Browsing by Author "Wilson, Philippe B."
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Item Metadata only Benchtop Low-Frequency 60 MHz NMR Analysis of Urine: A Comparative Metabolomics Investigation(MDPI, 2020-04-16) Leenders, Justine; Grootveld, Martin; Percival, Benita; Gibson, Miles; Casanova, Federico; Wilson, Philippe B.Metabolomics techniques are now applied in numerous fields, with the ability to provide information concerning a large number of metabolites from a single sample in a short timeframe. Although high-frequency (HF) nuclear magnetic resonance (NMR) analysis represents a common method of choice to perform such studies, few investigations employing low-frequency (LF) NMR spectrometers have yet been published. Herein, we apply and contrast LF and HF 1H-NMR metabolomics approaches to the study of urine samples collected from type 2 diabetic patients (T2D), and apply a comparative investigation with healthy controls. Additionally, we explore the capabilities of LF 1H-1H 2D correlation spectroscopy (COSY) experiments regarding the determination of metabolites, their resolution and associated analyses in human urine samples. T2D samples were readily distinguishable from controls, with several metabolites, particularly glucose, being associated with this distinction. Comparable results were obtained with HF and LF spectrometers. Linear correlation analyses were performed to derive relationships between the intensities of 1D and 2D resonances of several metabolites, and R2 values obtained were able to confirm these, an observation attesting to the validity of employing 2D LF experiments for future applications in metabolomics studies. Our data suggest that LF spectrometers may prove to be easy-to-use, compact and inexpensive tools to perform routine metabolomics analyses in laboratories and ‘point-of-care’ sites. Furthermore, the quality of 2D spectra obtained from these instruments in half an hour would broaden the horizon of their potential applications.Item Open Access Benchtop NMR Spectroscopy and Spectral Analysis of the cis- and trans-Stilbene Products of the Wittig Reaction(ACS, 2019-07-16) Edgar, Mark; Percival, Benita; Gibson, Miles; Masania, Jinit; Beresford, Ken; Wilson, Philippe B.; Grootveld, MartinBenchtop NMR spectrometers are now becoming more widely employed in university teaching laboratories. These low-field instruments are increasingly used in reaction monitoring and product purity applications. NMR spectra obtained using these spectrometers (40–80 MHz) tend to suffer from significant overlap of signals when compared to those obtained at 300–400 MHz or above, and therefore, some reactions may be less suited to analysis using such benchtop systems. While some reactions can be modified to make them more amenable to analysis on low-field benchtop spectrometers, the fact remains that many common undergraduate laboratory chemistry reactions remain as a stalwart of the university education system. Therefore, there is currently a major requirement for benchtop NMR analysis to improve in order to facilitate student understanding. Herein, it is demonstrated that a combination of spectral analysis and simulation at low-fields (40–80 MHz) allows the fine structure of second-order effects and overlapping spectra to be deduced, enabling an improved understanding of the low-field benchtop NMR technique within undergraduate student cohorts. The evolution of well-resolved and distinct multiplets at 400 MHz to complex, overlapping multiplets at 40–80 MHz also serves as a useful guide for laboratory demonstrators and academic staff when explaining the advantages of such benchtop systems. The Wittig reaction has been a standard reaction practical session in many university teaching laboratories since the 1980s, the products of which are a mixture of cis- and trans-stilbenes. This reaction serves as an ideal example of how benchtop NMR spectrometers and analysis can support chemistry teaching laboratories.Item Open Access Computational modelling of a caged methyl cation: structure, energetics and vibrational analysis(ACS, 2018-01-16) Wilson, Philippe B.; Williams, Ian H.DFT calculations for CH3+ within a constrained cage of water molecules permit the controlled manipulation of distances rax and req to “axial” and “equatorial” waters. Equatorial CH···O interactions catalyze methyl transfer (MT) between axial waters. Variation in rax has a greater effect on CH bond lengths and stretching force constants in the symmetric SN2-like transition structures than variation in req. In-plane bending frequencies are insensitive to these variations in cage dimensions, but axial interactions loosen the out-of-plane bending mode (OP) whereas equatorial interactions stiffen it. Frequencies for rotational and translational motions of CH3+ within the cage are influenced by rax and req. In particular, translation of CH3+ in the axial direction is always coupled to cage motion. With longer rax, CH3+ translation is coupled with asymmetric CO bond stretching, but with shorter rax, it is also coupled with OP (equivalent to the umbrella mode of trigonal bipyramidal O···CH3+···O); the magnitude of the imaginary MT frequency increases steeply as rax diminishes. This coupling between CH3+ and its cage is removed by eliminating the rows and columns associated with cage atoms from the full Hessian to obtain a reduced Hessian for CH3+ alone. Within a certain range of cage dimensions, the reduced Hessian yields a real frequency for MT. The importance of using a Hessian large enough to describe the reaction coordinate mode correctly is emphasized for modeling chemical reactions and particularly for kinetic isotope effects in enzymic MT.Item Open Access A computational study of the influence of methyl substituents on competitive ring closure to α- and β-lactones(Royal Society of Chemistry, 2017-08-18) Wilson, Philippe B.; Williams, Ian H.Ring-closure of substituted 2-chlorosuccinates to α- or β-lactones has been studied by means of MP2/6-311+G(d,p)//MP2/6-31+G(d) calculations in water treated as a polarised continuum (PCM) and in vacuum. Optimised geometries have been obtained for 2-chlorosuccinate and its 2-methyl, 3,3-dimethyl, and 2,3,3-trimethyl derivatives, along with the transition structures and products for intramolecular nucleophilic displacement leading to the 3- or 4-membered rings. Relative enthalpies and Gibbs free energies of activation and reaction are presented, along with key geometrical parameters, and changes in electrostatic-potential-derived atomic charges. The difference in free-energy barriers for α- and β-lactone formation from the 2-methyl substrate at 298 K is less than 1 kJ mol−1. Primary 14C kinetic isotope effects calculated for substitution at C2 are significantly smaller for α-lactone formation than for β, suggesting a possible way to distinguish between the competing pathways of reaction. The B3LYP method without dispersion corrections predicts the wrong relative stability order for methyl-substituted succinate dianions in PCM water.Item Embargo Critical evaluation of anharmonic corrections to the equilibrium isotope effect for methyl cation transfer from vacuum to dielectric continuum(Taylor & Francis, 2015-02-11) Wilson, Philippe B.; Williams, Ian H.Harmonic and anharmonic vibrational frequencies are computed for isotopologues of methyl cation in vacuum and in a polarised continuum model (PCM) dielectric continuum (ϵ = 80) within Gaussian09. Comparison of results in vacuum for two methods (B3LYP and second-order Møller–Plesset perturbation theory) and three basis sets (6-31+G(d), cc-aug-PVDZ, cc-aug-PVQZ) with published anharmonic frequencies obtained from an accurate vibrational configuration interaction (VCI) method shows the smallest root mean square error in the frequencies from B3LYP/6-31+G(d) with anharmonic corrections. Using this method to calculate isotopic partition function ratios (IPFRs) for all six pairs of CH3+, CH2D+, CHD2+ and CD3+ gives better results for anharmonic frequencies than for unscaled harmonic frequencies, but scaled harmonic frequencies give even better results for less cost. The scaling factor is simply the ratio of the sum of the anharmonic VCI frequencies to the sum of the harmonic B3LYP/6-31+G(d) frequencies, which corresponds to the dominance of zero-point energy changes in determining the IPFRs. Both the scaled and unscaled harmonic frequencies provide reasonable estimates for the equilibrium isotope effects (EIEs) upon transfer of methyl cation from vacuum to PCM ‘water’, but the anharmonic PCM calculations give erratic results. The use of scaled B3LYP/6-31+G(d) harmonic frequencies is recommended for the estimations of EIEs rather than expensive anharmonic corrections.Item Open Access Determination of Heavy Metals Present in the Hypoglycemic Karela Powder: An Analytical Assay(E-Cronicon, 2017-07-20) Ruparelia, K. C.; Wilson, Philippe B.; Sousa, M. C.; Juma, Nazmin; Desai, Unmesh; Grootveld, Martin; Arroo, R. R. J.; Zeka, K.Diabetes is a common health condition associated with heightened glucose content in the blood due to impaired insulin production/function. Considering current societal trends, the number of patients with this condition is growing fast. To help this subset of the population, researchers are investigating natural products exhibiting hypoglycaemic effects. It is well known that one third of patients with diabetes mellitus use some form of complementary or alternative medicine. One plant that has received some attention for its anti-diabetic properties is bitter melon, or Momordica charantia, commonly referred to as bitter gourd, karela and balsam pear.Item Open Access Errors in DFT Integration Grids and Their Potential Impact on Chemical Shift Calculations(Wiley, 2019-09-09) Wilson, Philippe B.; Grootveld, Martin; Kamerlin, S. C. L.Item Metadata only Evaluations of the Peroxidative Susceptibilities of Cod Liver Oils by a 1H NMR Analysis Strategy: Peroxidative Resistivity of a Natural Collagenous and Biogenic Amine-Rich Fermented Product(MDPI, 2020-03-12) Percival, Benita; Wann, Angela; Zbasnik, Richard; Schelgel, Vicki; Edgar, Mark; Ampem, Gilbert; Le Gresley, Adam; Wilson, Philippe B.; Naughton, Declan; Grootveld, Martin; Zhang, JieHigh-resolution 1H nuclear magnetic resonance (NMR) analysis was employed to molecularly screen the lipid, lipid oxidation product (LOP), and antioxidant compositions of four natural (unrefined) cod liver oil (CLO) products. Products 1–3 were non-fermented CLOs, whilst Product 4 was isolated from pre-fermented cod livers. Supporting analytical data that were acquired included biogenic amine, flavanone, tannin, phenolic antioxidant, α-tocopherol, and oxygen radical absorbance capacity (ORAC) determinations by recommended HPLC, LC/MS/MS, or spectrophotometric methods. SDS-PAGE, HPLC, and 1H NMR analyses investigated and determined collagenous antioxidants and their molecular mass ranges. 1H NMR analysis of aldehydic LOPs was employed to explore the susceptibilities/resistivities of each CLO product to peroxidation that is induced by thermal stressing episodes (TSEs) at 180°C, or following prolonged (42 day) storage episodes at 4 and 23 °C. Product 4 displayed extremely high ORAC values, which were much greater than those of Products 1–3, and that were predominantly ascribable to significant levels of peroxidation-blocking and/or aldehyde-consuming collagenous polypeptides/peptides and ammoniacal agents therein. Significantly lower levels of toxic aldehydes were generated in the pre-fermented Product 4 during exposure to TSEs, or the above long-term storage episodes. These results confirmed the enhanced peroxidative resistivity of a fermented, antioxidant-fortified natural CLO product over those of non-fermented unrefined products. Product 4: Green Pasture Blue Ice™ Fermented Cod Liver Oil.Item Open Access Influence of Equatorial CH⋅⋅⋅ O Interactions on Secondary Kinetic Isotope Effects for Methyl Transfer(Wiley, 2015-02-01) Wilson, Philippe B.; Williams, Ian H.DFT calculations for methyl cation complexed within a constrained cage of water molecules permit the controlled manipulation of the “axial” donor/acceptor distance and the “equatorial” distance to hydrogen-bond acceptors. The kinetic isotope effect k(CH3)/k(CT3) for methyl transfer within a cage with a short axial distance becomes less inverse for shorter equatorial C⋅⋅⋅O distances: a decrease of 0.5 Å results in a 3 % increase at 298 K. Kinetic isotope effects in AdoMet-dependent methyltransferases may be m∧odulated by CH⋅⋅⋅O hydrogen bonding, and factors other than axial compression may contribute, at least partially, to recently reported isotope-effect variations for catechol-O-methyltransferase and its mutant structures.Item Open Access Influence of Equatorial CH⋅⋅⋅O Interactions on Secondary Kinetic Isotope Effects for Methyl Transfer(Wiley, 2016-01-28) Wilson, Philippe B.; Williams, Ian H.DFT calculations for methyl cation complexed within a constrained cage of water molecules permit the controlled manipulation of the “axial” donor/acceptor distance and the “equatorial” distance to hydrogen-bond acceptors. The kinetic isotope effect k(CH3)/k(CT3) for methyl transfer within a cage with a short axial distance becomes less inverse for shorter equatorial C⋅⋅⋅O distances: a decrease of 0.5 Å results in a 3 % increase at 298 K. Kinetic isotope effects in AdoMet-dependent methyltransferases may be m∧odulated by CH⋅⋅⋅O hydrogen bonding, and factors other than axial compression may contribute, at least partially, to recently reported isotope-effect variations for catechol-O-methyltransferase and its mutant structures.Item Metadata only Kinetic Isotope Effects(Royal Society of Chemistry, 2016-11-25) Williams, Ian H.; Wilson, Philippe B.Methods for calculation of kinetic isotope effects and their application to reactions catalysed by enzymes are surveyed, including consideration of cut-off approximations both old and new, empirical bond-order–bond-energy approaches, quantum-mechanical cluster methods, and hybrid quantum mechanics/molecular mechanical methods. The unifying feature is the use of a Hessian matrix of force constants within the harmonic approximation. The merits of methods appropriate for supramolecular systems, including enzymes, are discussed in contrast to commonly used methods developed for gas-phase molecules, and the importance of averaging in conformationally flexible systems is emphasised.Item Open Access Low-Field, Benchtop NMR Spectroscopy as a Potential Tool for Point-of-Care Diagnostics of Metabolic Conditions: Validation, Protocols and Computational Models(MDPI, 2018-12-27) Percival, B.C.; Grootveld, Martin; Gibson, M.; Osman, Y.; Molinari, M.; Jafari, F.; Sahota, T. S.; Martin, M.; Casanova, F.; Mather, M.L.; Edgar, M.; Masania, J.; Wilson, Philippe B.Novel sensing technologies for liquid biopsies offer promising prospects for the early detection of metabolic conditions through omics techniques. Indeed, high-field nuclear magnetic resonance (NMR) facilities are routinely used for metabolomics investigations on a range of biofluids in order to rapidly recognise unusual metabolic patterns in patients suffering from a range of diseases. However, these techniques are restricted by the prohibitively large size and cost of such facilities, suggesting a possible role for smaller, low-field NMR instruments in biofluid analysis. Herein we describe selected biomolecule validation on a low-field benchtop NMR spectrometer (60 MHz), and present an associated protocol for the analysis of biofluids on compact NMR instruments. We successfully detect common markers of diabetic control at low-to-medium concentrations through optimised experiments, including α-glucose (≤2.8 mmol/L) and acetone (25 µmol/L), and additionally in readily accessible biofluids, particularly human urine. We present a combined protocol for the analysis of these biofluids with low-field NMR spectrometers for metabolomics applications, and offer a perspective on the future of this technique appealing to ‘point-of-care’ applications.Item Metadata only Metabolomic studies of lipid storage disorders, with special reference to Niemann-Pick type C disease: A critical review with future perspectives.(MDPI, 2020-04-05) Percival, Benita; Gibson, Miles; Wilson, Philippe B.; Platt, Frances M.; Grootveld, MartinLysosomal storage disorders (LSDs) are predominantly very rare recessive autosomal neurodegenerative diseases.Sphingolipidoses, a sub-group of LSDs, result from defects in lysosomal enzymes involved in sphingolipid catabolism, and feature disrupted storage systems which trigger complex pathogenic cascades with other organelles collaterally affected. This process leads to cell dysfunction and death, particularly in the central nervous system. One valuable approach to gaining insights into the global impact of lysosomal dysfunction is through metabolomics, which represents a discovery tool for investigating disease-induced modifications in the patterns of large numbers of simultaneously-analysed metabolites, which also features the identification of biomarkers Here, the scope and applications of metabolomics strategies to the investigation of sphingolipidoses is explored in order to facilitate our understanding of the biomolecular basis of these conditions. This review therefore surveys the benefits of applying ’state-of-the-art’ metabolomics strategies, both univariate and multivariate, to sphingolipidoses, particularly Niemann-Pick type C disease. Relevant limitations of these techniques are also discussed, along with the latest advances and developments. We conclude that metabolomics strategies are highly valuable, distinctive bioanalytical techniques for probing LSDs, most especially for the detection and validation of potential biomarkers. They also show much promise for monitoring disease progression and the evaluation of therapeutic strategies and targets.Item Metadata only Molecular Composition of and Potential Health Benefits Offered by Natural East African Virgin Sunflower Oil Products: A 400 MHz 1H NMR Analysis Study(Open Access Publications, 2019-03-18) Percival, B.; Savel, Etienne; Ampem, G.; Gibson, M.; Edgar, Mark; Jafari, F.; Frederick, Kianna; Woodason, Katy; Wilson, Philippe B.; Grootveld, MartinObjectives: Sunflower oil (SFO) is regularly employed for cosmetic, emollient and food frying purposes, the latter representing its foremost use globally. Therefore, full investigations of the molecular composition and quality of sunflower oil products are a major requirement. In this study, high-field 1H NMR analysis was employed to explore the molecular composition and authenticities of East African virgin (EAV) SFO products, particularly their acylglycerol fatty acid contents, together with those of selected minor constituents. Results acquired were statistically compared to those acquired on commercially-available, EU-approved refined SFO products via NMR-linked multivariate chemometrics strategies. Methodology: High-field 1H NMR spectra of EAV and refined SFOs (n = 55 and 4 respectively) were acquired at an operating frequency of 400 MHz. Their triacylglycerol fatty acid, triacylglycerol hydrolysis product, and sterol and stanol contents were determined via intelligent frequency bucketing and electronic integration of selected resonances. Univariate analysis-of-variance, and multivariate ROC curve evaluations were conducted to determine the magnitude and statistical significance of analyte concentration differences between these two sample classifications. Further multivariate NMR-linked chemometrics analyses such as principal component, random forest and support vector machine classification analyses were also utilised for this purpose. Key Results: Multicomponent 1H NMR analysis demonstrated that EAV SFOs had significantly higher and lower contents of monounsaturated fatty acids (MUFAs) and polyunsaturated fatty acids (PUFAs), respectively, than those of refined SFOs. Furthermore, significantly higher concentrations of ‘health-friendly’, cholesterol-blocking sterols and stanols were also found in these virgin products. Major Conclusions: 1H NMR analysis provides much valuable molecular information regarding the composition and virginal status of SFOs. The high [MUFA]:[PUFA] content ratio of unrefined EAV SFO products renders them more suitable and safer for commercial or domestic deep-frying episodes than refined SFOs (MUFAs are much more resistant to thermally-induced peroxidation than PUFAs). These products also potentially offer valuable health benefits in view of their high natural sterol and stanol contents.Item Metadata only Potential Adverse Public Health Effects Afforded by the Ingestion of Dietary Lipid Oxidation Product Toxins: Significance of Fried Food Sources(MDPI, 2020-04-01) Grootveld, Martin; Percival, Benita; Leenders, Justine; Wilson, Philippe B.Exposure of polyunsaturated fatty acid (PUFA)-rich culinary oils (COs) to high temperature frying practices generates high concentrations of cytotoxic and genotoxic lipid oxidation products (LOPs) via oxygen-fueled, recycling peroxidative bursts. These toxins, including aldehydes and epoxy-fatty acids, readily penetrate into fried foods and hence are available for human consumption; therefore, they may pose substantial health hazards. Although previous reports have claimed health benefits offered by the use of PUFA-laden COs for frying purposes, these may be erroneous in view of their failure to consider the negating adverse public health threats presented by food-transferable LOPs therein. When absorbed from the gastrointestinal (GI) system into the systemic circulation, such LOPs may significantly contribute to enhanced risks of chronic non-communicable diseases (NCDs), e.g. , cancer, along with cardiovascular and neurological diseases. Herein, we provide a comprehensive rationale relating to the public health threats posed by the dietary ingestion of LOPs in fried foods. We begin with an introduction to sequential lipid peroxidation processes, describing the noxious effects of LOP toxins generated therefrom. We continue to discuss GI system interactions, the metabolism and biotransformation of primary lipid hydroperoxide LOPs and their secondary products, and the toxicological properties of these agents, prior to providing a narrative on chemically-reactive, secondary aldehydic LOPs available for human ingestion. In view of a range of previous studies focused on their deleterious health effects in animal and cellular model systems, some emphasis is placed on the physiological fate of the more prevalent and toxic α,β-unsaturated aldehydes. We conclude with a description of targeted nutritional and interventional strategies, whilst highlighting the urgent and unmet clinical need for nutritional and epidemiological trials probing relationships between the incidence of NCDs, and the frequency and estimated quantities of dietary LOP intake.Item Open Access Progress in Low Field Benchtop NMR Spectroscopy in Chemical and Biochemical Analysis(Elsevier, 2019-02-23) Grootveld, Martin; Percival, B.C.; Osman, Y.; Edgar, Mark; Molinari, M.; Mather, M.L.; Casanova, F.; Wilson, Philippe B.The employment of spectroscopically-resolved NMR techniques as analytical probes have previously been both prohibitively expensive and logistically challenging in view of the large sizes of high-field facilities. However, with recent advances in the miniaturisation of magnetic resonance technology, low-field, cryogen-free “benchtop” NMR instruments are seeing wider use. Indeed, these miniaturised spectrometers are utilised in areas ranging from food and agricultural analyses, through to human biofluid assays and disease monitoring. Therefore, it is both intrinsically timely and important to highlight current applications of this analytical strategy, and also provide an outlook for the future, where this approach may be applied to a wider range of analytical problems, both qualitatively and quantitatively.Item Open Access Q6: A comprehensive toolkit for empirical valence bond and related free energy calculations(ELSEVIER, 2018-01-04) Bauer, Paul; Barrozo, Alexandre; Purg, Miha; Amrein, Beat Anton; Esguerra, Mauricio; Wilson, Philippe B.; Major, Dan Thomas; Aqvist, Johan; Kamerlin, Shina Caroline LynnAtomistic simulations have become one of the main approaches to study the chemistry and dynamics of biomolecular systems in solution. Chemical modelling is a powerful way to understand biochemistry, with a number of different programs available to perform specialized calculations. We present here Q6, a new version of the Q software package, which is a generalized package for empirical valence bond, linear interaction energy, and other free energy calculations. In addition to general technical improvements, Q6 extends the reach of the EVB implementation to fast approximations of quantum effects, extended solvent descriptions and quick estimation of the contributions of individual residues to changes in the activation free energy of reactions.Item Open Access Recent Advances in Avian Egg Science: A Review(Elsevier, 2017-07-14) Wilson, Philippe B.Eggs and egg products form an integral part of the food chain. As such, research into egg structure, function, and production has made an important contribution to the field of poultry science. The past decade has seen significant advances in avian egg science research, with work supplementing our understanding of the nature of the avian egg, and its biological, chemical, and physical properties. Eggshell color, strength, and chemical composition, poultry nutrition, and genetics have all been intensively studied recently, with significant progress being made in a number of these areas. Indeed, with the prevalence of robust theoretical techniques, it is now commonplace to combine experimental investigations with theory, providing a balanced and interdisciplinary perspective.Item Embargo Ruthenium (II)-Catalyzed C–H Functionalization Using the Oxazolidinone Heterocycle as a Weakly Coordinating Directing Group: Experimental and Computational Insights(ACS, 2016-07-14) Leitch, Jamie A.; Wilson, Philippe B.; McMullin, Claire L.; Mahon, Mary F.; Bhonoah, Yunas; Williams, Ian H.Herein, we report the ruthenium-catalyzed ortho C–H alkenylation of a wide range of N-aryloxazolidinone scaffolds. Alkenylation was achieved with complete monoselectivity with a scope of 27 examples in 2-MeTHF. Yields ranged from 23 to 94%, producing highly decorated oxazolidinone scaffolds. A kinetically relevant C–H cleavage was also observed with a kinetic isotope effect (KIE) of ∼2. Density functional theory calculations provided information about mechanism, detailing the β-hydride elimination as the most energetically challenging step of 13.5 kcal mol–1. In-depth computational kinetic studies also predicted a KIE of 2.17 for C–H cleavage and an intrinsic KIE for the reaction of 2.22, in line with the experimentally observed valueItem Embargo Solvent Effects on Isotope Effects: Methyl Cation as a Model System(ACS, 2014-07-17) Wilson, Philippe B.; Williams, Ian H.; Weaver, Paul; Grieg, Ian R.The isotopic sensitivity (CH3+ vs CD3+) of the equilibrium between the methyl cation in vacuum and in solution has been investigated. Two alternative options for describing the shape of the solute cavity within the widely used polarized continuum model for implicit solvation were compared; the UFF and UA0 methods give equilibrium isotope effects (EIEs) that vary as a function of the dielectric constant in opposite directions. The same isotope effect was also obtained as the average over 40 structures from a hybrid quantum mechanical/molecular mechanical molecular dynamics simulation for the methyl cation explicitly solvated by many water molecules; the inverse value of the EIE agrees with UFF but not UA0. The opposing trends may be satisfactorily explained in terms of the different degrees of exposure of the atomic charges to the dielectric continuum in cavities of different shapes.