Three-dimensional potential energy

There is another useiiil way of depicting the ideas embodied in the variable transition state theory of elimination reactions. This is to construct a three-dimensional potential energy diagram. Suppose that we consider the case of an ethyl halide. The two stepwise reaction paths both require the formation of high-energy intermediates. The El mechanism requires formation of a carbocation whereas the Elcb mechanism proceeds via a caibanion intermediate. 

Three-dimensional potential energy diagrams of the type discussed in connection with the variable E2 transition state theory for elimination reactions can be used to consider structural effects on the reactivity of carbonyl compounds and the tetrahedral intermediates involved in carbonyl-group reactions. Many of these reactions involve the formation or breaking of two separate bonds. This is the case in the first stage of acetal hydrolysis, which involves both a proton transfer and breaking of a C—O bond. The overall reaction might take place in several ways. There are two mechanistic extremes ... 

There are examples of each of these mechanisms, and a three-dimensional potential energy diagram can provide a useful general framework within which to consider specific addition reactions. The breakdown of a tetrahedral intermediate involves the same processes but operates in the opposite direction, so the principles that are developed will apply equally well to the reactions of the tetrahedral intermediates. Let us examine the three general mechanistic cases in relation to the energy diagram in Fig. 8.3. 

Fig. 8.3. Three-dimensional potential energy diagram for addition of a proton and nucleophile to a caibonyl group, (a) Proton transfer complete before nucleophilic addition begins (b) nucleophilic addition complete before proton transfer begins (c) concerted proton transfer and nucleophilic addition.

Figure 10. Three-dimensional potential-energy surface for the H + C2H3 C2H4 addition reaction. The lower left plot is taken in the symmetry plane of the vinyl radical. The other plots are taken in parallel planes at distances of O.S. O a.u. from the symmetry plane (1 a.u. = 0.52918 A). Solid contours are positive, dashed contours are negative, and the zero-energy contour (defined to be the energy of the reactant asymptote) is shown with a heavy sohd fine. The contour increment is 1 kcalmoU. Reproduced from [57] by pentrission of the PCCP Owner Societies.

The saddle point on a three-dimensional potential-energy surface, characterized by one negative force constant in the harmonic force constant matrix. 

J. E. Stevens, R. K. Chaudhuri, and K. F. Freed, Global three-dimensional potential energy surfaces of H2S from the ab initio effective valence shell Hamiltonian method. J. Chem. Phys. 105, 8754 (1996). 

Fig. 10 The three-dimensional potential energy surface describing the motion of protons between N6(A) and 04(T) and between N3(T) and N1(A) shows two critical points in the ground state. The deeper minimum corresponds to the amine/keto structure of AT and a shallow one to the imine/enol structure (A T ). Upon absorption of a UV photon the initaly delocalized excitonic states (1) undergo a rapid localization on f 10 ps timescale for single bases and 100 ps timescale for stacked base pairs to form a charge transfer (CT) states. The subsequent CT states passing through a conical intersection are carried back to the ground state.

Figure 7-1. Three-dimensional potential energy surfaces (a) Energy hypersurface for FSSF SSF2 isomerization (detail). Reproduced with permission [19] copyright (1977) American Chemical Society (b) Potential energy surface of the molecular rearrangement of Agl3, with the corresponding structures indicated on the sides [20], Copyright (2005) American Chemical Society.

The detailed results of these calculations have been given elsewhere Then we shall only recall the main features of the three-dimensional potential energy surface,... 

In 2004 Nanbu and Johnson [110] re-examined the isotope effects in NNO photolysis using a three dimensional potential energy surface, the added degree of freedom being NN vibration. This allowed an investigation of the effect of this degree of freedom on the dynamics, and of the vi = 1 vibrational state, both of which impact the absorption cross section. The NN bond can absorb some of the impulse... 

Figure 3. Collinear CASSCF one-dimensional cuts of the three-dimensional potential energy functions for the doublet and quartet states of CC>2+ possibly involved in the predissociation of CO2+(C2 g+). The other Rco distance is set to the equilibrium geometry of the neutral molecule (2.2 Bohr). The energies of the dissociation limits and electronic states are shifted to known experimental values. Strictly speaking, the g-u symmetry is only applicable for Rco = 2.2 Bohr (from [13]).

Figure I 2.3 A three-dimensional potential energy surface that illustrates the difficulty of distinguishing between a "stepwise" reaction, which involves an intermediate, and "concerted" reaction, which does not. The local minimum labeled I on the potential energy surface could plausibly be called an intermediate for the B C reaction since the minimum energy path must traverse the region of I. However, it is not clear whether it should be called an intermediate for the A —> B or A — C reactions since some paths include I but some do not. The concepts of stepwise and concerted reactions are thus not well defined for reactions of the A —> B or A —> C type.

The nature of vibrationally and rotationally predissociating states of atom-diatom Van der Waals molecules and the fundamental considerations governing their predissociation are discussed. Particular attention is focussed on the influence of the potential energy surface and the information about it which might be extracted from accurate measurements of predissociation lifetimes. Most of the results discussed pertain to the molecular hydrogen-inert gas systems, and details of previously unpublished three-dimensional potential energy surfaces for diatomic hydrogen with krypton and xenon are presented. 

Recent discussions have been on reactions with two major changes in a single step and these may be described by a three-dimensional potential-energy surface. A qualitative picture of the surface for a reaction (Eqn. 109) is all that is necessary to... 

Fig. 4. Three-dimensional potential-energy diagram for the reaction AH-I-B A -I-The dotted line represents the reaction coordinate and the double arrow the vibration mode of the hydrogen in the transition state (Eqns. 27 and 28).

P. Siegbahn and B. Liu, An accurate three-dimensional potential energy surface for H J. Chem. Phys. 68 2457 (1978). 

The three-dimensional potential energy function was determined from the electronic energies of 150 selected conformations. Calculations were performed at the RHF/MP2 level with the 6-31lG(d,p) basis set. All the structures were fully optimized taking into account in some way the interactions with the remaining vibration modes. 

The reactions of P-donor nucleophiles with the metal carbonyl cluster Rh4COi2 have been studied over a considerable time period.It is widely accepted that the reaction is associative. This latest investigation is aimed at quantifying the effects of the electronic and steric properties of the nucleophiles upon the kinetic parameters. A rapid substitution reaction step using an excess of the nucleophile was monitored by SF spectrophotometry. Second-order rate constants were obtained from the variation of the pseudo-first-order rate constants with nucleophile concentration. Contributions to these constants from the properties steric effect, TT-activity, and, in addition, an aryl effect of the nucleophiles were assessed in a multi-parameter equation. The outcome is a successful understanding of the relative reactivities of many P-donors toward the rhodium cluster. The data were also represented by a three-dimensional potential energy surface. 

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