2.1 Synthesis of N-substituted tropinone and granatanone derivatives

The higher N-alkyl analogues of tropinone 1 and granatanone 2 were prepared via an adapted two-step literature procedure [46], except for the N-benzyl derivatives (Scheme 1).

Tropinone and granatanone were N-methylated with methyl iodide to yield the corresponding quaternary salts. The quaternary salts were reacted with appropriate primary amines in an ethanol–water mixture. In most cases, fair or good overall yields of the desired products were obtained (30–82%). For the tert-butyl derivatives, incomplete reactions and low yields as well as problems with purification were encountered. Granatanone tert-butyl derivative 2c was obtained in 6% yield and satisfactory purity by PTLC. The reaction medium for N-tert-butylnortropinone (1c) had to be changed to DMSO, to obtain the product in acceptable yield (14%). N-benzyl derivatives 1e and 2e were conveniently obtained (75 and 77% yield, respectively) via Robinson–Schopf synthesis according to a previously published procedure [47]. The amine hydrochlorides for the spectroscopic studies were prepared from the amino ketones by vacuum evaporation with excess hydrochloric acid followed by drying. With the compounds in hand, we performed the experimental study of the N-invertomer equilibriums in solution.

2.2 Theoretical study of N-invertomer distributions

In this study, we chose a DFT functional with two basis sets and CPCM [48,49] to model solvent effects. The density functional calculations at the B3LYP/6-31G(d) level are not computationally demanding and are popular with organic chemists. The results from calculations at this level of theory have proven to be useful in the exploration of organic mechanisms and equilibrium states in both the gas and liquid phases [50–53]. This method also displayed excellent performance for aldol reactions of bicyclical amino ketones [22]. Therefore, this basic set was employed as the basis set of choice. In addition, reportedly a more accurate but much more computationally demanding B3LYP/6-311++G(3d,3p) level of theory was included for comparison for these particular structures. This basis set was chosen due to the satisfactory results obtained for the investigation of the N-methyl invertomer distributions for tropanes and granatanes [40]. All of the electronic structure calculations were performed using the GAUSSIAN 09 suite of programs. The equilibrium constant K (representing N-invertomer ratio) was calculated with the formula:

For comparison, distributions in the gas phase were also calculated at the same levels of theory and temperatures as for solution calculations. The calculated relative free energies, obtained from the DFT calculations, together with corresponding ratios of the equatorial to axial forms (Fig. 1) are listed in Table 1 (gas phase), Table 2 (water), and Table 3 (methanol). For comparison, Tables 2 and 3 contain also experimental data obtained directly from NMR spectra (vide infra).

In the gas phase (Table 1), a general dominance of the equatorial forms for the tropane analogues (with the exception of N-isopropyl and N-phenyl) and the axial forms for the granatane analogues was observed. The gas phase calculations also indicated a shift to a higher content of equatorial forms upon protonation of the nitrogen atom in tropanes. In the granatanes, a shift to the axial form was observed. To verify the reliability of the chosen computational methods, a direct comparison with experiment is needed.

2.3 NMR study of N-invertomer distributions

We used a proven approach used by Sturm [26] and by us [40] for the N-methyl analogues based on integration of signals in inverse gated ¹³C NMR experiments. The ¹³C NMR spectra of some of the free amines 1 and 2 in methanol at –90 °C and many amines 1 and 2 hydrochlorides in water at room temperature exhibited separate signals for both N-invertomers (Tables 4 and 5). The basis for this phenomenon has been presented by Glaser et al. [55]. The separation of signals in ¹³C NMR spectra is a result of decreased rate of inversion on the nitrogen atom. Lowering temperature to ca.–100 °C [26] or protonation of the amine nitrogen atom slows down the inversion process enough to make the separate N-invertomers observable at the NMR time scale. The presence of excess acid increases the rate of exchange of hydrogens on amine nitrogen resulting often in sharper signals. Increasing the lifetimes of the two equilibrating invertomers enables the recording of spectra for two separate invertomers at the so-called NMR slow exchange limit (SEL) for isomer interconversion, e.g., at low temperature or for the protonated amine at room temperature. The separation of signals with decreasing temperature for the carbon atoms most sensitive to syn-γ effect is exemplified in Fig. 2. The syn-γ effect in tropanes is due to the relative shielding or de-shielding of carbon atoms C(2,4) and C(6,7) related to the axial or equatorial disposition of the N-alkyl group and associated position of the lone electron pair [26].

It should be remembered that signals (chemical shifts) at the NMR fast exchange limit (FEL) for interconversion (recorded at room temperature for free amines) correspond to a time-averaged structure. Therefore, the position of the time-averaged signal for a specific carbon of both invertomers recorded at room temperature is found within a shift range set by separated signals (shifts) of the same carbon recorded at lowered temperature. Because of technical limitations, not all signals of the carbons may be separated (peaks may be broadened if the effect is subtle). When the invertomer ratio is higher than the signal-to-noise ratio for the major invertomer, the minor invertomer may be undetected, which results in an apparent lack of signal separation for any atom. Using our previous experience [40], by analogy with the described syn-γ effect applied to tropanes by Sturm [26], and correlation spectroscopy, the split signals were assigned to the specific carbons of two N-invertomers. As previously observed for granatanone (2 R = Me) [40], tropanes 1b–d, 1f and all granatanes 2 exhibited no detectable splitting of signals at –90 °C (Table 4) or even at lower temperatures (up to solvent freezing, ca. –105 °C). However, the signals in the spectra of these compounds shifted slightly as the temperature decreased from room temperature to –90 °C. For these cases, we concluded that only one N-invertomer was observed within the detection limits of the experiments at low temperatures. The content of the major invertomers was estimated from the signal-to-noise ratio in the spectra (Table 3, the actual ratio of major/minor invertomers was equal or higher than the signal-to-noise ratio). For cases where no minor invertomer was visible, comparing the position of signals in the ¹³C NMR spectra of the invertomer observed at –90 °C with the positions of the corresponding signals at room temperature, which are the time-averaged signals for both invertomers (the axial and the equatorial), we could infer the relative position of the undetected, minor invertomer signals to the major signals (as upfield or downfield to the detected invertomer). This inference combined with the syn-γ effect shown in the predicted relative position of invertomer signals of C(2,4) and C(6,7/8) by a computational model enabled the assignment of the split signals’ chemical shifts to the axial or the equatorial form (the assignments are shown in Tables 4 and 5). According to the computational model, the ¹³C shifts were calculated using the DFT optimised geometry and the SCF GIAO method as implemented in GAUSSIAN 09.

The calculated shifts for the relevant atoms and the experimental shifts for the free amines are compared in Table 4. The relative position of the calculated and experimental signals could not be used for invertomer identification in two cases (1c and 1d). In these cases, the experimental and predicted shifts for C(6,7) did not follow the trend. Thus, the dominating invertomer was assumed to be the one predicted on the basis of the calculated equilibrium distributions. To sum up, using the observed NMR shifts at low temperature and at room temperature (Table 4) and the invertomer distributions obtained from DFT calculations (Table 3), we accept that all granatanes and tropanes 1b, 1d, and 1f, at low temperatures in methanol solution, exhibit dominating invertomers with the N-axial group, which is in contrast to tropanes 1a, 1c, and 1e.

The room-temperature NMR spectra of the hydrochlorides of amines 1 and 2 in water exhibited the separation of many signals into resonances corresponding to species with axial and equatorial N-substituents analogous to their N-methyl analogues [39]. We assigned the signals (Table 5) based on literature data [39], correlation spectroscopy, and correspondence to the spectra of free amines (Table 4). The results from the calculations and the shift predictions from SCF GIAO also supported the assignments in the protonated amines, except 1b•HCl, where one pair of signals did not follow the trend (Table 5). However, for some of the protonated forms, no separation of signals of C(2,4) and C(6,7/8) corresponding to the separate invertomers was observed (Table 5). In these cases, the assignment could not be verified by the relative shielding prediction and was based only on calculated invertomer dominance (Table 2). We can conclude that, at room temperature in water, the preferred isomer of protonated granatanes has the axial N-substituent, while for tropanes the opposite N-equatorial isomer is preferred.

The experimental relative ratio of isomers (Tables 2 and 3) was obtained by dividing peak areas of signals corresponding to the same carbon atom (typically the carbonyl) in both isomeric species in the inverse gated ¹³C NMR spectra. In cases where no minor invertomer was detected, the signal-to-noise ratio was used as an estimate of the minimum value of the major-to-minor isomer ratio.

2.4 Comparisons and discussion of the calculated and experimental distributions

The invertomer distributions in methanol and water observed in the inverse gated ¹³C NMR experiments are quantitatively compared with the distributions calculated by the computational methods (Tables 2 and 3). The accuracy of methods, such as B3LYP, is only moderate, and this functional is able to predict stereoselectivities with errors of less than 0.5 kcal/mol [56]. Variation in the results of this order would yield a variation in the invertomer distribution ratio on the order 2.3 at T = 298 K and ca. 4 at T = 183 K.

To obtain a quantitative estimate of the accuracy of the theoretical methods, the mean (average) absolute deviation (MAD) values are defined as:

are reported in Tables 2 and 3. In the above formula, n is the number of experimental results available, ratio_exp denotes the measured distribution, and ratio_calc represents the distribution calculated with a given computational method. Summation is extended over all the species for which the experimental distributions are available. Of course, a smaller MAD value indicates that the results from a given method agree more closely with the experimental data.

For the tert-butyl derivative 1c and its salt (Tables 2 and 3), the signals from the minor invertomers were too weak to observe by ¹³C NMR spectroscopy under the experimental conditions used. The relative amounts of N-invertomers were estimated from the signal-to-noise ratio for the major invertomers. The S/N was limited by the experimental time and solubility. Therefore, the experimental ratio of invertomers for the nortropinone tert-butyl derivatives was estimated as greater than 22.5 for 1c and greater than 43.6 for 1c•HCl. A comparison of these experimental data with those obtained from the calculations resulted in a very high relative error and overstated MAD values. The exclusion of these uncertain cases would improve the MAD values for B3LYP/6-31g(d) and B3LYP/6-311++g(3d,3p) in Table 3 to 83 and 105, respectively, and in Table 2 to 58 and 91, respectively. This indicates a good overall agreement of the computational methods with experimental results and points towards the simpler basis set as better choice for this type of problem.

The calculated ratio of equatorial/axial isomers for the tert-butyl nortropane derivative 1c in methanol at –90 °C reached the very high value of ca. 300 for the free amine and more than 50,000 for the protonated one; this stems from the calculated difference in the free energy of invertomers (ΔG of equatorial to axial inversion) ca. 2.1 and 4 kcal/mol for the free and the protonated forms, respectively (Table 3). This high invertomer ratios stand out from the other results; however, considering the commonly accepted A values [57,58] for the tert-butyl substituent (4.9 kcal/mol [59]) and the expected preference of the substituent in the tropane system, this is a reasonable result [60]. The lower free energy of inversion for derivatives with the bulky isopropyl and the benzyl group can be rationalized by their axial form attaining the lowest energy conformations in which the C–H bond is positioned between the pseudoaxial hydrogens of the C(4) and C(2) carbons of the tropane system (Fig. 3a and b). In case of the tert-butyl group, which has no such C–H bond but a C–CH₃ group instead (Fig. 3c), much higher destabilising interactions in the axial N-invertomer are expected. The differences between the tert-butyl, and isopropyl and ethyl groups observed experimentally and calculated for the tropane system are less than the corresponding A values (ΔG° 4.9, 2.1, 1.8 kcal/mol, respectively [57,58]). This can be rationalized based on the flattening of the piperidone ring, compared to the cyclohexanone for which the A values are given, and the resulting diminished interactions with pseudoaxial hydrogens at C(2) and C(4). The flat phenyl substituent may adopt the lowest energy conformation with lessened steric interactions with the piperidone ring (Fig. 3d) favouring also the axial invertomer of the free amine (entry 7 in Tables 1, 2 and 3). In granatane derivatives, the interactions within the piperidine ring (equatorial N-substituent) are expected to be stronger than within the flattened piperidone ring (axial N-substituent). This accounts for reversed invertomer preferences in the granatane series; both free amines and protonated amine favoured the axial invertomers (Tables 1, 2 and 3).

The calculated invertomer ratios for free amines (Table 3) agreed qualitatively and reasonably well quantitatively with the experimental values. Experiments and calculations provided complementary data indicating that in methanol and water the free amine equatorial isomers dominated in the N-benzylnortropinone and especially in the N-tert-butylnortropinone. The axial forms dominated in the remaining tropanones, except 1a (N-ethyl) and all of the norgranatanone derivatives. The experimental results for protonated amines in water (HCl salts) were also qualitatively and fairly quantitatively reproduced by the calculations (Table 2). Both basis sets yielded a fairly good level of accuracy for reproducing the experimental results for free and protonated amines (Tables 2 and 3) with slightly lower MAD values for the 6-31G(d). Therefore, based on the much lower computational demands of the 6-31G(d) basis set, this level of theory is recommended for this type of problem. It can also be inferred, from both experiments and calculations, that the protonation of nitrogen in the nortropinone derivatives shifts the equilibrium toward the equatorial N-invertomers. Especially striking was the reversal of the dominant configuration of the N-isopropyl and N-phenyl groups of tropanones (e.g., for Ph from 0.29 to 12.3, experiment for 1d, entry 7, Table 3 versus entry 8, Table 2). According to experiment, the invertomer distributions in the norgranatanone derivatives appeared to be affected in the same way by protonation, but the axial forms remained dominant. According to both levels of theory, protonation in the granatane analogues shifted the invertomer equilibriums to some degree, and the direction of this shift was dependent on the N-substituent and temperature. In addition, in some cases, the predicted direction of the equilibriums shifts differed based on the basis set used. The protonation effect in the computed equilibriums in the granatanone series were within the errors of the method and as such could be regarded as inconclusive. However, the axial preference of the N-substituents in the protonated granatanones was clear. The found N-invertomers preference for the granatanes and for isopropyl and phenyl tropane derivatives agrees qualitatively with previous works [24,25,40]. For the rest of tropanes, e.g. benzyl derivative 1e, the differences with previous reports may be accounted for by the different solvents used (methanol and water in this study vs. CDCl₃ [23]). The calculations, despite the known limited accuracy of the DFT methods, ca. 0.5 kcal/mol [56], and the relatively simple methodology commonly used by organic chemists (using comparisons of the lowest energy conformations and the B3LYP with moderate basis set) gave fairly good overall agreement with experiments.

4.1 General methods

Magnetic resonance spectra were recorded on a Bruker AVANCE II 400 spectrometer using 5-mm probes, operating at 400 MHz for ¹H and 100 MHz for ¹³C. The chemical shifts are reported in ppm downfield of tetramethylsilane. The chemical shifts were determined relative to residual CD₂HOD (¹H δ 3.31) and internal CD₃OD (¹³C δ 49.0) as secondary references for the methanol-d₄ solutions and relative to DSS (¹H and ¹³C δ 0.0) for the aqueous solutions. For low-temperature measurements, the temperatures of the probe were calibrated with methanol. No-D NMR spectroscopy [45] was used for experiments in non-deuterated solvents (i.e., H₂O, CH₃OH). In this case, the spectra were recorded using shimming of the FID signal. Quantification of the ¹³C signals was achieved using inverse gated mode spectra. When required, the analysis and assignment of the ¹H and ¹³C NMR data were supported by homonuclear (COSY) and heteronuclear (HSQC and HMBC) correlation experiments.

4.2 General procedure for the synthesis of N-substituted tropanones 1 and granatanones 2

Step 1. Tropinone (1, R = Me) or granatanone (2, R = Me) (5.00 mmol, 1.00 equiv) was dissolved in acetone (5 mL). Methyl iodine (5.50 mmol, 1.10 equiv) was added dropwise over 45 min, and the reaction was stirred at room temperature for 1 h. The methiodide precipitate was filtered, washed with acetone and hexane and dried over P₂O₅ [46].