Probing the Influence of Anomeric Effects on the Lithium Ion Affinity in

Sep 10, 2010 - Lithium ion affinities of methanediamine (MDA), N,N,N′,N′-tetramethylmethanediamine (TMMDA), 1,3- diazacyclohexane (DAC), trans-3 ...
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Probing the Influence of Anomeric Effects on the Lithium Ion Affinity in 1,3-Diaza Systems: A Computational Study Manoj K. Kesharwani,† Walter Thiel,‡ and Bishwajit Ganguly*,† Analytical Science Discipline, Central Salt & Marine Chemicals Research Institute (Council of Scientific and Industrial Research), BhaVnagar 364 002, Gujarat, India, and Max-Planck-Institut fu¨r Kohlenforschung, Kaiser Wilhelm-Platz 1, D-45470, Mu¨lheim an der Ruhr, Germany ReceiVed: May 13, 2010; ReVised Manuscript ReceiVed: August 17, 2010

Lithium ion affinities of methanediamine (MDA), N,N,N′,N′-tetramethylmethanediamine (TMMDA), 1,3diazacyclohexane (DAC), trans-3,5-diazabicyclo[4.4.0]decane (trans-3,5-DBD), trans-1,3-diazabicyclo[4.4.0]decane (trans-1,3-DBD), cis-1,3-diazabicyclo[4.4.0]decane (cis-1,3-DBD), 1,5-diazabicyclo[3.3.1]nonane (DBN), trans-decahydro-8a,9a-diazaanthracene (trans-DDA), cis-decahydro-8a,9a-diazaanthracene (cis-DDA), 1,3-diazetidine (DAT), 1,3-imidazolidine (IMD), and 1,3-diazepane (DAP) have been studied by using density functional theory (DFT) and correlated ab initio methods. Possible conformers of these compounds were optimized at the B3LYP/6-31+G* level, and relative energies were evaluated at the MP2/6-311+G**//B3LYP/ 6-31+G* level. The experimental lithium ion affinities for reference molecules (i.e., ammonia and trimethylamine) are well-reproduced at these levels of theory. NBO analysis shows the influence of anomeric effects (nN f σ*C-N hyperconjugative interactions) on the conformational stability of the title compounds; however, the electrostatic and steric contributions included in the NBO Lewis term also affect the stabilities in some cases. The influence of anomeric effect is apparent in cis-DDA, where the nitrogen involved in nN f σ*C-N hyperconjugative interaction (cis-DDA-Li2) has a lithium ion affinity 1.7 kcal/mol lower than the nitrogen not involved in nN f σ*C-N hyperconjugative interaction (cis-DDA-Li1). In general, the computed lithium ion affinities were found to be conformationally dependent. The NBO results showed that the lithium ion affinities are also governed by the interplay of nN f σ*C-N hyperconjugative interactions and the steric strain caused upon lithiation. Further, the ring size also influences the lithium ion affinities in the 1,3-diaza monocyclic systems. In some complexes multiple coordination of the lithium ion is possible by inversion of one of the nitrogen atoms. SCHEME 1

Introduction The stereoelectronic behavior of X-C-Y containing systems (X, Y ) OR, NR2, Hal), known as the anomeric effect, has been extensively studied.1–4 In an X-C-Y system, the anomeric effect is due to an nX f σ*C-Y two electron-two orbital interaction2 (negative hyperconjugation3 in valence bond terms) and is manifest4 in (1) structural parameters, e.g., shorter or longer anomeric bonds and larger anomeric bond angles, and (2) stereoselective reactivity (Scheme 1). The electrostatic model of dipole interaction, which was originally applied to explain the destabilization of the equatorial conformations in sugars, is based on the notion that nx/A-Y dipole-dipole repulsion destabilizes the anti conformation. This has also been proposed to be the origin of the anomeric effect.5 Compared with the abundant research efforts on stereoelectronic effects in neutral molecules, much less attention had been paid to these effects in charged systems and coordination complexes. These are of considerable interest owing to their mechanistic and synthetic implications (concerning the relative stability of conformers, structural properties, coordination sites and strengths, relative reactivities, nucleophilic reactions of molecular systems subject to stereoelectronic effects, etc.). Negative hyperconjugation may be used to control, in a predictable manner, the specific interaction pathways in neutral * Corresponding author, [email protected]. † Central Salt & Marine Chemicals Research Institute. ‡ Max-Planck-Institut fu¨r Kohlenforschung.

and charged complex heterocyclic systems.6 It has been established that the anomeric effect in C-O-C-O-C-containing molecules makes them weaker bases than the corresponding simple ethers, and differential protonation of oxygen lone pairs in unsymmetrical C-O1-C2-O3-C moieties indeed shows that the lone pair engaged in n f σ* interaction has a lower proton affinity than the “free” one: for example, the preferred site of protonation of 1,3-dioxane is axial, since the equatorial lone pair is hyperconjugatively delocalized.7 The geometric parameters (mainly bond lengths) are affected by and diagnostic for this stereoelectronic behavior, in line with experimental observations. By contrast, the COCCOC species are stronger bases than the COCOC (anomeric) species and approach regular ethers in their strength. The gauche forms of dimethoxyethane and 1,4-dioxane are stronger bases than the corresponding anti forms, and anti (equatorial) protonation is preferred over gauche

10.1021/jp1043656  2010 American Chemical Society Published on Web 09/10/2010

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(axial) protonation, unless ditopic protonation is possible. Clearly, both the anomeric and the gauche effect play a significant role for the formation, relative stability, and reactivity of these charged species.

LA(M) ) E(Li+) + E(M)-E(MLi+)

The coordination behavior of anomeric and gauche conformers toward the lithium cation has also been reported.8 A combined computational and structural study has shown the conformational dependence of lithium affinity to COCCOC (gauche) and COCOC (anomeric) species. Molecules containing the N-C-N moiety have been explored less than the analogous oxygen systems. There is only an electron diffraction (ED) study on N,N,N′,N′-tetramethylmethanediamine9 and few reliable 13C NMR conformational equilibrium studies of the highly relevant 1,3-diazane systems.10 The complexity of the systems containing N-C-N moieties results from a peculiar combination of steric and stereoelectronic effects and hydrogen-bond-type interactions. The cumulative influence of these three effects makes it difficult to interpret the experimental results. Natural bond orbital (NBO) analysis of N-C-N systems indicates that the preference for the anti lp-N-C-N orientation is mainly due to charge delocalization. This hyperconjugative stabilization is generally dominant while the electrostatic and steric contributions included in the Lewis term are less important than delocalization.11 The participation of a nitrogen lone pair in an anomeric interaction should be accompanied by an increased pyramidality at nitrogen. Imposing planarity at nitrogen leads to the shortening of the L(C-Nplanar) bond and to an increase in the total energy.12 The two manifestations of the anomeric effect are in apparent conflict: better np f σ* overlap is achieved by a p-type orbital in the planar NR2 geometry, but with an energetic penalty due to the cost of rehybridization (planarization).3a It is in this context that we now present the results of a computational investigation of the lithium ion affinity of acyclic N-C-N systems such as methanediamine (MDA) and N,N,N′,N′-tetramethylmethanediamine (TMMDA). Lithium ion affinities have also been calculated for a number of cyclic N-C-N systems, namely, 1,3-diazacyclohexane (DAC), trans-3,5-diazabicyclo[4.4.0]decane (trans-3,5-DBD), trans1,3-diazabicyclo[4.4.0]decane(trans-1,3-DBD),cis-1,3-diazabicyclo[4.4.0]decane (cis-1,3-DBD), 1,5-diazabicyclo[3.3.1]nonane (DBN), trans-decahydro-8a,9a-diazaanthracene (trans-DDA), cis-decahydro-8a,9a-diazaanthracene (cis-DDA), 1,3-diazetidine (DAT), 1,3imidazolidine (IMD), and 1,3-diazepane (DAP). Such cyclic systems are devoid of intramolecular hydrogen bonding and can provide a much clearer picture of anomeric effect on lithium ion affinities for 1,3-diaza moieties. We have compared the calculated geometrical parameters with those of related theoretical and experimental literature results to elucidate the coordination behavior and the stereoelectronic effects in these molecules.

The geometries of the free and lithiated aza compounds were fully optimized at the B3LYP/6-31+G* level13 with Gaussian 03.14 Single point calculations were done at the MP2/6311+G** level using B3LYP optimized geometries.15 All MP2 calculations were performed with the frozen-core (FC) approximation. CBS-QB3 calculations16 were also performed to examine the reliability of MP2 results. The CBS-QB3 results for the bond separation reactions devised to examine the lithium ion affinities for ammonia and trimethylamine were in good agreement with the corresponding MP2/6-311+G**//B3LYP/ 6-31+G* results, suggesting that MP2 is adequate for such studies (Scheme 2). CBS-QB3 is known to be accurate for energy predictions within (1 kcal/mol.16 The NBO analysis17 for neutral and lithiated species was carried out with B3LYP/ 6-31+G* geometries at the same level of theory. According to the NBO method, the total SCF energy, Etot can be decomposed in two terms. The Lewis energy, ELew, is associated with the localized B3LYP wave function and is obtained by zeroing all the orbital interactions, that is deleting the off-diagonal elements of the Fock matrix. The delocalization energy, Edel, corresponding to all the possible interactions between orbitals is calculated as Edel ) Etot - ELew. ELew includes all energy contributions apart from delocalization effects. These are, in particular, steric and electrostatic effects which cannot be separated within the NBO method. The procedure to calculate the degree of pyramidality at nitrogen is given in Scheme 3. To find structural information on systems related to those included in this study, we conducted searches of Cambridge Structural Database (CSD) for the lithiated N-C-N systems.18 These searches led to the retrieval of lithiated trimethylamine, whereas no data were found for the other systems. Results and Discussion Figure 1a shows the relative energies and geometries of the TT, TG, and GG conformers of MDA calculated at B3LYP/631+G* level of theory. Relative MP2/6-311+G** energies at the B3LYP optimized geometries are also given in Figure 1a. The letters “T” and “G” represent the approximate value (T ) 180°, G ) 60°) of the lp-N1-C-N2 and N1-C-N2-lp dihedral angles, in this order. Both B3LYP and MP2 favor the TT conformer for MDA, consistent with previous theoretical SCHEME 2

Computational Methods Calculations were performed for MDA, TMMDA, DAC, trans-3,5-DBD, trans-1,3-DBD, cis-1,3-DBD, trans-DDA, cisDDA, DBN, DAT, IMD, and DAP as well as for ammonia, trimethylamine, and the ammonia dimer that serve as reference molecules. Gas phase lithium ion affinities (LAs) were determined from the difference between the calculated total energies of the reactants (i.e., the neutral molecule M and the lithium cation) and of the corresponding ion-molecule complex.

M + Li+ f MLi+

SCHEME 3

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Figure 1. B3LYP/6-31+G* optimized geometries, important bond lengths (Å) and bond angles (deg), degree of pyramidality of nitrogens (χN), relative energies (kcal/mol), and calculated lithium ion affinities of various stable conformers of (a) MDA and (b) TMMDA. MP2/6-311+G**// B3LYP/6-31+G* lithium ion affinities are given in parentheses. Key: gray ) carbon; blue ) nitrogen; pink ) lithium; white ) hydrogen.

results.11,19 The stability of TT conformer can be attributed to the two anomeric nN f σ*C-N hyperconjugative interactions that are possible (double anomeric effect). The least stable GG conformer allows for no nN f σ*C-N hyerconjugative interactions. The anomeric effect is manifested in the computed structural parameters of these conformers. The calculated N-C-N angles for TT, TG, and GG are 119.7°, 113.7°, and 107.4°, respectively. The double anomeric effects in the TT conformer widen the N-C-N angle, whereas the smallest value is obtained for the GG conformer (Figure 1a). The bond length variations are also in accord with the anomeric interactions in these cases (Figure 1a). They are significant in MDA-TG, where the C-N bond with the nitrogen involved in anomeric interaction is shorter (1.451 Å) than the other one (1.473 Å). NBO analysis performed at B3LYP/6-31+G* level for the TT, TG, and GG conformers of MDA shows the contributions of Lewis and delocalization energies (Table 1). Comparing the Lewis and delocalization energies, it appears that steric factors destabilize the TT conformer of MDA by 6.0 and 8.5 kcal/mol relative to the TG and GG conformers, whereas hyperconjugative delocalization stabilize it by 6.6 and 9.4 kcal/mol, respectively (Table 1).

The opposite conformational preference is observed for N,N,N′,N′-tetramethylmethanediamine (TMMDA) (Figure 1b). The GG conformer without any nN f σ*C-N hyperconjugative interactions is computed to be the most stable conformer for TMMDA. The B3LYP/6-31+G* structural parameters suggest that anomeric effects are again operative in the TT conformers, since the relative C-N bond lengths and N-C-N bond angles vary in a similar fashion as in MDA (Figure 1b). The NBO analysis indicates that the relative energies of the two conformers are dominated by steric effects, which largely get compensated by the hyperconjugative delocalization energy (Table 1). The steric factors destabilize the TT conformer of TMMDA by 24.6 kcal/mol compared to the GG conformer, whereas there is significant stabilization from nN f σ*C-N hyperconjugative interactions (20.3 kcal/mol) in the former conformer (Table 1). The steric crowding of methyl groups seems to contribute to the destabilization of the TT conformer of TMMDA. The calculated conformational energies for 1,3-diazacyclohexane (DAC) show that the conformer with equatorial nitrogen lone pairs (DAC-TT) is more stable than that with axial lone pairs (DAC-GG) (Figure 2a).19a,20 However, the conformer with one axial and one equatorial nitrogen lone pair (DAC-TG) is

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TABLE 1: B3LYP/6-31+G* Calculated Relative Energies (Etot) and Contributions of Hyperconjugation (Edel) and Lewis Energies (ELew) for the Stable Conformers of Various Diaza Compounds (all values in kcal/mol) Etot MDA TT TG GG TMMDA TT GG DAC TT TG GG trans-3,5-DBD TT TG GG trans-1,3-DBD TG GG cis-1,3-DBD TG GG DAT GG1 GG2 IMD TT GG DAP TT TG GG

Edel

ELew

0.0 0.6 0.9

0.0 6.6 9.4

0.0 -6.0 -8.5

4.4 0.0

-20.3 0.0

24.6 0.0

0.1 0.0 2.7

-5.1 0.0 2.6

5.2 0.0 0.1

0.0 0.2 2.8

0.0 5.2 8.3

0.0 -5.0 -5.6

0.0 2.6

0.0 2.2

0.0 0.4

0.0 2.9

0.0 1.9

0.0 1.0

1.0 0.0

0.0 5.2

6.2 0.0

0.0 0.3

0.0 1.1

0.8 0.0

0.0 0.3 2.9

0.0 7.1 15.5

12.6 5.7 0.0

comparable in energy with DAC-TT. The stability order of DAC conformers seems to be governed by a delicate balance between steric and hyperconjugative delocalization effects (Table 1). In the TT conformer, each lone pair is in optimal position for nN f σ*C-N hyperconjugative interactions and is thus stabilized by 5.1 kcal/mol relative to the TG conformer in which only one lone pair is involved in nN f σ*C-N interactions. However, 1,3-flag-pole type interactions destabilize the TT conformer by 5.2 kcal/mol compared with TG (Table 1). The least stable GG conformer does not allow for any nN f σ*C-N hyperconjugative interactions. The extended bicyclic trans-3,5diazabicyclo[4.4.0]decane (trans-3,5-DBD) shows the same conformational stability order as observed for DAC at both levels of theory (Figure 2b). We have also considered 1,3-diaza bicyclic systems, with one of the nitrogens at the junction of the rings, i.e., the trans- and cis-form of 1,3-diazabicyclo[4.4.0]decane (trans-1,3-DBD and cis-1,3-DBD). In these cases, calculations were performed only with TG and GG conformers. The calculated relative energies suggest that the TG conformer is preferred over the GG conformer in both cases (Figure 3), mainly due to the more favorable nN f σ*C-N hyperconjugative interactions (Table 1). Furthermore, the effects of imperfect TT, TG, and GG arrangement of nitrogen lone pairs were examined for 1,3-diaza moieties in four-, five-, and seven-membered rings, i.e., 1,3diazetidine (DAT), 1,3-imidazolidine (IMD), and 1,3-diazepane (DAP), respectively. In the case of DAT, the imperfect TT conformer cannot be realized due to geometric constraints; however, two imperfect GG forms are possible (Figure 4a). IMD optimizations converged to imperfect TT and GG forms, with the former conformer being energetically preferred by 0.7 kcal/

mol (Figure 4b). The NBO analysis for the IMD conformers suggests that the TT form is more stable than the GG form because of its larger delocalization energy (Table 1). The TT conformer is also favored in DAP, again due to the larger delocalization energy compared to the TG and GG forms (Figure 4c and Table 1). Lithium Ion Affinities. The calculated lithium ion affinities for the reference systems ammonia and trimethylamine are shown in Figure 5. The MP2/6-311+G** results for ammonia and trimethylamine (40.6 and 41.4 kcal/mol, respectively) are in good agreement with experiment.21 The CSD search provided an experimental structure for the complex between the lithium ion and trimethylamine.22 The calculated bond lengths in the complex Me3N · Li+ are in good agreement with the observed crystal structure (Figure 5), and the degree of pyramidality at nitrogen is also similar (33.0° calculated and 36.0° X-ray). The lithium ion affinity of the NH3 dimer toward formation of (NH3)2 · Li+ is computed to be 75.8 kcal/mol (Figure 5). Lithium Ion Affinity of Methanediamine (MDA). The three conformations TT, TG, and GG forms of MDA were considered. In TT, double nN f σ*C-N hyperconjugative delocalization is possible, compared with only one such interaction in TG and none in GG. It is important to see how the lithium ion affinity varies for such systems. Figure 1a shows the relative energies and geometries of the complexes between the TT, TG, and GG conformers of MDA and the lithium ion affinity at B3LYP/631+G* and MP2/6-311+G**//B3LYP/6-31+G* levels of theory. The MP2/6-311+G** lithium ion affinity of the TT conformer (MDA-Li1) is similar to that of ammonia and lower than that of trimethylamine (Figures 1a and 5). The optimizations for the TG and GG complexes converged to the same structure, in which Li+ is coordinated with both nitrogen atoms in a fourmembered ring complex (Figure 1a). Thus, the least stable GG form, devoid of any anomeric effect, provides the platform for the most stable lithium ion complex (MDA-Li2) whose geometry is coplanar with a small N-Li+-N angle. The strain caused by this small angle presumably lowers the lithium ion affinity compared to ammonia dimer (Figure 1a). The lithium ion obviously prefers to coordinate with more than one nitrogen atom, and hence it is not possible to segregate the lithium ion affinities for the heteroatoms involved in anomeric and nonanomeric interactions. Therefore, additional calculations were performed with constrained geometries of MDA-TG. In the TG conformer, one of the nitrogen atoms is involved in nN f σ*C-N hyperconjugative delocalization, but not the other one. The calculated lithium ion affinities are markedly different for these two nitrogen atoms (Figure 6). The nitrogen lone pair involved in nN f σ*C-N hyperconjugative interaction (MDA-Li3) has a lithium ion affinity (40.7 kcal/mol) nearly equal to MDA-TT and ammonia, whereas the nitrogen lone pair not involved in nN f σ*C-N hyperconjugative interaction (MDA-Li4) has a lower lithium ion affinity (38.6 kcal/mol), presumably arising from 1,3-bond pair type repulsive interactions (Figure 6). Lithium Ion Affinity of N,N,N′,N′-Tetramethylmethanediamine (TMMDA). In N,N,N′,N′-tetramethylmethanediamine (TMMDA), the unstable TT conformer yields a lithium ion affinity (46.3 kcal/mol), which is higher than that of trimethylamine and of the TT conformer of MDA (Figures 1b and 5). Interestingly, the other nitrogen atom inverts in the lithiated form of TMMDA-TT such that it can form weak intramolecular C-H · · · N type interactions with the substituted methyl groups. The computed C-H · · · N distance in the lithiated TT complex is 2.65 Å. The GG conformer, devoid of any anomeric effect, provides the platform for the most stable lithium ion complex

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Figure 2. B3LYP/6-31+G* optimized geometries, important bond lengths (Å) and bond angles (deg), degree of pyramidality of nitrogens (χN), relative energies (kcal/mol), and calculated lithium ion affinities of various stable conformers of (a) DAC and (b) trans-3,5-DBD. MP2/6-311+G**// B3LYP/6-31+G* lithium ion affinities are given in parentheses. Key: gray ) carbon; blue ) nitrogen; pink ) lithium; white ) hydrogen.

(TMMDA-Li2). Lithium coordinates with both nitrogen atoms of the GG form of TMMDA, and the geometry is again coplanar with a small N-Li+-N angle. The lithium ion affinity (56.6 kcal/mol) is lower than that of the ammonia dimer (75.8 kcal/ mol) due to the strain caused by the smaller N-C-N angle. Lithium Ion Affinity of 1,3-Diazacyclohexane (DAC). The lithium ion affinities of the TT, TG, and GG conformers of less

flexible 1,3-diazacyclohexane (DAC) were examined (Figure 2a). The C-N-C-N-C fragment in the TT conformer is subject to a second-order anomeric effect, i.e., nN f σ*C-N two electron-two orbital mixing, whereas the TG form has one such interaction and the GG form none. The calculated lithium ion affinity for the TT conformer of DAC is 42.7 kcal/mol and thus higher than that of the TT conformer of MDA. The lithium ion

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Figure 3. B3LYP/6-31+G* optimized geometries, important bond lengths (Å) and bond angles (deg), degree of pyramidality of nitrogens (χN), relative energies (kcal/mol), and calculated lithium ion affinities of various stable conformers of (a) trans-1,3-DBD and (b) cis-1,3-DBD. MP2/6311+G**//B3LYP/6-31+G* lithium ion affinities are given in parentheses. Key: gray ) carbon; blue ) nitrogen; pink ) lithium; white ) hydrogen.

affinity calculated for the nitrogen lone pair involved in nN f σ*C-N hyperconjugative interaction (DAC-Li2) is 44.0 kcal/ mol, whereas the one on the other nitrogen atom is 58.8 kcal/ mol (DAC-Li3) (Figure 2a). In the latter case, both nitrogen atoms coordinate with the lithium ion which is made possible by the inversion of one of them (Figure 2a). The GG conformer has the highest lithium ion affinity in this series because of the ditopic coordination of the lithium ion with the nitrogen atoms of DAC. To segregate the influence of anomeric effect on the lithium ion affinity with DAC, additional calculations were performed with constrained geometries of the DAC-TG conformer. The

MP2 results show that the lithiation of the nitrogen lone pair, which is not involved in the nN f σ*C-N hyperconjugative interaction, gives a lower lithium ion affinity than in the opposite case where the nitrogen lone pair is engaged in such an interaction (Figures 2a and 7). This situation is similar as in the MDA lithium complexes, presumably due to the large 1,3flag-pole type interactions. Lithium Ion Affinity of 1,3-Diaza Bicyclic and Tricyclic Systems. Lithium ion affinities were calculated for three different forms of diazabicyclo[4.4.0]decane, viz., trans-3,5-diazabicyclo[4.4.0]decane (trans-3,5-DBD), trans-1,3-diazabicyclo[4.4.0]decane (trans-1,3-DBD), and cis-1,3-diazabicyclo[4.4.0]decane (cis-

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Figure 5. B3LYP/6-31+G* optimized geometries, important bond lengths (Å), degree of pyramidality of nitrogens (χN), relative energies (kcal/mol), and calculated lithium ion affinities of ammonia and trimethylamine. MP2/6-311+G**//B3LYP/6-31+G* lithium ion affinities are given in parentheses. Key: gray ) carbon; blue ) nitrogen; pink ) lithium; white ) hydrogen.

Figure 6. B3LYP/6-31+G* optimized geometries, important bond lengths (Å) and bond angles (deg), degree of pyramidality of nitrogens (χN), and calculated lithium ion affinities of TG conformer of MDA. MP2/6-311+G**//B3LYP/6-31+G* lithium ion affinities are given in parentheses. Calculations for lithium complexes were performed with constrained geometries. Key: gray ) carbon; blue ) nitrogen; pink ) lithium; white ) hydrogen.

Figure 4. B3LYP/6-31+G* optimized geometries, important bond lengths (Å) and bond angles (deg), degree of pyramidality of nitrogens (χN), relative energies (kcal/mol), and calculated lithium ion affinities of various stable conformers of (a) DAT, (b) IMD and (c) DAP. MP2/ 6-311+G**//B3LYP/6-31+G* lithium ion affinities are given in parentheses. Key: gray ) carbon; blue ) nitrogen; pink ) lithium; white ) hydrogen.

1,3-DBD). The calculations were done for all three TT, TG, and GG conformers of trans-3,5-DBD, whereas only the TG and GG forms were considered for trans-1,3-DBD and cis-1,3-DBD. In trans-3,5-DBD the fused ring system influences the lithium ion affinities of the TT, TG, and GG forms, which are generally higher than those of the corresponding forms of DAC (parts a and b of Figure 2), similar molecular size effects were also seen in protonation studies.23 In the TG form of trans-1,3-DBD, the lithium ion can bind either to N3 (trans-1,3-DBD-Li1) or to N1 (trans-

Figure 7. B3LYP/6-31+G* optimized geometries, important bond lengths (Å), and calculated lithium ion affinities of TG conformer of DAC. MP2/6-311+G**//B3LYP/6-31+G* lithium ion affinity is given in parentheses. Calculation for lithium complex was performed with constrained geometry. Key: gray ) carbon; blue ) nitrogen; pink ) lithium; white ) hydrogen.

1,3-DBD-Li2) (Figure 3a). The lithium ion affinity of nitrogen lone pair involved in nN f σ*C-N hyperconjugative interaction (trans1,3-DBD-Li1) is computed to be 0.9 kcal/mol higher than that of the nitrogen in the junction of the ring (trans-1,3-DBD-Li2) (Figure 3a), presumably due to 1,3-repulsions between the lithium and hydrogen atoms in trans-1,3-DBD-Li2. The GG conformer shows ditopic coordination of the lithium ion (trans-1,3-DBD-Li3) similar to trans-3,5-DBD (Figures 2b and 3a). In the TG form of cis-1,3-DBD, the computed lithium ion affinity (45.5 kcal/mol) of the nitrogen lone pair involved in

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Figure 8. B3LYP/6-31+G* optimized geometries, important bond lengths (Å) and bond angles (deg), degree of pyramidality of nitrogens (χN), and calculated lithium ion affinities of (a) cis-DDA and (b) trans-DDA. MP2/6-311+G**//B3LYP/6-31+G* lithium ion affinities are given in parentheses. Key: gray ) carbon; blue ) nitrogen; pink ) lithium; white ) hydrogen.

nN f σ*C-N hyperconjugative interaction is slightly higher than the corresponding value (44.5 kcal/mol) for trans-1,3-DBD (parts a and b of Figure 3). Lithiation at the junction nitrogen atom N1 of the TG form causes inversion of the second nitrogen, which leads to ditopic coordination of the lithium ion and a large lithium ion affinity of 61.4 kcal/mol. In the GG form, there is also ditopic coordination of the lithium ion, with an even larger lithium ion affinity of 64.6 kcal/mol (Figure 3b), which is the highest value found in the presently studied 1,3-diaza systems. However, this is still lower than the reference value for 1,4-diaza systems from ethane-1,2-diamine (67.6 kcal/mol, see Figure S1, Supporting Information).24 The four-membered ring formed upon ditopic lithiation of the 1,3-diaza system is more strained than the five-membered ring formed with 1,4diaza systems, which diminishes the lithium ion affinity in the former case. In trans- and cis-1,3-DBD, the nitrogen atoms are secondary and tertiary in nature. The lithium ion affinities computed for these systems, however, does not give the comparative results with or without nN f σ*C-N hyperconjugative interaction due to nitrogen inversion. To circumvent this situation, we have calculated the lithium ion affinity with tricyclic cis and trans form of decahydro-8a,9a-diazaanthracene (cis-DDA and transDDA). These scaffolds provide an opportunity to freeze the nitrogen atoms in the ring system, and they are tertiary in nature. In the case of TG form (cis-DDA), the lithium ion affinity with the nitrogen involved in nN f σ*C-N hyperconjugative interaction is 46.8 kcal/mol (cis-DDA-Li2), which is 1.7 kcal/mol lower than the lithium ion affinity calculated for the nitrogen not involved in nN f σ*C-N hyperconjugative interaction (cis-DDALi1) (Figure 8a). This result clearly shows that the nitrogen lone pair involved in hyperconjugative interaction is less available for lithiation. The GG form of DDA (trans-DDA) shows ditopic coordination with lithium ion and the computed

Figure 9. B3LYP/6-31+G* optimized geometries, important bond lengths (Å) and bond angles (deg), degree of pyramidality of nitrogens (χN), and calculated lithium ion affinity of DBN. MP2/6-311+G**// B3LYP/6-31+G* lithium ion affinity is given in parentheses. Key: gray ) carbon; blue ) nitrogen; pink ) lithium; white ) hydrogen.

lithium ion affinity is 64.5 kcal/mol (Figure 8b). We also studied 1,5-diazabicyclo[3.3.1]nonane (DBN), where the tertiary nitrogen atoms are involved in nN f σ*C-N hyperconjugative interaction and frozen at the junction in the ring system. The calculated lithium ion affinity of DBN is 43.6 kcal/mol (Figure 9), which is lower than lithium ion affinity computed for the nitrogen not involved in nN f σ*C-N hyperconjugative interaction (cis-DDA-Li1). Lithium Ion Affinity of 1,3-Diazetidine (DAT), 1,3-Imidazolidine (IMD), and 1,3-Diazepane (DAP). The effect of imperfect T and G alignment of the nitrogen lone pair on the lithium ion affinity of DAT, IMD, and DAP was examined at the B3LYP/6-31+G* and MP2/6-311+G** levels of theory. The MP2 lithium ion affinity of the DAT-GG1 conformer is higher than that of the reference molecules ammonia and trimethylamine (Figures 4a and 5). The DAT-GG2 conformer undergoes ditopic coordination with the lithium ion, but the computed lithium ion affinity is much lower than in other cases of ditopic coordination, presumably due to the ring strain in the formed complex (Figure 4a). Going from DAT-GG1 to

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IMD-TT, the nitrogen lone-pair becomes more involved in nN f σ*C-N hyperconjugation which should slightly reduce the lithium ion affinity (by 0.3 kcal/mol at the MP2 level, see parts a and b of Figure 4). In the GG conformer of IMD, the eclipsing interaction between the C-H and N-Li bonds is expected to diminish the lithium ion affinity, which is indeed slightly lower than that of IMD-TT (Figure 4b). The lithium ion affinity for ditopic coordination of IMD is 53.4 kcal/mol (IMD-Li2), which lies in between the lithium ion affinity of ditopic coordination of four-membered DAT (50.9 kcal/mol) and six-membered DAC (58.8 kcal/mol). These results show that the lithium ion affinity with ditopic coordination can be enhanced by means of the ring size of 1,3-diaza compounds. The computed lithium ion affinities of DAC-TT and IMD-TT are almost identical (Figures 2a and 4b) which, according to NBO analysis, can be attributed to counteracting effects arising from the interplay of delocalization and Lewis energies (Figure S2 in the Supporting Information). The 1,3-diaza compounds IMD, DAC, and DAP contain five-, six-, and seven-membered rings, respectively. The computed lithium ion affinities for the corresponding TT conformers are 42.6 (IMD-Li1), 42.7 (DAC-Li1), and 43.5 kcal/mol (DAPLi1) (Figures 4b, 2a, and 4c). The higher value for DAP can be ascribed to the larger flexibility of the seven-membered ring which may help to reduce the steric strain after lithiation (Figure S2 in the Supporting Information). The TG conformer of DAP has an even larger lithium ion affinity (45.2 kcal/mol, Figure 4c), presumably again because of less ring strain after lithiation compared with the TT conformer (Figure S3 in the Supporting Information). The lithiation of the TG conformer of DAP at the nitrogen not involved in nN f σ*C-N type hyperconjugative interaction leads to ditopic coordination, since the second nitrogen undergoes inversion to facilitate coordination. The resulting lithium ion affinity for DAP-TG is 60.5 kcal/mol, which is only slightly lower than the value of 62.7 kcal/mol for the ditopic coordination in DAP-GG (Figure 4c). Bond Distances and Vibrational Frequencies. The C-N bond distances correlate well with the corresponding frequencies in these lithium ion complexes (Table 2). Lithiation disrupts the nN f σ*C-N hyperconjugative delocalization and lengthens the corresponding C-N bonds. The calculated frequencies of such lithiated C-N bonds are lower than those of normal C-N bonds (Table 2). In the MDA system, the N1 nitrogen undergoes lithiation in both MDA-Li1 and MDA-Li3 (Figures 1a and 4), which causes the C2-N1 bond to be longer than C2-N3 in both cases (Table 2). Comparing the influence of lithiation on C-N bond lengths of MDA-Li1 and MDA-Li3, it appears that the nN f σ*C-N hyperconjugative delocalization is stronger than the nN f σ*C-H hyperconjugative delocalization, which is also reflected in the stretching frequencies of these C-N bonds (Table 2). Turning to MDA-Li4, the lone-pair at N3 is involved in lithiation, whereas the lone-pair at N1 engages in nN f σ*C-N hyperconjugative delocalization, and hence the C2-N3 bond is longer than C2-N1 (Figure 4 and Table 2). In TMMDALi1, the lone-pair at N1 participates in lithiation, whereas the lone-pair at N3 is involved in nN f σ*C-H hyperconjugative delocalization (Figure 1b), which results in a longer C2-N1 bond and lower frequency compared with C2-N3 (Table 2). The cyclic systems DAC, trans-3,5-DBD, trans-1,3-DBD, cis1,3-DBD, cis-DDA, DAT, IMD, and DAP also show similar changes in the C-N bond distances and the corresponding frequencies as observed for the acyclic systems (Table 2). The significant difference in the stretching frequencies for the

Kesharwani et al. TABLE 2: B3LYP/6-31+G* Calculated C-N Bond Distances (Å) and Corresponding Stretching Frequencies (cm-1, in parentheses) for Lithium Complexes of Various 1,3-Diaza Systems MDA MDA-Li1 MDA-Li3 MDA-Li4 TMMDA TMMDA-Li1 DAC DAC-Li1 DAC-Li2 DAC-Li4 trans-3,5-DBD trans-3,5-DBD-Li1 trans-3,5-DBD-Li2 trans-1,3-DBD trans-1,3-DBD-Li1 trans-1,3-DBD-Li2 cis-1,3-DBD cis-1,3-DBD-Li1 cis-DDA cis-DDA-Li1 cis-DDA-Li2 DAT DAT-Li1 IMD IMD-Li1 IMD-Li3 DAP DAP-Li1 DAP-Li2

C2-N1

C2-N3

1.535 (845) 1.498 (917) 1.425 (1250)

1.415 (1127) 1.439 (1112) 1.528 (868)

1.513 (972)

1.439 (1068)

1.427 (1188) 1.496 (1043) 1.440 (1133)

1.524 (851) 1.441 (1162) 1.516 (855)

1.427 (1183) 1.492 (1029)

1.523 (817) 1.444 (1169)

1.444 (1155) 1.511 (899)

1.491 (1005) 1.430 (1196)

1.443 (1103)

1.495 (1060)

1.508 (951) 1.449 (1115)

1.436 (1195) 1.483 (1115)

1.521 (907)

1.466 (1058)

1.528 (826) 1.549 (812)

1.433 (1159) 1.439 (1164)

1.527 (818) 1.437 (11890)

1.417 (1218) 1.498 (848)

lithiated and non-lithiated nitrogen atoms can thus serve as an indicator for probable sites of lithiation in such systems. Conclusions We have reported DFT and MP2 calculations to examine the lithium ion affinities of anomeric N-C-N acyclic systems, such as MDA and TMMDA, and of cyclic systems, such as DAC, trans-3,5-DBD, trans-1,3-DBD, cis-1,3-DBD, DBN, transDDA, cis-DDA, DAT, IMD, and DAP. Conformational preferences for MDA, TMMDA, and DAC are in good agreement with previously reported results. NBO analysis shows that the conformational stabilities are generally governed by a delicate balance between hyperconjugative delocalization and steric factors. The calculated lithium ion affinities of 1,3-diaza systems are found to be conformationally dependent. The methylsubstituted TMMDA-TT shows higher lithium ion affinity compared to parent MDA-TT. Similar enhancement in lithium ion affinity was also observed between the ammonia and trimethylamine systems. Further, in the case of TMMDA-TT, the higher lithium ion affinity is partly associated due to the noncovalent C-H · · · N type interactions. In general, the TG forms of cyclic systems leads to ditopic coordination with lithium ion due to concomitant inversion of the nitrogen atom involved in nN f σ*C-N hyperconjugative interactions. Such cyclic systems exhibiting anomeric effect (TG) have lower lithium ion affinity compared to the cases where such effects are not possible (GG) just as observed on protonation.7a The anomeric effect was further exhibited with cis-decahydro-8a,9adiazaanthracene (cis-DDA), where the nitrogen involved in nN f σ*C-N hyperconjugative interaction (cis-DDA-Li2) has a lithium ion affinity 1.7 kcal/mol lower than the nitrogen not involved in nN f σ*C-N hyperconjugative interaction (cis-DDA-

Anomeric Effects on Lithium Ion Affinity Li1). In the monocyclic 1,3-diaza systems, the lithium ion affinities are higher in the more flexible seven-membered ring (DAP) compared to the five-membered (IMD) and sixmembered (DAC) ring systems. Here the increase in the molecular size of 1,3-diaza systems enhances the lithium ion affinity. NBO analysis suggests that in both cyclic and acyclic systems the lithium ion affinity is governed by the interplay of delocalization and the steric strain. The computed C-N stretching frequencies correlate with the variation of the C-N bond lengths upon lithiation of the studied 1,3-diaza systems; they can serve as an indicator for probable sites of lithiation. Acknowledgment. B.G. thanks the INSA/DFG bilateral exchange program for financial support. M.K.K. is grateful to UGC, New Delhi, India for the award of a fellowship. We thank the reviewers for their comments and suggestions that have helped us to improve the paper. Supporting Information Available: B3LYP/6-31+G* optimized Cartesian coordinates of all stationary points. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) (a) The Anomeric Effect and Associated Stereoelectronic Effects; Thatcher, G. R. J., Ed.; ACS Symposium Series No. 539; American Chemical Society: Washington, DC, 1993. (b) Juaristi, E.; Cuevas, G. Tetrahedron 1992, 48, 5019. (c) Kirby, A. J. The Anomeric Effect and Related Stereoelectronic Effects at Oxygen; Springer: Berlin, 1983. (d) Anomeric Effect. Origins and Consequences; Szarek, W. A., Horton, D., Eds.; ACS Symposium Series No. 87; American Chemical Society: Washington, DC, 1979. (e) Deslongchamps, P. Stereoelectronic Effects in Organic Chemistry; Wiley: New York, 1983. (f) Lemieux, R. U. Pure Appl. Chem. 1971, 25, 527. (g) Romers, C.; Altona, C.; Buys, H. R.; Havinga, E. Top. Stereochem. 1969, 4, 39. (2) (a) Altona, C. PhD Thesis, University of Leiden, 1964. (b) David, S.; Eisenstein, O.; Hehre, W. J.; Salem, L.; Hoffmann, R. J. Am. Chem. Soc. 1973, 95, 3806. (3) (a) Reed, A. E.; Schleyer, P. v. R. Inorg. Chem. 1988, 27, 3969. (b) Salzner, U.; Schleyer, P. v. R. J. Org. Chem. 1994, 59, 2138. references cited therein. (4) (a) Schleifer, L.; Senderowitz, H.; Aped, P.; Tartakovsky, E.; Fuchs, B. Carbohydr. Res. 1990, 206, 21. (b) Fuchs, B.; Schleifer, L.; Tartakovsky, E. NouV. J. Chim. 1984, 8, 275. (c) Fuchs, B.; Ellencweig, A.; Tartakovsky, E.; Aped., P. Angew. Chem., Int. Ed. Engl. 1986, 25, 287. (d) Aped, P.; Apeloig, Y.; Ellencweig, A.; Fuchs, B.; Goldberg, I.; Karni, M.; Tartakovsky, E. J. Am. Chem. Soc. 1987, 109, 1486. (e) Aped, P.; Schleifer, L.; Fuchs, B.; Wolfe, S. J. Comput. Chem. 1989, 10, 265. (f) Senderowitz, H.; Aped, P.; Fuchs, B. HelV. Chim. Acta 1990, 73, 2113. (g) Senderowitz, H.; Aped, P.; Fuchs, B. J. Comput. Chem. 1993, 14, 944. (h) Senderowitz, H.; Aped, P.; Fuchs, B. Tetrahedron 1993, 49, 3879. (i) Senderowitz, H.; Fuchs, B. J. Mol. Struct.: THEOCHEM 1997, 395/396, 123. (j) Alder, R. W.; Carniero, T. M. G.; Mowlam, R. W.; Orpen, A. G.; Petillo, P. A.; Vachon, D. J.; Weisman, G. R.; White, J. M. J. Chem. Soc., Perkin Trans. 2 1999, 589.

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