Electron error statistics

Table 1 Summary of Error Statistics and Parameters for the Three parameter Correction using the CCSD(T) Electron Correlation Met hod. All units are kcal mol ...

Table 2 CCSD basis set error statistics for sample test sets of reaction energies and atomization energies computed with different CCSD-F12 models and cc-pVXZ-F12 basis sets. All values in kJ/mol per valence electron. Reproduced with permission in modified form from Ref. 55. Copyright 2010 American Institute of Physics.

The core and valence monopole populations used for the MaxEnt calculation were the ones of the reference density (electrons in the asymmetric unit iw = 12.44 and nvalence = 35.56). The phases and amplitudes for this spherical-atom structure, union of the core fragment and the NUP, are already very close to those of the full multipolar model density to estimate the initial phase error, we computed the phase statistics recently described in a multipolar charge density study on 0.5 A noise-free data [56],... 

Our statistical analysis reveals a large improvement from cc-pCV(DT)Z to cc-pCV(TQ)Z see Fig. 1.4. In fact, the cc-pCV(TQ)Z calculations are clearly more accurate than their much more expensive cc-pcV6Z counterparts and nearly as accurate as the cc-pcV(56)Z extrapolations.The cc-pCV(TQ)Z extrapolations yield mean and maximum absolute errors of 1.7 and 4.0 kJ/mol, respectively, compared with those of 0.8 and 2.3 kJ/mol at the cc-pcV(56)Z level. Chemical accuracy is thus obtained at the cc-pCV(TQ)Z level, greatly expanding the range of molecules for which ab initio electronic-structure calculations will afford thermochemical data of chemical accuracy. 

BB. Most molecule-based descriptors, such as logP, PSA, and molecular electronic properties, were used to construct models with a variety of statistical tools. The best performing models can approach the limit of experimental error, which was estimated to be 0.3 log units. 

In the experiment, the transmission intensities for the excited and the dark sample are determined by the number of x-ray photons (/t) recorded on the detector behind the sample, and we typically accumulate for several pump-probe shots. In the absence of external noise sources the accuracy of such a measurement is governed by the shot noise distribution, which is given by Poisson statistics of the transmitted pulse intensity. Indeed, we have demonstrated that we can suppress the majority of electronic noise in experiment, which validates this rather idealistic treatment [13,14]. Applying the error propagation formula to eq. (1) then delivers the experimental noise of the measurement, and we can thus calculate the signal-to-noise ratio S/N as a function of the input parameters. Most important is hereby the sample concentration nsam at the chosen sample thickness d. Via the occasionally very different absorption cross sections in the optical (pump) and the x-ray (probe) domains it will determine the fraction of excited state species as a function of laser fluence. 

Since for a given measuring time nlrut It, and acc /e2i> where /el is the electron beam current, it can be seen that when acc /Jtrue the statistical error is optimal and independent of ItV Second, the coincidence rate is restricted by the maximum allowable singles count rates in either channel (—106— 107 cps, as discussed earlier). 

Figure 2.7. The X-ray observables surface brightness profile and projected gas temperature and their simple derivatives, deprojected temperature, gas density, and gas pressure for the regular galaxy A478 (Sun et al. 2003). (top left) Surface brightness (0.5 - 5 keV) distribution, (upper right) electron density, (lower left) gas temperature, (lower right) gas pressure. Only statistical uncertainties are shown (1 a random errors). In the temperature profile, the data points with small circles are projected temperatures, while the data points with large filled circles are deprojected (three dimensional) values.

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