Comparison with high precision experimental

In the next two subsections, we describe collections of calculations that have been used to probe the physical accuracy of plane-wave DFT calculations. An important feature of plane-wave calculations is that they can be applied to bulk materials and other situations where the localized basis set approaches of molecular quantum chemistry are computationally impractical. To develop benchmarks for the performance of plane-wave methods for these properties, they must be compared with accurate experimental data. One of the reasons that benchmarking efforts for molecular quantum chemistry have been so successful is that very large collections of high-precision experimental data are available for small molecules. Data sets of similar size are not always available for the properties of interest in plane-wave DFT calculations, and this has limited the number of studies that have been performed with the aim of comparing predictions from plane-wave DFT with quantitative experimental information from a large number of materials. There are, of course, many hundreds of comparisons that have been made with individual experimental measurements. If you follow our advice and become familiar with the state-of-the-art literature in your particular area of interest, you will find examples of this kind. Below, we collect a number of examples where efforts have been made to compare the accuracy of plane-wave DFT calculations against systematic collections of experimental data. 

Here we call the heavy particle the muon, having in mind that the precise theory of hyperfine splitting finds its main application in comparison with the highly precise experimental data on muonium hyperfine sphtting. However, the theory of nonrecoil corrections is valid for any hydrogenhke atom. 

Included in Table III is the comparison of the transition frequencies calculated from the energies obtained in our calculations with the experimental transition frequencies of Dabrowski [125]. To convert theoretical frequencies into wavenumbers, we used the factor of 1 hartree = 219474.63137 cm . For all the frequencies our results are either within or very close to the experimental error bracket of 0.1 cm . We hope that the advances in high-resolution spectroscopy will inspire remeasurements of the vibrational spectrum of H2 with the accuracy lower than 0.1 cm. With such high-precision results, it would be possible to verify whether the larger differences between the calculated and the experimental frequencies for higher excitation levels, which now appear, are due to the relativistic and radiative effects. 

Theoretical results described above find applications in numerous high precision experiments with hydrogen, deuterium, helium, muonium, muonic hydrogen, etc. Detailed discussion of all experimental results in comparison with theory would require as much space as the purely theoretical discussion above. We will consider below only some applications of the theory, intended to serve as illustrations, their choice being necessarily somewhat subjective and incomplete (see also detailed discussion of phenomenology in the recent reviews [1, 2]). 

Such a situation will often arise if the model does indeed fit the data well, and if the measurement process is highly precise. Recall that the F-test for lack of fit compares the variance due to lack of fit with the variance due to purely experimental uncertainty. The reference point of this comparison is the precision with which measurements can be made. Thus, although the lack of fit might be so small as to be of no practical importance, the F-test for lack of fit will show that it is statistically significant if the estimated variance due to purely experimental uncertainty is relatively very small. 

The LDA results describe the experimental trends quite well. It is noticed, that the distances X-X and A-X as well as the lattice parameters are underestimated for AuSb2 and FeS2, a typical effect of the local density approximation. The theoretical unit cell of SIP2 is slightly expanded in comparison to the experimental result, which was assumed to be a high pressure phase [7]. All position parameters u are reproduced with sufficient precision. 

Matrix isolation experimental techniques [1-10] stand out among many other modern chemical research methods with regard to their ability to provide direct comparisons with quantum mechanical calculations. The use of photoexcitation methods to induce reactions [7-9] as well as the applications of multiple spectroscopic techniques to study such photochemical reactions allows for close control of the reaction parameters. Most of the high temperature and entropy effects, otherwise very large in thermochemical reactions, are therefore not present here and thus some of the limitations associated with applications of precise quantum mechanical calculations to kinetic processes disappear. 

Because of the unusually high sensitivity of a precise experimental value of Op to possible physics beyond the Standard Model, theoretical predictions of the contributions to of these theories are of great interest. In general any new particles or interactions which couple to the muon or to the photon contribute to Op, whose value then provides a sum rule for physics [53]. In comparison with experimental data from the higher energy colliders (LEP II, Tevatron, LHC), an Op value with a precision of 0.35 ppm, as projected for the current BNL experiment, provides a comparable or greater sensitivity to a composite structure... 

Another study focusing on the comparison between theoretical and experimental densities is that of Tsirelson el al. on MgO.133 Here precise X-ray and high-energy transmission electron diffraction methods were used in the exploration of p and the electrostatic potential. The structure amplitudes were determined and their accuracy estimated using ab initio Hartree-Fock structure amplitudes. The model of electron density was adjusted to X-ray experimental structure amplitudes and those calculated by the Hartree-Fock model. The electrostatic potential, deformation density and V2p were calculated with this model. The CPs in both experimental and theoretical model electron densities were found and compared with those of procrystals from spherical atoms and ions. A disagreement concerning the type of CP at ( , 0) in the area of low,... 

A method based on the comparison of experimental and calculated kinetic dependencies of the dynamic surface tension can be more precise in comparison with the use of Eq. (5.253) [77, 85, 89, 92, 93]. Mitrancheva et al. presented the most detailed data and compared calculated dynamic surface tension with results obtained for solutions of TRITON X-100 using three different experimental methods the inclined plate, the oscillating jet and the maximum bubble pressure methods [93]. The inclined plate method yielded values of i2 different from the results of the two other techniques. This discrepancy is probably connected with the differences in the attainable surface age. Thus the inclined plate method can be used only at relatively high surface life times when the surface tension tends asymptotically to equilibrium, and when the accuracy of determination of i2 decreases. In addition the insufficiently investigated peculiarities of the liquid flow along the inclined plane can be another source of experimental errors [93]. 

Much of the diflBculty with these comparisons results from apparent points of inflection in the experimental log (fca/ a ) vs. log (S/D) plots that occur within the approximate range 0.01 < (S/D) < 0.03. Further work is needed to permit more precise characterizations of the locations of these inflection points. The present authors are not aware of the existence of any previous high-precision falloff results measured within the above noted range for a chemically activated system. The sensitive region in which the discrepancies between measured and simulated... 

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