Isomers of Alkali Metal (Methylbenzyl)allylamides: A Theoretical Perspective.

Recent studies of alkali metal N-(α-methylbenzyl)allylamides containing lithium, sodium, and potassium have shown unique rearrangements in NMR experiments. It was found that lithium isomers favored the formation of aza-allyl and aza-enolate complexes that could exist in a solution for a substantial amount of time. As the radius of the metal ion increases going from lithium to potassium, so does the preference for the formation of the imine structure. For sodium, the aza-allyl complex could still be isolated, whereas the imine structure was only found to be stable on the scale of several hours for potassium. In this work, ab initio calculations were used to shed light on this phenomenon. Decomposition of intermolecular interaction energies of the aza-allyl, aza-enolate, and imine complexes showed that for lithium, the formation of aza-allyl and aza-enolate complexes was driven by electrostatic interactions. For potassium, the dispersion component of the metal interaction with the ligand proved to be more important for the stability of the imine structure. The presence of the imine formation in potassium and partially in sodium was found to be due to the reduced electrostatic nature of these larger metals. The assignment of the experimental NMR spectra was further confirmed with the natural bond order (NBO) analysis as well as the partial charge calculations. Analysis of orbital energies, specifically those of the highest occupied molecular orbitals (HOMOs), as well as the deformation energies of each of the ligands, were also considered. Through these procedures, an understanding of the tendency for each metal to have a unique isomerization pathway was gained.

Introduction

Asymmetric synthesis using alkali metal complexes is an important and widely researched area.[1−5] Reaction pathways often depend on the alkali metal, with the metal identity having a significant impact on their thermodynamics. Understanding how alkali metals interact with organic molecules is crucial to their application as reagents and catalysts in synthesis. This can be seen in such cases as the deprotonation of arene, aromatic heterocyclic metallocene, and metal π-arene substrates (Scheme ).[6]

Scheme 1

Chemical Pathways of Rearrangements of Sodium and Potassium (S)-N-(α-Methylbenzyl)methallylamide

In the course of our research of unsaturated alkali metal amides, the persistent occurrence of sigmatropic rearrangements (often accompanied by decomposition pathways and frequently with a loss of chirality where present) has sparked our interest.[7−12] In particular, the structural chemistry and the driving forces behind these rearranged products have not been well understood.

Anionic sigmatropic rearrangements have been the subject of extensive research,[13] with examples in the anionic oxy-Cope rearrangement[14] and more recently, the anionic amino-Cope rearrangement,[15] both of which display remarkable rate acceleration when compared to the thermally driven rearrangements of the neutral compounds.

The initial report of the anionic oxy-Cope rearrangement found that ion-pair separation promoted the accelerating effect.[14] Similarly, the initial report of the anionic amino-Cope rearrangement found that some of the amino dienes used required the use of a n-BuLi/t-BuOK mixture to facilitate rearrangement, as n-BuLi alone gave alternative or no reactivity.[15] The same group found interesting solvent effects on the rearrangements: the use of higher polarity solvents correlated with higher yields, but regioselectivity was dramatically affected.[16] Most recently, it was found that the use of potassium as the counter ion in the anionic rearrangements of sulfonamide-based amino-Cope substrates was detrimental when compared with lithium or sodium.[17] It was suggested that this is due to potassium promoting dissociation of the molecule formed. These examples demonstrate the need to better understand how the interactions between an organic anion and alkali metal cation affect the propensity for sigmatropic rearrangements to occur.

Our own work has found that separation of the ion pair in unsaturated alkali metal amides promotes a series of sigmatropic rearrangements, ultimately leading to an aza-enolate structure in the most separated ion pairs.[7] The substrates used are also substructures of some of the dienes used for amino-Cope rearrangements,[18] so any rearrangement to an aza-allyl or aza-enolate structure will clearly impact the outcome of these reactions.

It has been previously established that there exists a relationship among the size of the metal counter ion used, the density of the Lewis donor used, and the facility of the occurrence of rearrangements. A predictable trend was established, in which N,N,N′,N″,N″-pentamethyldiethylenetriamine (PMDETA), which is a tridentate donor, induces a rearrangement to the aza-enolate isomer in all complexes, regardless of the metal used. The use of N,N,N′,N′-tetramethylethylenediamine (TMEDA), a bidentate donor, with lithium or sodium tends to cause rearrangement to the aza-allyl form, while the use of tetrahydrofuran (THF), a monodentate donor, depends heavily upon the metal identity, as well as the amount of THF used (multiple equivalents of THF can act as a pseudo-polydentate donor). Until recently, all of the potassium complexes studied rearranged to the aza-enolate form regardless of the Lewis donor used; however, the discovery of another intermediate anion form on the route to aza-enolate formation[19] has prompted us to take a closer look at the effect of metal–anion interaction.

The purpose of this study was to analyze the thermodynamic stability of all possible isomers of alkali metal N-(α-methylbenzyl)methallylamides and gain insight into the reason for why potassium is able to undergo an additional isomerization to form an imine complex. This was achieved using quantum chemical methods to calculate Gibbs free energies of formation of four main isomerization products including allyl-amide, aza-allyl, aza-enolate, and imine isomers shown in Chart . Both the structural and energetic factors were analyzed to provide the theoretical underpinning for the unusual difference among lithium, sodium, and potassium metals. It is assumed that the bond between an alkaline metal ion and isomers of N-(α-methylbenzyl)methallylamides is ionic; our previous study identified that in inorganic salts containing either a lithium or a sodium cation, the process of charge transfer between the inorganic anion and the metal ion took place, thus making the metal–anion bond partially covalent.[20] The covalency factor was especially pronounced in the case of lithium and strongly depended on the anion type. In this study, the interaction energy between the metal ion and isomers of N-(α-methylbenzyl)methallylamides was calculated and decomposed into electrostatic and dispersion components. In addition to explaining the trends found in the previously measured NMR spectra for sodium and potassium complexes,[19] new NMR spectra for lithium isomers were produced from a precursor of (S)-α-methylbenzylamine added to a 1:1 mixture of n-BuLi and PMDETA or TMEDA in hexane to complete the analysis of the effect of the alkali metal nature on isomerization.

Chart 1

Structures Studied Based on the N-(α-Methylbenzyl)methallylamide Ligand

Theoretical Procedures

All geometry optimizations were performed using the Gaussian09 quantum chemical package.[21] The hybrid meta-GGA functional of density functional theory (DFT), M06-2X,[22] was used for geometry optimizations in combination with Dunning’s double-ζ basis set, cc-pVDZ.[23] To simulate the THF solvent used experimentally, the conductor-like polarizable continuum model (CPCM) was applied to implicitly emulate its bulk behavior.[24,25] All structures were subjected to a full conformational search, wherein sp2 and sp3 hybridized groups were rotated by 180 and 120°, respectively. For each metal complex as well as for the ligand on its own, conformers within 10 kJ mol–1 were used for further analysis. Improved electronic energies were calculated at the M06-2X/aug-cc-pVTZ level of theory coupled with the CPCM solvent model and THF as solvent.

Gibbs free energies of the most stable conformers determined from single-point energy calculations were calculated using the standard physical chemistry formulae, as shown in eq .[26,27]where E is the electronic energy, ZPVE refers to the zero-point vibrational energy, TC is the thermal correction, T is the temperature, and S is the entropy calculated based on the harmonic oscillator and rigid rotor approximations. Both TC and S components were calculated using the in-house thermochemistry code.[28,29] Room temperature was used in all calculations.

Partial atomic charges for the lowest-energy conformers of each isomer in Chart were calculated using the Geodesic scheme,[30] as implemented in the GAMESS-US software package.[31,32] The net charge transfer from the alkali metal to the ligand was also estimated.

Interaction energies between the metal ion and the ligand were calculated, as shown in eq . The spin ratio scaled Møller–Plesset second-order perturbation theory (SRS-MP2)[33]/cc-pVTZ[23] method was used in these calculations. For potassium, Ahlrichs’ TZV basis set was applied.[34] SRS-MP2 has been shown to be accurate for a wide variety of interactions and thus can be easily applied in these systems.[35] The HF component of interaction energy was corrected for basis set superposition error using the Boys and Bernardi counterpoise correction.[36]For the decomposition of interaction energy, the HF component of interaction energy was used to estimate the electrostatic contribution in the system, whereas the SRS-MP2 electron correlation component was used to calculate the dispersion contribution. In SRS-MP2 calculations, it was necessary to include the inner shell electrons for each of the alkali metals to ensure all interaction energy was accounted for. In this case, the 1s2 orbital for lithium, the 1s22s22p6 orbitals for sodium, and the 1s22s22p63s23p6 orbitals for potassium were all calculated. Our previous studies established the involvement of these core electrons in bonding with negatively charged ligands due to increased polarization by the latter.[20] Deformation energies were calculated by comparing the SRS-MP2/cc-pVTZ energy of the ligand in each of its four states indicated in Chart optimized in the presence of the metal with the ligand optimized on its own as an anion.

Results and Discussion

To determine the stability of the mono-lithio complexes with different density donors, we attempted the synthesis of these compounds to allow for a comparison with the sodium and potassium complexes. Addition of (S)-N-(α-methylbenzyl)methallylamine to a 1:1 mixture of n-BuLi and PMDETA or TMEDA in hexane yielded a yellow oil, which was washed with hexane and dried under vacuum to produce a yellow solid. Typically, complexes supported by PMDETA are more susceptible to full rearrangement and TMEDA can sustain intermediates for a longer duration, thus providing information as to which isomers can be stable and also which is the most stable overall.

The 1H and 13C NMR spectra of the PMDETA-coordinated complex i share characteristic features of the aza-enolate structure with those seen in previously reported examples.[7,10,19,37] In particular, the disappearance of the distinctive quartet and doublet in the 1H NMR spectra corresponding to the α-methylbenzyl moiety and appearance of a pair of signals at 3.81 and 3.44 ppm show that a rearrangement to the aza-enolate form has occurred (see Figure ).

Figure 1

NMR spectra of potassium compounds in d8-THF (top), TMEDA-complexed lithium compound in d6-benzene (middle), and PMDETA-complexed lithium compound in d6-benzene (bottom), all samples were tested 5 days after dissolution.

The NMR spectrum of the lithium TMEDA complex ii showed almost exclusively the aza-allyl form. This structure is, again, analogous to the aza-allyl structures observed previously with lithium and sodium.[19,37−39] The rearrangement was confirmed by the disappearance of the methylene and terminal alkenyl protons, at 2.94 and 4.83 and 4.97 ppm, respectively. These were replaced by the signals of the terminal methyl groups at 1.96 and 1.85 ppm and an alkenyl signal from the remaining proton adjacent to the nitrogen atom at 6.59 ppm (see Figure ).

Samples of the lithium complexes in both PMDETA and TMEDA contained significant quantities of the starting material due to incomplete metallation, likely resulting from competing dilithiation of the amine. It appears that precomplexation of the lithium source to the Lewis donor (i.e., formation of n-BuLi·PMDETA or n-BuLi·TMEDA) is necessary to achieve monometallated complexes. Addition of the reagents in a different order results in dilithiation of the amine or the formation of a complicated and intractable reaction mixture. The formation of complexes i and ii in the presence of PMDETA and TMEDA, respectively, is in agreement with our previous studies on these systems.[7] No evidence for the formation of the imine-type structure was found.

In contrast, the NMR spectrum of the potassium complex in d8-THF showed the presence of many isomers simultaneously for extended periods of time; a sample left for 5 days continued to show a mixture of the aza-enolate, aza-allyl, and imine isomers in a 7:12:10 ratio (see Figure ). This indicates that there must be a relatively small energy barrier between all three isomers and the ability to move between them for a considerable amount of time, before shifting to the most stable aza-enolate product, as observed in previous studies for the potassium complexes. The imine complex is not observed when the potassium product is complexed with TMEDA or PMDETA (these instead yield the aza-enolate complex, as shown in Scheme ), nor has it been observed when using sodium under any conditions.

Scheme 2

Chemical Pathways of Rearrangements of Lithium (S)-N-α-(Methylbenzyl)methallylamide

To this end, the potassium ion was the only metal ion that could produce three isomers, aza-allyl, aza-enolate, and imine, and have these remain stable for several weeks, slowly converting to aza-enolate over time. For the lithium ion, the preference for the formation of either aza-enolate or aza-allyl depended on the chelating agent that was used due to high reactivity of the cation. In the case of the sodium ion, the formation of aza-enolate and aza-allyl depended on the type of solvent used, with aza-enolate being formed in the course of several weeks regardless of the solvent used. Imine was not detected in either lithium or sodium.

These NMR results gave a starting point to search for structures to test computationally to try to identify the stability of each metal–ligand complex and why it is that each metal gives such different NMR spectra.

Initially, the conformational search of all possible conformations showed a large variety among different conformers. An average of 16 conformations was tested for each structural isomer, with between three and seven conformers falling within 10 kJ mol–1 of each other. Analysis of the lowest-energy conformers revealed no notable changes between metals with similar ligand–metal interaction sites present, other than the expected difference in bond length caused by the increasing van der Waals radius on the alkali metal ion (see Figure ). This finding indicates that the difference in the thermodynamic stability of the isomers is likely to originate from energetic factors.

Figure 2

Lowest-energy conformation for potassium isomers.

Although visually the isomers were found to be quite similar among the three alkali metal ions, a thorough analysis shows that the bond distances between the metal atom and the closest carbon and nitrogen atoms change significantly (see Table ). As expected, with increasing atomic radius on the metal ion, the distance between the metal and closest atom increases from 1.94 Å on average for Li to 2.73 Å on average for K. For each alkali metal, the M–N bond (where M is Li, Na, and K) does not vary between the four isomers, with only a slight increase of 0.1 Å being observed for the imine. In each complex, the short M–N distance is accompanied by a longer M–C1 bond (see Chart ), approximately by 0.9 Å regardless of the alkali metal, except for the imine isomer shown in Chart . For the latter, the M–C1 distance is only 0.4 Å longer than the M–N bond distance for Li and Na and as little as 0.2 Å in the case of K. This indicates that the larger sized potassium cation forms bonds with both the carbon and nitrogen atoms simultaneously (see Figure ). A short N–C1 bond between the nitrogen and carbon atoms sharing the metal ion in the imine isomer is also indicative of the π conjugation in the imine.

Table 1

Bond Distances of the Metal Ion (M) from the Closest Carbon and Nitrogen for Each Isomer and Corresponding Sums of Covalent Radii Calculated Using ref (41)

metal	isomer	M–N bond length (Å)	M–C1 bond length (Å)
Li	allyl-amide	1.884	2.935
Li	aza-allyl	1.923	2.952
Li	imine	2.020	2.454
Li	aza-enolate	1.946	2.799
Li	covalent radii	1.990	2.010–2.040
Na	allyl-amide	2.235	3.161
Na	aza-allyl	2.266	3.202
Na	imine	2.406	2.786
Na	aza-enolate	2.295	3.163
Na	covalent radii	2.370	2.390–2.420
K	ally-amide	2.673	3.392
K	aza-allyl	2.703	3.745
K	Iimine	2.816	3.004
K	aza-enolate	2.713	3.512
K	covalent radii	2.740	2.760–2.790

Figure 3

Optimized structure of the potassium imine isomer. Bond lengths between potassium and closest ligand atoms are shown.

To determine whether the metal ion–ligand bonding is covalent in nature or the product of long-range dispersion interactions, the covalent radius concept was considered. Covalent radii of alkali metals were taken from a study by Cordero et al.,[40] in which the first 96 atoms of the periodic table were analyzed using crystal structures from the Cambridge Structural Database (CSD) to determine maximum lengths of covalent bonds for all two-atom combinations. The lengths of these covalent bonds were then fitted by summing covalent radii of corresponding atoms to best predict the measured covalent bonds, thus giving realistic estimates of the covalent radius for each atom. In this work, the covalent radii of Li, Na, and K were used to estimate the nature of their bonding in the studied isomers. The sums of covalent radii for both M–C1 and M–N bonds are given in Table . In all of the isomers except for imines, the M–N bond was found to be inside the sum of the covalent radii, indicating that these might be covalent bonds, whereas the M–C1 bond is placed outside the range. In the case of the imine isomer, the M–N bond was also found to be outside the distance for all three alkali metals. However, it should be noted that in the study on covalent radii,[40] the covalent radius of potassium had a relatively high standard deviation of 0.13 Å, thus suggesting that the K–N bond in the imine may also have some covalent nature. In the cases of lithium and sodium complexes, further clarification is necessary to confirm that the M–N bond is covalent in nature. This is achieved with partial atomic charge calculations discussed further in the text.

The allyl-amide isomer is known to be the least thermodynamically favorable product. Therefore, the relative Gibbs free energies of the possible isomers with respect to the initial isomer, allyl-amide, are shown in Figure . There is a striking difference in thermodynamic stabilities of the sodium and potassium ions, with the former having clear energetic differences among the isomers. In all metal ions proceeding the allyl-amide, the imine isomer was the least thermodynamically stable complex. It has to be noted that the horizontal lines in Figure represent thermodynamically stable isomers, with the dashed lines not representing activation barriers between isomers. Due to the predominantly ionic bonding between metal ions and ligands, the location of transition states connecting the possible isomers was not possible. It has to be noted that the DFT functional selected in this study, M06-2X, in combination with aug-cc-pVTZ produces average errors between 2 and 36 kJ mol–1 for the well-known databases of noncovalent interactions.[41] It is well accepted that DFT functionals of the meta-GGA type have a systematic error of at least 10 kJ mol–1. Therefore, any variation in Gibbs free energies of the alkali complexes studied here within this systematic error must be considered to have similar stability.

Figure 4

Gibbs free energies (ΔG, kJ mol–1) of isomerization reactions involving lithium, sodium, and potassium metals relative to the allyl-amide structure.

The aza-enolate is by far the most thermodynamically stable isomer in the case of the sodium ion. The aza-allyl isomer is 33.8 kJ mol–1 less stable, whereas the imine is 56.9 kJ mol–1 less stable. The trend is different for the potassium ion. The aza-enolate isomer was also found to be the most thermodynamically stable, with two other isomers exhibiting a similar thermodynamic stability. The aza-enolate is more stable than the imine by as little as 12.5 kJ mol–1. Due to the presence of the systematic error in the level of theory used, this difference can be as little as 2.5 kJ mol–1, making the two isomers energetically indistinguishable. This indicates that the potassium imine can be formed. Aza-enolate was found to be the most stable isomer, and this finding is in agreement with prior experimental data[37] that the imine isomer could be detected in the early stages of the synthesis in the presence of potassium, slowly converting to the aza-enolate. For lithium, the imine isomer was the second least stable by 23.9 kJ mol–1, again favoring the formation of aza-allyl and aza-enolate. The difference in their Gibbs free energy was found to be as little as 0.3 kJ mol–1. This indicates that both isomers can be easily accessed at room temperature, as seen in the NMR results in Figure . In the previous study, it was identified that the chelating agent could tip the balance toward one of the isomers.[42] In the current study, we experimentally demonstrated above that a tridentate such as PMDETA favored the formation of aza-enolate, whereas a two-dentate ligand such as TMEDA gave the aza-allyl.

Partial atomic charges showed that as the metal ion size increased from lithium to potassium, so did the positive charge on the ion, thus indicating that the net charge transfer from the ligand to the metal decreased. Therefore, the larger metals (sodium and potassium) donate a smaller portion of their valence electrons to the ligand, causing them to be more cationic (see Table ). Charge transfer can be considered as an indication of covalency of a given bond, with increased charge transfer leading to increased covalency. Of the four possible isomers, imine showed the least positive charge on the metal ion, suggesting that this isomer undergoes the largest net charge transfer from the metal to the nitrogen and carbon atoms involved in the bonding, thus increasing the degree of covalency. This finding is rather surprising considering that the imine isomer is the least stable for all ions. The lithium atom showed a net charge transfer of >0.27e in all four isomers, which corresponds to the highest degree of covalency, as was also demonstrated by our group for a series of lithium salts.[20] The partial charges on the nitrogen center for the allyl-amide, aza-allyl, aza-enolate, and imine are reflected by corresponding net charge-transfer values, with the charge becoming less negative with increasing charge transfer. For all three metal ions, the variation in charge transfer among the four possible products is as small as 0.09e, thus highlighting the fact that charge transfer is not responsible for differences in the stability of the isomers studied. The net charge-transfer values in the imine isomer do not follow the M–N distances discussed above, with the largest net charge transfer resulting in the longest M–N bond in the case of potassium. The analysis of highest occupied molecular orbitals (HOMOs) of the four isomers further confirms the presence of charge transfer as an appreciable amount of the ligand electron density is delocalized in the area of the metal–ligand bond (Figure ).

Table 2

Geodesic Atomic Charges (q, e) on Alkali Metal Ions (M) and the Nitrogen Atom for Each Isomer

M	structural isomer	q(M)	q(N)
Li	allyl-amide	0.73	–0.89
Li	aza-allyl	0.69	–0.84
Li	imine	0.58	–0.25
Li	aza-enolate	0.63	–0.58
Na	allyl-amide	0.79	–0.85
Na	aza-allyl	0.77	–0.82
Na	imine	0.70	–0.25
Na	aza-enolate	0.77	–0.89
K	allyl-amide	0.82	–0.87
K	aza-allyl	0.85	–0.91
K	imine	0.79	–0.39
K	aza-enolate	0.82	–0.88

Figure 5

HOMOs for each isomer with potassium: (i) allyl-amide, (ii) aza-allyl, (iii) aza-enolate, and (iv) imine.

The imine isomer represents an outlier as the charge on the nitrogen is not as negative falling in the range of −0.25 to −0.39e. The analysis of the partial charge on the adjacent benzylic carbon atom indicates that this atom is positively charged within the error of calculations in all isomers, including imines. This causes the M–N bond to lengthen as the metal ion is forced to keep away from the positively charge carbon. Therefore, the imine isomer can potentially be formed for alkali metals that have small net charge transfer with the ligand and therefore are more mobile to hop between interaction sites on the ligand.

The natural bond order (NBO) and molecular orbital analyses were performed to study the bond type of each covalent bond present in the ligand according to Figure . It is not surprising that the metal–nitrogen bond is not assigned any bond type as it is clearly ionic in nature. The NBO analysis confirmed that in each structure a distinct double bond was present where it would be expected, as shown in Chart (for more details on the NBO data, see Table S6 in the Supporting Information).

It was clearly identified from HOMO energies of each isomer and metal ion presented in Table that of the four isomers, imine has the highest orbital energy regardless of the metal ion, thus making it the least electronically stable isomer. Apart from this finding, trends established in HOMO energies do not follow those of Gibbs free energy in Figure . Results of HOMO energies of the lithium isomers contradict experimental findings and Gibbs free-energy trends. The aza-enolate HOMO is only 0.17 eV less stable than that of the allyl-amide, whereas the HOMO of the aza-allyl is a further 0.45 eV higher in energy. These findings suggest that the formation of the aza-allyl isomer should be difficult, which goes against the experimental observation. Of the three metal ions, only sodium complexes follow experimental findings, with the aza-enolate complex not only having the lowest HOMO energy but also being separated from the next stable isomer, the allyl-amide, by 0.3 eV. For potassium, the relatively high HOMO energy of −4.40 eV of the imine isomer (0.4 eV higher than the next more stable isomer) indicates that it is less likely to be formed. Contrary to this, the trend in Gibbs free energy clearly showcases that the imine isomer can be formed. Orbital energies can be used with caution and must not be overanalyzed. Electron correlation effects, including charge transfer, are not directly included in orbital energies, even when calculated with DFT. Therefore, HOMO energies cannot be used as a reliable criterion to rank the thermodynamic stability of alkali metal complexes. The charge-transfer effect, in particular, appears to be important for these molecular systems, and hence their relative stability must be predicted with Gibbs free energy calculated using levels of theory that accurately account for electron correlation effects.

Table 3

HOMO Energy of Each Complex in eV Calculated with M06-2X aug-cc-pVTZ

structural isomer	Li	Na	K
allyl-amide	–5.73	–5.34	–5.06
aza-allyl	–5.11	–4.81	–4.79
imine	–4.69	–4.50	–4.40
aza-enolate	–5.56	–5.63	–5.03

To further elucidate the nature of the metal–ligand bond, interaction energies between the metal and the ligand were decomposed into electrostatic and dispersion components (see theoretical methodology). Overall, the interaction energies in metal alkali complexes are strong ranging from up to −1174 kJ mol–1 for lithium to −909 kJ mol–1 for potassium, shown in Figure . For each metal ion, there is a variation in the metal–ligand interaction strength among four isomers. In this case, it is seen that in all cases allyl-amide has the highest interaction energy, up to −1174 kJ mol–1 despite being the least stable isomer, largely due to its strong electrostatic interactions (making up >90% of interaction energy in all cases). The imine isomer is seen to be the weakest interacting isomer in all three metals, up to 125.7 kJ mol–1 lower than the allyl-amide complex, largely due to its reliance on the relatively weak dispersion energy. It is not surprising that the interaction strength decreases going from lithium to sodium and to potassium, with sodium interacting on average 167.9 kJ mol–1 less than lithium and potassium interacting on average 99.6 kJ mol–1 less than sodium—a significant decrease of >250 kJ mol–1 from lithium to potassium. As the metal-ion size increases, electrostatic energy decreases on average by 182.5 kJ mol–1 from lithium to sodium and 131.7 kJ mol–1 from sodium to potassium. Meanwhile, the dispersion component of interaction energy slightly increases on average by 14.6 kJ mol–1 from lithium to sodium and 32.0 kJ mol–1 from sodium to potassium. The latter in particular is a significant increase in dispersion energy, nearly doubling on going from sodium to potassium complexes. Lithium and sodium isomers are predominantly driven by electrostatic forces contributing 99 and 97%, respectively. Of the four possible isomers, the imine isomer has the largest contribution from dispersion forces for both ions: −40.0 kJ mol–1 for Li and −50.0 kJ mol–1 for Na. This is also manifested in shorter metal–ligand distances and increased net charge transfer, thus resulting in thermodynamically stable complexes that are less likely to undergo transition among isomers. This process will require the metal ion to be able to move further away from the ligand by 0.075–0.1 Å in two most stable isomers—aza-enolate and aza-allyl—to form the imine isomer. Given the strength of the metal–ligand bond in the lithium and sodium complexes, this is highly unlikely. For the potassium complexes, dispersion starts to contribute a non-negligible amount between 7.35% in aza-enolate and 9.22% in imine. Coupled with the least charge transfer and lowest electrostatic interaction energies among the alkali metal ions studied here, the potassium ion is likely to be the most mobile ion, thus resulting in a rather similar thermodynamic stability of the aza-allyl and imine isomers (see Figure ). Therefore, it is not surprising that all three isomers, aza-allyl, aza-enolate, and imine, could be detected experimentally. For the lithium complexes, the net charge transfer is largest in the aza-allyl and aza-enolate isomers. This suggests that when one isomer is formed it is highly unlikely that the lithium cation would allow for any further rearrangement to take place.

Figure 6

Dispersion and electrostatic interaction between an alkali metal and a ligand for different isomers.

It might be perceived contradictory that increased charge transfer does not lead to an increase in the dispersion component of interaction energy. Charge transfer is a consequence of the orbital overlap between interacting species due to bond shortening, which results in the exchange component of interaction energy becoming more positive and the electrostatic component much more negative. In our previous study, we demonstrated that an increase in charge transfer and hence covalency mainly leads to an increase in the electrostatic component, 100 kJ mol–1 on average.[20] The electron correlation component was very low (on the scale of several kJ mol–1) compared with 500–600 kJ mol–1 of the overall interaction energy. In this work, large charge-transfer values are observed for both lithium and sodium, which is reflected in the overall large interaction energy (<−800 kJ mol–1).

Although there is evidence in the Gibbs free-energy data suggesting that the aza-enolate isomer is favored in the sodium complex, the interaction energies indicate that this should not be the case. This comes as a result of the aza-enolate being 93.5 and 53.4 kJ mol–1 lower in interaction energy than the largely unstable allyl-amide isomer and the aza-allyl isomers, respectively. To investigate other causes of the experimentally and computationally observed stability of the sodium aza-enolate isomer, deformation energies were considered. As shown in Table , sodium complexes tend to have a highly negative deformation energy for the allyl-amide and aza-allyl isomers, −21.5 and −14.4 kJ mol–1, respectively, suggesting that these isomers need to overcome a relatively large energy barrier to enter a favorable geometry to interact with the metal. Conversely, the aza-enolate is only at −5.8 kJ mol–1 deformation energy, suggesting that the ligand is closer to its global energy minimum when it interacts with sodium. The ligand in the imine isomer has only −1.8 kJ mol–1 of deformation energy. However, as a result of the imine complex having the weakest interaction energy and the largest contribution from dispersion forces (5.63%) relative to the other sodium isomers, this is likely not to be sufficient to form the isomer on the time scale of NMR measurements. This susceptibility for the aza-enolate to form a complex with sodium could explain its preference as the most stable sodium isomer as confined with thermodynamic calculations and experimental results. Contrary to the sodium and lithium complexes, the ligand does not need to undergo structural changes when forming a bond with the potassium ions, which is demonstrated by low deformation energies below −3.9 kJ mol–1. This is in accord with the presented findings on lowest charge-transfer numbers between the potassium cation and the ligand in all isomers studied, further confirming the ability of the potassium cation to freely move around the ligand backbone. Therefore, it is not surprising that the three isomers, aza-allyl, imine, and aza-enolate, do not show large fluctuations in their thermodynamic stability.

Table 4

Deformation Energy for Ligands in kJ mol–1

isomer	Li	Na	K
allyl-amide	–22.8	–21.5	–3.9
aza-allyl	–13.9	–14.4	–0.9
imine	–7.5	–1.8	–3.7
aza-enolate	–11	–5.8	–0.6

Conclusions

Here, we presented a study of the thermodynamic stability of four possible alkali-metal allyl-amide isomers. Of the three metals studied, sodium was shown to have the largest variation in the thermodynamic stability of the four isomers. Aza-enolate is most thermodynamically stable, with the imine and aza-allyl isomers being 56.9 and 33.8 kJ mol–1 less stable, respectively. This clearly indicates the preference of sodium to form the aza-enolate isomer. It is also in agreement with previous experimental data that confirmed the formation of the most stable isomer, aza-enolate, in as little as one day in the case of potassium when water was present to catalyze the reaction.

In the case of lithium complexes, Gibbs free energies of the aza-enolate and aza-allyl isomers are only 0.3 kJ mol–1 apart, indicating that both isomers can be equally formed. This finding has been confirmed experimentally, with the preference for one of the isomers strongly depending on a chelating agent. The formation of the imine isomer was found to be 24.2 kJ mol–1 less preferable, and therefore the formation of this isomer has never been observed for Li. Due to strong electrostatic forces and a large net charge transfer of >0.3e in aza-enolate and aza-allyl, it is unlikely for the imine isomer to form as the lithium cation must move by 0.075–0.1 Å away from the nitrogen atom on the ligand to allow for the C=N bond to form. To confirm this finding, we also synthesized both lithium aza-allyl and aza-enolate complexes and found that they had comparable solution-state structures to previously synthesized alkali metal complexes.

In the case of potassium, all three rearranged isomers, imine, aza-allyl, and aza-enolate, were predicted to have similar thermodynamic stabilities within 12.5 kJ mol–1, with aza-enolate being the most thermodynamically stable isomer. Compared to lithium and sodium, this starkly similar stability was attributed to three factors: (1) decreased interaction strength of the metal–ligand bond by >200 kJ mol–1 with respect to lithium complexes, (2) decreased net charge transfer between the potassium ion and the ligand (below 0.2e), and (3) significant increase in the dispersion contribution of up to 58.3 kJ mol–1. The potassium ion can easily move between the nitrogen and carbon centers on the ligand, thus resulting in various isomers.

These findings support the experimental observation of the existence of all three isomers for the potassium metal and absence of the imine isomer for the sodium metal. From this, a clear trend was found in the tendency for each metal to prefer different interaction types, varying from the electrostatic nature of lithium interactions accompanied by strong charge transfer and ligand deformation energy to the dispersion-driven interactions present in potassium with moderate charge transfer and ligand deformation energy.

Experimental Section

(S)-N-(α-Methylbenzyl)methallylamine: (S)-α-methylbenzylamine (6.06 g, 50 mmol) was dissolved in THF (40 mL), followed by addition of nBuLi (31 mL [1.6 M solution in hexanes], 50 mmol) at −89 °C (isopropanol/liquid nitrogen). The solution was stirred for 2 h while warming to 0 °C. 3-Bromo-2-methylpropene (6.75 g, 50 mmol) was then added dropwise, and the resultant solution was allowed to warm to room temperature and stirred overnight. The resultant orange solution was quenched with water (50 mL), THF was evaporated in vacuo, and then extracted with diethyl ether (3 × 40 mL). The organic phase was washed with brine and dried over Na2SO4, and then the solvent was removed in vacuo to yield a pale-yellow liquid. This was distilled in vacuo to produce a colorless oil, which was stored under N2 over 4 Å molecular sieves (7.84 g, 89%). Bp: 40 °C/0.1 mmHg. 1H NMR (400 MHz, C6D6, 30 °C): δ 7.29 (2H, m, ortho-H), 7.20 (2H, m, meta-H), 7.10 (1H, m, para-H), 4.97 (1H, s, CH2C(CH3)=CH2), 4.83 (1H, s, CH2C(CH3)=CH2), 3.59 (1H, q, 3J = 6.6 Hz, PhC(H)CH3), 2.94 (1H, d, 2J = 14.4 Hz, CH2C(CH3)=CH2), 2.92 (1H, dd, 3J = 14.4 Hz, CH2C(CH3)=CH2), 1.63 (3H, s, CH2C(CH3)=CH2), 1.19 (3H, d, 3J = 6.6 Hz, PhC(H)CH3), 1.00 (1H, bs, NH). 13C NMR (100 MHz, C6D6, 30 °C): δ 146.5 (ipso-C), 144.9 (CH2C(CH3)=CH2), 128.7 (meta-C), 127.1 (para-C), 127.0 (ortho-C), 110.5 (CH2C(CH3)=CH2), 57.9 (PhC(H)CH3), 53.9 (CH2C(CH3)=CH2), 25.0 (PhC(H)CH3), 20.9 (CH2C(CH3)=CH2)

[PhC(=CH2)=NLiCH2CH(CH3)2·PMDETA], 1: nBuLi (1.25 mL, 1.6 M in hexanes, 2 mmol) was added to 10 mL of hexane, followed by PMDETA (0.42 mL, 2 mmol). The solution was cooled to −89 °C, and (S)-N-(α-methylbenzyl)methallylamine (0.35 g, 2 mmol) was added, forming a yellow oil. Upon warming to room temperature, a gummy yellow solid was obtained, which was washed with hexane (2 × 20 mL) and dried under vacuum to yield a yellow solid. 1H NMR (400 MHz, C6D6, 30 °C): δ 8.02 (2H, m, ortho-H), 7.20 (2H, m, meta-H), 7.11 (1H, m, para-H), 3.81 (1H, d, 2J = 1.6 Hz, PhC=CH2), 3.44 (1H, d, 2J = 1.6 Hz, PhC=CH2), 3.22 (2H, d, 3J = 6.5 Hz, NCH2), 2.50 (1H, nonet, 3J = 6.6 Hz, CH2CH(CH3) 2), 1.85 (15H, bs, CH3–PMDETA), 1.65 (8H, bs, CH2–PMDETA), 1.27 (6H, d, 3J = 6.6 Hz, CH(CH3)2). 13C NMR (100 MHz, C6D6, 30 °C): δ 164.1 (PhC=CH2), 151.9 (ipso-C), 127.9 (meta-C), 127.6 (ortho-C), 125.6 (para-C), 65.1 (=CH2), 61.9 (NCH2), 57.2 (CH2–PMDETA), 45.5 (CH3–PMDETA), 27.6 (CH(CH3)2), 22.9 (CH(CH3)2). 7Li NMR (156 MHz, C6D6, 30 °C): δ 2.98 (bs), 2.15 (bs), 1.74 (bs), 0.34 (s).

(S)-[PhCH(CH3)NLi=CH=C(CH3)2·TMEDA]n, 2: nBuLi (1.25 mL, 1.6 M in hexanes, 2 mmol) was added to 10 mL of hexane, followed by TMEDA (0.30 mL, 2 mmol). The solution was cooled to −89 °C, and (S)-N-(α-methylbenzyl)methallylamine (0.35 g, 2 mmol) was added, forming a yellow oil. Upon warming to room temperature, a gummy yellow solid was obtained, which was washed with hexane (2 × 20 mL) and dried under vacuum to yield a yellow solid. 1H NMR (400 MHz, C6D6, 30 °C): δ 7.47 (2H, d, 3J = 7.4 Hz, ortho-H), 7.22 (2H, t, 3J = 7.5 Hz, meta-H), 7.08 (1H, t, 3J = 7.3 Hz, para-H), 6.59 (1H, bs, N=CH), 4.24 (1H, bs, PhCH), 1.96 (3H, bs, =C(CH3)2), 1.85 (3H, bs, =C(CH3)2), 1.64 (12H, bs, CH3–TMEDA), 1.56 (4H, CH2–TMEDA), 1.51 (3H, d, 3J = 6.6 Hz, PhCHCH3). 13C NMR (100 MHz, C6D6, 30 °C): δ 152.6 (ipso-C), 147.4 (N=CH), 128.6 (meta-C), 127.2 (ortho-C), 125.9 (para-C), 64.5 (PhCH), 56.3 (CH2–TMEDA), 45.2 (CH3–TMEDA), 28.0 (PhCHCH3), 24.1 (=C(CH3)2, 17.7 (=C(CH3)2)). 7Li NMR (156 MHz, C6D6, 30 °C): δ 2.80 (bs), 2.11 (bs), 1.58 (bs), 0.78 (s).