Scaling functions angular momentum

Figure 4. The average change in the squared value of the classical orbital angular momentum ((A/. )) and the standard deviation of the A/. distribution

Figure 4. Cumulative reaction probability for the H2 + OH - H2O + H reaction as a function of total energy for total angular momentum 7 = 0 (Ref. 11) (a) logarithmic scale (b) linear scale.

Here we look at some details of the cumulative reaction probability of the reaction of H + H2 and discuss what picture can be obtained from the analytical expressions of the current theory. Figure 7.7 shows the cumulative reaction probability N E) as a function of the energy E both in linear and log scales. The result of the harmonic approximation (dotted curve) and that of the NF theory (solid curve) are compared. The calculation uses the potential energy surface of Mielke et al. The total angular momentum is fixed to zero for simplicity. This allows us to take the zeroth order approximation as in eqn (7.11), i.e. a collection of harmonic oscillators and a parabolic barrier. Readers interested in the extension of the theory to include the rotational motions should refer to the literature. ... 

The second example is the hydrogen atom tunneling in the triatomic molecule HO2 for zero total angular momentum (/ = 0). In this case an analytical DMBE (double many-body expansion) potential function is available [126]. Since the quantum mechanically exact calculation can be carried out, the numerical results based on the present semi-classical theory are compared with the exact results. The exact numerical calculations are carried out in the hyperspherical elliptic coordinates (p, f, r]) [127,128], which are convenient for describing a light atom transfer between two heavy atoms. The coordinate p is called hyperradius, which represents the mass scaled radius of the hypersphere and is defined as... 

Fig. 8.17. Gaussian exponents of the carbon correlation-consistent basis sets of cardinal numbers 2-5 on a logarithmic scale with tight functions to the left and diffuse functions to the right. The exponents of the valence-correlating orbitals present in the cc-pVXZ root sets are located in the middle and are plotted using larger dots, the exponents of the core-correlating orbitals are located on the left, and the diffuse functions of the augmented aug-cc-p(C)VXZ sets are located on the right. For each angular momentum, we have plotted the exponents for cardinal numbers X = 2 at the bottom and X = 5 at the top.

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