Electron excitation probability atomic orbitals approximation

Excited states of the hydrogen molecule may be formed from a normal hydrogen atom and a hydrogen atom in various excited states.2 For these the interelectronic interaction will be small, and the Burrau eigenfunction will represent the molecule in part with considerable accuracy. The properties of the molecule, in particular the equilibrium distance, should then approximate those of the molecule-ion for the molecule will be essentially a molecule-ion with an added electron in an outer orbit. This is observed in general the equilibrium distances for all known excited states but one (the second state in table 1) deviate by less than 10 per cent from that for the molecule-ion. It is hence probable that states 3,4, 5, and 6 are formed from a normal and an excited atom with n = 2, and that higher states are similarly formed. 

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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