9: Molecular Spectroscopy
- Page ID
- 456276
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- 9.1: The Electromagnetic Spectrum
- Electromagnetic radiation—light—is a form of energy whose behavior is described by the properties of both waves and particles. Some properties of electromagnetic radiation, such as its refraction when it passes from one medium to another are explained best by describing light as a wave. Other properties, such as absorption and emission, are better described by treating light as a particle.
- 9.3: Rotation of Linear Molecules
- The rotational energy levels of a diatomic molecule in 3D space is given by the quantum mechanical solution to the rotating rigid rotor.
- 9.4: Microwave Rotational Spectroscopy
- Microwave rotational spectroscopy uses microwave radiation to measure the energies of rotational transitions for molecules in the gas phase. It accomplishes this through the interaction of the electric dipole moment of the molecules with the electromagnetic field of the exciting microwave photon.
- 9.5: The Selection Rule for the Rigid Rotor
- A selection rule describes how the probability of transitioning from one level to another cannot be zero. This presents a selection rule for rigid rotors that transitions are forbidden for Δl=0.
- 9.6: Rotational Spectra of Polyatomic Molecules
- To consider the rotational energy of molecules, it is useful to divided molecules into five categories: Diatomic, linear, symmetric tops, spherical tops, and asymmetric tops. The principle moments of inertial of polyatomic molecules: Rotation of the molecule can take places about any axis passing through the center of mass. There are two unique axes that are at 90º of each other, and about which the moment of inertia is a minimum or a maximum.
- 9.7: The Harmonic Oscillator and Infrared Spectra
- Infrared (IR) spectroscopy is one of the most common and widely used spectroscopic techniques employed mainly by inorganic and organic chemists due to its usefulness in determining structures of compounds and identifying them. Chemical compounds have different chemical properties due to the presence of different functional groups.
- 9.8: The Harmonic Oscillator Selection Rule
- Transitions with Δv= ±1, ±2, ... are all allowed for anharmonic potential, but the intensity of the peaks become weaker as Δv increases. v=0 to v=1 transition is normally called the fundamental vibration, while those with larger Δv are called overtones. Δv=0 transition is allowed between the lower and upper electronic states with energy E1 and E2 are involved, i.e. (E1, v''=n) →→ (E2, v'=n), where the double prime and prime indicate the lower and upper quantum state.
- 9.9: Vibrational Overtones
- Combination bands, overtones, and Fermi resonances are used to help explain and assign peaks in vibrational spectra that do not correspond with known fundamental vibrations. Combination bands and overtones generally have lower intensities than the fundamentals. Hot bands will also be briefly addressed.
- 9.10: Vibrational Spectroscopy Techniques
- Infrared and Raman spectroscopy are two experimental methods that are commonly used by chemists to measure vibrational frequencies ( ωe ).
- 9.11: Rotations Accompany Vibrational Transitions
- Below, will learn how the rotational transitions of molecules can accompany the vibrational transitions. It is important to know how each peak correlates to the molecular processes of molecules. Rovibrational spectra can be analyzed to determine average bond length.
- 9.12: Unequal Spacings in Vibration-Rotation Spectra
- As molecules are excited to higher rotational energies they spin at a faster rate. The faster rate of spin increases the centrifugal force pushing outward on the molecules resulting in a longer average bond length. Looking back, B and l are inversely related. Therefore the addition of centrifugal distortion at higher rotational levels decreases the spacing between rotational levels.
- 9.13: Unequal Spacings in Pure Rotational Spectra
- Vibrational energy which is a consequence of the oscillations/ vibrations of the nuclei along inter nuclear axis, is possible only when the distance between the nuclei is not fixed/ rigid; that means the separation between the two nuclei is flexible/ elastic (non-rigid rotator). Consequently, centrifugal force, when the molecule is rotating, tends to fly the reduced mass μ away from the axis of rotation. To keep the mass rotating about the axis, there must be some restoring force to counter bal
- 9.14: Normal Modes in Polyatomic Molecules
- Normal modes are used to describe the different vibrational motions in molecules. Each mode can be characterized by a different type of motion and each mode has a certain symmetry associated with it. Group theory is a useful tool in order to determine what symmetries the normal modes contain and predict if these modes are IR and/or Raman active. Consequently, IR and Raman spectroscopy is often used for vibrational spectra.
- 9.15: Irreducible Representation of Point Groups
- Each of these coordinates belongs to an irreducible representation of the point the molecule under investigation. Vibrational wavefunctions associated with vibrational energy levels share this property as well. The normal coordinates and the vibration wavefunction can be categorized further according to the point group they belong to. From the character table predictions can be made for which symmetries can exist.
- 9.16: Group Theory Determines Infrared Activity
- Group theory makes it easy to predict which normal modes will be IR and/or Raman active. If the symmetry label of a normal mode corresponds to x, y, or z, then the fundamental transition for this normal mode will be IR active. If the symmetry label of a normal mode corresponds to products of x, y, or z (such as \(x^2\) or yz) then the fundamental transition for this normal mode will be Raman active.
- 9.17: Raman- Application
- If one can extract all of the vibrational information corresponds a molecule, its molecular structure can then be determined. In the field of spectroscopy, two main techniques are applied in order to detect molecular vibrational motions: Infrared spectroscopy (IR) and Raman spectroscopy. Raman Spectroscopy has its unique properties which have been used very commonly and widely.
- 9.18: Raman- Theory
- The phenomenon of Raman scattering of light was first postulated by Smekai in 1923 and first observed experimentally in 1928 by Raman and Krishnan. Raman scattering is most easily seen as the change in frequency for a small percentage of the intensity in a monochromatic beam as the result of coupling between the incident radiation and vibrational energy levels of molecules. A vibrational mode will be Raman active only when it changes the polariazbility of the moleculeat.