Solution reactions dynamical effects

Krause, J. L., Whitnell, R. M., Wilson, K. E. and Yan, Y. J. (1994) "Classical quantum control with application to solution reaction dynamics,in Gauduel, Y. and Rossky, P. J.(eds.), Ultrafast reaction dynamics and solvent effects, AIP Press, New York,pp.3- 15. 

The interiors of proteins are more densely packed than liquids [181], and so the participation of the atoms of the protein surrounding the reactive system in an enzyme-catalysed reaction is likely to be at least as important as for a reaction in solution. There is experimental evidence which indicates that protein dynamics may modulate barriers to reaction in enzymes [10,11]. Ultimately, therefore, the effects of the dynamics of the bulk protein and solvent should be included in calculations on enzyme-catalysed reactions. Dynamic effects in enzyme reactions have been studied in empirical valence bond simulations Neria and Karplus [180] calculated a transmission coefficient of 0.4 for proton transfer in triosephosphate isomerase, a value fairly close to unity, and representing a small dynamical correction. Warshel has argued, based on EVB simulations of reactions in enzymes and in solution, that dynamical effects are similar in both, and therefore that they do not contribute to catalysis [39]. 

Another class of reactions whose understanding may require the inclusion of quantum effects consists of proton transfer reactions. The light mass of the proton indicates that such quantum effects might be quite important, but there have been attempts to simulate this process purely classically (primarily in the gas phase). An interesting method that lies in between gas phase calculations and full solution phase molecular dynamics is the supermolecule method used by Nagaoka et al. to calculate the dynamics of formamidine in water solvent. This system is quite interesting from the perspective of solution reaction dynamics because the transition state for this reaction incorporates a water molecule from the solvent. The overall process consists of two proton transfers, one from the formamidine molecule to the solvent water molecule and another one from the other end of the solvent water molecule back to the formamidine. 

Benjamin et al. consider bimolecular solution reaction dynamics from a stereochemical perspective, showing that the dynamics leading to the proper relative orientation between reactants can be studied computationally. This work was motivated by the considerable knowledge that had been gained from studying steric effects of gas phase reactions. The reactions studied by Benjamin et al. (Cl + CI2 and Cl -I- HCl in Ar solvent and Sn2, i.e.. Cl -I- CH3CI, in... 

This is no longer the case when (iii) motion along the reaction patir occurs on a time scale comparable to other relaxation times of the solute or the solvent, i.e. the system is partially non-relaxed. In this situation dynamic effects have to be taken into account explicitly, such as solvent-assisted intramolecular vibrational energy redistribution (IVR) in the solute, solvent-induced electronic surface hopping, dephasing, solute-solvent energy transfer, dynamic caging, rotational relaxation, or solvent dielectric and momentum relaxation. 

Many additional refinements have been made, primarily to take into account more aspects of the microscopic solvent structure, within the framework of diffiision models of bimolecular chemical reactions that encompass also many-body and dynamic effects, such as, for example, treatments based on kinetic theory [35]. One should keep in mind, however, that in many cases die practical value of these advanced theoretical models for a quantitative analysis or prediction of reaction rate data in solution may be limited. 

Van der Zwan G and Hynes J T 1982 Dynamical polar solvent effects on solution reactions A simple continuum model J. Chem. Phys. 76 2993-3001... 

Chemical reaction dynamics is an attempt to understand chemical reactions at tire level of individual quantum states. Much work has been done on isolated molecules in molecular beams, but it is unlikely tliat tliis infonnation can be used to understand condensed phase chemistry at tire same level [8]. In a batli, tire reacting solute s potential energy surface is altered by botli dynamic and static effects. The static effect is characterized by a potential of mean force. The dynamical effects are characterized by tire force-correlation fimction or tire frequency-dependent friction [8]. 

An examination of the autocorrelation function (0(0) <2(0) annucleophilic attack step in the catalytic reaction of subtilisin is presented in Fig. 9.4. As seen from the figure, the relaxation times for the enzymatic reaction and the corresponding reference reaction in solution are not different in a fundamental way and the preexponential factor t 1 is between 1012 and 1013 sec-1 in both cases. As long as this is the case, it is hard to see how enzymes can use dynamical effects as a major catalytic factor. 

FIGURE 9.4. The autocorrelation function of the time-dependent energy gap Q(t) = (e3(t) — 2(0) for the nucleophilic attack step in the catalytic reaction of subtilisin (heavy line) and for the corresponding reference reaction in solution (dotted line). These autocorrelation functions contain the dynamic effects on the rate constant. The similarity of the curves indicates that dynamic effects are not responsible for the large observed change in rate constant. The autocorrelation times, tq, obtained from this figure are 0.05 ps and 0.07ps, respectively, for the reaction in subtilisin and in water. 

Effect of enzyme dynamics on catalytic activity, 41, 317 Effective charge and transition-state structure in solution, 27, 1 Effective molarities of intramolecular reactions, 17, 183 Electrical conduction in organic solids, 16, 159 Electrochemical methods, study of reactive intermediates by, 19, 131 Electrochemical recognition of charged and neutral guest species by redox-active receptor molecules, 31, 1... 

Actually, all of the above results are in contradiction to the currently conventional view [32-35] that solvent dynamical effects for electronically adiabatic ET reactions are determined by solvent dynamics in the R and P wells, and not the barrier top region. This misses the correct picture, even for fairly cusped barrier. Instead, it is the solvent dynamics occurring near the barrier top, and the associated time dependent friction, that are the crucial aspects. It could however be thought possible that, for cusped barrier adiabatic ET reactions in much more slowly relaxing solvents, the well dynamics could begin to play a significant role. However, MD simulations have now been carried out for the same ET solute in a solvent where the... 

Even for purely adiabatic reactions, the inadequacies of classical MD simulations are well known. The inability to keep zero-point energy in all of the oscillators of a molecule leads to unphysical behavior of classical trajectories after more than about a picosecond of their time evolution." It also means that some important physical organic phenomena, such as isotope effects, which are easily explained in a TST model, cannot be reproduced with classical molecular dynamics. So it is clear that there is much room for improvement of both the computational and experimental methods currently employed by those of us interested in reaction dynamics of organic molecules. Perhaps some of the readers of this book will be provide some of the solutions to these problems. 

The higher reactivity of the PVMI-Co(III) complex is attributed to the electrostatic domain of the polymer complex, as in the above PVP system. When the PVMI chain contracts, the charge density in the polymer domain increases and the reaction rate also increases. On the other hand, when the polymer chain expands, the electrostatic domain is weakened, which produces a fall in reactivity. These results confirm that the conformation of the polymer complex is closely related to the strength of its electrostatic domain and to the reaction rate. The effects of the polymer chain on reactivity are to be understood not only in terms of static chemical environment but also as dynamic effects which vary with the solution conditions, e.g. pH, ionic strength, solvent composition, temperature, and so on. 

The environmental effects are caused by the micro-environments constituted by the domain of a polymer ligand. The electrostatic domain of a polymer-metal complex was demonstrated in the reaction of the polymer-Co(ni) complex with ionic species (Section IVA), and was shown to be utilized in the catalytic activity of the polymer-Cu complex (Section VIA). In another case, the hydrophobic domain was predominant, ie. in the reaction with hydrophobic substrates (Sections IVB and VIIC). The environmental effects of a polymer ligand also include dynamic effects, Which vary with the solution conditions (Section IIIC). 

The force controls the remarkably persistent coherence in products, a feature that was unexpected, especially in view of the fact that all trajectory calculations are normally averaged (by Monte Carlo methods) without such coherences. Only recently has theory addressed this point and emphasized the importance of the transverse force, that is, the degree of anharmonicity perpendicular to the reaction coordinate. The same type of coherence along the reaction coordinate, first observed in 1987 by our group, was found for reactions in solutions, in clusters, and in solids, offering a new opportunity for examining solvent effects on reaction dynamics in the transition-state region. 

Dynamics effects, which were described in previous sections, on reaction pathways, concerted-stepwise mechanistic switching, and path bifurcation have in most cases been examined for isolate systems without medium effects. Since energy distribution among vibrational and rotational modes and moment of inertia of reacting subfragment are likely to be modified by environment, it is intriguing to carry out simulations in solution. The difference or similarity in the effect of dynamics in the gas phase and in solution may be clarified in the near future by using QM/MM-MD method. Such study would provide information that is comparable with solution experiment and help us to understand reaction mechanisms in solution. 

The knowledge of the two-minima energy surface is sufficient theoretically to determine the microscopic and static rate of reaction of a charge transfer in relation to a geometric variation of the molecule. In practice, the experimental study of the charge-transfer reactions in solution leads to a macroscopic reaction rate that characterizes the dynamics of the intramolecular motion of the solute molecule within the environment of the solvent molecules. Stochastic chemical reaction models restricted to the one-dimensional case are commonly used to establish the dynamical description. Therefore, it is of importance to recall (1) the fundamental properties of the stochastic processes under the Markov assumption that found the analysis of the unimolecular reaction dynamics and the Langevin-Fokker-Planck method, (2) the conditions of validity of the well-known Kramers results and their extension to the non-Markovian effects, and (3) the situation of a reaction in the absence of a potential barrier. 

Han P, Bartels DM (1994) Encounters of H and D atoms with 02 in water relative diffusion and reaction rates. In Gauduel Y, Rossky P (eds) AIP conference proceedings 298. "Ultrafast reaction dynamics and solvent effects." AIP Press, New York, 72 pp Hasegawa K, Patterson LK (1978) Pulse radiolysis studies in model lipid systems formation and behavior of peroxy radicals in fatty acids. Photochem Photobiol 28 817-823 Herdener M, Heigold S, Saran M, Bauer G (2000) Target cell-derived superoxide anions cause efficiency and selectivity of intercellular induction of apoptosis. Free Rad Biol Med 29 1260-1271 Hildenbrand K, Schulte-Frohlinde D (1997) Time-resolved EPR studies on the reaction rates of peroxyl radicals of polyfacrylic acid) and of calf thymus DNA with glutathione. Re-examination of a rate constant for DNA. Int J Radiat Biol 71 377-385 Howard JA (1978) Self-reactions of alkylperoxy radicals in solution (1). In Pryor WA(ed) Organic free radicals. ACS Symp Ser 69 413-432... 

The mechanistic borderline between E2 and ElcB mechanisms has been studied under various conditions.1,2 The mechanism of the elimination reaction of 2-(2-fluoroethyl)-1-methylpyridinium has been explored explored by Car-Parrinello molecular dynamics in aqueous solution.3 The results indicated that the reaction mechanism effectively evolves through the potential energy region of the carbanion the carbon-fluoride bond breaks only after the carbon-hydrogen bond. 

In this chapter we consider dynamical solvent effects on the rate constant for chemical reactions in solution. Solvent dynamics may enhance or impede molecular motion. The effect is described by stochastic dynamics, where the influence of the solvent on the reaction dynamics is included by considering the motion along the reaction coordinate as (one-dimensional) Brownian motion. The results are as follows. 

K. Ando and S. Kato, Dielectric relaxation dynamics of water and methanol solutions associated with the ionization of /V,/V-dimcltiylanilinc theoretical analyses, J. Chem. Phys., 95 (1991) 5966-82 D. K. Phelps, M. J. Weaver and B. M. Ladanyi, Solvent dynamic effects in electron transfer molecular dynamics simulations of reactions in methanol, Chem. Phys., 176 (1993) 575-88 M. S. Skaf and B. M. Ladanyi, Molecular dynamics simulation of solvation dynamics in methanol-water mixtures, J. Phys. Chem., 100 (1996) 18258-68 D. Aheme, V. Tran and B. J. Schwartz, Nonlinear, nonpolar solvation dynamics in water the roles of elec-trostriction and solvent translation in the breakdown of linear response, J. Phys. Chem. B, 104 (2000) 5382-94. 

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