The least motion path

We first comment on the so-called least motion path (LMP), in which the two H atoms move away from the CO atoms, maintaining a Czv symmetry, as shown in Fig. 16.6. Earlier calculations of all sorts indicate that this path does not cross 

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Fig. 8. a) Non-least-motion approach of two methylenes. The sequence 1-2—3 shows the mutual orientation of the two fragments with decreasing distance, b) Energy variation along the least-motion path (i) and along the least-energy path (2). The abscissa scale is the C-C distance (A). The vertical bar is 1 eV on the ordinate energy scale. 

In the photolysis of methyl-(3,5,5-trialkyl-3,5-dihydro-[l,2,3]triazol-4-ylidene)-amine (34) in solution, aziridine imines are formed quantitatively, about 85% on the non-least-motion path and 15% on the least-motion path (90CB2195). The gas-phase pyrolysis of 34 affords only the product of the former path (93CB2683). 

If it is a real intermediate and not too short-lived, it is likely that the thermodynamically most stable product will be formed, and this seems to be the usual case. Examples are found in the decompositions of 25-27, which follow the least-motion path, and 31-37, which follow the non-least-motion path. The most obvious exception is the triazolinone system 30 (Scheme 1). 

If a major contributor to least motion effects in. solution is the varying degrees of solvent reorganisation required for varying degrees of nuclear motion, then it is not clear what function of atomic displacements should be minimised to determine the least motion path. Following Hine (1966a), the square of the atomic displacement has been minimised, but if solvation forces are involved, this will be accurate only for small displacements. 

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. 

Two singlet silylenes dimerize to give a ground-state disilene with a substantial barrier via the least-motion path and without a barrier via the non-least-motion path. On the other hand, two triplet silylenes dimerize to give adiabatically an excited state of disilene. 

A ground-state methylene ( Bi) and an excited-state silylene ( B,) give a ground-state silaethylene without a barrier in the least-motion path, and an excited-state methylene ( Ai) and a ground-state silylene also give a ground-state silaethylene without a barrier in the non-least-motion path. 

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. 7. Diabatic (SS and TT) and adiabatic (Ej) curves for the dimerization of methylenes 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.)... 

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. 

Frlmer, Bartlett, Boschung and Jewett (32) have recently observed by means of deuterium and tritium Isotope effects that the transition states In the attack of singlet oxygen on 4-methyl-2,3 dlhydro-4H-pyrans deviate from the "least motion" path for the direct formation of either dloxetane or allyllc hydroperoxide, toward the type of transition state to be expected If perepoxlde formation were the rate determining step. Any final Judgment the perepoxlde as an Intermediate In dloxetane formation must await evidence as specific as that which has eliminated It In the competitive photo-epoxldatlons. 

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