Torsional dependence

Jiang, X., C-H. Yu, M. Cao, S. Q. Newton, E. F. Paulus, andL. Schafer. 1997. cfr/ifr Torsional Dependence of Peptide and Protein Backbone Bond-Lengths and Bond-Angles Comparison of Crystallographic and Calculated Parameters. J. Mol. Struct. 403, 83-93. 

Fig. 7.6 The torsional dependence of the central C-C bond distances in some substituted ethanes. All curves are graphs of relative values taken from L. Schafer, J. D. Ewbank, V. J. Klimkowski, K. Siam, and C. van Alsenoy, J. Mol. Struct. 135 (1986) 141, and L. Schafer, M. Cao, M. Ramek, B. J. Teppen, S. Q. Newton, and K. Siam, J. Mol. Struct, in press.

Figure 3.51 also contains a dissection of the total energy ( totai) into Lewis (ii(L)) and non-Lewis (ElSL>) components. The localized Lewis component E" corresponds to more than 99.3% of the full electron density, and so incorporates steric and classical electrostatic effects in nearly exact fashion. Yet, as shown in Fig. 3.51, this component predicts local minima (at 70° and 180°) and maxima (at = 0° and 130 ) that are opposite to those of the full potential. In contrast, the non-Lewis component E (NL) exhibits a stronger torsional dependence that is able to cancel out the unphysical behavior predicted by (L), leading to minima correctly located near 0° and 120°. Thus, the hyperconjugative interactions incorporated in E(SL> clearly provide the surprising stabilization of 0° and 120° conformers that counter the expected steric and electrostatic effects contained in ElL>. 

Figure 3.52 Leading hyperconjugative stabilizations in CFH2CH = CH2, showing the torsional dependence of n-o (solid lines) and a-n interactions (dotted lines) for the C—F (crosses) and two C—FI bonds (triangles, circles) of the—CFF12 group. The sum of all six interactions is shown as the heavy solid line (squares), which may be compared with the total barrier potential in Fig. 3.51.

Figure 3.76 The torsion-dependent composition of the croNf NLMO of the3 n -> 7t excited state of the model aminoketone shown in Fig. 3.75.

The factors influencing the conformational stability in open chain molecules have previously been treated extensively in review articles (see for example Ref.6 and 107 ). The aim of the present section is to study torsional potential functions of a series of molecules of principal importance, in particular related to the results of electron-diffraction investigations. The bulk contents of information obtainable from an electron-diffraction intensity curve of a molecule carrying out torsional motion, are not concerned with the torsional motion at all. The part of the intensity curve giving information about the torsion, is distributed over the same range of the intensity curve as where the torsional independent information may be obtained. In the RD-curve the contribution from the torsional dependent part is more clearly separated. To illustrate this and the general influence of torsional motion, three simple molecules with three-fold torsional barriers have been selected (Figs. 3-5)... 

Fig. 3. Radial distribution curves for hexachloroethane. The vertical lines give the Cl Cl positions in gauche ( ) and anti (a). Curve A is experimental, the dashed line combined with the other part, indicates the torsional dependent contribution, obtained by subtracting the theoretical torsional insensitive part from the experimental curve. Curves B-E are theoretical torsional dependent distribution curves. (B) based on a rigid, staggered model with ug = 14.3, ua = 6.7 (pm). (C-E) calculated for large amplitude models, using framework vibrations and a torsional potential 5-V3 (1 +cos 30) with V3 equal to 12.5,4.2, andO(kJ /mol), respectively. The scaling between A and the other curves is somewhat arbitrary, and the damping factors and modification functions slightly different...

Table 3. Some torsional dependent observed quantities for molecules with symmetric end-groups. Central distance (R) and u-values in pm, torsional amplitude (a ) in °, Fourier term (Vn) in kJmol"1...

Whether a staggered model will reproduce the torsion sensitive distance distribution with sufficient accuracy for intermediate barriers, or a weighted sum over Gaussian peaks has to be applied, will also depend on the total change in the torsion dependent distance compared to the u-values of the said distance. 

For bicyclopropyl each geometric species contains two torsion dependent C. .. C-distances. The positions of these distances are given in Fig. 10 both for anri and gauche. The effect of the large torsional amplitude in bicyclopropyl is demonstrated by the broad torsional dependent area in the RD-curve without well defined peaks. This is in contrast to the well defined nnri-peak in the corresponding part of the RD-curve for 1,3-butadiene. 

The maximum time step depends on the highest frequencies (usually R-H bonds). One of the main problems in dynamics calculations is that the movements leading to appreciable conformational changes usually have lower frequencies (milliseconds, e. g., torsions). Depending on the size of the molecule the computation of such long time intervals is usually prohibitive due to the CPU time and storage space involved. 

The similarity to the A A state bonding representation is conspicuous (the only difference lying in the half-occupancy of Uq in the A state vs. Uq in the C state), and the adiabatic relaxation patterns might be expected to be similar. The similarity of initial A- vs. C-state relaxation is also suggested by the small-angle torsional dependence in Figure... 

Torsional dependence of the electronic energies of the ground state and singlet and triplet n,n states of ethene. (Adapted from references 108a and 108b.)... 

For the classical vibrational analysis ( which does not yet consider -dependent modes) we know that the conformational dependence of the IR and Raman spectra (frequencies and intensities) of polyaromatic molecules linked by "single" C-C bonds should be very small for small deviation out of planarity. As fully discussed in other simple cases [ 142,143 ] in principle the lowering of the symmetry produced by the conformational twisting should give IR /Raman activity originally silent for the fully coplanar higher symmetry system. Slight frequency shifts of a few torsionally dependent normal modes can also be predicted and calculated. 

Most conspicuous in Fig. 6.4 are the steric variations (x s, dotted lines) of the three methyl protons as they successively twist into coplanarity with the adjacent kn lone pair (with Hg achieving such coplanarity at 30° for the dihedral range shown in Fig. 6.4). However, the sum of the three Mn o ch interactions is constant (as the rigid Csv symmetry of the methyl group demands), so these repulsions make no net contribution to the overall methyl torsional dependence. Instead, the most important CH methyl repulsion is expected to be that with the lone pair (circles, solid line),... 

The potential F(t) is shown in Fig. 10 while the normal mode frequencies versus x are presented in Fig 11. The bending frequencies, in particular, are seen to have a strong dependence on the torsional angle (up to 20%). Another source of coupling that can be included in our formalism is the torsional dependence of the rotation constants, which is also on the order of 20%. 

The overall faetor of 2J +1, not included in these formulae, thus cancels in the final expression. The result for J = 0 versus energy above the dissociation limit, 48.4 kcal/mol, is shown in Fig. 15. For comparison, the HO-RR and hindered rotor approximations are also presented. It is seen that the HO-RR method gives results that are about a factor 2-3 too low at most energies. Clearly, the harmonic approximation is inappropriate for the TS. The separable hindered rotor approximation gives an improvement over the HO-RR method. It corrects about half of that error, but still yields results that are about a factor of 1.5 too small. The coupling induced by the torsional dependence of the vibrational frequencies and rotational constants is seen to have a clear and potentially observable effect upon the rate coefficient. The lifetimes predicted by RRKM theory are of the same order of magnitude as the experimental observations. 

---