Intrinsic accuracy

The intrinsic accuracy of mismatch measurements is ample. For example, a 1 /um layer that is mismatched by 220 ppm from an InP substrate gives a peak splitting of 28 this can be measured to about 2%, giving a resolution of 4-5 ppm. The peaks begin to merge below about 100 ppm but splitting down to about 50 ppm can be handled by simple methods smaller splittings can be... 

Intrinsic Accuracy. Intrinsic accuracy indicates the bias caused by sample matrix and sample preparation. In this approach, a stock solution is prepared by using known quantities of related substance and drug substance. The stock solution is further diluted to obtained solutions of lower concentrations. These solutions are used to generate linearity results. In addition, these linearity solutions of different concentrations are spiked into placebo. The spiked solutions are prepared according to the procedure for sample analysis. The resulting solutions, prepared from the spiked solution, are then analyzed. If the same stock solution is used for both linearity and accuracy and all of these solutions are analyzed on the same HPLC run, the response of linearity (without spike into matrix) and accuracy (with spike into matrix) can be compared directly. Any differences in response indicate the bias caused by matrix interference or sample preparation. To determine the intrinsic accuracy at each concentration level, one can compare the peak area of accuracy (with matrix) with that of linearity (without matrix) at the same concentration (Figure 3.11). This is the simplest approach, and one would expect close to 100% accuracy at all concentration levels. 

In this approach, similar to the determination of intrinsic accuracy, the accuracy solutions are prepared by spiking a known quantity of authentic samples and drug... 

More recently, Fisher information has been studied as an intrinsic accuracy measure for concrete atomic models and densities [43, 44] and also for quantum mechanics central potentials [45]. Also, the concept of phase space Fisher information, where position and momentum variables are included, was analyzed for hydrogenlike atoms and the isotropic harmonic oscillator [46]. The net Fisher information measure is found to correlate well with the inverse of the ionization potential and dipole polarizability [44]. 

Consider the Fisher information for locality [1,2], called intrinsic accuracy, which historically predates the Shannon entropy by about 25 years being proposed at about the same time that the final form of quantum mechanics was shaped. This local measure of the information content of the continuous (normalized) classical probability density p r) reads... 

The Fisher information, reminiscent of von Weizsacker s [70] inhomogeneity correction to electronic kinetic energy in the Thomas-Fermi theory, charactoizes the compactness of the probability density. For example, the Fisher information in normal distribution measures the inverse of its variance, called invariance, while the complementary Shannon entropy is proportional to the logarithm of variance, thus monotonically increasing with the spread of Gaussian distribution. Therefore, Shannon entropy and intrinsic accuracy describe complementary facets of the probability density the former reflects the distribution s ( spread ( disorder , a measure of uncertainty), while the latter measures its narrowness ( order ). 

Now, for the first time, the intrinsic accuracy of a semiempirical method can be accurately determined. Hitherto, incomplete optimizations precluded any such determination. 

Before considering the whole of shifts, we shall recall here some of the problems connected with the accuracy of the reported values. Indeed the intrinsic accuracy of the published values depends... 

In this section we will focus on the results of calculations with the singles and doubles coupled cluster method with a perturbative estimate of connected triple excitations, CCSD(T) (for open-shell systems there are a number of variants of this approach " ). The atomic calculations discussed above, as well as numerous molecular calculations, have shown that the intrinsic accuracy of this method is very high for the atomic and molecular properties of interest here. Thus, use of this method eliminates most significant issues related to the accuracy of the method used. Further, to the extent that the variations in the CCSD(T) results with basis set are similar to those of other methods for treating electron correlation, the conclusions drawn from these studies will be generally applicable. 

Although orbital wave functions, such as Hartree-Fock, generalized valence bond, or valence-orbital complete active space self-consistent field wave functions, provide a semi-quantitative description of the electronic structure of molecules, accurate predictions of molecular properties cannot be made without explicit inclusion of the effects of dynamical electron correlation. The accuracy of correlated molecular wave functions is determined by two inter-related expansions the many-electron expansion in terms of antisymmetrized products of molecular orbitals that defines the form of the wave function, and the basis set used to expand the one-electron molecular orbitals. The error associated with the first expansion is the electronic structure method error the error associated with the second expansion is the basis set error. Only by eliminating the basis set error, i.e., by approaching the complete basis set (CBS) limit, can the intrinsic accuracy of the electronic structure method be determined. 

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