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85033278618
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note
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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 E+ δE 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.
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47
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85033282419
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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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48
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49
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85033324306
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note
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1000 corresponding classical numbers are 506, 755, and 1004, respectively. Because of the polyad structure the quantum mechanical number of states N(E) 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.
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50
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85033306958
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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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51
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0031281042
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Schinke, R.6
Yamashita, K.7
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52
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85033284919
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note
-
2 with the value of ∈ being the same within one figure. The plots are always viewed along the R axis, i.e., in the direction perpendicular to the (r.γ)-plane. Especially the wave functions of highly excited states (or their backbones) are not confined to the (r,γ)-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
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85033323937
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note
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SN. Because these states substitute the real [r1A]-type states (0,0,P), we have changed the nomenclature.
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-
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56
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85033285702
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note
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We also performed classical as well as quantum mechanical two-dimensional calculations with R fixed at its equilibrium for γ=0 and found that the 2D and 3D molecules are remarkably different, which, shows that all three modes are coupled.
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59
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0001100505
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R. Prosmiti, S. C. Farantos, R. Guantes, F. Borondo, and R. M. Benito, J. Chem. Phys. 104, 2921 (1996).
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Benito, R.M.5
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62
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0009658546
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