Dissociative path

Figure 9.3 Cross-section and top views of selected states along the O2 dissociation path on Pt(lll), from the initial state (t-b-t) to the dissociated product state (fee x 2). The third image is the transition state. (Reproduced with permission from Xu et al. [2004].)...

Sulfate monoesters can react by dissociative paths, and this is the favored path. Whether such reactions are concerted or involve a very short-lived sulfur trioxide intermediate has been the subject of debate. ° Benkovic and Benkovic reported evidence suggesting that the nucleophile is present (though there is little bond formation) in the transition state for the reaction of amines with p-nitrophenyl sulfate. Alkyl esters of sulfuric or sulfonic acids normally react with C-0 cleavage only when this is disfavored, as in aryl esters, does one see S-0 cleavage. Sulfate diester... 

In this case, the dissociative path via 20 looks slightly favored thongh a concerted path looks possible. For this reaction the likely mechanism would be as follows ... 

Fig. 2. CH4 hydrate stability curves (laboratory data) showing CH4 hydrate dissociation paths (schematic) in the depressurization method.

Figure A.17 Most likely dissociation path of CO on Rh(lll). In the transition state, CO bends across a rhodium atom, which gives optimum overlap between Rh d and CO 2p orbitals (from deKoster etal. [211).

Such conclusions have been initially regarded with reluctance by some experimentalists [40], Despite its potential interest, the new alternative does not fit the large body of experimental observations available so far. As pointed out by Fischer and Hofmann [40], kinetic studies are not consistent with the associative mechanism and are clearly in favor of a dissociative path. However, in a recent kinetic study, Waters, Bos, and Wulff (WBW) [41] have provided the first example of a bimolecular reaction of a... 

In spite of the fact that we have introduced the factor of exp(—) in equation (47), our analytical expression for the dipole moment does not have a qualitatively correct asymptotic behaviour for the bond lengths r,—> 00. The function does not converge to the dipole moment of the NH2 fragment if we remove a hydrogen atom. However, neither does it diverge The calculated dipole moment values at large r, are around 2-3 D depending on which dissociation path we use. Obviously, the asymptotic behaviour of the dipole moment is of no importance for the simulations carried out in the present work we are only concerned with molecular states well below dissociation. 

The results were interpreted as a two-term rate law for an irreversible reaction, b representing the second-order rate constant for attack by Cl ion and a an unusual dissociative path (Sec. 4.6). More recent work indicates that at the low [Cl ] concentrations used, reaction (1.53) is reversible and Eqn. (1.54) is better interpreted in terms of a reversible reaction as depicted in (1.53) in which in (1.54), b = and a = A , As a check the value of b/a = K is close to that estimated for reaction (1.53). 

P ta-Rearranged Products. Very little quantitative data concerning their formation has been published. They might be formed by both the dissociative Path A or the concerted Path B. Yields are apparently independent of the solvent polarity. As with the or/Ao-products, their formation is also possible when the para-position of the original aryl ester is substituted with — I, + M substituents (chlorine, methoxy). Photochemically they are very stable in polar solvents, whereas in nonpolar ones they can photopinacolize with a considerable quantum yield. 

Phenols. Presumably they arise exclusively via dissociative Path A, subsequent radical diffusion from the solvent cage, and abstraction of a hydrogen from the solvent (65 -> 74). The yields are (1) increased with decreasing viscosity of the reaction medium (2) higher in nonpolar and lower in polar solvents (3) practically independent of the hydrogen-donating ability of the solvent and (4) increased if a radical counterpart of a phenoxy radical, i.e., an acyl radical, decarbonylates in the solvent cage for structural reasons. 

Figure 1. Schematic representation of resonances in the continuum of a polyatomic molecule ABC(X) dissociating into products AB(X, 0) and C. The left-hand side shows an absorption-type cross section <7abs( ) with a rich resonance pattern. The term p(E) is the density of states at the energy E and N r(E) is the number of states at the TS, orthogonal to the dissociation path, that are accessible at energy E. Several experimental schemes for a spectroscopic analysis of resonances are also indicated. (Reprinted, with permission of the Royal Society of Chemistry, from Ref. 34.)...

Plotting the stationary wave functions of the system facilitates the assignment of the resonances in terms of vibrational quantum numbers (if there is any) and illustrates the overall dissociation path. For this reason we usually consider the so-called total wave function kg (Chapter 2 of Ref. 4), that is, a... 

In addition, CH2 radicals arc also produced. The energetic consideration rules out the direct dissociation path at 2660 A... 

In some molecules there is another, slower dissociation path known as predissociation. In this case the crossing to the dissociative state is the rate-limiting step, and this may take place after many vibrations in the absorption spectrum the vibrational sub-levels remain sharp, but the rotational levels are blurred (Figure 4.28). 

The energetics of several dissociation paths of the CH4He2+ dication was also... 

A clean formation of [Rh(OEP)]2 proceeds via thermolysis [269] or photolysis [273] with loss of dihydrogen from or autoxidation of the hydride RhH(OEP) (path p). The tetramesitylporphyrin complex, Rh(TMP) [61], does not dimerize at all due to the sterically hindrance created by the two ortho-methyl groups of each phenyl ring (see Ru(TMP) ), however, the meta-methyl groups of the rhodium(II) derivative prepared from tetra-kis(3,5-xylyl) porphyrin [H2(TXP)] do not prevent dimerization, and the complex is isolated as a dimer [Rh(TXP)] 2 which dissociates (path — q) prior to chemical reactions. Photolysis of RhMe(TMP) [274] (path r) is another suitable access to Rh(TMP) [271]. 

Fig. 1.11. (cont.) The Si and S2 potential energy surfaces have been calculated by Nonella and Huber (1986) and Suter, Briihlmann, and Huber (1990), respectively, whereas the PES for the So state is approximated by the sum of two uncoupled Morse oscillators. The shaded circles indicate the equilibrium region of the ground electronic state where the dissociative motion in the excited electronic states starts and the heavy arrows illustrate the subsequent dissociation paths. Detailed discussions of the absorption spectra and the vibrational state distributions of NO follow in Chapters 7 and 9. 

Fig. 1.12. Two-dimensional polar plots of the potential energy surfaces (denoted below by Vx, Va, and Ve) of the three lowest electronic states of H2O. One of the O-H bonds is frozen at its equilibrium in the electronic ground state. The contours represent the potential energy as the other H atom swings around the O atom. Energies and distances are given in eV and A, respectively. The energy is normalized such that H + OH(2II, re) and H + OH(2E, re), respectively, correspond to E — 0. Vx is the empirical fit of Sorbie and Murrell (1975) whereas Va and Vb have been calculated by Staemmler and Palma (1985) and by Theodorakopoulos, Petsalakis, and Buenker (1985), respectively. The heavy arrows illustrate the main dissociation paths in the excited states.

However, the total dissociation wavefunction is useful in order to visualize the overall dissociation path in the upper electronic state as illustrated in Figure 2.3(a) for the two-dimensional model system. The variation of the center of the wavefunction with r intriguingly illustrates the substantial vibrational excitation of the product in this case. As we will demonstrate in Chapter 5, I tot closely resembles a swarm of classical trajectories launched in the vicinity of the ground-state equilibrium. Furthermore, we will prove in Chapter 4 that the total dissociation function is the Fourier transform of the evolving wavepacket in the time-dependent formulation of photodissociation. The evolving wavepacket, the swarm of classical trajectories, and the total dissociation wavefunction all lead to the same general picture of the dissociation process. 

Relation (6.40) represents a dynamical mapping which is mediated by Hamilton s equations of motion in the upper state and ultimately by the forces —dV/dR and —dV/dr and the torque —dV/d y. The energy dependence is mainly determined by the slope dV/dR of the potential in the direction of the dissociation path while dV/dr and dV/d y control the vibrational and rotational state distribution of the fragment. 

Figure 8.2 depicts a typical potential energy surface (PES) for a symmetric molecule ABA with intramolecular bond distances R and R2] the ABA bond angle is assumed to be 180° (collinear configuration). The PES is symmetric with respect to the line defined by Ri = R2 it has a saddle point at short distances and decreases monotonically from the saddle point out into the two identical product channels A + BA and AB + A (see also Figure 7.18). The shaded area indicates the Franck-Condon (FC) region accessed via photon absorption and the two arrows illustrate the main dissociation paths for the quantum mechanical wavepacket or, equivalently, a swarm of classical trajectories. Because no barrier obstructs dissociation, the majority of trajectories immediately evanesce in either one of the two product channels without ever returning to the vicinity of the FC point.

Fig. 8.2. Typical potential energy surface for a symmetric triatomic molecule ABA. The potential energy surface of H2O in the first excited electronic state for a fixed bending angle has a similar overall shape. The two thin arrows illustrate the symmetric and the anti-symmetric stretch coordinates usually employed to characterize the bound motion in the electronic ground state. The two heavy arrows indicate the dissociation path of the major part of the wavepacket or a swarm of classical trajectories originating in the FC region which is represented by the shaded circle. Reproduced from Schinke, Weide, Heumann, and Engel (1991).

Fig. 8.9. Contour plot of the potential energy surface of H2O in the BlA state as a function of the H-OH dissociation bond Rh-oh and the HOH bending angle a the other O-H bond is frozen at the equilibrium value in the ground electronic state. The energy normalization is such that E = 0 corresponds to H(2S ) + OH(2E, re). This potential is based on the ab initio calculations of Theodorakopulos, Petsalakis, and Buenker (1985). The structures at short H-OH distances are artifacts of the fitting procedure. The cross marks the equilibrium in the ground state and the ellipse indicates the breadth of the ground-state wavefunction. The heavy arrow illustrates the main dissociation path and the dashed line represents an unstable periodic orbit with a total energy of 0.5 eV above the dissociation threshold.

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