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Highly excited vibrational states of HCP and their analysis in terms of periodic orbits: The genesis of saddle-node states and their spectroscopic signature
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46.Of course, a periodic orbit does not have an initial point in the phase space. With initial point we mean here that particular point at which the tracing of the periodic orbit from E to is started. A more rigorous procedure would be to choose, for example, the maximum value of r along the PO for a particular energy. That would change the various curves in the bifurcation diagram but not the general appearance nor the bifurcation points.
47.More information about the calculated periodic orbits can be found at the www site http://www.cc. forth. gr/farantos/articles/hcp/data/
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49.The accuracy of the quantum calculations can be approximately assessed by comparing the number of quantum mechanical states at a particular energy with the corresponding number extracted from the volume of the classical phase space. For the energy of the 250th state, the phasespace volume gives 253. For and the corresponding classical numbers are 506, 755, and 1004, respectively. Because of the polyad structure the quantum mechanical number of states is not a smooth function of E, which partly explains the relatively large deviations for the smaller energies. Overall, however, the agreement is very good.
50.The results of the quantum mechanical calculation together with the assignment can be obtained by anonymous ftp from ftp. gwdg. de, directory/ftp/public/mpsf/schinke/hcp/quantum. results.
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52.All the wave function plots shown in this article have been obtained from a 3D plotting routine, which allows to rotate objects, that depend on three variables, in space. In all cases we show one particular contour with the value of ε being the same within one figure. The plots are always viewed along the R axis, i. e., in the direction perpendicular to the (r, g)-plane. Especially the wave functions of highly excited states (or their backbones) are not confined to the (r, g)-plane but arranged in the 3D space. Therefore, showing 2D projections, with one coordinate fixed or integrated over, makes their appearance less informative. The shading emphasizes the 3D character of the wave functions. After testing various ways of plotting we came to the conclusion that these representations are optimal.
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55.In paper I the states had been labeled Because these states substitute the real -type states we have changed the nomenclature.
56.We also performed classical as well as quantum mechanical twodimensional calculations with R fixed at its equilibrium for and found that the 2D and 3D molecules are remarkably different, which shows that all three modes are coupled.
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