University of Birmingham From crystalline to amorphous calcium pyrophosphates: A solid state Nuclear Magnetic Resonance perspective

Hydrated calcium pyrophosphates (CPP, Ca 2 P 2 O 7 · nH 2 O) are a fundamental family of materials among osteoarticular pathologic calcifications. In this contribution, a comprehensive multinuclear NMR (Nuclear Magnetic Resonance) study of four crystalline and two amorphous phases of this family is presented. 1 H, 31 P and 43 Ca MAS (Magic Angle Spinning) NMR spectra were recorded, leading to informative fingerprints characterizing each compound. In particular, different 1 H and 43 Ca solid state NMR signatures were observed for the amorphous phases, depending on the synthetic procedure used. The NMR parameters of the crystalline phases were determined using the GIPAW (Gauge Including Projected Augmented Wave) DFT approach, based on first-principles calculations. In some cases, relaxed structures were found to improve the agreement between experimental and calculated values, demonstrating the importance of proton positions and pyrophosphate local geometry in this particular NMR crystallography approach. Such calculations serve as a basis for the future ab initio modeling of the amorphous CPP phases.


Introduction
Crystalline calcium pyrophosphate dihydrates (CPPD, Ca 2 P 2 O 7 ·2H 2 O) are among the most common forms of pathologic articular minerals: their prevalence increases with age, impacting on 17.5% of the population after the age of 80. 1 Although often asymptomatic, they are frequently involved or associated with acute articular arthritis such as pseudogout, and, more rarely, with chronic polyarthritis and destructive arthropathy; current treatments are mainly directed at relieving the symptoms of joint inflammation but not at inhibiting calcium pyrophosphate (CPP) formation nor at dissolving these crystals. 2,3,4 CPP have been identified in vivo as two polymorphs of CPPD: 5 a triclinic form with a known structure, 6 and a monoclinic form with a recently solved structure 7 (respectively denoted as t-CPPD and m-CPPD). Other crystalline forms of hydrated calcium pyrophosphates have been synthesized in vitro and characterized, including a dimorphic monoclinic tetrahydrate (CPPT: Ca 2 P 2 O 7 ·4H 2 O), referred to as m-CPPT α and m-CPPT β. 8,9 Recently, Gras et al. 7 performed a systematic investigation of the synthesis of pure hydrated calcium pyrophosphates. They described the pH and temperature conditions leading to the formation of m-CPPT β, t-CPPD and m-CPPD, 10 as well as the identification of a new monohydrated calcium pyrophosphate phase exhibiting monoclinic symmetry, referred to as m-CPPM (CPPM: Ca 2 P 2 O 7 ·H 2 O), 11 and an unreferenced highly metastable trihydrated monoclinic calcium pyrophosphate phase derived from the structure of m-CPPT β. 12 The preparation of amorphous phases of biological interest, noted a-CPP (Ca 2 P 2 O 7 ·nH 2 O), has also been reported by Slater et al. 13 and Gras et al., 10 and it was found that these phases are particularly stable compared to amorphous calcium orthophosphate and amorphous calcium carbonate. 4 Several characterizations have been performed on all the hydrated calcium pyrophosphate phases mentioned above by several approaches, including powder XRD (X Ray diffraction) and vibrational spectroscopies, providing information on the configuration of the pyrophosphate groups. 10 It was observed that pyrophosphate ions in CPP phases have a wide range of P-O-P angles (between 123.1 and 134.1°). 8,9 This angle is important in understanding the relationship between the various CPP forms and their stability and transformation ability. Developing complementary tools for the characterization of hydrated calcium pyrophosphates is of particular interest, especially to understand the structure of phases like m-CPPD, for which the positioning of protons may be very difficult based exclusively on X-ray powder diffraction data, particularly considering that single crystals suitable for diffraction structure resolution are not yet available. Indeed, this phase has the highest inflammatory potential of all CPP phases, and it would be of interest to determine its structure in detail in order to understand the inflammation mechanism, which is possibly based on rupture of lysosome phospholipid membranes induced by pyrophosphate groups on the surface of the crystals. 14,15,16,17 Solid state NMR is a technique which is attracting increasing attention for the study of synthetic and natural biomaterials 18 including calcium phosphate phases. 19,20,21,22,23,24,25,26,27 Indeed, solid state NMR can provide detailed atomic-scale information on the local structure around nuclei like 31 P, even in disordered and amorphous phases, and is therefore highly complementary to other analytical tools like XRD and IR (Infra Red) or Raman spectroscopies. NMR studies of calcium pyrophosphate phases have been very limited to date.
To the best of our knowledge, 31 P NMR has only been applied to the characterization of the crystalline α-and β-Ca 2 P 2 O 7 anhydrous phases, and of a hydrated amorphous calcium pyrophosphate of composition ~ Ca 2 P 2 O 7 ·4H 2 O 13,28 In the latter case, the hydrolysis of the P-O-P bridge upon heat treatment was demonstrated using 1 H MAS, 31 P MAS and 1 H-31 P 5 cross-polarisation (CP) MAS NMR experiments. With regards to 43 Ca NMR, only the anhydrous α-Ca 2 P 2 O 7 phase has been analyzed to date, 29 showing that the two crystallographically-inequivalent Ca sites can be unambiguously resolved at 14.1 T. Although 43 Ca is a more challenging nucleus than 31 P, 30,31 given its quadrupolar nature, 32 low natural abundance (0.014 %) and small magnetic moment (leading it to be a member of the group of so-called low-γ nuclei), 33 recent studies have shown that it can be very sensitive to subtle changes in Ca local environments. 34,35,36 Finally, even more challenging isotopes like oxygen-17 which usually require isotopic enrichment have been completely neglected so far.
The purpose of this study is to demonstrate, using a combined experimental-computational approach, how solid state NMR can be used for the structural investigation of calcium pyrophosphate phases, whether hydrated or anhydrous, and whether crystalline or amorphous. For this purpose, the 31 P, 43 Ca and 1 H MAS NMR spectra of a series of crystalline CPP phases (m-CPPD, t-CPPD, m-CPPT β and m-CPPM) are first reported, followed by those of amorphous calcium pyrophosphates. Then, we report the results of firstprinciples calculations of the NMR parameters of the crystalline calcium pyrophosphate phases, which were carried out using the Gauge-Including Projector Augmented Wave (GIPAW) approach. 37,38 The comparison between experimental and calculated NMR parameters not only validates the structural models of each compound allowing the assignment of P and Ca sites in crystalline phases, but also helps determine what atomic-scale information can be determined by solid state NMR. Interpretations of the NMR spectra of amorphous calcium pyrophosphate are given, a phase that has recently been proposed as an interesting component of bone cements. 39 2. Materials and methods 6

Syntheses
Crystalline hydrated calcium pyrophosphates m-CPPD, t-CPPD and m-CPPT β were synthesized following the methods previously published by Gras et al., 10 by double decomposition between a potassium pyrophosphate solution and a calcium nitrate solution mixed into a buffer solution at a controlled temperature. The crystalline m-CPPM phase was prepared starting from m-CPPT β crystals and heating them at 110°C for 30 min as previously reported by Gras et al. 12 The amorphous calcium pyrophosphate phases, of general formula Ca 2 P 2 O 7 .xH 2 O (with x ~ 4), 10,13 were prepared using two different synthetic procedures. According to Gras,10 precipitation at a controlled temperature (25°C) and pH (5.8) was used (compound referred to as "sample A" thereafter). According to Slater et al. 13 a precipitation at room temperature without any specific control/monitoring of the pH was also performed (compound referred to as "sample B" thereafter). In the latter case, the amorphous phase was also heat treated to 140 and 220 °C, in view of further solid state NMR characterizations of the transformations under temperature.

General characterization
XRD measurements were performed using a Seifert XRD-3000TT diffractometer with a Cu Kα radiation (Cu Kα 1 λ = 1.54060 Å and Cu Kα 2 λ = 1.54443 Å), and equipped with a graphite monochromator. The XRD patterns were obtained between 2 and 70° (2θ) with a step size of 0.02° and a scan step time of 16 s at 298 K. The corresponding XRD powder patterns can be found in supporting information ( Figure S1). The other characterization performed on the crystalline and amorphous synthesized phases, using notably vibrational spectroscopies, 7 can be found in previous publications. 10 Temperature regulation was used during the experiments, to ensure that the temperature inside the rotor was ~ 10 °C. Prior to all experiments, the magic angle was carefully set in order to obtain the best 31 P MAS resolution, avoiding the reintroduction of any CSA or dipolar interaction which would broaden the spectra.

43 Ca solid state NMR
Natural abundance 43  Details of the recycle delays, number of transients acquired, and total experimental times needed for each sample at both fields can be found in Table S1 (in supplementary information). 20 transients were acquired, with recycle delays ranging from 4 to 16 s (depending on the sample). The 1 H chemical shifts were referenced externally to adamantane, used as a secondary reference (at 1.8 ppm with respect to tetramethylsilane, TMS). Temperature regulation was used during the experiments, to ensure that the temperature inside the rotor was ~ 10° C.

Calculations of NMR parameters
The first principles calculations based on the GIPAW 48 method were performed within Kohn-Sham DFT (Density Functional Theory) using the QUANTUM-ESPRESSO code. 49 The crystalline structure is described as an infinite periodic system using periodic boundary conditions. The NMR calculations were performed as follows: for hydrated phases, proton positions geometry optimization was carried out, starting from the published experimental structures of t-CPPD 50 , m-CPPT β 51 and m-CPPD,7 allowing the positions of protons to relax using the VASP (Vienna Ab Initio Simulation Package) code. 52 In the case of m-CPPM, 12 all atomic positions were relaxed to obtain a better agreement with the experimental data (see later in the text). The 1 H-relaxed structures are named "Rel H" hereafter, and the fully relaxed structure of m-CPPM is referred to as "Rel tot". The α-Ca 2 P 2 O 7 53 structure was calculated without further relaxation. For NMR calculations, the PBE generalized gradient approximation 54 was used and the valence electrons were described by norm conserving pseudopotentials 55 in the Kleinman-Bylander form. 56

10
The wave functions were expanded on a plane wave basis set with a kinetic energy cut-off of 80 Ry. The integral over the first Brillouin zone was performed using a Monkhorst-Pack 2×2×2 k-point grid. The principal components V xx , V yy , and V zz of the electric field gradient (EFG) tensor defined with |V zz | ≥ |V xx | ≥ |V yy | were obtained by diagonalisation of the tensor. The quadrupolar interaction was then characterized by the quadrupolar coupling constant C Q and the asymmetry parameter η Q , which are defined as C Q = eQV zz /h and  33 − δ iso | ≥ |δ 11 − δ iso | ≥ |δ 22 − δ iso |, and δ iso = 1/3(δ 11 + δ 22 + δ 33 ). The CSA parameters are defined by δ CSA = δ 33 − δ iso (anisotropy) and η CSA = |(δ 22 − δ 11 )/δ CSA | (asymmetry). MAS experiments. 26,61 The number of isotropic lines is thus directly related to the number of inequivalent P sites in the asymmetric unit of a given structure. Here, it is explicitly assumed that residual 31 P-31 P homonuclear dipolar couplings can be safely ignored in the simulations as they are much smaller (in Hz) than CSA effects.

Results and discussion
All simulations of the 31 P MAS NMR spectra are presented in Figure S2. As expected from the crystal structures, two distinct 31 P resonances are observed for each compound. For all spectra, the relative intensity of the two resonances differs from the expected 1:1 ratio, because the measurements were performed only for the purpose of determining the 31 P NMR parameters δ iso , δ CSA and η CSA , and thus in conditions which do not necessarily ensure full relaxation of the different 31 P resonances. The observed range for δ iso ( 31 P) is ~ −12 to −5 ppm (average value ~ −7.7 ppm), in agreement with data already published in the literature. 13,28 Concerning δ CSA , the observed range is ~ 59 to 86 ppm, and the average value for all sites is ~ 77 ppm. The average values of δ iso ( 31 P) and δ CSA are fully compatible with the data obtained for a-CPP. In the case of a-CPP (Figure 1), a minor resonance centered at ~ 0 ppm is observed. As suggested by Slater et al., 13 such a contribution can be safely assigned to PO 4 3− or HPO 4 2− moieties, caused by the presence of traces of orthophosphates in the precursors used to prepare CPP phases, and/or resulting from the partial hydrolysis of pyrophosphates under ageing. 10,13 As a matter of fact, the relative intensity of this particular resonance was found to increase with time (see supporting information, Figure S3).
Studying calcium pyrophosphates represents a challenge in terms of first principles calculations of 31 P chemical shifts, as the experimental resonances are closely separated (~ 1 ppm in the case of t-CPPD, see Table 1). The accuracy of the GIPAW method applied to 31 P has been reviewed previously. 63 Generally, the precision of such calculations depends explicitly on the accuracy of the corresponding structural data (obtained mainly by means of X-ray and/or neutron diffraction), 38 which means that the NMR data can act as constraints for the further refinement of a crystallographic structure. In the case of α-Ca 2 P 2 O 7 , t-CPPD and m-CPPT β, good agreement is obtained between the experimental and calculated values both in terms of δ iso ( 31 P) and δ CSA . We notice that the calculated isotropic value for P1 in m-CPPT β is underestimated. Nevertheless, P1 and P2 can unequivocally be assigned.
The case of m-CPPD is an interesting one as it demonstrates the importance of proton relaxation. Indeed, starting from the published structure, 10 the assignment of P1 and P2 is not straightforward, because when assigning the sites based on the relative values of δ iso ( 31 P), there is a contradiction with the relative order of the δ CSA values (and vice versa). In contrast, starting from the m-CPPD relaxed structure (Rel H in Table 1 The spectrum of a-CPP is characterized by a broadening of the unique resonance corresponding to a distribution of δ iso ( 31 P). Such a distribution is related to variations of P-O bond lengths and P-O-P angles, and also to a distribution in the relative proximity of neighbouring Ca 2+ cations and water molecules in these more disordered structures.
Interestingly, the 31 P MAS NMR spectrum is not sensitive to the synthetic protocol used for the preparation of the amorphous phase (see Figure S4). 14

43 Ca MAS NMR
The natural abundance 43 Ca MAS NMR spectra of the crystalline phases were recorded at two different magnetic fields, in order to better constrain the quadrupolar parameters C Q and η Q extracted (Figures 3 and S5). Indeed, for 43 Ca, 1D experiments at a single magnetic field are generally insufficient to extract these parameters. 30 Moreover, given that high magnetic fields, large volume rotors and rather long experimental times (see Table   S1) are usually essential for natural abundance 43  As shown in Figure 3, the 43 Ca isotropic chemical shift is sensitive enough to readily distinguish the various CPP forms both in terms of δ iso ( 43 Ca) and C Q ( 43 Ca). The 43 Ca MAS NMR spectra were fitted using pure second-order quadrupolar lineshapes 62 (see Table 2 and As a first attempt to correlate 43 Ca NMR parameters to the local environment of calcium in these materials, the calculated δ iso ( 43 Ca) was plotted as a function of the average Ca-O bond distance (see Figure 4 and Table S2). δ iso ( 43 Ca) globally decreases as the average Ca-O bond distance increases, in agreement with the different trends reported so far for other inorganic compounds of different oxygen-bonded families. 29,30 Interestingly, by looking more specifically at the different Ca local environments in the structures and analyzing in more detail the nature and number of the oxygen-bonded ligands coordinated to Ca, a better analysis could be proposed. Indeed, depending on the structures, the Ca 2+ can be between 6-and 8-coordinated, and the ligands can be either only O atoms belonging to pyrophosphates, or to water molecules. As shown in Figure 4, the nature of the oxygenated ligand (pyrophosphate or water) does not appear to have a big influence, but when separating the Ca sites according to their coordination number, different zones can be clearly distinguished, depending on whether the Ca is 6-, 7-or 8-coordinated. This shows that the two main parameters which appear to govern the δ iso ( 43 Ca) in the case of calcium pyrophosphates are the average Ca…O bond distance and the coordination number around the Ca. Finally, we note that similar trends were also observed using experimental δ iso ( 43 Ca) values, rather than the calculated ones.
The high sensitivity of δ iso ( 43 Ca) towards its local environment shows that it is a highly relevant tool of investigation of the structure of a-CPP at the atomic scale. In Figure 5, the high field 43  High field 43 Ca NMR was actually found to be a highly relevant tool of analysis of other related a-CPP phases. Indeed, depending on the synthetic protocol (control or not of the pH during the precipitation of a-CPP), 43 Ca MAS NMR spectra presented subtle differences (see Figure S6 for the comparison of samples A and B), showing that the structures of these materials actually slightly differ, despite the similarities in the 31 P MAS NMR data (see Figure S4). Finally, it is worth noting that the effect of heat-treatment of a-CPP could also be followed by 43 Ca MAS NMR ( Figure S7). Indeed, despite rather symmetrical lineshapes at 20.0 T, a broadening of the signal was clearly observed after having heated the a-CPP phase 16 at 220 °C, indicating an increase of the distribution of the 43 Ca NMR parameters, possibly due to the formation of hydrogen-phosphate anions within the material, as previously evidenced by 1 H and 31 P MAS NMR. 13 All in all, 43 Ca NMR appears as a valuable tool for investigation of hydrated calcium pyrophosphates, which would deserve to be looked into more systematically, as it can provide complementary information about their structure at the atomic scale. A comparison with GIPAW calculated 1 H chemical shifts (Table S3) is also presented in Figure 6 for t-CPPD, m-CPPD, m-CPPM and m-CPPT β. As already stated in the 31 P discussion, the scatter of the calculated values is more pronounced in the case of m-CPPD.

1 H MAS NMR
This observation tends to suggest that it should be possible to improve the positioning of the protons in the structure using the 1 H chemical shifts as constraints. shifts observed at room temperature correspond to averages. Freezing local dynamics would lead to determine "static" isotropic chemical shifts which could be compared safely to GIPAW predictions and act therefore as pertinent constraints for structure refinement.

Conclusion
In this contribution, several hydrated calcium pyrophosphate phases (both crystalline and amorphous) were characterized by multinuclear MAS NMR. It was demonstrated that 31 P and 43 Ca MAS NMR spectroscopies are suitable for the clear distinction of the various phases.
Even in the case of amorphous samples, subtle variations of the resonance lines were 18 observed by 43 Ca MAS NMR depending on the synthetic protocol and heat treatment temperature. Moreover, 1 H NMR was found to be informative about differences in the H-bond networks within these phases.
All crystalline structures were then studied in the context of NMR crystallography, using GIPAW as a theoretical bridge between experimental and computed data. All in all, a fairly good agreement was observed for the three studied nuclei, provided that a relaxation of the structures (focusing especially on proton positions) was carried out. Nonetheless, discrepancies remained for the hydrated phases, which may be due to the fact that NMR calculations do not take into account any temperature/local motion effects. Previous studies have indeed shown that these factors could induce significant differences between experimental and computational data. 38 Concerning a-CPP phases, important structural features have been derived from multinuclear solid state NMR analyses. First of all, the 31 P MAS spectra are rather insensitive to the synthetic protocols: it demonstrates that the 31 P NMR parameters are mostly determined by the local geometry of the P 2 O 7 4species (angle, bond lengths) and not by the localization of the calcium cations and the water molecules. This is clearly not the case when considering 43 Ca and 1 H NMR parameters. In particular, 1 H MAS spectra seem suitable to distinguish local environments comparable to those observed in m-CPPT β and m-CPPM crystalline phases, though contents in water molecules are comparable from one sample to another one.
Slater et al. 13 already pointed out structural similarity between m-CPPT β and a-CPP by pair distribution functions (PDF) analysis. This structural similarity was furthermore linked to comparable behavior regarding hydrolysis reactions. Thus it has been observed that m-CPPT β, m-CPPM and a-CPP are hydrolyzed at high temperature but this is not the case for t-CPPD and m-CPPD samples. 10,12 Based on the elemental composition of the amorphous calcium pyrophosphate phases, and on the structural information gathered here by 1 H, 43 Ca and 31 P MAS NMR, realistic structural models for these amorphous phases are currently being developed. Following the pioneering approach initiated by Charpentier 37 and very recent results presented by the same author, 69 the idea is to compare the calculated NMR values for computational models of this material with the experimental ones, in order to propose a realistic model. This study will be presented in a forthcoming publication.
Finally, the contribution of this study in structural refinement of poorly known hydrated CPP phases is a first step towards the understanding of in vivo phenomena related to osteoarthritis: structureinflammatory response relationships, potential precursor phase formation and evolution, role of trace elements in CPP crystal formation occurring in associated diseases like hypomagnesaemia, 70 Wilson's disease (copper excess) 71 and haemochromatosis (iron excess). 72 In addition, some applications of CPP compounds in the biomaterial field can be envisioned. 39

Acknowledgements
The French/UK CNRS PICS project QMAT is acknowledged. D. Laurencin  10.0 kHz (left) and ~ 2.8 to 5.0 kHz (right). For the slow MAS spectra, the exact rotation frequency, ν r , is specified in Figure S2 for each sample. For each spectrum, the arrow indicates the region of the isotropic resonances (two in general, except in the case of a-CPP).
All other lines correspond to spinning sidebands from which CSA parameters can be extracted. In the case of a-CPP, the minor component at δ iso ~ 0 ppm is assigned to orthophosphate species (see main text). MAS rotation frequency: between 4 and 6 kHz. For details on the relaxation delay and number of scans for each sample, see Table S1. The fitting of the different MAS NMR spectra can be found in Figure S5.    Table S1]. MAS rotation frequency: 5 kHz. Comparison between the 43 Ca MAS spectra of samples A and B are presented in Figure S6.  Table S3).  Table 1: Experimental and calculated 31 P chemical shift tensor (CSA) data for m-CPPD, m-CPPM, t-CPPD, m-CPPT β. The definitions of δ CSA and η CSA are given in the experimental section. In the case of m-CPPD, results obtained before and after relaxation of the proton positions ("Rel H") are presented. In order to validate the combined experimental/computational approach, both sets of data were added for α-Ca 2 P 2 O 7 (anhydrous phase). The maximum error on experimental δ iso values was estimated to 0.15 ppm.   43 Ca chemical shift and quadrupolar parameters for α-Ca 2 P 2 O 7 , m-CPPD, t-CPPD, m-CPPT β and m-CPPM. The definitions of C Q and η Q are given in the experimental section. In the case of m-CPPD, results obtained before and after relaxation of the proton positions (Rel H) are presented. The spectra from which the experimental values were determined are shown in Figure S5, together with their simulation.
Errors were estimated to ~2-3 ppm on δ iso and ~ 0.2-0.4 MHz on C Q , except for the m-CPPM phase for which the fitting was performed at only one magnetic field (thus leading to larger errors