Frequency scale

Despite these simplifications, a typical or F NMR spectrum will nomially show many couplings. Figure BTl 1.9 is the NMR spectrum of propan-1-ol in a dilute solution where the exchange of OH hydrogens between molecules is slow. The underlymg frequency scale is included with the spectrum, in order to emphasize how the couplings are quantified. Conveniently, the shift order matches the chemical order of die atoms. The resonance frequencies of each of the 18 resolved peaks can be quantitatively explained by the four... 

Figure Bl.11.9. Integrated 250 MHz H NMR spectrum of dilute propan-1-ol in dinrethylsulfoxide solvent. Here, the shift order parallels the chemical order. Arr expansion of the H2-I nrultiplet is included, as is the implicit frequency scale, also referenced here to TMS = 0.

Octave bands are divided, on a logarithmic frequency scale, into three equally wide one-third octave bands. This is done often when more exact data of sound spectra are needed. Table 9.14 shows the standardized one-third octave band series. 

Octave band frequency The band in frequency scale that is split into bands, each assigned a sound power level, that is twice the power level of the lower limit. 

System Calc. Frequency Scaled Exp. Symmetry Intensity... 

Here are the predicted frequencies (scaled, in cm ) in the gas phase and in solution ... 

The following table lists recommended values of og for the v.irunij jy, ] includes the published frequency (scaled) associated with carbonyl stretch in the gas phase for each compound that we gave in Chapter 4 ... 

Sum This type of modulation, which is described in the example above, generates a series of frequencies that include the fundamental shaft speeds, both input and output, and fundamental gear-mesh profile. The only difference between the real frequencies and the ghost is their location on the frequency scale. Instead of being at the actual shaft-speed frequency, the ghost appears at frequencies equal to the sum of the input and output shaft speeds. Figure 44.40 illustrates this for a speed-increaser gearbox. 

Without any restrictions we may shift the origin of the frequency scale to the centre of gravity of the spectrum ... 

One possibility for this was demonstrated in Chapter 3. If impact theory is still valid in a moderately dense fluid where non-model stochastic perturbation theory has been already found applicable, then evidently the continuation of the theory to liquid densities is justified. This simplest opportunity of unified description of nitrogen isotropic Q-branch from rarefied gas to liquid is validated due to the small enough frequency scale of rotation-vibration interaction. The frequency scales corresponding to IR and anisotropic Raman spectra are much larger. So the common applicability region for perturbation and impact theories hardly exists. The analysis of numerous experimental data proves that in simple (non-associated) systems there are three different scenarios of linear rotator spectral transformation. The IR spectrum in rarefied gas is a P-R doublet with either resolved or unresolved rotational structure. In the process of condensation the following may happen. 

Our solid state NMR findings suggest that three distinct groups of pectins differing in mobility on the kHz frequency scale, coexist in at least two different areas of the onion cell wall. 

Instead of considering a spectrum as a signal which is measured as a function of wavelength, in this chapter we consider it measured as a function of time. The frequency scale in the Fourier domain is given in cycles (v) per second (Hz) or radians (to) per second (s" ). These units are related by 1 Hz = 2k s" . 

TABLE 4.2. Selected experimental and B3LYP/6-31G(d) calculated IR frequencies (scaled by 0.96) for diphenyloxiranone (16) and 6is-(4-methoxyphenyl)oxiranone (17). ... 

Table 8-7. Frequency scaling factors, rms deviation, proportion outside a 10 % error range and listings of problematic cases [cm-1] for several methods employing the 6-31G(d) basis set. Taken from Scott and Radom, 1996.

Intramethyl couplings in ellipses. Upper and lower set of sign combinations fit spectrum equally well. (B) NMR spectra of AcAlaNHMe in 42%/wt CsPFO in D20. Frequency scale with 0 Hz = 0 ppm. (a) Isotropic spectrum at 47°C. (b) Oriented LX-NMR spectrum at 25°C. (c) Simulated spectrum using best-fit coupling constants shown in (A). From Poon et al., (2000)./. Am. Chem. Soc. 122, 5642-5643, 2000, Reprinted with permission from the American Chemical Society. 

The frequency scale detected by 13C-resolved H spin-lattice relaxation time in the rotating frame Tq) 1 evaluated from the 13C CPMAS spectra42 is similar to that of the 13C T2C values and line-shape analysis16 for 13C (or 15N) or 2H nuclei, as illustrated in Figure 3. It is demonstrated... 

In the solid, dynamics occurring within the kHz frequency scale can be examined by line-shape analysis of 2H or 13C (or 15N) NMR spectra by respective quadrupolar and CSA interactions, isotropic peaks16,59-62 or dipolar couplings based on dipolar chemical shift correlation experiments.63-65 In the former, tyrosine or phenylalanine dynamics of Leu-enkephalin are examined at frequencies of 103-104 Hz by 2H NMR of deuterated samples and at 1.3 x 102 Hz by 13C CPMAS, respectively.60-62 In the latter, dipolar interactions between the 1H-1H and 1H-13C (or 3H-15N) pairs are determined by a 2D-MAS SLF technique such as wide-line separation (WISE)63 and dipolar chemical shift separation (DIP-SHIFT)64,65 or Lee-Goldburg CP (LGCP) NMR,66 respectively. In the WISE experiment, the XH wide-line spectrum of the blend polymers consists of a rather featureless superposition of components with different dipolar widths which can be separated in the second frequency dimension and related to structural units according to their 13C chemical shifts.63... 

Frequency scale. This scale is used to help align the chart paper and to tell you during the run where in the spectrum the instrument is. 

Line-up mark. A line, here at the number 4000, that you use to match up the numbers on the instrument frequency scale with the same numbers on the chart paper. 

The zero-point vibrational energy (Ezpv) is obtained from harmonic B3LYP/VTZ+1 frequencies scaled by 0.985 in the case of Wl theory. For W2 theory, anharmonic values of Ezpv from quar-tic force fields at the CCSD(T)/VQZ+1 (or comparable) level are preferred where this is not feasible, the same procedure as for Wl theory is followed as a fallback solution . 

Values of Ezpv derived from B3LYP/VTZ+1 harmonic vibrational frequencies scaled by 0.985. Same remark applies to W2h, Wl, Wlh and Wlc data given. d For systems where W2h and Wlh are equivalent to W2 and Wl, respectively, entries have been left blank. 

The time-temperature superposition, implying that the functional form does not appreciably depend on temperature (see e.g. [34, 111]). For instance, mechanical or rheological data corresponding to different temperatures can usually be superimposed if their time/frequency scales are shifted properly taking a given temperature Tr as reference. 

Note (SCF frequencies scaled by 0.91 correlated frequencies scaled by 0.95). 

A iH NMR spectrum is a graph of resonance frequency (chemical shift) vs. the intensity of Rf absorption by the sample. The spectrum is usually calibrated in dimensionless units called "parts per million" (abbreviated to ppm) although the horizontal scale is a frequency scale, the units are converted to ppm so that the scale has the same numbers irrespective of the strength of the magnetic field in which the measurement was made. The scale in ppm, termed the 6 scale, is usually referenced to the resonance of some standard substance whose frequency is chosen as... 

Put class interval in the X-axis Put frequency scale on the Y-axis... 

Compound Solvent Screening-constant scale referred to internal MeNCb or NO3-" Frequency scale J referred to Me4N+X- N Resonance half-height width (Hz)... 

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