Reaction force partitioning

Keywords Chemical reaction prediction. Conceptual density functional theory, Ehrenfest force, Electronic stress tensor, Reaction force partitioning. Quantum theory of atoms in molecules... 

Since chemical reactions can be seen as a sequence of chemical events that involves the electronic activity taking place during the reaction, a descriptor of this activity becomes important to get insights into the reaction mechanism. The reaction electronic flux (REF), which was defined as the derivative of the electronic chemical potential with respect to the reaction coordinate, has been shown to be an adequate descriptor of the electronic activity. This chapter is focused on the definitions, usefulness, and applications of the REF, the reaction force, the reaction force constant, and the partition of the activation energy. 

Values of and Qb can be calculated for molecules in the gas phase, given structural and spectroscopic data. The transition state differs from ordinary molecules, however, in one regard. Its motion along the reaction coordinate transforms it into product. This event is irreversible, and as such occurs without restoring force. Therefore, one of the components of Q can be thought of as a vibrational partition function with an extremely low-frequency vibration. The expression for a vibrational partition function in the limit of very low frequency is... 

Chymotrypsin, 170,171, 172, 173 Classical partition functions, 42,44,77 Classical trajectories, 78, 81 Cobalt, as cofactor for carboxypeptidase A, 204-205. See also Enzyme cofactors Condensed-phase reactions, 42-46, 215 Configuration interaction treatment, 14,30 Conformational analysis, 111-117,209 Conjugated gradient methods, 115-116. See also Energy minimization methods Consistent force field approach, 113 Coulomb integrals, 16, 27 Coulomb interactions, in macromolecules, 109, 123-126... 

Similar to the standard SBC, GSBP partitions the system into inner and outer regions and the effects of the outer region on the inner, reaction region are represented implicitly within the total effective potential (potential of mean force) [36],... 

To what extent is the partitioning of simple aliphatic and benzylic a-CH-substituted carbocations in nucleophilic solvents controlled by the relative thermodynamic driving force for proton transfer and nucleophile addition reactions It is known that the partitioning of simple aliphatic carbocations favors the formation of nucleophile adducts (ksjkp > 1, Scheme 2) and there is good evidence that this reflects, at least in part, the larger thermodynamic driving force for the nucleophilic addition compared with the proton transfer reaction of solvent (A dd U Scheme 6).12 21,22,24... 

The more favorable partitioning of [1+ ] to form [l]-OH than to form [2] must be due, at least in part, to the 4.0 kcal mol-1 larger thermodynamic driving force for the former reaction (Kadd = 900 for conversion of [2] to [l]-OH, Table 1). However, thermodynamics alone cannot account for the relative values of ks and kp for reactions of [1+] that are limited by the rate of chemical bond formation, which may be as large as 600. A ratio of kjkp = 600 would correspond to a 3.8 kcal mol-1 difference in the activation barriers for ks and kp, which is almost as large as the 4.0 kcal mol 1 difference in the stability of [1]-OH and [2]. However, only a small fraction of this difference should be expressed at the relatively early transition states for the reactions of [1+], because these reactions are strongly favored thermodynamically. These results are consistent with the conclusion that nucleophile addition to [1+] is an inherently easier reaction than deprotonation of this carbocation, and therefore that nucleophile addition has a smaller Marcus intrinsic barrier. However, they do not allow for a rigorous estimate of the relative intrinsic barriers As — Ap for these reactions. 

The very small value of ks/kp = 0.00063 for partitioning of [4+] reflects the strong aromatic stabilization of naphthalene [5]. This will reduce the activation barrier for deprotonation, provided aromaticity is partly developed in the reaction transition state. Thus, this aromatic stabilization results in both a large 20 kcal mol"1 (K 1015) driving force for the dehydration of [4]-OH to give [5],44,99 and a very small barrier for deprotonation of [4+] (kp > 1.6 x 1010 s 1). 

Fig. 6.1 An aspartate amino acid partitioned into quantum and classical (MM) regions. The functional group of the side chain, involved in the chemical reaction, lies within the quantum region and the backbone atoms are treated by using a molecular mechanics force field.

The driving force for the mass transfer of the solute in the three-phase system can be determined with the solvent/water partition coefficient, just as the partition coefficient for gas/liquid phases, the Henry s Law constant, is used to determine the driving force for the mass transfer of ozone. A solute tends to diffuse from phase to phase until equilibrium is reached between all three phases. This tendency of a solute to partition between water and solvent can be estimated by the hydrophobicity of the solute. The octanol/water partition coefficient Kow is a commonly measured parameter and can be used if the hydrophobicity of the solvent is comparable to that of octanol. How fast the diffusion or transfer will occur depends not only on the mass transfer coefficient in addition to the driving force but also on the rate of the chemical reaction as well. 

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