DMBE

In the remainder of this section, we focus on the two lowest doublet states of Li3. Figures 3 and 4 show relaxed triangular plots [68] of the lower and upper sheets of the 03 DMBE III [69,70] potential energy surface using hyper-spherical coordinates. Each plot corresponds to a stereographic projection of the... 

Figure 11. Perspective view [60] of a relaxed triangular plot [68] for the two DMBE adiabatic potential energy surfaces of H3 using hyperspherical coordinates.

DMBE III calculation, permutational symmetry, dynamic Jahn-Teller and geometric phase effects, 699—711 Double degeneracy, geometric phase theory, Jahn-Teller models, 2-4, 31-33 Dynamic phase, properties, 210... 

Figure 19. Scattering resonances of 2F collinear models of the dissociation of H3 obtained by Manz et al. [143] on the Karplus-Porter surface and by Sadeghi and Skodje on a DMBE surface [132], The energy is defined with respect to the saddle point. The dashed lines mark the bifurcations of the transition to chaos 1, 5, and 3 are the numbers of shortest periodic orbits, or PODS, in each region.

The DMBE method has also been successfully applied to chemically stable triatomic molecules so far H02(,X2A")141 and 03(X /t ).159 In this subsection, we survey some of these results. 

Although the change in the quadrupole moment of OH expressed by equation (123d) (the first nonzero permanent electric moment is always independent of the choice of origin21 ) was not taken into account in building up the H02 DMBE potential of ref. 141, it is likely that the associated error will have no practical significance. 

Figure 15. DMBE potential111 for an 0(3P) atom moving around a OH(X 2/7) molecule fixed at the equilibrium geometry, with the center of the bond at the origin. Note the presence (contour K on the right) of the metastable minimum for the C., hydrogen-bonded species OH - O. The contours in this figure (and the following ones till Fig. 19) are equally spaced by 0.01 t, starting at A = — 0.211 Eh (close to the equilibrium Cs geometry of the H02 molecule).

Figure 19. Triangular plot of the H02(X2/4") DMBE potential141 with the molecular perimeter fixed at the equilibrium value 4 — 7.56a0 see Fig. 3).

Figure20. Triangular plot of the O iX 1 A,) DMBE potential159 with the molecular perimeter fixed at the average value of the perimeters for the C2l. equilibrium structure and the D h cyclic structure (4 = 8.52a0). Contours are equally spaced by 0.007E, starting at A = — 0.221...

A final word concerns the n-body problem with n > 3. Here the main problem is the rate of convergence of the EHF and corr series expansions, which we have discussed in Section IV.C. Although we may consider the knowledge of the potential-energy surface in its full dimensionality to be of fundamental importance in the case of four or five atoms, we suspect that the same may not be true for systems with a larger number of atoms, since the main role in the system chemical reactivity may then be attributed to three, four, or five atoms which define the active molecular center. Currently under way are studies for the H03 and 04 systems, and we hope, by using the DMBE... 

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