Frozen phonon technique

The organization of the lectures is as follows. A brief review of the theoretical techniques is given in Sec. II. This includes a discussion on the density functional formalism, generation of ab Initio pseudopotentials, and techniques for band structure calculations. The bulk systems are discussed in Sec. III. The static structural properties are presented in Sec. IIIA. These results establish the accuracy of the calculations. Examples will be given for semiconductors, insulators, and transition metals. The vibrational properties are discussed in Sec. IIIB. Phonon frequencies are calculated using the frozen phonon technique. 

Phonon Dispersions. The frequency and eigenvecCor of an individual phonon mode can be obtained using the frozen phonon technique. 28,31-35 approach, the usual Born-Oppenheimer... 

The frozen phonon technique has been applied with equal success to the metals.The only added complication in these calculations is that a large number of fc-points in the Brillouin zone is needed to sample over the Fermi surface for convergent results because of the small energies involved. 

An advanced approach to lattice dynamics involves the precise determination of the crystalline total energy as a function of the lattice displacement associated with a particular phonon. This method is commonly referred to as the frozen-phonon method. It utilizes first-principles band-structure techniques to obtain the total energy for each frozen-in position of the lattice. The phonon frequency can then be obtained from the resultant potential-energy curve. 

If the molecule has dynamic motions on the timescale of the EPR experiment, this motion will lead to relaxation effects on the EPR line. Depending on the timescale and size of these motions, these effects may be observable directly in the cw-EPR spectrum or indirectly by pulsed EPR measurements of the relaxation times. In many cases, different dynamics may simultaneously contribute to the relaxation behavior of the electron spin system, as, for example, vibrational and rotational motion, conformational dynamics, phonon coupling to the frozen solvent, and nuclear spin dynamics. In these cases, it will be difficult to obtain specific information from these relaxation measurements. On the other hand, it is possible to highlight a specific time-scale window by the selection of pulse sequences and microwave frequencies that can lead, in favourable cases, to a direct relation between measured relaxation times and interesting molecular dynamics at the paramagnetic site. In these cases, very interesting molecular dynamical aspects of electron-transfer, catalytic, or photo-reactions, unobservable by other structural methods, can be studied directly by pulse-EPR techniques. 

Lattice vibrations in Si were also studied by the first-principle LCAO method in Ref. 7 the frozen core approximation (which is implicitly used in all pseudopot tial calculations) was verified by an all-electron calculation. The same technique was later applied to phonons in transition metals (Nb, Mo, Zr) in Ref. 42 and 43. This method, as well as the st important results achieved, are summarized in a recent review... 

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