Reaction path definition

The choice of reaction path definition used as the reference for such a constrained dynamics is arbitrary any path may be used in practice. However, a natural choice in order to ensure that the simulation moves along the bottom of the potential energy valley connecting reactants/products with TS is the intrinsic reaction path (IRP) of Fukui.46,47 IRP by definition goes along the bottom of such a valley. IRP simply corresponds to a steepest descent path in a mass-weighted coordinates ... 

Density functional methods are competitive with the above traditional wave function methods for numerous applications such as the computation of ground-state PES. A few applications of transition metal photochemistry have been proposed on the basis of the A-SCF approach implying several approximations on the excited-state reaction-path definition by symmetry constraints not always appropriate in a coordinate driving scheme. Excited-state gradients have been recently implemented in DFT for various functionals, the feasibility of the approach having been tested for small molecules... 

The explicit expression for lAI depends on the definition of the reaction path because A defines kinetic motion off the reaction path during which R is constrained to be fixed. For many reaction path definitions, such constrained motion implies a complicated expression for lAI. However, if R is defined as the separation of the centers of mass of the two fragments, a general expression for lAI has been found (see paper I) ... 

Another drawback of the SDPs is the impossibility to detect bifurcations of a valley path [1,15,16], whereas the reaction path definition by VF-GE gives us the possibility to determine bifurcations. 

Attention should be paid to the fact that the ratio of Pd and phosphine ligand in active catalysts is crucial for determining the reaction paths. It is believed that dba is displaced completely with phosphines when Pd2(dba)3 is mixed with phosphines in solution. However the displacement is not eom-plcte[16]. Also, it should be considered that dba itself is a monodentate alkene ligand, and it may inhibit the coordination of a sterically hindered olefinic bond in substrates. In such a case, no reaction takes place, and it is recommended to prepare Pd(0) catalysts by the reaction of Pd(OAc)2 with a definite amount of phosphinesflO]. In this way a coordinatively unsaturated Pd(0) catalyst can be generated. Preparation of Pd3(tbaa)3 tbaa == tribenzylidene-acetylacetone) was reported[17], but the complex actually obtained was Pd(dba)2[l8],... 

An IRC calculation examines the reaction path leading down from a transition structure on a potential energy surface. Such a calculation starts at the saddle point and follows the path in both directions from the transition state, optimizing the geometry of the molecular system at each point along the path. In this way, an IRC calculation definitively connects two minima on the potential energy surface by a path which passes through the transition state between them. 

This observation is the first part of the cancellation puzzle [20, 21, 27, 29]. We know from Section lll.B that we should be able to solve it directly by applying Eq. (19), which will separate out the contributions to the DCS made by the 1-TS and 2-TS reaction paths. That this is true is shown by Fig. 9(b). It is apparent that the main backward concentration of the scattering comes entirely from the 1-TS paths. This is not a surprise, since, by definition, the direct abstraction mechanism mentioned only involves one TS. What is perhaps surprising is that the small lumps in the forward direction, which might have been mistaken for numerical noise, are in fact the products of the 2-TS paths. Since the 1-TS and 2-TS paths scatter their products into completely different regions of space, there is no interference between the amplitudes f (0) and hence no GP effects. 

The definition of a reduced dimensionality reaction path starts with the full Cartesian coordinate representation of the classical A-particle molecular Hamiltonian,... 

The electrophilic attack of nitric oxide on a bent nitrosyl is now realized to be the path by which hyponitrite-bridged Co species are formed. Reaction (93) was known since the time of Werner (217), but the black and red isomers of [Co(NO)(NH3)5]2+ obtained from this reaction defied definitive characterization for many years. It has now been established that the black isomer is a mononuclear, octahedral complex of Co(III) and NO- (218) while the red isomer is a hyponitrite bridged system containing two Co(III) ions (219). 

For definiteness, consider barrierless adsorption-desorption reaction (2). In the variational TST, the position qf of transition complex TCad in the reaction path (see Figures 9.1 and 9.2) corresponds to a maximum of the Helmholtz free energy cf(qr) of the trial transition complex TCad( r) considered as a function of the reaction coordinate. 

One of the most useful static methods of microscopic chemical kinetics is based on the definition of the reaction path as introduced by Fukui. This method offers information on reactions in terms of the intrinsic reaction coordinate (62,144). A theoretical analysis of the minimum energy path was given in Section III,B. Fukui s definition is equivalent to Eq. (34). 

With suitable definitions of search functions, EA methods can also be used to locate more features on the PES than just low-energy local and global minima. Chaudhury et al. [144,145] have implemented methods for finding first-order saddle points and reaction paths, applying them to LJ clusters up to n=30. It remains to be tested, however, if these method can be competitive with deterministic exhaustive searches for critical points for small systems [146], on the one hand, and with the large arsenal of methods for finding saddles and reaction paths between two known minima for larger systems [63], on the other hand. 

For convenience, the constants are taken to include the two po.ssible reaction paths, combination and disproportionation. Attention must be paid to the definition of the k a to avoid confusion in the use of factors of 2. 

It might be supposed that stereochemical evidence would be rather definite in distinguishing from Sn2 reaction paths. In /SVl a stable carbonium ion is formed as an intermediate following ionization [Eq. (XVI.1.2)]. If the carbon center is originally asymmetric and the starting compound, RX, is optically active, then the product, R Y, would be racemic. This turns out to be true in many cases. However, when the atom adjacent... 

Whilst this scheme is not intended to be fully definitive it does illustrate that the predominant reaction path will depend on the relative values of 2. K, fei7, fe42, 1 14, 24) and fei6 and on the equilibrium value of [C H2 + 1 06] /[C H2 + 1 ]. For most alkanes, except methane, reactions (2), (3), (17) and (42) are all possible, but reaction (14) will be highly... 

The main effect is already taken into account if symmetry numbers are included in the densities of states. The symmetry number is a correction to the density of states that allows for the fact that indistinguishable atoms occupy symmetry-related positions and these atoms have to obey the constraints of the Pauli principle (i.e. the wave function must have a definite symmetry with respect to any permutation), whereas the classical density of states contains no such constraint. The density of states is reduced by a factor that is equal to the dimension of the rotational subgroup of the molecule. When a molecule is distorted, its symmetry is reduced, and so its symmetry number changes by a proportion that is equivalent to the number of indistinguishable ways in which the distortion may be produced. For example, the rotational subgroup of the methane molecule is T, whose dimension is 12, whereas the rotational subgroup of a distorted molecule in which one bond is stretched is C3, whose dimension is 3. The ratio of these symmetry numbers, 4, is the number of ways in which the distortion can occur, i.e. the reaction path degeneracy. 

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