Sub-Nanometer-Range Structural Effects From Mg2+ Incorporation in Na-Based Borosilicate Glasses Revealed by Heteronuclear NMR and MD Simulations.

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.

1H and 13C chemical shift-structure effects in anhydrous ß-caffeine and four caffeine-diacid cocrystals probed by solid-state NMR experiments and DFT calculations.

By using density functional theory (DFT) calculations, we refined the H atom positions in the structures of ß-caffeine (C), α-oxalic acid (OA; (COOH)2), α-(COOH)2·2H2O, ß-malonic acid (MA), ß-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 ß-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.

Improved reweighting protocols for variationally enhanced sampling simulations with multiple walkers.

In molecular dynamics simulations utilizing enhanced-sampling techniques, reweighting is a central component for recovering the targeted ensemble averages of the "unbiased" system by calculating and applying a bias-correction function c(t). We present enhanced reweighting protocols for variationally enhanced sampling (VES) simulations by exploiting a recent reweighting method, originally introduced in the metadynamics framework [Giberti et al. J. Chem. Theory Comput., 2020, 16, 100-107], which was modified and extended to multiple-walker simulations: these may be implemented either as "independent" walkers (associated with one unique correction function per walker) or "cooperative" ones that all share one correction function, which is the hitherto only explored option. When each case is combined with the two possibilities of determining c(t) by time integration up to either t or over the entire simulation period , altogether four reweighting options result. Their relative merits were assessed by well-tempered VES simulations of two model problems: locating the free-energy difference between two metastable molecular conformations of the N-acetyl-L-alanine methylamide dipeptide, and the recovery of an a priori known distribution when one water molecule in the liquid phase is perturbed by a periodic free-energy function. The most rapid convergence occurred for large cooperative walkers, regardless of the upper integration limit, but integrating up to t proved advantageous for small walker ensembles. That novel reweighting method compared favorably to the standard VES reweighting, as well as to current state-of-the-art reweighting options introduced for metadynamics simulations that estimate c(t) by integration over the collective variables. For further gains in computational speed and accuracy, we also introduce analytical solutions for c(t), as well as offering further insight into its features by approximative analytical expressions in the "high-temperature" regime.

Nuclear Magnetic Resonance and Metadynamics Simulations Reveal the Atomistic Binding of l-Serine and O-Phospho-l-Serine at Disordered Calcium Phosphate Surfaces of Biocements.

Interactions between biomolecules and structurally disordered calcium phosphate (CaP) surfaces are crucial for the regulation of bone mineralization by noncollagenous proteins, the organization of complexes of casein and amorphous calcium phosphate (ACP) in milk, as well as for structure-function relationships of hybrid organic/inorganic interfaces in biomaterials. By a combination of advanced solid-state NMR experiments and metadynamics simulations, we examine the detailed binding of O-phospho-l-serine (Pser) and l-serine (Ser) with ACP in bone-adhesive CaP cements, whose capacity of gluing fractured bone together stems from the close integration of the organic molecules with ACP over a subnanometer scale. The proximity of each carboxy, aliphatic, and amino group of Pser/Ser to the Ca2+ and phosphate species of ACP observed from the metadynamics-derived models agreed well with results from heteronuclear solid-state NMR experiments that are sensitive to the 13C-31P and 15N-31P distances. The inorganic/organic contacts in Pser-doped cements are also contrasted with experimental and modeled data on the Pser binding at nanocrystalline HA particles grown from a Pser-bearing aqueous solution. The molecular adsorption is driven mainly by electrostatic interactions between the negatively charged carboxy/phosphate groups and Ca2+ cations of ACP, along with H bonds to either protonated or nonprotonated inorganic phosphate groups. The Pser and Ser molecules anchor at their phosphate/amino and carboxy/amino moieties, respectively, leading to an extended molecular conformation across the surface, as opposed to an "upright standing" molecule that would result from the binding of one sole functional group.

Refined Structures of O-Phospho-l-serine and Its Calcium Salt by New Multinuclear Solid-State NMR Crystallography Methods.

O-phospho-l-serine (Pser) and its Ca salt, Ca[O-phospho-l-serine]·H2O (CaPser), play important roles for bone mineralization and were recently also proposed to account for the markedly improved bone-adhesive properties of Pser-doped calcium phosphate-based cements for biomedical implants. However, the hitherto few proposed structural models of Pser and CaPser were obtained by X-ray diffraction, thereby leaving the proton positions poorly defined. Herein, we refine the Pser and CaPser structures by density functional theory (DFT) calculations and contrast them with direct interatomic-distance constraints from two-dimensional (2D) nuclear magnetic resonance (NMR) correlation experimentation at fast magic-angle spinning (MAS), encompassing double-quantum-single-quantum (2Q-1Q) 1H NMR along with heteronuclear 13C{1H} and 31P{1H} correlation NMR experiments. The Pser and CaPser structures before and after refinements by DFT were validated against sets of NMR-derived effective 1H-1H, 1H-31P, and 1H-13C distances, which confirmed the improved accuracy of the refined structures. Each distance set was derived from one sole 2D NMR experiment applied to a powder without isotopic enrichment. The distances were extracted without invoking numerical spin-dynamics simulations or approximate phenomenological models. We highlight the advantages and limitations of the new distance-extraction procedure. Isotropic 1H, 13C, and 31P chemical shifts obtained by DFT calculations using the gauge including projector augmented wave (GIPAW) method agreed very well with the experimental results. We discuss the isotropic and anisotropic 13C and 31P chemical-shift parameters in relation to the previous literature, where most data on CaPser are reported herein for the first time.

Assessment of new symmetry-based dipolar recoupling schemes for homonuclear magnetization exchange between quadrupolar nuclei in two-dimensional correlation MAS NMR.

We provide an extensive experimental and numerical evaluation of MQ-phase (S)M supercycles with M={3,4} of three groups of symmetry-based homonuclear dipolar recoupling rf-pulse sequences, [Formula: see text] , for establishing proximities among half-integer spin quadrupolar nuclei under moderately fast magic-angle-spinning (MAS) conditions in single-quantum-single-quantum (1Q-1Q) correlation NMR experiments. The relative merits of the (S)M schemes for variations in resonance offsets and rf-amplitude errors were assessed by numerically simulated magnetization transfers in spin-3/2 pairs with variable isotropic chemical shifts and quadrupolar coupling constants. Experimental demonstrations of 23Na (spin-3/2) NMR on Na2MoO4·2H2O and 27Al (spin-5/2) NMR on AlPO-CJ19 [(NH4)2Al4(PO4)4HPO4·H2O] are presented at 14.1 T and 24 kHz MAS. We recommend using the (SR221)3 or (SR221)4 supercycles for samples that exhibit small chemical-shift dispersions (<3 kHz), and any (SRNNN/2)3 scheme with N⩾10 for larger spreads of isotropic chemical shifts. However, because the (SRNNN/2)3 sequences recouple heteronuclear dipolar interactions, their application to proton-bearing samples requires high-power proton decoupling during the mixing period. Alternatively, the (SR241)3 and (SR241)4 schemes may be employed in the absence of proton decoupling, but with poorer compensation to resonance-offsets and rf-amplitude errors.

The Monetite Structure Probed by Advanced Solid-State NMR Experimentation at Fast Magic-Angle Spinning.

We present a solid-state nuclear magnetic resonance (NMR) spectroscopy study of the local 31 P and 1 H environments in monetite [CaHPO 4 ; dicalcium phosphate anhydrous (DCPA)], as well as their relative spatial proximities. Each of the three 1 H NMR peaks was unambiguously assigned to its respective crystallographically unique H site of monetite, while their pairwise spatial proximities were probed by homonuclear 1 H- 1 H double quantum-single quantum NMR experimentation under fast magic-angle spinning (MAS) of 66 kHz. We also examined the relative 1 H- 31 P proximities among the inequivalent {P1, P2} and {H1, H2, H3} sites in monetite; the corresponding shortest internuclear 1 H- 31 P distances accorded well with those of a previous neutron diffraction study. The NMR results from the monetite phase were also contrasted with those observed from the monetite component present in a pyrophosphate-bearing calcium phosphate cement, demonstrating that while the latter represents a disordered form of monetite, it shares all essential local features of the monetite structure.

Direct Experimental Evidence for Abundant BO4-BO4 Motifs in Borosilicate Glasses From Double-Quantum 11B NMR Spectroscopy.

By using double-quantum-single-quantum correlation 11B nuclear magnetic resonance (NMR) experiments and atomistic molecular dynamics (MD) simulations, we resolve the long-standing controversy of whether directly interlinked BO4-BO4 groups exist in the technologically ubiquitous class of alkali/alkaline-earth based borosilicate (BS) glasses. Most structural models of Na2O-B2O3-SiO2 glasses assume the absence of B[4]-O-B[4] linkages, whereas they have been suggested to exist in Ca-bearing BS analogs. Our results demonstrate that while B[4]-O-B[4] linkages are disfavored relative to their B[3]-O-B[3]/B[4] counterparts, they are nevertheless abundant motifs in Na2O-B2O3-SiO2 glasses over a large composition space, while the B[4]-O-B[4] contents are indeed elevated in Na2O-CaO-B2O3-SiO2 glasses. We discuss the compositional and structural parameters that control the degree of B[4]-O-B[4] bonding.

Structure-composition trends in multicomponent borosilicate-based glasses deduced from molecular dynamics simulations with improved B-O and P-O force fields.

We present a comprehensive molecular dynamics (MD) simulation study of composition-structure trends in a set of 25 glasses of widely spanning compositions from the following four systems of increasing complexity: Na2O-B2O3, Na2O-B2O3-SiO2, Na2O-CaO-SiO2-P2O5, and Na2O-CaO-B2O3-SiO2-P2O5. The simulations involved new B-O and P-O potential parameters developed within the polarizable shell-model framework, thereby combining the beneficial features of an overall high accuracy and excellent transferability among different glass systems and compositions: this was confirmed by the good accordance with experimental data on the relative BO3/BO4 populations in borate and boro(phospho)silicate networks, as well as with the orthophosphate fractions in bioactive (boro)phosphosilicate glasses, which is believed to strongly influence their bone-bonding properties. The bearing of the simulated melt-cooling rate on the borate/phosphate speciations is discussed. Each local {BO3, BO4, SiO4, PO4} coordination environment remained independent of the precise set of co-existing network formers, while all trends observed in bond-lengths/angles mainly reflected the glass-network polymerization, i.e., the relative amounts of bridging oxygen (BO) and non-bridging oxygen (NBO) species. The structural roles of the Na+/Ca2+ cations were also probed, targeting their local coordination environments and their relative preferences to associate with the various borate, silicate, and phosphate moieties. We evaluate and discuss the common classification of alkali/alkaline-earth metal ions as charge-compensators of either BO4 tetrahedra or NBO anions in borosilicate glasses, also encompassing the less explored NBO-rich regime: the Na+/Ca2+ cations mainly associate with BO/NBO species of SiO4/BO3 groups, with significant relative Na-BO4 contacts only observed in B-rich glass networks devoid of NBO species, whereas NBO-rich glass networks also reveal substantial amounts of NBO-bearing BO4 tetrahedra.

Medium-Range Structural Organization of Phosphorus-Bearing Borosilicate Glasses Revealed by Advanced Solid-State NMR Experiments and MD Simulations: Consequences of B/Si Substitutions.

The short and intermediate range structures of a large series of bioactive borophosphosilicate (BPS) glasses were probed by solid-state nuclear magnetic resonance (NMR) spectroscopy and atomistic molecular dynamics (MD) simulations. Two BPS glass series were designed by gradually substituting SiO2 by B2O3 in the respective phosphosilicate base compositions 24.1Na2O-23.3CaO-48.6SiO2-4.0P2O5 ("S49") and 24.6Na2O-26.7CaO-46.1SiO2-2.6P2O5 ("S46"), the latter constituting the "45S5 Bioglass" utilized for bone grafting applications. The BPS glass networks are built by interconnected SiO4, BO4, and BO3 moieties, whereas P exists mainly as orthophosphate anions, except for a minor network-associated portion involving P-O-Si and P-O-B[4] motifs, whose populations were estimated by heteronuclear 31P{11B} NMR experimentation. The high Na+/Ca2+ contents give fragmented glass networks with large amounts of nonbridging oxygen (NBO) anions. The MD-generated glass models reveal an increasing propensity for NBO accommodation among the network units according to BO4 < SiO4 < BO3 ≪ PO4. The BO4/BO3 intermixing was examined by double-quantum-single-quantum correlation 11B NMR experiments, which evidenced the presence of all three BO3-BO3, BO3-BO4, and BO4-BO4 connectivities, with B[3]-O-B[4] bridges dominating. Notwithstanding that B[4]-O-B[4] linkages are disfavored, both NMR spectroscopy and MD simulations established their presence in these modifier-rich BPS glasses, along with non-negligible B[4]-NBO contacts, at odds with the conventional structural view of borosilicate glasses. We discuss the relative propensities for intermixing of the Si/B/P network formers. Despite the absence of pronounced preferences for Si-O-Si bond formation, the glass models manifest subtle subnanometer-sized structural inhomogeneities, where SiO4 tetrahedra tend to self-associate into small chain/ring motifs embedded in BO3/BO4-dominated domains.

Proton Environments in Biomimetic Calcium Phosphates Formed from Mesoporous Bioactive CaO-SiO2-P2O5 Glasses in Vitro: Insights from Solid-State NMR.

When exposed to body fluids, mesoporous bioactive glasses (MBGs) of the CaO-SiO2-P2O5 system develop a bone-bonding surface layer that initially consists of amorphous calcium phosphate (ACP), which transforms into hydroxy-carbonate apatite (HCA) with a very similar composition as bone/dentin mineral. Information from various 1H-based solid-state nuclear magnetic resonance (NMR) experiments was combined to elucidate the evolution of the proton speciations both at the MBG surface and within each ACP/HCA constituent of the biomimetic phosphate layer formed when each of three MBGs with distinct Ca, Si, and P contents was immersed in a simulated body fluid (SBF) for variable periods between 15 min and 30 days. Directly excited magic-angle-spinning (MAS) 1H NMR spectra mainly reflect the MBG component, whose surface is rich in water and silanol (SiOH) moieties. Double-quantum-single-quantum correlation 1H NMR experimentation at fast MAS revealed their interatomic proximities. The comparatively minor H species of each ACP and HCA component were probed selectively by heteronuclear 1H-31P NMR experimentation. The initially prevailing ACP phase comprises H2O and "nonapatitic" HPO42-/PO43- groups, whereas for prolonged MBG soaking over days, a well-progressed ACP → HCA transformation was evidenced by a dominating O1H resonance from HCA. We show that 1H-detected 1H → 31P cross-polarization NMR is markedly more sensitive than utilizing powder X-ray diffraction or 31P NMR for detecting the onset of HCA formation, notably so for P-bearing (M)BGs. In relation to the long-standing controversy as to whether bone mineral comprises ACP and/or forms via an ACP precursor, we discuss a recently accepted structural core-shell picture of both synthetic and biological HCA, highlighting the close relationship between the disordered surface layer and ACP.

Coarse-Grained Molecular Dynamics Simulations of Membrane-Trehalose Interactions.

It is well established that trehalose (TRH) affects the physical properties of lipid bilayers and stabilizes biological membranes. We present molecular dynamics (MD) computer simulations to investigate the interactions between lipid membranes formed by 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and TRH. Both atomistic and coarse-grained (CG) interaction models were employed, and the coarse graining of DMPC leads to a reduction in the acyl chain length corresponding to a 1,2-dilauroyl-sn-glycero-3-phosphocholine lipid (DLPC). Several modifications of the Martini interaction model, used for CG simulations, were implemented, resulting in different potentials of mean force (PMFs) for DMPC bilayer-TRH interactions. These PMFs were subsequently used in a simple two-site analytical model for the description of sugar binding at the membrane interface. In contrast to that in atomistic MD simulations, the binding in the CG model was not in agreement with the two-site model. Our interpretation is that the interaction balance, involving water, TRH, and lipids, in the CG systems needs further tuning of the force-field parameters. The area per lipid is only weakly affected by TRH concentration, whereas the compressibility modulus related to the fluctuations of the membrane increases with an increase in TRH content. In agreement with experimental findings, the bending modulus is not affected by the inclusion of TRH. The important aspects of lipid bilayer interactions with biomolecules are membrane curvature generation and sensing. In the present investigation, membrane curvature is generated by artificial buckling of the bilayer in one dimension. It turns out that TRH prefers the regions with the highest curvature, which enables the most favorable situation for lipid-sugar interactions.

Molecular dynamics simulations and NMR spectroscopy studies of trehalose-lipid bilayer systems.

The disaccharide trehalose (TRH) strongly affects the physical properties of lipid bilayers. We investigate interactions between lipid membranes formed by 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and TRH using NMR spectroscopy and molecular dynamics (MD) computer simulations. We compare dipolar couplings derived from DMPC/TRH trajectories with those determined (i) experimentally in TRH using conventional high-resolution NMR in a weakly ordered solvent (bicelles), and (ii) by solid-state NMR in multilamellar vesicles (MLV) formed by DMPC. Analysis of the experimental and MD-derived couplings in DMPC indicated that the force field used in the simulations reasonably well describes the experimental results with the exception for the glycerol fragment that exhibits significant deviations. The signs of dipolar couplings, not available from the experiments on highly ordered systems, were determined from the trajectory analysis. The crucial step in the analysis of residual dipolar couplings (RDCs) in TRH determined in a bicelle-environment was access to the conformational distributions derived from the MD trajectory. Furthermore, the conformational behavior of TRH, investigated by J-couplings, in the ordered and isotropic phases is essentially identical, indicating that the general assumptions in the analyses of RDCs are well founded.

Direct ¹7O NMR experimental evidence for Al-NBO bonds in Si-rich and highly polymerized aluminosilicate glasses.

By using solid-state (17)O NMR spectroscopy, we provide the first direct experimental evidence for bonds between Al and non-bridging oxygen (NBO) ions in aluminosilicate glasses based on rare-earth (RE) elements, where RE = {Lu, Sc, Y}. The presence of ∼10% Al-NBO moieties out of all NBO species holds regardless of the precise glass composition, at odds with the conventional structural view that Al-NBO bonds are absent in highly polymerized and Si-rich aluminosilicate glass networks.

Na/Ca Intermixing around Silicate and Phosphate Groups in Bioactive Phosphosilicate Glasses Revealed by Heteronuclear Solid-State NMR and Molecular Dynamics Simulations.

We characterize the intermixing of network-modifying Na(+)/Ca(2+) ions around the silicate (QSi(n)) and phosphate (QP(n)) tetrahedra in a series of 16 Na2O­CaO­SiO2­P2O5 glasses, whose P content and silicate network connectivity were varied independently. The set includes both bioactive and bioinactive compositions and also encompasses two soda-lime-silicate members devoid of P, as well as two CaO­SiO2 glasses and one Na2O­SiO2­P2O5 glass. The various Si/P↔Na/Ca contacts were probed by molecular dynamics (MD) simulations together with heteronuclear magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) experimentation utilizing (23)Na{(31)P} and (23)Na{(29)Si} REDOR, as well as (31)P{ (23)Na} and (29)Si{(23)Na} REAPDOR. We introduce an approach for quantifying the extent of Na(+)/Ca(2+) ordering around a given QP(n) or QSi(n) group, encoded by the preference factor 0⩽ PM ⩽ 1 conveying the relative weights of a random cation intermixing (PM = 0) and complete preference/ordering (PM = 1) for one of the species M, which represents either Na(+) or Ca(2+). The MD-derived preference factors reveal phosphate and silicate species surrounded by Na(+)/Ca(2+) ions intermixed nearly randomly (PM ≲ 0.15), except for the QSi(4) and QSi(1) groups, which manifest more significant cation ordering with preference for Na+ and Ca2+, respectively. The overall weak preferences are essentially independent of the Si and P contents of the glass, whereas PM primarily correlates with the total amount of network modifiers: as the latter is increased, the Na/Ca distribution around the {QP(0), QSi(1), QSi(2)} groups with preference for Ca2(+ )tend to randomize (i.e., PCa decreases), while the PNa-values grow slightly for the {QP(1), QSi(3), QSi(4)} species already preferring coordination of Na. The set of experimental preference factors {PCa} for the orthophosphate (QP(0)) groups extracted from (31)P{(23)Na} REAPDOR NMR-derived M2(P­Na) dipolar second moments agrees well with the MD-generated counterparts. Our results on the Na/Ca intermixing in soda-lime-silicate glasses are discussed in relation to previous reports, highlighting the dependence of the conclusion on the approach to data evaluation.

Two heteronuclear dipolar results at the price of one: quantifying Na/P contacts in phosphosilicate glasses and biomimetic hydroxy-apatite.

The analysis of S{I} recoupling experiments applied to amorphous solids yields a heteronuclear second moment M(2)(S-I) that represents the effective through-space dipolar interaction between the detected S spins and the neighboring I-spin species. We show that both M(2)(S-I) and M(2)(I-S) values are readily accessible from a sole S{I} or I{S} experiment, which may involve either S or I detection, and is naturally selected as the most favorable option under the given experimental conditions. For the common case where I has half-integer spin, an I{S} REDOR implementation is preferred to the S{I} REAPDOR counterpart. We verify the procedure by (23)Na{(31)P} REDOR and (31)P{(23)Na} REAPDOR NMR applied to Na(2)O-CaO-SiO(2)-P(2)O(5) glasses and biomimetic hydroxyapatite, where the M(2)(P-Na) values directly determined by REAPDOR agree very well with those derived from the corresponding M(2)(Na-P) results measured by REDOR. Moreover, we show that dipolar second moments are readily extracted from the REAPDOR NMR protocol by a straightforward numerical fitting of the initial dephasing data, in direct analogy with the well-established procedure to determine M(2)(S-I) values from REDOR NMR experiments applied to amorphous materials; this avoids the problems with time-consuming numerically exact simulations whose accuracy is limited for describing the dynamics of a priori unknown multi-spin systems in disordered structures.

Computer-intensive simulation of solid-state NMR experiments using SIMPSON.

Conducting large-scale solid-state NMR simulations requires fast computer software potentially in combination with efficient computational resources to complete within a reasonable time frame. Such simulations may involve large spin systems, multiple-parameter fitting of experimental spectra, or multiple-pulse experiment design using parameter scan, non-linear optimization, or optimal control procedures. To efficiently accommodate such simulations, we here present an improved version of the widely distributed open-source SIMPSON NMR simulation software package adapted to contemporary high performance hardware setups. The software is optimized for fast performance on standard stand-alone computers, multi-core processors, and large clusters of identical nodes. We describe the novel features for fast computation including internal matrix manipulations, propagator setups and acquisition strategies. For efficient calculation of powder averages, we implemented interpolation method of Alderman, Solum, and Grant, as well as recently introduced fast Wigner transform interpolation technique. The potential of the optimal control toolbox is greatly enhanced by higher precision gradients in combination with the efficient optimization algorithm known as limited memory Broyden-Fletcher-Goldfarb-Shanno. In addition, advanced parallelization can be used in all types of calculations, providing significant time reductions. SIMPSON is thus reflecting current knowledge in the field of numerical simulations of solid-state NMR experiments. The efficiency and novel features are demonstrated on the representative simulations.

Assessing the phosphate distribution in bioactive phosphosilicate glasses by 31P solid-state NMR and molecular dynamics simulations.

Melt-derived bioactive phosphosilicate glasses are widely utilized as bone-grafting materials for various surgical applications. However, the insight into their structural features over a medium-range scale up to ∼ 1 nm remains limited. We present a comprehensive assessment of the spatial distribution of phosphate groups across the structures of 11 Na2O-CaO-SiO2-P2O5 glasses that encompass both bioactive and nonbioactive compositions, with the P contents and silicate network connectivities varied independently. Both parameters are known to strongly influence the bioactivity of the glass in vitro. The phosphate distribution was investigated by double-quantum (31)P nuclear magnetic resonance (NMR) experiments under magic-angle spinning (MAS) conditions and by molecular dynamics (MD) simulations. The details of the phosphate-ion dispersion were probed by evaluating the MD-derived glass models against various scenarios of randomly distributed, as well as clustered, phosphate groups. From comparisons of the P-P interatomic-distance spreads and the statistics of small phosphate clusters assessed for variable cutoff radii, we conclude that the spatial arrangement of the P atoms in phosphosilicate glasses is well-approximated by a statistical distribution, particularly across a short-range scale of ≤ 450 pm. The primary distinction is reflected in slightly closer P-P interatomic contacts in the MD-derived structures over the distance span of 450-600 pm relative to that of randomly distributed phosphate groups. The nature of the phosphate-ion dispersion remains independent of the silicate network polymerization and nearly independent of the P content of the glass throughout our explored parameter space of 1-6 mol % P2O5 and silicate network connectivities up to 2.9.

Toward a rational design of bioactive glasses with optimal structural features: composition-structure correlations unveiled by solid-state NMR and MD simulations.

The physiological responses of silicate-based bioactive glasses (BGs) are known to depend critically on both the P content (n(P)) of the glass and its silicate network connectivity (N(BO)(Si)). However, while the bioactivity generally displays a nonmonotonic dependence on nP itself, recent work suggest that it is merely the net orthophosphate content that directly links to the bioactivity. We exploit molecular dynamics (MD) simulations combined with ³¹P and ²9Si solid-state nuclear magnetic resonance (NMR) spectroscopy to explore the quantitative relationships between N(BO)(Si), n(P), and the silicate and phosphate speciations in a series of Na2O-CaO-SiO2-P2O5 glasses spanning 2.1 ≤ N(BO)(Si) ≤ 2.9 and variable P2O5 contents up to 6.0 mol %. The fractional population of the orthophosphate groups remains independent of n(P) at a fixed N(BO)(Si)-value, but is reduced slightly as N(BO)(Si) increases. Nevertheless, P remains predominantly as readily released orthophosphate ions, whose content may be altered essentially independently of the network connectivity, thereby offering a route to optimize the glass bioactivity. We discuss the observed composition-structure links in relation to known composition-bioactivity correlations, and define how Na2O-CaO-SiO2-P2O5 compositions exhibiting an optimal bioactivity can be designed by simultaneously altering three key parameters: the silicate network connectivity, the (ortho)phosphate content, and the n(Na)/n(Ca) molar ratio.

New interatomic potential parameters for molecular dynamics simulations of rare-earth (RE = La, Y, Lu, Sc) aluminosilicate glass structures: exploration of RE3+ field-strength effects.

Sets of self-consistent oxygen-rare earth (RE = La, Y, Lu, Sc) interatomic potential parameters are derived using a force-matching procedure and utilized in molecular dynamics (MD) simulations for exploring the structures of RE2O3-Al2O3-SiO2 glasses that feature a fixed molar ratio n(Al)/n(Si) = 1 but variable RE contents. The structures of RE aluminosilicate (AS) glasses depend markedly on the RE(3+) cation field strength (CFS) over both short and intermediate length-scales. We explore these dependencies for glasses incorporating the cations La(3+), Y(3+), Lu(3+) and Sc(3+), whose CFSs increase due to the concomitant shrinkage of the ionic radii: R(La) > R(Y) > R(Lu) > R(Sc). This trend is mirrored in decreasing average RE(3+) coordination numbers (Z(RE)) from Z(La) = 6.4 to Z(Sc) = 5.4 in the MD-derived data. However, overall the effects from RE(3+) CFS elevations on the local glass structures are most pronounced in the O and {Al([4]), Al([5]), Al([6])} speciations. The former display minor but growing populations of O([0]) ("free oxygen ion") and O([3]) ("oxygen tricluster") moieties. The abundance of AlO5 polyhedra increases significantly from ≈10% in La-based glasses to ≈30% in their Sc counterparts at the expense of the overall dominating AlO4 tetrahedra, whereas the amounts of AlO6 groups remain <5% throughout. We also discuss the Si([4])/Al([p]) (p = 4, 5, 6) intermixing and the nature of their oxygen bridges, where the degree of edge-sharing increases together with the RE(3+) CFS.