Root mean-square splitting

Sum Square Splitting and Root Mean Square Splitting as Measures of Configurational Splitting... 

The triplet-state splittings of tyrosine were first observed by electron paramagnetic resonance (EPR) more than two decades ago.l30 32) The initial characterization of the splittings was limited to a measurement of >, a root-mean-square zfs defined by... 

It should be mentioned that another validation technique, called leverage correction [1], is available in some software packages. This method, unlike cross validation, does not involve splitting of the calibration data into model and test sets, but is simply an altered calculation of the RMSEE fit error of a model. This alteration involves the weighting of the contribution of the root mean square error from each calibration... 

Secondly come methods depending on W asastjema s Criterion (36) that the distance D should be split into structural radii in the ratio of the Electron Cloud radii y at approximately their root-mean-square values yrms-... 

The absorption spectrum of Cp3Nd(NCCH3) in a single crystal form at liquid nitrogen temperatures showed a truncated crystal field splitting pattern could be derived. The parameters of an empirical Hamiltonian were fitted [41] with the energies of 41 levels with a root mean square deviation of 26 cm1. 

If we put the originally taken nucleus of nonzero size into the usual electronic shell and observe the interactions, we should take the Coulomb forces of the nucleus with electrons into account (eq. (8.2.5)) (Figure 8.2b). This event shifts both levels. The displacement value is in the order of 10 eV. (Attention should be paid to the fact that it is impossible to draw the levels and splitting in Figure 8.2 to the right scale on the background of main transition 10 eV, we must depict details of 10" -10 eV, the difference is 11 orders of value less.) However, it is important that the nucleus in ground and excited states can have different radii (different root mean square radii (r )) and displacements of those two levels are different (however, (/i(0,0,0) ) in both cases is the same). Measurements show that this difference is of the order 10 eV. So, transition frequency o) decreases by the value Aco 10" /10 —10 Hz (in comparison with 10 Hz). 

In this instrument ions produced in the source are accelerated to a given velocity. The unresolved beam is then injected into a field-free region and the ions drift towards the collector. The velocities will be inversely proportional to the square roots of the masses. This means that a pulse of ions will split up according to the ionic masses. The unresolved beam thus becomes resolved in time. Provided that the response time of the electronics is sufficiently fast a spectrum can be recorded. Obviously an average over many such pulses is necessary to provide a reliable signal. Once again the electronics lie at heart of this problem, which demands very fast amplifiers. Initially the time-of-flight mass spectrometer (TOF) was the province of physicists and later of chemists but, with the tremendous advance in electronics, instruments are now produced that are capable of routine operation by relatively untrained operators. 

---