Wavenumber unit

Conversions from units of gauss into frequency or wavenumber units involves the g-value ... 

If we consider FTIR instrumentation then the situation is trickier, since the equivalent resolution in nm varies across the spectrum. But even keeping the spectrum in its natural wavenumber units, we again find that, except for rotational fine structure of gases, the natural bandwidth of many (most) absorbance bands is greater than 10 wavenumbers. So again, using that figure shows the typical user how he can expect his own measured spectra to behave. 

Raman spectra are usually represented by the intensity of Stokes lines versus the shifted frequencies 12,. Figure 1.15 shows, as an example, the Raman spectrum of a lithium niobate (LiNbOs) crystal. The energies (given in wavenumber units, cm ) of the different phonons involved are indicated above the corresponding peaks. Particular emphasis will be given to those of higher energy, called effective phonons (883 cm for lithium niobate), as they actively participate in the nonradiative de-excitation processes of trivalent rare earth ions in crystals (see Section 6.3). 

Fig. 28. Time-resolved phosphorescence spectra of quinoxaline in durene host observed at 1.38 K and at (a) 30 msec, (b) 450 msec, and (c) 1500 msec after excitation cutoff. The ordinate scale is normalized with respect to the 0 - 0" band. The numbers shown in (c) represent the vibrational frequencies (in wavenumber unit) measured from the 0 - 0" band (21639 cm r). The arrows indicate the bands whose relative intensities are remarkably enhanced at later times after the excitation cutoff. (From Yamauchi and Azumi, Ref. >)...

We note, furthermore, that Eq. 5.1 and most of the following relationships are here expressed in the International System of Units (SI), also called the mks system conversion to cgs units is readily accomplished by replacing the factor l/(47i o) by unity. For comparison with measurements, it is customary to use frequencies v in wavenumber units (cm-1). Conversion to these units is accomplished by replacing frequency co (in units of radians/second) by 2ncv, where c designates the speed of light in vacuum furthermore, we replace (5(co) by the identical 3(v)/2nc. 

We note that in the definition of moments, we have used frequency v in units of cm-1. Other units of frequency are sometimes chosen instead of the experimentalist s standard use of frequency in wavenumber units (cm-1), angular frequencies co = 2ncv are the most likely choice of theorists, which leads to different dimensions of the moments, and to the appearence of factors like powers of 2nc. We note, moreover, that in the early days of collisional induction studies the zeroth moment yo was defined without the hyperbolic cotangens function, Eqs. 5.6. For the vibrational bands (hco 3> kT), the old and new definitions are practically identical. However, for the ro to translational band substantial differences exist. The old definition of yo was never intended to be used for the far infrared [314] only Eq. 5.6 gives total intensity in that case. 

The Bi are the rotational constants of molecule i in the vibrational ground state in wavenumber units. P( is the normalized Boltzmann factor. 

Raman spectrum of aqueous HN03 at 25"C. Signals at 1 360,1 049. and 720 cm 1 arise from N03 anion. Signals denoted by asterisks are from undissociated HN03. The wavenumber unit, cm, is 1/wavelength. 

The following table provides a conversion between wavelength and wavenumber units, for use in infrared spectrophotometry. 

Some spectra are recorded on a wavenumber scale, which is inversely proportional to wavelength. The most common wavenumber unit is the reciprocal centimetre, which is related to wavelength units as follows ... 

Figure 1.1. The electromagnetic spectrum, classified according to frequency (v), wavelength (X), and wavenumber units (v). There is no established convention for the division of the spectrum into different regions we show our convention.

Finally, we note that this discussion of the RKR method has been given in energy units (J). The equations must be divided throughout by he if the equivalent expressions in wavenumber units, for example, are required. 

The spectral shape of the vibrational band differs from a Lorentzian. The deviation is evident for the wings, a factor of —20 below the maximum, and necessitates an accurate determination of neighboring bands and the baseline level. The isotropic Raman linewidth Sv (FWHM) is predicted to be smaller by a few percent than the Lorentzian width <5vl = (tcT2) 1 (FWHM in wavenumber units) for the same T2 (45). The numbers for the example DMSO in Table 1 (last three lines) give some experimental... 

The system CH3LCDCI3 was studied by IR and Raman spectroscopy two decades ago (56-58). The vi frequency in wavenumber units is a>o/2jtc = 2950 cm 1 in the neat liquid and varies approximately linearly with dilution. The linewidth (isotropic scattering component) in the neat... 

Term values and rotational constants are sometimes defined in wavenumber units (e.g. T — E/hc), and sometimes in frequency units (e.g. T = E/h). When the symbol is otherwise the same, it is convenient to distinguish wavenumber quantities with a tilde (e.g. v, f, A, B, C for quantities defined in wavenumber units), although this is not a universal practice. 

The force constants in dimensionless normal coordinates are usually defined in wavenumber units by the... 

Eq. 2.1-8 gives the frequency v (in Hz, s ) of the vibration. In vibrational spectroscopy, it is common to measure frequencies in wavenumber units i> (waves per unit length), which is the reciprocal wavelength A ... 

The flux through a spectrometer within a small spectral region is appropriately described by Eq. 3.1-1. In this book, the optical properties are usually related to wavenumbers (Eq. 3.1-9) by the spectral radiance Lc, (radiance per wavenumber), by the spectral optical conductance Gy (optical conductance per wavenumber), and by Ai>, the bandwidth of the instrument (in wavenumber units) ... 

Fig. 2a-c Solid-state absorption and luminescence spectra of a NITPy b NITBzImH c [Gd(hfac)3]NITBzImH at 5 K. Alphabetical labels denote maxima summarized in Tables 1 and 2. Energy intervals in wavenumber units are indicated by horizontal double arrows... 

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