A Method of Calculating the Kamlet–Abboud–Taft Solvatochromic Parameters Using COSMO-RS

There is demand for safer and bio-based solvents, brought on by legislation and sustainability objectives. The prediction of physical properties is highly desirable to help design new molecules. Here we present an in silico approach to obtain calculated Kamlet–Abboud–Taft solvatochromic parameters using virtual experiments. The tautomerisation equilibrium of methyl acetoacetate and dimedone was calculated in different solvents with COSMO-RS theory and converted into estimates of solvent dipolarity and hydrogen bond accepting ability, respectively. Hydrogen bond donating ability was calculated as a function of the electron deficient surface area on protic solvents. These polarity descriptors correlate with rate constants and equilibria, and so ability of calculated Kamlet–Abboud–Taft solvatochromic parameters to recreate experimental free energy relationships was tested with sixteen case studies taken from the literature. The accuracy of the calculated parameters was also satisfactory for solvent selection, as demonstrated with a 1,4-addition reaction and a multicomponent heterocycle synthesis.


Experimental determination of Kamlet-Abboud-Taft (KAT) parameters.
N,N-Dimethyl-4-nitroaniline, N,N-diethyl-4-nitroaniline, or 4-nitroanisole can be used to obtain π*, a measure of solvent polarity. In this work N,N-diethyl-4-nitroaniline was used to obtain data for 6,8dioxabicyclo[3.2.1]octan-4-ol (levoglucosanol). Marcus used several dyes and took an average π* value. 1 The UV absorbance of these dyes changes frequency depending on the dipolarity (or polarisability for polyhalogenated solvents or aromatic solvents) of the medium it is dissolved in. The π* scale is normalised between the response of cyclohexane (363 nm, π* = 0.00) and dimethyl sulphoxide (412 nm, π* = 1.00). Therefore it is possible for solvents to have π* values outside of this scale, should they be less polar than cyclohexane or more polar than dimethyl sulphoxide. The λmax of N,N-diethyl-4-nitroaniline in levoglucosanol is 407 nm, equating to a π* value of 0.89.
To obtain a value of hydrogen bond accepting ability (β), a second dye is required. This is the dealkylated equivalent of the first (e.g. 4-nitroaniline or 4-nitrophenol). In non-hydrogen bonding solvents, the responses of the two dyes are linearly proportional. A deviation of the UV response from this trend is observed when hydrogen bond interactions with the solvent are possible. The magnitude of the deviation is proportional to β. The scale is normalised to hexamethyl phosphoramide (originally defined as β = 1.00, but in Marcus' data set slightly higher due to the choice of dyes). The proportionality between the pair of dyes in non-hydrogen bonding solvents is not perfect, and so very weak hydrogen bonding (β < 0.10) cannot be discerned. Marcus reported low β values due to the use of several pairs of dyes and taking the average. The λmax of 4-nitroaniline in levoglucosanol is 378 nm (β = 0.58).
Reichardt's dye is used to obtain α in an equivalent manner to how β is obtained ( Figure S1). 2 Nitroanisole and Reichardt's dye have a proportional λmax in aprotic solvents. Protic solvents deviate from this correlation, and the magnitude of deviation is the basis of the α scale. Methanol (α = 1.00) is indicated with an arrow on Figure  S1. The base line (solid line) is subject to minor deviations which means accurate determination of very small α values is not possible. The dashed line in Figure S1 marks the α = 0.10 equivalence line, which is within the accuracy of the base line. It is common to assign α values below 0.1 (including negative values) as zero for this reason. An empirical equation is also available to separate the effect of solvent dipolarity from the response of Reichardt's dye to give the α value of a solvent if π* is already known. 3 Figure S1. The experimental determination of α values.
The large dataset of Marcus reports the average KAT parameter (π*, β, α) obtained from up to five dyes. 1 This elaborate approach is not practiced anymore. Instead, one set of dyes is used as described above. 4 This means that different KAT parameter values will be reported for the same solvent depending on the author and their methods. Using a dataset with KAT parameters from different sources introduces an inconsistency and should be avoided if possible. We required a large dataset for this work and so used Marcus' data. This means the calculated KAT parameters are predictions of the average response of different dyes. Out of necessity, when we have tested the predictive model on a secondary dataset, the prediction is of what the Marcus average value would have been and not the value we have at our disposal. This needs to be considered when applying this work and evaluating the error of the calculation. Fortunately in the majority of cases the choice of dyes does not have a dramatic impact on the values of the KAT parameters.
Tautomerisation and an explanation of the solvent effect.
The reactions chosen as the basis for solvent polarity estimations were the tautomerisation of 1,3-dicarbonyl compounds. There is a quantitative linear correlation between keto-enol tautomerisation equilibria, expressed as ln(KT), and solvent polarity. 5 This is an example of a linear solvation energy relationship (LSER), a sub-set of free energy relationships with the following general form where XYZ is an energy dependent variable (e.g. log(k), ln(K)) and XYZ0 is a constant (see equation 1). Other variables may be included if statistically relevant, such as molar volume to account for cavity effects.
If the dicarbonyl compound is acyclic, such as methyl acetoacetate, enol concentration is inversely proportional to solvent dipolarity (π*). The enol-tautomer forms an intramolecular hydrogen bond, and this species has a lower value dipole than the diketo-tautomer. Thus non-polar solvents favour higher concentrations of the enoltautomer. If the dicarbonyl compound is cyclic (e.g. dimedone), the equilibrium position is proportional to the solvent's hydrogen bond accepting ability (β). This is because the enol-tautomer is conformationally restricted, meaning an intramolecular hydrogen bond is impossible (Scheme S1). Instead a hydrogen bond with a solvent molecule occurs. As a consequence the concentration of the enol-tautomer is higher in hydrogen bond accepting solvents.

Section 2. Calculations
Software.  Figure S2 shows representative σ-surfaces, σ-profiles, and σ-potentials. Qualitative and quantitative descriptions of these calculations can be found elsewhere. 6,7,8,9,10 To briefly summarise, the foremost output of COMSOtherm is the σ-surface, a polarity map of the surface of a molecule. Red represents electron rich regions of the molecular surface, green is neutral and blue areas are electron deficient. A σ-surface is generated for each energetically relevant conformer, and thermodynamic calculations (such as the virtual equilibria calculated in this work) consider the distribution of conformers. The σ-profile is a graphical interpretation of the σ-surface, which contains information about the electron donating and electron accepting ability of the molecule. Regions to the left of the σ-profile represent electron accepting functionalities. Its integral is the electron deficient surface area. Regions to the right of the σ-profile represent electron donating functionalities. The area under this portion of the σ-profile is the electron rich surface area. The lipophilic surface area is centred. One further analysis performed in COMSOtherm is the σ-potential. The σ-potential shows the affinity (quantified as chemical potential) of a surface segment with an external screening charge. Lipophilic solvents that do not stabilise charges have characteristic "U-shaped" curves. Conversely, the σ-potential of water and alcohol solvents are the opposite, as they are able to interact favourably with positive and negative charges. The affinity of dipolar aprotic solvents towards cations and electron accepting molecules is captured with an "S-shaped" σpotential ( Figure S2). Equilibria were calculated using the 'Reaction' function of COSMOtherm in the chosen solvent. Solvent densities for molar volume predictions were calculated using the 'Density' function of COSMOtherm. Solvent σ-profiles and σ-moments were accessed for each solvent and exported to Microsoft Excel. Regression analysis to produce free energy relationships were conducted in Microsoft Excel. The P-value of variables was used to confirm statistical significance. Screenshots of the calculation of the virtual equilibrium constant for dimedone in levoglucosanol are provided in Figure S3. COSMOtherm can be run on the Microsoft Windows operating system and has a user-friendly interface that allows organic chemists and other non-computational chemists to explore solvent effects and design solvents without needing to understand the underlying theory or to write in source code. For the multi-component heterocycle synthesis, the predicted solubility of the product was required to enable solvent selection. The Hansen solubility parameters of solvents were calculated using HSPiP (5th edition 5.0.03, developed by Abbott, Hansen and Yamamoto) utilising the Y-MB neural network molecular breaking technique, if not available in the HSPiP database. The Hansen solubility parameters of the solute were calculated after fitting a solubility sphere to the experimental solubility data (see Section 7).
Experimental data for the KT of methyl acetoacetate is available for a small selection of solvents, 5 and exhibits an inverse correlation with the dipolarity of the solvent. The same trend is calculated by COSMOtherm (Table  S1). Due to the difference in magnitude between experimental and virtual equilibrium constants, the former were normalised by scaling between the smallest and largest value, thereby producing a scale between zero and one. Virtual equilibrium constants were consequently adjusted by preserving the relationship to experimental values. The normalised calculated equilibrium constants, expressed as ln(KT), were plotted against experimental π* values. The resulting linear relationship provides estimates of π* simply by using the gradient and intercept values to transform a normalised virtual ln(KT) value of a solvent. Acidic solvents defy the correlation due to the stabilisation of the diketo-tautomer (Scheme S2). 5 Graphical analyses are provided in Figure S4.  The method of calculating β is identical to that of π* except dimedone is now the substrate (Table S2). The equilibrium is directly proportional to β. The solvent training set does not include highly basic solvents (β > 0.8). Graphical analyses are provided in Figure S5. The issue of basic solvents disobeying the predictive method was also experienced by Diorazio, 11 and Waghorne. 12 No resolution had been found. Diorazio et al. examined just four basic solvents, achieving one satisfactory prediction of β and three with errors exceeding 0.20. 11 Waghorne et al. investigated a larger number of basic solvents, but alcohols and amines were not modelled correctly and removed from subsequent analysis. 12

The α calculation.
The σ-profile of a solvent describes the electronic charge as a function of molecular surface area ( Figure S2). The central region shows the surface area of a molecule that is neutral (uncharged). Negatively charged areas are further right, and electron deficient areas to the left. The σ-profile in this latter portion is zero for aprotic solvents. Alcohols and other protic solvents have some electron deficient surface area at the location of a hydrogen bond donating functionality (e.g. the hydrogen atom in an alcohol group). A linear regression fitting experimental α values to σ-profiles (for the lowest energy conformation of each of the 175 solvents in Marcus' dataset) revealed only a portion of the electron deficient surface area has a statistically relevant contribution to the model. This region is highlighted in Figure S6, which shows the σ-profile of ethanol. Equation 2 was subsequently used to calculate the α values of solvents. A training set was not used to obtain α values, unlike the calculation of π* and β.
The model generally underestimates the α values of aliphatic monoalcohols, which in the context of the whole data set is balanced by an overestimation of aromatic alcohols, water, and occasionally phenols and carboxylic acids. Due to the data fitting exercise performed on the primary data set as a whole, aprotic solvents are assigned α values of 0.03 due to the constant in equation 2. Any solvent with a calculated α < 0.10 has been corrected to zero, as is accepted practice for experimental values ( Figure S1). One functionality that can give rise to a valid α value below 0.1 would be a ketone, due to tautomerisation. Solvents with C-H acidity, including some nitriles and chlorohydrocarbons are not recognised as having a measurable α value by this method. Marcus reports low α values because that data is the average value obtained from a number of different dyes, some of which will record relatively large α values. The largest calculation error is 2chloroethanol. The hydrogen bond donating ability of 2,2,2-trifluoroethanol was also underestimated, but the predicted α value of hexafluoroisopropanol was correct to 2 decimal places (1.96), so there is not a systematic error for halogenated alcohols. The MAE of the α predictions was 0.06 (r = 0.965 when correlated to experimental values), reduced to 0.05 (r = 0.966) after the correction to aprotic solvents was applied. A literature method is accurate to r = 0.944. 11 This approach was adapted from the previous work of Palomar et al. 13 However there are some significant differences. Palomar et al. used the entire span of the σ-profile to deduce the response of Reichardt's dye instead of α. The UV spectrum of Reichardt's dye responds to the hydrogen bond donating ability (α) and dipolarity (π*) of the solvent it is dissolved in, and can be used in its own right as a scale of solvent polarity. 14 When extending the model to predict the α values of an additional 23 solvents, 2-methoxyethanol and ethyl lactate in particular resulted in poor accuracy. This was discovered to be due to intramolecular hydrogen bonds concealing the hydrogen bond donating ability of the solvent. COSMO-RS theory allows solvents to be modelled as a realistic distribution of conformers. The lowest energy conformers of 2-methoxyethanol and ethyl lactate are stabilised by intramolecular hydrogen bonds ( Figure S7). This interaction is broken in the second lowest energy conformation of ethyl lactate, whereby the proton rotates out of the plane of the molecule. The proportion of electron deficient molecular surface area is now much increased. There are two conformers of 2methoxyethanol that exhibit intramolecular hydrogen bonding, but in the third lowest energy conformation the alcohol group is directed away from the ether functionality. The difference in σ-profiles is shown with an example in Figure S7.
It is possible to select specific conformers for virtual experiments in COSMOtherm. The conformers of ethyl lactate and 2-methoxyethanol without intramolecular hydrogen bonding were isolated and used to provide a revised prediction of α. This resulted in an improved estimation of α (Table S3). Three further solvents in the secondary dataset also had intramolecular hydrogen bonds. In these cases, the calculation of an accurate α value was prevented because all the determined conformers were hydrogen bonding (i.e. diethylene glycol methyl ether) or very unfavourable conformations were required. High energy conformations become unrepresentative of the actual solvent composition. The α values of ionic liquids were not successfully calculated. Ionic liquids are typically aprotic, but interactions of the cation with electron donating molecules replicate a hydrogen bond donor interaction. As shown in Figure S8, the 1-butyl-3-methylimidazolium [bmim] cation does not have any surface area with sufficiently high and localised electron deficiency to register a non-zero α value. Instead, the positive charge is resonant, and consequently there is a large proportion of the cation surface with a weak positive charge.

Kamlet-Abboud-Taft (KAT) parameter data set.
A separate supplementary spreadsheet (Excel file) is available containing experimental KAT parameters, virtual ln(KT) values, calculated KAT parameters and their correctional factors.
The primary solvent data set obtained from Marcus was amended in the following ways: Due to missing π* data, styrene, furan, n-propyl acetate, methyl propanoate, methyl benzoate, N,N-diethyl formamide, and Nmethyl caprolactam were removed. Eucalyptol, 15 2-methyltetrahydrofuran, 16 ethylene carbonate, 17 and dimethyl carbonate, 18 also lacked π* data, but alternative values were found. The contentious data for glycerol was updated to a newer version. 15 The secondary dataset, 15,16,18,19,20,21,22,23,24,25,26 and ionic liquids, 27,28,29 were collated from various sources. A systematic error analysis for uncorrected and corrected calculated π* and β values is provided in Figure S9. A graphical analysis of corrected and uncorrected calculated α values is provided in Figure S10.

Deep eutectic mixtures.
COSMOtherm allows a mixture of solvents to be chosen as the medium for a virtual reaction, and so no modification to the method is required to calculate π* or β. The components of deep eutectic solvents interact strongly with each other, and so it was interesting to see if the polarity of representative examples could be modelled. The MAE of π* calculations was 0.08, and for β calculations it was equal to 0.10 (reduced to 0.08 if discounting the high β values above 0.80). The data is sourced from different publications, 30,31,32 and so the consistency across the dataset is not high. The approach to determining α values is not possible to directly recreate for a mixture. The addition of two (or potentially more) σ-profiles will significantly overestimate hydrogen bond donating ability.

Linear solvation energy relationships (LSERs) with experimental and calculated data.
Sixteen free energy relationships from the literature were reproduced using experimental KAT parameters, and the calculated KAT parameters (uncorrected and corrected) obtained from the virtual experiments (Scheme S3 to Scheme S16). 5,17,19,26,27,33,34,35,36,37,38 Comparing the correlations to the experimental data, XYZ (see equation 1), be it ln(k), ln(K), etc., showed a satisfactory recreation of the relationships in-silico. Solvents with KAT parameters that cannot be corrected were removed from the corresponding correlations. The free energy relationships were recalculated using KAT parameters preferentially from the Marcus dataset, and any coefficients with a P-value greater than 0.01 were eliminated. In case study 12 (the biocatalysed Fischer esterification) the molar volume was calculated using a predicted density from COSMOtherm. Scheme S10. Case studies 8-10. Alkylhalide solvolysis. Case study 8: X = Cl; Case study 9: X = Br; Case study 10: X = I. 35 Scheme S11. Case study 11. Fischer esterification. 27 Catalysed by p-toluenesulphonic acid.
Scheme S16. Cyanoamidation. 38 Product enantioselectivity is a function of solvent polarity.

Failed approaches for KAT parameter estimations.
Other methods of KAT parameter prediction, all using COSMO-RS theory, were attempted but without success. In order to prevent other practitioners from expending their time on these unworkable models, they are briefly described here.
The obvious manner to obtain a prediction of the KAT parameters is to model the solvent effect on the ground and excited states of the dyes used in experiment. We attempted to model the difference in chemical potential between the ground state and excited state of nitroanilines in solution. Unfortunately it was difficult to obtain a reliable molecular geometry and charge distribution of an excited state without resorting to more expensive computational models. Pursuing this would have been contrary to the purpose of designing a model that is rapid to implement for novel solvents.
The second failed attempt was based on the σ-profile of the solvents. A portion of this molecular surface charge histogram served for the calculation of α (as documented earlier), but unexpectedly did not permit a reliable estimation of β. This may be due to hydrogen bond donating ability (as measured on the α scale) resulting from a single acidic proton on a molecule, whereas electron rich areas of a molecule may be delocalised and although cumulatively the σ-profile gives the appearance of a basic molecule, there may not be a focused point of charge that will engage in hydrogen bonding. Similarly, it would appear the failure to represent dipolarity (π*) is due to the σ-profile not accounting for the relative position of charges, which for a dipolar molecule are orientated to create a dipole.
The alternative σ-potential was also investigated. Each σ-potential consists of 61 datapoints. These were redefined using principal component analysis (PCA) in Origin following the procedure of Aubry. 6 Four PCA variables accounted for 97% of data variance in Marcus' KAT parameter dataset. These 4 variables did not result in accurate correlations with the KAT parameters, and were especially poor for π*. The σ-potential is based on interactions with point charges, which could in theory approximate hydrogen bonding, but not dipole-dipole interactions between molecules.
The final method was to use the σ-moments generated as part of the description of molecules in COSMO-RS theory. These parameters have been used to successfully estimate the Abraham solute parameters. 39 It was found the statistically relevant σ-moments (by regression analysis) were not logical descriptors of the KAT parameters: for instance the two relevant independent variables that produced a prediction of β actually represent the hydrogen bond donating ability of the solvent, which is what α describes. This method was not pursued further due to logical inconsistencies such as this.

Comparing different probes.
There are a number of enolisable substrates that have equilibrium constants dictated by solvent polarity, and could be superior to methyl acetoacetate and dimedone for predicting KAT parameters in virtual experiments. ethyl acetoacetate and dimedone. Table S5 demonstrates that no improvement could be made by substituting t-butyl picolyl ketone in for methyl acetoacetate or by using anthracene ketone in place of dimedone. The fact that each probe's solvent dataset is different (due to the availability of experimental data) means this is not a thorough analysis, but it is indicative of the quality of the virtual ln(KT) accuracy with methyl acetoacetate and dimedone.

Direct equilibrium calculations.
It is prudent to reiterate why it is important to calculate the KAT parameters when it is possible to directly model individual processes. The primary reason is because access to the (calculated) KAT parameters then allows us to build a catalogue of potential solvents we have designed, from which to pick suitable candidates depending on what application we investigate next. The method can be reproduced by other COSMOtherm users, while the data disclosed here for commercially available solvents can be used by all. Working on an application-by-application basis would mean intuitively (or randomly) creating or selecting potential solvents and performing the virtual reaction each time, with no predictable relevance to other applications. Another benefit is that with calculated KAT parameters, reaction kinetics can be modelled (albeit indirectly) with COSMO-RS, a thermodynamic model. The computation speed for the calculation of β or π* (from virtual tautomerisations) is a few seconds. Computational kinetics and equilibria studies are often successful in obtaining the right order of a series of rate constants or equilibrium constants, but the absolute values are harder to obtain without referencing experimental data. The KAT parameters operate on a normalised scale that automatically corrects this systematic error without having to normalise each case study individually.
Three virtual equilibria were calculated in COSMOtherm to show this limitation. This information is in the supplementary spreadsheet. The isomerisation of 3-benzoyl camphor (case study 3), 33 2-isopropyl-5-methoxy-1,3-dioxane (case study 4), 33 and the energy difference between the rotomers of chloroacetaldehyde (case study 5), 33 show reasonable proportionality between virtual experiments and reality. However, as is true of the tautomerisation of methyl acetoacetate and dimedone, the correlation is strong but not necessarily in absolute terms. This is resolved when calculated KAT parameters are used. When directly modelling the reaction equilibrium of more complex systems (case study 1 and 2), the results had no similarity to experiment. This is in contrast to the successful free energy relationship approach using KAT parameters. 5

2-(3-Oxo-1,3-diphenyl-propyl)-malonic acid dimethyl ester (4).
Dimethyl malonate (3, 1.2 mmol, 0.156 g) and trans-chalcone (1 mmol, 0.208 g) were dissolved in the chosen solvent (5 mL), potassium phosphate (0.17 mmol) added, and the resulting suspension stirred at room temperature for 24 hours. Samples were taken at 15, 30, 45, 60, 120 and 240 minutes, and finally at 24 hours. Analysis was performed with a Hewlett-Packard 6890 series gas chromatograph using a flame ionisation detector and a ZB-HT5 fused silica column (30 m x 0.25 mm x 0.25 μm). The inlet was set at a temperature of 300 °C with a split ratio of 60, and an initial oven temperature of 50 °C before ramping at 30 °C min -1 to 300 °C, which was then held for 5 minutes. The total run time for each sample was 13 minutes 20 seconds. Kinetic profiles were created using the integrated second order rate law as explained by Wells Where: [3] = initial concentration of first reactant; x = initial concentration of second reactant; [4] = concentration of product.
Isolation of the product was only undertaken for the purpose of characterisation to verify the intended reaction had occurred. To do so, the base was removed by filtration, washed with acetone and the combined organic phase concentrated in vacuo to give 2-(3-oxo-1,3-diphenyl-propyl)-malonic acid dimethyl ester as a white powder. Analysis was consistent with the literature. 42

Michael addition free energy relationship.
A multivariate regression analysis was conducted to establish the relationship between ln(k) and solvent polarity using the values in Table S6. P-values were used to discard variables that were not statistically relevant (namely α and π*, the addition of which did not improve the correlation). The resulting empirical linear solvation energy relationship is shown as equation 4, and the values of ln(k) when solving the equation with experimental and calculated values of β and Vm are given in Table S7

Solubility study.
The tetrahydropyridine 5 was determined to have Hansen solubility parameters of δD = 20.4 MPa ½ , δP = 10.0 MPa ½ , δH = 4.6 MPa ½ . In theory solvents with similar Hansen solubility parameters will dissolve this substrate, and dissimilar solvents will not. The boundary between solvents and non-solvents can be plotted as the radius of a sphere centred on the solute within the three dimensions defined by the Hansen solubility parameters. The radius (Ra) can only be determined experimentally, and was found to be 9.9 MPa ½ . For this study a soluble system was defined as a 0.5 M solution. In some cases a suspension occurred, in which case the solvent was designated as a poor solvent for the purpose of calculating the Hansen sphere. In Table S8 the test solvents for the solubility study are listed in order of increasing 'relative energy difference' (RED), defined as the vector between solute and solvent in Hansen space divided by Ra. Thus a solvent with a RED equal or less than 1 theoretically should dissolve the substrate. As an empirical theorem the definition of the Hansen sphere is not precise, and there are 4 solvents at the sphere boundary wrongly in or out of the sphere. One solvent is a clear outlier, that being 2-MeTHF. These contradictions are marked with an asterisk in Table S8. The solvents for this solubility study were chosen for their diversity in order to obtain a strong fit for the Hansen sphere. Tetrahydropyridine synthesis free energy relationship.
Following the same principle as for the previous Michael addition case study, a free energy relationship was constructed to correlate reaction productivity with the KAT parameters. A free energy relationship was arrived at in the usual manner using the data in Table S9 (equation 7, not using data for levoglucosanol), which can then be used to predict yields (Table S10). The calculated π* value of levoglucosanol was obtained from the virtual tautomerisation of methyl acetoacetate (ln(K) = 8.29, normalised to 0.16). The free energy relationship in equation 7 was replicated using uncorrected (equation 8) and corrected (equation 9) values of π* to form the correlation instead of experimental values of π* (also without levoglucosanol). The proportionality between ln(K') and π* is retained.

6,8-Dioxabicyclo[3.2.1]octan-4-ol (levoglucosanol).
To a solution of sodium borohydride (3.63 g, 96 mmol) in water (40 mL) in an ice bath was added dihydrolevoglucosenone (7.57 g, 60 mmol) dropwise. The mixture was stirred overnight, and allowed to warm to the ambient temperature. Then chloroform (3 x 50 mL) was added and separated, and the combined organic extracts combined, dried with magnesium sulphate, and concentrated in vacuo to give 6,  44 The product consists of diastereoisomers in an approximate 6:1 molar ratio favouring the endo-diastereomer ( Figure S11).