The crystal structures of monoclinic paracetamol, its cocrystal with oxalic acid (ParaOA), and its HCl monohydrate salt (ParaHCl) were refined by density functional theory (DFT) calculations and contrasted with the initial X-ray diffraction (XRD) structures. Two independent, but largely consistent, assessments were made: (i) comparisons between 1H and 13C chemical shifts obtained from magic-angle spinning (MAS) nuclear magnetic resonance (NMR) experiments and those predicted by plane-wave DFT calculations before and after geometry optimization; (ii) direct 1H–1H distance evaluations by a recently introduced NMR crystallography method that offers straightforward structure assessments due to interatomic-distance constraints from one double-quantum–single-quantum (2Q–1Q) 1H NMR correlation experiment. For both the 1H/13C chemical shift and 1H–1H distance assessments, the geometry-optimized ParaHCl structure offered a markedly better match than the initial XRD structure, while the XRD structure of paracetamol revealed excellent agreement with the NMR data, with only marginal improvements offered by the DFT optimization. The XRD-derived structure of ParaOA also agreed well with the NMR chemical shift/distance constraints: While the computed 13C chemical shifts showed better agreement with those from MAS NMR, slightly larger discrepancies were observed for the 1H chemical shifts and the 1H–1H distances. We also discuss the chemical shifts and present the first 1H and 13C MAS NMR-peak assignments for the ParaHCl and ParaOA structures.

We demonstrate that the entire set of bridging oxygen (BO; O^[2] coordinations), non-bridging O (NBO; O^[1]), and O tricluster (O^[3]) populations may be deduced for an aluminosilicate (AS) glass by knowledge of its composition and the {AlO₄, AlO₅, AlO₆} populations that are readily extracted from routine ²⁷Al magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) experiments. The protocol exploits a recently deduced empirical expression for estimating the hitherto experimentally inaccessible fractional O^[3] population, which is employed to solve for the O^[1] and O^[2] populations. The method typically reproduced previously published NBO fractions derived by ¹⁷O MAS NMR experiments within ±0.02, which is almost within experimental uncertainties. The primary utility of the method, however, is for the vast majority of AS glasses for which expensive ¹⁷O enrichment is not available, and notably so for glass systems where the ¹⁷O MAS NMR spectrum manifest significant overlap between the resonances from the BO and NBO sites, such as AS glasses comprising Li⁺, Na⁺, and Mg²⁺. Predicted O^[𝑞] speciations of Mg²⁺-bearing glasses are presented and discussed. The NBO predictions of the new protocol compares markedly more favorably to experimental data than alternative options. The close structural relationship between the O^[3] and high-coordination Al^[5] and Al^[6] species are discussed. The new expressions also shed further light onto previously proposed and heavily debated (non)correlations between the populations of NBO, O triclusters, and AlO₅ groups in tecto-aluminosilicate glasses which are formally free of NBO species.

The degree of disorder across the subnanometer scale of an oxide glass is largely governed by the relative propensities of its network formers (F) and modifiers (M) to coordinate the bridging oxygen (BO) and non-bridging oxygen (NBO) species, as well as the (non)preferential interlinking of the various network-forming polyhedra. This paper and its sequel examine the bonding-preference concept, which quantifies the degree of preference or reluctance of two atom species to interlink. Unified and consistent definitions of bonding preferences are presented along with critical reviews of previous reports in the field, which remain sparse due to the substantial experimental challenges to quantify bonding preference in glasses and rendering computational modeling the main tool. Because the preference/reluctance for bond formation marks the deviation from a statistical atom/ion intermixing, a rigorous formulation of the latter is required. Potential pitfalls for defining the statistical reference case are discussed. With particular focus on glasses with F={Al, B, Si} as network formers, this article targets the (relative) F–BO/NBO and M–BO/NBO bonding preferences pertaining to the first coordination shells of the {F, M, O} species in the glass, while the preferential F–O–F' interlinking and M^z+–FO_p associations are examined in the sequel article.

Our previous paper (Edén and Stevensson, J. Non-cryst. Solids 673 (2026) 123865) discussed the bonding preferences of the first-coordination spheres of the bridging oxygen (BO) and non-bridging oxygen (NBO) species with the network formers (F) and modifiers (M) in oxide glasses. This paper moves the spotlight onto the F and M second coordination spheres, encompassing the preferential intermixing of the FO_p network polyhedra along with the relative propensities of distinct network-modifier species (e.g., Na⁺ and Ca^2＋) to charge-balance the various anionic moieties of the glass network. The importance of accounting for the relative F–NBO and F'–NBO bonding affinities is frequently overlooked when assessing the preferred and disfavored F–O–F' linkages in aluminosilicate and/or borosilicate (BS) glass networks. This aspect is illustrated in the context of B^[p]–O–B^[q] linkage preferences in BS glasses, as well as for assessing the relative preferences for forming B^[4]–O–Si and B^[4]–O–B^[3] bridges, whose quantifications are revised and improved relative to an earlier study. Particular attention is given to the Al^[4]–O–Al^[4] and B^[4]–O–B^[4] linkages that have traditionally been postulated to be largely absent but have nonetheless been shown to exist to variable amounts in many Al and/or B bearing oxide glasses. We also review the results of a recent nuclear magnetic resonance (NMR) approach employed for estimating the relative preferences of B^[3]–O–Si and B^[4]–O–Si linkage formation in BS glasses, as well as the relative propensities of Na⁺ and Ca^2＋ cations to associate with the silicate and phosphate groups in phosphosilicate glasses.

Physical-property alterations were probed in three series of aluminosilicate (AS) glasses with 𝑥MgO–(25 − 𝑥)Na₂O–(20 + 𝑦)Al₂O₃–(55 − 𝑦)SiO₂ stoichiometries (in mol%), where 0 ⩽ 𝑥 ⩽ 25 and 𝑦 = {0, 5, 10}. The members of each glass branch feature progressively increasing MgO-for-Na₂O substitutions but share a fixed Al₂O₃ content of 20, 25, or 30 mol% along with a constant net amount of 25 mol% of networkmodifier oxides. We established composition–structure–property relationships for several measured physical properties, encompassing the nanohardness (𝐻), reduced elastic modulus (𝐸_r), crack resistance (CR), glass transition temperature (𝑇_g), and the density-related molar volume (𝑉_m) and glass compactness (𝐶; atom-packing efficiency). All mechanical properties increase for an increasing number density of O  and/or the ²⁷Al NMR-derived average coordination number of Al , where formation of high Al-coordination AlO₅ and AlO₆ polyhedra boost that accompanies the replacements of Na₂O by MgO. Both the hardness and reduced elastic modulus increase linearly with each of and . A key finding is that the observed mechanical-property enhancements for increasing MgO-for-Na₂O substitution do not stem directly from the Mg²⁺ cations per se, but rather from the concurrently increased number of strong bonds forming between O and Al of the network-forming AlO₅ and AlO₆ polyhedra, along with the increased O number density accompanying each 2Na⁺ → 1Mg²⁺ replacement. We also discuss property–composition trends in other AS glass systems subject to systematic oxide substitutions, encompassing Al₂O₃-for-SiO₂ replacements.

Oxygen sites coordinating three network-forming cations in aluminosilicate (AS) glasses—i.e., O^[3] coordination species referred to as “oxygen triclusters”—was proposed 60 years ago and has since then been heavily debated because irrefutable experimental proof for their existence is still lacking. We introduce a protocol for predicting the O^[3] population from the average coordination number of Al () and the fraction of non-bridging O (NBO) species, which are available from routine ²⁷Al and ¹⁷O NMR experiments, respectively. Although O^[3] species were proposed for balancing the negatively charged [AlO_4/2]^- groups that typically dominate the Al speciation in AS glasses, recent computational modeling reveals a stronger propensity for the higher-coordination Al^[5] (AlO₅) and Al^[6] (AlO₆) species to coordinate O triclusters for charge-compensation. We discuss the structural roles of the O^[3] and Al^[5]/Al^[6] entities, all of which remain unclear despite extensive previous research. For a large set of AS glasses involving various  M⁺, M²⁺, and M³⁺ cations, the fractional O^[3] population () increases concurrently with the net number of Al^[5] and Al^[6] sites in the glass, but decreases for increasing M^z+ cation potential. Both O^[3] and Al^[5]/Al^[6] species have been suggested to enhance the glass hardness and crack resistance. For AS glasses involving various trivalent rare-earth cations, the microhardness correlated better with the average coordination number of Al () than with , as did the crack resistance of a limited set of Ca AS glasses. Nevertheless, contributions from O^[3] sites cannot be excluded for the latter glasses and further studies are needed for firm conclusions.

By using density functional theory (DFT) calculations, we refined the H atom positions in the structures of β-caffeine (C), α-oxalic acid (OA; (COOH)₂), α-(COOH)₂·2H₂O, β-malonic acid (MA), β-glutaric acid (GA), and I-maleic acid (ME), along with their corresponding cocrystals of 2 : 1 (2C–OA, 2C–MA) or 1 : 1 (C–GA, C–ME) stoichiometry. The corresponding ¹³C/¹H chemical shifts obtained by gauge including projector augmented wave (GIPAW) calculations agreed overall very well with results from magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy experiments. Chemical-shift/structure trends of the precursors and cocrystals were examined, where good linear correlations resulted for all COO¹H sites against the H⋯O and/or H⋯N H-bond distance, whereas a general correlation was neither found for the aliphatic/caffeine-stemming ¹H sites nor any ¹³C chemical shift against either the intermolecular hydrogen- or tetrel-bond distance, except for the ¹³COOH sites of the 2C–OA, 2C–MA, and C–GA cocrystals, which are involved in a strong COOH⋯N bond with caffeine that is responsible for the main supramolecular stabilization of the cocrystal. We provide the first complete ¹³C NMR spectral assignment of the structurally disordered anhydrous β-caffeine polymorph. The results are discussed in relation to previous literature on the disordered α-caffeine polymorph and the ordered hydrated counterpart, along with recommendations for NMR experimentation that will secure sufficient ¹³C signal-resolution for reliable resonance/site assignments.

We discuss the prospects for accurate ¹¹B magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) spectral deconvolutions for reaching beyond the readily extracted borate speciations offered by the integrated resonances of the coexisting B^[3] and B^[4] species of the respective BO₃ and BO₄ network groups in borosilicate (BS) glasses. We critically review hitherto proposed ¹¹B^[3] and ¹¹B^[4] NMR-peak assignments relating to their neighboring Si, B^[3] and B^[4] species, as quantified by MAS NMR spectral deconvolution. Guidance to these resonance assignments was offered from double-quantum–single-quantum (2Q–1Q) ¹¹B MAS NMR experiments that inform about the B^[p]–O–B^[q] network linkages. The NMR spectral deconvolutions from two BS glass series with low nonbridging oxygen (NBO) contents and fixed molar ratios n_Si/n_B = {1.0, 2.0} but variable network-modifying cations of alkali metals and Mg²⁺ revealed a dominance of B^[4]–O–Si linkages, yet with a significant dependence on the BO₃ population of the glass, which was rationalized by the different propensities for B^[4]–O–{Si, B^[3], B^[4]} linkage formation. For BS glasses with comparable B and Si contents, we recommend three-peak deconvolutions of the ¹¹B^[4] spectral region, whose ¹¹B^[4](mSi) sites differ in their (average) numbers of m B^[4]–O–Si and 4 – m B^[4]–O–B^[p] bonds, where B^[p] may assume B^[3] or B^[4]. We also discuss the structural origin of the two rather arbitrarily classified “ring” and “non-ring” B^[3] entities, where 2Q–1Q ¹¹B NMR suggests the former to primarily constitute BO₃ groups that coexist with BO₄ moieties in (superstructural) ring units largely devoid of bonds to Si, whereas the “non-ring” B^[3] sites involve linkages to all of B^[3], B^[4], and Si, with B^[3]–O–Si linkages prevailing. The limitations of ¹¹B NMR spectral deconvolutions are discussed, including the remaining challenges in analyzing NBO-rich BS glasses.

Magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) experiments and molecular dynamics (MD) simulations were employed to investigate Na2O-B2O3-SiO2 and MgO-Na2O-B2O3-SiO2 glass structures up to ≈0.3 nm. This encompassed the {Na[p]}, {Mg[p]}, and {B[3], B[4]} speciations and the {Si, B[p], M[p]}-BO and {Si, B[p], M[p]}-NBO interatomic distances to the bridging oxygen (BO) and nonbridging oxygen (NBO) species, where the superscript indicates the coordination number. The MD simulations revealed the dominance of Mg[5] coordinations, as mirrored in average Mg2+ coordination numbers in the 5.2-5.5 range, which are slightly lower than those of the larger Na+ cation but with a narrower coordination distribution stemming from the higher cation field strength (CFS) of the smaller divalent Mg2+ ion. We particularly aimed to elucidate such Na+/Mg2+ CFS effects, which primarily govern the short-range structure but also the borosilicate (BS) glass network order, where both MD simulations and heteronuclear double-resonance 11B/29Si NMR experiments revealed a reduction of B[4]-O-Si linkages relative to B[3]-O-Si upon Mg2+-for-Na+ substitution. These effects were quantified and discussed in relation to previous literature on BS glasses, encompassing the implications for simplified structural models and descriptions thereof.

We examine the borate group intermixing in a series of 25 borosilicate (BS) glasses from the [0.5M₍₂₎O–0.5Na₂O]–B₂O₃–SiO₂ systems with M = {Li, K, Rb, Mg, Ca} along with ternary K₂O–B₂O₃–SiO₂ and Na₂O–B₂O₃–SiO₂ glasses by double-quantum–single-quantum (2Q–1Q) ¹¹B correlation nuclear magnetic resonance (NMR) experiments. The alterations of the fractional populations of B^[3]–O–B^[3], B^[3]–O–B^[4], and B^[4]–O–B^[4] linkages in the glass networks were monitored for variable n_Si/n_B molar ratios, nonbridging O contents of the glass, and the (average) cation field strength (CFS) of the M^z+/Na⁺ network modifiers. A significant B^[4]–O–B^[4] bonding is observed in all glasses, thereby conclusively demonstrating that the normally assumed “BO₄–BO₄ avoidance” is far from strict in BS glasses, regardless of the M^z+ field strength. We show that the degree of B^[4]–O–B^[4] bonding depends foremost on its underlying BO₄ population and to a lesser degree on the NBO content of the glass; we also provide a straightforward prediction of the B^[4]–O–B^[4] population in an arbitrary BS glass from parameters readily obtained by routine ¹¹B NMR. The propensity for forming B^[4]–O–B^[4] linkages increases concurrently with either the CFS or the amount of glass network modifiers, roughly scaling as the square root of the “effective CFS” that encompasses both parameters. Although BO₃–BO₃ and BO₃–BO₄ pairs remain favored throughout all examined BS glass networks, the borate group intermixing randomizes significantly for increasing effective CFS, out of which the amount and charge of the glass-network modifier cations dominate over their size. Our results are discussed in relation to the two prevailing but formally mutually exclusive “random network” and “superstructural unit” models of borate and BS glasses.