain consistent results, and to check the effect of different exchange-correlation approximations or the vdW interaction. Unless otherwise stated, the results presented in the next sections were obtained using GGA+U 50 and vdW corrections using the scheme of Grimme. 48,49 U ef f =U-J was chosen to be 3 eV in all cases. Additional tests were made to check that reasonable values of U ef f do not qualitative change our conclusions. The planewave cutoff energy was set to 300 eV. The calculated slab included 5 Ag atomic layers intercalated by 7 vacuum layers in the vertical direction, and a 7×7 lateral supercell. The positions of all atoms in the molecule and the first three Ag layers were relaxed vertically and laterally until forces were smaller than 0.05 eV/Å. The projected density of states (PDOS) of NiPc have been used to compare single (1×1×1) and multiple (5×5×1) k point calculations, which converge after applying a broadening of 100 meV to the data. Based on that, the results for a single k point with the latter broadening are used in the following. Charge transfer and local magnetic moments have been calculated using a Bader charge analysis. 51,52

III. GAS-PHASE TMPC
Before discussing the effects of adsorption on the molecular electronic and magnetic structure, we briefly introduce the chemical configuration of gas-phase TMPc, as well as the electronic structure obtained from spinpolarized calculations, which will be used later as a reference.
TMPc are characterized by a rather simple and stable molecular structure, where the TM ion bonds to four isoindole (pyrrole + benzene) ligands via their pyrrole N (N p ). That leaves the ion in a [TM] 2+ state, and the molecule with the square planar D 4h symmetry. Under this symmetry group, the d-states transform as b 2g (d xy ), b 1g (d x 2 −y 2 ), a 1g (d z 2 ), and e g (d xz ,d yz = d π ). Depend- ing on their symmetry and energy position, these orbitals mix to a different degree with 2p-states of the C and N atoms. The highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO) of the Pc ring are represented by delocalized a 1u and 2e g π-orbitals, respectively, with marginal contribution from the TM d-states. The TM-related MO can be classified in two groups according to their parallel (b 2g , b 1g = d ) or perpendicular (a 1g , e g = d ⊥ ) orientation with respect to the molecular plane, and hence, the substrate. Figure 1 shows the spin-up and spin-down energy levels of TMPc near the frontier orbitals obtained within the GGA+U scheme. The 3d contribution in each MO is indicated between parentheses; the molecular magnetic moments are discussed in Sect. VI. Our calculations show that the electronic structure of the Pc ring is barely affected by the TM ion. This is clearly seen in the a 1u and 2e g ligand orbitals: the a 1u MO, with negligible dcontribution, appears at the same energy in all molecules. The 2e g energy varies slightly with the d configuration of the TM ion as this orbital exhibits a finite d π contribution that ranges from 7% in FePc to 1% in CuPc.
The evolution of the electronic configuration of the central [TM] 2+ ions cannot be rationalized by the simple filling of one-electron energy levels split by the ligand field, due to the strong d-d correlation and the energydependent hybridization with ligand states. The situation is most critical for the ground state of FePc, where the quasidegeneracy between different electronic terms 3,53 has led to a long-standing debate in literature. [54][55][56][57][58][59] The discussion of such differences is beyond the scope of this paper. However, the spin moment that we obtain for this molecule is S=1, independently of the DFT functional and in good agreement with previous work. 3,53-59 CoPc, with one electron more, presents a robust 2 A 1g (S=1/2) ground state with a single a 1g (d z 2 ) hole, in agreement with x-ray absorption measurements. 3 NiPc, with d 8 , has a singlet (S=0) 1 A 1g ground state. The TM spin is recovered in CuPc, with a single hole in b 1g (d x 2 −y 2 ), resulting in a doublet (S=1/2) 2 B 1g ground state.

A. Adsorption geometry
The adsorption of individual TMPc has been studied by STM. Their topographic appearance already reflects differences that allow us to classify them in two groups: the TM ion appears as a protrusion in FePc and CoPc and a depression in NiPc and CuPc, as shown in Figs. 2 (a) and 3. The different contrast is due to the large (small) coupling of the TM d ⊥ (d ) orbitals near the Fermi level (E F ) with the tip states. 60 As typical for TMPc on metals, the molecules adsorb with the aromatic plane parallel to the surface. Atomically resolved images of the surface reveal two different azimuthal orientations of the TM-N p ligand axis [ Fig. 2 (b)], corresponding to ±30 • with respect to the (100) surface lattice vectors. Previous systematic ab-initio calculations of CuPc on Ag(100) revealed that this orientation, with the TM ion located on the Ag hollow site, corresponds to the minimum of the adsorption energy. 2 A similar adsorption site has been found for CuPc on Cu(100) (Ref. 61). The rotation of the Pc macrocycle with respect to the substrate high symmetry directions was attributed to bond optimization between aza-N (N a ) and Ag atoms. This study confirms the leading role of the N a -Ag interaction, as both theory and experiment find very similar adsorption configurations for all TMPc, independently of the central TM ion (see Fig. 2b).
The calculations also show that TMPc become slightly concave after deposition, with the periphery of the molecule slightly further from the surface. This effect is most pronounced in the case of FePc. The molecules also induce a small distortion of the substrate, pushing the Ag atoms below N p slightly below the surface plane and the Ag atoms below N a slightly above it. The molecule-substrate distances, calculated as the difference in the z coordinate between the TM atom and the Ag atom below N p , are shown in Table I. The distance obtained with LDA is ∼2.5Å for the four molecules. This method is known to overbind, compensating for the absence of van der Waals (vdW) forces. These forces are included in the GGA+vdW method. The results with GGA+vdW show that z increases to ∼2.7Å, keeping it TM-independent. Similar values were also found using both methods for CoPc adsorbed on Cu(111) (Ref. 34). On the less reactive Au(111) surface, however, distances obtained with LDA for different TMPc do not level out and still reflect a TM-dependent behavior. 33,36 In our case, we can separate the effect of the interaction between the TM ion and the substrate by using plain GGA, i.e., by switching off the vdW interaction. Using this method, we find that FePc and CoPc, with z = 2.76 and 3.08Å respectively, are significantly closer to the surface than NiPc and CuPc, with z = 3.59 and 3.47Å respectively. The stronger TM-Ag interaction of FePc and CoPc is attributed to the direct participation of the d-orbitals to the molecule-substrate bonds. 26,33,36 The vdW interaction introduced by GGA+vdW can be estimated by the correction added to the total energy calculated by GGA alone. This correction is larger by about 1 eV for NiPc and CuPc compared to FePc, which compensates for the lack of direct TM-substrate interaction in the former species and results in the nearly TM-independent bond length reported in Table I.  (Table I)  it has been shown that the chiral contrast observed by STM is not related to nuclear distortions, but originates from the asymmetric electronic interaction between the a 1u and 2e g orbitals and Ag states. This asymmetry is due to the misalignment between surface and molecular symmetry axes, where the +30 • and −30 • configurations imprint chiral charge distortion of opposite sign. Here we extend this study to FePc, CoPc, and NiPc, and quantify the contribution of conformal distortions to the chiral contrast. We use the height difference between two opposite C atoms at the benzene ring as a measure of their torsion (see Table I and Fig. 2b). Its small value, close to the calculation's accuracy, obtained for all TMPc confirms the electronic origin of chirality. This is in line with the voltage dependence of the chiral contrast, and the fact that it is only observed in CuPc and NiPc in spite of the similar geometry found for all molecules. Electronic chirality is imprinted to each MO to a different degree, depending on their spatial distribution and hybridization with the substrate, with maximum effect in orbitals exhibiting a nodal plane on the TM-N p ligand axis (see Fig. 5). The a 1u MO exhibits the strongest distortion because of its double lobe structure at the benzene ring, where the asymmetry of charge distortion is maximum. The chiral contrast at the 2e g MO, also with nodal planes on the ligand axis, varies with energy: at positive bias it is strongly reduced, but becomes more intense when shifted to negative bias due to charge transfer. The MOs with significant TM-d contribution do not have nodal planes on the ligand axis, and hence do not present any significant chirality. This leads to a voltage-dependent chiral appearance of the TMPc that depends solely on the specific electronic structure of each molecule, as shown in Fig. 3. CuPc and NiPc are strongly chiral at negative bias due to the asymmetry of the a 1u orbital and of the partially occupied 2e g orbital, and achiral at positive bias, where tunneling occurs via a more symmetric 2e g resonance. In CoPc and FePc, on the other hand, the 2e g orbital only appears at positive bias, where the chiral contrast is insignificant. Furthermore, TM-d states and other other interface-related resonances with maximum intensity on the ligand axis hinder the chirality of the a 1u state.

V. ELECTRONIC STRUCTURE
In this section we present scanning tunneling spectroscopy (STS) measurements of the molecules adsorbed on the Ag(100) surface. The energy of the MOs and other interface-related features is obtained from individual dI/dV spectra, whereas maps of the dI/dV intensity at specific energies reveals their symmetry and spatial distribution within the molecule. Experimental results are then compared to the theoretical density of states projected onto different MOs, which allows us to assign the observed dI/dV peaks to specific orbitals, providing insight into the formation of hybridized moleculesubstrate states, charge transfer, and molecular mag-netism.
A. Scanning tunneling spectroscopy Figure 4(a) shows the dI/dV spectra of FePc to CuPc recorded by positioning the STM tip on the central TM atom (red curves) and on a peripheral benzene ring (blue curves). The a 1u and 2e g resonances corresponding to the HOMO and LUMO of the gas-phase Pc ring can be easily identified by studying the spatial distribution of the dI/dV peaks of the spectra acquired on benzene, as shown in Fig. 5. The intensity distribution of these resonances is similar to that found for other substrates, 20 except for the chiral fingerprint discussed in the previous Section. The energy position of the a 1u state is similar in all TMPc, varying continuously from -1.14 V in CoPc to −1.40 V in CuPc (FePc was not measured in this energy range). On the other hand, the spectral distribution of the 2e g state critically depends on the TM ion: in FePc and CoPc, a single unoccupied peak is observed at +0.39 and +0.47 V, respectively, as expected for the Pc LUMO. Conversely, CuPc and NiPc exhibit two peaks around the Fermi level, located at -0.29/+0.35 V and -0.35/+0.35 V, respectively. Both peaks, however, can be associated with the 2e g state due to their similar spatial distribution. The position of the lowest energy peak below E F indicates that this orbital is partially occupied. The energy splitting of ∼ 0.65−0.70 eV is within the range of the Coulomb repulsion energies obtained for π-orbitals in aromatic complexes of similar size. 41,62, 63 We therefore assign the peaks at negative and positive bias to single and double occupation of the 2e g state, respectively, in agreement with the results reported in Ref. 7. The sharp peak appearing between the two 2e g "Coulomb blockade" peaks is the Kondo resonance associated to the unpaired ligand spin, 7 which will be discussed further in Section VI. Note that the short electron lifetime of empty orbitals in molecules coupled to metals prevents their double occupation by tunneling electrons, which would lead to similar "Coulomb blockade" peaks in the 2e g state of FePc and CoPc.
Spectra recorded on the TM ions, shown as red curves in Fig. 4(a), allow us to identify the MOs with dcharacter. The broad peak shifting downwards with increasing d-occupation from FePc to NiPc can be related to d ⊥ states, easiest to observe due to their effective coupling with the STM tip. In CuPc, these states are situated below the probed energy range. The localization of this peak on the TM ion is confirmed by the dI/dV map of CoPc at -510 mV [ Fig. 5(b)]. In this molecule, the d ⊥ resonance appears well below E F , suggesting the complete filling of the a 1g (d z 2 ) orbital, and hence a switch in the charge transfer channel from the ligand 2e g to TMd states compared to NiPc and CuPc. In FePc, the tail of the d ⊥ peak crosses E F , suggesting that these states are not fully occupied, similarly to FePc on Au(111) (Ref. 3).
Contrary to the d ⊥ -states, the perturbation of the d - states due to adsorption appears to be minor. Although confinement in the molecular plane makes them difficult to access by STS, some features in the spectra of NiPc and CuPc can be tentatively assigned to the b 1g (d x 2 −y 2 ) state. In the pristine molecules, this orbital is singly occupied in CuPc and unoccupied in NiPc (see Fig. 1).
The intensity corresponding to the unoccupied b 1g state is masked by a step-like interface resonance feature (IR 1 ) that we observe around +0.2 V in all molecules. However, both CuPc and NiPc exhibit a larger dI/dV signal in this energy range compared to CoPc and FePc, which suggests that there is an additional orbital contributing to the tunneling current above E F . The singly occupied b 1g state in CuPc can be assigned to the small hump observed around -0.4 V, close to where the 2e g resonance on the benzene spectra presents a pronounced valley. This valley, absent in NiPc at this energy, is tentatively assigned to a Fano resonance originating from the tunneling interference between the occupied b 1g and the more hybridized 2e g states, analogous to that occurring between resonant and direct channels in impurity and quantum dot systems. [64][65][66] Indeed, the dip observed in NiPc at -1.4 V, where d ⊥ states overlap with the a 1u orbital, might have a similar origin, supporting the presence of Fano peaks in these molecules.
In addition to MO resonances that maintain the original character of the TMPc states, we find additional interface resonances that originate from strong hybridization with Ag electrons (see Fig. 6). The IR 1 resonance observed at +0.2 V [ Fig. 4(a)] is common to all TMPc and only observed on Ag(100). This resonance could originate from the hybridization of molecular states with the  Fig. 4(b). The topography of FePc recorded during the acquisition of the maps is displayed on the left side.
lowest lying unoccupied surface state of Ag(100), which is close in energy. 67 In FePc, we observe an additional feature (IR 2 ) between the a 1u and d ⊥ states, which we identify with an interface state with intensity at the benzene rings, similar to that reported for CoPc on Au(111) (Ref. 20).

B. Density of states calculated by DFT
In order to correlate the features observed in the dI/dV spectra with the molecular electronic structure, we have computed the PDOS projected onto the TM-d states as well as on the MOs of the TMPc, as shown in Fig. 4. In general, we find fair agreement between the measured and calculated resonances, supporting the assignment of the spectral features to specific MO based on the symmetry and spatial distribution of the dI/dV intensity.
The strongest hybridized states are the a 1g MOs of FePc and CoPc, as expected owing to their dominant d z 2 character. The TM d z 2 -electrons hybridize with the Ag-sp z states, confirming the strong, direct substrate-TM interaction discussed in Section IV. Additionally, in the case of FePc and CoPc, two 2e g and one e g state are mixed together, projecting onto one occupied and one empty spin-down resonances (see Fig. 4c). Mixing is induced by hybridization with the substrate, showing that the picture of slightly distorted MO is no longer valid in this case. This is in line with the appearance of interface resonance as those observed in STS maps (IR 2 in Fig. 6). For NiPc and CuPc, hybridization with the substrate turns out to be much smaller, and the PDOS resembles that of the gas-phase molecules of Fig. 1. In these two cases the confinement of the b 1g orbital in the molecular plane and its σ character reduces hybridization with Ag electrons, diminishing the charge transfer to this orbital. Hence, it appears unoccupied in NiPc and singly occupied in CuPc, as in the gas-phase.
The a 1u orbital, fixed at about -1.30 eV, is the only MO that is not affected by the d-occupation of the TM ion. In the case of FePc, the spin up and spin down a 1u states are exchange-split due to the single-configurational nature of DFT. This broken symmetry reflects the strong spin-polarization of the whole molecule. The position of the 2e g MO, on the other hand, depends strongly on the type of TM ion and reveals a transition in the interaction with the substrate. As in the dI/dV spectra, the PDOS shows that this state is unoccupied in FePc, partially occupied in CoPc, and acquires a charge of approximately one electron in NiPc and CuPc. The splitting between occupied and unoccupied 2e g states is not fully reproduced in the calculations due to the well-known electronic gap problem in DFT, which is especially critical for delocalized π-orbitals. 68 The origin of the charge-transfer behavior with TM can be unfolded by using gas-phase anions to study pure transfer without hybridization. We find that the TMd dependent behavior is the same as in adsorbates. In [FePc] 1− and [CoPc] 1− the effect of the extra electron is complex and the extra charge is not easily assigned to a single MO. It rather induces a reorganization of the charge within the molecule. In [NiPc] 1− and [CuPc] 1− the behavior is simpler, with the extra electron going to 2e g . The observed behavior is also in agreement with transport results in electron-doped thin films. 69 In summary, although the net amount of transferred charge is about one electron in all cases (see Table II), its effect on the molecule depends on the d occupation of the ion. This difference is driven by the interplay between energy alignment and Coulomb repulsion in the d and 2e g states, as well as their degree of hybridization with the substrate. The similarity between results obtained by calculating gas-phase anions and adsorbates indicates that the leading role of the substrate is that of a charge reservoir. However, the strong (weak) hybridization of the d ⊥ (d ) states further stabilizes the different charge donation channels, promoting charge transfer to TM-d states in FePc and CoPc, and inhibiting it in NiPc and CuPc.

VI. MAGNETIC PROPERTIES
The magnetic properties of TMPc on Ag(100) are addressed using STS through the analysis of dI/dV spectra close to E F . The presence of sharp zero bias resonances can be used to detect the formation of local magnetic moments screened by the Kondo effect. 70,71 This occurs as itinerant electrons belonging to the substrate couple antiferromagnetically to a localized spin, forming a many-body singlet state at temperatures below the characteristic Kondo energy k B T K . dI/dV maps of the Kondo spectral features further allow us to measure the spatial distribution of the spin density for unpaired electrons. We note, however, that, although the presence of a Kondo resonance is a signature of a local moment, its absence is not a proof of a nonmagnetic ground state, since the resonance can also be experimentally inaccessible due to the low T K in weakly interacting spins. In such a case, STS data have to be contrasted with complementary experiments, such as x-ray magnetic circular dichroism, 3,32 or, as in the present case, with theoretical calculations. Figure 7 shows the dI/dV spectra measured near E F for the four molecules at the position of the TM ion (red curves) and benzene ligand (blue curves). FePc and CoPc present featureless spectra, which indicate that the Kondo interaction between these molecules and the Ag(100) surface is either absent or too weak to be observed at 5 K. Relatively flat Co spectra were reported also for CoPc adsorbed on Au(111), for which it was concluded that the filling of the a 1g state leads to a complete quenching of the molecular magnetic moment. 19 This interpretation has been recently questioned based on a mixed-valence model of x-ray absorption spectra. 3 In both cases, the quenching of the CoPc magnetic moment appears to be a robust result. On the other hand, FePc does present a Kondo resonance on Au(111), although different interaction strengths have been reported. 14, 16 We attribute the absence of Kondo peaks on Ag(100) to a stronger interaction with the substrate, as reflected by the substantial hybridization of the d ⊥ states, which may lead to a mixed-valence configuration of FePc, as discussed later.

A. Kondo effect probed by STS
In contrast with FePc and CoPc, NiPc and CuPc present many characteristic signatures of low-energy excitations around E F . Such excitations have been discussed in detail in Ref. 7. Here we report a summary of these results for comparison with theory as well as to provide a complete picture of TMPc adsorbed on Ag(100). The most prominent feature of the NiPc and CuPc spectra is the presence of an intense zero bias resonance with maximum intensity at the ligand position. This is rather unusual for metal-organic adsorbates since, in most cases, Kondo resonances are associated to the spin of the TM ions. 14,16,19,24,25 Here, the zero bias peak is assigned to an elastic Kondo resonance (K e ) arising from the unpaired spin located in the 2e g orbital of CuPc and NiPc. This interpretation is supported by the temperature dependence of the peaks full width at half maximum (Γ K ) and maximum intensity (G K ). Figure 8 shows that both parameters follow expressions derived from Fermi liquid theory 72 and numerical renormalization group (NRG): 73 (2) where α and ξ are parameters that depend on the total spin of the molecule. Fitting the values of Γ K with Eq. 1 leads to a Kondo temperature of T K = 27 ± 2 K for CuPc. The logarithmic behavior of G K makes it more sensitive to the scattering of the data, but we find that expressions for both S=1/2 and (the underscreened) S=1 fit reasonably well the data by using T K = 27 K. The two possible spin states will be discussed later.
We notice that NiPc and CuPc present very similar Kondo resonances in spite of the S=0 ground state of the Ni ion and S=1/2 ground state of Cu. Indeed, we estimate a Kondo temperature T K = 29 K for NiPc from Γ K measured at 5 K. Moreover, the intensity of both CuPc and NiPc resonances closely follows the contour of the 2e g orbital, as revealed by the remarkable similarity of the dI/dV maps reported in Figs. 7(e) and (f) compared to with the single occupancy of this orbital discussed in Section V. The relation between energy, width, and Coulomb repulsion potential, with values of = −0.30 eV, Γ ∼ 0.30 eV, and U = 0.65 eV, respectively, is also characteristic of the Kondo regime, for which | |, | + U | ≥ Γ.
The direct observation of the "Coulomb blockade" peaks and the Kondo resonance allows, unlike in previous studies of molecular adsorbates, for a univocal identification of the MO associated to the unpaired spin. As the spin participating to the many-body Kondo state originates from a single orbital, we expect a well-defined value of T K over the whole molecule, as confirmed by our observations. This is in contrast with the variations of T K found for Co porphyrins adsorbed on Cu(111), which suggest a spatially-dependent, multiple orbital origin of the Kondo interaction, possibly due to strong intermixing of TM and ligand orbitals near E F (Ref. 40).

B. Inelastic vibrational and Kondo excitations
The dI/dV spectra of NiPc and CuPc recorded on the TM ions [red curves in Figs. 7(c) and (d)] present a complex series of peaks and conductance steps in addition to the elastic Kondo resonance observed at zero bias. It is well-known that inelastic excitations induce step-like increases in the differential conductance spectra symmetrically distributed in energy around E F . 74,75 In Kondo systems, the coherent coupling of the Kondo state with such excitations leads to additional peaks at the energies of the inelastic conductance steps. 76 Unlike quantum dots, where the reduced orbital level-spacing favors the coupling of Kondo and electronic excitations, 77 the origin of such side peaks in small aromatic molecules is restrained to vibrational 41,78-80 (K v ) or magnetic 39,73,[81][82][83] (K ts ) excitations. In the present case, by comparing the energy of the K v peaks with that of the Raman vibrational modes of gas-phase CuPc, 84 we find that the inelastic features found at the position of the Ni and Cu ions [ Fig. 9(a)] correspond to vibrational excitations that involve distortion of the TM-N p bonds. 7 Note that the vibrational spectra of NiPc and CuPc are nearly identical, as shown by the twin d 2 I/dV 2 spectra displayed in the bottom graph. The step-like and peak-like contributions to the inelastic conductance can be obtained by fitting the dI/dV spectra with step and Lorentzian functions, as shown in Fig. 9(a). From the fit of the spectra we observe that both NiPc and CuPc present more intense conductance steps at negative bias and more intense Kondo peaks at positive bias. These inverted correlation between vibrational and Kondo features has also been observed for TCNQ molecules adsorbed on Au(111), and has been attributed to the competition between the purely inelastic channel and the one including the Kondo effect. 41

C. Inelastic triplet-singlet and Kondo excitations
In contrast to the spectra of the TM ions, the spectrum of NiPc recorded on benzene does not present signatures of finite-bias excitations. The CuPc benzene spectrum, however, presents two side-peaks at ±21 ± 1 meV, shown in Fig. 9(b). These side-peaks are assigned to intramolecular magnetic excitations, 7 owing to the presence of two spins in CuPc, one localized on the Cu d x 2 −y 2 state, 32 and the other in the 2e g ligand state. This interpretation is supported by the gas-phase calculation of charged molecules presented later. The energy of the side peaks provides a direct estimate of the intramolecular exchange coupling (J) between d-and π-spins. The observation of an intense Kondo peak at zero bias, on the other hand, indicates that the CuPc ground state is magnetic, namely a triplet (S=1) state where the metal and ligand spins are aligned parallel to each other, whereas the excited state is a singlet (S=0) state.
The similarity between the elastic Kondo resonances of NiPc and CuPc, with S=1/2 and S=1 respectively, can be explained by the fact that the total CuPc spin is underscreened due to the very weak coupling between the b 1g (d x 2 −y 2 ) orbital and the substrate. Thus, only the 2e g ligand spin is effectively screened by the substrate in the temperature range accessible by our STM.

D. Multi-orbital non-crossing approximation of the Kondo resonance associated to the ligand spin
Although spin excitations coupled to the Kondo effect have already been observed in transport experiments with molecular junctions, 39,73,81-83 the precise configuration of the molecule-metal bonding provided by STM and the assignment of the Kondo-screened spin to a specific orbital allow us to model our results by mapping the electronic structure of CuPc/Ag(100) calculated by DFT onto an impurity Hamiltonian. Our model describes the interaction between the 2e g orbital and the substrate by an SU(4) Anderson Hamiltonian, where two-fold spin degeneracy coexists with the two-fold orbital degeneracy on the same footing, and an infinite repulsive Coulomb term (see Ref. 85 for more details). DFT calculations show that the interaction between the ion b 1g state and the substrate can be neglected, as reflected by the small hybridization-induced broadening obtained for this orbital, which is a factor of 20 smaller than that of the 2e g state. The Hamiltonian includes a molecular exchange term −JS L · S T M , which couples the ligand spin (S L ) to the TM spin (S T M ). The 2e g on-site energy is fitted to = -0.35 eV, and the spectral density of the coupling with the substrate is assumed to have rectangular shape with magnitude Γ = 0.1 eV and band half-width of 10 eV.
The PDOS onto the 2e g state, calculated within the non-crossing approximation at T=5 K (see Ref. 85), is compared with the experimental dI/dV spectra in Fig. 9(b). For STM studies this comparison is a firstorder approximation that takes into account that the tunneling conductance is proportional to the local DOS. Moreover, our calculations are performed in equilibrium. At typical STM parameters, the non-equilibrium modification of NCA equations 86 for slowly varying substrate DOS, reduce to corrections smaller than 1/1000 th in the tunneling current. Hence, in these STM studies, the equilibrium spectral function is an excellent approximation to compare with the experiment. This is confirmed by the correct reproduction of the Kondo features observed for NiPc and CuPc when we set the intramolecular coupling term to 0 meV and 25 meV respectively, as shown in the bottom graph of Fig. 9(b). In the case of ferromagnetic coupling, the finite-bias features correspond to inelastic Kondo replicas that originate from spin excitations. Decomposition into spin channels yields that the Stokes satellite (positive bias) is in the S = 0 channel, whereas the anti-Stokes peak (negative bias) as well as the Kondo peak are in the S = 1 channel. 85,87 E. Magnetic moments calculated by DFT By calculating the saturation magnetic moments of TMPc, DFT provides complementary results to the analysis of the Kondo spectra reported above. Moreover, in addition to supporting the interpretation of the STS data, DFT allows us to construct a quantitative picture of the effect of the different charge transfer mechanisms on the molecular magnetic properties. Table II summarizes the magnetic moments calculated for the neutral and anionic form of gas-phase TMPc as well as for TMPc adsorbed on Ag(100). We notice that, although the amount of charge transferred from the substrate to the molecules is similar in all cases, the total magnetic moment is reduced in FePc and CoPc, whereas it is increased in NiPc and CuPc with respect to the neutral gas-phase TMPCs. The calculations confirm that the magnetic moment of the TM ions in NiPc and CuPc is not perturbed upon adsorption, owing to the small hybridization of the planar b 1g orbital with the substrate states. This is in agreement with previous results obtained by XMCD on CuPc/Ag(100) (Ref. 32) and with the coexistence of TM and ligand spins in CuPc inferred from the Kondo spectra. We recall that, due to the underestimation of correlation effects in DFT, the ligand spin is just barely present in the calculations with adsorbates. For NiPc, we calculate a small magnetic moment of 0.14µ B , while for CuPc the moment is just slightly larger than the 1µ B corresponding to the unpaired spin in the b 1g orbital. Since charge transfer is close to one electron, one way to estimate the magnitude of the ligand spin using DFT is to consider gas-phase anions as a proxy of adsorbed TMPc. In such a case the number of electrons belonging to the molecule is fixed and the calculations can be constrained to yield the minimum energy spin state. Figure 10 displays the spin density of neutral and anionic gas-phase molecules, where we clearly observe the additional ligand spin of NiPc and CuPc upon charge transfer. In CuPc, the spin density originating from the b 1g orbital is also observed, distributed over the Cu ion and N p atoms.    FePc and CoPc present a more complicate picture compared to the simple addition of one spin in NiPc and CuPc, partly because of the strong hybridization with the substrate discussed in Section V B. In both cases, the magnetic moment is reduced upon adsorption. The extra electron donated by the surface is not easily assigned to a single MO, inducing a reorganization of the charge within the molecule. We use the results obtained for gas-phase anions to disentangle the different mechanisms responsible for the quenching of the magnetic moment. As shown in Fig. 11, the spin density of FePc follows the same distribution in the gas-phase anion and in the adsorbed molecule. This similarity can also be checked by comparing their element-resolved magnetic moments in Table III, which are very similar in both cases. Thus, regardless of the strong hybridization of adsorbed FePc, the main features of the spin moment distribution are again captured by the simple addition of one electron to the gas-phase system. The true nature of the ground state of FePc on Ag (100), however, might be more complex than suggested by the calculated spin density distribution, due to the interplay of several MO close to E F and dynamic electron correlation effects that are not included in DFT. The computed electronic structure for FePc yields a S=1/2 system when adsorbed on Ag (100), same as for the gas-phase anion. However, the adsorbate exhibits a more complex configuration due to the presence of multiple molecular orbitals at the Fermi level. This could result in either a mixed-valence system, given the Fermi level crossing and strong interaction of the a 1g orbital with the substrate, or a more complex Kondo behavior with a low-temperature Kondo phase originating in the many less-coupled orbitals near the Fermi energy. This complex behavior makes FePc/Ag(100) an interesting candidate to study very low temperature Kondo physics in a multi-orbital system.
CoPc represents another case of nontrivial charge transfer occurring upon adsorption. For example, the a 1g orbital is filled, but new empty d π states appear above E F , as shown in Figs. 4(b) and (c). Moreover, the anion is not a good model for the adsorbed molecule. As shown in Table II and Fig. 10, the anion is in a S=0 state, due to antiferromagnetic coupling between spins residing in different MOs, while in the adsorbed case we find a non-integer spin magnetic moment of 0.63µ B . This non-integer spin, together with the absence of a Kondo interaction, could indicate that CoPc is in the mixed-valence regime, with charge fluctuating between the CoPc d and Ag states, similar to results obtained for CoPc on Au(111) using x-ray absorption spectroscopy.    ) for FePc in the neutral and anionic gas-phase, and in the adsorbate, using GGA+U.

F. Intramolecular exchange coupling
The TM-ligand spin coupling observed via the inelastic Kondo interaction in CuPc can be studied in gasphase [CuPc] 1− . Here, the energy of ferromagnetic and antiferromagnetic spin configurations can be computed by fixing the total spin of the molecule. The ferromagnetic (triplet) alignment is favored over the antiferromagnetic (singlet) one. The triplet ground state is in agreement with the zero-bias Kondo resonance observed experimentally. From the energy difference between triplet and singlet states, evaluated using the parallel spin (E ↑↑ ) and antiparallel spin (E ↑↓ ) energies, and taking the correct singlet and triplet configurations to yield J = 2(E ↑↓ −E ↑↑ ), we extract the exchange coupling constant J for the anion, J = 38 meV. The discrepancy with J = 21 meV measured for CuPc/Ag(100) can be explained by surface screening, which is expected to significantly reduce exchange correlation effects involving hybridized orbitals.
The distribution of the spin density in [FePc] 1− and [CoPc] 1− , shown in Fig. 10, reveals a different type of intramolecular spin correlation. Both neutral and anionic molecules exhibit antiferromagnetically aligned TM and ligand spins, indicating that the spin contrast is not directly due to the interaction with the substrate, but is intrinsic to the molecule and related to the pristine TM spin, which extends to nearby C and N atoms upon the formation of MOs with mixed d-and π-character. Such intramolecular antiferromagnetic spin coupling is a result of the large exchange splitting of the d-levels of the Fe and Co ions. This induces spin-dependent mixing of the d and ligand states, leading to the formation of spin-polarized MOs with different spatial distribution. A similar mechanism can be invoked to explain the site-and energydependent spin contrast recently measured for CoPc deposited on Fe(110), for which the total molecular moment is zero. 23

VII. CONCLUSIONS
The adsorption, electronic, and magnetic structure of four TMPc (M = Fe, Co, Ni, and Cu) adsorbed on Ag(100) have been systematically studied using STM, STS, and ab-initio DFT calculations within the LDA, GGA, GGA+vdW, and GGA+U approximations.
We find that all molecules adsorb with the macrocy-cle plane parallel to the surface and the TM-N p ligand axis rotated by ±30 • with respect to the high-symmetry surface lattice vectors. The comparison between DFT results using different approximations evidences differences in the TM-Ag interaction, but the leading role of vdW forces leads to similar molecule-substrate distances and azimuthal rotation angles. The rotation between molecular and surface symmetry axes imprints chirality to the frontier electronic orbitals without perturbing the structural conformation of the molecules. This can only be observed in NiPc and CuPc at negative voltages, due to the contribution of the a 1u and partially occupied 2e g orbitals to the tunneling current and minor influence of the d-channels in the same energy region. The electronic structure of adsorbed TMPc is modified mainly due to charge transfer from the substrate. Although all molecules receive approximately one electron, charge is transferred to the ligand 2e g orbital in NiPc and CuPc, and to multiple MOs in FePc and CoPc, inducing internal charge reorganization. This difference is related to both energy level alignment and Coulomb repulsion. In addition, whereas FePc and CoPc exhibit strongly hybridized d ⊥ -states near E F , those are shifted down in energy in NiPc and CuPc, which display unperturbed d -states in this energy range. The electronic configuration of the Ni and Cu ions is not significantly affected by adsorption.
Both charge transfer and hybridization tend to reduce the magnetic moment of FePc and CoPc. The computed electronic structure of FePc indicates a S=1/2 system when adsorbed on Ag(100), with a strong presence of MOs near the Fermi energy that could indicate either a mixed-valence system, given the strong interaction of the a 1g orbital with the substrate, or a more complex Kondo behavior with a low-temperature Kondo phase originating in the many less-coupled orbitals near the Fermi energy. The non-integer moment obtained for CoPc and the existence of a substantial molecular DOS at the Fermi energy (see Fig. 4), together with the absence of a Kondo resonance in this molecule, suggest a mixed-valence configuration. Opposite to the moment reduction in FePc and CoPc, the spin multiplicity is actually enhanced by charge transfer in NiPc and CuPc, due to the induction of a ligand spin in the 2e g orbital. This transforms NiPc into a paramagnetic molecule and induces a triplet ground state in CuPc, where the ligand spin is exchangecoupled to the TM magnetic moment.
The interaction between the 2e g ligand spin of NiPc and CuPc and the substrate gives rise to a Kondo interaction, which induces a prominent zero bias resonance delocalized over the perimeter of the molecules. Coherent coupling between Kondo spin flip and vibrational excitations induces inelastic Kondo resonances in both NiPc and CuPc. In CuPc, the total magnetic moment is underscreened as the Kondo energy scale of the TM spin is orders of magnitude smaller than the one of the 2e g ligand spin. However, the additional magnetic degree of freedom due to the TM spin leads to the coupling of Kondo and inelastic triplet-singlet excitations. The coexistence of different nonequilibrium Kondo processes related to vibrational and spin transitions in CuPc opens up the possibility to study the timescale and spatial localization of multiple spin excitation and relaxation channels within a single molecule, as reported in more detail in Ref. 7.
In general, we show that charge transfer and hybridization of MOs orbitals have profound effects on the electronic configuration, magnetic moment, and transport properties of metal-organic complexes adsorbed on a metallic substrate. Such effects in TMPc do not depend monotonically on the electronic configuration of the TM ions. Rather, the energy position, symmetry, and spin polarization of the pristine MOs has to be considered within a comprehensive picture of the charge transfer process. Importantly, the magnetic moment of adsorbed TMPc can be either reduced or enhanced depending on the relative energy of the d ⊥ and π-levels, and their degree of hybridization with the substrate. Further, the possibility of inducing additional ligand spins upon adsorption may be relevant to establish magnetic coupling in extended molecular structures assembled on metal surfaces.