Inelastic nuclear motion

The problem of cross-section calculation for various inelastic collisions is mathematically equivalent to the solution of a set (in principle, infinite) of coupled wave equations for nuclear motion [1]. Machine calculations have been done recently to obtain information about nonadiabatic coupling in some representative processes. Although very successful, these calculations do not make it easy to interpret particular transitions in terms of a particular interaction. It is here that the relatively simple models of nonadiabatic coupling still play an important part in the detailed interpretation of a mechanism, thus contributing to our understanding of the dynamic interaction between electrons and nuclei in a collision complex. 

Whilst with techniques of optical spectroscopies the dynamics of nuclei is monitored indirectly by changes of the electron distribution during the normal mode (reflected via changes of dipole moments or polarizabilities), the inelastic neutron scattering follows the nuclear motion directly. As com-... 

The electron excitation process is caused by the interaction with the incoming atom or molecule. Since we have seen that some charge transfer takes place from the metal to the incoming atom/molecule the simplest model assumes that this charged particle can induce the e-h excitation through its interaction with the electrons. In this approach the e-h processes are viewed as additional inelastic (nonadiabatic) processes taking place on top of the adiabatic electronic adjustment connected with the charge transfer and the Bom-Oppenheimer construction of the adiabatic surfaces used for the nuclear motion. In order to facilitate the theoretical treatment of these inelastic processes, it is convenient to introduce the concept of second quantization. 

Historically, hydrogen exchange experiments (i.e., the replacement of one isotope of hydrogen bound to an O, N, or S atom in the protein interior by another isotope from the solvent water) provided some of the earliest evidence for the existence of conformational fluctuations in proteins. More recently, a wide range of experimental methods (such as fluorescence quenching and depolarization, nuclear magnetic resonance relaxation, infrared and Raman spectroscopy, and X-ray and inelastic neutron scattering) have been used to study the motions in proteins. However, it is primarily the application of theoretical methods, particularly molecular dynamics simulations, that have... 

Significant complementary data on the metal sites in proteins have also been obtained using the technique of nuclear inelastic scattering spectroscopy (NIES), also known as nuclear resonance vibrational spectroscopy. NIES probes the vibrational modes which directly involve motion of Mossbauer-active nuclei such as Fe. Thus the spectra are dominated by Fe-ligand modes associated with actual displacement of the Fe atom, such as the low frequency doming modes of heme.The NIES technique has also had a definitive role in the study of Fe(II) mono- and polymeric spin-crossover species and that work has been well reviewed recently. Spin-crossover complexes are the topic of separate discussion in Section 4 below. 

The concept of a potential energy surface, arising from the adiabatic approximation, is the basis of both the classical and quantum-mechanical treatment of the dynamics of elastic, inelastic and reactive collisions. The adiabatic potential energy V(x) governs the internal motions of atoms in an isolated system and determines the solutions of the nuclear wave equation (6.1) However, the results of a collision process will be entirely determined by the interaction potential V(x) only if the translation and rotation motion of the overall system do not influence its internal motions ... 

Phonons are quasiparticles, which are quantized lattice vibrations of all atoms in a solid material. Oscillating properties of the individual atoms in nonequivalent positions in a compound, however, are not necessarily equivalent. The dynamics of certain atoms in a compound influence characteristics such as the vibration of the impurity or doped atoms in metals and the rare-earth atom oscillations in filled skutterudite antimonides. Therefore, the ability to measure the element-specific phonon density of states is an advantageous feature of the method based on nuclear resonant inelastic scattering. Element-specific studies on the atomic motions in filled skutterudites have been performed (Long et al. 2005 Wille et al. 2007 Tsutsui et al. 2008). 

Inelastic neutron scattering is used for the smdy of transmission or absorption neutron energy spectra, particularly the side-group motion in polymers. All data reported so far for polymers have been concerned with symmetric top molecules. Three spectrometries are available at present (1) slow neutron spectrometry, which studies slow neutron excitation functions with continuous-energy neutron sources (2) fast neutron spectrometry, which smdies the spectra of neutrons produced in nuclear reaction and (3) monoenergetic slow neutron spectrometry, which smdies the spectra of neutrons corresponding to the inelastic scattering from atoms in solids or fluids. 

Nuclear magnetic resonance and inelastic neutron scattering have both been used to study the local dynamical response of the ring motions in PANl [57,58] and in PPV films [59,60]. The NMR experiments are able to detect the two aforementioned types of motion, ring flips and librations. At lower temperatures the ring motion is almost exclusively librational with modest torsional excursions about an equilibrium position. At elevated temperatures there are pronounced flips, approaching a full 180° of rotation. 

Nuclear spin-lattice relaxation of gas-phase molecules occurs primarily via the spin-rotation (SR) mechanism. The magnitude of the magnetic field generated by the rotational motion of the molecule changes at a rate that is dependent on the rotationally inelastic collision frequency. Scalar coupling of the nuclear spin angular momentum to this time-dependent field provides an efficient relaxation pathway that is generally not available in condensed phases where rotational motion is hindered. For medium-sized molecules, and Ti values are typically on the order of a few hundred milliseconds... 

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