High-Accuracy Computational Strategies

Calculate Eint values on the left side of Table 2 (Eq. 

Reproduce the electronic energies discussed in the proceedings section and check the size consistency of the results obtained with the SCF and CISD methods. 

Although quantum mechanical studies of weak interactions can be traced back to Slater s 1929 work on He, ° the first supermolecule ab initio 

---

These results certainly appear very promising and reassuring in terms of our computational strategies, which emphasize that rigorous validation of QSAR models as well as conservative extrapolation are responsible for a very high hit rate (Tables 16.1 and 16.2). However, additional developments of methodology are certainly required to improve model accuracy since quantitative agreement between actual and predicted anticonvulsant activity is not excellent. 

Marti S, V Moliner, M Tunon, IH Williams (2005) Computing kinetic isotope effects for chorismate mutase with high accuracy. A new DFT/MM strategy. J. Phys. Chem. B 109 (9) 3707-3710... 

As can be deduced, for m > 2, expression (2.67) leads to cross derivatives by x and y, whose evaluation is rather cumbersome. To alleviate this difficulty, only one fictitious point can be considered at each side of the interface and hence only the zero- and first-order jump conditions are implemented. While this notion gives reliable solutions, an alternative quasi-fourth-order strategy has been presented in [28] for the consideration of higher order conditions and crossderivative computation. A fairly interesting feature of the derivative matching method is that it encompasses various schemes with different orders that permit its hybridization with other high-accuracy time-domain approaches. 

Theoretical description of the chemisorption bond and calculation of adsorption energies are nowadays mainly based on application of density functional theory (DFT) [28]. This approach has developed to a computational strategy of comparable accuracy to the traditional correlated quantum chemical methods, but at much lower costs, and is now widely used to calculate bond energies to fairly high accuracy comparable to experimental data [29], but sometimes also at variance [30]. 

As reported in Chap. 2, all aftertreatment devices have to be described mathematically with high accuracy. Therefore, aU chemical reactions and heat transfer phenomena are represented in a chemical and physical form. Since computational time has to be kept short, global reactions and rate formulations based on Lang-muir-Hinshelwood type are considered. Moreover, the calibration of the models represents a major step in the modeling work, requiring time and costs and directly affects the accuracy of the simulation of exhaust aftertreatment systems. For the development of control strategies, it is necessary to consider all affected aspects of the powertrain in form of a virtual test bench. The overall simulation tool includes the catalytic parts but also devices like sensors and ECU functions, which interact... 

When selecting the strategy for a computational study, we advocate the use of accurate ab initio calculations whenever this is feasible, because reliable theoretical predictions can be obtained at high theoretical levels (ideally through a convergence toward the solution of the time-independent Schrodinger equation). We recommend the use of semiempirical methods in cases where a complete ab initio or DFT study is impractical. It is essential in such cases to establish the expected accuracy of the semiempirical results, either by comparisons with the available literature data or by separate calibrations. In this context it is usually helpful to perform some checks against ab initio or DFT calculations (if possible). The next section includes examples of such studies. 

---