Computational and Experimental 1H-NMR Study of Hydrated Mg-Based Minerals

Magnesium oxide (MgO) can convert to different magnesium-containing compounds depending on exposure and environmental conditions. Many MgO-based phases contain hydrated species allowing 1H-nuclear magnetic resonance (NMR) spectroscopy to be used in the characterization and quantification of proton-containing phases; however, surprisingly limited examples have been reported. Here, 1H-magic angle spinning (MAS) NMR spectra of select Mg-based minerals are presented and assigned. These experimental results are combined with computational NMR density functional theory (DFT) periodic calculations to calibrate the predicted chemical shielding results. This correlation is then used to predict the NMR shielding for a series of different MgO hydroxide, magnesium chloride hydrate, magnesium perchlorate, and magnesium cement compounds to aid in the future assignment of 1H-NMR spectra for complex Mg phases.


Introduction
Magnesium oxide (MgO) is used in many engineering applications because of its unique material properties. For example, its high thermal conductivity contributes to its use as a stable refractory material [1], and its structure makes it an ideal basic oxide model [2,3]. MgO has also been used for construction [4,5], optics [6,7], medicine [8,9], fertilizers [10], electronics [11,12], catalysis [13], chemical warfare agent decontamination [14], high temperature super conductors [15], hydrogen storage [16,17], and nuclear waste storage [18,19]. For many of these applications, the performance of MgO depends on property reproducibility that may be impacted by impurities or defects formed from the conversion of MgO to other magnesium-containing phases due to environmental exposure. In many cases, the resulting MgO conversion phases are disordered or amorphous in nature, making their characterization by scattering techniques challenging. For example, our interest is the identification of protonated impurities in MgO [20]: a material that is currently used as an engineered barrier for carbon remediation at the DOE Waste Isolation Pilot Plant (WIPP) located near Carlsbad, New Mexico.
Nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for characterizing disordered solids where diffraction methods may fail. Despite its usefulness, only a few publications have reported solid state 1 H-NMR spectra for MgO-based compounds [3,[20][21][22][23][24][25][26]. Previous studies noted that the 1 H chemical shifts in basic environments are shifted to lower frequencies (~0 ppm), while acidic environments exhibit higher frequency chemical shifts (~4.5 ppm) [27]. In a previous study, at least six different proton environments were observed (but not fully assigned) in nominally pure MgO between 1.2 and −1.8 ppm [3]. Extensive NMR characterization (including 1 H-NMR) of hydrous ringwoodite (γ-Mg 2 SiO 4 ) [28], hydroxyl-clinohumite (4Mg 2 SiO 4 ·Mg(OH) 2 ) [29], and hydrous wadsleyite (β-Mg 2 SiO 4 ) have also been published [30][31][32]. Most computational NMR efforts on MgO-related phases have focused on 25 Mg and 17 O, but for low concentration impurity or defect phases these nuclei can be difficult to address experimentally. There has been at least one thorough computational effort using density functional theory (DFT) to model OH groups on irregularities in MgO surface states [2]. In this work, we report the 1 H magic angle spinning (MAS) NMR spectra for a set of MgO-based minerals, which are reaction products of MgO with different environmental constituents. Using computational NMR methods, the correlation between the predicted NMR chemical shielding and the experimental NMR chemical shift is developed to allow 1 H-NMR chemical shift referencing in Mg oxide compounds. These computational NMR methods are then extended to develop a starting database of 1 H-NMR chemical shifts of proton-containing Mg phases not readily isolated or available.

Results and Discussion
MgO can convert to a variety of different compounds, including naturally occurring minerals, by incorporating new coordinating species during environmental exposure. These include hydroxylated, hydrated, nitrated, and sulfonated magnesium phases derived from either MgO or MgCO 3 through simple conversion reactions (Scheme 1). These new Mg-containing species may act as impurities or defects within the original bulk materials, which could ultimately impact the targeted material performance.
Molecules 2020, 24, x 2 of 15 hydrous ringwoodite (γ-Mg2SiO4) [28], hydroxyl-clinohumite (4Mg2SiO4·Mg(OH)2) [29], and hydrous wadsleyite (β-Mg2SiO4) have also been published [30][31][32]. Most computational NMR efforts on MgOrelated phases have focused on 25 Mg and 17 O, but for low concentration impurity or defect phases these nuclei can be difficult to address experimentally. There has been at least one thorough computational effort using density functional theory (DFT) to model OH groups on irregularities in MgO surface states [2]. In this work, we report the 1 H magic angle spinning (MAS) NMR spectra for a set of MgO-based minerals, which are reaction products of MgO with different environmental constituents. Using computational NMR methods, the correlation between the predicted NMR chemical shielding and the experimental NMR chemical shift is developed to allow 1 H-NMR chemical shift referencing in Mg oxide compounds. These computational NMR methods are then extended to develop a starting database of 1 H-NMR chemical shifts of proton-containing Mg phases not readily isolated or available.

Results and Discussion
MgO can convert to a variety of different compounds, including naturally occurring minerals, by incorporating new coordinating species during environmental exposure. These include hydroxylated, hydrated, nitrated, and sulfonated magnesium phases derived from either MgO or MgCO3 through simple conversion reactions (Scheme 1). These new Mg-containing species may act as impurities or defects within the original bulk materials, which could ultimately impact the targeted material performance.

Model Hydroxylated and Hydrated Magnesium Compounds
The 1 H-MAS-NMR spectra for a series of different Mg minerals is shown in Figure 1 with the experimental chemical shifts summarized in Table 1. Brucite, Mg(OH)2, is formed from the absorption of water by MgO and is a common hydrogen-containing phase observed in environmentally exposed materials [20]. The 1 H NMR spectrum of Mg(OH)2 is shown in Figure 1a. The dominant resonance at δ = +0.05 ppm (93%) is assigned to the hydroxyl proton in Mg(OH)2, while the minor resonance at δ = +4.9 ppm (7%) is attributed to a water containing phase in this material. In cement applications, Mg(OH)2 may cause structural expansions inducing stress, cracking, and failure in concrete and is therefore important to identify [5]. Nitromagnesite, MgNO3·6H2O, is a highly water-soluble magnesium salt and can be formed by mixing magnesium sulfate with calcium nitrate, or by simply exposing MgO, Mg(OH)2, or magnesium carbonate (MgCO3) to nitric acid [33]. The 1 H-MAS-NMR spectrum of nitromagnesite is shown in Figure 1b, with the major resonance at δ = +4.0 ppm assigned to the bound water protons, while the small sharp resonance at δ = +4.5 ppm results from mobile surface adsorbed water in this sample. Heating nitromagnesite leads to decomposition of the salt rather than dehydrating it, producing undesirable NO3. Bischofite, MgCl2·6H2O, can be formed by the neutralization of dilute HCl by MgO. The 1 H-NMR spectrum of bischofite is shown in Figure 1c

Model Hydroxylated and Hydrated Magnesium Compounds
The 1 H-MAS-NMR spectra for a series of different Mg minerals is shown in Figure 1 with the experimental chemical shifts summarized in Table 1. Brucite, Mg(OH) 2 , is formed from the absorption of water by MgO and is a common hydrogen-containing phase observed in environmentally exposed materials [20]. The 1 H NMR spectrum of Mg(OH) 2 is shown in Figure 1a. The dominant resonance at δ = +0.05 ppm (93%) is assigned to the hydroxyl proton in Mg(OH) 2 , while the minor resonance at δ = +4.9 ppm (7%) is attributed to a water containing phase in this material. In cement applications, Mg(OH) 2 may cause structural expansions inducing stress, cracking, and failure in concrete and is therefore important to identify [5]. Nitromagnesite, MgNO 3 ·6H 2 O, is a highly water-soluble magnesium salt and can be formed by mixing magnesium sulfate with calcium nitrate, or by simply exposing MgO, Mg(OH) 2 , or magnesium carbonate (MgCO 3 ) to nitric acid [33]. The 1 H-MAS-NMR spectrum of nitromagnesite is shown in Figure 1b, with the major resonance at δ = +4.0 ppm assigned to the bound water protons, while the small sharp resonance at δ = +4.5 ppm results from mobile surface adsorbed water in this sample. Heating nitromagnesite leads to decomposition of the salt rather than dehydrating it, producing undesirable NO 3 . Bischofite, MgCl 2 ·6H 2 O, can be formed by the neutralization of dilute HCl by MgO. The 1 H-NMR spectrum of bischofite is shown in Figure 1c with the bound water protons observed at δ = +4.3 ppm. The formation of bischofite phases may impact the refractory application of MgO, since MgCl 2 has a melting point (987 K) almost three times lower than MgO [33]. Epsomite, MgSO 4 ·7H 2 O, can be formed by the reaction of MgO with dilute sulfuric acid to produce MgSO 4 , which is stable in the heptahydrate form up to 48 • C in air and high relative humidity (RH). Above this temperature (or in low RH), dehydration occurs to form the hexahydrate, until finally heating between 200-300 • C produces an anhydrous phase [33]. The loss of water during dehydration changes the crystal structure (i.e., the heptahydrate's orthorhombic structure evolves to a monoclinic structure in the hexahydrate). The 1 H-NMR spectrum of epsomite is shown in Figure 1d, with the bound water proton environment assigned to the δ = +5.0 ppm resonance. A mobile surface adsorbed water environment is observed at δ = +4.4 ppm. Magnesium bromide, MgBr 2 ·6H 2 O, is produced by reacting MgCO 3 with HBr and can form both anhydrous and hexahydrate forms [33]. The 1 H-NMR spectrum of the hexahydrate phase is shown in Figure 1d, with the water proton resonance at δ = +4.1 ppm. Magnesium carbonate can exist in many forms, including multiple minerals. The most common is the anhydrous salt magnesite MgCO 3 . The 1 H-NMR spectra of several common hydrated magnesium carbonate salts are shown, including hydromagnesite (4MgCO 3 ·Mg(OH) 2 ·4H 2 O, Figure 1f, artinite (MgCO 3 ·Mg(OH) 2 ·3H 2 O, Figure 1g, and dypingite (4MgCO 3 ·Mg(OH) 2 ·5H 2 O, Figure 1h. These NMR spectra show a hydroxyl proton environment at δ~−1.3 ppm along with multiple water proton species between +5.0 and +7.0 ppm. The multiple overlapping water proton environments are further characterized using two-dimensional (2D) double quantum (DQ)-single quantum (SQ) NMR correlation experiments discussed in a later section. The hydroxyl resonance was asymmetric such that two different hydroxyl environments were included to improve the deconvolution of this spectral region. There is no clear resolution of the different hydroxyl environment, though the 2D DQ-SQ NMR correlation experiments also supports the argument of overlapping hydroxyl species. For artinite (MgCO 3 ·Mg(OH) 2 ·3H 2 O, an additional hydroxyl environment at δ = −0.1 ppm was also observed and is clearly identified in the 2D DQ-SQ correlation experiments (see below). Two different commercial sources of dypingite were analyzed and produced equivalent NMR spectra (Supplementary Materials, Figure S1, electronic supplementary information ESI). An acidic proton at δ = 16.9 ppm was seen for hydromagnesite and dypingite (<1%). Minor unidentified impurity phases between δ = +0.7 and +1.1 ppm were also present [30]. While the NMR spectra for these three carbonates phases are similar, the ratio of the hydroxyl and hydrating water proton concentration might also be used to support the proposed structure. Artinite (MgCO 3 ·Mg(OH) 2 ·3H 2 O) has the largest [OH]/[H 2 O] ratio of 2/6 (25%/75%) and compares to the 22%/73% ratio observed experimentally ( Figure    Deconvolution of the 1 H-magic angle spinning (MAS) nuclear magnetic resonance (NMR) spectra for (a) brucite, Mg(OH) 2  The experimental NMR results for all the compounds listed in Table 1 represent only two major types of proton environments (hydroxyl and coordinating water) with subtle differences in the coordination environments giving rise to small changes in the 1 H-NMR chemical shifts. The very small variations further support the argument that computational NMR efforts are needed to help characterize proton containing magnesium phases (Section 2.2).

Two-Dimensional Double Quantum NMR
To further characterize the multiple proton environments in the carbonate series 4MgCO 3 ·Mg(OH) 2 ·4H 2 O, MgCO 3 ·Mg(OH) 2 ·3H 2 O, and 4MgCO 3 ·Mg(OH) 2 ·5H 2 O, 2D DQ-SQ NMR correlation spectra were obtained. As an example, Figure 2a is the 2D DQ-SQ NMR spectrum for hydromagnesite (4MgCO 3 ·Mg(OH) 2 ·4H 2 O), while Figure 2b in the DQ-SQ spectrum for artinitie (MgCO 3 ·Mg(OH) 2 ·3H 2 O). The 2D DQ-SQ NMR correlation spectrum for dypingite (4MgCO 3 ·Mg(OH) 2 ·5H 2 O) was very similar to the hydromagnesite spectrum ( Figure 2a) and is provided in Figure S2 for comparison (ESI). In these 2D-NMR correlation experiments, cross peaks are observed at spectral frequencies for protons that are spatially near each other with significant 1 H-1 H dipolar coupling to produce the DQ coherence. Cross peaks on the diagonal (filled circles) are auto-correlation resonances and arise from dipolar coupling (spatially near each other) between equivalent 1 H environments. Off diagonal cross peaks (solid lines) result from dipolar coupling between two different 1 H environments. The 2D DQ-SQ NMR correlation spectra show multiple cross peaks and allow for improved spectral separation between the different 1 H environments. To further characterize the multiple proton environments in the carbonate series 4MgCO3·Mg(OH)2·4H2O, MgCO3·Mg(OH)2·3H2O, and 4MgCO3·Mg(OH)2·5H2O, 2D DQ-SQ NMR correlation spectra were obtained. As an example, Figure 2a is the 2D DQ-SQ NMR spectrum for hydromagnesite (4MgCO3·Mg(OH)2·4H2O), while Figure 2b in the DQ-SQ spectrum for artinitie (MgCO3·Mg(OH)2·3H2O). The 2D DQ-SQ NMR correlation spectrum for dypingite (4MgCO3·Mg(OH)2·5H2O) was very similar to the hydromagnesite spectrum ( Figure 2a) and is provided in Figure S2 for comparison (ESI). In these 2D-NMR correlation experiments, cross peaks are observed at spectral frequencies for protons that are spatially near each other with significant 1 H-1 H dipolar coupling to produce the DQ coherence. Cross peaks on the diagonal (filled circles) are auto-correlation resonances and arise from dipolar coupling (spatially near each other) between equivalent 1 H environments. Off diagonal cross peaks (solid lines) result from dipolar coupling between two different 1 H environments. The 2D DQ-SQ NMR correlation spectra show multiple cross peaks and allow for improved spectral separation between the different 1 H environments. For hydromagnesite (Figure 2a), two water resonances are more clearly observed at δ = +5.5 ppm and + 7.0 ppm, with both water environments having auto-correlation peaks (solid blue and orange circles). This means that the water protons are spatially close to other water protons in equivalent environments (as expected). There is also some off-diagonal intensity between these two water resonances, suggesting that the water environments are spatially near each other but are not in rapid exchange on the NMR time scale (chemical shift difference). The water and hydroxyl protons (δ = −1.2 ppm) also reveal a strong off-diagonal correlation peak (solid blue and orange lines), confirming that the water and hydroxyl proton environments are spatially near each other (i.e., dipolar coupled). Note that the hydroxyl cross peak reveals slightly different hydroxyl chemical shifts (minor slope in DQ dimension) but is not resolved in the 2D projections or the one dimensional (1D) 1 H-MAS-NMR spectra (Figure 1f). The hydroxyl protons (δ ~ −1.3 ppm) also show a weak auto-correlation peak (solid red circle) but can be seen in the DQ projection, demonstrating that these hydroxyl protons have limited spatial interactions with equivalent hydroxyl proton environments. Finally, the small sharp resonance at δ ~ +1 ppm shows a vanishing weak auto-correlation peak (yellow solid circle) but reveals no other cross peaks. This means that this proton environment is spatially near similar protons but is spatially isolated from all the other protons in these materials. A minor isolated For hydromagnesite (Figure 2a), two water resonances are more clearly observed at δ = +5.5 ppm and + 7.0 ppm, with both water environments having auto-correlation peaks (solid blue and orange circles). This means that the water protons are spatially close to other water protons in equivalent environments (as expected). There is also some off-diagonal intensity between these two water resonances, suggesting that the water environments are spatially near each other but are not in rapid exchange on the NMR time scale (chemical shift difference). The water and hydroxyl protons (δ = −1.2 ppm) also reveal a strong off-diagonal correlation peak (solid blue and orange lines), confirming that the water and hydroxyl proton environments are spatially near each other (i.e., dipolar coupled). Note that the hydroxyl cross peak reveals slightly different hydroxyl chemical shifts (minor slope in DQ dimension) but is not resolved in the 2D projections or the one dimensional (1D) 1 H-MAS-NMR spectra (Figure 1f). The hydroxyl protons (δ~−1.3 ppm) also show a weak auto-correlation peak (solid red circle) but can be seen in the DQ projection, demonstrating that these hydroxyl protons have limited spatial interactions with equivalent hydroxyl proton environments. Finally, the small sharp resonance at δ~+1 ppm shows a vanishing weak auto-correlation peak (yellow solid circle) but reveals no other cross peaks. This means that this proton environment is spatially near similar protons but is spatially isolated from all the other protons in these materials. A minor isolated unidentified phase has been observed in previous studies on Mg silicates [30,32], while a δ = +1.1 ppm resonance has been reported for hydrous Chondrodite, Mg 5 Si 2 O 8 (OH) 2 [25], as well as Talc, Mg 3 Si 4 O 10 (OH) 2 [26]. The existence of this auto-correlation peak in the 2D DQ-SQ NMR correlation spectrum also argues that this proton is not simply probe background but is indeed a unique proton containing phase. Similarly, for artinite (Figure 2b), two water environments are observed at δ = 7.1 and δ = + 5.2 ppm with strong auto-correlation peaks (solid blue and orange circles). The off-diagonal cross peaks between the water and hydroxyl protons (δ = −1.4 ppm) are also observed (solid blue and orange lines), confirming these proton environments are spatially near each other. Unique to artinite is the presence of a strong auto-correlation peak neat δ~0.0 ppm (green circle) arising from isolated hydroxyl protons. The hydroxyl protons are only spatially near equivalent hydroxyl protons (giving rise to an auto-correlation peak) but show no dipolar coupling to water proton environments. This contrasts with the hydromagnesite (Figure 2a) and dypingite ( Figure S2) spectra, where the hydroxyl environments are isolated from each other and are instead dipolar coupled to nearby water protons. These 2D 1 H-DQ-SQ-NMR correlation experiments reveal how it is possible to improve resolution between different proton species as well as probe the spatial arrangement of the different proton environments.

Chemical Shift Referencing
To compare NMR results, both the experimental and calculated chemical shifts (δ) are defined with respect to the isotropic trace of the chemical shielding tensor σ iso .
where σ re f is the chemical shielding tensor for a reference compound. It has been established that the DFT gauge-including projector augmented wave (GIPAW) method (used here) has a linear relationship between the variation in the experimental (δ exp ) and calculated chemical shifts δ calc [36], and that σ exp re f and σ calc re f are not necessarily equivalent. This linear variation is given by This leads to the correlation relationships between the calculated and experimental values for systems where a structure is available  Table 1 (bold) and are plotted in Figure 4. Table S1 provides the complete list of predicted 1 H-NMR chemical shieldings and shifts for the reference compounds. The δ exp range from −3.2 ppm (NaOH) to +5.0 ppm (MgSO 4 ·7H 2 O), while the σ calc iso range from +34.5 to +22.9 ppm. Using Equation (3), α = 0.701, σ exp re f = 21.52 ppm, and σ calc re f = 30.7 ppm. This compares well with the σ calc re f of + 31.0 ppm reported based on referencing to the single Mg(OH) 2 chemical shift [31], and to the +29.76 ppm and +29.59 ppm recently reported for semi-and fully-hydrated wadsleyite [32]. In the future, this chemical shielding correlation could be improved by including experimental NMR for additional compounds with an isolated hydroxyl proton environment (δ < 0 ppm).  [31], and to the +29.76 ppm and +29.59 ppm recently reported for semi-and fully-hydrated wadsleyite [32]. In the future, this chemical shielding correlation could be improved by including experimental NMR for additional compounds with an isolated hydroxyl proton environment (δ < 0 ppm).  Additionally, the selected reference compounds include hydrogen bond lengths from 1.62Å (nitromagnesite and bischofite) to 2.53Å (brucite). The relationship between hydrogen bond length (OH . . . O) and δ has been previously noted by Pourpoint et al. [37] and Xue and Kanzaki [38], with increasing hydrogen bond lengths resulting in a decrease in the calculated δ value. Our results indicate the same trend ( Figure 5) and compounds with isolated hydroxyls exhibit lower δ values than those that contain molecular water. Because the referenced compounds include such a large range of hydrogen bonding lengths, the fitting discussed above can be applied to a variety of materials with proton containing phases. Additionally, the selected reference compounds include hydrogen bond lengths from 1.62Å (nitromagnesite and bischofite) to 2.53Å (brucite). The relationship between hydrogen bond length (OH … O) and δ has been previously noted by Pourpoint et al. [37] and Xue and Kanzaki [38], with increasing hydrogen bond lengths resulting in a decrease in the calculated δ value. Our results indicate the same trend ( Figure 5) and compounds with isolated hydroxyls exhibit lower δ values than those that contain molecular water. Because the referenced compounds include such a large range of hydrogen bonding lengths, the fitting discussed above can be applied to a variety of materials with proton containing phases.

Predicted Chemical Shifts for Hydrogen Containing MgO Phases
In addition to the MgO minerals used for the development of the chemical shift/shielding correlation above (Figure 4) Table 2. These compounds have all been suggested as conversion species of MgO and therefore could be probed by 1 H-MAS-NMR. Unfortunately, samples of these phases were not readily available, precluding experimental

Predicted Chemical Shifts for Hydrogen Containing MgO Phases
In addition to the MgO minerals used for the development of the chemical shift/shielding correlation above (Figure 4) Table 2. These compounds have all been suggested as conversion species of MgO and therefore could be probed by 1 H-MAS-NMR. Unfortunately, samples of these phases were not readily available, precluding experimental measurements of their chemical shifts. As expected, 1 H chemical shifts of the Mg hydroxides are predicted to fall into a very narrow range between δ = 0.0 and +0.8 ppm, while the MgCl 2 hydrate water protons have chemical shifts that are predominantly in the δ = +4.0 to +5.0 range. The 1 H environments in the Mg perchlorates are predicted to have unique chemical shifts in the δ~+3 ppm range. The Mg-cements and layered NaOH compounds are predicted to have very complex and rich chemical shift signatures ranging from δ = −2.3 to 11.6 ppm. The small 1 H chemical shifts ranges will make it difficult to uniquely identify a given phase based simply on 1D 1 H-NMR spectra, but 2D NMR correlation experiments will improve the resolution while also providing the means to identify the multiple 1 H environments arising from a single compound. These results also allow one to quantify the different general proton environments (i.e., hydroxyl, hydrating water, acidic, etc.) that exist in a material. It is hoped that future research into different MgO phases may benefit from these calculated 1 H-NMR shieldings and shifts for spectral assignment.

Materials
Mg-based compounds were used as-received except where otherwise stated with the purity provided by the vendor. Reagent grade brucite Mg(OH) 2

Experimental NMR
The solid state 1 H-magic angle spinning (MAS) NMR experiments were performed on a Bruker Avance III spectrometer (Bruker, Billerica, MA, USA) at a proton observation frequency of 600.1 MHz, using a 2.5 mm broadband MAS probe spinning at 30 kHz. Spectra were obtained using a rotor-synchronized Hahn Echo pulse sequence with a 4 s recycle delay and a π/2 pulse length of 2.5 µs. To assure quantitative spectra, the recycle delay was chosen to allow for complete spin lattice (T 1 ) relaxation. To correct for the impact of spin-spin relaxation (T 2 ) on the Hahn Echo spectra, the signal intensity for the zero-time echo delay (τ = 0) was obtained from the S(τ) versus τ correlations, as shown in Figure S3. For the samples reported here, the impact of differential T 2 relaxation was most notable when comparing multiple water and hydroxyl environments, such as observed in the Mg carbonate series of materials. Due to frictional heating, the sample temperature was nominally 325 K. The 2D DQ-SQ 1 H-MAS-NMR correlation spectra were obtained at a 25 kHz spinning speed using an offset compensated back-to-back (BaBa) multiple pulse sequence for excitation and reconversion of the multiple quantum coherences [39], using a single rotor-period rotor period excitation (τ DQ = 40 µs, N c = 1), with phase-sensitive detection in the F1 dimension via the States time-proportional phase incrementation method. 1 H-NMR chemical shifts were referenced to the secondary standard adamantane (δ = +0.8 ppm) with respect to TMS (δ = 0 ppm). The DMFIT software was used for all NMR spectral deconvolutions [40].

Computational NMR
Crystal structures were imported from the Crystallography Open Database (COD) [41], and structural relaxation was performed using periodic density functional theory (DFT) calculations with the Quantum Espresso [42] open source electronic structure code. Norm-conserving pseudopotentials [43] with the generalized gradient approximation in the form of Perdew, Burke, and Ernzerhof (PBE) [44] were implemented. An energy cut-off of 90 Ry and a 6x6x6 k-point matrix were used with high levels of convergence (total energy convergence threshold = 4 × 10 −8 , force convergence threshold = 2 × 10 −5 , self-consistent energy threshold = 1 × 10 −10 ). Dispersion corrections were not included in the simulations. Tests indicated that the computational 1 H-NMR isotropic chemical shifts were not impacted by the dispersion correction, changing between 0.1 to 0.5 ppm for the crystal structures studied here when it was included. For the initial identification of low-energy structures, the lattice parameters were changed iteratively to identify the lowest energy structure, which was then used as the starting point for a variable cell relaxation. Computational NMR chemical shifts were calculated using the gauge-including projector augmented wave (GIPAW) method [45], which has been proven successful at investigating 1 H-NMR chemical shifts in proton containing MgO phases [2,23,46]. Refer to [47,48] for a more thorough description of the GIPAW method and its application to different oxide and ceramic systems. Absolute shielding tensors for the computational crystalline systems were calculated from fully converged all-electron calculations.

Conclusions
The 1 H-MAS-NMR spectra of crystalline Mg-based phases was combined with periodic DFT NMR calculations to produce a correlation between the computed chemical shielding tensor and the experimental chemical shift to be used for referencing hydroxylated and hydrated Mg materials. This correlation was used to predict 1 H-NMR chemical shifts for multiple Mg-and Na-based proton containing phases that have been proposed in literature, as a demonstration that computational NMR methods provide a powerful tool for the assignment of solid state 1 H-NMR spectra. The small 1 H chemical shifts range for these materials and significant spectral overlap hampers the identification of unique species in complex phases, but the development of very high-speed MAS-NMR and improved homonuclear decoupling techniques will continue to improve spectral resolution. In addition, the introduction of 2D heteronuclear NMR correlation experiments ( 1 H-17 O, 1 H-23 Na etc.) would also prove beneficial in separating different proton species in complex proton containing Mg phases and is being pursued.
Supplementary Materials: The following are available online, Figure S1: 1 H-MAS-NMR spectra of dypingite from two different commercial sources, Figure S2: 2D DQ-SQ 1 H-MAS-NMR correlation experiments for dypingite, Figure S3: The variation of water and hydroxyl intensity for the Mg carbonate series of minerals, Table S1: Computational 1 H-NMR chemical shieldings (σ) and chemical shifts (δ) for 7 proton containing reference structures along with the atomic coordinates for reference minerals: brucite, nitromagnesite, epsomite, bischofite, wadsleyite, OH-chondrodite, and sodium hydroxide.