Quantum Monte Carlo reactions

Solvent effects were found to have minimal influence on the excitation energies of phenol in aqueous solution using a quantum Monte Carlo simulation , which is in line with experimental observations on its absorption spectra " . Reaction field calculations of the excitation energy also showed a small shift in a solution continuum, in qualitative agreement with fluorescent studies of clusters of phenol with increasing number of water molecules " . The largest fluorescent shift of 2100 cm was observed in cyclohexane. 

In this review, almost all of the simulations we have described use only classical mechanics to describe the nuclear motion of the reaction system. However, a more accurate analysis of many reactions, including some of the ones that have already been simulated via purely classical mechanics, will ultimately require some infusion of quantum mechanical methods. This infusion has already taken place in several different types of reaction dynamics electron transfer in solution, > i> 2 HI photodissociation in rare gas clusters and solids,i i 22 >2 ° I2 photodissociation in Ar fluid,and the dynamics of electron solvation.22-24 Since calculation of the quantum dynamics of a full solvent is at present too time-consuming, all of these calculations involve a quantum solute in a classical solvent. (For a system where the solvent is treated quantum mechanically, see the quantum Monte Carlo treatment of an electron transfer reaction in water by Bader et al. O) As more complex reaaions are investigated, the techniques used in these studies will need to be extended to take into account effects involving electron dynamics such as curve crossing, the interaction of multiple electronic surfaces and other breakdowns of the Born-Oppenheimer approximation, the effect of solvent and solute polarization, and ultimately the actual detailed dynamics of the time evolution of the electronic degrees of freedom. 

For systems containing a few electrons—such as the molecular ion H3, the dimer He-He, the trimer He3, the pair He-H, and the molecule H2—a quantum Monte Carlo method provides absolute accuracies of better than 0.01 kcal/ mol without systematic error. When an exact potential energy surface for the reaction H + Fi2—>Fi2 -l- H is needed, a quantum Monte Carlo method is the best choice, providing 60,000 points on the surface with accuracies of 0.01 kcal/mol or better. ... 

Exact quantum Monte Carlo calculations by Diedrich and Anderson ° have produced a potential energy surface for the reaction H -I- H2 —> H2 -l- H accurate to within 0.01 kcal/mol at the saddle point and within 0.10 kcal/mol or better elsewhere on the surface. The method used is that of cancellation... 

Figure 8 Rate constants k T) for the reaction OH + H2 — H2O + H. Results are shown for diffusion quantum Monte Carlo calculations (DMC) and for the more approximate Morse quadratic-quartic (MQQ) procedure. (From Ref. 132.)...

Progress in the theoretical description of reaction rates in solution of course correlates strongly with that in other theoretical disciplines, in particular those which have profited most from the enonnous advances in computing power such as quantum chemistry and equilibrium as well as non-equilibrium statistical mechanics of liquid solutions where Monte Carlo and molecular dynamics simulations in many cases have taken on the traditional role of experunents, as they allow the detailed investigation of the influence of intra- and intemiolecular potential parameters on the microscopic dynamics not accessible to measurements in the laboratory. No attempt, however, will be made here to address these areas in more than a cursory way, and the interested reader is referred to the corresponding chapters of the encyclopedia. 

Specific solute-solvent interactions involving the first solvation shell only can be treated in detail by discrete solvent models. The various approaches like point charge models, siipennoleciilar calculations, quantum theories of reactions in solution, and their implementations in Monte Carlo methods and molecular dynamics simulations like the Car-Parrinello method are discussed elsewhere in this encyclopedia. Here only some points will be briefly mentioned that seem of relevance for later sections. 

The calculation of the potential of mean force, AF(z), along the reaction coordinate z, requires statistical sampling by Monte Carlo or molecular dynamics simulations that incorporate nuclear quantum effects employing an adequate potential energy function. In our approach, we use combined QM/MM methods to describe the potential energy function and Feynman path integral approaches to model nuclear quantum effects. 

Another aspect that has been theoretically studied109,124,129 is experimental evidence that Diels-Alder reactions are quite sensitive to solvent effects in aqueous media. Several models have been developed to account for the solvent in quantum chemical calculations. They may be divided into two large classes discrete models, where solvent molecules are explicitly considered and continuum models, where the solvent is represented by its macroscopic magnitudes. Within the first group noteworthy is the Monte Carlo study... 

Beyond the clusters, to microscopically model a reaction in solution, we need to include a very big number of solvent molecules in the system to represent the bulk. The problem stems from the fact that it is computationally impossible, with our current capabilities, to locate the transition state structure of the reaction on the complete quantum mechanical potential energy hypersurface, if all the degrees of freedom are explicitly included. Moreover, the effect of thermal statistical averaging should be incorporated. Then, classical mechanical computer simulation techniques (Monte Carlo or Molecular Dynamics) appear to be the most suitable procedures to attack the above problems. In short, and applied to the computer simulation of chemical reactions in solution, the Monte Carlo [18-21] technique is a numerical method in the frame of the classical Statistical Mechanics, which allows to generate a set of system configurations... 

Beyond Transition State Theory (and, therefore, beyond Monte Carlo simulations) dynamical effects coming from recrossings should be introduced. Furthermore, additional quantum mechanical aspects, like tunneling, should be taken into account in some chemical reactions. 

Tapia, O. and Lluch, J. M. Solvent effects on chemical reaction profiles. Monte Carlo simulation of hydration effects on quantum chemically calculated stationary structures, J. Chem.Phys., 83 (1983, 3970-3982... 

Tapia, O., Lluch, J. M., Cardenas, R. and Andres, J. Theoretical study of solvation effects in chemical reactions. A combined quantum chemical/Monte Carlo study ofthe Meyer-Schuster reaction mechanism in water, J. Am. Chem.Soc., Ill (1989), 829-835... 

---