Wigner and

Metallic hydrogen has been a holy grail of high-pressure research since Wigner and Fluntington suggested that... 

Equations (7-89), (7-40), (7-44), (7-46), (7-47), and (7-48) are sufficient for the calculation of many (7-coefficients. General formulas, too lengthy to be derived here, have been given by Wigner and Bacah.10 Wigner s formula is... 

A first step toward quantum mechanical approximations for free energy calculations was made by Wigner and Kirkwood. A clear derivation of their method is given by Landau and Lifshitz [43]. They employ a plane-wave expansion to compute approximate canonical partition functions which then generate free energy models. The method produces an expansion of the free energy in powers of h. Here we just quote several of the results of their derivation. 

The Woodward-Hoffmann rules have intellectual roots that can be traced back to Wigner-Witmer correlation rules (E. Wigner and E. E. Witmer, Z. Phys. 51 [1928], 859) and general correlation-diagram concepts (R. S. Mulliken, Rev. Mod. Phys. 4 [1932], 1) as employed, e.g., by K. F. Herzfeld, Rev. Mod. Phys. 41 (1949), 527. Alternative MO... 

In lack of analytical or numerical methods to obtain the spectra of complicated Hamiltonians, Wigner and Dyson analyzed ensembles of random matrices and were able to derive mathematical expressions. A Gaussian random matrix ensemble consists of square matrices with their matrix elements drawn from a Gaussian distribution... 

Transition state theory, a quasi-thermodynamic/statistical mechanical approach to the theory of reaction rates was developed in the early 1930s by a number of workers including H. Eyring, E. R Wigner, and J. C. Polanyi and was very quickly applied to the consideration of isotope effects on rates of simple molecular reactions. 

Theoretical descriptions of absolute reaction rates in terms of the rate-limiting formation of an activated complex during the course of a reaction. Transition-state theory (pioneered by Eyring "", Pelzer and Wigner, and Evans and Polanyi ) has been enormously valuable, and beyond its application to chemical reactions, the theory applies to a wider spectrum of rate processes (eg., diffusion, flow of liquids, internal friction in large polymers, eta). Transition state theory assumes (1) that classical mechanics can be used to calculate trajectories over po-... 

Diatomic hydrogen, H2, also exhibits a rich and remarkable complex soUd phase diagram. At low temperatures, when a H2-based solid is formed, electrons are confined in the H2 molecules and the soUd is thus a large-gap insulator. E. Wigner and H. B. Huntington predicted in 1935 the possibiUty of preparing... 

Fig. 5.14 The binding energy U as a function of the Wigner-Seitz radius fiws for sodium. The bottom of the conduction band, 1 is given by the lower curve to which is added the average kinetic energy per electron (the shaded region). (After Wigner and Seitz (1933).)...

We see that eqn (5.63) mirrors the behaviour found in Fig. 5.14 for sodium by Wigner and Seitz. At metallic densities the bottom of the conduction band is well described by the first contribution in eqn (5.63). As the atoms are brought together, the bonding state becomes more bonding until eventually the repulsive core contribution dominates, and the bottom of the conduction band rises rapidly. From eqn (5.63) the maximum binding energy of this state occurs for... 

The bottom of the sp NFE conduction band, 15 behaves in a similar fashion to that found by Wigner and Seitz in Fig. 5.14 for the alkali metal Na. Its volume dependence is also well described by a modified variant of the first term in eqn (5.63), namely... 

The first attempt to calculate realistic wave functions for electrons in metals is that of Wigner and Seitz (1933). These authors pointed out that space in a body-or face-centred cubic crystal could be divided into polyhedra surrounding each atom, that these polyhedra could be replaced without large error by spheres of radius r0, so that for the lowest state one has to find spherically symmetrical solutions of the Schrodinger equation (6) subject to the boundary condition that... 

The prototype potential surface invoked in chemical kinetics is a two-dimensional surface with a saddle equilibrium point and two exit channels at lower energies. The classical and quantal dynamics of such surfaces has been the object of many studies since the pioneering works by Wigner and Polanyi. Recent advances in nonlinear dynamical systems theory have provided powerful tools, such as the concepts of bifurcations and chaos, to investigate the classical dynamics from a new point of view and to perform the semiclassical... 

R. A. Marcus My interests in variational microcanonical transition state theory with J conservation goes back to a J. Chem. Phys. 1965 paper [1], and perhaps I could make a few comments. First, using a variational treatment we showed with Steve Klippenstein a few years ago that the transition-state switching mentioned by Prof. Lorquet poses no major problem The calculations sometimes reveal two, instead of one, bottlenecks (transition states, position of minimum entropy along the reaction coordinate) [2], and then one can use a method described by Miller and partly anticipated by Wigner and Hirschfelder to calculate the net dux. 

Calculation and Characterization of Molecular Potential Energy Surfaces, T. H. Dunning, Ed., JAI Press, London, 1990, Vol. 1, pp. 213-262. The Von Neumann-Wigner and Jahn-Teller Theorems and Their Consequences. 

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