Molecular spectroscopy rotation-vibration

This is the classic work on molecular rotational, vibrational and electronic spectroscopy. It provides a comprehensive coverage of all aspects of infrared and optical spectroscopy of molecules from the traditional viewpoint and, both for perspective and scope, is an invaluable supplement to this section. 

We find it convenient to reverse the historical ordering and to stait with (neatly) exact nonrelativistic vibration-rotation Hamiltonians for triatomic molecules. From the point of view of molecular spectroscopy, the optimal Hamiltonian is that which maximally decouples from each other vibrational and rotational motions (as well different vibrational modes from one another). It is obtained by employing a molecule-bound frame that takes over the rotations of the complete molecule as much as possible. Ideally, the only remaining motion observable in this system would be displacements of the nuclei with respect to one another, that is, molecular vibrations. It is well known, however, that such a program can be realized only approximately by introducing the Eckart conditions [38]. 

The treatment of electronic motion is treated in detail in Sections 2, 3, and 6 where molecular orbitals and configurations and their computer evaluation is covered. The vibration/rotation motion of molecules on BO surfaces is introduced above, but should be treated in more detail in a subsequent course in molecular spectroscopy. 

I. N. Levine (1975) Molecular Spectroscopy (John Wiley Sons, New York). A survey of the theory of rotational, vibrational, and electronic spectroscopy of diatomic and polyatomic molecules and of nuclear magnetic resonance spectroscopy. 

The vibrational and rotational motions of the chemically bound constituents of matter have frequencies in the IR region. Industrial IR spectroscopy is concerned primarily with molecular vibrations, as transitions between individual rotational states can be measured only in IR spectra of small molecules in the gas phase. Rotational - vibrational transitions are analysed by quantum mechanics. To a first approximation, the vibrational frequency of a bond in the mid-IR can be treated as a simple harmonic oscillator by the following equation ... 

Phospholipids, which are one of the main structural components of the membrane, are present primarily as bilayers, as shown by molecular spectroscopy, electron microscopy and membrane transport studies (see Section 6.4.4). Phospholipid mobility in the membrane is limited. Rotational and vibrational motion is very rapid (the amplitude of the vibration of the alkyl chains increases with increasing distance from the polar head). Lateral diffusion is also fast (in the direction parallel to the membrane surface). In contrast, transport of the phospholipid from one side of the membrane to the other (flip-flop) is very slow. These properties are typical for the liquid-crystal type of membranes, characterized chiefly by ordering along a single coordinate. When decreasing the temperature (passing the transition or Kraft point, characteristic for various phospholipids), the liquid-crystalline bilayer is converted into the crystalline (gel) structure, where movement in the plane is impossible. 

Molecular spectroscopy. This spectroscopy deals with the interaction of electromagnetic radiation with molecules. This results in transition between rotational and vibrational energy levels besides electronic transitions. 

Vibrational spectroscopy can help us escape from this predicament due to the exquisite sensitivity of vibrational frequencies, particularly of the OH stretch, to local molecular environments. Thus, very roughly, one can think of the infrared or Raman spectrum of liquid water as reflecting the distribution of vibrational frequencies sampled by the ensemble of molecules, which reflects the distribution of local molecular environments. This picture is oversimplified, in part as a result of the phenomenon of motional narrowing The vibrational frequencies fluctuate in time (as local molecular environments rearrange), which causes the line shape to be narrower than the distribution of frequencies [3]. Thus in principle, in addition to information about liquid structure, one can obtain information about molecular dynamics from vibrational line shapes. In practice, however, it is often hard to extract this information. Recent and important advances in ultrafast vibrational spectroscopy provide much more useful methods for probing dynamic frequency fluctuations, a process often referred to as spectral diffusion. Ultrafast vibrational spectroscopy of water has also been used to probe molecular rotation and vibrational energy relaxation. The latter process, while fundamental and important, will not be discussed in this chapter, but instead will be covered in a separate review [4],... 

One of the most important aims of our theoretical work is to assist in the interpretation and understanding of high-resolution molecular spectroscopy experiments. We have already been able [1] to provide assistance of this kind in that, with our calculated values for the rotational energies in the 4v2 vibrational state of we could verify (and, for a few transitions, refute) the tentative... 

Patel et al. °"> successfully operated parametric oscillators in the infrared region (2.5 - 25 pm) using the nonlinear characteristics of tellurium and selenium single crystals. This frequency range is important for the molecular spectroscopy of rotational-vibrational... 

It is anticipated that a course dealing with atomic and molecular spectroscopy will follow the student s mastery of the material covered in Sections 1- 4. For this reason, beyond these introductory sections, this text s emphasis is placed on electronic structure applications rather than on vibrational and rotational energy levels, which are traditionally covered in considerable detail in spectroscopy courses. 

One is familiar with the idea of discrete and definite electronic stales in molecules, as revealed by molecular spectroscopy. Each electronic stale possesses a number of vibrational states that are occupied to a great extent near the ground state at normal temperatures. Each vibrational state has, if the stcric conditions are enabling, a number of rotational states associated with it, and for gas molecules both the vibrational and the rotational states can easily be observed and measured spectroscopically. Correspondingly, the distribution of the vibrational states in solids (phonon spectra) is easily measurable. 

Much of the beauty of high-resolution molecular spectroscopy arises from the patterns formed by the fine and hyperfine structure associated with a given transition. All of this structure involves angular momentum in some sense or other and its interpretation depends heavily on the proper description of such motion. Angular momentum theory is very powerful and general. It applies equally to rotations in spin or vibrational coordinate space as to rotations in ordinary three-dimensional space. 

Although molecular inversion is a phenomenon which theoretically can occur in any nonplanar molecule, from the point of view of vibration-rotation spectroscopy inversion is of significance for relatively few molecules. Nevertheless, molecular inversion is ail interesting and important large-amplitude molecular motion. Inversion has pronounced effects on the spectra of certain molecules experimental as well as theoretical studies of these effects became an important part of the history of molecular spectroscopy. The results of these studies found also important applications, the best-known example being the celebrated NH3 molecular beam maser. 

Mills, I. A. Vibration-rotation structure in asymmetric- and symmetric-top molecules. In Molecular spectroscopy modern research, Rao, K. Narahari, Mathews, C. W. (eds.). New York Academic Press 1972. 

High resolution studies by conventional spectroscopy are genuinely hampered by Doppler-broadening of the rotation-vibration lines in the low pressure regime. Individual Doppler-shifted frequencies contribute to the (normalized) Doppler-broadened line shape, due to the distribution of molecular velocities along the direction of observation... 

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