Second overtone

Third overtone Second Combination-overtone (SCOT)... 

Overtone Overtone Overtone Overtone Second Second... 

First overtones Second overtones Medium Small Solids 0.1 -1 mm thick Cells with pathlengths 5 20 mm... 

Equations (6.5) and (6.12) contain terms in x to the second and higher powers. If the expressions for the dipole moment /i and the polarizability a were linear in x, then /i and ot would be said to vary harmonically with x. The effect of higher terms is known as anharmonicity and, because this particular kind of anharmonicity is concerned with electrical properties of a molecule, it is referred to as electrical anharmonicity. One effect of it is to cause the vibrational selection mle Au = 1 in infrared and Raman spectroscopy to be modified to Au = 1, 2, 3,. However, since electrical anharmonicity is usually small, the effect is to make only a very small contribution to the intensities of Av = 2, 3,. .. transitions, which are known as vibrational overtones. 

The fundamental vibrational frequency is that with n = 1, while the frequen-cies of the harmonics or overtones are obtained with n = 2,3,4. Specifically, n = 2 is called the second harmonic in electronics and the first overtone in musical acoustics. Both terms are employed, often erroneously, in the description of molecular vibrations (see Chapter 9). 

The D band, the disorder induced mode, normally appears between 1250 and 1450 cm. This band is activated in the first-order scattering process of sp2 carbons by the presence of in-plane substitutional hetero-atoms, vacancies, grain boundaries or other defects and by finite-size effects [134], The G band is the second-order overtone of the D band. 

Applying the exchange approximation and neglecting the zero-point energy terms, we may safely limit the representation of the Hamiltonian Hsf ex within the following reduced base which accounts for the ground states of each mode and for the first (second) overtone of the fast (bending) mode ... 

The second overtone has three half-wavelengths within the string. We can find the... 

Figure 8.1 The harmonic potential and the Morse potential, together with vibrational energy levels. The harmonic potential is an acceptable approximation for molecular separations close to the equilibrium distance and vibrations up to the first excited level, but fails for higher excitations. The Morse potential is more realistic. Note that the separation between the vibrational levels decreases with increasing quantum number, implying, for example, that the second overtone occurs at a frequency slightly less than twice that of the fundamental vibration.

The second set of problems in dynamics are those of scattering theory where the Hamiltonian is of the form H = H0 + V and the interaction V vanishes when the colliding particles are far apart. It is usually assumed that the H0 part is already solved and that the interesting or the hard part is to account for the role of V. For realistic systems, which are anharmonic, even the role of H() can be quite significant. An example that has received much recent attention is the reaction of vibrationally excited HOD with H atoms (Sinha et al., 1991 Figure 8.2). The large difference in the OH and OD vibrational frequencies means that the stretch overtones of HOD are primarily local in character (cf. Section 4.21). It follows that one can excite HOD to overtones localized preferentially on either one of the two bonds and that an approaching H atom will abstract prefer-... 

Liittke and Mecke (1949) investigated e.g. the position of the second overtone OH vibration of phenol in 18 solvents and found that, on changing from an inert solvent to a solvent which has a strong interaction with the phenol, the OH-band is displaced to longer wavelengths and broadened. In some cases a splitting of the OH-band into two components was also observed. 

There are two effects of the anharmonicity of the quantized energy levels described above, which have signiflcance for NIRS. First, the gap between adjacent energy levels is no longer constant, as it was in the simple harmonic case. The energy levels converge as n increases. Second, the rigorous selection rule that An = +1 is relaxed, so that weak absorptions can occur with n = 2 (flrst overtone band), or +3 (second overtone band), etc. 

What near-infrared spectral region will be targeted for the calibration development, for example, combination region, first combination/overtone, or second combination/overtone Each region will imply a different transmission path length, and hence cell or probe design. 

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