Spectrum/a

These equations indicate that the energy of the scattered ions is sensitive to the mass of the scattering atom s in the surface. By scanning the energy of the scattered ions, one obtains a kind of mass spectrometric analysis of the surface composition. Figure VIII-12 shows an example of such a spectrum. Neutral, that is, molecular, as well as ion beams may be used, although for the former a velocity selector is now needed to define ,. ... 

The actual line shape in a spectrum is a convolution of the natural Lorentzian shape with the Doppler shape. It must be calculated for a given case as there is no simple fomuila for it. It is quite typical in electronic... 

The spectral frequency range covered by the central lobe of this sinc fiinction increases as the piilselength decreases. For a spectrum to be undistorted it should really be confined to the middle portion of this central lobe (figure B 1.12.2). There are a number of examples in the literature of solid-state NMR where the resonances are in fact broader than the central lobe so that the spectrum reported is only effectively providing infonnation about the RF-irradiation envelope, not the shape of the signal from the sample itself... 

Another problem in many NMR spectrometers is that the start of the FID is corrupted due to various instrumental deadtimes that lead to intensity problems in the spectrum. The spectrometer deadtime is made up of a number of sources that can be apportioned to either the probe or the electronics. The loss of the initial part of the FID is manifest in a spectrum as a rolling baseline and the preferential loss of broad components of... 

Considerable spectroscopic data are required for the detemiination of the relative populations in die various internal quantum levels of the product from the relative intensities of various lines, or bands, in a spectrum. 

Recall that L contains the frequency or (equation (B2.4.8)). To trace out a spectrum, equation (B2.4.11)) is solved for each frequency. In order to obtain the observed signal v, the sum of the two individual magnetizations can be written as the dot product of two vectors, equation (B2.4.12)). 

Once the basic work has been done, the observed spectrum can be calculated in several different ways. If the problem is solved in tlie time domain, then the solution provides a list of transitions. Each transition is defined by four quantities the mtegrated intensity, the frequency at which it appears, the linewidth (or decay rate in the time domain) and the phase. From this list of parameters, either a spectrum or a time-domain FID can be calculated easily. The spectrum has the advantage that it can be directly compared to the experimental result. An FID can be subjected to some sort of apodization before Fourier transfomiation to the spectrum this allows additional line broadening to be added to the spectrum independent of the sumilation. 

In a coupled spin system, the number of observed lines in a spectrum does not match the number of independent z magnetizations and, fiirthennore, the spectra depend on the flip angle of the pulse used to observe them. Because of the complicated spectroscopy of homonuclear coupled spins, it is only recently that selective inversions in simple coupled spin systems [23] have been studied. This means that slow chemical exchange can be studied using proton spectra without the requirement of single characteristic peaks, such as methyl groups. 

If a spectrum lacks certain Lines or contains extra lines from additional unknown components, or if the true line positions are blurred, fuzzy set theory can improve the matching. 

Other methods consist of algorithms based on multivariate classification techniques or neural networks they are constructed for automatic recognition of structural properties from spectral data, or for simulation of spectra from structural properties [83]. Multivariate data analysis for spectrum interpretation is based on the characterization of spectra by a set of spectral features. A spectrum can be considered as a point in a multidimensional space with the coordinates defined by spectral features. Exploratory data analysis and cluster analysis are used to investigate the multidimensional space and to evaluate rules to distinguish structure classes. 

Multivariate data analysis usually starts with generating a set of spectra and the corresponding chemical structures as a result of a spectrum similarity search in a spectrum database. The peak data are transformed into a set of spectral features and the chemical structures are encoded into molecular descriptors [80]. A spectral feature is a property that can be automatically computed from a mass spectrum. Typical spectral features are the peak intensity at a particular mass/charge value, or logarithmic intensity ratios. The goal of transformation of peak data into spectral features is to obtain descriptors of spectral properties that are more suitable than the original peak list data. 

To define the state yon want to calculate, you must specify the m u Itiplicity. A system with an even ii n m ber of electron s n sn ally has a closed-shell ground state with a multiplicity of I (a singlet). Asystem with an odd niim her of electrons (free radical) nsnally has a multiplicity of 2 (a doublet). The first excited state of a system with an even ii nm ber of electron s usually has a m n Itiplicity of 3 (a triplet). The states of a given m iiltiplicity have a spectrum of states —the lowest state of the given multiplicity, the next lowest state of the given multiplicity, and so on. 

The metal is characterized by a spectrum containing two bright lines in the blue along with several others in the red, yellow, and green. It is silvery white, soft, and ductile. It is the most electropositive and most alkaline element. 

Mathematical manipulation (Fourier transform) of the data to plot a spectrum... 

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