The Principle of Least-Motion

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]  

Implicitely, as the principle of minimal structural changes, the PLM gained long ago currency among organic chemists as one of their basic concepts. The mathematical formulation of the PLM rests on a mechanical model of the molecule in which the energy of structural deformation, when initial reactants (r) turn into products (p), is assumed to be proportional to the sum of the squares of the changes in the positions of the nuclei common for r and p  

The direction of reaction associated with the minimal deformation energy is considered preferable. The changes in the coordiates qi corresponding to the values of permit conclusions to be drawn as to the reaction path and reaction coordinate. For example, in the case of the dehydrohalogenation of vinyl halogenides XXVIII considered earlier the calculated value of for trans-elimination of hydrohalogenide amounts to 0.32 A (/, = 1), while for the cis-elimination it is 1.24 A whence a conclusion may be made in favor of the former direction. 

The principal equation of the PLM [Eq. (1.31)] coincides with the standard relationships for the potential energy of small vibrations, hence it is valid only in the earliest stage of a reaction. There are suggestions [84, 89] that a promising 

Numerous reactions violate the PLM requirements. Thus, as may be seen from Fig. 1.9, the addition of hydrogen to methylene does not take place along the least motion path, i.e., with retention of C2V symmetry of the reacting system (Sect. 1.3.3.1). 

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It can be seen that the two bonds whose bond order is 1 are unchanged in the two products, but for the other four bonds there is a change. If the 1,4-diene is formed, the change is 5 + 5 + 5 -l- 5, while formation of the 1,3-diene requires a change of j + j + l + Since a greater change is required to form the 1,3-diene, the principle of least motion predicts formation of the 1,4-diene. This may not be the only factor, because the NMR spectrum of 46 shows that the 6 position has a somewhat greater electron density than the 2 position, which presumably would make the former more attractive to a proton. 

The stereochemistry of the electrocyclic ring opening following the attack of the nucleophile on the vinylic carbon appears to be governed by the principle of least motion . 

The isolation of the -isomer 139 was in fact unexpected, since all tetrasubstituted olefins previously obtained from thiirene dioxide have been assigned the cis-configuration with respect to the two phenyl substituents based on the principle of least motion during the ring opening to olefins ". It might well be, therefore, that the -isomer is obtained through the isomerization of the initially formed Z-isomer. 

Another question that has come up is why the addition of proton to carbanion occurs only at position 6 to give 1,4 diene and not at 2 or 4 to give a 1,3 diene This has been answered on the principle of least motion advanced by Hine according to which those reactions are favoured which involve the least change in atomic position and electronic configuration. 

CH2 reacts with ethylene to form cyclopropane. The symmetrical approach shown below appears to be the simplest. It also respects the principle of least motion, often invoked in the literature. Use FO analysis to show that this mechanism is improbable and to find the best approach. Assume that the carbene has a singlet configuration. 

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. 

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... 

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