Dynamical theories

Born M and Huang K 1954 Dynamical Theory of Crystal Lattices (Oxford Clarendon)... 

Although the field of gas-phase kinetics remains hill of challenges it has reached a certain degree of maturity. Many of the fiindamental concepts of kinetics, in general take a particularly clear and rigorous fonn in gas-phase kinetics. The relation between fiindamental quantum dynamical theory, empirical kinetic treatments, and experimental measurements, for example of combustion processes [72], is most clearly established in gas-phase kmetics. It is the aim of this article to review some of these most basic aspects. Details can be found in the sections on applications as well as in the literature cited. 

Troe J 1992 Statisticai aspects of ion-moiecuie reactions State-Selected and State-to-State Ion-Molecule Reaction Dynamics Theory ed M Baer M and C-Y Ng (New York Wiiey)... 

Baer T and Hase W L 1996 Unimolecular Reaction Dynamics. Theory and Experiments (New York Oxford University Press)... 

Quack M and Kutzelnigg W 1995 Molecular spectroscopy and molecular dynamics theory and experiment Ber. Bunsenges. Rhys. Chem. 99 231-45... 

Election nuclear dynamics theory is a direct nonadiababc dynamics approach to molecular processes and uses an electi onic basis of atomic orbitals attached to dynamical centers, whose positions and momenta are dynamical variables. Although computationally intensive, this approach is general and has a systematic hierarchy of approximations when applied in an ab initio fashion. It can also be applied with semiempirical treatment of electronic degrees of freedom [4]. It is important to recognize that the reactants in this approach are not forced to follow a certain reaction path but for a given set of initial conditions the entire system evolves in time in a completely dynamical manner dictated by the inteiparbcle interactions. 

M, Born and K. Huang, Dynamical Theory of Crystal Lattices Oxford University Press, 1954, pp. 166-177, 402 07,... 

M. Bom and K. Huang, Dynamical theory of Crystal Lattices, Oxford University Press, New York, 1954. 

Zukas, J.A. Impact Dynamics Theory and Experiment, US Army Ballistic Research Laboratory Technical Report No. ARBRL-TR-02271, Aberdeen Proving Ground, MD, 67 pp., October 1980. 

In the concepts developed above, we have used the kinematic approximation, which is valid for weak diffraction intensities arising from imperfect crystals. For perfect crystals (available thanks to the semiconductor industry), the diffraction intensities are large, and this approximation becomes inadequate. Thus, the dynamical theory must be used. In perfect crystals the incident X rays undergo multiple reflections from atomic planes and the dynamical theory accounts for the interference between these reflections. The attenuation in the crystal is no longer given by absorption (e.g., p) but is determined by the way in which the multiple reflections interfere. When the diffraction conditions are satisfied, the diffracted intensity ft-om perfect crystals is essentially the same as the incident intensity. The diffraction peak widths depend on 26 m and Fjjj and are extremely small (less than... 

The key here was the theory. The pioneers familiarity with both the kinematic and the dynamic theory of diffraction and with the real structure of real crystals (the subject-matter of Lai s review cited in Section 4.2.4) enabled them to work out, by degrees, how to get good contrast for dislocations of various kinds and, later, other defects such as stacking-faults. Several other physicists who have since become well known, such as A. Kelly and J. Menter, were also involved Hirsch goes to considerable pains in his 1986 paper to attribute credit to all those who played a major part. 

We can distinguish between static theories, which in essence give a description of the electron density, and dynamic theories, where an attempt is marie to measure the response of a molecule to (e.g.) an approaching N02" " ion. In recent years, the electrostatic potential has been used to give a simple representation of the more important features of molecular reactivity. It can be calculated quite easily at points in space ... 

Reynolds, O. Papers on Mechanical and Physical Subjects 2 (1881-1901) 51. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous and the law of resistance in parallel channels. 535. On the dynamical theory of incompressible viscous fluids and the determination of the criterion. 

We now move to the predictions based on the symmetry rule. Comparing the lowest excitation energies (the sixth column) with the results concerning the symmetry reduction obtained on the basis of the dynamic theory (the last column), we can draw a very clear-cut criterion for the symmetry reduction ... 

The symmetries of the lowest excited states listed in Table 1 are nothing but the symmetries to which the most soft second-order bond distortions belong. It is seen that the types of symmetry reduction predicted using the symmetry rule are in complete agreement with those obtained on the basis of the dynamic theory. 

It wiU be seen below that the actual geometrical structures of these radicals calculated using the dynamic theory support these conclusions. 

Next, we discuss the symmetries, bond lengths and spin densities for the anion and cation radicals of fulvalene (XXI) and heptafulvalene (XXIII) using the dynamic theory. We use the semiempirical open-shell SCF MO formalism in conjunction with the variable bond-length technique. 

Finally, electronically excited states are considered in the framework of the dynamic theory. In Fig. 8 are shown calculated bond lengths in the lowest excited states of heptalene (VII), azulene (XI) and the fulvalenes POCI-XXIII). 

The results of our calculations based on both the static and dynamic theories show that most of the nonbenzenoid cyclic conjugated systems examined exhibit in a greater or lesser degree a marked double-bond fixation. The static theory indicates that even in benzene there exists a hidden tendency to distort into a skewed structure and that such a tendency is actually realized in [4n-f-2] annulenes larger than a certain critical size. In nonalternant hydrocarbons bond distortion is a rather common phenomenon. Fulvenes, fulvalenes and certain peri-condensed nonalternant hydrocarbons undergo a first-order bond distortion, and... 

Sontherland, W, A Dynamical Theory of Diffusion for Non-Electrolytes and the Molecnlar Mass of Albnmin, Philosophical Magazine 9, 781, 1905. 

Interpretation of the images is still not straightforward even when there seems to be a simple one-to-one correspondence between black (or white) dots in the image and atom positions. Especially when quantitative data on interatomic distances is to be derived, detailed calculations based on many-beam dynamical theory ( ) must be applied to derive calculated images for comparison with experiment. For this purpose the experimental parameters describing the imaging conditions and the specimen thickness and orientation must be known with high accuracy. 

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