Reaction mechanisms static approach

In describing the PES-based approach for molecules in the gas phase we added the remark that the picture of the reaction mechanism we have described was static. The same remark also holds for the description of reactions in solution. In neglecting dynamical aspects we have greatly simplified the tasks of describing and interpreting the reaction mechanism, and at the same time we have lost aspects of the reaction that could be important. 

It is the purpose of this review to present an outline of both the dynamic and static approaches to theoretical studies of reaction mechanisms. The dynamic approach may be regarded—as far as the physics involved is concerned—as the more sophisticated of the two. However, it has limitations in answering many practical questions which a chemist may ask. The static approach, on the other hand, may seem not to be so sophisticated, but at present it provides answers to everyday chemistry in a variety of fields at different levels of theory. 

Let us finally consider implications of these findings for reaction mechanisms in metalloproteins. Therefore, we must take into account that, much like with Sabatier s approach, considerations about thermodynamic stability, which might go as a static phenomenon if it were not for the fact that chemical equilibrium is nothing but the ratio of forward and reverse reaction rates, hence it also is about dynamics and might be compared to other reaction rates, this approach being encouraged by the well-known structure-reaction rate relationships for both (at least benzenoid aromatic) substrates and square-planar or octahedral coordination complexes ... 

As observed in other systems, the obvious difficulty in elucidating reaction mechanisms based on static structural snapshots subsequently initiated structural-dynamic theoretical studies of metalloproteinases. The active site chemistry of zinc-dependent enzymes has been studied using a variety of theoretical approaches. For example, mixed quantum mechaiucal/molecular calculations and classical molecular dynamic simulations have been employed, especially studies using density functional methods on redox-active metal centers (42). 

The application of the VTST to reactions in solution has to face several computational problems, of the type we have discussed for the canonical static description of the reaction mechanism. Moreover, there is another important problem to face, not present when this approach is applied to reaction in vacuo, which literally adds new dimensions to the model. We shall consider now this point, even if shortly. 

In the present article, we report a study concerning the reaction mechanism of a prototype reaction using both static and dynamic approaches to explore a DFT potential surface. The static approach is the standard IRC model, while the dynamic one is based on a Carr-Parrinello method performed with localized (Gaussian) orbitals, the so-called atom-centered density matrix propagation (ADMP) model.25 Our aim is to elucidate the differences, and the common aspects, between the two approaches in the analysis of bond breaking/formation. To this end, we have chosen topological quantities as probe molecular descriptors. 

This approach is a static population-based metaheuristic that applies an abstraction of the chemical reactions as intensifiers (substitution, double substitution reactions) and diversifying (synthesis, decomposition reactions) mechanisms. The elitist reinsertion strategy allows the permanence of the best elements and thus the average fitness of the entire element pool increases with every iteration. The... 

The same principle was applied to investigating reaction mechanisms in which a strained bond is attacked, causing rupture in a reaction with the attacking species. This type of reaction is, however, difficult to assess using static calculations as the reaction itself cannot be followed and only one line of approach of a neighboring molecule is assessed. 

In addition, the results are extremely sensitive to the level of theory used for the PES, which make low-level methodological approaches non reliable. On the other hand, the static approach provides plausible photochemical mechanisms and discards others. In this context, single determinations of excited-state minima and CIXs with the ground state (approach A) are not safe procedures. Instead, the photochemical reaction path approach must be used (approach B). It corresponds to the determination of the most probable evolution of the molecule after light absorption to the brightest excited state towards a minimum or a state crossing by means of MEP computations and the location of the most relevant CK points for surface hopping. 

In the last years the theoretical organic chemistry has been increasingly extended beyond the gas phase realm of quantum mechanics to the study of the course of chemical reactions in solution. The success of these methods will indicate the begin of a new period for modeling chemistry in solution. Here, we mainly restrict our attention to a static solvent treatment. The discussion of the limitation of this approach was recently continued.Such studies assume the solvation to be in equilibrium with the chemical system at each point along a HP. This basic hypothesis may first be questioned from possibly different time scales of solvent relaxation and the chemical process and, secondly, from the motion of a (limited number) of solvent molecules which may form an important part of the motion of the whole system along the HP. But apart from dynamical nonequilibrium solvation effects and other limitations in the application of TST to reaction in solvents (see Chap. 1.4), static approaches will give much information on the intermolecular interactions and may represent a suitable ansatz for the estimation and interpretation of solvent effects in many cases. 

A survey of many such reactions suggests that there is no single, simple pattern that can be used to predict the outcome of photochemical nucleophilic substitutions, but rather a situation in which oneof at least three mechanisms may operate, and this has been borne out by more detailed mechanistic studies. One approach to rationalizing the preferred orientation in the excited-state reactions is to calculate electron densities at the various ring carbon atoms for a particular pattern of substituents, and to assume that preferential attack by a nucleophile will take place at the position of lowest electron density. This static reactivity leads to the prediction that a nitro group is meta-directing for direct nucleophilic attack in the excited state,... 

AG only gives a static description of the reaction. A dynamic study is required to resolve many remaining questions. How do the initial conditions (relative positions and velocities of the reactants) influence the reaction How should the reagents approach each other in order to achieve a reactive collision How is the energy of the system divided between electronic, translational, rotational and vibrational components after the collision Unfortunately, such calculations are difficult and only small systems can be treated by quantum dynamics at present. For more complicated structures, the potential surface is calculated using quantum mechanics and the dynamic aspects are treated using classical mechanics. To illustrate the kind of information that can be obtained from dynamic studies, let us consider the Sn2 reaction ... 

Let us consider first the in vacuo cases. Dynamical aspects of the reaction in vacuo may be recovered by resorting to calculations of semiclassical trajectories. A cluster of independent representative points, with accurately selected classical initial conditions, are allowed to perform trajectories according to classical mechanics. The reaction path, which is a static semiclassical concept (the best path for a representative point with infinitely slow motion), is replaced by descriptions of the density of trajectories. A widely employed approach to obtain dynamical information (reaction rate coefficients) is based on modern versions of the Transition State Theory (TST) whose original formulation dates back to 1935. Much work has been done to extend and refine the original TST. 

The key differences between the PCM and the Onsager s model are that the PCM makes use of molecular-shaped cavities (instead of spherical cavities) and that in the PCM the solvent-solute interaction is not simply reduced to the dipole term. In addition, the PCM is a quantum mechanical approach, i.e. the solute is described by means of its electronic wavefunction. Similarly to classical approaches, the basis of the PCM approach to the local field relies on the assumption that the effective field experienced by the molecule in the cavity can be seen as the sum of a reaction field term and a cavity field term. The reaction field is connected to the response (polarization) of the dielectric to the solute charge distribution, whereas the cavity field depends on the polarization of the dielectric induced by the applied field once the cavity has been created. In the PCM, cavity field effects are accounted for by introducing the concept of effective molecular response properties, which directly describe the response of the molecular solutes to the Maxwell field in the liquid, both static E and dynamic E, [8,47,48] (see also the contribution by Cammi and Mennucci). 

In recent years, there have been many attempts to combine the best of both worlds. Continuum solvent models (reaction field and variations thereof) are very popular now in quantum chemistry but they do not solve all problems, since the environment is treated in a static mean-field approximation. The Car-Parrinello method has found its way into chemistry and it is probably the most rigorous of the methods presently feasible. However, its computational cost allows only the study of systems of a few dozen atoms for periods of a few dozen picoseconds. Semiempirical cluster calculations on chromophores in solvent structures obtained from classical Monte Carlo calculations are discussed in the contribution of Coutinho and Canuto in this volume. In the present article, we describe our attempts with so-called hybrid or quantum-mechanical/molecular-mechanical (QM/MM) methods. These concentrate on the part of the system which is of primary interest (the reactants or the electronically excited solute, say) and treat it by semiempirical quantum chemistry. The rest of the system (solvent, surface, outer part of enzyme) is described by a classical force field. With this, we hope to incorporate the essential influence of the in itself uninteresting environment on the dynamics of the primary system. The approach lacks the rigour of the Car-Parrinello scheme but it allows us to surround a primary system of up to a few dozen atoms by an environment of several ten thousand atoms and run the whole system for several hundred thousand time steps which is equivalent to several hundred picoseconds. 

Our purpose here is to review spectroscopic approaches, optical and vibrational, applied to the determination of enzyme structure and dynamics. We focus on hydride transfer reactions in protein catalysis. Vibrational spectroscopy is especially useful in the study of the molecular mechanism of enzymes because it is structurally specific and is of high resolution bond distortions as small as 0.01-0.001 A can be discerned by vibrational spectroscopy. It is at this level of atomic resolution that enzyme induced bond distortions usually manifest themselves. In addition, both enthalpic and entropic factors can be characterized by vibrational spectroscopy, sometimes in quantitative terms. Although most of the chapter is concerned with the structures of static protein-ligand complexes, the dynamics of how these complexes are formed and depleted has recently become a viable topic for scientific... 

---