QM simulation

Figure 19(a) shows the QM simulation of the differential cross-section (DCS) in the HF + D channel, over the same extended energy range as in Fig. 5. The agreement with experiment is seen to be qualitatively reasonable. The forward-backward peaking and direct reaction swathe observed in the experiment also occur in the QM calculation, although the relative magnitudes are not consistent. Thus fully quantitative agreement between QM calculations and experiment in all of the reaction attributes must await further refinements of the PES, and/or a more rigorous treatment of the open-shell character of the F(2P) atom.90...

A number of tools have been employed for the analysis of simulation trajectories. Structural data can be extracted via RDFs, which can be independently obtained for any desirable atom-atom pair distribution, and from ADFs for any angle of relevance. CNDs supply a clear picture of different species being formed within the simulation time, which for QM simulations usually ranges between 10 and 50 ps. Therefore, different species observed means that for almost all experimental timescales these species are present simultaneously and that the experiment delivers a time-averaged picture of them. For the reactivity of solutes, however, the detailed species distribution is of great importance, in particular for understanding reaction mechanisms. It is possible to analyze RDF and ADF separately for all of the (differently coordinated) species, thus obtaining detailed structural information for each of them. 

QM/MM approaches where the solute is QM and the solvent MM are in principle useful for computing the effect of the slow reaction field (represented by the solute point charges) but require a polarizable solvent model if electronic equilibration to the excited state is to be included (Gao 1994). With an MM solvent shell, it is no more possible to compute differential dispersion effects directly than for a continuum model. An option is to make the first solvent shell QM too, but computational costs for MC or MD simulations quickly expand with such a model. Large QM simulations with explicit solvent have appeared using the fast semiempirical INDO/S model to evaluate solvatochromic effects, and the results have been promising (Coutinho, Canute, and Zemer 1997 Coutinho and Canute 2003). Such simulations offer the potential to model solvent broadening accurately, since they can compute absorptions for an ensemble of solvent configurations. 

The previous two sections of this review deal with classical simulation methods. A description of the activation of adsorbates by acidic sites, together with any bond breaking or bond formation that may take place, is the realm of quantum mechanical (QM) simulations. These types of calculations are particularly well-suited to zeolite-adsorbate systems when the cluster approximation is used. The active acidic site in the zeolite is modeled by a molecular cluster, formed by cutting out a small portion of... 

Most of other trajectories obtained in this study exhibited intermediate characters between trajectories (a) and (b). An important message was that the chemical reaction does not always proceed through the lowest energy pathway with optimal solvation. In conclusion, the simulations for the first time illustrated how the atoms in reacting molecules behave in solution at the molecular level, which was made possible by using full QM simulations with the recently developed FMO-MD methodology. 

The first strategy maintains the QM description of the solvent molecules but reduces their number and adopts a different description for other molecules (often adopting a continuum distribution) to take account of bulk effects in the calculation. These QM simulation methods, of which the first and most frequently used is the Car-Parrinello method [2], are in use since several years, and have largely passed the stage of benchmark examples. This strategy is the most satisfactory under the formal aspects we have at present, and will surely be employed more and more with increasing computer power, but will certainly not completely replace, in the foreseeable future, other strategies. 

The rapid growth of ab initio quantum mechanical (QM) simulations of condensed matter means that a comprehensive review of theoretical approaches and applications would in itself occupy a book. In this chapter the emphasis will be placed on QM studies of silicate and oxide systems. The key technologies will be identified and a critique of the possibilities and inadequacies of current theory presented. Although we discuss the technical details of implementation of QM methods, and some fundamental issues with regard to the description of electron interactions, the intention is to provide a general reference for non-experts in this field. Recent work based on semi-empirical approaches to QM simulations will not be reviewed (e.g. LaFemina, 1992 Goniakowski etal., 1993). 

Amorphous silica has also been studied recently using first principle molecular dynamics (Samthein et al., 1995). Such simulations are currently restricted to rather small unit cells (24 Si02 units) and short time spans ( 10 ps), unlike the simulations using interatomic potentials described in Chapter 9. Nevertheless, the direct simulation of the liquid phase followed by a rapid quench produces an amorphous state with structural and electronic properties in reasonable agreement with neutron diffraction and spectroscopic studies. QM simulations are able to treat a wide range of structural environments on an equal footing while providing information on both structural and electronic properties. 

Also, new MP2 Monte Carlo simulations of the liquid are important in evaluating these efforts [20]. However, perhaps the major problem for biological simulations isthat AIMD and other QM simulations are so computationally intensive that current studies of the pure liquid generally consist of less than 100 water molecules for less than 100 ps, somewhat like the situation 40 years ago for classical MD simulations. Thus, for computer simulations of most biological applications, empirical PEFs are still needed. 

Recent advances in first-principles molecular dynamics (MD) calculations, which follow the Newtonian dynamics of classically treated nuclei, have made electronic-structure calculations applicable to the study of large systems where previously only classical simulations were possible. Examples of quantum-mechanical (QM) simulation methods are Born-Oppenheimer molecular dynamics (BOMD), Car-Parrinello molecular dynamics (CPMD), tight-binding molecular dynamics (TBMD), atom-centered density matrix propagation molecular dynamics (ADMPMD), and wavepacket ab idtb molecular dynamics (WPAIMD). 

BF, in that they are designed to solve different problems. One general problem with QM/MM, whether conventional or designed for diffusive systems, is that particles at the boundary interact with other particles of both QM and MM character, and may prefer one over the other. This may result in either a density increase, or a density depletion at the boundary, which would not be present in a fiiUy QM simulation. This artifact may be reduced somewhat in the above-mentioned ONIOM-XS, Hot Spot, and LOTF, if the transition region is chosen sufficiently large, but in the BF method this issue is tackled in a more thorough manner. 

The previous sections presented the state of art in adaptive QM/MM methods. Since their debut in 1996 with the Hot Spot method, they have largely reduced the demand on computational resources, while improving structural properties and energy conservation. These methods have already been successfully applied to simulate the solvation stmcture of ions in liquid water [41, 43, 50, 51] and even aqueous chemical reactions [19, 23]. The validation procedure is usually based on comparison with experiments [50] or with the corresponding fully QM simulation [19, 23, 41]. 

However, as stated in the introduction, the bulk of the aqueous reactions of interest involve proton transfer in some form. Even with advanced adaptive QM/MM methods it is still not trivial to perform simulations on proton transfer processes, due to their delocalized nature. Therefore, considering an example system in which proton transfer and diffusion occur can serve as a tough crash test for adaptive QM/MM, and should demonstrate the limitations of the methods. We specifically focus on diffusion and Grothuss shuttling, which are particularly non-local, and will affect thermodynamic reaction quantities. The impact of the introduction of an adaptive QM/MM boundary will be quantified through comparison with fully QM simulations on the same system. To underline the limits of the methodology, the behavior of the proton transfer events and their deviation from expectation will be thoroughly discussed. 

Both our QM and QM/MM simulations show that hydroxide migration occurs in step-wise hops followed by long resting periods. The average hopping rates (counting all proton transfer events, not only the forward-hopping motions) are 1.67 and 0.48 ps for QM/MM and QM simulations respectively. 

Decorrelation is not complete on the time-scales of our simulations (c(t) in Fig. 2.19 does not decay to zero). Again, we observe a considerably faster decay (higher hopping-rate) in the QM/MM simulation than in the fully QM simulation. In both cases, the QH ion remains mainly in the active region. 

Guthrie MG, Daigle AD, Salazar MR (2009) Properties of a method for performing adaptive, multilevel QM simulations of complex chemical reactions in the gas-phase. J Chem Theory Comput 6 18-25... 

To defined the ReaxFF angle parameters we performed a QM-simulation on the H2O molecule where the H-O-H angle was adiabatically distorted from 72° to 134°. Figure 6.2 shows the QM- and ReaxFF results for this angle distortion energy. ReaxFF obtains an equilibrium angle of 103.3° for the isolated water molecule this angle opens up to a value of 105.6° in the Ice(cmc)-phase. 

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