Inversion and rotation barriers

Variable temperature H NMR has been employed by several groups to determine inversions and rotation barriers. Bolinger and Rauchfuss83 examined the inversion (Scheme 5) for the series (Cp)2Ti(E2R) (E = S, Se R = C2(C02Me)2, C2(CF3)2, C6H4Me). 

A number of azabicyclic derivatives have also been investigated (7 ICC 1104) as model compounds to study the effect of increasing the nitrogen inversion barrier upon the amide rotational barrier. From the experimental results and simplified MO pictures of the inversion and rotational mechanism, the authors (71CC1104) conclude that changes in the amide rotational barrier do not necessarily correspond to enhancement of the nitrogen inversion barrier. 

The same authors, in a different paper (93JA3494), have shown that the N-R substituent prefers to be equatorial and that the conformation about the exocyclic N-R bond is due to a rapid equilibrium between two nearly eclipsed conformations (cf. Scheme 37b). The second ground state of the dynamic process, the own-conformation (after 180° of rotation), could not be detected experimentally but was calculated by molecular dynamics to be less stable by 5.5 kcal/mol than the preferred, vy -conformers, e.g., 99h (cf. Scheme 37). The transition state in 99b-e and 99g-l occurs when the exocyclic substituent has its maximum interaction with an equatorial methyl group about 120° on either side of the ground state. The dynamic behavior of 99h,i and 99o (R = Bu) was also studied by the MM3 force field (99CEJ449) the authors concluded that the experimental barriers of 99h,i and 99o belong to a complex combination of ring inversion, N-inversion and rotation about the exocyclic bond. 

Before discussing structural effects on barrier heights, it is necessary to distinguish between the two processes planar nitrogen inversion and rotation about the C=N bond, which may both lead to interconversion of the isomers. Rotation about a non-activated C=N double bond is expected to be hindered by an energy barrier similar to the ethylene barrier, i.e. of the order of 50—60 kcal/mole 121.132) Thus, alkyl- and presumably also aryl-substituted imines, which show interconversion barriers below 30 kcal/mole (Table 6), undergo nitrogen inversion ). 

Ionization energies can be computed to about 0.2 eV rotational barriers to about 0.5 kcal/mol dipole moments to about 0.5 D barriers to inversion to about 2.5 kcal/mol infrared frequencies can be computed with about a 15% error (usuaHy too high) and protonation energies are accurate to about 1 piCunit. 

There is another mechanism for equilibration of the cation pairs A, Aj and B, Bj, namely, inversion at oxygen. However, the observed barrier represents at least the minimum for the C=0 rotational barrier and therefore demonstrates that the C-O bond has double-bond character. 

Closely related to conformational energy differences are barriers to single-bond rotation and to pyramidal inversion. Here the experimental data are restricted to very small systems and derive primarily from microwave spectroscopy, from vibrational spectroscopy in the far infrared and from NMR, but are generally of high quality. Comparisons with calculated quantities are provided in Table 8-3 for single-bond rotation barriers and Table 8-4 for inversion barriers. The same models considered for conformational energy differences have been surveyed here. 

As with conformational energy differences, SYBYL and MMFF molecular mechanics show marked differences in performance for rotation/inversion barriers. MMFF provides a good account of singlebond rotation barriers. Except for hydrogen peroxide and hydrogen disulfide, all barriers are well within 1 kcal/mol of their respective experimental values. Inversion barriers are more problematic. While the inversion barrier in ammonia is close to the experimental value, barriers in trimethylamine and in aziridine are much too large, and inversion barriers in phosphine and (presumably) trimethylphosphine are smaller than their respective experimental quantities. Overall,... 

MP2 models provide broadly similar results to the best of the density functional models for both rotation and inversion barriers. For rotation barriers, the MP2/6-311+G model provides improvement over MP2/ 6-31G. On the other hand, the two models yield very similar inversion barriers, perhaps reflecting the fact that bond angles involving nitrogen and phosphorous change only slightly between the two. 

Semi-empirical models are markedly inferior to all other models dealt with (except the SYBYL molecular mechanics model) for barrier calculations. Major trends in rotation barriers are often not reproduced, for example, the nearly uniform decrement in rotation barrier from ethane to methylamine to methanol. None of the semi-empirical models is better than the others in this regard. One the other hand, AMI is clearly superior to MNDO and PM3 in accounting for nitrogen inversion barriers. All in all, semi-empirical models are not recommended for barrier calculations. 

Semi-empirical models do not provide good descriptions of the energy barrier to ring inversion in cyclohexane. The MNDO model underestimates the barrier by a factor of three, and the AMI and PM3 models by almost a factor of two. This behavior is consistent with previous experience in dealing with single-bond rotation barriers. 

Compilations of experimental data relating to conformational energy differences and rotation/inversion barriers may be found in (a) T. A. Halgren andR.B. Nachbar,/. ComputationalChem., 17, 587 (1996) (b) T.A. Halgren,... 

---