Wavenumber scale

All infrared spectrophotometers are provided with chart recorders which will present the complete infrared spectrum on a single continuous sheet, usually with wavelength and wavenumber scales shown for the abscissa and with absorbance and percentage transmittance as the ordinates. More advanced instruments also possess visual display units on which the spectra can be displayed as they are recorded and on which they can be compared with earlier spectra previously obtained or with spectra drawn from an extensive library held in a computer memory. These modern developments have all led to quantitative infrared spectrophotometry being a much more viable and useful analytical procedure than it was just a few years ago. 

Wavenumbers scaled by optimized factors. Intensities for Raman active modes classified by the present authors on the basis of the calculated values. The intensities of two IR active vibrations were calculated to be equal (Ra) = Raman active, (IR) = infrared active [181]... 

Evidence exists that some of the lines correspond to the second type of complexes. Figure 20 shows with the same wavenumber scale the absorption in bulk as grown InP material and in proton and deuteron implanted material. It is clear that the two local modes of vibration are observed at exactly the same energies (2202.4 cm-1 and 2315.6 cm-1) in as grown and... 

Comments should be made here on the theoretical equivalence between Eqs (3.15) and (3.21). The fluorescence quantum yield <1>f, i.e. the number of photons emitted over the whole fluorescence spectrum divided by the number of absorbed photons, must of course be independent of the representation of the fluorescence spectrum in the wavelength scale (Eq. 3.15) or the wavenumber scale (Eq. 3.21) ... 

Box 3.3 Determination of fluorescence quantum yields from fluorescence spectra wavelength scale or wavenumber scale ... 

It should be noted that no such difficulty appears with the integral of an absorption spectrum because the absorption coefficient is proportional to the logarithm of a ratio of intensities, so that e(A) = e(v). For instance, in the calculation of an oscillator strength (defined in Chapter 2), integration can be done either in the wavelength scale or in the wavenumber scale. 

The spectra Fo(v) and Ca(v) are represented on the wavenumber scale and the fluorescence spectrum (F(v)) of the donor is normalized on this scale n is the refractive index, e iv) is the molar decadic extinction coefficient of the acceptor and To is the radiative lifetime (s) and R(nm) is the D-A center to center distant. For very strong coupling the rate is given by... 

In a typical IR absorption spectrum of an organic substance (Figure 6), the ordinate is transmittance and the abscissa is the wavenumber. A linear wavenumber scale is... 

Here FD (v) is the spectral distribution of donor emission expressed in number of quanta emitted per unit wave number interval and normalized to unity on a wavenumber scale ... 

Fig. 6. Geiser and Giidel s axial circular dichroism spectrum of [A-Cr(en),] [A-Ir(en)3]Cl6 KC1 6H20 at 8 K [37], The wavenumber scale is the same as in Fig. 5. The dotted line represents the room temperature solution spectrum of [A-Cr(en)3]3 +. The peak in the center with a slightly negative Ae was assigned as an electronic origin...

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 ... 

The advantage of the wavenumber scale is that it is linearly proportional to other energy units. Some of the relationships and conversion factors (see Appendix 8) are as follows ... 

Figure 15-3. Composite one-color R2PI spectrum of adenine (upper panel). Peak A is the origin band of the ntr transition, while peak D was assigned to be that of the ira transition. The wavenumber scale on the top is relative to the 0-0 band of the nil state. Starting from 800crrr1 above the 0-0 band, there appears a broad background underneath the sharp vibronic features. Fluorescence excitation spectrum of adenine (lower panel). The peaks denoted as C , D , and E , respectively, correspond to the R2PI peaks C, D, and E in the above R2PI spectrum. (Reprinted with permission from Ref. [8].)...

To calibrate the wavenumber scale, first reeord the spectrum of the sample and then place a polystyrene film in the sample beam and record a few of the main bands whose frequency is known and which do not coincide with the main bands in the spectrum... 

The Raman lines at larger wavelengths are much stronger they reflect those quanta which transfer radiation energy to the molecule by exciting its vibrations. The absolute wavelength scale and the absolute wavenumber scale are not well suited to represent the... 

Fig. 3.5-13 demonstrates the influence of sample and instrumental parameters on the intensities of the observed Raman lines, excited with the Nd YAG laser at 1064 nm. The lower abscissa shows the absolute wavenumber scale, the upper abscissa represents the Raman shift. The relative intensity of Raman radiation is calculated by Eq. 3.5-9, taking into account the absorption coefficient a cm ) of water (Fig. 3.5-3) and a constant Raman scattering coefficient (assumed to be equal to 1 cm ). The elastic scattering coefficients as parameters, r = 0, 10, 100, 500 cm , describe the properties of a liquid, a coarse, a medium, and a fine powder, respectively. The traces show the relative output voltage of a Germanium detector. 

For clarity, the wavenumber scale of the CH-stretching region is magnified besides the A type band at 2989.5 cm (t n), there is a B type band at higher wavenumbers whose rotation-vibration lines go through a marked intensity minimum (3105.5 cm ( 9). Further two A type bands of medium intensity (1443.5 cm 1 12 and a combination band at 1889.6 cm, assigned to r v -f i s) can be observed. 

Temperature information from CARS spectra derives from spectral shapes either of the 2-branches or of the pure rotational CARS spectra of the molecular constituents. In combustion research it is most common to perform thermometry from nitrogen since it is the dominant constituent and present everywhere in large concentration despite the extent of chemical reaction. The 2-branch of nitrogen changes its shape due to the increased contribution of higher rotational levels which become more populated when the temperature increases. Figure 6.1-21 displays a calculated temperature dependence of the N2 CARS spectrum for experimental parameters typically used in CARS thermometry (Hall and Eckbreth, 1984). Note that the wavenumber scale corresponds to the absolute wavenumber value for the 2320 cm 2-branch of N2 when excited with the frequency doubled Nd.YAG laser at 532 nm ( 18796 cm ), i. e. = 18796 -1- 2320 = 21116 cm. The bands lower than about 21100 cm are due to the rotational structure of the first vibrational hot band. 

Fig. 25. Emission spectra (time-integrated) of (a) Pt(2-thpy-hg)2 and (b) Pt(2-thpy-dg)2 dissolved in n-octane (Shpol skii matrix) at a concentration of 10 mol/1. Ag c = 457.9 nm. The wavenumber scale gives the separation from the respective electronic origin I (set to zero). For both compounds, origin I does not carry any emission intensity. All vibrational satellites that correspond to fundamentals are false origins, i. e. they are vibronically (Herzberg-Teller) induced. Several vibrational modes of the perprotonated compound are correlated to those of the perdeuterated one, they are connected by dotted lines. The spectrum (a) corresponds to the one reproduced in Fig. 13. (Compare Ref. [23])...

Using the wavenumber scale results in IR frequencies in a numerical range that is easier to report than the corresponding frequencies given in hertz (4000-400 cm compared to1.2x10 -1.2x10 Hz). 

Wavenumber is inversely proportional to wavelength and reported in reciprocal centimeters (cm" ). Wavenumber (v) is proportional to frequency (v). Frequency (and therefore energy) increases as the wavenumber increases. Using the wavenumber scale, IR absorptions occur from 4000 cm" -400 cm". ... 

IR spectra have both a wavelength and a wavenumber scale on the x axis. Wavelengths are recorded in pm (2.5-25). Wavenumber, frequency, and energy decrease from left to right. Where a peak occurs is reported in reciprocal centimeters (cm ). 

Figure 14.6 Rotational energies on wavenumber scale Ejjhc = BJ J + 1). Note (2/ + l)-fold degeneracy.

Figure 14.16 Vibrational Raman spectrum of CCI4 using 632.8-nm radiation. Note that the wavenumber scale increases right to left.

Figure 3.1 IR spectra from 950 to 1800 and from 2750 to 3600cm (A-E) and Raman spectra from 400 to 1800cm (F-J) of the protein concanavalin A (A, F), the protein bovine serum albumin (B, G), DNAfrom calf thymus (C, H), a lipid extract (D, I) and cholesterol (E, J). The wavenumber scale of the IR spectra in the interval 2750-3600cm is twofold compressed.

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