Why do ethyl [2-cyano-3-(n-butylamino)acryloyl]carbamate and its analogues stay as Z -isomers only ?

Density functional method and isodesmic reactions were used to explore relative stability between Z - and E -ethyl [2-cyano-3-(n-butylamino)acryloyl] carbamate ( 3 ). Hydrogen bonding stabilization (7.19 kcal/mol) in favor of Z - 3 and both steric hindrance (2.17 kcal/mol) and resonance stabilization (1.79 kcal/mol) in favor of E - 3 contribute the relative stability between Z - 3 and E - 3 , and that successfully explains why 3 stay as a Z -isomer only.


Introduction
Isodesmic reactions are not real chemical reactions and can be set up according to the criterion that the total number of each type of bond is identical in the reactants and products. 1They were designed to successfully predict the heat of formation, 1 substituent effects on the stability of functional groups, 2 and contribution of steric hindrance and resonance stabilization to the stability of E/Z-isomers 3a .
As shown in Scheme 1, ethyl (2-cyano-3-ethoxyacryloyl)carbamate (1) 3 and ethyl 2-cyano-3-ethoxyacrylate (2) 4 were found to stay as an E-isomer exclusively.E-1 is much more stable than Z-1 because of contribution of both resonance stabilization (1.47 kcal/mol) and steric hindrance (2.28 kcal/mol) in favor of E-1.3a These compounds are push-pull olefins, 5 and the barrier for the isomerization of Z-1 to E-1 was found as small as 19.6 kcal/mol experimentally.When we treated E-1 with n-BuNH 2 , t-BuNH 2 , or aniline in CDCl 3 and monitored the reactions with NMR spectrometry, we found that both E-and Z-isomers of 3, 4, or 5 were formed at the beginning but eventually all the E-isomers were converted to the corresponding the Z-isomers. 6(Scheme 2) It is clear that 3, 4, or 5 are all push-pull olefins and the isomerization barriers from the E-isomers to the Z-isomers should be low, so the E/Z isomerization is feasible at room temperature.In contrast to the fact that 1 completely stays as an E-isomer (Scheme 1), its nitrogen analogues 3, 4, and 5 exist as Z-isomers exclusively.To explain these facts, 3 was used as a model compound.We explored relative stability between Z-3 and E-3 and analyzed the contribution of steric hindrance, resonance stabilization, and hydrogen bonding stabilization to the stability of Z-3 and E-3 by means of density functional method and isodesmic reactions.

Computation
All the calculations reported here were performed with Gaussian98 program. 7All the structures of Z-3, Z-3a, E-3, E-3a, Z-4, E-4, Z-5, E-5, Z-6, E-6, Z-7, E-7, 8, 9, Z-10, E-10, Z-11, E-11, and 12 were optimized at level of B3LYP/6-31+G* without any symmetry restriction except that C-F, C=C and C=O of Z-11 and E-11 were kept in the same plane in order to mimic Z-10 and E-10.Vibration frequencies and zero-point vibration energies were calculated at the same level, and the zero-point vibration energies are scaled by 0.9804 according to the literatures. 1Their calculated energies are shown in Table 1.Many possible conformations have been optimized for each of the structures and the one with lowest energy was chosen.

Results and Discussion
As shown in Fig. 1, major conformers, Z-3 and Z-3a, were located for the Z-isomer of 3, and Z-3 is 13.9 kcal/mol more stable than Z-3a.All the enamine, nitrile, and C(O)NHC(O)OEt groups of Z-3 stay in a plane with an intramolecular hydrogen bonding of NH--O=C whose distance is 1.89Å.However, in Z-3a the C(O)NHC(O)OEt group is twisted away from its molecular plane formed by enamine and nitrile groups in order to avoid steric hindrance with the amino group.
Major conformers, E-3 and E-3a, were located for the E-isomer of 3 (Fig. 1), and E-3 is 7.17 kcal/mol more stable than E-3a.All the enamine, nitrile, and C(O)NHC(O)OEt groups of E-3 stay in a plane but there is no intramolecular hydrogen bonding.In contrast, in E-3a the C(O)NHC(O)OEt group is twisted away from its molecular plane formed by enamine and nitrile groups in order to avoid steric hindrance with the vinyl hydrogen.Based on the above analysis, ARKAT the more stable conformers for Z-and E-isomer of 3 are Z-3 and E-3, respectively, which have a common structure feature: s-cis conformation for C=C-C=O.By this way, they can pull the C(O)NHC(O)OEt group away from vinyl hydrogen or the amino group to avoid steric hindrance.Calculated thermodynamic data for the conformational and E/Z configurational isomerizations of 3 at the B3LYP/6-31+G* level are shown in Table 2. Experimental results indicate that E/Z isomerization of 3 from the E-isomer to the Z-isomer is spontaneous at room temperature, 6 but calculated ∆G values of E/Z isomerization from E-3 to Z-3a or from E-3a to Z-3a are 9.51 and 2.67 kcal/mol, respectively, indicating that these two thermodynamically unfavorable processes are not consistent with the experimental results.On the other hand, calculated ∆G values of E/Z isomerizations from E-3 to Z-3 or from E-3a to Z-3 are -2.64 and -9.49kcal/mol, respectively, indicating that these two processes are thermodynamically favorable.In addition, more than 99.99% of E-isomers of 3 stay as E-3, based on the equation of ∆G = -RT(lnK) 8 and its ∆G value of -6.84 kcal/mol.Therefore, E/Z isomerization of 3 from the Eisomer to the Z-isomer is supposed to involve isomerizations from E-3 to Z-3.Negative entropy (∆S) is not favorable for this process.The major factor, which dominates this isomerization, is enthalpy (∆H), which is close to the relative stability (∆E).At the B3LYP/6-31+G* level Z-3 is 3.36 kcal/mol more stable than E-3, and that is consistent with the experimental E/Z isomerization results, indicating that the relative stability between E-3 and Z-3 does explain why 3 stays as a Z-isomer only.Then we want to analyze why Z-3 is much more stable than E-3 according to four independent factors: dipole moment, steric hindrance, resonance stabilization, and hydrogen bonding stabilization.
As shown in Table 1, dipole moments of Z-3 and E-3 are 3.97 and 4.87 debye, respectively, at B3LYP/6-31+G* level.Chloroform is a nonpolar aprotic solvent with dielectric constant of 4.81 while acetonitrile is a dipolar aprotic solvent with dielectric constant of 36.6.9a Based on a useful rule of thumb -"like dissolves like", 9b acetonitrile may stabilize E-3 better than Z-3, while chloroform may stabilize Z-3 better than E-3.However, the only stable isomer of 3 in both chloroform and acetonitrile is Z-3, indicating that dipole moment is not a major factor to make Z-3 much more stable than E-3.
The isomers, E-3 and Z-3, can be divided into two systems: Z-4/E-5 and E-4/Z-5, respectively.Isodesmic reactions of Eq.1~4 were designed to explore contribution of steric hindrance, resonance stabilization, and hydrogen bonding stabilization to the stability of Z-4, E-5, E-4, and Z-5, respectively.Optimized structures of Z-4, E-4, Z-5, E-5, 8, 9 at the B3LYP/6-ARKAT 31+G* level are shown in Fig. 2. Therefore, the sum of ∆E 1 and ∆E 2 of Eq.1~2 is the estimate for the contribution of steric hindrance and resonance stabilization to the stability of E-3, and the contribution of steric hindrance, resonance stabilization, and hydrogen bonding stabilization to the stability of Z-3 is estimated by the sum of ∆E 3 and ∆E 4 of Eq.3~4.Based on the isodesmic reactions of Eq.1~4, the relative stability between Z-3 and E-3 should equal to (∆E 3 + ∆E 4 ) -(∆E 1 + ∆E 2 ) = 3.23 kcal/mol, which is close to their relative energy difference of 3.36 kcal/mol at the B3LYP/6-31+G* level.
Steric hindrance between vicinal substituents across C=C bond in E-4 and E-5 is around 0.0 kcal/mol.Because Van der Waals radii of NH is close to that of CH 2 , 8 in order to consider steric hindrance in Z-4 and Z-5, the pentyl group replaced n-butylamino substituent and Z-6, E-6, Z-7, and E-7 were designed for a significant reduction of resonance effect along two substituents across C=C.Optimized structures of Z-6, E-6, Z-7, and E-7 at the B3LYP/6-31+G* level are shown in Fig. 3. Therefore, steric hindrance [Es(Z-4)] in Z-4 is close to that [Es(Z-6)] in Z-6, which is estimated to be 0.27 kcal/mol by the isodesmic reaction of Eq.5.Similarly, steric hindrance [Es(Z-5)] in Z-5 is about the same as that [Es(Z-7)] in Z-7, which is approximately 2.44 kcal/mol based on the isodesmic reaction of Eq.6.The ∆E 1 , ∆E 2 , and ∆E 3 of Eq.1~3 include the contribution of repulsive steric hindrance and resonance stabilization to the stability of Z-4, E-5, and E-4, and their repulsive steric hindrance is just estimated, so the contribution of resonance stabilization to the stability of Z-4, E-5, and E-4 is approximately 19.26, 19.50, and 17.33 kcal/mol, respectively.On the other hand, ∆E 4 of Eq.4 includes the contribution of repulsive steric hindrance, resonance stabilization, and hydrogen bonding stabilization to the stability of Z-5, and its steric hindrance [Es(Z-5)] is 2.44 kcal/mol, so the contribution from both resonance stabilization and hydrogen bonding stabilization to the stability of Z-5 is approximately 26.83 kcal/mol.
To explore what the hydrogen bonding stabilization in Z-5 is, Z-10 was designed with N-F bond replacing N-H bond and its optimized structure at the B3LYP/6-31+G* level is shown in Fig. 4. The isodesmic reaction of Eq. 7 can estimate the contribution of steric hindrance and resonance stabilization to the stability of Z-10.To find out what the steric hindrance in Z-10 is, the 1-fluoropentyl group replaced N-fluoro-n-butylamino substituent and Z-11 and E-11 were designed for a significant reduction of resonance effect along two substituents across C=C.The optimized structures of Z-11 and E-11 at the B3LYP/6-31+G* level are shown in Fig. 4. Therefore, the steric hindrance [Es(Z-10)] in Z-10 is close to that [Es(Z-11)] in Z-11, which is estimated to be around 11.63 kcal/mol according to the isodesmic reaction of Eq. 8.Then, based on ∆E 7 of the isodesmic reaction of Eq.7 and Es(Z-10), the contribution of resonance stabilization [E R (Z-10)] to the stability of Z-10 is approximately 9.72 kcal/mol, which is small compared with the resonance stabilization in Z-4, E-5, and E-4.It is clear that the N-F substituent may change resonance stabilization when Z-5 is replaced by Z-10.To find out the change extent of this resonance stabilization, E-10 and the isodesmic reaction of Eq.9 were designed and the resonance stabilization difference between Z-5 and Z-10 is approximately equal to that between E-5 and E-10, which is 9.92 kcal/mol (= E R (E-5) -E R (E-10)).Based on this calculated resonance stabilization difference and E R (Z-10), the contribution of resonance stabilization [E R (Z-5)] to the stability of Z-5 is calculated to be 19.64 kcal/mol, which is reasonable compared with the ARKAT resonance stabilization in Z-4, E-5, and E-4.According to the calculated E R (Z-5), Es(Z-5), and ∆E 4 of Eq.4, the contribution of hydrogen bonding stabilization [E H (Z-5)] to the stability of Z-5 is estimated to be 7.19 kcal/mol, which is reasonable compared with known hydrogen bonding.

Conclusions
At the B3LYP/6-31+G* level Z-3 is 3.36 kcal/mol more stable than E-3, and that explains why 3 stays as a Z-isomer only.The relative stability between Z-3 and E-3 is contributed from 7.19 kcal/mol of hydrogen bonding stabilization in favor of Z-3 and both 2.17 kcal/mol of steric hindrance and 1.79 kcal/mol of resonance stabilization in favor of E-3.Intramolecular hydrogen bonding in Z-3 plays an important role in the relative stability between E-3 and Z-3.