Sébastien Dhers

Abhishake Mondal

David Aguilà

Juan Morua Ramirez

Sergi Vela

Pierre Dechambenoit

Mathieu Rouzieres

Jonathan R Nitschke

Rodolphe Clérac

Jean-Marie Lehn

Juan Ramírez

Mathieu Rouzières

Zhenjie Zhang

Lukasz Wojtas

Mohamed Eddaoudi

Michael J Zaworotko

Spin State Chemistry: Modulation of Ligand pKa by Spin State Switching in a [2´2] Iron(II) Grid-Type Complex

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

n INTRODUCTION

The search for materials having tunable properties is a very active research area. 1 In this context, special attention has been given to the modulation of magnetic properties by physical means such as temperature, 2 pressure and light, 2,3 or through chemical processes affecting the ligand field in complexes. 4 Spin crossover (SCO) complexes are interesting candidates, particularly iron(II) complexes, which exhibit a switching process between a paramagnetic high spin state (HS, S = 2) and a diamagnetic low spin state (LS, S = 0). 5 Polymetallic [2´2] grid-like complexes 6 with modulable properties can be seen as molecular precursors of metallosupramolecular architectures or materials due to their ability to generate ordered arrangements of multiple grid entities by self-assembly at the air-water interface, 7 through hydrogen-bond formation in the solid array 8 and on adsorption onto a graphite surface. 9 It has been shown that tetranuclear iron(II) [2´2] grids undergo multiple spin state switching under the action of three physical triggers, temperature, pressure and light. 2,10 The influence of hydrogen-bond donors, 11 as well as that of counterions and solvent, 12 have also been shown to allow the modulation of the magnetism of these architectures. On the other hand, [2´2] grids presenting ionizable N-H sites undergo reversible protonic modulation of optical and redox properties. 13 One thus expects that the magnetic properties of such entities may also be modulated by reversible ligand deprotonation without destruction of the initial complex. 2, 13 The hydrazine-based ditopic isomeric ligand H2L (Scheme 1) offers the opportunity to both generate [2´2] grid architectures by self-assembly and to study the protonic modulation of their physico-chemical properties, due to their ionizable N-H sites. The final step of the synthesis of such a ditopic ligand consists in the condensation reaction of one equivalent of 4,6-bis(hydrazino)-2-phenyl-pyrimidine with two equivalents of 2-pyridine-carboxaldehyde to yield ligand H2L. This ligand contains two complexation subunits of terpyridine (terpy) type, where the hydrazone function acts as an ionizable group whose acidity is greatly enhanced on complexation, as compared to the free ligands. Stepwise Transformation of the Molecular Building Blocks in a Porphyrin-Encapsulating Metal-Organic Material P orous metal-organic materials (MOMs) that incorporate reactive species (RS) such as metalloporphyrins, 1 metallosalens, 2 and polyoxometalates 3 are of topical interest because they can combine the physicochemical properties of the RS 4 with permanent porosity of the framework. 5 Such MOMs can thereby enable new approaches to gas storage, 6 separations, 7 luminescence, and catalysis, 8 including enzymatic catalysis. 8b MOMs that incorporate RS can be divided into two subgroups: those with RS as an integral part of nodes/linkers (RSMOMs) 9 and those that encapsulate or host RS in cages (RS@MOMs). 10 Encapsulation may be achieved directly through synthesis 11 or via postsynthetic modification (PSM). 12 Metalloporphyrins are attractive RS because of their value as catalysts 13 and dyes, 14 and we recently reported the generation of porphyrin-encapsulating MOMs (porph@MOMs) [START_REF]From a synthetic point of view, the use of an appropriate base to deprotonate the NH group of the free ligand, transforms this one in a nucleophilic reagent that is possible to alkylate thus opening a synthetic route toward new very diverse ligands[END_REF] that exhibit PSM through metal ion exchange 16 or metal salt incorporation. 17 The availability of such porph@MOMs offers the opportunity to study their PSM systematically and evaluate its impact on their properties such as gas sorption, luminescence, and catalysis. In addition, PSM can afford new compounds that cannot be directly synthesized.

PSM involving metal exchange in molecular building blocks (MBBs) is now widely studied and tends to focus upon Cd-and Zn-containing MOMs 18 because of the relative lability of complexes of d 10 ions (Cd 2+ , Zn 2+ , and Hg 2+ ). 19 The metal exchange process is typically monitored using atomic absorption ray diffraction (SCXRD) are rare. 16,20 Since Cd 2+ in cadmium porphyrins can be irreversibly exchanged with Cu 2+ , 21 the possibility of selective control of PSM in porph@MOMs exists if the MOM and the encapsulated RS exhibit different rates of exchange. In this work, we addressed such a situation through the study of crystals of porph@MOM-11 (P11), a Cd-sustained MOM that encapsulates CdTMPyP cations [H 2 TMPyP = mesotetra(N-methyl-4-pyridyl)porphine tetratosylate]. P11 was immersed in methanol solutions of Cd 2+ and/or Cu 2+ to study how the Cd 2+ /Cu 2+ mole ratio impacts PSM. Scheme 1 shows how porph@MOMs might generally undergo complete or partial metal exchange through control of the ratio of two metal ions.

The reaction of biphenyl-3,4′,5-tricarboxylic acid (H 3 BPT) 22 and Cd(NO 3 ) 2 with H 2 TMPyP afforded P11, a microporous MOM in which encapsulated cationic porphyrins occupy alternating channels. 17 P11 is based upon a 3,6-connected rtl net built from two 6-connected [Cd 2 (COO) 6 ] 2-MBBs [Figure 1a and Figure S1 The iron(II) [2´2] grid [Fe4(H2L)4] 8+ shown in Scheme 1 incorporates hydrazone groups, which act as soft ligands to assemble the iron(II) ions. The deprotonation of this two-site ligand H2L 14 changes its coordination properties from a weak-field ligand (non-deprotonated) to a strong-field ligand (deprotonated). Its deprotonation also confers to the ligand an anionic 15 character (-N --N=CH-, Scheme S1) thus leading to a stronger coordination with a larger splitting energy between the eg and t2g levels of the iron cations. In this configuration, all the electrons should be paired in the t2g level leading to a diamagnetic [Fe4L4] complex. However, given that a grid complex contains four Fe II cations, the spin crossover process may be more or less complete depending on the strength of the ligand field. This modulation of the magnetic properties is expected to depend on the degree of deprotonation of the grid, which contains a total of eight ionizable groups. Indeed, the influence of pH on iron(II) SCO complexes has been investigated mostly in the context of NMR contrast agents 16 and only a few pH switchable iron(II) SCO complexes have been reported just for single iron(II) sites. 17

Herein, we describe the synthesis of the iron(II) [2´2] grid complex, [Fe4(H2L)4] 8+ , and the study of the reversible modulation of its magnetic properties in the solid state and solutions depending on the protonation state of the four constituting ligands. We also demonstrate the remarkable effect of the iron(II) spin state switching on the pKa of the grid ligands, which induces the generation of selectively deprotonated magnetic entities and amounts conversely to a spin state modulated chemical reaction. The zinc(II) analogue is also reported and serves as a diamagnetic reference compound for the investigation of the iron(II) grid entities. The red needle crystals of Fe-8H were found to lose crystallinity rapidly once outside the mother liquor. Thus, a single-crystal was mounted immersed in oil and placed in the X-ray diffractometer directly at 120 K. The crystal structure was solved in the monoclinic C2/c space group, exhibiting a molecular [2´2] grid topology with the four fully protonated ligands: [Fe4(H2L)4](BF4)8•6MeCN (Fe-8H, Table S1, top part of Figure 1 and Figure S2). Together with the cationic complex, eight tetrafluoroborate anions ensure the electro-neutrality of the system and indicate the 8+ charge of the corresponding Fe-8H complex. In addition, acetonitrile molecules are located in the crystal lattice. The number of acetonitrile molecules (six) was derived from the electron density and void space volume calculated by PLATON. In the asymmetric unit, one of the BF4 - anions is disordered across two positions, as is the phenyl group of one of the H2L ligands. Two types of iron ions, Fe1 and Fe2, were found in the asymmetric unit, both exhibiting coordination number six. The bond distances between Fe1 and the corresponding nitrogen donor atoms (1.885(9) -2.060(7) Å, Table S3) suggest a low spin configuration. In contrast, the Fe2-N bond distances are in the range between both low and high spin configurations (1.971(7) -2.133(7) Å, Table S3) suggesting possible spin state disorder on this site. The H2L ligands show hydrogen bonding interaction between their corresponding acidic NH protons and (i) two BF4 -anions around the Fe2 site and (ii) one BF4 - anion and one acetonitrile molecule around the Fe1 centers.

The temperature of the same single crystal was then increased at 2 K min -1 up to 290 K. The collected structure was again solved in the monoclinic C2/c space group, with the same [2´2]-grid like geometry (Table S1). The complex is thus surrounded by the eight tetrafluoroborate anions, two of them being disordered. The number of acetonitrile molecules has been estimated to be two. Thus, the increase of temperature to 290 K seems to favor the loss of about four acetonitrile molecules. This desolvation effect is clearly seen in the reduction of the unit cell volume, which contracts from 11904.6(17) Å 3 at 120 K to 11151(3) Å 3 at 290 K (Table S1). The Fe2 site and its coordination sphere appears to be only slightly affected by the temperature change with Fe2-N bond distances ranging between 1.980 (8) and2.127(8) Å (Table 1 andTable S3). As observed at 120 K, the spin state of the Fe2 ion is thus in between LS and HS, in agreement with a possible spin state disorder on this site. On the other hand, the bond distances between the Fe1 site and the nitrogen donor atoms are much larger than at 120 K ranging between 2.081 (8) and 2.196(8) Å. This modification of the Fe1 coordination site indicates clearly a spin-state switching from LS at 120 K to HS at 290 K and reveals the occurrence of a spin-crossover process in Fe-8H.

Table 1. Summary of the Fe II spin states as deduced from the crystallographic data at 120 and 290 K for Fe-8H, Fe-6H, and Fe-4H.

Fe-8H

(red needles)

Fe-6H

(red blocks)

Fe-4H (red plates) 120 K 290 K 120 K 290 K 120 K Fe1 LS HS LS LS LS Fe2 LS-HS LS-HS LS-HS HS LS-HS Fe3 LS HS LS LS LS Fe4

LS-HS LS-HS LS-HS HS LS-HS

Note: the Fe3 and Fe4 sites are symmetry-equivalent to Fe1 and Fe2 in Fe-8H.

(b) Following the same procedure, a red block crystal of Fe-6H was mounted immersed in oil and placed in the X-ray diffractometer directly at 120 K. The crystal structure was collected and solved in the monoclinic P21/c space group (Table S1), exhibiting again a [2´2] grid-like complex. However, in this case, only six tetrafluoroborate anions were found in the structure, since two ligands exhibit a monodeprotonation giving the complex: [Fe4(H2L)2(HL)2](BF4)6•8MeCN (Fe-6H, bottom part of Figure 1 and Figure S3). Together with the anions, eight molecules of acetonitrile are located in the crystal lattice. At this temperature, three pyridyl moieties are significantly disordered. Similarly, one of the acetonitrile molecules is disordered across three different positions, while one of the BF4 -anions shows disorder between two different positions. Each of the six acidic NH protons is interacting with a molecule of tetrafluoroborate anion, while no H-bond acceptor is located close to the two deprotonated hydrazone groups. The [2´2] grid-like complex shows four crystallographically different iron sites (Figure 1, bottom). Fe1 and Fe3 are surrounded by two coordination pockets featuring one protonated and one deprotonated hydrazone group. The bond distances between the metal ion (Fe1 and Fe3) and the donor N atoms are in the range for a low spin configuration (1.875(3) -2.035(3) Å for Fe1, 1.872(4) -2.063 Å for Fe3, Table S4). In contrast, the coordination pockets around the Fe2 and Fe4 site feature two NH groups. The Fe2-N and Fe4-N bond distances do not point strongly toward a specific electronic configuration (2.010 -2.165 Å and 1.904(6) -2.113(4) Å, respectively; Table S4), although this feature could be influenced by the disorder exhibited by the pyridyl groups surrounding these two metal ions. The same single-crystal was allowed to warm to 290 K (2 K min -1 ), and the structure was again collected (Table S1). While the same space group was used to solve the structure (P21/c), the volume of the unit cell was found to be significantly larger (11437.0(8) and 11889.2( 18) Å 3 at 120 and 290 K, respectively). At this temperature, only one tetrafluoroborate anion was found to be disordered. The Fe-N bond distances around the two iron sites, Fe1 and Fe3, encapsulated by the coordination pocket featuring both protonated and deprotonated hydrazone group are very similar to the ones observed at 120 K, suggesting again a low spin configuration (1.871(4) -2.043(4) Å and 1.871(4) -2.053(4) Å for Fe1 and Fe3, respectively, Table S4). Thus, as expected, the deprotonation of the hydrazone group leads to a stronger ligand field and thus stabilizes the LS state of the coordinated iron metal ion. In contrast, the Fe-N bond distances around the Fe2 and Fe4 sites (surrounded by pockets featuring two non-deprotonated =N-NH-hydrazone groups) are now clearly in the range for a high-spin configuration (2.118(4) -2.247(4) Å and2.088(4) -2.244(4) Å for Fe2 andFe4, respectively, Table 1 andTable S4), evidencing a stabilization of the HS state at higher temperatures and suggesting the occurrence of a spincrossover phenomena at these metal ion sites.

(c)

The crystals of the third type, the red plates, were also collected at 120 K and solved in the monoclinic P21/c space group (Table S2), exhibiting the same [2´2] grid topology. In this case, however, the number of tetrafluoroborate anions is reduced to four, implying the deprotonation of altogether four hydrazone sites of the grid ligands to give [Fe4(HL)4](BF4)4•12MeCN (Fe-4H, top part of Figure 2 and Figure S4). At this temperature, the four iron metal ions are crystallographically independent. One of them ( Fe3) is disordered over two positions (Fe3a and Fe3b, respectively) as well as the two coordinating ligands surrounding this Fe site. The tetrafluoroborate (disordered over two positions) and acetonitrile molecules are located in the lattice void space.

The number of solvent molecules was estimated from the electronic density and void space volume calculated by PLATON. Remarkably, the arrangement of the half-deprotonated ligands leads to Fe1 and Fe3 sites surrounded by two deprotonated hydrazone groups, while the pockets surrounding Fe2 and Fe4 centers feature only non-deprotonated hydrazone group. Confirming the trend observed in the previous structures, the short Fe-N bond distances for the iron metal ions within the deprotonated hydrazone environments suggest a LS configuration (1.840( 7) -2.036(5) Å, 1.882(13) -2.206(10) Å and 1.875(13) -2.126(12) Å for Fe1, Fe3a and Fe3b respectively, Table S5). It should be noted that the high value observed for one of the distances surrounding Fe3 ions is probably induced by the disorder observed in this metal site. In contrast, the values observed for the metal ions surrounded by coordinating pockets featuring only non-deprotonated hydrazone groups point rather to a HS configuration at 120 K (2.086(6) -2.190(6) Å and 2.086(6) -2.197(6) Å for Fe2 and Fe4, respectively, Table 1 and Table S5) even if at this temperature a spin state disorder on these sites is likely to be present. As expected, each NH group of the ligand interacts with one BF4 - anion through hydrogen bonding. In contrast, no H-donor species were found surrounding the deprotonated hydrazone moieties.

(d)

The Zn-4H analogue was prepared as a reference complex by replacing iron(II) with zinc(II), in order to analyze the deprotonation pattern observed for Fe-4H. Single crystals of Zn-4H were obtained as crystalline red plates by diffusion of diethylether into the acetonitrile solution of the complex (see supporting information). The X-ray diffraction data on a single crystal were collected at 120 K and solved in the tetragonal P4/ncc group (Table S6), yielding a [2´2] grid-like complex similar to Fe-4H. The presence of four tetrafluoroborate anions confirms the half deprotonation of the four ligands wrapping the Zn-4H grid complex: [Zn4(HL)4](BF4)4•8H2O (bottom part of Figure 2 and Figure S5). The zinc [2´2] grid is geometrically more distorted than the Fe-4H analogue, but is also more crystallographically symmetrical, as the asymmetric unit contains only one ligand and one zinc center (Zn-N: 2.075 -2.261 Å). The tetrafluoroborate and water molecules are located in the lattice. The number of solvent molecules was estimated from the electronic density and void space volume calculated by PLATON. The good refinement of the structure and its high symmetry demonstrate that the deprotonation pattern for the Zn-4H grid is different from that of Fe-4H. Indeed, the four Zn II sites are surrounded by two HL ligands forming a coordination pocket with one deprotonated and one protonated hydrazone group.

(e) The fully protonated Zn II 4 [2´2] grid, Zn-8H, was also obtained and structurally characterized by X-ray diffraction (Table S6, Figures S6 andS7). Both Zn II grids, Zn-4H and Zn-8H, exhibit similar octahedricity values (S(Oh), see below) 18 to the corresponding Fe II grids (Table S7).

Determination and Analysis of the Magnetic Properties of the Fe II

4

[2´2] Grid Complexes. Magnetic susceptibility measurements were performed for the Fe-8H, Fe-6H, and Fe-4H complexes in the temperature range of 1.85 -300 K (Figure 3). The magnetic measurements shown in Figure 3 are reproducible below 300 K for Fe-8H and Fe-4H while for Fe-6H, the temperature cannot be increased above 270 K without losing the complete reversibility. The lack of reversibility is clearly linked to the partial loss of the acetonitrile molecules during the magnetic measurements. Therefore, only perfectly reversible magnetic data corresponding to the structurally characterized materials are discussed in the following. The cT products at highest accessible temperature for Fe-8H, Fe-6H, and Fe-4H (300, 270 and 300 K) are 6.6, 4.3 and 3.6 cm 3 K mol -1 , respectively. These values are intermediate between the ones expected for a fully high spin [Fe II HS]4 complex (12-16 cm 3 K mol -1 ; Fe II HS: S = 2 and g » 2.0 to 2.3, Curie constant of 3-4 cm 3 K mol -1 ) and for a diamagnetic [Fe II LS]4 species (Fe II LS S = 0, Curie constant of 0 cm 3 K mol -1 ). Upon decreasing the temperature, the cT product gradually decreases reaching to a plateau below 120 K at 2.4, 1.5 and 2.6 cm 3 K mol -1 for the Fe-8H, Fe-6H and Fe-4H grids, respectively. Analyzing the temperature dependence of the susceptibility, the proportions of HS Fe II centers are estimated at 48, 31 and 26 % at room temperature (taking a g factor of 2.15), and as 17, 11 and 19 % at 50 K, for Fe-8H, Fe-6H and Fe-4H respectively. This behavior clearly demonstrates an incomplete SCO for these complexes that never reach a fully low spin configuration (four Fe II LS sites) at low temperatures and neither a fully high spin configuration (four Fe II HS sites) before desolvation/decomposition of the material at high temperature. This result is also in agreement with the crystal structure analysis (vide supra), which indicates the systematic presence of spin state disorder on the Fe2 and Fe4 sites at 120 K for the three compounds (Table 1) and the absence of a high-spin configuration at 290 K. When the temperature is decreased below 20 K, a decrease in the cT product is also observed, indicating most likely the presence of spin-orbit coupling expected for Fe II centers in an octahedral coordination sphere, and possibly intramolecular antiferromagnetic coupling between the Fe(II) through the pyrimidine groups. 19 The field dependence of the magnetization for the [2´2] Fe II 4 grid (Figures S8-S10) has some notable characteristics: (i) the steady increase of the magnetization at low field without inflexion point ("S" shape curve) suggests the absence of significant magnetic interactions between the reminding magnetic sites; and (ii) a linear increase without clear saturation even at 1.8 K under 7 T. This high field behavior of the magnetization and the non-superimposable M vs H/T curves reveal most likely the presence of magnetic anisotropy expected for Fe II HS centers. The magnetization value obtained at 1.85 K under 7 T are 1.95, 1.25 and 2.47 µB, confirms the residual presence of Fe II HS ions in Fe-8H, Fe-6H and Fe-4H grid respectively. It is worth mentioning that preliminary solid-state reflectivity measurements on these three complexes indicate the absence of bulk photoactivity at 10 K and thus the impossibility to convert LS Fe II centers into HS ones using light irradiation in the visible range.

UV-Vis Spectroscopic Properties of the Fe II 4 [2´2] Grid Complexes upon Base Titration

The UV-Vis spectra of the grid Fe-8H (Figure 4) were measured in acetonitrile/chloroform (1:1) on addition of increasing equivalents of bis(dimethylamino)naphthalene (DMAN) base. The grid Fe-8H exhibits an absorption band at 372 nm, which is characteristic of the fully protonated grid complex. When two equivalents of base are added to give Fe-6H, the intensity of the band at 455 nm increases but diminishes after further base addition. A third band at 543 nm appears after adding more than 2 base equivalents, increasing in intensity until reaching a maximum intensity for the fully deprotonated species Fe-0H. Considering the ratio of molar absorption coefficient and the λmax obtained, and comparing it to the values known for [Fe(Hpaphy)2] 2+ and [Fe(paphy)2] (Table S8, Hpaphy = pyridine-2-aldehyde-2-pyridylhydrazone), these charge transfer bands observed appear to be of MLCT (Metal Ligand Charge Transfer) type. 14 The deprotonation affects markedly the color of the solution (Figure 4). UV-Vis spectra have also been measured between pH = 1 and pH = 13 in a 50:50 (v/v) mixture of acetonitrile and Britton-Robinson buffer, showing similar results (Figure S11).

H NMR Spectral Studies of the Fe II 4 [2´2]

Grid Complexes upon Acid/Base Titration. SCO phenomena have been observed in solution by 1 H NMR spectroscopy for Fe II 4 [2´2] grid-type complexes, 2a but remain scarce. 2b, 20 Mass spectrometry (see supporting information) was used to ensure that the species in solution were indeed the [2´2] grid structures observed in the solid state (Figures S12-S17). The titration of a solution of Fe-8H (followed by 1 H NMR in CD3CN/CDCl3 (1:1) at 25°C) with successive equivalents of DMAN or proton sponge showed chemical shifts ranging from around -40 to 200 ppm, with broad signals, and a shift of the signals towards the range for diamagnetic species as more equivalents of base were added (Figure S18). The titration produced a color change of the solution, from yellow to dark red (Figure 4, bottom), as well as a change in the solubility of the Fe-nH complex. The Fe-8H grid is soluble in acetonitrile but not in chloroform, whereas the opposite is true for Fe-0H. Hence the solvent mixture CD3CN/CDCl3 (1:1) was chosen for the NMR studies. The titration was also done in pure CD3CN (0 to 4 equivalents of base, up to the solubility limit) to allow for an increase in the maximum concentration in order to give a better NMR spectrum (Figure S19). The amount of exchange present in solution, known for grid structures, 13c plus the equilibrium between Fe-nH species, render complicated the observation of the paramagnetic peaks associated with the grid (Figures S18 andS19). Nevertheless, paramagnetic peaks are clearly observed for Fe-8H to Fe-4H, as expected from the crystal structures, and are in agreement with the presence of HS Fe II centers in the grid complexes. The titration also follows the expected trend, going from a strongly paramagnetic species for Fe-8H to a weakly paramagnetic Fe-4H system (containing less HS Fe II sites), then to LS diamagnetic Fe-2H to Fe-0H grids with no paramagnetic signal observed. The formally Fe-3H complex is the crossover species between paramagnetic and diamagnetic systems, and it is difficult to infer whether or not this species is still paramagnetic in solution.

To further investigate this magnetic behavior in solution upon deprotonation, the magnetic susceptibility was determined by 1 H NMR using the Evans method on the Fe-8H grid following the same titration procedure. The results obtained (Figure 5) agree completely with those qualitatively described above. The susceptibility value for Fe-8H is 0.047 cm 3 mol -1 (cT = 14 cm 3 K mol -1 ) in excellent agreement with the presence of four Fe II HS (with g = 2.16). Therefore, in solution, the Fe-8H complex is, or is close to, the fully paramagnetic configuration. Progressive addition of up to 8 equivalents of DMAN produced a marked decrease of the magnetic susceptibility to 0 cm 3 mol -1 between 5 and 6 equivalents of base (Figure 5). This decrease of the susceptibility on addition of base clearly revealed a dependence of the grid magnetic configuration with a number of HS or LS Fe II sites dependent upon the degree of deprotonation. Furthermore, back titration performed by adding progressively trifluoromethanesulfonic acid (CF3SO3H) resulted in a similar pattern for the magnetic susceptibility, showing the reversibility of this system upon protonation/deprotonation. This result also highlights the fully diamagnetic configuration in solution for species Fe-2H to Fe-0H. Here again it is difficult to be definitive about the magnetic state of Fe-3H, which seems to be still slightly paramagnetic but falls within the standard deviation range of diamagnetic species (Figure 5). On the other hand, the formally Fe-4H complex generated by adding four base equivalents is clearly not diamagnetic suggesting that the deprotonation of the four hydrazone groups does not lead to four LS Fe II sites in agreement with the structural and magnetic measurements in solid state (Table 1). The present titration results demonstrate a reversible Proton-Driven Spin State Switching (PD-SSS) without modification of the metal ion coordination in contrast to what has been observed in the tris(bipyridine)iron(II) system which shows also a proton-driven spin state switching but induced by a change in coordination state upon protonation (PD-CISSS). 17a

The [2´2] grid Zn-8H was also investigated as a diamagnetic model for Fe-8H. The base chosen for this titration was triethylamine (NEt3) to make sure that the base signals would not interfere with the diamagnetic grid signals. As in the case of Fe-8H, the solubility of the grid changes with deprotonation, with Zn-8H to Zn-4H being soluble in acetonitrile (Figure S20), and Zn-3H to Zn-0H being soluble in DMSO but not in acetonitrile or chloroform (Figure S21). In contrast to the iron grid, all 1 H NMR signals of Zn-8H correspond as expected a diamagnetic species over the titration range (from 0 to 8 equivalents of base) and can be assigned by COSY NMR (Figure S22). Both Fe-4H and Zn-4H seem to be pivotal species in their respective deprotonation series, as going from the 4H to 3H protonation states shows similar changes both in solubility and color.

As crystal structures only reflect the solid state and not the solution state observed by 1 H NMR, control experiments have been performed. In the case of the Fe complexes, two distinct 1 H NMR spectra were observed during the titration, the initial one being the same as that of a solution obtained by dissolution of Fe-8H crystals (Figures S18 andS19). After addition of 4 equivalents of base, the second distinct pattern was identified. This solution was then taken out of the NMR spectrometer and slow ether diffusion yielded crystals confirmed by X-Ray crystallography to be Fe-4H. To ensure that the crystals obtained were the only type present, several different crystals were tried, giving the same result. Therefore, the symmetrical deprotonation pattern observed for the Zn-4H grid (consisting of each metal ion site surrounded by two HL ligands forming a coordination pocket with one deprotonated and one nondeprotonated hydrazone group) is not observed for Fe-4H even after crystallization of the titrated solution. This result is consistent with the paramagnetic signature of the Fe-4H solution (Figure 5) as one would expect a symmetrical Fe-4H species to be fully diamagnetic with each Fe II center surrounded by one deprotonated ligand environment. It is worth mentioning that Zn-4H with the symmetrical deprotonation pattern has also been reproducibly isolated from the corresponding titrated NMR solution.

Computational studies on Fe II grids: Magnetic Configuration Energetics and Deprotonation Patterns. In order to investigate how the successive deprotonation of the bridging ligands affects the SCO properties within the grid, DFT computations have been performed to monitor the stability of the relevant magnetic configurations depending on the deprotonation pattern. These configurations are HS with four HS Fe II sites, LS with four LS Fe II sites and intermediate states with two HS and two LS Fe II centers either in opposite, noted IS-trans, or neighboring, noted IS-cis, sites of the grid, or with one HS and three LS Fe II centers referred to HLLL (Table S9). Other magnetic configurations have been computed and found of little interest for the discussion. The stability is discussed only in terms of electronic enthalpies (𝐻 "#"$ ) due to the difficulty to evaluate the vibrational enthalpy (𝐻 %&' ) and entropy (𝑆 %&' ) contributions. The 𝐻 "#"$ values for relevant magnetic configurations and deprotonation patterns of Fe-8H, Fe-6H, Fe-4H and Fe-3H are given in Table S9. To evaluate the magnetic configuration stability at a given temperature from our calculations and allow a direct comparison with experiment, we have assumed 𝛥𝐻 %&' = -3 kJ/mol, and 𝛥𝑆 *+* = 35 J/K•mol, which lie in the common range of values, and a Boltzmann distribution of states based on free enthalpies (𝛥𝐺 = 𝛥𝐻 "#"$ + 𝛥𝐻 %&' -𝑇𝛥𝑆 *+* ). The computational model consists of an isolated [2´2] grid, whose structure is optimized at different magnetic configurations to obtain 𝐻 "#"$ . Deviations from experimental measurements can be ascribed to crystal packing effects originated in the interactions with counterions, solvent molecules or other grids. These effects could be incorporated to our computational analysis by means of solid-state calculations with periodic boundary conditions. However, the size of the unit cells (ca. 1000 atoms) makes such analysis extremely expensive in the present case. The calculations for the Fe-8H complex indicate a HS ground configuration with a less stable LS state lying at about 21.1 kJ/mol (see Table S9), and also a IS-trans state that is slightly preferred over the IS-cis one (7.3 and 8.9 kJ/mol above HS, respectively). One of the reasons for the disfavored LS structure in the calculations is found by looking at the Fe II coordination spheres. Indeed, most of the LS Fe II centers in the structurally characterized grids (shown in Tables 2 andS7) have octahedricity values within the range 2.24-2.46 indicating a slightly distorted octahedral geometry. 17, 22 In contrast, the LS configuration for Fe-8H has a significantly-larger calculated S(Oh) value (ca. 2.60; Table S10) indicating that the Fe coordination sphere should be more distorted and, thus, disfavored. In the case of the Fe-6H complex, three deprotonation patterns have been explored: a single deprotonation of two different Fe centers in (i) cis and (ii) trans positions within the grid, or (iii) a double deprotonation in one center (i.e. homo). The results show that such homo pattern is clearly unfavorable with respect to the cis and trans ones, both showing similar stability. In light of these calculations, it is difficult to suggest which might be the most stable structure at room temperature, since multiple configurations should be thermally accessible. To illustrate the complexity, assuming the aforementioned 𝛥𝐻 %&' and 𝛥𝑆 *+* values, there would be four states with more than 5% population at 300 K, and the ratio of HS:IS:LS states would be ca. 1:1:0. This is in line with the poorly-defined 1 H NMR spectrum following the addition of two equivalents of base as observed in Figures S18 andS19, indicative of a superposition of multiple proton-transfer isomers. Similarly, at 120 K the ratio of HS:IS:LS states would be of ca. 1:9:0. For Fe-4H, we have explored two deprotonation patterns in which only one proton is removed from each of the four Fe II centers (so-called hetero) or two protons are removed from the same two Fe II centers (i.e. homo). In contrast with the results discussed for Fe-6H, the homo pattern is far more stable than the hetero one for all of the explored magnetic configurations. Concerning the stability, the LS configuration is the most stable one in terms of 𝐻 "#"$ , but the IS-trans lies very close in energy (1.0 kJ/mol) so it is likely thermally populated at moderate temperatures due to the favorable entropic contribution. Indeed, assuming the same 𝛥𝐻 %&' and 𝛥𝑆 *+* values as before, we would obtain a population of 93% of the IS-trans state at 120 K with the homo deprotonation pattern, which would be consistent with the crystallographic data (Table 1). Finally, for Fe-3H we have performed a less systematic study, whose purpose has been to evaluate (i) the preference for the homo deprotonation over the hetero one, and (ii) the possibility of accessible paramagnetic configurations. The two points are confirmed by our calculations; the hetero configuration lies 8 kJ/mol above the homo one, and the HLLL state is accessible since it is only 1.3 kJ/mol higher than the LS state, which means that at room temperature one would have 70% of HLLL state. These results are also in good agreement with the experimental data shown in Figure 5. Overall, the calculations clearly over-stabilize the HS configuration for the Fe-8H grid (8+ charge), and to some extent also for the Fe-6H grids (6+ charge). In turn, the HS/LS stability in the Fe-4H grids (4+ charge) seems to be better balanced. The origin for such decreasing error as we reduce the intrinsic charge of the grid might be associated to the decrease of the intermolecular interactions between the grids and their neighbors (either counterions, lattice-solvent molecules or other grids). Indeed, these interactions might have an important electrostatic contribution that is missing in our calculations, whose importance must certainly decrease along with the deprotonation. If this contribution were stabilizing the LS state (or penalizing the HS state), then the apparent errors in the mixed HS/LS state stability could be certainly ascribed to the absence of such electrostatic interactions in our computational model. Nevertheless, the deprotonation patterns observed by crystallography are supported by the present calculations, with the first two deprotonation steps (Fe-8H to Fe-6H) occurring in opposite sides of the grid (i.e. hetero) and the third and fourth steps (Fe-6H to Fe-4H) occurring in the already-deprotonated sites (i.e. homo).

Additional pKa calculations have also been performed on a truncated version of an isolated Fe II center (see supporting information). The numerical results show that the HS Fe II center has a higher pKa value than the LS site (Table S11). Overall the unexpected unsymmetrical deprotonation pattern seen in Fe-4H seems to be induced by the intramolecular cooperativity enforced by the ligands, as has been shown for similar Fe II [2´2] grids, both experimentally and theoretically. 12a,21 This effect can be monitored by Continuous Shape Measurements (CShM), which evaluate the octahedricity of the Fe-N6 coordination sphere, i.e. its distortion from an ideal octahedron (S(Oh) = 0), 18,22 and enable us to gain some relevant insight concerning the mutual influence between the Fe II centers in the studied grid (Table 2). First, the deprotonation of one coordination pocket not only affects the S(Oh) value of the Fe metal ion in that pocket but affects also the two neighboring Fe centers coordinated to the two ligands of the deprotonated coordination pocket and, indirectly, the whole grid. This is precisely what is expected from a system displaying intramolecular cooperativity, and can be illustrated, for instance, in the S(Oh) values of the HS configuration for the Fe-6H-Cis deprotonation pattern, in which the largest value corresponds to an Fe pocket that is not deprotonated (7.09, Table 2). This is surprising at first sight, but can be understood by looking at the actual structure of the grid, which presents a significant degree of distortion that stems from the Fe-N6 coordination sphere but is absorbed by the whole grid. As a result of this observation and for the sake of simplicity, our discussion in the next paragraph will be based on S(Oh) values averaged for the four Fe sites of the grid (see Avg. values in Tables 2 andS10). Indeed, the deprotonation affects differently the HS and LS Fe II centers. The S(Oh) value of HS centers increases from Fe-8H (6.50) to Fe-6H (6.61 for homo and trans, and 6.76 for cis) and then decreases from Fe-6H to Fe-4H (6.58). On the contrary, the S(Oh) value of the LS centers continuously decrease upon deprotonation from Fe-8H (2.59) to Fe-6H (2.42 for trans and cis, and 2.40 for homo) to Fe-4H (2.36) (Tables 2 andS10). This observation indicates that the coordination pockets of the ligand are better suited to coordinate a LS Fe II metal ion after deprotonation, whereas the opposite trend holds for a HS center. Making the fair assumption that, the larger the distortion of the Fe-N6 sphere, the larger the energy penalty, it would explain the progressive (de)stabilization of (HS)LS centers upon deprotonation that is captured in Table S9. Of course, the scenario is significantly more complex for IS and HLLL configurations so we have restricted our analysis to states in which all Fe centers are either HS or LS (Table S10). Even though other energy contributions are likely to contribute to the HS/LS relative stability, this analysis provides a microscopic interpretation to the magnetic configuration stability of the reported [2´2] grid.

Modulation of the magnetic configuration in the [Fe4(HnL4)] (n)+ (n = 4, 6, 8) complexes as a function of protonation state in light of the structural, magnetic and computational data. Remarkably, on reaching the conditions for deprotonation of four of the eight hydrazone N-H sites belonging to the four ligands of the [Fe4(H2L)4] 8+ complex (Fe-8H), the crystal structure of the corresponding complex [Fe4(HL4)] 4+ (Fe-4H) showed that a double deprotonation had occurred at two Fe II metal centers (Figure 2, top), the other two coordination centers remaining fully protonated. This result is in strong contrast with an expected symmetrical pattern of single deprotonation on each of the four coordination sites, as it is indeed observed in the crystal structure of the zinc analogue Zn-4H (Figure 2, bottom). Indeed, it was shown that for complexes of a ligand such as Hpaphy (Scheme 2), the pKa increases after the first ligand deprotonation. 14 An estimation of the acidity of the N-H site for Hpaphy gives pKa = 14.5. 23 In the [Fe II (Hpaphy)2] 2+ complex, the N-H site becomes much more acidic, due to the binding of the As stated above, Fe-8H exhibits a very unusual deprotonation behavior.

As for paphy complexes, two different pKas would be expected on the same metal center, pKa1(H2L/HL) and pKa2(HL/L), leading to the deprotonation pattern indeed observed for Zn-4H. The proposed explanation for the different deprotonation patterns observed for Fe-4H and Zn-4H is that the Fe II spin state switching from HS to LS affects the pKa of the corresponding N-H ligand site to a point that the pKa2(HL/L) of an LS coordination center becomes lower than the pKa1(H2L/HL) of a HS site. Following this reasoning, Fe-6H then also exhibits an interesting deprotonation pattern, as in that case a trans deprotonation is observed involving two different, diagonally located Fe II centers -as opposed to the removal of both protons on the same metal site. This cooperative effect between Fe II centers due to ligand rigidity within iron(II)

[2´2] grids has been evidenced before for multi-step spin crossover processes, both experimentally and theoretically. 12a,21 These results show that the SCO is facilitated first between Fe II from opposite corners but then hampered for further spin state switching. The experimental and theoretical data on our system lead us to similar conclusion on the importance of cooperativity and ligand rigidity in a grid complex, as evidenced by the CShM calculations (Table S10). DFT calculations also showed clearly that for a same ligand system, the pKa is lower for a LS Fe II site than it is for the HS analogue (Table S11). Relating the results of the calculations to the behavior of our system, the first double deprotonation step (Fe-8H to Fe-6H), rather than resulting from the influence of the Fe II spin state on the ligand pKa, is governed by the rigidity of the ligand which forces a deprotonation on two different sites. The second double deprotonation step (Fe-6H to Fe-4H) is in turn governed by the change in pKa induced by the SCO of the trans-located iron centers, now in the LS state. The reason is that the pKa1 of the two remaining HS iron centers must be higher than the pKa2 of the two LS iron centers that underwent SCO. The stability of this unsymmetrical deprotonation pattern for Fe-4H is well supported by the calculations on both grid stability and influence of Fe II spin state on pKa (Tables 2 andS11).

n

CONCLUSIONS

The data presented herein demonstrate the possibility of modulating the spin state of the Fe II sites and subsequently the magnetic properties of a [2´2] Fe II grid-like complex by variation of the degree of deprotonation of the hydrazine-based N-H sites of the ligand in the complex. Evidence has been provided, both in the solid state and in solution, towards understanding the strong influence of the spin-crossover process on the pKas of the grid ligands, which exhibit a unique deprotonation pattern.

The present study provides a demonstration of the effect of spin state switching of a chemical property, here on ligand pKa in a metallosupramolecular grid.

■ ASSOCIATED CONTENT P orous metal-organic materials (MOMs) that incorporate reactive species (RS) such as metalloporphyrins, 1 metallosalens, 2 and polyoxometalates 3 are of topical interest because they can combine the physicochemical properties of the RS 4 with permanent porosity of the framework. 5 Such MOMs can thereby enable new approaches to gas storage, 6 separations, 7 luminescence, and catalysis, 8 including enzymatic catalysis. 8b MOMs that incorporate RS can be divided into two subgroups: those with RS as an integral part of nodes/linkers (RSMOMs) 9 and those that encapsulate or host RS in cages (RS@MOMs). 10 Encapsulation may be achieved directly through synthesis 11 or via postsynthetic modification (PSM). 12 Metalloporphyrins are attractive RS because of their value as catalysts 13 and dyes, 14 and we recently reported the generation of porphyrin-encapsulating MOMs (porph@MOMs) [START_REF]From a synthetic point of view, the use of an appropriate base to deprotonate the NH group of the free ligand, transforms this one in a nucleophilic reagent that is possible to alkylate thus opening a synthetic route toward new very diverse ligands[END_REF] that exhibit PSM through metal ion exchange 16 or metal salt incorporation. 17 The availability of such porph@MOMs offers the opportunity to study their PSM systematically and evaluate its impact on their properties such as gas sorption, luminescence, and catalysis. In addition, PSM can afford new compounds that cannot be directly synthesized.

PSM involving metal exchange in molecular building blocks (MBBs) is now widely studied and tends to focus upon Cd-and Zn-containing MOMs 18 because of the relative lability of complexes of d 10 ions (Cd 2+ , Zn 2+ , and Hg 2+ ). 19 The metal exchange process is typically monitored using atomic absorption spectroscopy (AAS) and powder X-ray diffraction (PXRD), and examples where PSM has been followed using single-crystal X-

Scheme 1 .

 1 Scheme 1. Synthesis of the ditopic ionizable hydrazine-based ligand H2L and its self-assembly into the corresponding tetranuclear [Fe4(H2L)4] 8+ [2´2] grid complex by coordination with Fe II cations. Red spheres represent Fe metal ions. Hydrogen atoms that are colored in blue emphasize the deprotonation sites on the [2´2] grid.

  Scheme 1. Metal Ion PSM in porph@MOMs: (i) Partial PSM with Metal 2 in the Presence of Both Metal 1 and 2 (Bottom Left); (ii) Complete Exchange with Metal 2 (Bottom Right)

n

  RESULTS AND DISCUSSIONSynthesis of the ligand and of the corresponding Fe II [2´2] grid complexes. Several [2´2] grids, [Fe4(HnL4)] (n)+ (0 > n > 8, Fe-nH), were prepared and isolated by reaction of the corresponding ligand H2L with Fe(BF4)2 in a 1:1 molar ratio at room temperature in acetonitrile and in the case of n < 8, adding the corresponding amount of base (triethylamine) for deprotonation (see supporting information for detailed procedures). Subsequently, crystals of the [2´2] grid complexes in different states of ionization were obtained by slow diffusion of diethylether into the different solutions. Three single-crystal structures were determined by X-ray diffraction (see supporting information) and confirmed the expected [2´2] grid topology accompanied by 8, 6 and 4 BF4 - anions, depending on the degree of deprotonation of the grids: [Fe4(H2L)4](BF4)8•xMeCN (Fe-8H, red needles, x = 2 or 6 at 290 and 120 K, respectively), [Fe4(H2L)2(HL)2](BF4)6•8MeCN (Fe-6H, red blocks) and [Fe4(HL)4](BF4)4•12MeCN (Fe-4H, red plates). Unfortunately, and despite intensive efforts, no crystals were obtained for the other deprotonated states. Two Zn-based [2´2] grids, [Zn4(HnL4)] (n)+ (n = 8 and 4, Zn-8H and Zn-4H, respectively), were also prepared and isolated by reaction of the corresponding ligand with Zn(BF4)2 in a 1:1 molar ratio at room temperature in acetonitrile (in the case of n = 4, the corresponding amount of triethylamine was added). As zinc(II) is diamagnetic, the Zn-based complexes provide model systems to study the ligand behavior independently of the iron(II) SCO influence.

Figure 1 .

 1 Figure 1. Ball and stick representations of the crystal structures of the [Fe4(H2L)4](BF4)8•2MeCN complex, Fe-8H, with non-ionized ligands (top) and the doubly deprotonated [Fe4(H2L)2(HL)2]-(BF4)6•8MeCN complex, Fe-6H, (bottom) both at 290 K. Fe, N, C and H atoms are shown in red, blue, grey and white, respectively. All non-NH hydrogen atoms, acetonitrile and tetrafluoroborate molecules are omitted for clarity. Non-deprotonated NH sites are circled in red.

Figure 2 .

 2 Figure 2. Ball and stick representations of the crystal structures of [Fe4(HL)4](BF4)4•12MeCN complex, Fe-4H, (top) and [Zn4(HL)4](BF4)4•8H2O complex, Zn-4H, (bottom) at 120 K. Fe, Zn, N, C and H atoms are shown in red, green, blue, grey and white, respectively. All non-NH hydrogen atoms, acetonitrile and tetrafluoroborate molecules are omitted for clarity. Non-deprotonated NH sites are circled in red. Only one position for Fe3 (Fe3a) and its corresponding donor atoms are shown.

Figure 3 .

 3 Figure 3. Temperature dependence of cT product at 0.1 (between 1.85 and 50 K) and at 1 T (above 50 K) between 1.85 and 300 K for polycrystalline samples of Fe-8H, Fe-6H, and Fe-4H (where c is the magnetic susceptibility equal to M/H per mole of [2´2] Fe4 grid).

Figure 4 .

 4 Figure 4. (top) UV-Vis spectra of the grid Fe-8H after progressive addition of base in acetonitrile/chloroform (1:1); (bottom) corresponding pictures of Fe-8H solution after addition of base (0 to 8 eq., left to right).

Figure 5 .

 5 Figure 5. Evolution of the magnetic susceptibility (and cT product) of Fe-nH in CD3CN/CDCl3 (1:1) at 298 K on titration with DMAN base as observed by 1 H NMR using the Evans method. Error bars represent standard deviation over 3 experiments.

Table 2 .

 2 Calculated octahedricity parameters: S(Oh) values 18,22 as a measure of distortion of the Fe-N6 coordination sphere for 1 to 4 SCO centers in selected grids. Values of S(Oh) smaller than 4.42 indicate a geometry closer to the octahedron than to the trigonal prism, while S(Oh) values above 4.42 point toward a distorted trigonal prism geometry.

ABSTRACT:

  When immersed in solutions containing Cu(II) cations, the microporous metal-organic material P11 ([Cd 4 (BPT) 4 ]•[Cd(C 44 H 36 N 8 )(S)]•[S], BPT = biphenyl-3,4′,5-tricarboxylate) undergoes a transformation of its [Cd 2 (COO) 6 ] 2-molecular building blocks (MBBs) into novel tetranuclear [Cu 4 X 2 (COO) 6 (S) 2 ] MBBs to form P11-Cu. The transformation occurs in single-crystal to single-crystal fashion, and its stepwise mechanism was studied by varying the Cd 2+ /Cu 2+ ratio of the solution in which crystals of P11 were immersed. P11-16/1 (Cd in framework retained, Cd in encapsulated porphyrins exchanged) and other intermediate phases were thereby isolated and structurally characterized. P11-16/1 and P11-Cu retain the microporosity of P11, and the relatively larger MBBs in P11-Cu permit a 20% unit cell expansion and afford a higher surface area and a larger pore size.

18,22 Deprotonation Fe-8H Fe-6H-Trans Fe-6H-Cis Fe-6H-Homo Fe-4H-Homo HS

  The second deprotonation occurs at a higher pKa2 of 6.57 in aqueous solution (Scheme 2).14 These values offer an approximation of what one would expect for the iron(II) sites of the Fe-8H grid. Interestingly both [Fe(Hpaphy)2] 2+ and [Fe(paphy)2] species are diamagnetic complexes.

	doubly charged metal cation (pKa1 = 5.68).
		①	6.44	6.47	6.36	6.45	6.61
		②	6.51	6.77	7.07	6.58	6.58
	S(Oh)	③	6.58	6.75	7.09	6.91	6.53
		④	6.46	6.46	6.50	6.48	6.62
		Avg.	6.50	6.61	6.76	6.61	6.58
	LS
		①	2.58	2.39	2.45	2.40	2.32
		②	2.60	2.41	2.45	2.42	2.41
	S(Oh)	③	2.60	2.45	2.38	2.39	2.44
		④	2.58	2.42	2.40	2.40	2.28
		Avg.	2.59	2.42	2.42	2.40	2.36

24 Scheme 2. Acidity constants pKa of [Fe(Hpaphy)2] 2+ (left), [Fe(Hpaphy)(paphy)] + (middle) and Hpaphy (right).

■ ACKNOWLEDGMENTS

We thank the ERC (Advanced Research Grant SUPRADAPT 290585), the University of Strasbourg, the University of Bordeaux, the Région Nouvelle Aquitaine, the CNRS, the GdR MCM-2: Magnétisme et Commutation Moléculaires and the MOLSPIN COST action CA15128 for funding. S.V. is thankful to the LabEx-Chemistry of Complex Systems for a post-doctoral grant (ANR-10-LABX-0026CSC) and to the regional High-Performance Computing (HPC) center in Strasbourg for computational resources. J.M.L. thanks Jack Harrowfield and Mihail Stadler for discussions.

Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI: Experimental details about syntheses, crystal structures, physical characterizations and theoretical calculations (PDF) X-ray crystallographic data for Fe-8H (120 and 290 K ; CIF), Fe-6H (120 and 290 K ; CIF), Fe-4H (120 K ; CIF), Zn-8H (173 K ; CIF) and Zn-4H (120 K ; CIF)

Notes

The authors declare no competing financial interests.


Antoine Collin
email: antoine.collin@ephe.sorbonne.fr

Camille Ramambason

Yves Pastol

Elisa Casella

Alessio Rovere

Lauric Thiault

Benoit Espiau

Gilles Siu

Franck Lerouvreur

Nao Nakamura

Benoît Espiau

Lerouvreur

James L Hench

Russell J Schmitt

J Holbrook

Matthias Troyer

Neil Davies

Very high resolution mapping of coral reef state using airborne bathymetric LiDAR surface-intensity and drone imagery

Keywords: coral reefs, bathymetric LiDAR, drone coral reefs, state, LiDAR, drone, neural network 20

Introduction 21

Coral reefs host 25% of the marine biodiversity but are increasingly subject to global 22 ocean-climate changes and local anthropogenic activities [START_REF] Bellwood | Confronting the coral reef 14 crisis[END_REF]). Fine-scale 23 monitoring of coral reef ecosystems and associated ecosystem services is needed for 24 their management and spatial planning. Coral reef mapping usually relies on remote [START_REF] Madin | Ecological consequences of major hydrodynamic 26 disturbances on coral reefs[END_REF] sensing for cost-effectively identifying their structural complexity, benthic

( ) ∑ = i i i X n w k X h ) ( ) (
(1) 2

Neurons n i are hereinafter based on hyperbolic tangents. ANN constrained by a 3 single hidden layer provided with two neurons so the number of neurons to be in 4 synergy with the number of inputs (predictors, Fig. 3). Trained by the 275 calibration 5 samples, the ANN will be validated by the remaining 135 validation samples. 6 Figure 3 7

Performance analysis 8

The agreement between validation and classified pixels in the five ecological states was 9 quantified using the confusion matrix, from which overall, producer's and user's 10 accuracies (OA, PA and UA, respectively) were computed [START_REF] Congalton | Assessing the accuracy of remotely sensed data: 45 principles and practices[END_REF]. 11

PA and UA were calculated as the correctly classified pixels in each coral state divided 12 by the number of calibration pixels of the corresponding state, and the total number of 13 pixels that were classified in that state, respectively. OA was reckoned as the correctly 14 classified pixels in all states divided by the total number of pixels. 15

Results 16

Local coral reef state at very high resolution 17

The OA of the ANN classification reached a satisfactory performance (OA=0.75), [START_REF] Collin | Enhancing coral health detection using spectral diversity 19 indices from worldview-2 imagery and machine learners[END_REF] showing that the dual combination of LiDAR surface and intensity variables had a 19 robust explanatory power of the variability of coral reef states (

Moorea coral reef state at very high resolution 29

Insofar as the ANN prediction was adequate enough to be extended, the digital 30 ecological classification was mapped at the island scale. Moorea LiDAR DSM and DIM 31

were first rasterized at 0.5 m spatial resolution (Fig. 5a and5b) and then entered as 32 inputs to the ANN classification, which produced a digital model of coral reef 33 ecological state over the whole island (Fig. 5c

Very high resolution mapping of coral reef state using airborne 1 bathymetric

 1 Very high resolution mapping of coral reef state using airborne bathymetric LiDAR surface-intensity and drone imagery LiDAR surface-intensity and drone imagery 2 Very high resolution (VHR) airborne data enable detection and physical 3 measurements of individual coral reef colonies. The bathymetric LiDAR system, 4 as an active remote sensing technique, accurately computes the coral reef 5 ecosystem's surface and reflectance using a single green wavelength at the 6 decimetre scale over 1-to-100 km 2 areas. A passive multispectral camera 7 mounted on an airborne drone can build a blue-green-red (BGR) orthorectified 8 mosaic at the centimetre scale over 0.01-to-0.1 km 2 areas. A combination of these 9 technologies is used for the first time here to map coral reef ecological state at the 10 submeter scale. Airborne drone BGR values (0.03 m pixel size) serve to calibrate 11 airborne bathymetric LiDAR surface and intensity data (0.5 m pixel size). A 12 classification of five ecological states is then mapped through an artificial neural 13 network (ANN). The classification was developed over a small area (0.01 km 2 ) in 14 the lagoon of Moorea Island (French Polynesia) at VHR (0.5 m pixel size) and

4

  review and synthesis." Marine pollution bulletin 50(2): 125-146. 5 Goodman, J.A., J.P. Samuel, and R.P. Stuart. 2013. Coral reef remote sensing. A guide for 6 mapping, monitoring and management. Springer: Netherlands. 7 Hedley, J.D., C.M. Roelfsema, I. Chollett, A.R. Harborne, S.F. Heron, S. Weeks, W.J. Skirving, 8 A.E. Strong, C.M. Eakin, T.R.L. Christensen, V. Ticzon, S. Bejarano, and P.J. Mumby.

9 2016.Figure 1 . 7 Figure 2 .Figure 3 .Figure 4 .

 917234 Figure 1. (a) Moorea Island (French Polynesia) was surveyed by bathymetric LiDAR at island

Figure 5 .

 5 Figure 5. Digital (a) surface, (b) intensity (532 nm wavelength), and (c) coral reef state

2. Materials and methods 31 2.1. Study site 32

	1 1	reef bathymetry and derived terrain roughness at very high resolution (VHR) using the 2.2. Drone visible response
	2 2	photogrammetry approach (Leon et al. 2015; Casella et al. 2017). The 3D point cloud, A drone-based spectral survey (Fig. 1b) was carried out on 17 August 2015 using a
	26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 23 24 25 26 27 28 29 30 33 34 35 36 37 38 39 40 41 42 43 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 13 14 15 16 12 13 14 15 17 18 19 21 22 20	composition, and regime surrogates over large areas (Goodman, Samuel and Stuart 2013; Hedley et al. 2016). Spaceborne multispectral imagery demonstrates great spatial potential to accurately map coral reef colonies (Collin, Hench, and Planes 2012), habitats (Collin et al. 2016), health (Collin and Planes 2012; Collin, Archambault, and Planes 2014) and resilience (Rowlands et al. 2012; Knudby et al. 2013; Collin, Nadaoka, and Bernardo 2015). Airborne passive hyperspectral imagery, provided with dozens of spectral bands, enables coral reef benthos, substrates and bathymetry to be significantly improved (Leiper et al. 2014). Airborne (usually on manned aircraft) active light detection and ranging (LiDAR) is now the reference system for measuring bathymetry, outperforming waterborne sound detection and ranging (SoNAR) devices, which are strongly impeded by shallow features, specifically in the coastal realm where coral reefs thrive (Costa, Battista, and Pittman 2009). LiDAR-derived morphometry indices can reveal efficient proxies for ecosystem characteristics, for example, estimates of reef fish assemblages (Wedding et al. 2008). Yet despite the increase in discrimination power showed over benthic habitats bathed with turbid waters, LiDAR indices have not been used to date to exploit the spectral information associated with water-penetrating green LiDAR wavelength for coral reef monitoring (Collin, Archambault, and Long 2008; Collin, R e v i e w O n l y future states of the social-ecological system in support of scenario-based planning (Davies et al. 2016). We follow a drone-based assessment of ecological state (coral reef state classification; Table 1) and combine it with LiDAR-based data to spatially classify the coral reef state at VHR over a small area and then extend this to the whole island. Findings are discussed with a view to how this approach could advance an automated workflow for coral reef mapping. Figure 1 Table 1 The study site is located in the northern lagoon of Moorea Island (17°33′S, 149°50′W) in the Society Archipelago (French Polynesia, Fig. 1a). Moorea demonstrates a highly resilient coral reefs (Adjeroud et al. 2009), especially its outer slope, which following the extremely low coral cover (2%) due to 2007-2010 outbreak of corallivore crown-of-thorne sea star (Acanthaster planci) and 2010 Oli cyclone strike, is recovering to record rates close to 70% (Chancerelle, pers. comm.). Located inside the 46.83 km 2 Moorea lagoon, the study site covers 11 710 m 2 with maximum depth of 2 m. It is bathed in oligotrophic, thus clear, seawater including various taxa of reef building corals (Porites, Acropora, Pocillopora, Montipora), red calcareous algae (Lithothamnium), fleshy algae (red, brown and green) and a diversity of geomorphic features (rubble, sand and pavement). R e v i e w O n l y Archambault, F o r P e e r permitting 2D orthorectified BGR mosaics and 2.5D digital surface models (DSM), results from the multi-angle information of a single scene made possible by spatially-BGR camera (GoPro Hero 4) mounted on a consumer-grade drone (DJI Phantom 2). even acquisition of BGR imagery from a moving airborne drone flying at low altitude Calm sea and low sun elevation angle were optimal conditions for this survey. A series (from 30 to 150 m): so-called "structure-from-motion". The images and by-products of 360 geolocated BGR photographs, acquired at 30 m altitude at nadir, were mosaicked yield spatial resolution at centimetre scale (i.e., 0.03 m pixel size). Coral reef states can then processed using the photogrammetry software Agisoft Photoscan be significantly distinguished using the resulting 0.03 m BGR orthomosaic drone (http://www.agisoft.ru). Constrained by nine ground control points and three scale bars, dataset, enabling classification of reef ecological states. the resulting orthorectified mosaic (WGS 84 datum and UTM 6S projection) has 0.03 m Here we describe methodology for creating the first coral reef ecological state resolution (see Casella et al. 2017 for further details) and was therefore deemed as map at VHR based solely on regional airborne LiDAR "predictors" trained with local precise enough to be used as air-truth (Fig. 1c, Collin, Lambert, and Etienne 2018). A "response" imagery from drone. The bathymetric LiDAR Riegl VQ-820-G, mounted on total of 410 sampling points over the BGR orthomosaic, corresponding to as many a small plane or helicopter, serves as the remotely-sensed 1-to-100 km 2 predictors with four measurements of surface and intensity (green) per m 2 . The BGR GoPro, mounted on a consumer-grade airborne drone (DJI phantom 2), is used as the remotely-sensed 0.01-to-0.1 km 2 response. Spearheading machine learners in satellite-based coastal prediction (Collin, Etienne, and Feunteun 2017), an artificial neural network (ANN) LiDAR soundings, were visually interpreted by an expert and classified into five ecological states (Fig. 2a and Table 1), each one composed of 55 training and 27 F validation sub-datasets. o Figure 2 r classifier is developed to provide a robust, yet simple, algorithm linking the two datasets. Our study takes place on one of the best-studied islands in the world (Cressey 2015): Moorea (French Polynesia, Fig. 1), a volcanic island with fringing, barrier and outer coral reefs in the central South Pacific Ocean. It contributes to efforts to build a 4D model -an Island Digital Ecosystem Avatar (IDEA) -of Moorea and to simulate of r e e P 2.3
		3 4

and Long 2011; Collin, Long, and Archambault 2011). 44 Unmanned airborne vehicles (UAVs, or simply 'drones') are becoming an 45 integral component of the scientific toolbox for coral reef research and management. 46 Equipped with blue-green-red (BGR) spectral cameras, drones are able to measure coral 47

. LiDAR surface and intensity predictors 16

  , functions called neurons, n i (Heermann and Khazenie 1992): 1

		weighted, w i
		F o r
		P e
		e r
	24 25 26 27 28 29	fly for each sounding by converting the time between sea surface and bottom green echoes R e v into distance (knowing the light speed into water), and by recording the peak of bottom green echo, respectively. Maximum depth ever recorded by bathymetric LiDAR i e reached 76.1 m in Moorea Island during the studied survey (Pastol, Chamberlain, and Sinclair 2016) given the water clarity due to oligotrophic waters. Since our Moorea w
	30 31 32 33 34 35	study limits to the shallow waters (< 10 m depth), LiDAR intensity has been directly processed with no water correction. As each LiDAR surface and intensity sounding is duly located by the combination of HR global navigation satellite system and inertial O measurement unit, digital surface and intensity models (DSM and DIM, Fig. 2b and 2c) can be calculated using ordinary kriging method applied to LiDAR sounding clouds. n l LiDAR points and rasters were geographically referenced to WGS84 UTM 6S and y
	36	altimetrically zeroed as the mean sea level (SHOM 2016). Drone-derived imagery was
	37	registered with LiDAR data using a 1 st degree polynom function and resampled with
	38	cubic convolution.
	39	2.4. Artificial neural network classification
	40	Given their performance in a comparative analysis (Collin, Etienne, and Feunteun
	41	2017), we use an ANN approach as a classification procedure binding the drone-based
		air-truth and LiDAR-based variables.
		5

The airborne LiDAR campaign was conducted from 10 to 26 June 2015 (one month 17 before the drone flight) using a Riegl VQ-820-G hydrographic laser scanner mounted 18 on a small plane. The sensor was operated at 251 kHz, providing minimum sounding 19 density of four points per m 2 (0.5 m) and vertical accuracy of 0.15 m, computed from 20 43798 comparisons (Pastol, Chamberlain, and Sinclair 2016). This bathymetric LiDAR 21 pulses an electromagnetic radiation (532 nm wavelength, namely green) from the 22 aircraft and records its travel time in air and water by means of a waveform (Collin, 23 Archambault, and Long 2008). LiDAR surface and intensity are computed on-the-42 The ANN builds non-linear classifications by minimizing least squares using a 43 multi-layer perceptron classifying ecological state response, h(X), (Table 1) with the 44 LiDAR surface and intensity predictors, X, through a constant, k, and intermediate 45

Table 2

 2

	). Contrary to

  Authors gratefully thankService Hydrographique et Océanographique de la Marine for the 1 LiDAR acquisition control, and the IDEA Consortium for sparking this collaborative research. 2 This work was partly supported by French Polynesia government for LiDAR acquisition, the 3 ETH Zurich for purchasing satellite imagery, and the National Science Foundation through the 4 Meyer, B. Stoll, B. Swalla, D.M. Tartakovsky, H.T. Murphy, S. Turyshev, F. Valdvinos, 1 R. Williams, S. Wood, Consortium I. 2016. "Simulating social-ecological systems: the 2 Island Digital Ecosystem Avatars (IDEA) consortium." Gigascience 5:14. 3 Fabricius, K.E. 2005. "Effects of terrestrial runoff on the ecology of corals and coral reefs:

	1 1	4. Discussion nm, as the third harmonic of the 1064-nm laser), likely to detect the coral fluorescence C.
	2	as well as intermediate states (Sasano et al. 2012).
	2	4.1. Airborne drone as "air-truth"
	3 3 5	The five coral reef ecological states were based on VHR BGR orthorectified mosaic 4.3. Moorea coral reef states' spatial patterns Moorea Coral Reef LTER (OCE-1236905 and 1637396) and Physical Oceanography (OCE-
	4 4 6	derived from a consumer-grade multispectral camera driven by an airborne drone. This The coral reef state classification, spatially-classified at VHR, is a strong asset to outline 143133) programs. Two valuable referees and the editor are deeply acknowledged for the
	5 5 7	innovative procedure is supported by our knowledge of in situ coral reef features that hotspots of health coral reefs, thus of associated biodiversity and ecosystem services. manuscript improvement.
	F o r can be discriminated at the centimetre scale. Insofar as both ecological composition and structural complexity are easily deduced from the BGR dataset, relatively inexpensive drone deployment can be used to obtain air-truth data directly even in places with little technical capacity. The geolocated photographs can be remotely processed and analysed in the cloud, given a suitable internet connection. With an easy-to-implement flight planning mobile application, rapid surveys could be conducted at even very remote locations with little infrastructure/capacity after short-terms events such as cyclone/storm and bleaching. The number of states could be increased by either flying at lower altitude (to gain in spatial resolution) or using drone-mounted LiDAR that can enhance the vertical accuracy, for example, to differentiate coral from macroalgae F o r The centimetre and decimetre scales targeted in this study greatly enhance the spatial resolution of coral reefs' diagnoses and prognoses, surpassing other recent studies using object-based image analysis, which bottom at 2 m or 10 m (Phinn, Roelfsema, Mumby 2012; Roelfsema et al. 2013). LiDAR-based spatially-explicit classification, provided with decimetre sounding density over 100 km 2 , offers an unpublished map of Moorea coral reefs' health. Two main spatial patterns emerged from the spatially-explicit classification: westward polarization of healthy fringing reefs and northward polarization of healthy barrier reefs. Wide healthy fringing reefs along west shorelines strongly contrast with thin ones along eastern coast. This outstanding geographic difference is very susceptible to F o r 8 F 6 7 8 9 10 11 12 13 14 15 6 7 8 9 10 11 12 13 14 15 o r
	16 17 18 19 20 21 16 17 18 19 20 21	P e e r The use of this air-truth, in the form of a cost-efficient UAV-borne BGR (Leiper et al. 2014). orthomosaic, has a strong potential to be applicable to other worldwide coral lagoons and even to a large panel of coastal and aquatic areas, provided with relatively clear waters. This air-truth leverages a high ratio of covered space unit per time unit while collecting centimetre-scale data, considerably outperforming submerged acquisitions, P e e r be the consequence of the dominant easterly winds (i.e., Southeast trade winds), which entail significantly greater amounts of rain then carried sediment, which, in turn, deposit onto and stress coral colonies (Fabricius 2005), impeding development of eastern fringing coral reefs. P e P e More extended barrier reefs are obvious in the northern compared to southern lagoon. This patterning might be explained by the two dominant swell systems e r e r
	22 23 24 22 23 24 25 26 25 26 27 28 29 27 28 29	R e v i e w hindered by the very high viscosity of water. 4.2. Airborne LiDAR surface and intensity The gradient of ecological states (from 1, well-developed hard coral, to 5, sand) was positively correlated with both surface (r=0.93) and intensity (r=0.93), showing that R e v originating from South: 40% SE and 25% SSW (Etienne 2012). Swell average height tends to be higher than 4 m during Austral winter, what creates, at the reef, significant wave height greater than 8 m (e.g. Teahupoo spot in Southern Tahiti Iti, Etienne 2012). The exposure to this high to very high energy flow hinders the efficient settlement of R e R e coral larvae and breaks the coral assemblage structure (Madin and Connolly 2006). This v v coral coverage decreases with depth and LiDAR green reflectance. The coral shrinkage with depth can be explained by the coral growth and structural complexification towards the surface (as a photosynthetic symbiont), what corroborates results derived from a spaceborne reef health proxy (Collin, Hench, and Planes 2012). The negative i e w interpretation is corroborated by the third dominant swell system (22% NE, Etienne 2012), which constrains NE lagoon to exhibit slightly less extended barrier reefs compared to NW. i e i e w w
	30 31 32 33 34 35 36 30 31 32 33 34 35	O n l y trend between coral state and green reflectance coincides with in situ spectral measurements, making explicit a greater reflectance of increasingly depigmented blue-and brown-mode coral reefs in the coral health chart (Leiper et al. 2009). This increase in green reflectance (decrease in green absorbance) is linked to the loss of peridinin pigments contained in symbiotic zooxanthellae living in coral tissues (Collin and Planes 2012). Even if most bathymetric LiDAR systems use the single green wavelength, this electromagnetic radiation is relevant to distinguish coral reef state as highlighted in the O n l y 5. Conclusion This original research has demonstrated that airborne bathymetric LiDAR data are able to reliably map five ecological states in coral reef systems at VHR over shallow, clear O O waters. Reef state information can be gleaned from an airborne drone equipped with a multispectral imaging sensor. Novel findings can be summarized as follows: n l n l (1) Coral reef state at the colony-scale (pixel size = 0.03 m) can be sourced from a y y
	37 36	elaboration of both the green-purple and the "red edge"-green normalized difference BGR camera mounted on an airborne low-altitude drone;
	38 37	ratios (Collin, Hench, and Planes 2012; Collin, Archambault, Planes 2014, (2) LiDAR surface and intensity are powerful predictors of coral reef ecological
	39 38	respectively). state at the colony-scale (pixel size = 0.03 m);
	40 39 34 41 40 35 42 41 36 43 42 37 44 43 38 40 46 39 45 44	, 40364 × 34588 pixels). Moorea classes Inner classification results (UA) revealed that coral-and sand-dominant states (3) ANN is an efficient classification approach to predict ecological state based only are dominated by sand on pavement (56.8%), followed by Porites stony corals (14.1%) (1, 3 and 5) were successfully recognized, contrary to both assemblages of corals and LiDAR surface and intensity (OA=0.75); and Microalgae on rubble (13.8%), then Acropora/Pocillopora/Montipora stony corals rubble colonized by calcareous and micro-algae (2 and 4), respectively. We could (4) LiDAR surface and intensity are powerful predictors of ecological state at the with red calcareous algae (10.9%), and finally Acropora/Pocillopora/Montipora stony assume that the spectral mixing due to the presence of algae on relatively "pure" states landscape scale (pixel size = 0.5 m); corals (4.4%). Overall, the coverage of hard corals (from state 1 to 3) appears was not very effectively resolved by the ANN classifier built from only LiDAR surface (5) Healthy fringing and barrier coral reefs in Moorea are located on the western significantly greater in the leeward side than the windward side. Figure 5 innovative bathymetric LiDAR, augmented by an added spectral wavelength (i.e. 355 and intensity. We advocate the experiment of a coral reef state classification using an and northern parts of the lagoon, respectively.
		6 7 8 9

Table 1 .

 1 Ecological description of the five coral reefscape states identified on airborne drone 1 blue-green-red imagery (0.03 m spatial resolution) enabling a coral reef state classification to be 2 created and colour-coded.

	3
	Drone-
	based state
			Acropora/
	Ecological compositio n	Acropora/ Pocillopora/ Montipora stony corals	Pocillopora/ calcareous Montipora stony corals with red	Porites stony corals	Microalgae on rubble	Sand on pavement
			algae
	Structural	Very High	High	Medium	Low	Very low
	complexity	roughness	roughness	roughness	roughness	roughness
	Coral reef state	1	2	3	4	5
	Colour
	class
	4

Table 2 .

 2 Confusion matrix synthesizing the quality of the artificial neural network classification 5 applied to the independent 135 validation pixels (27 pixels per coral reef state). Page 15 of 14 http://mc.manuscriptcentral.com/tres Email: IJRS-Administrator@Dundee.ac.uk International Journal of Remote Sensing and Remote Sensing Letters

	6
					Reference class
		STATE	1	2	3	4	5	Total	UA
		1	21	2	2	0	0	25	0.84
	Classified class	2 3 4	4 1 0	17 3 1	3 20 1	1 2 19	0 1 7	25 27 28	0.68 0.74 0.68
		5	0	1	2	3	24	30	0.80
		Total	26	24	28	25	32	135
		PA	0.80	0.71	0.71	0.76	0.75
	7
	8
	9
	10

http://mc.manuscriptcentral.com/tres Email: IJRS-Administrator@Dundee.ac.uk International Journal of Remote Sensing and Remote Sensing Letters

Acknowledgements

45