Cervical Spine Manipulation and Causation of Cervical Artery Dissection: A Review of 10 Case Reports.

Recent media coverage of high-profile cases of cervical artery dissection (CAD) has ignited the discussion about the role of cervical spine manipulation (CSM) in causing cervical artery dissection. However, research does not support a causal association between cervical spine manipulation and cervical artery dissection in a healthy cervical spine. The objective of this study was to review the 10 most recent case reports of cervical spine manipulation and cervical artery dissection for convincing evidence of the causation of cervical artery dissection by cervical spine manipulation. Nine of 10 case reports showed no convincing evidence of a causal relationship between cervical spine manipulation and cervical artery dissection. The 10th case report was exceptional as the CSM was contraindicated by pre-existing cervical spine pathology. We conclude that these 10 case reports provide no convincing evidence of the causation of cervical artery dissection by cervical spine manipulation in a healthy cervical spine. One case report demonstrated that cervical spine manipulation can cause cervical artery dissection when performed in the presence of pre-existing cervical spine pathology. Therefore, we conclude that practitioners should exclude cervical spine pathology before performing cervical spine manipulation.

Diagnosis of Cervical Spinal Cord Multiple Sclerosis by a Chiropractic Physician: A Case Report.

We present a case report of diagnosis of cervical spine multiple sclerosis by a chiropractic physician. This unique case contributes an account of a challenging differential diagnosis to the literature. A 30-year-old male presented with a three-year history of diffuse left upper extremity motor strength deficits and paresthesia (numbness and tingling). The patient had seen multiple physicians for these symptoms with no diagnosis of multiple sclerosis and no advanced imaging. The differential diagnosis included lower cervical spine nerve root compression or neurological disorders such as amyotrophic lateral sclerosis, cerebral lesion, motor neuropathy, multiple sclerosis, or spinal cord lesion. MRI of the cervical spine with and without IV contrast revealed evidence of spinal cord multiple sclerosis. The patient was referred to a neurologist where the diagnosis of multiple sclerosis was confirmed. A 10-year follow-up showed the patient was controlling his condition with medications and had no disability. This case underscores the importance for physicians to consider neurological conditions and advanced imaging in the presence of diffuse motor strength deficits and paresthesia in the absence of injury, pain, or any other symptoms.

Polymorph Identification for Flexible Molecules: Linear Regression Analysis of Experimental and Calculated Solution- and Solid-State NMR Data.

The Δδ regression approach of Blade et al. [ J. Phys. Chem. A 2020, 124(43), 8959-8977] for accurately discriminating between solid forms using a combination of experimental solution- and solid-state NMR data with density functional theory (DFT) calculation is here extended to molecules with multiple conformational degrees of freedom, using furosemide polymorphs as an exemplar. As before, the differences in measured 1H and 13C chemical shifts between solution-state NMR and solid-state magic-angle spinning (MAS) NMR (Δδexperimental) are compared to those determined by gauge-including projector augmented wave (GIPAW) calculations (Δδcalculated) by regression analysis and a t-test, allowing the correct furosemide polymorph to be precisely identified. Monte Carlo random sampling is used to calculate solution-state NMR chemical shifts, reducing computation times by avoiding the need to systematically sample the multidimensional conformational landscape that furosemide occupies in solution. The solvent conditions should be chosen to match the molecule's charge state between the solution and solid states. The Δδ regression approach indicates whether or not correlations between Δδexperimental and Δδcalculated are statistically significant; the approach is differently sensitive to the popular root mean squared error (RMSE) method, being shown to exhibit a much greater dynamic range. An alternative method for estimating solution-state NMR chemical shifts by approximating the measured solution-state dynamic 3D behavior with an ensemble of 54 furosemide crystal structures (polymorphs and cocrystals) from the Cambridge Structural Database (CSD) was also successful in this case, suggesting new avenues for this method that may overcome its current dependency on the prior determination of solution dynamic 3D structures.

Plausible Mechanisms of Causation of Immediate Stroke by Cervical Spine Manipulation: A Narrative Review.

It has been proposed that cervical spine manipulation (CSM) can cause dissection in healthy cervical arteries, with resultant immediate stroke. However, research does not support a causal association between CSM and cervical artery dissection (CAD) in healthy cervical arteries. The objective of this study was to review the literature to identify plausible mechanisms of causation of immediate stroke by CSM. Immediate stroke is defined as a stroke occurring within seconds or minutes of CSM. Our review found plausible thromboembolic and thrombotic mechanisms of causation of immediate stroke by CSM in the literature. The common premise of these mechanisms is CAD being present before CSM, not occurring as a result of CSM. These mechanisms of causation have clinical and medicolegal implications for physicians performing CSM.

Impacted and Angulated Right Hip Fracture in a Patient Reporting No History of Trauma Presenting to a Chiropractic Physician: A Case Report.

A case involving a patient with an impacted and angulated femoral neck fracture presenting to a chiropractic physician is rare. This unique case contributes an account of a challenging differential diagnosis to the literature. A 65-year-old female, reporting no history of trauma, presented with a two-week history of right lower back and right anterior hip pain radiating down the front of the right thigh in the L2-L4 dermatome. The differential diagnosis included lumbar spine disc herniation and nerve root compression or a right hip abnormality. An MRI of the lumbar spine revealed L3-L4 and L4-L5 posterior disc bulges and right foraminal narrowing. She was subsequently referred to pain management and diagnosed with lumbar radiculopathy and neural foraminal stenosis. After three lumbar spine epidural injections and a period of conservative care, the patient's symptoms were 90% improved but not fully resolved. Subsequently, right hip X-rays were ordered. The x-rays revealed an impacted and angulated right femoral neck base fracture. At this time, the patient recalled a possible traumatic incident. The patient was immediately referred to an orthopedic surgeon. After a month's delay waiting for further advanced imaging, a total right hip replacement was performed. This case underscores the importance for physicians to recognize that patients may not be aware of their own history of trauma. It also highlights the need for physicians to consider the possibility of multiple concurrent pathologies and to order imaging for all areas of pain.

Nuclear spin diffusion under fast magic-angle spinning in solid-state NMR.

Solid-state nuclear spin diffusion is the coherent and reversible process through which spin order is transferred via dipolar couplings. With the recent increases in magic-angle spinning (MAS) frequencies and magnetic fields becoming routinely applied in solid-state nuclear magnetic resonance, understanding how the increased 1H resolution obtained affects spin diffusion is necessary for interpretation of several common experiments. To investigate the coherent contributions to spin diffusion with fast MAS, we have developed a low-order correlation in Liouville space model based on the work of Dumez et al. (J. Chem. Phys. 33, 224501, 2010). Specifically, we introduce a new method for basis set selection, which accounts for the resonance-offset dependence at fast MAS. Furthermore, we consider the necessity of including chemical shift, both isotropic and anisotropic, in the modeling of spin diffusion. Using this model, we explore how different experimental factors change the nature of spin diffusion. Then, we show case studies to exemplify the issues that arise in using spin diffusion techniques at fast spinning. We show that the efficiency of polarization transfer via spin diffusion occurring within a deuterated and 100% back-exchanged protein sample at 60 kHz MAS is almost entirely dependent on resonance offset. We additionally identify temperature-dependent magnetization transfer in beta-aspartyl L-alanine, which could be explained by the influence of an incoherent relaxation-based nuclear Overhauser effect.

Comparison of methods for 14N-1H recoupling in 14N-1H HMQC MAS NMR.

1H-detected 14N heteronuclear multiple-quantum coherence (HMQC) magic-angle-spinning (MAS) NMR experiments performed at fast magic-angle spinning (≥50 kHz) are finding increasing application, e.g., to pharmaceuticals. Of importance to the efficacy of these techniques is the recoupling technique applied to reintroduce the 1H-14N dipolar coupling. In this paper, we compare, by experiment and 2-spin density matrix simulations, two classes of recoupling scheme: first, those based on n = 2 rotary resonance, namely R3 and spin-polarisation inversion SPI-R3, and the symmetry based SR412 method and, second, the TRAPDOR method. Both classes require optimisation depending on the magnitude of the quadrupolar interaction, and thus there is a compromise choice for samples with more than one nitrogen site, as is the case for the studied dipeptide ß-AspAla that contains two nitrogen sites with a small and large quadrupolar coupling constant. Considering this, we observe better sensitivity for the TRAPDOR method, though noting the marked sensitivity of TRAPDOR to the 14N transmitter offset, with both SPI-R3 and SR412 giving similar recoupling performance.

Discovering the Solid-State Secrets of Lorlatinib by NMR Crystallography: To Hydrogen Bond or not to Hydrogen Bond.

Lorlatinib is an active pharmaceutical ingredient (API) used in the treatment of lung cancer. Here, an NMR crystallography analysis is presented whereby the single-crystal X-ray diffraction structure (CSD: 2205098) determination is complemented by multinuclear (1H, 13C, 14/15N, 19F) magic-angle spinning (MAS) solid-state NMR and gauge-including projector augmented wave (GIPAW) calculation of NMR chemical shifts. Lorlatinib crystallises in the P21 space group, with two distinct molecules in the asymmetric unit cell, Z' = 2. Three of the four NH2 hydrogen atoms form intermolecular hydrogen bonds, N30-H…N15 between the two distinct molecules and N30-H…O2 between two equivalent molecules. This is reflected in one of the NH21H chemical shifts being significantly lower, 4.0 ppm compared to 7.0 ppm. Two-dimensional 1H-13C, 14N-1H and 1H (double-quantum, DQ)-1H (single-quantum, SQ) MAS NMR spectra are presented. The 1H resonances are assigned and specific HH proximities corresponding to the observed DQ peaks are identified. The resolution enhancement at a 1H Larmor frequency of 1 GHz as compared to 500 or 600 MHz is demonstrated.

Elucidation of microbial lignin degradation pathways using synthetic isotope-labelled lignin.

Pathways by which the biopolymer lignin is broken down by soil microbes could be used to engineer new biocatalytic routes from lignin to renewable chemicals, but are currently not fully understood. In order to probe these pathways, we have prepared synthetic lignins containing 13C at the sidechain ß-carbon. Feeding of [ß-13C]-labelled DHP lignin to Rhodococcus jostii RHA1 has led to the incorporation of 13C label into metabolites oxalic acid, 4-hydroxyphenylacetic acid, and 4-hydroxy-3-methoxyphenylacetic acid, confirming that they are derived from lignin breakdown. We have identified a glycolate oxidase enzyme in Rhodococcus jostii RHA1 which is able to oxidise glycolaldehyde via glycolic acid to oxalic acid, thereby identifying a pathway for the formation of oxalic acid. R. jostii glycolate oxidase also catalyses the conversion of 4-hydroxyphenylacetic acid to 4-hydroxybenzoylformic acid, identifying another possible pathway to 4-hydroxybenzoylformic acid. Formation of labelled oxalic acid was also observed from [ß-13C]-polyferulic acid, which provides experimental evidence in favour of a radical mechanism for α,ß-bond cleavage of ß-aryl ether units.

Exploring the Potential of Multinuclear Solid-State 1 H, 13 C, and 35 Cl Magnetic Resonance To Characterize Static and Dynamic Disorder in Pharmaceutical Hydrochlorides.

Crystallographic disorder, whether static or dynamic, can be detrimental to the physical and chemical stability, ease of crystallization and dissolution rate of an active pharmaceutical ingredient. Disorder can result in a loss of manufacturing control leading to batch-to-batch variability and can lengthen the process of structural characterization. The range of NMR active nuclei makes solid-state NMR a unique technique for gaining nucleus-specific information about crystallographic disorder. Here, we explore the use of high-field 35 Cl solid-state NMR at 23.5 T to characterize both static and dynamic crystallographic disorder: specifically, dynamic disorder occurring in duloxetine hydrochloride (1), static disorder in promethazine hydrochloride (2), and trifluoperazine dihydrochloride (3). In all structures, the presence of crystallographic disorder was confirmed by 13 C cross-polarization magic-angle spinning (CPMAS) NMR and supported by GIPAW-DFT calculations, and in the case of 3, 1 H solid-state NMR provided additional confirmation. Applying 35 Cl solid-state NMR to these compounds, we show that higher magnetic fields are beneficial for resolving the crystallographic disorder in 1 and 3, while broad spectral features were observed in 2 even at higher fields. Combining the data obtained from 1 H, 13 C, and 35 Cl NMR, we show that 3 exhibits a unique case of disorder involving the + N-H hydrogen positions of the piperazinium ring, driving the chloride anions to occupy three distinct sites.

Correction: Optimisation of 1H PMLG homonuclear decoupling at 60 kHz MAS to enable 15N-1H through-bond heteronuclear correlation solid-state NMR spectroscopy.

Correction for 'Optimisation of 1H PMLG homonuclear decoupling at 60 kHz MAS to enable 15N-1H through-bond heteronuclear correlation solid-state NMR spectroscopy' by Jacqueline Tognetti et al., Phys. Chem. Chem. Phys., 2022, 24, 20258-20273, https://doi.org/10.1039/D2CP01041K.

Optimisation of 1H PMLG homonuclear decoupling at 60 kHz MAS to enable 15N-1H through-bond heteronuclear correlation solid-state NMR spectroscopy.

The Lee-Goldburg condition for homonuclear decoupling in 1H magic-angle spinning (MAS) solid-state NMR sets the angle θ, corresponding to arctan of the ratio of the rf nutation frequency, ν1, to the rf offset, to be the magic angle, θm, equal to tan-1(√2) = 54.7°. At 60 kHz MAS, we report enhanced decoupling compared to MAS alone in a 1H spectrum of 15N-glycine with at θ = 30° for a ν1 of ∼100 kHz at a 1H Larmor frequency, ν0, of 500 MHz and 1 GHz, corresponding to a high chemical shift scaling factor (λCS) of 0.82. At 1 GHz, we also demonstrate enhanced decoupling compared to 60 kHz MAS alone for a lower ν1 of 51 kHz, i.e., a case where the nutation frequency is less than the MAS frequency, with θ = 18°, λCS = 0.92. The ratio of the rotor period to the decoupling cycle time, Ψ = τr/τc, is in the range 0.53 to 0.61. Windowed decoupling using the optimised parameters for a ν1 of ∼100 kHz also gives good performance in a 1H spin-echo experiment, enabling implementation in a 1H-detected 15N-1H cross polarisation (CP)-refocused INEPT heteronuclear correlation NMR experiment. Specifically, initial 15N transverse magnetisation as generated by 1H-15N CP is transferred back to 1H using a refocused INEPT pulse sequence employing windowed 1H decoupling. Such an approach ensures the observation of through-bond N-H connectivities. For 15N-glycine, while the CP-refocused INEPT experiment has a lower sensitivity (∼50%) as compared to a double CP experiment (with a 200 µs 15N to 1H CP contact time), there is selectivity for the directly bonded NH3+ moiety, while intensity is observed for the CH21H resonances in the double CP experiment. Two-dimensional 15N-1H correlation MAS NMR spectra are presented for the dipeptide ß-AspAla and the pharmaceutical cimetidine at 60 kHz MAS, both at natural isotopic abundance. For the dipeptide ß-AspAla, different build-up dependence on the first spin-echo duration is observed for the NH and NH3+ moieties demonstrating that the experiment could be used to distinguish resonances for different NHx groups.

Eudicot primary cell wall glucomannan is related in synthesis, structure, and function to xyloglucan.

Hemicellulose polysaccharides influence assembly and properties of the plant primary cell wall (PCW), perhaps by interacting with cellulose to affect the deposition and bundling of cellulose fibrils. However, the functional differences between plant cell wall hemicelluloses such as glucomannan, xylan, and xyloglucan (XyG) remain unclear. As the most abundant hemicellulose, XyG is considered important in eudicot PCWs, but plants devoid of XyG show relatively mild phenotypes. We report here that a patterned ß-galactoglucomannan (ß-GGM) is widespread in eudicot PCWs and shows remarkable similarities to XyG. The sugar linkages forming the backbone and side chains of ß-GGM are analogous to those that make up XyG, and moreover, these linkages are formed by glycosyltransferases from the same CAZy families. Solid-state nuclear magnetic resonance indicated that ß-GGM shows low mobility in the cell wall, consistent with interaction with cellulose. Although Arabidopsis ß-GGM synthesis mutants show no obvious growth defects, genetic crosses between ß-GGM and XyG mutants produce exacerbated phenotypes compared with XyG mutants. These findings demonstrate a related role of these two similar but distinct classes of hemicelluloses in PCWs. This work opens avenues to study the roles of ß-GGM and XyG in PCWs.

Combining X-ray and NMR Crystallography to Explore the Crystallographic Disorder in Salbutamol Oxalate.

Salbutamol is an active pharmaceutical ingredient commonly used to treat respiratory distress and is listed by the World Health Organization as an essential medicine. Here, we establish the crystal structure of its oxalate form, salbutamol oxalate, and explore the nature of its crystallographic disorder by combined X-ray crystallography and 13C cross-polarization (CP) magic-angle spinning (MAS) solid-state NMR. The *C-OH chiral center of salbutamol (note that the crystal structures are a racemic mixture of the two enantiomers of salbutamol) is disordered over two positions, and the tert-butyl group is rotating rapidly, as revealed by 13C solid-state NMR. The impact of crystallization conditions on the disorder was investigated, finding variations in the occupancy ratio of the *C-OH chiral center between single crystals and a consistency across samples in the bulk powder. Overall, this work highlights the contrast between investigating crystallographic disorder by X-ray diffraction and solid-state NMR experiment, and gauge-including projector-augmented-wave (GIPAW) density functional theory (DFT) calculations, with their combined use, yielding an improved understanding of the nature of the crystallographic disorder between the local (i.e., as viewed by NMR) and longer-range periodic (i.e., as viewed by diffraction) scale.

Combining heteronuclear correlation NMR with spin-diffusion to detect relayed Cl-H-H and N-H-H proximities in molecular solids.

Analysis of short-to-intermediate range intermolecular interactions offers a great way of characterizing the solid-state organization of small molecules and materials. This can be achieved by two-dimensional (2D) homo- and heteronuclear correlation NMR spectroscopy, for example, by carrying out experiments at high magnetic fields in conjunction with fast magic-angle spinning (MAS) techniques. But, detecting 2D peaks for heteronuclear dipolar coupled spin pairs separated by greater than 3 Å is not always straightforward, particularly when low-gamma quadrupolar nuclei are involved. Here, we present a 2D correlation NMR experiment that combines the advantages of heteronuclear-multiple quantum coherence (HMQC) and proton-based spin-diffusion (SD) pulse sequences using radio-frequency-driven-recouping (RFDR) to probe inter and intramolecular 1H-X (X = 14N, 35Cl) interactions. This experiment can be used to acquire 2D 1H{X}-HMQC filtered 1H-1H correlation as well as 2D 1H-X HMQC spectra. Powder forms of dopamine·HCl and l-histidine·HCl·H2O are characterized at high fields (21.1 T and 18.8 T) with fast MAS (60 kHz) using the 2D HMQC-SD-RFDR approach. Solid-state NMR results are complemented with NMR crystallography analyses using the gauge-including projector augmented wave (GIPAW) approach. For histidine·HCl·H2O, 2D peaks associated with 14N-1H-1H and 35Cl-1H-1H distances of up to 4.4 and 3.9 Å have been detected. This is further corroborated by the observation of 2D peaks corresponding to 14N-1H-1H and 35Cl-1H-1H distances of up to 4.2 and 3.7 Å in dopamine·HCl, indicating the suitability of the HMQC-SD-RFDR experiments for detecting medium-range proximities in molecular solids.

A toolbox for improving the workflow of NMR crystallography.

NMR crystallography is a powerful tool with applications in structural characterization and crystal structure verification, to name two. However, applying this tool presents several challenges, especially for industrial users, in terms of consistency, workflow, time consumption, and the requirement for a high level of understanding of experimental solid-state NMR and GIPAW-DFT calculations. Here, we have developed a series of fully parameterized scripts for use in Materials Studio and TopSpin, based on the .magres file format, with a focus on organic molecules (e.g. pharmaceuticals), improving efficiency, robustness, and workflow. We separate these tools into three major categories: performing the DFT calculations, extracting & visualizing the results, and crystallographic modelling. These scripts will rapidly submit fully parameterized CASTEP jobs, extract data from the calculations, assist in visualizing the results, and expedite the process of structural modelling. Accompanied with these tools is a description on their functionality, documentation on how to get started and use the scripts, and links to video tutorials for guiding new users. Through the use of these tools, we hope to facilitate NMR crystallography and to harmonize the process across users.

Importance of Water in Maintaining Softwood Secondary Cell Wall Nanostructure.

Water is one of the principal constituents by mass of living plant cell walls. However, its role and interactions with secondary cell wall polysaccharides and the impact of dehydration and subsequent rehydration on the molecular architecture are still to be elucidated. This work combines multidimensional solid-state 13C magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) with molecular dynamics modeling to decipher the role of water in the molecular architecture of softwood secondary cell walls. The proximities between all main polymers, their molecular conformations, and interaction energies are compared in never-dried, oven-dried, and rehydrated states. Water is shown to play a critical role at the hemicellulose-cellulose interface. After significant molecular shrinkage caused by dehydration, the original molecular conformation is not fully recovered after rehydration. The changes include xylan becoming more closely and irreversibly associated with cellulose and some mannan becoming more mobile and changing conformation. These irreversible nanostructural changes provide a basis for explaining and improving the properties of wood-based materials.

Synergy of Solid-State NMR, Single-Crystal X-ray Diffraction, and Crystal Structure Prediction Methods: A Case Study of Teriflunomide (TFM).

In this work, for the first time, we present the X-ray diffraction crystal structure and spectral properties of a new, room-temperature polymorph of teriflunomide (TFM), CSD code 1969989. As revealed by DSC, the low-temperature TFM polymorph recently reported by Gunnam et al. undergoes a reversible thermal transition at -40 °C. This reversible process is related to a change in Z' value, from 2 to 1, as observed by variable-temperature 1H-13C cross-polarization (CP) magic-angle spinning (MAS) solid-state NMR, while the crystallographic system is preserved (triclinic). Two-dimensional 13C-1H and 1H-1H double-quantum MAS NMR spectra are consistent with the new room-temperature structure, including comparison with GIPAW (gauge-including projector augmented waves) calculated NMR chemical shifts. A crystal structure prediction procedure found both experimental teriflunomide polymorphs in the energetic global minimum region. Differences between the polymorphs are seen for the torsional angle describing the orientation of the phenyl ring relative to the planarity of the TFM molecule. In the low-temperature structure, there are two torsion angles of 4.5 and 31.9° for the two Z' = 2 molecules, while in the room-temperature structure, there is disorder that is modeled with ∼50% occupancy between torsion angles of -7.8 and 28.6°. These observations are consistent with a broad energy minimum as revealed by DFT calculations. PISEMA solid-state NMR experiments show a reduction in the C-H dipolar coupling in comparison to the static limit for the aromatic CH moieties of 75% and 51% at 20 and 40 °C, respectively, that is indicative of ring flips at the higher temperature. Our study shows the power of combining experiments, namely DSC, X-ray diffraction, and MAS NMR, with DFT calculations and CSP to probe and understand the solid-state landscape, and in particular the role of dynamics, for pharmaceutical molecules.

35 Cl-1 H Heteronuclear correlation magic-angle spinning nuclear magnetic resonance experiments for probing pharmaceutical salts.

Heteronuclear multiple-quantum coherence (HMQC) pulse sequences for establishing heteronuclear correlation in solid-state nuclear magnetic resonance (NMR) between 35 Cl and 1 H nuclei in chloride salts under fast (60 kHz) magic-angle spinning (MAS) and at high magnetic field (a 1 H Larmor frequency of 850 MHz) are investigated. Specifically, recoupling of the 35 Cl-1 H dipolar interaction using rotary resonance recoupling with phase inversion every rotor period or the symmetry-based SR42 1 pulse sequences are compared. In our implementation of the population transfer (PT) dipolar (D) HMQC experiment, the satellite transitions of the 35 Cl nuclei are saturated with an off-resonance WURST sweep, at a low nutation frequency, over the second spinning sideband, whereby the WURST pulse must be of the same duration as the recoupling time. Numerical simulations of the 35 Cl-1 H MAS D-HMQC experiment performed separately for each crystallite orientation in a powder provide insight into the orientation dependence of changes in the second-order quadrupolar-broadened 35 Cl MAS NMR lineshape under the application of dipolar recoupling. Two-dimensional 35 Cl-1 H PT-D-HMQC MAS NMR spectra are presented for the amino acids glycine·HCl and l-tyrosine·HCl and the pharmaceuticals cimetidine·HCl, amitriptyline·HCl and lidocaine·HCl·H2 O. Experimentally observed 35 Cl lineshapes are compared with those simulated for 35 Cl chemical shift and quadrupolar parameters as calculated using the gauge-including projector-augmented wave (GIPAW) method: the calculated quadrupolar product (PQ ) values exceed those measured experimentally by a factor of between 1.3 and 1.9.