Substitution energy surface

Substitution Energy Surface Can Be Placed Adjacent to the Elimination Surface S v 1 Competes with El Sn2 Competes with E2 Multivariable Decisions Nucleophilicity, Basicity, sp C-L Site Hindrance, Presence of Electron-Withdrawing Groups, Temperature, Electronegativity of the Leaving Group A Three-Dimensional Correlation Matrix... 

The substitution energy surface can be placed adjacent to the elimination surface since they share the C-L bond-breaking axis (Fig. 9.2). Now the factors that tilted each of the surfaces can be used to understand the substitution vs. elimination competition. 

Of the three common routes on the substitution energy surface (Fig. 4.2), only two substitution routes are energetically possible because the site of attack is a carbon atom (the pentacoordinate path is out). The two alternatives are the 5 2,... 

The use of isotopic substitution to detennine stmctures relies on the assumption that different isotopomers have the same stmcture. This is not nearly as reliable for Van der Waals complexes as for chemically bound molecules. In particular, substituting D for H in a hydride complex can often change the amplitudes of bending vibrations substantially under such circumstances, the idea that the complex has a single stmcture is no longer appropriate and it is necessary to think instead of motion on the complete potential energy surface a well defined equilibrium stmcture may still exist, but knowledge of it does not constitute an adequate description of the complex. 

Consider a reactant molecule in which one atom is replaced by its isotope, for example, protium (H) by deuterium (D) or tritium (T), C by C, etc. The only change that has been made is in the mass of the nucleus, so that to a very good approximation the electronic structures of the two molecules are the same. This means that reaction will take place on the same potential energy surface for both molecules. Nevertheless, isotopic substitution can result in a rate change as a consequence of quantum effects. A rate change resulting from an isotopic substitution is called a kinetic isotope effect. Such effects can provide valuable insights into reaction mechanism. 

A disadvantage of this technique is that isotopic labeling can cause unwanted perturbations to the competition between pathways through kinetic isotope effects. Whereas the Born-Oppenheimer potential energy surfaces are not affected by isotopic substitution, rotational and vibrational levels become more closely spaced with substitution of heavier isotopes. Consequently, the rate of reaction in competing pathways will be modified somewhat compared to the unlabeled reaction. This effect scales approximately as the square root of the ratio of the isotopic masses, and will be most pronounced for deuterium or... 

In highly exothermic reactions such as this, that proceed over deep wells on the potential energy surface, sorting pathways by product state distributions is unlikely to be successful because there are too many opportunities for intramolecular vibrational redistribution to reshuffle energy among the fragments. A similar conclusion is likely as the total number of atoms increases. Therefore, isotopic substitution is a well-suited method for exploration of different pathways in such systems. 

The VBSCF and EH-MOVB potential energy surfaces for the nucleophilic substitution reaction of HS and CH3CI are depicted in Figure 4-2. The energy contours determined using the EH-MOVB method (Figure 4-2A) are found to be in good accord... 

Smooth COSMO solvation model. We have recently extended our smooth COSMO solvation model with analytical gradients [71] to work with semiempirical QM and QM/MM methods within the CHARMM and MNDO programs [72, 73], The method is a considerably more stable implementation of the conventional COSMO method for geometry optimizations, transition state searches and potential energy surfaces [72], The method was applied to study dissociative phosphoryl transfer reactions [40], and native and thio-substituted transphosphorylation reactions [73] and compared with density-functional and hybrid QM/MM calculation results. The smooth COSMO method can be formulated as a linear-scaling Green s function approach [72] and was applied to ascertain the contribution of phosphate-phosphate repulsions in linear and bent-form DNA models based on the crystallographic structure of a full turn of DNA in a nucleosome core particle [74],... 

Gas-phase SN2 nucleophilic substitution reactions are particularly interesting because they have attributes of both bimolecular and unimolecular reactions.1 As discovered from experimental studies by Brauman and coworkers2 and electronic structure theory calculations,3 potential energy surfaces for gas-phase SN2 reactions of the type,... 

Classical trajectory calculations, performed on the PES1 and PESl(Br) potential energy surfaces described above, have provided a detailed picture of the microscopic dynamics of the Cl- + CH3Clb and Cl" + CH3Br SN2 nucleophilic substitution reactions.6,8,35-38 In the sections below, different aspects of these trajectory studies and their relation to experimental results and statistical theories are reviewed. 

The analytic potential energy surfaces, used for the Cl + CH3Clb and Cl + CHjBr trajectory studies described here, should be viewed as initial models. Future classical and quantum dynamical calculations of SN2 nucleophilic substitution should be performed on quantitative potential energy functions, derived from high-level ab initio calculations. By necessity, the quantum dynamical calculations will require reduced dimensionality models. However, by comparing the results of these reduced dimensionality classical and quantum dynamical calculations, the accuracy of the classical dynamics can be appraised. It will also be important to compare the classical and quantum reduced dimensionality and classical complete dimensionality dynamical calculations with experiment. 

Supercritical water (SCW) presents a unique combination of aqueous and non-aqueous character, thus being able to replace an organic solvent in certain kinds of chemical synthesis. In order to allow for a better understanding of the particular properties of SCW and of its influence on the rate of chemical reactions, molecular dynamics computer simulations were used to determine the free energy of the SN2 substitution reaction of Cl- and CH3C1 in SCW as a function of the reaction coordinate [216]. The free energy surface of this reaction was compared with that for the gas-phase and ambient water (AW) [248], In the gas phase, an ion-dipole complex and a symmetric transition... 

In another work, a series of substituted 2-aminoindans was analyzed using MM2-85108. The calculated potential energy surface for rotation around the CH—CH—CH2— N and CH—CH2—N—lp in model compound 70 is presented in Figure 9 and shows 9 minima. These were scrutinized as potential candidates for dopamine receptor agonists, according to several criteria The highest-energy conformation f (Erei = 7.3 kcalmol-1)... 

Abstract The Born-Oppenheimer approximation is introduced and discussed. This approximation, which states the potential energy surface on which the molecule vibrates/rotates is independent of isotopic substitution, is of central importance in... 

Equation 4.117 makes complete sense. One of the first things one learns in dealing with phase space integrals is to be careful and not over-count the phase space volume as has already been repeatedly pointed out. In quantum mechanics equivalent particles are indistinguishable. The factor n ni is exactly the number of indistinguishable permutations, while A accounts for multiple minima in the BO surface. It is proper that this factor be included in the symmetry number. Since the BO potential energy surface is independent of isotopic substitution it follows that A is also independent of isotope substitution and cannot affect the isotopic partition function ratio. From Equation 4.116 it follows... 

These equations express that (Taa + Haa) (Q) and (T bb+Hbb) (Q) constitute potential energy surfaces for the nuclear motions represented by Xav> and Xbw -The solution to our problem is readily found by substituting in Eqs. (4) and (4 ) the following expansions ... 

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