Repulsive potential curve

The slow peak was associated with the dissociation channel that produces an H atom and an X(2) fragment, while the fast peak was identified with the channel that produces the I( 3/2) fragment. From the polarization measurements they could obtain the anisotropy parameter 3, and this along with the TOF spectra could be used to derive the branching ratio between the two channels as a function of wavelength. Combining this information with the measured extinction coefficients, they were able to derive the partial extinction coefficients to the upper states that correlate with each of the channels. A modified 6 approximation was then combined with all of this information to calculate the upper repulsive potential curves that lead to dissociation into these products. Four upper states are involved in the dissociation in this region. The symmetries of these four states are 3nx, fjl, 3no, and The first two states produce... 

FIGURE 13. The dashed curve is part of a repulsive potential curve for IC1 constructed from experimental data (201). The solid line is taken from Child and Bernstein (216). Re denotes the ground state equilibrium distance and the horizontal line is the Franck-Condon region probed in the experiment. The figure was reproduced from reference (201) with permission of Elsevier Science Publishers. 

As has been described, the creation and relaxation of a core hole excited state involving shake-up, shake-off, and single and multiple electron autoionization and Auger decay, generally leaves the system with two or more holes in bonding orbitals, which essentially means that bond has disappeared and often the system is left on a repulsive potential curve. The importance of such multiple-electron excited states has been discussed for bond rupture and desorption for covalently bonded species (Ramaker 1983a, b,c Madey et al. 1981 Jaeger et al. 1982 Treichler et al. 1985). 

The slope of the repulsive potential at R" (or at the R" values of the two maxima in the v" = 1 probability distribution) may be determined from the width of ct(E). The vertical excitation energy of the repulsive state at JR" is determined by the E at which a E) reaches its maximum value. In this semi-classical approximation, the repulsive potential curve can be determined from a E) provided that /i(i .) varies no more rapidly than linearly in R (Child, et al., 1983). When a sufficient quantity of cr E) data is obtained from free-bound absorption or emission transitions originating from several bound vibrational levels, it is then also possible to determine the shape of the bound potential (Le Roy, et al., 1988). The /(-dependence of /i(JR) 2 can arise from two sources (i) the /(-dependence of the fractional contributions of several different A-S basis states to a single relativistic adiabatic fi-state (ii) /(-variation of the transition moment between A S basis states arising from the molecule to separated atom evolution of the LCAO characters of the occupied orbitals (iii) /(-variation of the configurational character (Configuration Interaction) of either electronic... 

One need only consider the energy dependence of the differential Franck-Condon factor. For small He, this factorization may be justified in the same way as in the case of second-order energy shifts of bound states. The variation of T and 5E with v and J provides information about the initially unknown shape of the repulsive potential curve. 

Figure 7.19 Pictorial descriptions of the phase difference between bound and continuum vibrational wavefunctions. The top part of the figure shows the crossing bound and repulsive potential curves and the two paths between which the phase shift is to be determined. The lower part of the figure represents the classical phase-space trajectories for motion on Vj (ellipse) and V2 (parabola). The shaded area is the phase difference between the two paths, (o) Outer wall crossing. Path I (single arrows) is the most direct dissociation path ai to Rc on Vj, Rc to oo on V2. Path II (double arrows) is the shortest indirect path 01 to i to Rc on Vi, Rc to a2 to oo on V2. (6) Inner wall crossing. The phase difference is between the shortest ( i to Rc on V, Rc to a2 to oo on V2) and next longer ( i to 01 to Rc on Vi,Rc to oo on V2) path.

When the minimum of a predominantly repulsive potential curve is considered negligible, it may be represented by a so-called anti-Morse curve ... 

Fig. 29 a—c. Potential energy curves corresponding to different mechanisms of radiative recombination, a Recombination on a repulsive potential curve, b recombination on an attractive potential curve, c recombination via inverse predissociation... 

In this case, the recombining atoms approach each other along a repulsive potential curve 1 (see Fig. 29 a) and, according to the Franck-Condon principle, emit a photon hv near the classical inflection point R, forming a molecule in the ground... 

A few quantum-chemical ab initio calculations predicted structure, stability, and some other molecular properties for the ion. SCF, CASSCF, and MRSD Cl calculations with various basis sets up to triple-zeta plus polarization quality gave repulsive potential curves for the ground state X (1cr) (2a) (3cr), energies of -848.9 (SCF) or -872.8 (Cl) kJ/mol, and a zero activation energy for the deprotonation (or exothermic charge-separation) reaction + [3, 4]. On the other hand, ground-state potential curves with a very... 

From the relationship between the photo-excitation and absorption spectrum, photodissociation quantum yields are in general unity when a molecule is excited to the repulsive potential curve as shown in Fig. 2.1. On the other hand, when an absorption spectrum has a band stmcture and a molecule is excited to a bound state as shown in Fig. 2.2, photodissociation quantum yields are in general 0 < cp < 1 and the value has to be determined experimentally. 

In addition, O3 has weak absorption bands called the Chappuis bands in the visible range and the Wulf bands in further longer wavelengths as shown in Fig. 4.2. These bands corresponds to the forbidden transitions to the lower electronically excited states that cross with repulsive potential curve dissociating into the ground states of an O atom and O2 molecule. 

The fluorescence induced by the second laser allows the accurate determination of the molecular parameters for those excited states on which the fluorescence transitions from are terminating. The LIF method can therefore be extended by stepwise excitation to the investigation of many molecular states which may not even have been found before. Of particular interest are dissociating excited states with repulsive potential curves below bound states E. These continuous states often cannot be studied by direct absorption from the ground state because the Franck-Condon factors for the transitions may be quite small. As an example of such investigations we mention the two-step excitation of the iodine molecule I2 (Fig.8.29). Selected (V, J ) levels in the B rig state are populated by optical pumping with a cw dye laser. Starting from these levels a krypton laser excites further levels in a... 

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