Potential energy surface Jacobi coordinates

By the introduction of the (x, y) coordinate system, one has reduced the problem to the motion of a particle of mass (i in a two-dimensional rectilinear space (x, y). Thus, the problem of the collision between an atom and a diatomic molecule in a collinear geometry has been converted into a problem of a single particle on the potential energy surface expressed in terms of the coordinates x and y rather than the coordinates rAB and rBc The coordinates x and y which transform the kinetic energy to diagonal form in such way that the kinetic energy contains only one (effective) mass are referred to as mass scaled Jacobi coordinates. 

Figure 4. Contour plots of the potential-energy surfaces for HCO, HNO, and HO2. The left-hand side shows the (R, r) dependence, with the angle 7 being fixed at the equilibrium in the well. The right-hand side highlights the (R, 7) dependence, with r fixed at the equilibrium. The spacing of the contours is 0.25 eV and the lowest contour is 0.25 eV above the minimum. Energy normalization is so that E = 0 corresponds to H + XO(re). The Jacobi coordinates R, r, and 7 are as described in the text, with 7 = 180° corresponding to H-X-O. (Reprinted, with permission of the Royal Society of Chemistry, from Ref. 34.)...

We consider the photodissociation of a linear triatomic molecule, ABC — A + BC(n), where n specifies the final vibrational state. The appropriate Jacobi coordinates R and r are defined in Figure 2.1 and the nuclear Hamiltonian is given in (2.39). For simplicity, we assume that only one chemical dissociation channel exists. Figures 1.11 and 2.3 depict typical potential energy surfaces appropriate for this section. 

The potential energy surfaces for the Li2+(X Sg+)Xe system have been computed as a function of the Jacobi coordinate V(/ e, R, y) and for six different angles y and a fixed distance for the Li2+(X Sg ) ionic molecule corresponding to the equilibrium distance. The distance R is the separation between the xenon atom and the center of mass of the Li2+(X Eg+) ionic molecule, and y is the angle between R and the Li2+ internuclear axis. These potential energy surfaces have been determined including the three-body interactions. The potential energy surfaces of the Li2+(X Sg+)-Xe... 

In order to simulate the experimental emission spectrum (panel c) we have performed 3D wave-packet d3mamical calculations d20 Jacobi coordinates and the so-called DMBE potential energy surfaces of Varan-das et The result (for J = 0) is displayed in panel b and seen to... 

Fig. 17. One-dimensional cuts through the X A and AAA potential energy surfaces along the Jacobi dissociation coordinate K (a) and the Jacobi bending angle 7 (b). The potential is minimized in the other two coordinates. 7 = 0 corresponds to linear HNO. The horizontal lines in (a) indicate the two zero-point energies. Reprinted, with permission of the American Institute of Physics, from Ref. 113.

Fig. 1.2. Schematic depiction of a collinear A -h BC AB + C potential energy surface and different ways of choosing coordinates, (a) Jacobi coordinates for arrangement a (A -h BC) and c (AB -h C), (b) reaction path ( natural coordinates ) coordinates, (c) hyper-spherical (here simply polar) coordinates. (Adapted from W. H. Miller, in Methods in Computational Molecular Physics S. Wilson, G. H. F. Diercksen (Eds.), NATO ASI Series B 293 (Plenum, NY, 1992), p. 519.

Fig. 1 Adiabatic potential energy surface (PES) for the (a) entrance F + HCl(v = 0) and (b) exit Cl + HF(v = 3) channels expressed in the appropriate Jacobi coordinates (R,y) calculated using the DHTSN-PES of ref. 28. Each contour line eorresponds to 0.1 kcal/mol. The ground adiabatic barrier to reaction is 3.46 kcal/mol.

The linearly structure (HCN)2 cluster was studied by SCF and Cl calculations. Results available so far are within the framework of a collinear model only, given the fact that a full, reliable potential surface for this system is not available yet. We note that calculations of vibrational predissociation lifetimes that we carried out for this system in the framework of a preliminary collinear treatment have shown that to obtain lifetimes compatible with the experimental ones, the energy released from the excited C-H stretching mode must necessarily be mostly dumped into C-H bending and rotational excitation of the fragments. This means that the collinear treatment is unacceptable even qualitatively for describing the predissociation dynamics. However a collinear treatment may be a reasonable approximation for the spectroscopy of those modes that do not involve bending excitations. Table 1 shows the results of SCF and Cl calculations for several of the transition frequencies. Jacobi ("collision") coordinates seemed an intuitively reasonable choice for the SCF calculation, and were employed here. 

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