Pathway, minimum energy

Figure A3.5.6. Minimum energy pathway for the reaetion of Cl with CH Br.

Figure 11-7. Minimum energy pathways on the Si surface of cytosine connecting the Si minimum to two Si/So conical intersections. The five singlet state energies at the MRCI level are shown. Energies are given in eV with respect to the ground state minimum energy, ciIJ represents conical intersection between states S/, Sj. (From Ref. [157])...

For the sake of simplicity, the minimum-energy pathways (which according to our calculations on coordination and preinsertion intermediates are expected to be similar) are assumed identical, independent of the symmetry (stereospecificity) of the catalyst. However, the plots for the syndiospecific (Figure 1.1 lb) and isospecific (Figure 1.11c) models are different since, as previously discussed, the stereoselectivities for the primary and secondary insertions are in favor of the same or opposite monomer enantiofaces, respectively. 

The key observation is that there is a systematic relationship between the geometrical parameters defining the reaction . When the Y-M bond is lengthened (Ar) under the various influences of a particular crystal and molecular environment, the rest of the tetrahedral structure (YMX angle, M-X bond length, r,) responds in a standard, predictable, way. [See, for example, the correlation shown in Fig. 5, which is discussed also by Dunitz (1979).] This must represent, in the particular circumstances, the most favourable, i.e. the minimum energy, pathway for the structural change... 

Given the definition of the geometry of the transition states in TST as the highest energy point in the minimum energy pathway from reactants to products, the formal definition of MEP is as follows. The MEP is, in one direction, the path of steepest descents from the transition state to reactants while, in the other direction, it is the path of steepest descents from transition state to products. For reasons which will not be discussed here, the formal definition of MEP includes the statement that the pathway is expressed in mass scaled Cartesian coordinates of the position of the atoms (introduced in Chapter 3, e.g. x is replaced by x = ). This simplifies... 

The potential energy is illustrated in Fig. 6.3a. While one can in principal calculate the exact quantum mechanical Born-Oppenheimer surface, the figure presents a semi-empirical surface constructed to yield the exact spectral properties of reactants and products and the correct activation energy (taken as the difference in energy between the energy (potential) in the reactant valley (x = oo) and the maximum of the MEP (minimum energy pathway).)... 

The aim of the present study is to investigate the validity of the pairwise additivity of two-body and three-body potentials for He2Br2. These results are compared with ah initio calculations" and a simple model of the three-body potential is proposed to determine well depths and equilibrium structures for different isomeric configurations of the complex, as well as the minimum energy pathways through them. Additionally, variational methods are used to calculate the vibrational states of He2Br2. The wavefunctions of the lower states are analyzed in terms of probability distributions of the internal coordinates and the zero-point energy of the vdW cluster is evaluated. 

Figure A7.1 The effect of an enzyme on the minimum energy pathway of a simple enzyme catalysed reaction involving a single substrate. (TS = transition state.) The heights of the energy barriers TSi, ts2 and ts3 will vary depending on which step in the enzyme controlled route is the rate controlling step...

HF Surfaces for Ss2 Reactions.—We now return to the review of the reactions which have been studied at the single-determinantal SCF level of approximation. The majority of these studies have concentrated on mapping out the minimum energy pathways between reactants and products. Such reaction pathways for a number of Ss2 displacement reactions have been determined. The systems which... 

Conformational interconversion is a process that cannot be observed experimentally. However, the energy profile associated with interconversion can be mapped using molecular mechanics. Then, representative structures along the minimum energy pathway can be predicted and visualized. For example, the mechanism of conversion from the X to the <5 conformer of [Co(en)(NH3)4]3+ has been calculated in this way11801. 

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