Single-valued adiabatic state

Single-valued diabatic potentials, non-adiabatic coupling, two-state molecular system... 

Single-valued potential, adiabatic-to-diabatic transformation matrix, non-adiabatic coupling, 49-50 topological matrix, 50-53 Skew symmetric matrix, electronic states adiabatic representation, 290-291 adiabatic-to-diabatic transformation, two-state system, 302-309 Slater determinants ... 

Fig. 14. Change in ealcile saturation state during single-step adiabatic boiling (vapour saturation pressure) of aquifer water from four wet-steam wells in three areas Krafla. Iceland Momotnmho. Nicaragua and Zunil. Guatemala. A positive Sl-value corresponds to oversaluralion and a negative value to undersaturation. An SI of zero corresponds with equilibrium. SI is on a log Scale so an Sl-value of +1 indicates tenfold oversaturation. The numbers indicate well numbers. The calculated Sl-values for the aquifer waters (dots) depart a little from equilibrium. In view of all errors involved in the calculation of the Sl-values. the departure front equilibrium is. however, not significant. Nine that variations in Sl-values are more accurately calculated than absolute values.

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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