Accuracy types

Before performing a validation method for a certain application, the scope of the method and its validation criteria should be defined first. The parameters to be investigated include compounds, matrices, types of formation, qualitative or quantitative method, detection or quantitation limit, linear range, precision and accuracy, types of equipment that will be used, and the location of the system. These steps of the validation method are illustrated in Fig. 1, which has been modified from Ref. [11],... 

Method Accuracy Type of measurement Measurement influenced by Usable for VRLA Cost... 

To type crude oils (see Figure 2.13). This method uses an extremely accurate compositional analysis of crudes to determine their source and possible migration route. As a result of the accuracy It is possible to distinguish not only the oils of individual accumulations in a region, but even the oils from the different drainage units within a field. If sufficient samples were taken at the exploration phase of a field, geochemistry allows one to verify cross flow and preferential depletion of units during later production. 

Two different types of calibration marks are used in our experiments, planar circles and circular balls. The accuracy of the calibration procedure depends on the accuracy of the feature detection algorithms used to detect the calibration marks in the images. To take this in account, a special feature detection procedure based on accurate ellipses fitting has been developed. Detected calibration marks are rejected, if the feature detection procedure indicates a low reliability. 

Class WAVEFORM Transducer type Thickness range Accuracy... 

The simplest use of an NMR spectnim, as with many other branches of spectroscopy, is for quantitative analysis. Furthennore, in NMR all nuclei of a given type have the same transition probability, so that their resonances may be readily compared. The area underneath each isolated peak in an NMR spectnim is proportional to the number of nuclei giving rise to that peak alone. It may be measured to 1% accuracy by digital integration of the NMR spectnim, followed by comparison with the area of a peak from an added standard. 

For every type of angle including three atoms, two parameters (force constant fe and reference value 0q) are needed. Also, as in the bond deformation case, higher-order contributions such as that given by Eq. (23) are necessary to increase accuracy or to account for larger deformations, which no longer follow a simple harmonic potential. 

The accuracy of a molecular mechanics or seim-eni pineal quantum mechanics method depends on the database used to parameterize the method. This is true for the type of molecules and the physical and chemical data in the database. Frequently, these methods give the best results for a limited class of molecules or phen omen a. A disad van tage of these methods is that you m u si have parameters available before running a calculation. Developing param eiers is time-consuming. 

Another approach is spin-coupled valence bond theory, which divides the electrons into two sets core electrons, which are described by doubly occupied orthogonal orbitals, and active electrons, which occupy singly occupied non-orthogonal orbitals. Both types of orbital are expressed in the usual way as a linear combination of basis functions. The overall wavefunction is completed by two spin fimctions one that describes the coupling of the spins of the core electrons and one that deals with the active electrons. The choice of spin function for these active electrons is a key component of the theory [Gerratt ef al. 1997]. One of the distinctive features of this theory is that a considerable amount of chemically significant electronic correlation is incorporated into the wavefunction, giving an accuracy comparable to CASSCF. An additional benefit is that the orbitals tend to be... 

As discussed in the previous chapters, discretization of the solution domain into an appropriate computational mesh is the first step in the finite element simulation of field problems. Main factors in the selection of a particular mesh design for a problem are domain geometi-y, type of the finite elements used in the di.scretization, required accuracy and cost of computations. In this respect, the accuracy of computations depends on factors such as ... 

Hybrid grids are used for very complex geometries where combination of structured mesh segments joined by zones of unstructured mesh can provide the best approach for discretization of the problem domain. The flexibility gained by combining structured and unstructured mesh segments also provides a facility to improve accuracy of the numerical solutions for field problems of a complicated nature. Figure 6.3 shows an example of this type of computational mesh. 

Density functionals can be broken down into several classes. The simplest is called the Xa method. This type of calculation includes electron exchange but not correlation. It was introduced by J. C. Slater, who in attempting to make an approximation to Hartree-Fock unwittingly discovered the simplest form of DFT. The Xa method is similar in accuracy to HF and sometimes better. 

A basis set is a set of functions used to describe the shape of the orbitals in an atom. Molecular orbitals and entire wave functions are created by taking linear combinations of basis functions and angular functions. Most semiempirical methods use a predehned basis set. When ah initio or density functional theory calculations are done, a basis set must be specihed. Although it is possible to create a basis set from scratch, most calculations are done using existing basis sets. The type of calculation performed and basis set chosen are the two biggest factors in determining the accuracy of results. This chapter discusses these standard basis sets and how to choose an appropriate one. 

There are several types of basis functions listed below. Over the past several decades, most basis sets have been optimized to describe individual atoms at the EIF level of theory. These basis sets work very well, although not optimally, for other types of calculations. The atomic natural orbital, ANO, basis sets use primitive exponents from older EIF basis sets with coefficients obtained from the natural orbitals of correlated atom calculations to give a basis that is a bit better for correlated calculations. The correlation-consistent basis sets have been completely optimized for use with correlated calculations. Compared to ANO basis sets, correlation consistent sets give a comparable accuracy with significantly fewer primitives and thus require less CPU time. 

Another related issue is the computation of the intensities of the peaks in the spectrum. Peak intensities depend on the probability that a particular wavelength photon will be absorbed or Raman-scattered. These probabilities can be computed from the wave function by computing the transition dipole moments. This gives relative peak intensities since the calculation does not include the density of the substance. Some types of transitions turn out to have a zero probability due to the molecules symmetry or the spin of the electrons. This is where spectroscopic selection rules come from. Ah initio methods are the preferred way of computing intensities. Although intensities can be computed using semiempirical methods, they tend to give rather poor accuracy results for many chemical systems. 

Transition state theory calculations present slightly fewer technical difficulties. However, the accuracy of these calculations varies with the type of reaction. With the addition of an empirically determined correction factor, these calculations can be the most readily obtained for a given class of reactions. 

There is no one best method for describing solvent effects. The choice of method is dependent on the size of the molecule, type of solvent effects being examined, and required accuracy of results. Many of the continuum solvation methods predict solvation energy more accurately for neutral molecules than for ions. The following is a list of preferred methods, with those resulting in the highest accuracy and the least amount of computational effort appearing first ... 

The parameters in the original parameterization are adjusted in order to reproduce the correct results. These results are generally molecular geometries and energy differences. They may be obtained from various types of experimental results or ah initio calculations. The sources of these correct results can also be a source of error. Ah initio results are only correct to some degree of accuracy. Likewise, crystal structures are influenced by crystal-packing forces. 

---