Approach angle

In an intramolecular cyclization, attack on the end of the double bond closest to the radical center (an exocyclic cyclization) achieves the proper approach angle. Attack on the other olefinic carbon requires that the radical reach across the double bond to achieve the proper approach angle. This is a higher energy path and is kinetically disfavored. The same arguments hold for cyclizations which can produce six- or seven-membered rings. 

Lewin, M., Guilhaus, M., Wildgoose, J., Hoyes, J., and Bateman, B. (2002). Ion dispersion near parallel wire grids in orthogonal acceleration time-of-flight mass spectrometry Predicting the effect of the approach angle on resolution. Rapid Commun. Mass Spectrom. 16 609-615. 

Barrier heights in bimolecular reactions depend on the approach angle. For example, in D + H2 — H + HD (and its isotopic variants), the lowest barrier is found when D attacks along the bond axis of H2, that is, collinearly. 

Fig. 3.1.1 A potential energy surface for a direct bimolecular reaction. The surface corresponds to a reaction like D + H — H—>D — H + Hata fixed approach angle, say in a collinear configuration specified by the D-H and H-H distances. These distances are measured along the two perpendicular axes. (Note that in this figure all energies above a fixed cut-off value Emax have been replaced by max.)...

Fig. 3.1.3 Energy along the reaction coordinate for the reaction D + H — H —> D — H + H (and its isotopic variants), as a function of the approach angle. Note that the lowest barrier is found for the collinear approach. [Adapted from R.D. Levine and R.B. Bernstein, Molecular reaction dynamics and chemical reactivity (Oxford University Press, 1987).]...

Fig. 3.1.4 Contour plot of a potential energy surface for the reaction A + BC —> AB + C. The surface is shown as a function of the two internuclear distances Rab and Rbc at a fixed approach angle. The barrier (marked with an arrow) occurs in the entrance channel, i.e., an early barrier.

Because of the entrance channel regiospecificity, the question has often been asked is it possible that the different OH level distributions relative to the gas phase are simply due to the restricted set of hydrogen approach angles and impact parameters We think not, because this would require the HOCO1 intermediate to behave quite nonstatistically, and under the present experimental conditions this seems unlikely. This will be discussed further in subsection 3.2.4. 

When the two transition states are compared, the radical approach angle in the transition state of 5-exo-trig manner is closer to a = 109° than that in 6-endo-trig manner. 

Bridging electrophiles, as in epoxidation, are fairly well behaved in the sense 5.132, possibly because the acute approach angle does not leave room for the medium-sized group to sit inside. Bromination, however, is reversible in the first step, and the stereochemistry actually observed, although often in the sense 5.132, is partly governed by the relative ease with which each of the diastereoisomeric epibromonium ions is opened. As a consequence, the ratio of diastereoisomers is not reliably a measure of the relative rates of attack on the diastereotopic faces of the alkene. 

The electroresistivity probe, recently proposed by Burgess and Calder-bank (B32, B33) for the measurement of bubble properties in bubble dispersions, is a very promising apparatus. A three-dimensional resistivity probe with five channels was designed in order to sense the bubble approach angle, as well as to measure bubble size and velocity in sieve tray froths. This probe system accepts only bubbles whose location and direction coincide with the vertical probe axis, the discrimination function being achieved with the aid of an on-line computer which receives signals from five channels communicating with the probe array. Gas holdup, gas-flow specific interfacial area, and even gas and liquid-side mass-transfer efficiencies have been calculated directly from the local measured distributions of bubble size and velocity. The derived values of the disper-... 

The potentials of the different states of the Cq+ -Uracil collision system may then be calculated along the reaction coordinate R for different approach angles 0, from perpendicular (0 = 90°) to planar geometry (0 = o°) (Figure 3a), in order to take into account the anisotropy of the process. This requires, of course, extensive... 

Figure 2.3 Typical configurations on discrete/obstacle scale. Normal approach angle 0 small enough (i.e. cos0 > 2w/d) for independent wakes to be formed (approximately parallel to the approach wind). Note the complex forms of obstacle wakes, in which swirl may persist.

Figure 2.5 Normal approach angle

At around 2.0 A, the calculated approach angle H... C=0 is ca. 120° and the pyramidalization becomes appreciable, although still rather small the angle between H... C and the H-C-H plane is ca. 65°. An angular displacement of 10° from the minimum energy path either in the H... C = O plane or in the lateral sense seems to require 1 to 1.5 kcalmoP. Below 2.0 A this funnel narrows considerably and... 

Since the approach angle was not optimized in these calculations, a separate assessment of the factors governing deviation from the direction normal to the carbonyl plane was made. Energy optimization for the model supermolecule HCHO-l-H" (fixed distance 1.5 A) and overlap calculations for H" and jt (C=0) were carried out for approach angles from 90° to 115° by increments of 5°. The optimal angle was found to be 110°. The authors concluded that the deviation is due almost entirely to the interaction with the 7t (C=O) orbital, since maximal overlap is obtained for 105°. 

The initial approach angle (C-H-M) of about 130° was rationalized in terms of a proposed interaction between the C - H o bond and an empty metal d orbital, and back-donation from a filled d orbital to a a orbital of the C-H system, but this angle may also result from geometrical factors. The role of steric and conformational effects in the balance between cyclometallation and attack on an external substrate (such as an alkane), was discussed in the context of the above reaction path. The conclusion was that sterically uncongested metal systems are more likely to activate alkanes, than to undergo cyclometallation. 

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