K Jenni
email: ]jenni@ph2.uni-koeln.de

S Kunkemöller

P Steffens

Y Sidis

R Bewley

Z Q Mao

Y Maeno

M Braden
email: ]braden@ph2.uni-koeln.de

Neutron scattering studies on spin fluctuations in Sr 2 RuO 4

The magnetic excitations in Sr2RuO4 are studied by polarized and unpolarized neutron scattering experiments as a function of temperature. At the scattering vector of the Fermi-surface nesting with a half-integer out-of-plane component, there is no evidence for the appearance of a resonance excitation in the superconducting phase. The body of existing data indicates weakening of the scattered intensity in the nesting spectrum to occur at very low energies. The nesting signal persists up to 290 K but is strongly reduced. In contrast, a quasi-ferromagnetic contribution maintains its strength and still exhibits a finite width in momentum space.

I. INTRODUCTION

A quarter century after the discovery of superconductivity in Sr 2 RuO 4 [START_REF] Maeno | Superconductivity in a layered perovskite without copper[END_REF] its character and its pairing mechanism remain mysterious. Inspired by the ferromagnetic order appearing in the metallic sister compound SrRuO 3 [START_REF] Koster | Structure, physical properties, and applications of SrRuO3 thin films[END_REF] it was initially proposed that ferromagnetic fluctuations drive the superconductivity in Sr 2 RuO 4 rendering its superconductivity similar to the A-phase of superfluid 3 He [START_REF] Baskaran | Why is Sr2RuO4 not a high Tc superconductor? Electron correlation, Hund's coupling and p-wave instability[END_REF][START_REF] Rice | Sr2RuO4: an electronic analogue of 3 He?[END_REF]. For a long time chiral p-wave superconductivity with spin-triplet pairing has been considered to best describe the majority of experimental studies [START_REF] Mackenzie | The superconductivity of Sr2RuO4 and the physics of spin-triplet pairing[END_REF][START_REF] Maeno | Evaluation of Spin-Triplet Superconductivity in Sr2RuO4[END_REF] although the absence of detectable edge currents [START_REF] Hicks | Limits on superconductivityrelated magnetization in Sr2RuO4 and PrOs4Sb12 from scanning SQUID microscopy[END_REF] and the constant Knight-shift observed for fields perpendicular to the Ru layers [START_REF] Murakawa | Measurement of the 101 Ru-Knight Shift of Superconducting Sr2RuO4 in a Parallel Magnetic Field[END_REF] were not easily explained in this scenario [START_REF] Kallin | Chiral p-wave order in Sr2RuO4[END_REF]. Further insight was gained from experiments performed under large uniaxial strain that revealed a considerable enhancement of the superconducting transition temperature by more than a factor two [START_REF] Hicks | Strong Increase of Tc of Sr2RuO4 Under Both Tensile and Compressive Strain[END_REF][START_REF] Steppke | Strong peak in Tc of Sr2RuO4 under uniaxial pressure[END_REF], similar to the enhancement in the eutectic crystals [START_REF] Maeno | Evaluation of Spin-Triplet Superconductivity in Sr2RuO4[END_REF]. However, the breaking of the four-fold axis should split the superconducting transition of the chiral state in contradiction with a single anomaly appearing in the specific heat under strain [START_REF] Li | High sensitivity heat capacity measurements on Sr2RuO4 under uniaxial pressure[END_REF]. Furthermore, the strain dependence of the transition temperature close to zero strain is flat [START_REF] Hicks | Strong Increase of Tc of Sr2RuO4 Under Both Tensile and Compressive Strain[END_REF][START_REF] Barber | Role of correlations in determining the Van Hove strain in Sr2RuO4[END_REF], whereas one expects a linear dependence for the chiral state.

The picture of chiral p-wave superconductivity was fully shaken, when the two experiments yielding the strongest support for triplet pairing [START_REF] Ishida | Spin-triplet superconductivity in Sr2RuO4 identified by 17O Knight shift[END_REF][START_REF] Duffy | Polarized-Neutron Scattering Study of the Cooper-Pair Moment in Sr2RuO4[END_REF] were revised. The new studies of the Knight shift in NMR [START_REF] Pustogow | Constraints on the superconducting order parameter in Sr2RuO4 from oxygen-17 nuclear magnetic resonance[END_REF][START_REF] Ishida | Reduction of the 17O Knight Shift in the Superconducting State and the Heat-up Effect by NMR Pulses on Sr2RuO4[END_REF] and those of the polarized neutron diffraction [START_REF] Petsch | Reduction of the spin susceptibility in the superconducting state of Sr2RuO4 observed by polarized neutron scattering[END_REF] reveal an unambiguous drop of the electronic susceptibility that is inconsistent with spin-triplet pairs parallel to Ru layers.

Since then, numerous proposals for the superconducting state were made mostly invoking some d-wave state and the discussion of the superconducting pairing has become very active [START_REF] Røising | Superconducting order of Sr2RuO4 from a three-dimensional microscopic model[END_REF][START_REF] Rømer | Knight Shift and Leading Superconducting Instability from Spin Fluctuations in Sr2RuO4[END_REF][START_REF] Wang | Theory of Chiral p-Wave Superconductivity with Near Nodes for Sr2RuO4[END_REF][START_REF] Wang | Spin-orbit coupling and spin-triplet pairing symmetry in Sr2RuO4[END_REF][START_REF] Suh | Stabilizing even-parity chiral superconductivity in Sr2RuO4[END_REF][START_REF] Rømer | Theory of straininduced magnetic order and splitting of Tc and TTRSB in Sr2RuO4[END_REF][START_REF] Kivelson | A proposal for reconciling diverse experiments on the superconducting state in Sr2RuO4[END_REF][START_REF] Sharma | Momentum-resolved superconducting energy gaps of Sr2RuO4 from quasiparticle interference imaging[END_REF]. The observations of broken timereversal symmetry in muon spin relaxation experiments [START_REF] Luke | Time-reversal symmetry-breaking superconductivity in Sr2RuO4[END_REF][START_REF] Grinenko | Superconductivity with broken time-reversal symmetry inside a superconducting s-wave state[END_REF] and in measurements of the magneto-optical Kerr effect [START_REF] Xia | High Resolution Polar Kerr Effect Measurements of Sr2RuO4: Evidence for Broken Time-Reversal Symmetry in the Superconducting State[END_REF] may require interpretations other than the chiral p-wave scenario. Many theories discuss a superconducting state with a complex combination of components [START_REF] Røising | Superconducting order of Sr2RuO4 from a three-dimensional microscopic model[END_REF][START_REF] Rømer | Knight Shift and Leading Superconducting Instability from Spin Fluctuations in Sr2RuO4[END_REF][START_REF] Wang | Theory of Chiral p-Wave Superconductivity with Near Nodes for Sr2RuO4[END_REF][START_REF] Wang | Spin-orbit coupling and spin-triplet pairing symmetry in Sr2RuO4[END_REF][START_REF] Suh | Stabilizing even-parity chiral superconductivity in Sr2RuO4[END_REF][START_REF] Rømer | Theory of straininduced magnetic order and splitting of Tc and TTRSB in Sr2RuO4[END_REF][START_REF] Kivelson | A proposal for reconciling diverse experiments on the superconducting state in Sr2RuO4[END_REF].

Assuming a simple boson-mediated pairing following BCS theory, phonons and magnetic fluctuations or a combination of both [START_REF] Schnell | Unconventional superconducting pairing symmetry induced by phonons[END_REF] can be relevant. There are anomalies in the phonon dispersion that could be fingerprints of electron phonon coupling [START_REF] Braden | Structural analysis of Sr2RuO4[END_REF][START_REF] Braden | Lattice dynamics and electron-phonon coupling in Sr2RuO4 : Inelastic neutron scattering and shellmodel calculations[END_REF]. The phonon mode that describes the rotation of the RuO 6 octahedra around the c axis exhibits an anomalous temperature dependence and severe broadening [START_REF] Braden | Structural analysis of Sr2RuO4[END_REF]. This mode can be associated with the structural phase transition and with the shift of the van Hove singularity in the γ band through the Fermi level. Both effects occur upon small Ca substitution [START_REF] Fang | Magnetic phase diagram of Ca2-xSrxRuO4 governed by structural distortions[END_REF][START_REF] Friedt | Structural and magnetic aspects of the metal-insulator transition in Ca2-xSrxRuO4[END_REF]. In addition, the Ru-O bond-stretching modes that exhibit an anomalous downwards dispersion in many oxides with perovskite-related structure [START_REF] Braden | Giant phonon anomalies in the bond-stretching modes in doped BaBiO3: comparison to cuprates manganites and nickelates[END_REF] exhibit an anomalous dispersion in Sr 2 RuO 4 as well [START_REF] Braden | Lattice dynamics and electron-phonon coupling in Sr2RuO4 : Inelastic neutron scattering and shellmodel calculations[END_REF]. Comparing the first-principles calculated [START_REF] Wang | Phonon dispersion in Sr2RuO4 studied by a first-principles cumulative force-constant approach[END_REF] and measured [START_REF] Braden | Lattice dynamics and electron-phonon coupling in Sr2RuO4 : Inelastic neutron scattering and shellmodel calculations[END_REF] phonon dispersion in Sr 2 RuO 4 the agreement is worst for these longitudinal bond-stretching modes, which exhibit a flatter dispersion indicating better screening compared to the density functional theory (DFT) calculations. Note, however, that perovskite oxides close to charge ordering exhibit a much stronger renormalization of the zone-boundary modes with breathing character that is frequently labeled overscreening [START_REF] Braden | Giant phonon anomalies in the bond-stretching modes in doped BaBiO3: comparison to cuprates manganites and nickelates[END_REF][START_REF] Braden | Dispersion of the high-energy phonon modes in Nd1.85Ce0.15CuO4[END_REF].

On the other side there is clear evidence for strong magnetic fluctuations deduced from NMR [START_REF] Imai | 17O NMR Evidence for Orbital Dependent Ferromagnetic Correlations in Sr2RuO4[END_REF] and inelastic neutron scattering (INS) experiments [START_REF] Sidis | Evidence for Incommensurate Spin Fluctuations in Sr2RuO4[END_REF][START_REF] Braden | Inelastic neutron scattering study of magnetic excitations in Sr2RuO4[END_REF][START_REF] Servant | Magnetic excitations in the normal and superconducting states of Sr2RuO4[END_REF][START_REF] Braden | Anisotropy of the Incommensurate Fluctuations in Sr2RuO4: A Study with Polarized Neutrons[END_REF][START_REF] Iida | Inelastic neutron scattering study of the magnetic fluctuations in Sr2RuO4[END_REF][START_REF] Iida | Two-Dimensional Incommensurate Magnetic Fluctuations in Sr2(Ru0.99Ti0.01)O4[END_REF][START_REF] Steffens | Spin Fluctuations in Sr2RuO4 from Polarized Neutron Scattering: Implications for Superconductivity[END_REF]. The dominating magnetic signal is incommensurate and stems from nesting in the one-dimensional bands associated with d xz and d yz orbitals, see Fig. 1. The relevance of this instability towards an incommensurate spin-density wave (SDW) is underlined by the observation of static magnetic order emerging at this q position in reciprocal space for minor substitution of Ru by Ti [START_REF] Braden | Incommensurate Magnetic Ordering in Sr2Ru1-x Tix O4[END_REF] or of Sr by Ca [START_REF] Carlo | New magnetic phase diagram of (Sr,Ca)2RuO4[END_REF][START_REF] Kunkemöller | Spin-density-wave ordering in Ca0.5Sr1.5RuO4 studied by neutron scattering[END_REF]. A repulsive impurity potential was recently proposed to form the nucleation center for the magnetic ordering that should strongly couple to charge currents [START_REF] Zinkl | Impurity induced double transitions for accidentally degenerate unconventional pairing states[END_REF]. Furthermore, the temperature dependence of these incommensurate magnetic fluctuations in pure Sr 2 RuO 4 agrees with a closeness to a quantum critical point [START_REF] Braden | Inelastic neutron scattering study of magnetic excitations in Sr2RuO4[END_REF]. These nesting-induced magnetic fluctuations can easily be explained by DFT calculations using the random phase approximations (RPA) [START_REF] Mazin | Competitions in Layered Ruthenates: Ferromagnetism versus Antiferromagnetism and Triplet versus Singlet Pairing[END_REF] but their relevance for the superconducting pairing remains controversial [START_REF] Huo | Spin density wave fluctuations and p-wave pairing in Sr2RuO4[END_REF]. Inelastic neutron scattering in the superconducting state can exclude the opening of a large gap for these nesting-driven [START_REF] Kunkemöller | Absence of a Large Superconductivity-Induced Gap in Magnetic Fluctuations of Sr2RuO4[END_REF]. Since magnetic excitations are particle hole excitations one expects in the most simple isotropic case a magnetic gap comparable to twice the superconducting one, which can be safely excluded. However, the anisotropy of the gap function and interactions can strongly modify the magnetic response in the superconducting state. A more recent TOF inelastic neutron scattering experiments confirms the absence of a large gap but reports weak evidence for suppression of spectral weight at very low energies [START_REF] Iida | Horizontal Line Nodes in Sr2RuO4 Proved by Spin Resonance[END_REF]. This experiment also claims the occurrence of a spin resonance mode at the nesting position with a finite perpendicular wave-vector component, which would point to an essential modulation of the superconducting gap perpendicular to the RuO 2 layers but which is inconsistent with the results of this work.

In addition to the incommensurate nesting-induced fluctuations, macroscopic susceptibility [START_REF] Maeno | Two-Dimensional Fermi Liquid Behavior of the Superconductor Sr2RuO4[END_REF], NMR [START_REF] Imai | 17O NMR Evidence for Orbital Dependent Ferromagnetic Correlations in Sr2RuO4[END_REF][START_REF] Mukuda | 17O NMR probe of spin fluctuations in triplet superconductor Sr2RuO4[END_REF] and also polarized inelastic neutron scattering experiments [START_REF] Braden | Anisotropy of the Incommensurate Fluctuations in Sr2RuO4: A Study with Polarized Neutrons[END_REF][START_REF] Steffens | Spin Fluctuations in Sr2RuO4 from Polarized Neutron Scattering: Implications for Superconductivity[END_REF] reveal the existence of magnetic fluctuations centered at the origin of the Brillouin zone, which typically can be associated with ferromagnetism. Futhermore, a small concentration Co doping can lead to static short-range ferromagnetic order [START_REF] Ortmann | Competition Between Antiferromagnetism and Ferromagnetism in Sr2RuO4 Probed by Mn and Co Doping[END_REF]. All techniques find almost temperature independent quasi-ferromagnetic excitations in pure Sr 2 RuO 4 . This ferromagnetic response qualitatively agrees with a recent dynamical mean field theory (DMFT) analysis of magnetic fluctuations [START_REF] Strand | Magnetic response of Sr2RuO4: Quasi-local spin fluctuations due to Hund's coupling[END_REF], which finds essentially local magnetic fluctuations superposed on the well known nesting signal. However, the neutron data disagree with a fully local character as they show a finite q dependence [START_REF] Steffens | Spin Fluctuations in Sr2RuO4 from Polarized Neutron Scattering: Implications for Superconductivity[END_REF]. The quasi-ferromagnetic fluctuations also disagree with the expectations for a nearly ferromagnetic system that exhibits paramagnon scattering [START_REF] Steffens | Spin Fluctuations in Sr2RuO4 from Polarized Neutron Scattering: Implications for Superconductivity[END_REF][START_REF] Moriya | Spin Fluctuations in Itinerant Electron Magnetism[END_REF]. SrRuO 3 clearly exhibits such paramagnon scattering with its well-defined structure in q and energy space [START_REF] Jenni | Interplay of Electronic and Spin Degrees in Ferromagnetic SrRuO3: Anomalous Softening of the Magnon Gap and Stiffness[END_REF].

Here we present additional neutron scattering experiments on the magnetic fluctuations in Sr 2 RuO 4 , which focus on several aspects that are particularly relevant for the superconducting pairing mechanism involving mag- netic fluctuations or for the general understanding of magnetic excitations in a strongly correlated electron system. We discuss the possibility of important out-of-plane dispersion in the magnetic response in the superconducting and normal states, the shape of nesting scattering away from the peak position and the non-local character of the quasi-ferromagnetic response.

II. EXPERIMENTAL

INS experiments were carried out on the ThALES [START_REF] Jenni | Interplay of magnetic excitations and superconductivity in Sr2RuO4[END_REF][START_REF] Jenni | superconducting state of Sr2RuO4[END_REF] and IN20 [START_REF] Jenni | Electronic interaction in the unconventional superconductor Sr2RuO[END_REF] triple-axis spectrometers (TAS) at the Institut Laue Langevin and on the LET [START_REF] Braden | Low-energy magnetic excitations in the superconducting state of Sr2RuO4: opening of a gap?[END_REF] timeof-flight (TOF) spectrometer at the ISIS Neutron and Muon Source. We used an assembly of 12 Sr 2 RuO 4 crystals with a total volume of 2.2 cm 3 in all experiments. At Kyoto University, the crystals were grown using the floating zone method and similar crystals were studied in many experiments [START_REF] Mackenzie | The superconductivity of Sr2RuO4 and the physics of spin-triplet pairing[END_REF][START_REF] Maeno | Evaluation of Spin-Triplet Superconductivity in Sr2RuO4[END_REF]. The crystal assembly was oriented in the [100]/[010] scattering plane (corresponding to a vertical c axis) to study the in-plane physics of the Ru layers. Additionally, with the instruments ThALES and LET it was possible to access parts of the q space perpendicular to the plane which enables an analysis of the out-of-plane dispersion of the magnetic response. To conduct experiments inside the superconducting phase a dilution refrigerator was used, reaching a temperature of ∼200 mK, well below the transition temperature of ∼1.5 K. ThALES and LET are operating with a cold neutron source providing the energy resolution to study the magnetic response down to ∼200 µeV. The TOF spectrometer LET records data simultaneously with four different values of the incidental energies, E i and resolutions, while the energy resolution of the TAS ThALES is determined by the chosen final neutron wave vector k f of 1.57 Å-1 combined with the collimations. On ThALES the best intensity to background ratio was achieved by using a Si(111) monochromator and PG(002) analyzer combined with a radial collimator in front of the analyzer for further background reduction. The same configuration was also used in an earlier study [START_REF] Kunkemöller | Absence of a Large Superconductivity-Induced Gap in Magnetic Fluctuations of Sr2RuO4[END_REF].

A polarized neutron scattering experiment was performed on the thermal TAS IN20 using Heusler crystals as monochromator and analyzer. A spin flipper in front of the analyzer enabled the polarization analysis. The scans were performed with a fixed final momentum of k f = 4.1 Å-1 , where the graphite filter in front of the analyzer cuts higher order contaminations. Longitudinal polarization analysis was performed with a set of Helmholtz coils.

III. RESULTS AND DISCUSSION

A. q dependence of fluctuations associated with nesting

The TOF technique enables an imaging of the complete Q-E-space, which gives insight on the distribution of scattering intensity in the reciprocal space. Throughout the paper, the scattering vector Q=(H,K,L) and the propagation vector in the first Brillouin zone q=(q h ,q k ,q l ) are given in reciprocal lattice units (rlu). We mostly consider only the planar wave vector Q 2d =(H,K) projection. Fig. 2 shows the inelastic scattering plotted against the H,K components of the scattering vector in the superconducting phase. The four different panels display sections of the two-dimensional (H,K) plane for different incident energies and hence different resolutions. The intensities are fully integrated along the energy transfer (depending on the incident energy) and along the out-of-plane component of the scattering vector, -0.7< L <0.7. The high scattering intensities at the incommensurate positions (±0.3,0.3), (±0.3,0.7), and (±0.7,0.7) are clearly visible, arising from the well known antiferromagnetic fluctuations [39-41, 43, 44]. Additionally there are ridges of scattering intensities connecting these positions in [ξ,0] and [0,ξ] directions that were first reported in [START_REF] Iida | Inelastic neutron scattering study of the magnetic fluctuations in Sr2RuO4[END_REF][START_REF] Iida | Two-Dimensional Incommensurate Magnetic Fluctuations in Sr2(Ru0.99Ti0.01)O4[END_REF]. The arc visible in Fig. 2(d) connecting (-0.3,0.3) and (0.3,0.3) is a spurious signal; it does not appear for the other incidental energies.

Neglecting electronic dispersion perpendicular to the planes and assuming an idealized scheme of flat onedimensional bands originating from the d xz and d yz orbitals, one expects nesting induced magnetic excitations FIG. 2. In-plane scattering in the superconducting phase (T = 0.2 K). The TOF data at four different incidental energies display the magnetic scattering distribution in the ab plane. The intense signal at the incommensurate positions (0.3,0.3), (0.7,0.7), and (0.3,0.7) is visible for all Ei. Additionally there is magnetic scattering between the incommensurate positions in [ξ,0] and [0,ξ] directions, respectively. To increase the statistics the data is integrated over the maximum L range of [-0.7,0.7] and full E range depending on the incidental energy (1.75< E <10 for Ei = 14.13meV, 0.8< E <6.7 for Ei = 8.78meV, 0.7< E <4.5 for Ei = 5.64meV, and 0.5< E <3.5 for Ei = 4.52meV). The overlayed rectangles in (a) represent the integration area of the one-dimensional cuts displayed in Fig. 3(a)-(c).

for any two-dimensional vector Q 2d =(0.3,ξ) and (ξ,0.3) and accordingly a peak at (0.3,0.3) [START_REF] Mazin | Competitions in Layered Ruthenates: Ferromagnetism versus Antiferromagnetism and Triplet versus Singlet Pairing[END_REF]. The peaks clearly dominate but the ridges are also detectablemostly for the positions connecting the nesting peaks, i.e. 0.3< ξ <0.7. This is in accordance with the calculation of the bare susceptibility which shows an enhanced signal only between the peaks, i.e. for the paths from (0.3,0.3) to (0.7,0.3) [START_REF] Mazin | Competitions in Layered Ruthenates: Ferromagnetism versus Antiferromagnetism and Triplet versus Singlet Pairing[END_REF].

To analyze the ridge scattering and the anisotropy of the incommensurate signals in detail, Fig. 3(a) shows one-dimensional cuts along the ridge in [ξ,0] direction calculated from the data taken with E i =14.13 meV (Fig. 2(a)). By subtracting the background obtained from the average of (ξ,0.15) and (ξ,0.45), shown in Fig. 3(b) and (c) respectively, we isolate the signal along the line (ξ,0.3) shown in Fig. 3(d). The ridge scattering is mainly detectable between the peaks at the incommensurate positions, as it is visible in the two one-dimensional cuts representing the background parallel to the ridge on both sides (Fig. 3(b) and(c)). While the (ξ,0.15) cut exhibits only a weak signal around (-0.3,0.15) the (ξ,0.45) cut shows clearly two peaks at the (-0.7,0.45) and (-0.3,0.45) positions representing the ridges in [0,ξ] direction. The rounding of the one-dimensional Fermisurface sheets suppresses the susceptibility at (0.3,ξ) with ξ lower than 0.3, but this suppression is not abrupt. Besides the ridge scattering we may also confirm the pronounced asymmetry of the nesting peak with a shoulder near (0.25,0.3) and equivalent positions. This shoulder was reported in [START_REF] Braden | Inelastic neutron scattering study of magnetic excitations in Sr2RuO4[END_REF] and was also found in the full RPA calculations.

The asymmetry of the nesting peaks and the ridge scattering between the incommensurate positions can also be seen in the data of lower incident energies (see Fig. 3(e) and (f)). The one-dimensional cuts for different K values confirm the asymmetric shape of the nesting peaks. A thorough analysis of the pure magnetic signal as in the case of E i = 14.13 meV is not possible due to uncertainty in the background. Furthermore, the ridge scattering is less pronounced in the data obtained with lower incident energies, which indicates a higher characteristic energy of the ridge scattering. This further explains why the much weaker scattering in the ridges has not been detected in early TAS studies [START_REF] Sidis | Evidence for Incommensurate Spin Fluctuations in Sr2RuO4[END_REF][START_REF] Braden | Inelastic neutron scattering study of magnetic excitations in Sr2RuO4[END_REF][START_REF] Servant | Magnetic excitations in the normal and superconducting states of Sr2RuO4[END_REF].

B. Search for gap opening or a resonance mode below Tc

The opening of a superconductivity-induced gap in the spectrum of magnetic fluctuations would have strong impact on the discussion of the superconducting character in Sr 2 RuO 4 . Previous INS experiments using a TAS revealed the clear absence of a large gap at the nesting position [START_REF] Kunkemöller | Absence of a Large Superconductivity-Induced Gap in Magnetic Fluctuations of Sr2RuO4[END_REF], whereas a recent TOF experiment reports a tiny gap although the statistics remained very poor [START_REF] Iida | Horizontal Line Nodes in Sr2RuO4 Proved by Spin Resonance[END_REF]. Studying the magnetic response of Sr 2 RuO 4 in its superconducting phase by INS is challenging, because one needs to focus on small energies of the order of 0.2 to 0.5 meV. At these energies the signal in the normal state is at least one order of magnitude below its maximum strength at 6 meV, and the required high-energy resolution further suppresses statistics. Fig. 4 presents the TOF data obtained with E i = 3 meV by calculating the energy dependence at the nesting position integrated over all L values. The full L integration is needed to enhance the statistics. In Fig. 4 (a) and (b) we compare the raw data for both temperatures with the background signal. In (c) the background subtracted magnetic response in the superconducting phase is compared to that in the normal phase. There is no evidence for the opening of a gap within the statistics of this TOF experiment. Also a resonance at a finite energy cannot be detected. Admittedly the statistics of this TOF data is too poor to detect small signals or their suppression.

Following the claim of Iida et al. [START_REF] Iida | Horizontal Line Nodes in Sr2RuO4 Proved by Spin Resonance[END_REF] the TOF data is also analyzed in terms of a possible resonance mode appearing at a finite value of the L component, i.e. at (0.3,0.3,0.5). Therefore, the L dependence of the magnetic signal at (0.3,0.3,L) is determined by background subtraction and compared for the two temperatures (see Fig. 5). The different panels represent the energy ranges from reference 53, where a resonance appearing at 0.56 meV is proposed for L=0.5. In our data shown in Fig. 5(b), there is no difference visible between superconducting and normal phase at L=±0.5.

To study the low-energy response and its L dependence in more detail and with better statistics the TAS is better suited since measurements can be focused to single Q,E points. Using ThALES and its high flux and energy resolution constant Q scans at the incommensurate position (0.3,0.7,L) with L=0, 0.25, and 0.5 were mea-FIG. 5. L dependence of incommensurate signal at low energies extracted from TOF data. Constant E cuts with an integration width of 0.2 meV at the incommensurate position (0.3,0.3,L) were adjusted for the measured background at the same energy at (0.09,0.41,L) and corrected for the Bose factor. The L dependence of the magnetic response in the superconducting phase (blue) is compared to the normal phase (red). Additionally, the square of the Ru 1+ form factor is depicted in each panel (black dashed line). There is no evidence for a peak at L=0.5.

sured to investigate the L dependence of the low energy response (see Fig. 6). This incommensurate position was chosen due to a better signal-to-noise ratio compared to (0.3,0.3,L) and because the larger |Q| value allows one to reach finite L values by tilting the cryostat. Similar to Fig. 4 (a) and (b) the raw data for two temperatures is shown in Fig. 6 (a)-(c). The background was measured by rotating ω by 20 degrees for each L value and then combining all three backgrounds to an average. For all L values the intensity of the incommensurate signal increases approximately linearly for small energies, following the established single relaxor behavior. Comparing the two temperatures there is no difference noticable for any L value down to the energy resolution. Especially around 0.56 meV where Iida et al. [START_REF] Iida | Horizontal Line Nodes in Sr2RuO4 Proved by Spin Resonance[END_REF] propose a resonance at the incommensurate position (0.3,0.3,0.5) the two temperatures yield comparable signals. It should be noted here that while the incommensurate positions (0.3,0.3,0) and (0.3,0.7,0) are crystallographically not equivalent both positions become equivalent with the L component 0.5, see Fig. 1. Therefore, the data taken at (0.3,0.3,0.5) and (0.7,0.3,0.5) can be compared. To emphasize the absence of a resonance mode around 0.56 meV the data from Fig. 6 is plotted with a larger energy binning to further increase the statistics (see Fig. 7, which also indicates the broad energy integration used in [START_REF] Iida | Horizontal Line Nodes in Sr2RuO4 Proved by Spin Resonance[END_REF]). There is no significant deviation from the general linear behavior for any L value at low temperatures detectable. Iida et al. [START_REF] Iida | Horizontal Line Nodes in Sr2RuO4 Proved by Spin Resonance[END_REF] report an increase of signal of ∼60% for L=0.5 in the superconducting phase, which clearly is incompatible with our data that offer higher statistics.

Since no L dependence of the magnetic low energy response can be established (Fig. 6 and7) we merge the data and compare it with the former published lowenergy dependence of the incommensurate signal [START_REF] Kunkemöller | Absence of a Large Superconductivity-Induced Gap in Magnetic Fluctuations of Sr2RuO4[END_REF] (see Fig. 8). The new experiments below T c fully confirm that the nesting excitations in Sr 2 RuO 4 do not exhibit a large gap, i.e. a magnetic gap comparable to twice the superconducting one. Combining all the previous and new data there is, however, some weak evidence for the suppression of magnetic scattering at very low energies below 0.25 meV. With the neutron instrumentation of today it seems very difficult to further characterize the suppression of the small signal at such low energy.

For the previously assumed superconducting state detailed theoretical analyzes of the magnetic response were reported [START_REF] Huo | Spin density wave fluctuations and p-wave pairing in Sr2RuO4[END_REF], but concerning the more recently proposed superconducting symmetries [START_REF] Røising | Superconducting order of Sr2RuO4 from a three-dimensional microscopic model[END_REF][START_REF] Rømer | Knight Shift and Leading Superconducting Instability from Spin Fluctuations in Sr2RuO4[END_REF][START_REF] Wang | Theory of Chiral p-Wave Superconductivity with Near Nodes for Sr2RuO4[END_REF][START_REF] Wang | Spin-orbit coupling and spin-triplet pairing symmetry in Sr2RuO4[END_REF][START_REF] Suh | Stabilizing even-parity chiral superconductivity in Sr2RuO4[END_REF][START_REF] Rømer | Theory of straininduced magnetic order and splitting of Tc and TTRSB in Sr2RuO4[END_REF][START_REF] Kivelson | A proposal for reconciling diverse experiments on the superconducting state in Sr2RuO4[END_REF][START_REF] Sharma | Momentum-resolved superconducting energy gaps of Sr2RuO4 from quasiparticle interference imaging[END_REF] such investigations lack. The d x 2 -y 2 state deduced from quasiparticle interference imaging [START_REF] Sharma | Momentum-resolved superconducting energy gaps of Sr2RuO4 from quasiparticle interference imaging[END_REF] exhibits nodes at Fermi-surface positions that are connected through the nesting vector. This implies that even at very low energies, the nesting induced excitations are not fully suppressed in such d x 2 -y 2 superconducting state, in agreement with the experimental absence of a large gap in the nesting spectrum [START_REF] Kunkemöller | Absence of a Large Superconductivity-Induced Gap in Magnetic Fluctuations of Sr2RuO4[END_REF]. Within the d x 2 -y 2 superconducting state the nesting vector also connects Fermi-surface regions with maximum and minimum gap values and it connects either two regions of the β sheet or one β region with an α region. Therefore the conditions for a spin-resonance mode are more complex and less favorable than in the case of the FeAs-based superconductors, where the s +-superconducting symmetry and the nesting magnetic fluctuations perfectly match each other [START_REF] Mazin | Unconventional superconductivity with a sign rever-sal in the order parameter of lafeaso1-xfx[END_REF].

C. Shape of the quasi-ferromagnetic fluctuations

The polarization analysis of inelastic neutron scattering provides the separation of the magnetic from any other scattering contribution. It is therefore possible to identify a tiny magnetic response that is little structured in q space. This technique was used to detect quasi-ferromagnetic fluctuations and to determine their strength in comparison to the incommensurate fluctuations in Sr 2 RuO 4 [START_REF] Steffens | Spin Fluctuations in Sr2RuO4 from Polarized Neutron Scattering: Implications for Superconductivity[END_REF]. We wished to extend this study focusing on the q dependence of the magnetic quasiferromagnetic response. Recent DMFT calculations [START_REF] Strand | Magnetic response of Sr2RuO4: Quasi-local spin fluctuations due to Hund's coupling[END_REF] find evidence for local fluctuations superposing the wellestablished nesting excitations, which qualitatively agree with the experimental quasi-ferromagnetic signal. However, while the neutron experiments indicate a finite suppression of the quasi-ferromagnetic response towards the boundaries of the Brillouin zone, the DMFT calculation obtains an essentially local feature without such q dependence.

The polarized neutron study was performed on the thermal TAS IN20 and the results are shown in Fig. 9. An example of the raw data with different spin channels that are needed for the polarization analysis, is given in Fig. 9(a) where a diagonal constant energy scan at 8 meV, reaching from the zone boundary (0.5,0.5) over the incommensurate position (0.7,0.3) to the zone center (1,0), is shown. The x, y, z indices refer to the common coordinate system used in neutron polarization analysis in respect to the scattering vector Q [START_REF] Steffens | Spin Fluctuations in Sr2RuO4 from Polarized Neutron Scattering: Implications for Superconductivity[END_REF]. The three spin flip channels SF x , SF y , and SF z clearly exhibit a maximum at the incommensurate position. While SF y and SF z exhibit comparable amplitudes SF x carries the doubled intensity as it senses both magnetic components perpendicular to the scattering vector. There is an enhancement of magnetic excitations polarized along the c direction, that can be seen in the stronger SF y and that was studied in reference 42. Assuming a polarization independent background, 2I(SF x )-I(SF y )-I(SF z ) yields the background free magnetic signal, see discussion in reference 45. sented in [START_REF] Steffens | Spin Fluctuations in Sr2RuO4 from Polarized Neutron Scattering: Implications for Superconductivity[END_REF]. Additionally, the data at 290 K indicates a significant drop of the incommensurate nesting signal, which however still is finite and clearly observable. The temperature dependence of the incommensurate signal was first discussed in reference 39, where the neutron scattering results are compared to the NMR results from reference 38. The incommensurate signal was found to strongly decrease with increasing temperature up to room temperature while the ferromagnetic component of the NMR is nearly temperature independent. Also the previous polarized neutron experiment found the quasi-ferromagnetic contribution to be almost identical at 1.6 and 160 K [START_REF] Steffens | Spin Fluctuations in Sr2RuO4 from Polarized Neutron Scattering: Implications for Superconductivity[END_REF]. As indicated in Fig. 9(b) the quasi-ferromagnetic signal does not change up to 290 K, so that the peak heights of incommensurate and quasi-ferromagnetic contributions are comparable at ambient temperature. Taking the much broader q shape of the quasi-ferromagnetic excitations into account, the qintegrated spectral weight of the latter clearly dominates. Around room temperature the quasi-ferromagnetic fluctuations possess thus a larger impact on any integrating processes such as electron scattering. The quasi-ferromagnetic fluctuations at 290 K, however, do not exhibit a local character as the signal is significantly reduced at the antiferromagnetic zone boundary (0.5,0.5,0) (Fig. 9(c)). This confirms the conclusion of Steffens et al. [START_REF] Steffens | Spin Fluctuations in Sr2RuO4 from Polarized Neutron Scattering: Implications for Superconductivity[END_REF] that the quasi-ferromagnetic fluctuations are sharper in q space than expected from the calculations. Also at the other zone boundary (0.5,0,0) there is no significant magnetic signal detectable (see Fig. 10).

IV. CONCLUSION

Polarized and unpolarized neutron scattering experiments were performed to study several aspects of the magnetic fluctuations in Sr 2 RuO 4 that are particularly relevant for a possible superconducting pairing scenario. The TOF instrument LET yields full mapping of the excitations and reveals the well-studied incommensurate fluctuations at (0.3,0.3) in the two-dimensional reciprocal space. There is also ridge scattering at (0.3,ξ) reflecting the one-dimensional character of the d xz and d yz bands, as first reported in references 43 and 44. These ridges are stronger between the four peaks surrounding (0.5,0.5), i.e. for ξ>0.3, but the suppression of the signal at smaller ξ is gradual. The TOF data confirm the pronounced asymmetry of the nesting peaks. Concerning the study of the nesting fluctuations at very low energy in the superconducting phase, TAS experiments yield higher statistics due to the possibility to focus the experiment on the particular position in Q,E space. Data taken at different out-of-plane components of the scattering vector exclude a sizeable resonance mode emerging at L=0.5 in the superconducting phase. Only by combining the results of several experiments one can obtain some evidence for the suppression of spectral weight at very low energies.

With neutron polarization analysis the magnetic excitations were further characterized at 290 K. The incommensurate nesting signal is strongly reduced but still visible, while the quasi-ferromagnetic contribution is almost unchanged. At this temperature there is a suppression of this quasiferromagnetic scattering at the Brillouin-zone boundaries, which underlines that this response is not fully local.

FIG. 1 .

 1 FIG. 1. Fermi surface of Sr2RuO4 for kz = 0. The bands are based on LDA+SO calculations from [60] and marked by different colors. The black arrow represents the dominant nesting vector between the one-dimensional sheets α (red) and β (blue). The incommensurate positions of the in-plane nesting signal are marked by different symbols. The circles represent the crystallographically equivalent positions (±0.3,±0.3) and (±0.7,±0.7). The positions (±0.3,±0.7) and (±0.7,±0.3) shown by stars are equivalent to those on the diagonals only in a purely two-dimensional picture, because (1 0 0) is not an allowed Bragg peak in the body-centered lattice.

FIG. 3 .

 3 FIG. 3. Magnetic scattering along the connection of the incommensurate positions. (a)-(c) show one-dimensional cuts from Fig. 2(a) along the (ξ,K) paths for K = 0.15 (a), 0.3 (b), and 0.45 (c). The background at both sides of the incommensurate positions is displayed in (a) and (c) (represented by the same colored rectangles in 3(a)). An averaged background is formed from both (gray open circles) and fitted with a linear contribution and two Gaussians (black solid line). This is compared to the incommensurate signal in (b). In (d) the linear background contribution (black dashed line) is subtracted and the signal along the [ξ,0] direction is fitted with two skew Gaussians for the incommensurate signal and a broad Gaussian fixed at ξ = 0.5 (red area) taking into account the ridge scattering. (e) and (f) represent one-dimensional cuts for different K and two different incident energies 8.78 meV and 5.64 meV taken from Fig. 2(b) and (c). The integration range in [0,ξ] direction is ±0.025 around the K value and the scans are shifted vertically for better visibility.

FIG. 4 .

 4 FIG. 4. Low energy dependence of incommensurate signal below and above the superconducting transition extracted from TOF data. (a) and (b) display the energy scans at at q=(0.3,0.3) below (T = 0.2 K) and above (T = 2 K) the superconducting phase transition. The background in both panels is derived from the constant Q cut at (0.09,0.41) for both temperatures (|Q IC | = |Q bg |). To increase statistics the TOF data with an incidental energy of 3 meV is fully integrated over L (range [-0.7,0.7]) and symmetrized by folding in q space at (0.3,0.7) along the (1,-1,0) plane. The H and K component is integrated with the range [0.25,0.35] (c) Background subtraction and Bose factor correction yields the pure magnetic response at low energies which is compared inside and outside the superconducting phase.

FIG. 6 .

 6 FIG.6. L dependence of incommensurate signal at low energies extracted from TAS data. The constant q scans were conducted at the incommensurate positions (0.3,0.7,L) with L = 0, 0.25, and 0.5 in the superconducting and normal phase. The background for each L is measured after ω rotation of 20 deg, thus keeping |q| constant, and later averaged for all scans, yielding the presented background (black circles) and its fit (gray). The intensity is normalized with 1980000 monitor counts which corresponds to a measuring time of about 15 min per point.

FIG. 9 .

 9 FIG.9. Polarized neutron analysis of the scattering along the diagonal of the 1 st Brillouin zone. (a) Example of constant energy scans for all three spin flip channels displays the increased scattering at the incommensurate position (0.7,0.3,0) at 8 meV and 1.6 K. The polarization analysis of all channels yields the purely magnetic scattering signal displayed in (b) for different energies and temperatures. The black circles represent data of the previously reported polarization analysis, taken from[START_REF] Steffens | Spin Fluctuations in Sr2RuO4 from Polarized Neutron Scattering: Implications for Superconductivity[END_REF]. This data set was as well measured at 8 meV and 1.6 K. (c) The magnetic signal at 290 K can be described by the susceptibility model used in[START_REF] Steffens | Spin Fluctuations in Sr2RuO4 from Polarized Neutron Scattering: Implications for Superconductivity[END_REF] (light red line). The intensity in (a) is normalized with 7800000 monitor counts which corresponds to a measuring time of about 20 minutes per point.

Fig. 9 (

 9 FIG.10. Comparison of magnetic scattering (T=1.6 K) at prominent points in k-space with L=0. The magnetic signal was extracted using the polarization analysis (2I(SFx)-I(SFy)-I(SFz)) and is displayed for the points in the Brillouin zone and different energies: Γ point, the incommensurate position, and the different zone boundaries X and M. The inset magnifies the intensity region around zero.

We acknowledge stimulating discussions with Ilya Eremin.

This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -Project number 277146847 -CRC 1238, project B04, the JSPS KAKENHI Nos.

JP15H05852 and JP17H06136, and the JSPS core-to-core program.


Houssein Nasrallah

Pengbo Lyu

Guillaume Maurin

Mohamad El-Roz

Highly efficient CO 2 reduction under visible-light on noncovalent Ru•••Re assembled photocatalyst: evidence on the electron transfer mechanism

Keywords: Artificial photosynthesis, CO2 photoreduction, supramolecular assembly, electron transfer

Herein, two complexes: Pyrene modified photosensitizer (RuPy) and catalyst (ReCOPy) were synthetized and combined to form a novel bimetallic supramolecular assembly RuPy•••ReCOPy via a combination of π-π stacking and hydrogen bond interactions. This supramolecular assembly was further characterized by electrochemical and spectroscopic techniques in order to determine its redox and photochemical properties. This novel RuPy•••ReCOPy supramolecular assembly was demonstrated to display a high level of performance for the photocatalytic conversion of CO2 conversion into CO with turn over frequency and CO quantum yield much higher (TOF: 18 h -1 , ΦCO: 0.77) than the value obtained for the benchmark system Ru(bpy)3Cl2 (Ru) with Re(bpy)(CO)3Cl (ReCO) (5.3 h -1 , ΦCO : 0.38). Time resolved spectroscopy and Density Functional Theory calculations revealed that an electron transfer mechanism is at the origin of the highly photocatalytic performance of RuPy•••ReCOPy.

INTRODUCTION

In the recent years, the use of CO2 as an alternative carbon source has become increasingly attractive for the production of useful carbon compounds, i.e. HCOOH, MeOH, CH4 and CO, among others. [START_REF] Li | Cocatalysts for selective photoreduction of CO2 into solar fuels[END_REF][START_REF] Corma | Photocatalytic reduction of CO2 for fuel production: possibilities and challenges[END_REF][START_REF] Aresta | Catalysis for the valorization of exhaust carbon: from CO2 to chemicals, materials, and fuels[END_REF] In particular, CO2 reduction using photocatalysts to mimic the solar light driven photosynthesis is a topical subject. In this field, the photocatalytic systems envisaged so far are split into three categories: isemiconductor systems, [START_REF] Sohn | Recent progress and perspectives in the photocatalytic CO2 reduction of Ti-oxidebased nanomaterials[END_REF][START_REF] Shehzad | A critical review on TiO2 based photocatalytic CO2 reduction system: Strategies to improve efficiency[END_REF][START_REF] Sánchez-Rodríguez | Semiconducting Nanocrystalline Bismuth Oxychloride (BiOCl) for Photocatalytic Reduction of CO2[END_REF][START_REF] Liu | Recent advancements in gC3N4-based photocatalysts for photocatalytic CO2 reduction: a mini review[END_REF][START_REF] Ong | Rational Design of Carbon-Based 2D Nanostructures for Enhanced Photocatalytic CO2 Reduction: A Dimensionality Perspective[END_REF] ii-biohybrid systems [START_REF] Yadav | A photocatalystenzyme coupled artificial photosynthesis system for solar energy in production of formic acid from CO2[END_REF][START_REF] Chaudhary | Visible Light-driven CO2 Reduction by Enzyme Coupled CdS Nanocrystals[END_REF][START_REF] Chen | Integration of enzymes and photosensitizers in a hierarchical mesoporous metal-organic framework for light-driven CO2 reduction[END_REF][START_REF] Miyaji | Artificial co-enzyme based on carbamoyl-modified viologen derivative cation radical for formate dehydrogenase in the catalytic CO2 reduction to formate[END_REF] and iii-organometallic complexes. This later strategy was initiated by Lehn et al. in 1983 using Re(bpy)(CO)3Cl catalyst to convert CO2 into CO. [START_REF] Hawecker | Efficient photochemical reduction of CO2 to CO by visible light irradiation of systems containing Re(bipy)(CO)3X or Ru(bipy)3 2+ -Co 2+ combinations as homogeneous catalysts[END_REF][START_REF] Hawecker | Electrocatalytic reduction of carbon dioxide mediated by Re(bipy)(CO)3Cl (bipy= 2, 2′-bipyridine)[END_REF] A wide range of metal-based complexes, i.e. Ru, Rh, Co and Mn have been further demonstrated to show even higher photocatalytic activities for CO2 conversion. [START_REF] Li | Photocatalytic CO2 reduction over metal-organic framework-based materials[END_REF][START_REF] Luo | From molecular metal complex to metal-organic framework: the CO2 reduction photocatalysts with clear and tunable structure[END_REF] Generally, a photosensitizer (PS) is required in tandem with the co-catalyst (Cat) to enable absorption of visible light and transfer the electron from a sacrificial electron donor to the Cat. Typically, Ishitani et al. reported several supramolecular photocatalysts by covalent linking of different photosensitizers and co-catalysts. In these systems, an efficient and faster electron transfer (ET) via intramolecular process was demonstrated to impact substantially their catalytic performance. [START_REF] Kamata | Photoelectrochemical CO2 Reduction Using a Ru(II)-Re(I) Supramolecular Photocatalyst Connected to a Vinyl Polymer on a NiO Electrode[END_REF][START_REF] Koike | Investigation of excited state, reductive quenching, and intramolecular electron transfer of Ru(II)-Re(I) supramolecular photocatalysts for CO2 reduction using time-resolved IR measurements[END_REF][START_REF] Kumagai | Hybrid Photocathode Consisting of CuGaO2 p-Type Semiconductor and a Ru(II)-Re(I) Supramolecular Photocatalyst: Non-Biased Visible-Light-Driven CO2 Reduction with Water Oxidation[END_REF][START_REF] Kuramochi | Iridium(III) 1-Phenylisoquinoline Complexes as a Photosensitizer for Photocatalytic CO2 Reduction: A Mixed System with a Re(I) Catalyst and a Supramolecular Photocatalyst[END_REF][START_REF] Sato | Highly efficient supramolecular photocatalysts for CO2 reduction using visible light[END_REF][START_REF] Tamaki | Supramolecular Photocatalysts for the Reduction of CO2[END_REF][START_REF] Tamaki | Red-Light-Driven Photocatalytic Reduction of CO2 using Os(II)-Re(I) Supramolecular Complexes[END_REF][START_REF] Tamaki | Development of highly efficient supramolecular CO2 reduction photocatalysts with high turnover frequency and durability[END_REF][START_REF] Ueda | A Visible-Light Harvesting System for Efficient CO2 Reduction Using a Supramolecular Ru(II)-Re(I) Photocatalyst Adsorbed in Periodic Mesoporous Organosilica[END_REF] A faster ET from the photosensitizer to the metallic center of the catalyst reduces the undesirable deactivation process of the PS excited state. Reducing the distance between the PS and the Cat via non-covalent interactions is an alternative promising strategy developed recently for making the ET more efficient. This allows adjusting the PS/Cat ratio, simplifying the synthesis process comparing to covalently linked PS-Cat, expanding their use and adaptation with other PS/Cat moiety and/or their potential adsorption on conductive support, etc. In this context, Kubiak et al. reported, recently, intramolecular ET by assembling Ru(dac)(bpy)2(PF6)2 and Re(dac)(CO)3Cl (dac = 4,4′-bis(methyl acetamidomethyl)-2,2′-bipyridine, bpy = 2,2′-bipyridine) via (-NH---O=C-) hydrogen bond interactions resulting in a substantial improvement of the CO2 conversion as compared to the combination of Re(dac)(CO)3Cl with the commercial Ru(bpy)3PF6. [START_REF] Machan | Supramolecular assembly promotes the electrocatalytic reduction of carbon dioxide by Re(I) bipyridine catalysts at a lower overpotential[END_REF][START_REF] Cheung | Improving photocatalysis for the reduction of CO2 through non-covalent supramolecular assembly[END_REF] Another system stabilized by π-π stacking interactions was reported, recently, by He et al, with Re[4,4′-di(pyren-1-yl)-2,2′-bipyridine](CO)3Cl (4.4'dipyrenyl-Re) as co-catalyst in the presence of Ru(bpy)3Cl2 enabling an efficient conversion of CO2 into CO. [START_REF] Qiu | A rhenium catalyst with bifunctional pyrene groups boosts natural light-driven CO2 reduction[END_REF] This intermolecular π-π stacking was found to boost ET leading to a turnover number (TON) twice higher than that obtained using the commercial Re(bpy)CO3Cl. On the other hand, the 4.4'-dipyrenyl-Re was active for CO2 photoreduction without the photosensitizer under solar light. This led to a light harvesting enhancement due to the π-π conjugation between the pyrene and the bipyridine groups of the catalyst as well as to the accelerated intermolecular ET through the stacked pyrenes. Very recently, Lu et al. reported a series of Ru(Phen) 3 2+ complexes (Phen: 1, 10-Phenanthroline) modified by pyrene as photosensitizers in association with cobalt-complex based catalyst for CO2 photoreduction. [START_REF] Wang | Improving photosensitization for photochemical CO2to-CO conversion[END_REF] The significant enhancement, observed with one of the modified photosensitizer, was assigned to an improvement of their photosensitization due to a long-lived excited state and suitable excited-state oxidation potential. It is also well documented that the π-π interactions enable the immobilization of pyrene modified catalysts on the surfaces of carbon allotropes for recycling purposes, i.e. reduced graphene oxide, carbon nanotubes and C60 among others. [START_REF] Chen | π-π stacking interaction: a nondestructive and facile means in material engineering for bioapplications[END_REF][START_REF] Christopher | The nature of π-π interactions[END_REF][START_REF] Vriamont | Catalysis with gold complexes immobilised on carbon nanotubes by π-π stacking interactions: Heterogeneous catalysis versus the boomerang effect[END_REF][START_REF] Nasrallah | Non covalent immobilization of pyrene-tagged ruthenium complexes onto graphene surfaces for recycling in olefin metathesis reactions[END_REF][START_REF] Karami | Catalytic activity and facile recovery of a cyclometalated N-heterocyclic carbene palladium (II) complex immobilized by non-covalent interactions on reduced graphene oxide[END_REF] Typically, Gray et al. reported the synthesis of a series of bipyridine-based complexes containing two pyrenes moieties to be immobilized on carbon electrode via π-π stacking for electrochemical CO2 reduction. [START_REF] Gupta | Immobilization and electrochemical properties of ruthenium and iridium complexes on carbon electrodes[END_REF][START_REF] Blakemore | Noncovalent immobilization of electrocatalysts on carbon electrodes for fuel production[END_REF] Herein, we report two ruthenium and rhenium-based complexes, i.e. RuPy and ReCOPy respectively, containing both, two pyrenes linked via -CH2-NH-CO-bonds with the bipyridine moieties (Fig. 1). The so-designed complexes are assembled to produce a photocatalytic supramolecular PS/Cat system via an unconventional combination of π-π stacking and hydrogen bond interactions. In addition to the short separating distance between PS and Cat, we demonstrated that the π-π stacking promotes an efficient ET mediated by the pyrene moieties to achieve an outstanding conversion of CO2 under visible light. Time resolved photoluminescence experiments were further combined with Density Functional Theory (DFT simulations) to shed light into the efficient electron transfer at the origin of the remarkable performances of this novel supramolecular photocatalytic system.

EXPERIMENTAL SECTION

Materials

1,8-diazabicyclo[5.4.0]undec-7-ene (DBU), 4,4 ' -Dimethyl-2,2-bipyridine and the complex Re(bpy)(CO)3Cl were purchased from TCI chemicals. Ru(bpy)2Cl2.6H2O, Ru(bpy)3Cl2, ReCO5Cl, DMF, SOCl2 and 1pyrenemethylamine hydrochloride were purchased from Merck company. Commercially available acetonitrile, toluene, THF, DMF were used without any distillation. 4,4 ' -Dimethyl-2,2-bipyridine (5.0 g) in heated H2SO4 (125 mL, 70-80 °C) was oxidized by adding solid potassium dichromate (24 g) slowly. The temperature was held consistently between 70 and 80 °C during the transfer. The deep green mixture was then poured over 800 mL of ice/ H2O, affording a light-yellow precipitate that was isolated by vacuum filtration and was washed with H2O. The solid was then refluxed in 50% HNO3 (150 mL) for 4 h. The cooled solution was then poured over ice and diluted with 800 mL of H2O. A white powder was isolated by vacuum filtration and washed with H2O (5 g, 73%). 1 H NMR (400 MHz, DMSO-d6) δ (ppm): 13.83 (2H, br s, R-COOH), 8.92 (d, J= 5.1 Hz, 2H), 8.85 (s, 2H), 7.92 (dd, J=4.9, 1.2 Hz, 2H).

Complexes RuPy and

N 4,4' -bis(1-pyrenylmethyl)-[2,2´-dipyridyl]-4,4´-dicarboxamide (Ligand-Bpy-Py).

The acid chloride of 2,2´-bipyridine-4,4´-dicarboxylic acid was prepared by refluxing 0.37 g (1.5 mmol) of the 4,4-dicarboxylic acid-2,2-bipyridine acid in 15 mL of thionyl chloride for 6 h. Remaining thionyl chloride was removed under vacuum. In a separate flask, 0.8 g (3 mmol) of 1-pyrenemethylamine hydrochloride were combined with 150 mL of dry acetonitrile and 0.9 mL of 1,8-diazabicyclo [5.4.0]undec-7-ene (DBU). The resulting solution was transferred to the solid bipyridine-acid chloride via cannula. The mixture was stirred for 12 h at room temperature, at which time 20 mL of saturated sodium bicarbonate and 130 mL of distilled water were added to form a beige precipitate. The precipitate was collected by filtration and washed with deionized water. The precipitate was dried under vacuum to give 0.62 g (61%) of an offwhite solid.

fac-(N 4,4' -bis(1-pyrenylmethyl)-[2,2´-dipyridyl]-4,4´-dicarboxamide)tricarbonylcholoro rhenium (I) (ReCOPy).

A solution of Re(CO)5Cl (18 mg, 0.049 mmol) with Ligand-Bpy-Py (30 mg, 0.044 mmol) in 1 mL of toluene was refluxed 18 h at 110ᵒC under argon. The solution was centrifuged to give an orange solid. The solid material was redissolved in THF before being centrifuged once more. The obtained solution was then concentrated and dried by rotary evaporation to obtain 30 mg of an orange precipitate. (Yield = 68%). 1 H NMR (400 MHz, DMSO-d6) δ (ppm) 9.92 (t, J =3.7 Hz, 2H), 9.18 (d, J= 3.8 Hz, 2H), 9.12 (s, 2H), 8.46 (d, J= 6.1 Hz, 2H), 8.34-8.24 (m, 9H), 8.07-8.18 (m, J= 5.27Hz, 9H), 8.08 (t, J = 5 Hz, 2NH amide), 5.32 (d, J = 4 Hz, 4H). ESI-MS (positive) m/z: found 999.14 (ReCOPyNa), calculated 999.13 (ReC49H30N4O5ClNa).

Electrochemistry

Electrochemical measurements were realized with a PowerEase 300W Power Supply, 230 VAC. All experiments were performed in DMF, the supporting electrolyte was 0.1 M tetrabutylammonium hexafluorophosphate (TBAPF6), using a standard three-electrode configuration: 2 mm diameter. Platinum disk working electrode, a silver wire immersed in a solution of 0.1 M TBAPF6 served as a reference electrode and the counter electrode was a Pt wire. The ferrocenium/ferrocene (Fc +/0 ) couple was used as an external reference in all experiments to calibrate potentials. Voltammetry collected for solution-soluble redox couples with typically concentrations of 3 × 10 -4 M with scan rate of 100 mV/s.

Photocatalytic tests

The photocatalytic CO2 reduction was tested in an in-situ reactor developed in the LCS laboratory and presented in Fig. S5. The reactor is made from glass with horizontal tubes which ensuring the FTIR beam pathway through CaF2 windows. The reactor is equipped with air circulator system for cooling and two gas inlet and outlet. The visible irradiation is ensured from the top through a removable quartz window. The quartz and CaF2 windows are attached to the reactor with screw fittings and the tightness is obtained by adapted Teflon O-rings. The total internal volume of the reactor is 160 ± 5 ml. All IR spectrum measurements with the in situ FTIR reactor were monitored in real time with 5 min per spectrum of time resolution. IR spectra of the reactor headspace were recorded using Nicolet 6700 IR spectrometer (Thermo Fisher 14 Scientific) equipped with an MCT detector. All photocatalytic tests presented in this work were performed in batch configuration and at room temperature. As a light source, Xe-lamp 16 (LC8 Hamamatsu, 200 W) with pass-high filter at 390 nm was used. Complexes were dissolved in DMF/H2O mixture (10/1.8 ml) and the solution was bubbled with saturated with CO2 for one hour with a flow rate of 8 ml min -1 . Then, triethanolamine (TEOA) was introduced as electron donor (220 mg in 1 mL) in the reactor where the CO2 bubbling was maintained for additional 15 minutes.

RESULTS AND DISCUSSION

Electro-photochemical characterizations

Two complexes were synthesized in this study, namely ReCOPy and RuPy (Fig. 1c). The first one was prepared according to the protocol reported in a previous study which considered this complex for the electro-catalytic reduction of CO2. [START_REF] Blakemore | Noncovalent immobilization of electrocatalysts on carbon electrodes for fuel production[END_REF] RuPy was synthetized, for the first time in this work, from the equimolar mixture of Ru(bpy)2Cl2 and Bpy-Py ligand. The other two commercial homologues Ru and ReCO complexes were used for comparison.

The electrochemical analysis was performed in order to determine the redox potentials of the different systems. The cyclic voltammetry (CVs) of Ru and ReCO complexes agrees well with the literature. [START_REF] Cheung | Improving photocatalysis for the reduction of CO2 through non-covalent supramolecular assembly[END_REF] A first reduction from Ru 2+ to Ru + and from Re + to Re 0 occurs at -1.77 V and at -1.79 V, respectively, with reversible oxidation bands at -1.71 V and -1.70 V, respectively (Fig. 2). Regarding the ReCOPy complex, the reduction band of ReCO + /ReCO 0 is shifted to -1.96 V with a quasi-reversible oxidation band at -1.86V.

On the other hand, The CV analysis of the RuPy complex showed a first oxidation band of RuPy 2+ / RuPy + at -1.73V. In addition to the UV-visible absorption data (bad gap values), these reduction potential values will be used later for calculating the energetic positions of the HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) of the corresponding complexes. The UV-Vis spectra of the complexes highlight the interaction of pyrene function with the metal center (Fig. 3a). The absorption bands, located at 458 nm and 370 nm for Ru and ReCO, respectively, are assigned to the metal to ligand charge transfer (MLCT). [START_REF] Thompson | Ru(bpy)3] 2+* and other remarkable metal-to-ligand charge transfer (MLCT) excited states[END_REF][START_REF] Whang | An electron-reservoir Re (I) complex for enhanced efficiency for reduction of CO2 to CO[END_REF] However, a red-shift of ca. 20 nm is noted in MLCT absorbance range for both RuPy and ReCOPy complexes (478 and 405 nm, respectively). This red-shift consolidates the hypothesis of the electron delocalization between the metal center and the pyrene indicating strong interactions between them. It should be noted that no significant influence of the grafted pyrene group on the absorbance coefficient was observed in this work, in contrast to what has been observed when pyrene is directly linked to the bipyridine group of Re(bpy)(CO)3Cl. [START_REF] Qiu | A rhenium catalyst with bifunctional pyrene groups boosts natural light-driven CO2 reduction[END_REF] In the last case, a significant increase in the coefficient molar absorption of the MLCT is observed in addition to the red-shift. This difference can be explained by a higher delocalization of the electron between the directly-linked pyrene and the 4,4'dipyrenyl-Regroup via a single bond. In contrast, the contribution of the pyrene in the electron delocalization is probably lower for ReCOPy, however the structure flexibility is higher owing to the presence of -CH2-NH-CO-linker, which is more suitable, in our case, for promoting the desired interaction with RuPy photosensitizer. In order the investigate the interaction between RuPy and ReCOPy, a mixture of ratio 1:1 All photocatalytic tests were carried out under similar visible light irradiation condition, in DMF, using triethanolamine (TEOA) as sacrificial electron donor and after saturation of the catalytic batch reactor with CO2. The gas phase was monitored during the reaction by in-situ FTIR and the amount of CO produced was quantified following the characteristic bands at 2116 and 2171 cm -1 (Fig. 4b) as reported in our recent works.

[40] It should be noted that the CO is formed selectively from the CO2 reduction as demonstrate Figure S8 using labelled CO2 ( 13 CO2). All tests were reproduced at least two times and the error bars were estimated to be less than ±10% (Fig. S9). The reactor temperature was maintained at around 25°C by air cooling circuit. The selectivity toward CO vs HCOOH formation was >99% in all cases, under our reaction conditions as further confirmed by gas chromatography (Fig. S9).

An equimolar mixture of complexes RuPy•••ReCOPy (1:1) was found to produce around 0.1 mmol of CO after one hour with an initial reaction rate V0 of 0.12 mmol.h -1 and turn over frequency (TOF) of 18±2 h -1 .

These results were compared to those obtained with the commercial Ru and ReCO complexes, tested under the same conditions. Remarkably, our new RuPy•••ReCOPy s system shows a substantially higher activity with a TOF three times higher than the value obtained for Ru•••ReCO (18 vs 5.3 h -1 , respectively) as well as four-fold higher initial reaction rate V0 (0.12 vs 0.03 mmol.h -1 , respectively). (Table S1) Additionally, a very high quantum yield (Φco) for CO formation was calculated to be 0.77 for RuPy•••ReCOPy and 0.38 in case of Ru•••ReCO .Comparing the relative TOF and Φco with that reported in the literature when mononuclear homogeneous counterparts (PS + Cat) are used as reference allows ranking our system as one of the four most efficient counterpart systems reported in the literature (Table S2). This observation emphasizes a major role of the pyrene function on TOF and reaction rate in the photocatalytic process (Fig. 4a). However, the absorbance behaviors of the photosensitizers as well as the redox potentials of the different complexes cannot justify this gap between both systems. In order to better understand this showed a poor conversion (TOF = 2.2 h -1 ) (Fig. 4c). These results seem contradictory to what has been reported recently on the benefit effect of the pyrene-modified photosensitizer [START_REF] Qiu | A rhenium catalyst with bifunctional pyrene groups boosts natural light-driven CO2 reduction[END_REF][START_REF] Wang | Improving photosensitization for photochemical CO2to-CO conversion[END_REF] where a higher efficiency of Ru•••ReCOPy systems (as well as for RuPy•••ReCO) is expected with respect to Ru•••ReCO.

The very low activity indicates that ET between the pyrene modified RuPy/ReCOPy structures and unmodified Ru/ReCO structures are not favorable despite the suitable redox potentials of the different couples. The effect of PS:Cat ratio on the photocatalytic activity of the system was also investigated. The tests with different RuPy:ReCOPy ratios were performed under similar conditions and the results are reported in Fig. 4d andS12. A lower concentration of the PS or Cat (ratio 0.5:1 and 1:0.5) led to a significant decrease of the TOF (8.3 h -1 and 14.8 h -1 respectively). Moreover, a higher concentration of the photosensitizer (RuPy:ReCOPy 2:1) or of the catalyst (RuPy:ReCOPy 1:2) causes a dramatic drop of the performance (TOF = 13.4 h -1 and 7.9 h -1 , respectively). These observations are different from that obtained with a covalent supramolecular PS-Cat where the highest activities were observed with 1:3 and 1:2 of PS:Cat ratios. [START_REF] Tamaki | Photocatalytic CO2 reduction with high turnover frequency and selectivity of formic acid formation using Ru (II) multinuclear complexes[END_REF][START_REF] Gholamkhass | Architecture of supramolecular metal complexes for photocatalytic CO2 reduction: Ruthenium-rhenium Bi-and tetranuclear complexes[END_REF][START_REF] Tamaki | Supramolecular photocatalysts for the reduction of CO2[END_REF] In order to figure out the role of the linked pyrene function on the complexes, a complementary experiment was performed by adding free pyrene (4 equivalent relative to the PS) to the RuPy•••ReCOPy with the idea that free pyrene can interact with the pyrenes of the complexes and consequently minimize the possible π-π interactions between the RuPy and ReCOPy (It should be noted that free pyrene couldn't interfere with the light absorption in the visible irradiation range). As excepted, a decrease of the catalytic activity was observed (Fig. 4c), with two times lower TOF (8.2 h -1 ) than that observed for pyrene-free system and close to that observed for Ru•••ReCO complex used as reference. It to be noted that our new system RuPy•••ReCOPy (1:1) displays a lower stability with respect to Ru•••ReCO system in these conditions. A total deactivation was observed after ≈70 minutes (Fig. S10). In order to clarify the origin of this deactivation, a set of additional experiments was performed, e.g. the CO2

purging and/or introduction of RuPy or ReCOPy moiety after the total deactivation. We evidenced that the activity can be only recovered by adding a fresh Cat (ReCOPy) to the solution showing that the degradation or the poisoning of this Cat is the only responsible of the deactivation process (Fig. 5a). However, the synergistic increase of the activity after adding "fresh" RuPy to solution containing only ReCOPy, and previously irradiated for 240 minutes under CO2 atmosphere in presence of TEOA, discarded the hypothesis of the catalyst photo-degradation (Fig. 5b). Therefore, the poisoning of this latter seems to be more realistic and probably due to the formation of a sub-product obtained from a possible reaction of the catalyst with the sub-product of electron donor (e.g. TEOA • ). [44]. These experiments highlighted further the nature of the RuPy/ReCOPy interactions. The synergistic activity observed after adding the fresh ReCOPy to

Time resolved emission of 3 MLCT and 3 IL excited state of PS.

Adjusting the excited-state lifetime of the photosensitizers is a key factor for an efficient reduction of CO 2 over PS/Cat system. Hence, the excited-state properties of Ru and RuPy were explored by measuring the time resolved photoluminescence (TR-PL) and absorption transient (AT) (Fig. 6). The PL of Ru and RuPy were significantly quenched as exposed to air (Fig. 6a), indicating the phosphorescence emission process, which mainly derived from the triplet state. 45 The TR-PL spectrum of Ru showed a typical 3 MLCT emission at 620 nm in DMF (Fig. 6a; Fig. S13). The 3 MLCT emission of RuPy is centered at 670 nm (Fig. 6b, Fig. S13), red-shifted for 50 nm with respect to Ru. This red-shift confirms the strong electrostatic interactions between the Ru-center and pyrenyl, in agreement with the UV-visible absorbance results. These results are confirmed by the absorption transient. For the Ru (Fig. 6c), absorption transient (AT) bands centred at 370 nm, and 560 nm and assigned to T1 and T2 transients, respectively are observed, with λexc=532nm (as well as with λexc=355nm), with a similar kinetic decay of the bleaching (at 450-460 nm, 630 and 660 nm). For RuPy, the corresponding AT bands are red-shifted, in agreement with the PL and UV-visible absorbance, and centered at 380 nm and 570 nm with a similar kinetic decay of the bleaching (at 450-480 nm, 670 and 710 nm). The bleaching in the 600-700 nm region is mainly assign to the phosphorescence emission due to radiative relaxations of the triplet state. The lifetimes of the PL, AT and bleaching are very close for Ru as well as for RuPy. The kinetic decay trace of the RuPy's PL and AT revealed 1.3-1.5 times higher excitedstate lifetime than that of 3 Ru for a similar concentration (1.08-1.30 µs vs 0.75-0.90 µs, respectively). The

3 RuPy was also demonstrated to be 2.5 times less sensitive toward O2 (Table 1). More surprising, a new distinctive AT band at 520 nm was selectively observed for RuPy with a longer lifetime of 35 µs (Insert of Fig. 6d). The sensitivity of this AT toward oxygen confirms that it corresponds to a triplet state and can probably be correlated to a formation of an exciplex 3 (RuPy•••RuPy) and/or to an intermolecular charge separation. Moreover, the quenching of 3 RuPy by TEOA was found 2.8 times higher than that for 3 Ru (2.11×10 6 M -1 s -1 vs 7.4×10 5 M -1 s -1 , respectively), indicating a faster electron transfer from the electron donor to the RuPy. It should be noted that the quenching rate constants calculated from the emission (Fig S11 ) are very similar to that calculated from the AT. A characteristic shoulder with a very short lifetimes (<10 ns)

was selectively observed for RuPy (Fig. S13a), representative of a dual emission emerged in the PL spectrum. The PL emission spectra of RuPy after excitation at 355 nm confirmed this inspection (Fig. S13bd) with additional emissions centred at 400 nm and 520 nm. This emission could be assigned to the pyrene moiety. Consequently, PL studies of pyrene molecule and of the RuPy's ligand were performed. The PL measurement results indicated that this emission corresponds to the intra-ligand triplet excited state ( 3 IL).

Therefore, observing this 3 IL upon 532 nm excitation (no absorption of pyrene and the ligand at 532 nm)

substantiates the electron/energy transfer between the Ru-center to the pyrene part. The significant decrease of the 3 IL lifetime of pyrene (Py), in the following order Py(200ns)<ReCOPY(120 ns)<Bpy-Py(100 ns)<RuPy(85ns), confirms this assumption (Fig. S13g). We should keep in mind that the electron transfer is promoted only after the reduction of the 3 PS to PS - which is achieved by an electron transfer from the electron donor to the 3 PS. Therefore, other quenching process can also play a role in the decrease of this transfer as 3 PS-3 PS self-quenching and 3 PS-Cat quenching.

The different rate constants of the 3 MLCT quenching of the Ru and RuPy are reported in Fig. S14 and summarized in Table 1. Interestingly, the self-quenching of 3 RuPy is three times lower than that of 3 Ru.

However, the quenching of 3 MLCT of Ru by ReCOPy is 500 times higher with respect to 3 Ru/ReCO. This quenching is in part promoted by the pyrene-moiety as demonstrated from the rate constant of the 3 Ru with pyrene (Table 1). The 3 Ru/Py quenching is 6 times higher than that for 3 RuPy/Py (and much higher than that the ET from TEOA), which could explain the very low activity of Ru/ReCOPy dual system. However, despite the low quenching rate of the 3 MLCT of RuPy by pyrene, the lifetime of 3 Py is dramatically affected with similar quenching rate constant founded with 3 Ru. This outweighs on a π-π interaction between the pyrene-moiety of RuPy with pyrene. On the other hand, the quenching of the 3 MLCT of RuPy by ReCO is four times lower than that with ReCOPy which could not explain the very low efficiency of RuPy/ReCO binary system compared to RuPy/ReCOPy. The different data allow building the energetic diagram of the HOMO and LUMO, for the different complexes (see ESI for more details) as well as the energetic levels of the different excited states (basing on the AT experiments) of the Ru and RuPy photosensitizers (Fig. S15).

It should be noted that the electron transfer occurs from the reduced photosensitizer *(PS •-), to the catalyst.

The *(PS •-) is formed from the oxidation of the electron donor and the 3 PS. Therefore, a longer lifetime of RuPy excited state(s) is highly desired as well as a lower quenching is critical for promoting the ET from the TEOA to the 3 PS as well as from the reduced [START_REF] Becke | Density-functional thermochemistry. III. The role of exact exchange[END_REF] with the Lee-Yang-Parr correlation functional [START_REF] Lee | Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density[END_REF] (B3LYP) implementing the empirical dispersion function (D3) [START_REF] Grimme | A consistent and accurate ab initio parameterization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu[END_REF] and associated with a triple zeta basis set TZVP [START_REF] Schäfer | Fully optimized contracted Gaussian-basis sets of triple zeta valence quality for atoms Li to Kr[END_REF] (except for Ru and Re which were described using the LANL2DZ basis set). [START_REF] Hay | Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals[END_REF] Other computational details can be found in ESI. Their corresponding most stable conformations are reported in Fig. S16-S22) and their associated PS/Cat interaction energies (Eint) are summarized in Table 2.

Table 2. Summary of the DFT-calculated interaction energy (Eint) for the different systems (expressed in kJ mol -1 ). The interaction energy between the two components of each system was calculated as Eint=E(system)-E(complex 1)-E(complex 2) where E(system) is the total energy of the system assembling the two complexes 1 and 2 while E(complex 1) and E(complex 2) are the total energies of complex 1 and 2 taken individually, respectively. ( 1) and ( 2) correspond to two possible geometries for the ReCOPy/RuPy system, (1) being the most energetically favorable one. The determination of the interaction energy for the RuPy-RuPy system was not performed since we used a charged cation model to treat RuPy.

System

Eint (kJ mol -1 )

Ru•••ReCO -156 RuPy•••ReCO -190 Ru•••ReCOPy -195 ReCOPy•••ReCOPy -261 RuPy•••ReCOPy (1) - 295
RuPy•••ReCOPy (2) - 227
These calculations revealed two plausible geometries for our new RuPy•••ReCOPy system (labeled 1 and 2

in Table 1) as illustrated in Fig. 7a and7b. The configuration (1) corresponds to the most energetically stable geometry resulting from the N-H/C=O hydrogen bond (d ≈ 1.9 Å) and the bipyridine-pyrene π-π stacking (d ≈ 2.8 Å) between the PS and the Cat leading to the supramolecular assembly. In addition, a remarkable intramolecular alignment of pyrene functions can be clearly observed and assigned to an intramolecular π-π stacking (d ≈ 3.4 Å). The configuration (2) is less stable and corresponds to a supramolecular assembly stabilized mainly via inter-and intra-molecular pyrene-pyrene π-π stacking (d ≈ 3.4 Å) as well as a N-H/C=O hydrogen bonds (d ≈ 1.9 Å); however, in contrast to configuration (1), the bipyridine-pyrene π-π stacking interactions are absent. These configurations 1 and 2 are associated with interaction energies between RuPy and ReCOPy (-295 and/or -227 kJ.mol -1 respectively) significantly higher than the value obtained between Ru and ReCO in the respective complex (-156 kJ mol -1 ). This result highlights that the introduction of pyrene in both Ru and ReCO leads to a substantial enhancement of the intermolecular interactions between the PS and Cat. These interactions energies are also significantly higher than the values calculated for Ru•••ReCOPy (-195 kJ.mol -1 ) and RuPy•••ReCO (-190 kJ.mol -1 ) (Table 2 and Color code: carbon(grey), hydrogen (white), nitrogen (blue), (green), oxygen (red), ruthenium (purple) and rhenium (yellow). The distances are reported in Å.

Mechanistic investigation

After discarding the absorbance impact in the enhancement of the activity of RuPy•••ReCOPy vs Ru-ReCO and based on the tests with other binary systems' combinations (Fig. 4 and S10), on the excited-state lifetimes, on the quenching rate constant and on the DFT calculations, we concluded that the higher activity is mainly attributed to a faster ET between RuPy and ReCOPy. The modelling shows two possible pathways as illustrated in Fig. 8: (i) Following a preliminary MLCT from ruthenium center to the bipyridine (bpy) and the electron then migrates from the pyrene towards the bipyridine-rhenium center to trigger the CO2 photoreduction; (ii) The electron migrates from the bipyridine of RuPy towards the pyrene moieties of Re and reaches the bipyridine-rhenium center after an intermolecular transfer (Fig. 8). The interaction energy calculated by DFT between the two complexes (Table 2) allows investigating the pathway (ii) as preferential. However, pathway (i) cannot be discarded since the DFT calculations did not take into account other factors such as the solvation effect. Consequently, with the stronger interaction between RuPy and ReCOPy, both ET pathways can occur simultaneously and/or separately for ensuring a fast ET.

CONCLUSION

The newly designed RuPy•••ReCOPy supramolecular photocatalytic system was demonstrated to show an enhanced conversion efficiency of CO2 to CO under visible light. This supramolecular assembly is promoted by non-covalent NH/CO hydrogen bond and π-π staking interactions between the catalyst and the photosensitizer. Remarkably, the calculated TOF was found three times higher than the value previously reported for the conventional Ru•••ReCO photocatalytic system (18 h -1 vs 5.3 h -1 ). These reaction rates and photocatalytic activity enhancement is due to an efficient electron transfer from RuPy to ReCOPy mediated by the pyrene moieties and the stronger interactions between RuPy and ReCOPy as compared to Ru and ReCO. The electron delocalization between the pyrene moieties and the complexes was confirmed by UV-Vis study and TR-PL showing the electron transfer pathway from ruthenium center to the pyrene moiety in RuPy and from the pyrene moiety to the rhenium center in ReCOPy. Additionally, the faster electron transfer from the electron donor to the RuPy comparing with Ru was also concluded form the quenching of the 3 MLCT with TEOA. These findings shed light on the importance of the electron transfer efficiency and pathway for enhancing the performance of the photo-catalytic system for the CO2 photoreduction.

Fig. 1 .

 1 Fig. 1. ReCOPy and RuPy complexes combined in this work to design a novel supramolecular assembly via hydrogen bond and π-π stacking.

ReCOPy preparation 2 . 2 . 1 . 4 , 4 '

 22144 -Dicarboxylic acid-2,2-bipyridine (HOOC-Bpy-COOH).

Fig. 2 .

 2 Fig. 2. Cyclic voltammetry for the ReCO, ReCOPy, Ru and RuPy complexes in DMF. Conditions: 100 mV/s, 0.1 M TBAPF6, Pt working electrode, Pt wire counter electrode, Ag/AgCl reference electrode. Referred to ferrocenium/ferrocene couple.

-

  2+ à Ru + Ru + à Ru 0 Ru 0 à Ru + Ru + à Ru 2+ Re 0 à Re + Re + à Re 0 2+ à Ru + Ru + à Ru 0 Ru 0 à Ru + Ru + à Ru 2+ Re 0 à Re + Re + à Re 0 ReCO Ru ReCOPy RuPy of complexes was analyzed by UV-Vis (RuPy•••ReCOPyexp) and the obtained spectra was compared with that of theoretical calculated from the addition of the individual RuPy and ReCOPy spectra (RuPy•••ReCOPycalc). (Fig. 3b) The subtraction of the two spectra RuPy•••ReCOPyexp˗RuPy•••ReCOPycalc indicates the presence of band-edge shifts with a modification in some band intensity. 321 and 339 nm resulting from the band-shift of pyrene at 330 and 345 nm, respectively. On the other hand, the characteristic bands 278 and 345 nm of pyrene was more intense in the RuPy•••ReCOPyexp spectrum. In addition, a bleaching were observed at 473 and 350 nm and attributed to the MLCT and metal centered d-d transitions (MC), respectively. This bleaching is accompanied with a relative increase of the band intensity centered at 290 nm and assigned to π-π * transitions ( * LC) of the ligand. [39] These observations confirm the interaction between RuPy and ReCOPy in solution through the pyrene moieties which indicate a plausible formation of supramolecular assembly of RuPy•••ReCOPy. It should be noted, that the relative low intensity due to the interaction could probably due to the fact of the ReCOPy•••ReCOPy interaction. Therefore, the difference, is the additional impact of the RuPy•••ReCOPy interaction in respect to the self-ReCOPy interaction.

Fig. 3 . 3 . 2 .

 332 Fig. 3. (a) UV-Visible spectra of Ru, RuPy photosensitizers and of ReCO, ReCOPy co-catalysts in DMF. Insert: zoom on the region of the MLCT bands. (b) Normalized spectra of RuPy-ReCOPy (1:1) mixture (RuPy-ReCOPyexp) and of mathematic addition of RuPy and ReCOPy (RuPy•••ReCOPycalc) with the difference between the two spectra, respectively. [Ru] = [RuPy] = [ReCO] = [ReCOPy] = 0.4 mM, [RuPy•••ReCOPyexp] : [RuPy] = [ReCOPy] = 0.2 mM *characteristic bands of pyrene 3.2. Photocatalytic performance.

  performance, equimolar mixtures of PS (Ru or RuPy) and Cat (ReCO or ReCOPy) binary combinations were further explored and tested under similar conditions. The combination of RuPy•••ReCO was tested with 1:1 ratio and surprising negligible activity was detected (TOF = 0.4 h -1 ). Moreover, Ru•••ReCOPy (1:1)

Fig. 4 .

 4 Fig. 4. Evolution of the CO amount during the photocatalytic reduction of CO2 under visible light over: a) RuPy•••ReCOPy and Ru•••ReCO; c) Ru•••ReCOPy, RuPy•••ReCO and RuPy•••ReCOPy+pyrene; d) Evolution of the TOF vs the ratio of RuPy:ReCOPy. b) Characteristic IR CO band evolutions in the first 30 minutes of irradiation for RuPy•••ReCOPy and Ru•••ReCO. Reaction condition: [Ru]=[RuPy]= 0.38 mM; [ReCO]=[ReCOPy)] = 0.38 mM; [TEOA]= 0.12 M; [H2O] = 8.3 M; VolDMF= 11 ml; Xe-Lamp; Irradiance~10 mW/cm 2 ; Filter pass high for 𝜆>390 nm; errors estimated lower than 10% on three reproducible experiments. TOFs were always based on the amount of Re complexes.

  RuPy•••ReCOPy or RuPy to the ReCOPy revealed the reversibility and the advantage of the non-covalent nature of the interactions between the PS and the Cat.

Fig. 5 .

 5 Fig. 5. a) Evolution of the CO amount during the photocatalytic reduction of CO2 after 2 hours of bubbling CO2 on deactivated RuPy•••ReCOPy system and adding of RuPy and ReCOPy. (b) Evolution of the CO amount during the photocatalytic reduction of CO2 over ReCOPy system before and after adding (indicated with arrow) of RuPy photosensitizer.

Fig. 6 .

 6 Fig. 6. (a) and (b) correspond to the nanosecond emission spectra (140ns/spectrum) of the 3 MLCT of Ru and RuPy, respectively. In insert: normalized kinetic decay trace of 3 MLCT emission of Ru and RuPy monitored at 620 nm and 670 nm, respectively, under air (i) and argon (ii) atmospheres. (c) and (d) report the evolution vs the time (140ns/spectrum) of the absorption transition (AT) of Ru and RuPy. Insert of Fig. d: normalized kinetic decay traces of the AT at 520 nm (i) and 570 nm (ii). λ exc = 532 nm, [RuPy]=1.7 mM; [Ru]= 3 mM; all spectra were recorded under Ar at 298K.

  𝜆emission=620nm; (b) 𝜆emission=650nm; (c) rate constant of the 3 Ru/ 3 Ru or 3 RuPY/ 3 RuPy selfquenching. 𝜆exc=532 nm; (d) rate constant of the 3 Pymoiety quenching of (𝜆emission=400nm; 𝜆exc=355 nm). Error estimated at 5%.

3. 4 .

 4 Molecular Insight into the preferential arrangements of the PS/Cat systems DFT calculations were performed on the different PS/Cat systems to identify the nature and strength of interactions between their constitutive components (see computational details in ESI). The geometry of the Ru•••ReCO, RuPy•••ReCO, Ru•••ReCOPy, ReCOPy•••ReCOPy and RuPy•••ReCOPy systems were DFToptimized using the Becke Three-Parameter Hybrid exchange functional

Fig. S17

  Fig.S17 and S18) confirming the synergistic role played by the pyrene functions present in both PS and Cat. The interaction energy for the ReCOPy•••ReCOPy complex (-261 kJ.mol -1 ) was also found to be much

Fig. 7 .

 7 Fig. 7. DFT-calculations on the RuPy•••ReCOPy system: a) the most stable configuration (1), b) plausible configuration (2) and c) charge differences for the most stable RuPy•••ReCOPy (1) complex upon the excitation to the second excited state. Green and white colors represent the charge accumulation and depletion regions respectively.Color code: carbon(grey), hydrogen (white), nitrogen (blue), (green), oxygen (red), ruthenium (purple) and rhenium (yellow). The distances are reported in Å.

Fig. 8 .

 8 Fig. 8. The two possible electron pathways in the RuPy•••ReCOPy photocatalytic systems based on the analysis of the experimental and theoretical data.

2.2.3. N 4,4' -bis(1-pyrenylmethyl)-[2,2´-dipyridyl]-4,4´-dicarboxamide)-bis(2,2′-bipyridine dichloro ruthenium (II) (RuPy).

	1 H NMR (400 MHz, DMSO-d6) δ (ppm), 9.73 (t, J = 3.6 Hz, 2H), 8.86-8.84 (m, 4H), 8.51, (d,
	J= 6Hz, 2H), 8.34-8.26 (m, 9H), 8.18 (m, 5H), 8.13 (d, J= 5.3 Hz, 2H), 8.08 (t, J = 4.4 Hz, 2NHamide), 5.28
	(d, J= 3.7 Hz, 4H).
	A solution of Ru(2,2′-bipyridine)2Cl2 (21 mg, 0.044 mmol) with Ligand-Bpy-Py (30 mg, 0.044 mmol) in
	0.6 mL of DMF was refluxed 18 h at 153 ᵒC under argon. The product was precipitated by addition of diethyl
	ether and sonicated during five minutes. The product was collected by centrifugation and washed with
	additional diethyl ether. The obtained solution was then dried by rotary evaporation to obtain 26 mg of dark
	red powder. (Yield = 50%) 1 H NMR (400 MHz, DMSO-d6) δ (ppm) 9.95 (t, J = 3.5 Hz, 2H), 9.40 (s, 2H),
	8.83 (t, J = 5.2 Hz, 4H), 8.52 (d, J = 6.4 Hz, 2H), 8.33-8.23 (m, 9H), 8.20-8.12 (m, 9H), 8.09 (t, J = 5 Hz,
	2H), 7.96-7.89 (m, 4H), 7.74 (d, J = 3.6 Hz, 2H), 7.68 (d, J = 3.6 Hz, 2H), 7.54-7.51 (m, 2H), 7.46-7.43 (m,
	2H), 5.30 (d, J = 4.4 Hz, 4H). 1 H NMR (125 MHz, DMSO-d6) δ (ppm) 163.13 (CO), 157.67 (CIV),
	156.81(CIV), 156.76 (CIV), 152.52 (CH), 152.09 (CH), 151.53 (CH), 141.73 (CIV), 138.67 (CH), 138.63
	(CIV), 132.57 (CIV), 131.21 (CIV), 130.71(CIV), 130.69(CIV), 128.60 (CIV) 128.44 (CH), 128.41 (CH), 128.14
	(CH), 127.83 (CH), 127.67 (CH), 126.77 (CH), 126.25 (CIV), 125.81 (CH), 125.66 (CH), 125.21 (CH),
	125.01 (CH), 124.48 (CVI), 124.33 (CIV), 123.87 (CH), 122.55 (CH), 41.74 (CH2). ESI-MS (positive) m/z:
	found 542.14 (RuPy/2 -2Cl), calculated 539.14 (RuC66H46N8O2) 2+ .

Table 1 .

 1 3 PS •-to the Cat. Consequently, the higher lifetime of the RuPy's excited-state and its lower quenching with respect to that of Ru can justify, in part, the highest activity of the RuPy•••ReCOPy system (in comparison to Ru•••ReCO). However, this cannot explain the gap in the performance between RuPy•••ReCOPy and RuPy•••ReCO, where the energetic diagram reveals similar LUMO levels of ReCO with respect to ReCOPy. Therefore, other factors should be taken into account to elucidate this phenomenon. Stern-Volmer-quenching constants with Ru and RuPy measured at 298K from the PL kinetic decays at 620 nm and 650 nm, respectively, in presence of different quencher. (M -1 s -1 ) kq x 10 8 (M -1 s -1 )

	PS	3 Ru (a)	3 RuPy (b)
	Q kq x 10 8 O2 299	117
	Ru/RuPy (c)	4.47	1.71
	ReCOPy	14.10	2.90
	ReCO	0.07	0.55
	TEOA	0.0021	0.0027
	Py	5.19
		(13.1 (d)

Acknowledgements

This work is supported by European Regional Development Fund (ERDF), Normandy region, as part of the project: RAPHYD (Recherche pour les Applications Energétiques de l'Hydrogène). We thank Mr. Adel Noon for his participation in this work during his internship and Mr. Adrien Lanel for In-situ FTIR reactor designing. This work was granted access to the HPC ressources of CINES under the allocation A0100907613 made by GENCI.

Supplementary materials

The following information are available in ESI: Ligand and complexes synthesis, NMR data, details for photocatalytic tests (in-situ reactor, calibration curve for CO quantification, FTIR spectra…), additional times resolved photoluminescence results (nanosecond emission and AT spectra, Stern-Volmert plots), energy level of HOMO and LUMO determination details and all optimized structure are presented in Fig. S1-S5.

S1-S22 and Table