Semi-classical approximation, free energy

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... 

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