Ferromagnetic Ligand Holes in Cobalt Perovskite Electrocatalysts as Essential Factor for High Activity Towards Oxygen Evolution

Please note that technical editing may introduce minor changes to the text and/or graphics, which may alter content. The journal’s standard Terms & Conditions and the ethical guidelines, outlined in our author and reviewer resource centre, still apply. In no event shall the Royal Society of Chemistry be held responsible for any errors or omissions in this Accepted Manuscript or any consequences arising from the use of any information it contains. Accepted Manuscript


Introduction
Water oxidation enables conversion of electricity into storable hydrogen, needed for clean energy and a sustainable economy. In water electrolysis, the oxygen evolution reaction (OER) is the rate limiting step of the overall process. Therefore much attention has devoted to understand the rationale behind triplet state O 2 evolution in order to develop active, stable and abundant catalysts that accelerate it 1 . In 1980 Matsumoto and co-workers examined the OER activity of the La 1-X Sr X Fe 1-Y Co Y O 3-δ (0 ≤ X ≤ 1 and 0 ≤ Y ≤ 1) family of perovskites in alkaline solution 2 ; even though the group could not synthesise the (Co~4 + ) SrCoO 3-δ composition, they predicted that it will show the lower overpotentials. The La 0.2 Sr 0.8 Fe 0.2 Co 0.8 O 3-δ structure was obtained by Matsumoto as an excellent and stable electrocatalyst for OER; similar compositions and oxidation states typically lead to good catalysts 3,4,5 . In the smaller La 1-X Sr X CoO 3-δ group, SrCoO 3-δ shows the optimum OER kinetic and is, in fact, one of the best catalysts 6,7 .
In 1984 Bockris and Otagawa described the electrocatalytic activity of perovskite oxides in terms of molecular orbital theory 8 ; they show that the antibonding (AB) 3d-metal orbitals directed towards the ligands (O) overlap with the lobes of the reactants forming AB σ*-type orbitals, e g -2p shells in octahedral coordination. The authors explained that the catalysts having occupied e g -2p levels achieve high rates of oxygen evolution due to mild bonding between the catalyst and the intermediates. Separately, Goodenough has established the foundations of the theoretical understanding of the electronic and magnetic transitions in metal oxides 9,10 . These works have been key to derive the significant influence of quantum spin exchange interactions (QSEI) in the orbital chemistry of magnetic catalysts, also known as spintro-catalysis 11 . Due to the impact of QSEI in compositions with open-shell configurations, 12 conventional electronic analysis in heterogenous catalysis like the d-band centre model / band theory 13 are insufficient to describe the highlycorrelated electrons; and then lead to rough approximations for the catalytic activity of materials based-on Earth-abundant magnetic elements. As in spintronics, the spins of many electrons can act together, affect the magnetic and electronic properties of a material, and influence significantly its catalytic behaviour.
QSEI reduce the electronic repulsions and are key for charge mobility in magnetic systems 12 . A ferromagnetic (FM) conduction band indicates that the physics of the itinerant electrons is significantly influenced by Fermi holes, a fundamental requirement for optimal electrocatalysts based on 3d-metals 11,14 . By looking carefully, we can see examples where magnetic structures associate overall with active heterogeneous catalysis. FM oxides show better activity than Pt in the oxidation of nitrous oxide (NO has doublet ground state) 15,16 , FM nitrides improve ammonia synthesis 17 , or Co doping in MoS 2 induces FM 18 and enhances the activity in various reactions. In addition of particular interest for electrocatalysis, interatomic FM orderings leads to favourable spin-charge transport, avoiding antiferromagnetic (AFM) electronic localization. 12 Fully AFM insulators like LaCrO 3 or LaFeO 3 are poor oxygen catalysts 19,20 . Spin selection in polarized density of states facilitates the oxidation/reduction of triplet state O 2 . 21,22 Nature has evolved excellent magnetic catalysts from abundant 3d-metals, e.g. during photosynthesis 23 , via engineering QSEI.
In a broad context, the rationalisation of the orbital physics in magnetic structures is important in theoretical heterogenous catalysis, because it will allow to study activities across the whole periodic table based on the interplay between chemical composition, and electronic configuration. Successful catalytic design based on orbital occupation 14,24 may proceed from the rigorous analysis of the quantum chemistry 25 . In the La 1-X Sr X Co Y O 3-δ family two ends for the OER activity can be defined: LaCoO 3 as the less active and SrCoO 3-δ as the most efficient. The orbital physics behind the intrinsic activity of SrCoO 3-δ is unknown, as well as the effect of the iron ions in compositions like La 0.2 Sr 0.8 Fe 0.2 Co 0.8 O 3-δ . Also, the specific orbital configuration of LaCoO 3 at room temperature is controversial, because three spin states representing the 3d-2p AB-orbitals in octahedral coordination, t 2g 6 e g 0 (low spin, LS), t 2g 4 e g 2 (high spin, HS) and t 2g 5 e g 1 (intermediate spin, IS), are accessible for the Co 3+ -O bonds. LaCoO 3 presents the following, not fully understood, electronic transitions as a function of temperature 26,27 :  0 K < T < 35 K: bulk cobalt cations are preferentially in the Low-Spin (LS) t 2g 6 e g 0 diamagnetic state.  110 K < T < 350 K: a mixture of approximately 50% LS and 50 % HS cobalt cations forms a semi-conductive paramagnetic (PM) phase.  350 K < T < 650 K: the semi-conductive phase coexists with a metallic phase, possibly due to the presence of IS cations. An insulator-to-metal transition occurs near 450 K. The phases of LaCoO 3 accommodate diverse Jahn-Teller (JT) distortions as the XRD patterns indicate 28,29 . Below 90 K (Tab. 1) the experimental Co-O distances are similar, 1.918-1.934 Å, and shorter than those at higher temperatures 28 .
Different electronic configurations coexist in cobalt-based oxides; the present manuscript explains via DFT(GGA+U) calculations the electronic structure behind the poor or good OER activity in the La 1-X Sr X Fe 1-Y Co Y O 3-δ series. The initial comparison between theory and experiment is based on bulk properties; and it serves to calibrate the method. Finally, we explore the mechanism for oxygen evolution on the most efficient SrCoO 3-δ , looking for a quantification of the specific influence of QSEI in the valence open-shells in reaction steps.

Theoretical methods
We have performed periodic Density Functional Theory (DFT) calculations using VASP (Vienna Ab-initio Simulation Package), a program that combines ab-initio energy calculations with plane-wave basis sets [30][31][32][33] . The electron-ion interactions for the atoms are described by the projector augmented wave method developed by Blöchl 34,35 . The exchange-correlation energy has been calculated within the generalized gradient approximation using the Perdew-Burke-Ernzerhof functional revised for solids 36 . We used a cut-off energy of 400 eV for the expansion of the wave function into plane waves. The Monkhorst-Pack scheme has been chosen for the integration in the reciprocal space 37 . We have used the so-called DFT+U approach for the corrections accounting for the strong correlation among the electrons at the Co and Fe atoms 38 . The Hubbard +U correction is desirable in 3d-metals to consider explicitly non-local interactions between localized electrons 39 . The value of U is a constant, thus, in order to get accurate results, a structuredependent parametrization of U is necessary 40 . An initial calibration of GGA +U method was performed in order to match the electronic configurations of the LaCoO 3 and SrCoO 3-δ catalysts. The lattice parameters for monoclinic I2/a LaCoO 3 were optimized using a single unit cell, 4 La, 4 Co and 12 oxygen atoms, versus U. Optimizations indicate that for U 2.0 -2.5 the Hubbard correction is suitable to both experimental Jahn-Teller distortions 29,41 (see Table 1) and expected relative stability of competing electronic configurations 21 . The reciprocal space has been sampled with a (7x7x5) k-point grid for the ground-state optimized lattice parameters (experimental within brackets): a = 5.309 Å (5.367), b = 5.417 Å (5.433), c = 7.719 Å (7.637),  = 90.8º (91.0). The SrCoO 3-δ (001) slab model has lattice parameters of a = 5.333 Å, b = 5.333 Å and c = 30.0 Å and about 15 Å vacuum gap. The reciprocal space has been sampled with a (5x5x1) k-point grid. The climbing-image nudged elastic band (cNEB) method is used to determine minimum-energy paths, via 8 images and a spring constant of 5.0 eV/Å 2 . All the plots and the iso-surfaces for spin densities (0.03 e -/Å 3 iso-value) have been realized using VESTA 42 .

Results and discussion
In our calculations, the LaCoO 3 ground-state has all the Co 3+ cations in LS configuration. The t 2g 6 e g 0 structure presents no JT distortion and the predicted Co-O distance is about  1.893 Å. The density of states (DOS), Fig. 1a, shows that LS LaCoO 3 is an insulator with a band gap of about 0.5 eV. The second most stable phase is the ¾ LS + ¼ HS configuration, Fig. 1b; the interatomic exchange interactions are favourably ferromagnetic, because the e g band is overall more empty than occupied 9 .  Both ¾ LS + ¼ HS and ¾ LS + ¼ IS structures present JT distortions on the cobalt atoms with localized magnetic moments, see Tab. 1. The DOS for ¾ LS + ¼ HS LaCoO 3 also has a band gap of 0.5 eV, while ¾ LS + ¼ IS is a half-metal. This last configuration, less stable, is not detected experimentally. At room temperature LaCoO 3 possesses a narrow optical gap < 1.0 eV 43 ; and our calculations predict a band gap of 0.5 eV (Fig. 1a ã nd 2). The LS t 2g 6 e g 0 configuration has a band gap because of the energy difference between the fully occupied t 2g 6 and the empty e g 0 levels; effect due to the splitting of 3d-shells in the crystal-field. A similar thing occurs between the fully occupied valence band in the HS t 2g 6 e g 2 cobalt atoms and the conduction band. However, for IS t 2g 5 e g 1 e g 0 t 2g 0 configurations, the degenerate and semi-occupied 3d-shells form metallic bands.

Please do not adjust margins
Please do not adjust margins The FM ½ LS + ½ HS ordering is slightly more stable than the AFM configuration, and above 120 K entropy disorders the spins. These structures accessible at 300 K present cooperative Jahn-Teller type distortions with 5% of maximum deviation b etween the average experimental distances and the calculated ones. Both LS and HS Co 3+ atoms show localization of spin density within the 3d-metal and 2p-oxygen orbitals. This suggests the presence of a mixed valence occupations and enhanced 3d-2p hybridization with the increment of on-site magnetism. Overall, the electrocatalytic activity of LaCoO 3 observed at room temperature is at least initially restricted by the limited charge conductivity.  SrCoO 3-δ is a FM conductor (T C = 305 K) with a total magnetization of 2.5μ B per octahedral shell 44 and a percentage of oxygen vacancies typical of Co 4+ oxides 6 . Calculations on the SrCoO 3 and SrCoO 2.75 stoichiometries result in FM metallic ground states with a total spin of 2.5μ B within Co-O bonds, in perfect agreement with experimental data. Fig. 3 shows the conduction band constituted by the frontier t 2g -2p and e g -2p orbitals, for the majority and minority of spin. The on-site QSEI in the open-shells are crucial to investigate the correct electron paring and the partial population of the AB-orbitals. The alternate orientation pattern in the adjacent orthogonal atomic 3d-orbitals reduces the electronic repulsions, without JT elongations and instead with some short Co-O bonds of 1.83 Å. A hypothetical AFM configuration, about 0.8 eV higher in energy from the FM configuration, recovers the JT distortions, with an elongation of some Co-O bonds to about 1.93 Å.
The admirable agreement between the GGA+U calculations and the experimental structural, electronic and magnetic properties for the two oxidation extremes, LaCoO 3  All the compositions in the La 1-X Sr X CoO 3-δ family are extended FM gapless conductors apart from LaCoO 3 45 , p-type semi-conductor. In their ground-states, the AB-eigenvectors show a concomitant increment of the 3d-2p hybridization with the magnetization, which is maximum in SrCoO 3 (Fig. 3 and 4). The participation of the 2p-orbitals of the ligands in the AB-shell at the conduction band increases with the number of Fermi holes. The relative number of t 2g -2p electrons with minority spin decreases with the increasing oxidation states, and the magnetic density in the Co-O bonds growths, favoured by the QSEI.  The presence of Fe ions increases the magnetism due to their own t 2g 3 e g 1 shells, while the spin-polarization overall decreases on the Co-O AB-orbitals. Overall La 0.25 Sr 0.75 Co 0.75 Fe 0.25 O 3-δ has less FM ligand holes, this explains that iron atoms serve to increase the stability of the Co~4 + oxides, but not the intrinsic OER activity. The trend shown in Fig. 4 is mathematically expressed by Eq. 1, that is derived from Eq. 3 by assuming that . For the La 1-X Sr X CoO 3-δ family, gives almost a quantitative prediction of the relative OER .
activity. The composition with the highest OER activity has a maximum value. The validity of this derivation should . serve to compare the relative intrinsic OER activity of different structures and 3d-metals by using .

Eq. 1)
The enthalpy of any chemical event mainly depends upon three kinds of energy terms, Eq. 2. In magnetic catalysts, the additional non-classical , .
are indispensable to understand ℎ magnetic catalysts, since spin-potentials are responsible of the electronic conductivity and important in the orbital interactions, but how much? Limiting our study to the formation triplet O 2 , Fig. 5 shows the thermodynamic steps of two possible mechanisms over a SrCoO 3-δ (001) surface for oxygen evolution. We compare between hypothetical closeshell (non-spin-polarized) calculations (Fig. 5 top) and the openshell spin-polarized mechanisms (Fig.5 bottom). QSEI reduce the energy of open-shells by a contribution of around 3±0.5 eV; this is not a trivial value. The kinetic is also significantly improved in the spin-polarized calculations, the activation barriers and the adsorption energies decrease considerably between 15% and 35% in comparison with the fictious close- It is also consistent with the role of lattice oxygen in the computational work of Yoo and co-workers 47 .
The peculiar property of the highly oxidised mixed-valence SrCoO 3-δ composition is the ability to insert nucleophilic lattice oxygen towards the formation of O 2 *; which after desorption, leaves concomitant oxygen vacancies. These mobile vacancies can be rapidly occupied by oxygen atoms through the diffusion of bulk atoms and by gas phase intermediates, alike. This phenomenon creates a high turnover in the numbers of the active centres at the surface 48 . Then excellent OER activities seem associated with an overall Mars-van Krevelen type mechanism that is characteristic of total oxidations 48,49 .
We already knew that coupled mixed-valence spin acceptors (or donors), showing preferential FM interactions in the partially occupied AB e g -2p orbitals, are good conductors and excellent oxygen spintro-catalysts 24 . Furthermore, prototypical oxides for OER are those structures with metals in a high oxidation state, and then sufficiently electronegative. Eq. 3 correlates the overall activation energy of FM catalysts with the specific influence of , added via a Heisenberg type ℎ exchange term 14,22 . Eq. 3 means that 3d-2p hybridization and magnetization of the AB-eigenvectors, , is an important design factor in . = + every technology involving oxygen production and evolution 24 . Eq. 3 also explains that the trends for 3d-metals do not follow the simple parabolic behaviours postulated by band theory 49 . For instance, Mott insulators governed by antiferromagnetic (AFM) superexchange interactions are less active oxygen electro-catalysts indicating -. ∆ .

•
. > Magnetism is not a simple catalytic descriptor, on the contrary, it reflects multiple interrelated electronic properties. These factors are spin-dependent charge conductivity, oxidation state, ligand holes, intermediate bonding, reduction of the electronic repulsions. Since the nature of the magnetic coupling (whether AFM or FM) is related to electrostatic potentials, covalency and electron occupancy, spin-potentials strongly influence OER activity, and provide a physical sense to the statistical evaluation of descriptors done in the group of Shao-Horn 50 . In comparison with other theoretical descriptors in oxygen electrocatalysis, the recent calculations by Tripkovic and co-workers on the series LaMO 3 (M = Cr, Mn, Fe, Co, Ni) show the ineffectiveness of trying to differentiate the electrocatalytic activities of magnetic systems simply from the binding energies of species like O* and OH* 51 .
We report the suitability of the GGA+U method in the description of the electronic structure of La 1-X Sr X Fe 1-Y Co Y O 3-δ compositions; what it is not a surprise since GGA+U is a wellestablished approach to try to capture the physics of strongly correlated catalysts 52 . Computational studies on correlated oxides without Hubbard corrections are more in error when calculating reactions. In addition, if spin polarization is not even included on magnetic oxides the reported values are too inaccurate, what lead to multiple errors like the overestimation of the activity of insulating materials.

Conclusions
Are quantum spin exchange interactions a fundamental electronic factor in the catalytic activity of magnetic oxides? Yes, they are.
We have seen that the inter-atomic magnetic moment accumulated in the bonds of Co-based perovskites relates with charge conductivity, Fermi holes in the ligands, spin-selection and moderate binding energies. Consequently, are ℎ indispensable to understand the behaviour of magnetic materials, and for determining their electrocatalytic activity and selectivity. Expected conclusion considering that are materials of interest in spintronics. The increment of oxidation state for Co from LaCo III O 3 to SrCo IV O 3-δ induces an improvement of O 2 release, in addition to good spin-conductivity, consequently an enhancement of the OER activity indicated by maximum and . In the highly .
active SrCoO 3-δ , the initial formation of the O-O bond is governed by spin-transfer from the ligands to the electronegative metal atoms (Co), in a mechanism guided by . ℎ

Conflicts of interest
The authors declare no conflicts of interest.