Reaction paths least-motion path

The so-called least-motion path has been popular for many years. In the original formulation, the elementary reactions that involve the least change in the atomic and electronic configurations are favored (160,161). This hypothesis has found numerous applications in organic and inorganic chemistry (162-167). However, it is necessary to admit that there exist rather numerous exceptions, primarily due to the fact that the non-least-motion pathway is symmetry allowed while the least-motion path is symmetry forbidden (168,169). Dimerization of singlet carbenes is a typical example. 

These results can be easily rationalized in terms of a diabatic surface analysis. For illustrative purposes, we report here the diabatic surface analysis for the dimerization of methylenes and for the coupling reaction of methylene and silylene along the least-motion path the fragments here are in one case two CH2 and in the other case a CHj and a SiH2. The geometry of the CH2 fragment in both reactions is assumed to be equal to the geometry of ethylene (Rch=1-07A and = 115.9 ), while that of the SiHj... 

Fig. 8. Diabatic (SS and TT) and adiabatic (E-r) curves for the coupling reaction of CHj and SiH2 along the least-motion path. TT denotes the curve associated with the triplet-triplet IFC. (From Bernardi and Robb. Reproduced by permission of Taylor and Francis Ltd, Publishers.)... 

The situation is less clear for the reaction between methylene and silylene here, in fact, an inspection of Fig. 8 for large values of R shows an avoided crossing of the TT and SS diabatic curves, leading to a small barrier. However, because of the limitations of these computations, this finding has to be taken with caution. Actually, a recent calculation indicates that silaethylene also dissociates through a least-motion path into a triplet methylene and a triplet silylene. The comparison between these two types of result for the reaction between methylene and silylene shows that it can be misleading in some cases to draw conclusions based only on diabatic curves rather than on the more informative diabatic surfaces. ... 

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). 

Consider as an example a reaction of the degenerate rearrangement of the 71-complex of chromium naphthalene-tricarbonyl XLIII. It would be natural to assume as an intermediate structure or a transition state the structure XLIIIa in which the group Cr(CO)3 is located between two nuclei on the least-motion path. 

In some cases orbital symmetry rules can label the least-motion approach of two reacting fragments as forbidden. Semi-empirical MO calculations, such as EHT ones, can then be used to pick out the minimum-energy path, as outlined in the foregoing section. Another example is given by the reactions 17) ... 

For 5-alkylidenetetrazolines (33) three reaction paths have to be considered. They afford either N-methyl ketene imines and methyl azide, or, in addition to molecular nitrogen, a 3-alkylidenediaziridine (least-motion path) or a methyliminoaziridine (non-least-motion path). As was shown by... 

Basch in 1970 carried out one of the first MCSCF calculations on a polyatomic system216 in an investigation of the least-motion, coplanar approach of two methylenes to give C2H4. For two closed shell, singlet state methylenes, the reaction path is purely repulsive, and the reaction occurs for two appropriately oriented bent triplet methylenes. 

The situation with respect to the photobehavior of 7-chlorocoumarin is interesting (Fig. 11). There are two reaction pathways in this crystal one that favors the formation of the vyn-IIII isomer arising from reaction between the transla-tionally related molecules with a center-to-center distance of 4.54 A and another that would yield the anti-HT dimer, corresponding to the reaction between the centrosymmetrically related molecules, the center-to-center distance being 4.12 A. Experiment clearly shows that only the yy -HH dimer is obtained—not the one that would correspond to the path of least motion. This is supported by the results of the lattice energy calculations. The implication is that the shape of the free volume is anisotropic, with the larger volume or extension in the direction of the translational periodicity of 4.54 A. 

As can be seen, this index attains its maximal value of unity for two identical structures (9 = 9,

monotonously decreases. The use of this index for the formulation of the least motion principle arises from the following simple idea. Let us assume that we are on a reaction path at point characterised by the wave function P(, q> ) and we are looking for such an infinitesimally close structure (9, (p) for which the transformation (9,

requires minimal change in electronic configuration. This condition is equivalent to a search of the direction along which the derivative of K at the point = 9 and q> = q> attains its minimum. This directional derivative can be mathematically described as (27),... 

Let us discuss now the most important conclusions that can be deduced from these figures. First, the most important conclusion concerns the comparison of the values of functional L along the optimal allowed and forbidden reaction paths. As can be seen, the value for the allowed conrotatory cyclisation is lower in absolute value than in the forbidden one. This confirms the intuitive expectation of the least motion principle that the extent of electron reorganisation should be smaller in allowed reactions than in the forbidden ones. On the basis of this primary test of reliability of the proposed model it is, in the next step, possible to start with the analysis and the classification of the reaction mechanisms for both individual reactions. Especially interesting in this connection is again the thermally forbidden disrotatory cyclisation. The reason for this... 

In order to assess the relative reactivity of different diacetylene monomers the packing parameters can be analysed in terms of a reaction along a least motion reaction path, i.e. the molecules simultaneously rotate and translate along the stacking direction In this model maximal reactivity is expected for d 5 A and 45°. 

---