Computational methods accuracy

A highly readable account of early efforts to apply the independent-particle approximation to problems of organic chemistry. Although more accurate computational methods have since been developed for treating all of the problems discussed in the text, its discussion of approximate Hartree-Fock (semiempirical) methods and their accuracy is still useful. Moreover, the view supplied about what was understood and what was not understood in physical organic chemistry three decades ago is... 

The many approaches to the challenging timestep problem in biomolecular dynamics have achieved success with similar final schemes. However, the individual routes taken to produce these methods — via implicit integration, harmonic approximation, other separating frameworks, and/or force splitting into frequency classes — have been quite different. Each path has encountered different problems along the way which only increased our understanding of the numerical, computational, and accuracy issues involved. This contribution reported on our experiences in this quest. LN has its roots in LIN, which... 

It is possible to use computational techniques to gain insight into the vibrational motion of molecules. There are a number of computational methods available that have varying degrees of accuracy. These methods can be powerful tools if the user is aware of their strengths and weaknesses. The user is advised to use ah initio or DFT calculations with an appropriate scale factor if at all possible. Anharmonic corrections should be considered only if very-high-accuracy results are necessary. Semiempirical and molecular mechanics methods should be tried cautiously when the molecular system prevents using the other methods mentioned. 

Size-consistency and size-extensivity are issues that should be considered at the outset of any study involving multiple molecules or dissociated fragments. As always, the choice of a computational method is dependent on the accuracy desired and computational resource requirements. Correction formulas are so simple to use that several of them can readily be tried to see which does best for... 

This last definition should be carefully appHed as either an interpolation or an extrapolation, particularly for empirical computational methods based on diverse observations. It is critical that users of molecular modeling tools understand where it is appropriate to apply a technique and where it is not, and what degree of accuracy can be expected. 

Computational methods have played an exceedingly important role in understanding the fundamental aspects of shock compression and in solving complex shock-wave problems. Major advances in the numerical algorithms used for solving dynamic problems, coupled with the tremendous increase in computational capabilities, have made many problems tractable that only a few years ago could not have been solved. It is now possible to perform two-dimensional molecular dynamics simulations with a high degree of accuracy, and three-dimensional problems can also be solved with moderate accuracy. 

Uses raw data from field tests to compute hydraulic conductivity computed value is evaluated by the expert system for its correctness with regard to these considerations site-specific geological characteristics, validity of test procedures, accuracy of the raw data, and the computational method. System is written in Arity-Prolog on a PC. 

With the availability of sophisticated computational methods, combined with the ever increasing speed of computers and the latest parallel computing technology, quantum chemical calculations with chemical accuracy for larger systems are now readily available. Thus, computational chemistry will play a major role in solving many of the unresolved and challenging problems in sulfur chemistry. 

A computational method which is suitable for studies of this nature should fulfill certain basic requirements (a) it should be sufficiently economical to allow computation of full potential-energy curves for comparatively large number of states, (b) the calculated potential curves for bound states should give rise to vibrational and rotational constants which are in reasonable agreement with experiment when a comparison is possible, (c) the calculated total energies of all the states should be of comparable accuracy, and (d) the ordering of the states should be correct. 

Are existing methods able to meet the four criteria of speed, accuracy, transferability, and interpretability The following is meant to be an illustrative, not exhaustive, brief survey of how some popular methods fall short on one or more of these criteria. For recent, comprehensive overviews of computational methods, references [14] and [17] are recommended. 

Finally, we should mention that experimental data serving as a benchmark for the appraisal of computational methods must be highly accurate. Setting the goal of 2 kcal/mol for useful accuracy of calculated thermochemical data means of course, that a still better level of accuracy must be reached by experimental measurements. The high accuracy of... 

The key feature of the systems to be considered in this book is that they have short memories that is, the effects of perturbations diminish with the passage of time. In the example of this chapter, the carbon dioxide pressure returns to a value of 1 within a century or two of the perturbation, regardless of the size of the initial perturbation. In this kind of system, computational errors do not grow as the calculation proceeds instead, the system forgets old errors. That is why the reverse Euler method is useful despite its simplicity and limited accuracy. The many properties of the environment that are reasonably stable and predictable can, in principle, be described by equations with just this kind of stability, and these are the properties that can be simulated using the computational methods described in this book. 

CFD may be loosely thought of as computational methods applied to the study of quantities that flow. This would include both methods that solve differential equations and finite automata methods that simulate the motion of fluid particles. We shall include both of these in our discussions of the applications of CFD to packed-tube simulation in Sections III and IV. For our purposes in the present section, we consider CFD to imply the numerical solution of the Navier-Stokes momentum equations and the energy and species balances. The differential forms of these balances are solved over a large number of control volumes. These small control volumes when properly combined form the entire flow geometry. The size and number of control volumes (mesh density) are user determined and together with the chosen discretization will influence the accuracy of the solutions. After boundary conditions have been implemented, the flow and energy balances are solved numerically an iteration process decreases the error in the solution until a satisfactory result has been reached. 

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