Quantum Mechanical Foundations of Molecular Spectroscopy. Max DiemЧитать онлайн книгу.
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1.5 Molecular Spectroscopy
Example 1.2 in the previous section describes an emission process in atomic spectroscopy, a subject covered briefly in Chapter 9. Molecular spectroscopy is a branch of science in which the interactions of electromagnetic radiation and molecules are studied, where the molecules exist in quantized stationary energy states similar to those discussed in the previous section. However, these energy states may or may not be due to transitions of electrons into different energy levels, but due to vibrational, rotational, or spin energy levels. Thus, molecular spectroscopy often is classified by the wavelength ranges of the electromagnetic radiation (for example, microwave or infrared spectroscopies) or changes in energy levels of the molecular systems. This is summarized in Table 1.1, and the conversion of wavelengths and energies were discussed in Eqs. (1.11)–(1.15) and are summarized in Appendix 1.
Table 1.1 Photon energies and spectroscopic rangesa.
| ν photon | λ photon | Ephoton [J] | Ephoton [kJ/mol] | Ephoton [m−1] | Transition | |
|---|---|---|---|---|---|---|
| Radio | 750 MHz | 0.4 m | 5×10−25 | 3×10−4 | 2.5 | NMRb |
| Microwave | 3 GHz | 10 cm | 2×10−24 | 0.001 | 10 | EPRb |
| Microwave | 30 GHz | 1 cm | 2×10−23 | 0.012 | 100 | Rotational |
| Infrared | 3×1013 Hz | 10 μm | 2×10−20 | 12 | 105 | Vibrational |
| UV/visible | 1015 | 300 nm | 6×10−19 | 360 | 3×106 | Electronic |
| X‐ray | 1018 | 0.3 nm | 6×10−16 | 3.6×105 | 3×109 | X‐ray absorption |
a) For energy conversions, see Appendix 1.
b) The resonance frequency in NMR and EPR depends on the magnetic field strength.
In this table, NMR and EPR stand for nuclear magnetic and electron paramagnetic resonance spectroscopy, respectively. In both these spectroscopic techniques, the transition energy of a proton or electron spin depends on the applied magnetic field strength. All techniques listed in this table can be described by absorption processes although other descriptions, such as bulk magnetization in NMR, are possible as well. As seen in Table 1.1, the photon energies are between 10−16 and 10−25 J/photon or about 10−4–105 kJ/(mol photons). Considering that a bond energy of a typical chemical (single) bond is about 250–400 kJ/mol, it shows that ultraviolet photons have sufficient energy to break chemical bonds or ionize molecules. In this book, mostly low energy photon interactions will be discussed, causing transitions in spin states, rotational, vibrational, and electronic (vibronic) energy levels.
Most of the spectroscopic processes discussed are absorption or emission processes as defined by Eq. (1.18):
(1.18)
However, interactions between light and matter occur even when the light's wavelength is different from the specific wavelength at which a transition occurs. Thus, a classification of spectroscopy, which is more general than that given by the wavelength range alone, would be a resonance/off‐resonance distinction. Many of the effects described and discussed in this book are observed as resonance interactions where the incident light, indeed, possesses the exact energy of the molecular transition in question. IR and UV/vis absorption spectroscopy, microwave spectroscopy, and NMR are examples of such resonance interactions.
The off‐resonance interactions between electromagnetic radiation and matter give rise to well‐known phenomena such as the refractive index of dielectric materials. These interactions arise since force is exerted by the electromagnetic radiation on the charged particles of matter even at off‐resonance frequencies. This force causes an increase in the amplitude of the motion of these particles. When the frequency of light reaches the transition energy between two states, an effect known as anomalous dispersion of the refractive index takes place. This anomalous dispersion of the refractive index always accompanies an absorption process. This phenomenon makes it possible to observe the interaction of light either in an absorption or as a dispersion measurement, since the two effects are related to each other by a mathematical relation known as the Kramers–Kronig relation. This aspect will be discussed in more detail in Chapter 5.
The normal (nonresonant) Raman effect is a phenomenon that also is best described in terms of off‐resonance models, since Raman scattering can be excited by wavelengths that are not being absorbed by molecules. A discussion of nonresonant effects ties together many well‐known aspects of classical optics and spectroscopy.