Computational feasibility

Many of the faster work stations can provide throughput similar to that observed on a crowded, shared supercomputer, especially for codes that do not benefit greatly from vectorization. The availabihty of such machines for less than 50,000 (much less for academic users) has once again changed concepts of what is computationally feasible. Many more people can perform computations that a few years ago were the sole domain of those with access to large-scale computing faciUties, and this trend is expected to continue. 

Gaussian includes many different model chemistries. The theoretical model chemistries in Gaussian have been subjected to the testing procedure described previously and so may be recommended for general use with any system for which they are computationally feasible. 

If it is computationally feasible, improve on the structure by using it as the starting point for a more accurate optimization (using a larger basis set and/or run at a higher level of theory). 

In order to calculate total energies with a chemical accuracy of 1 kcal/mol, it is necessary to use sophisticated methods for including electron correlation and large basis sets, which is only computationally feasible for small systems. Instead the focus is usually on calculating relative energies, trying to make the errors as constant as possible. 

Our results demonstrate that the augmented space recursion and the orbital peeling method in conjunction with the LMTO formalism, constitute a viable and computationally feasible approach to the calculation of phase stability in binary substitutionally disordered alloys. ... 

Unfortunately the complete calculation of the principal polarizabilities of a polyatomic molecule including the Silberstein interactions is very complex. Possibly electronic calculators will make this computation feasible for an array of molecules such as the... 

An important advance in making explicit polarizable force fields computationally feasible for MD simulation was the development of the extended Lagrangian methods. This extended dynamics approach was first proposed by Sprik and Klein [91], in the sipirit of the work of Car and Parrinello for ab initio MD dynamics [168], A similar extended system was proposed by van Belle et al. for inducible point dipoles [90, 169], In this approach each dipole is treated as a dynamical variable in the MD simulation and given a mass, Mm, and velocity, p.. The dipoles thus have a kinetic energy, JT (A)2/2, and are propagated using the equations of motion just like the atomic coordinates [90, 91, 170, 171]. The equation of motion for the dipoles is... 

Considering a trade-off between knowledge that is required prior to the analysis and predictive power, stoichiometric network analysis must be regarded as the most successful computational approach to large-scale metabolic networks to date. It is computationally feasible even for large-scale networks, and it is nonetheless far more predictive that a simple graph-based analysis. Stoichiometric analysis has resulted in a vast number of applications [35,67,70 74], including quantitative predictions of metabolic network function [50, 64]. The two most well-known variants of stoichiometric analysis, namely, flux balance analysis and elementary flux modes, constitute the topic of Section V. 

The analysis of large-scale systems is computationally feasible and does not require extensive information about the involved enzymatic rate equations and their associated parameter values. 

Water Potentials. The ST2 (23), MCY (24), and CF (2J5) potentials are computationally tractable and accurate models for two-body water-water interaction potentials. The ST2, MCY and CF models have five, four, and three interaction sites and have four, three and three charge centers, respectively. Neither the ST2 nor the MCY potentials allow OH or HH distances to vary, whereas bond lengths are flexible with the CF model. While both the ST2 and CF potentials are empirical models, the MCY potential is derived from ab initio configuration interaction molecular orbital methods (24) using many geometrical arrangements of water dimers. The MCY+CC+DC water-water potential (28) is a recent modification of the MCY potential which allows four body interactions to be evaluated. In comparison to the two-body potentials described above, the MCY+CC+DC potential requires a supercomputer or array processor in order to be computationally feasible. Therefore, the ST2, MCY and CF potentials are generally more economical to use than the MCY+CC+DC potential. 

There are several future research directions for this project. First, results from the FMO reaction check are not infallible due to the qualitative nature of this check. A more precise, yet computationally feasible model may be possible. Second, more work remains in the WLN rearranger a full system based on our concepts would require knowledge of the entire complement of WLN rules. It may also be desirable to adopt or develop another, more computationally tractable line notation for the purpose of synthetic analysis. Finally, we would like to extend our work to more reaction classes to examine its potential in more detail. 

The electron correlation problem remains a central research area for quantum chemists, as its solution would provide the exact energies for arbitrary systems. Today there exist many procedures for calculating the electron correlation energy (/), none of which, unfortunately, is both robust and computationally inexpensive. Configuration interaction (Cl) methods provide a conceptually simple route to correlation energies and a full Cl calculation will provide exact energies but only at prohibitive computational cost as it scales factorially with the number of basis functions, N. Truncated Cl methods such as CISD (A cost) are more computationally feasible but can still only be used for small systems and are neither size consistent nor size extensive. Coupled cluster... 

The semi-empirical methods ignore all the core electrons and consider only the outer shell of valence electrons. Many other types of simplification are also made to make the computation feasible in a reasonable length of time. These simplifications make the results less accurate, but make it possible to study larger molecules. 

Carefully established correlations between nuclear magnetic resonance (NMR) shifts and atomic electron populations in weU-defined series of closely related compounds can prove valuable for the evaluation of atomic charges in similar systems that are at, or beyond, the limits of practical computational feasibility. We certainly could make good use of them. [Also remember the insight gained with the help of Fig. 5.2 it led to Eq. (5.10).]... 

It is generally true that quantum chemists would like to perform all calculations to the highest possible accuracy. However, this is often computationally feasible only for small systems, because of the rapid increase in computer time and perhaps storage requirements of the calculations with increasing size of the molecule. In many cases it is not even necessary to perform such calculations for the purposes of prediction or interpretation, since the accuracy to which results need be known is often inversely proportional to the size of the system. That is, for diatomic molecules it is generally necessary to compute spectroscopic constants or intensities very accurately, because these quantities can often be determined to high accuracy by experiment. For systems of a dozen or more atoms it is seldom necessary to have such accurate results, because the experimental accuracy is lower and the problems quantum chemists are called on to answer will consequently often involve lower accuracy. 

First, the role of system design on the details of convection and solute segregation in industrial-scale crystal growth systems has not been adequately studied. This deficiency is mostly because numerical simulations of the three-dimensional, weakly turbulent convection present in these systems are at the very limit of what is computationally feasible today. New developments in computational power may lift this limitation. Also, the extensive use of applied magnetic fields to control the intensity of the convection actually makes the calculations much more feasible. 

The problem of combining dynamics with quantum chemistry is at the forefront of current research. The best method to be used will emerge as a compromise between quantum mechanical rigor and computational feasibility.99... 

Implicit solvation models have proved themselves very effective in providing a computationally feasible way to simulate the microscopic environment of molecules in solution [1-3] accurate free energy of solvation can be computed, and the spectroscopic properties of solutes can be corrected to take into account solvent effects. 

A simple but effective strategy ( corrected LR, or cLR) aimed at overcoming this intrinsic limit of the nonlinear effective solute Hamiltonian when applied to LR approaches has been first proposed by Caricato et al. [33], With such a strategy, the state-specific solvent response is recovered within the linear response approach. As a result, the LR-SS differences in vertical excitation energies are greatly reduced (still keeping the computational feasibility of LR schemes). 

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