Principles of Least Motion PLM

The possibility that reacting species prefer to react along those paths in which they undergo the least modification has always been intuitively attractive. At one time or another, so-called principles of minimum structural change or deformation, configurational change, and minimum atomic and electronic motion have been invoked (Wheland, 1960 Hine, 1966). To account for Michael s rule of favored anti 1,2-addition, Pfeiffer formulated acetylenes as tram-heat structures in 1904 Frankland (1912) suggested that anti elimination is favored by an inherent tendency to centric symmetry. The more conscious applications of PLM by Muller after 1886, are probably misapplications of the principle, since they were usually concerned with complex pyrolytic reactions above 1000° (Muller and Peytral, 1924). 

Wheland (1960) made the point in several ways that these principles could lead to absurd errors. When ethyl chloride is treated with hydroxide ion, we obtain ethanol, not dimethyl ether but when iso-bornyl chloride is treated in the same way we obtain camphene after a deep-seated skeletal rearrangement. Although nucleophilic substitution at an ethylenic center goes with retention (Miller and Yonan, 1957), the Walden inversion undercuts any general principle of minimum configurational change. Likewise, an early PLM representation of the 

Beckmann rearrangement in 98 had to give way to 99 which is in accord with observation (Meisenheimer and Theilacker, 1932). Nevertheless, Hine (1966) believes he has found a variety of reactions whose course PLM appears to control. Moreover, we too have used PLM arguments in the section on substitution reactions (III E). 

Initially, Hine (1966a) related PLM to the London-Eyring-Polanyi approach to three-center reactions. Since this method cannot easily be applied to most systems of interest, approximate methods have to be used. One of these minimizes bond motions and bond distortions. The geometric changes in pentadienyl or cyclohexadienyl anions brought about by protonation (Bates et al., 1967) in equation (192) are assumed to be roughly parallel to changes in bond order (BO). For deuteriation on the end carbons, 27(BO)2 = 2(2/3)2 + 2(l/3)2 = 10/9 for deuteriation 

To retain PLM as a guiding idea rather than a principle, we would limit its scope and rename it, the Hypothesis of Least Motion (HLM). Given that other factors are constant, one should consider HLM. Of the elementary paths from A to B, for example, one is of lowest free energy and presumably involves the least motion. It becomes more hazardous to extend this idea to evaluate two elementary paths A to B versus A to C. Our own attitude to HLM is ambivalent because of its simplicity, there should be no hesitation about applying HLM widely, even indiscriminately having done this, one should assess the results critically. 

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A tacit assumption in the change from tetrahedron to bipyramid is that the principle of least motion (PLM see a later section) holds. On this basis, the choices in Table 7 were set up. According to the energy criterion supplied by Van Der Voorn and Drago (1966), symmetrical substitution with inversion, i.e. equatorial in—equatorial out, or axial in—axial out, should be the rule for trigonal bipyramidal transitionstates. 

STEREOSELECTION IN STEPS OP ORGANIC REACTIONS 301 D. Principles of Least Motion (PLM)... 

Back in 1938 Rice and Teller [88] formulated the general principle which stated that those elementary reactions are the most favored which exhibit the fewest possible alterations in the positions of atomic nuclei and in electronic configuration. The part referring to the electron configuration was later developed into the Woodward-Hoffmann rules, while that concerning the nuclear shifts became known as the principle of least motion of nuclei or simply the principle of least-motion (PLM) [89,90] ... 

Rearrangements. "—Cyclopropyl-Allyl Rearrangement. This is one of the molecular rearrangements which has been investigated by calculations based upon the principle of least motion (PLM). ° In agreement with more sophisticated theoretical methods, PLM leads to the correct prediction of which of the two disrotatory openings will occur in the cyclopropyl-allyl transformation. 

PLM (Principle of Least Motion) favors axial over equatorial entry and departure. 

In contrast to the explanations based on steric considerations, the principle of least motion unambiguously predicts that abstraction of the 3-exo-H is much easier than that of the 3-endo-H in the 2-norbornanone series. Indeed, the parameter EmXn (see above), which expresses the amount of the coordinate variations of the nuclei, is much smaller for 3-exo-H (2.46 A2 for 2-norbornanone) than for 3-endo-H (5.94 A2) (Tee et al., 1974). However, as emphasised by the authors of this work the success of the PLM method does not necessarily imply that least motion of atoms is itself the factor which determines the stereochemical pathway. It may well transpire that the least-motion type of calculation, by virtue of its geometric constraints and... 

PBA poly(butyl acrylate) PLM principle of least motion... 

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