Parametric Improvement

In Section 1.1, parametric methods for improving tlie quality of correlated electronic-structure calculations were discussed in detail. Similarly, in Section 8.4.3, the mild parameterization of density functional methods to give maximal accuracy was described. Given that background, and the substantial data presented in diose earlier chapters, this section will only recapitulate in a rough categorical fashion tlie various approaches whose development was motivated by a desire to compute more accurate thermochemical quantities. 

Most attention has been focused on the computation of Eeiec, because even fairly modest levels of theory can compute molecular geometries and vibrational frequencies sufficiently accurately to give good ZPVEs and thermal contributions, particularly if the frequencies are scaled by an appropriate factor (see Section 9.3). The simplest approach to improved feiec estimation is to scale it as a raw value as well, and tliis is the formalism implicit in the PCI-80 and SAC methods described in Section 7.7.1. 

At a higher level of complexity, correlation energies are computed assuming tliat effects associated with basis-set incompleteness and, say, truncated levels of perturbation theory, 

The G2 and G3 methods go beyond extrapolation to include small and entirely general empirical corrections associated with the total numbers of paired and unpaired electrons. When sufficient experimental data are available to permit more constrained parameterizations, such empirical corrections can be associated with more specific properties, e.g., with individual bonds. Such bond-specific corrections are employed by the BAG method described in Section 7.7.3. Note that this approach is different from those above insofar as the fundamentally modified quantity is not Feiec, but rather A/7. That is, the goal of the method is to predict improved heats of formation, not to compute more accurate electronic energies, per se. Irikura (2002) has expanded upon this idea by proposing correction schemes that depend not only on types of bonds, but also on their lengths and their electron densities at their midpoints. Such detailed correction schemes can offer very high accuracy, but require extensive sets of high quality experimental data for their formulation. 

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Development of road maps or structured innovation plans would probably work for parametric improvements around the structure, but the basic structure itself is unpredictable and cannot be regulated because the future cannot be predicted. Road maps can plan the incremental improvements, which lead to important changes, but they cannot plan breakthrough or leap frog types of discoveries. 

While simulations reach into larger time spans, the inaccuracies of force fields become more apparent on the one hand properties based on free energies, which were never used for parametrization, are computed more accurately and discrepancies show up on the other hand longer simulations, particularly of proteins, show more subtle discrepancies that only appear after nanoseconds. Thus force fields are under constant revision as far as their parameters are concerned, and this process will continue. Unfortunately the form of the potentials is hardly considered and the refinement leads to an increasing number of distinct atom types with a proliferating number of parameters and a severe detoriation of transferability. The increased use of quantum mechanics to derive potentials will not really improve this situation ab initio quantum mechanics is not reliable enough on the level of kT, and on-the-fly use of quantum methods to derive forces, as in the Car-Parrinello method, is not likely to be applicable to very large systems in the foreseeable future. 

The first point to remark is that methods that are to be incorporated in MD, and thus require frequent updates, must be both accurate and efficient. It is likely that only semi-empirical and density functional (DFT) methods are suitable for embedding. Semi-empirical methods include MO (molecular orbital) [90] and valence-bond methods [89], both being dependent on suitable parametrizations that can be validated by high-level ab initio QM. The quality of DFT has improved recently by refinements of the exchange density functional to such an extent that its accuracy rivals that of the best ab initio calculations [91]. DFT is quite suitable for embedding into a classical environment [92]. Therefore DFT is expected to have the best potential for future incorporation in embedded QM/MD. 

At the end of the chapter, techniques for alchemical transformations were presented. We showed that, in order to avoid rapid changes in free energy and improve the efficiency of the calculation, the parametrization of the Hamiltonian is critical and soft-core potentials should be used [see (4.50)]. A popular approach is the technique of A dynamics which leads to an improved sampling. In this approach A is a variable in the Hamiltonian system [see (4.51)]. Umbrella sampling, metadynamics or ABF can be used to reduce the cost of A dynamics simulations. 

Enhancement of x2 will lead to improvement (in terms of efficiency per interaction volume) in the following applications up-conversion in the visible or near U.V. of powerful I.R. laser radiation, frequency modulation of a laser carrier beam, optical parametric oscillation and amplification for solid state infrared tunable coherent devices. 

As described by Wilhelm et alS55 an alternative operating procedure has been developed in order to improve the separation obtained, where separation is defined as the ratio of concentrations in the upper and lower reservoirs, or in a reservoir and the feed. The technique has become known as parametric pumping because changing an operating parameter, such as temperature, may be considered as pumping the adsorbate into a reservoir at one end of a bed and, by difference, depleting the adsorbate in a reservoir at the other end. 

A useful source of continuously tunable radiation from the near UV to the near-IR with unexplored potential in fluorescence studies is the optical parametric oscillator (OPO). These devices have been around since the 1960s(73) and have received a lot of coverage recently in laser and optoelectronic journals/74 This resurgence of interest in OPOs has been brought about by recent improvements in nonlinear crystals and the development of all-solid-state pump-laser sources with the required levels of coherence and intensity. 

Growing better crystals can certainly improve threshold and output power. As soon as the problems of frequency stabilization have been solved satisfactorily the parametric oscillator will surpass conventional devices in its intensity and resolving power... 

The development and technical perfection of widely tunable, monochromatic devices, such as dye lasers and optical parametric oscillators, now already at the stage of industrial manufacture, will certainly facilitate and improve many spectroscopic investigations, replacing in some experiments both light source and monochromator. 

Although based on a simplified parametric description of the electronic structure of the molecule and of the leads, the framework discussed in this section has the advantage of leading directly to the computation of measurable quantities (the I-V curves). Thus, it is possible to relate the experimental observations to the quantum-mechanical properties of the systems under investigation, e.g., the electronic energy-level structure of the molecule and the relation of such levels to the energy of the leads. A timely improvement in this direction will come from the implementation of manageable methods, which combine a parameter-free atomistic description of the electronic... 

An improved version of the MTD approach would be of real interest as a mono-parametric Free-Wilson-type method (due to their meaning, the MTD and Free-Wilson parameters belong to the same class). The topological description of the molecular structure assures the easy to use character of the MTD method, and the hypermolecule concept allows to study widely differing structures within the data basis. 

There has been much recent progress in the application of density functional theory (DFT) to the calculation of shift tensors, and several methods are presently available. The sum-over-state (SOS) DFT method developed by Malkin et al. (70) does not explicitly include the current density, but it has been parametrized to improve numerical accuracy. Ziegler and coworkers have described a GIAO-DFT method (71) that is available as part of the Amsterdam density functional package (72). An alternate method developed by Cheeseman and co-workers (73) is implemented in Gaussian 94 (74). 

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