Adiabatic electronic energy

Here, I(co) is the Fourier transform of the above C(t) and AEq f is the adiabatic electronic energy difference (i.e., the energy difference between the v = 0 level in the final electronic state and the v = 0 level in the initial electronic state) for the electronic transition of interest. The above C(t) clearly contains Franck-Condon factors as well as time dependence exp(icOfvjvt + iAEi ft/h) that produces 5-function spikes at each electronic-vibrational transition frequency and rotational time dependence contained in the time correlation function quantity <5ir Eg ii,f(Re) Eg ii,f(Re,t)... 

Figure 12. Cross sections of the adiabatic electronic energy hypersurfaces of Li,. The lowest five doublet states with the electronic configuration (laif(le ) (2a/)f (x) are shown (21). Key , B, , A, A,A, and, B,.

We may summarize the two cases in a simple but approximate way as follows When the nuclear kinetic energy is much smaller than the spacings between the adiabatic electronic energy surfaces Ga(R), these surfaces serve as potential energy surfaces for nuclear motion. When the nuclear kinetic energy is comparable to or larger than the spacings between the t/o.(R), the adiabatic approximation may, and often does, break down. 

Since E o is the width of the electronic resonance state no it is related to the imaginary part of the adiabatic electronic energy... 

Population dynamics in response to the laser fields First of all, we examine the population d3mamics of the two low-lying states. Since we study the time-dependent response of these electronic states to laser fields, the ordering of the states with respect to the adiabatic electronic energy does not make an invariant sense. Hence we simply call the first... 

From the standard quantum mechanical expression for the rate of nonadiabatic electron-transfer, it is apparent that the pure electronic coupling matrix element (V) and adiabatic electronic energy gap (O) are important factors for consideration of dispersive kinetics of the DA —> D A electron-transfer process, where D s donor and A s acceptor. By necessity, we assume that these two variables are uncorrelated. We begin by considering dispersive kinetics from a distribution of Q-values. Next we present some of our experimental data that speak to the question of dispersive kinetics from a distribution of V-values. 

To conclude this subsection we observe that the utilization of the standard Fermi-Golden rule rate expression, which leads to Eq. 1, is subject to a number of constraints. In particular, when the adiabatic electronic energy gap between P BH and P B "H is too small ( kT at room T) its use would be questionable. Nevertheless, even in this case an exact theoretical treatment of the problem is unlikely to reveal dispersive kinetics at room T from the Q distribution. 

On the basis of a nonadiabatic electron-transfer theory, which exposes the homogeneous width of the nuclear factor from low frequency modes (phonons), and hole burning data we conclude that this nonexponentiality is not due to a distribution of values, f, for the relevant adiabatic electronic energy gap(s) 2. Dispersive kinetics from f in the low temperature limit are judged to be unlikely. Nevertheless, the expression (. 2) for the average electron-transfer rate constant suggests that samples which exhibit sufficiently different Fj-values for the P-band should have measurably different values for in... 

Finally, in brief, we demonstrate the influence of the upper adiabatic electronic state(s) on the ground state due to the presence of a Cl between two or more than two adiabatic potential energy surfaces. Considering the HLH phase, we present the extended BO equations for a quasi-JT model and for an A -1- B2 type reactive system, that is, the geometric phase (GP) effect has been inhoduced either by including a vector potential in the system Hamiltonian or... 

Figure 6. Diabatic and corresponding adiabatic potential energy along a relevant reaction coordinate for normal electron transfer...

H3 (and its isotopomers) and the alkali metal triiners (denoted generally for the homonuclears by X3, where X is an atom) are typical Jahn-Teller systems where the two lowest adiabatic potential energy surfaces conically intersect. Since such manifolds of electronic states have recently been discussed [60] in some detail, we review in this section only the diabatic representation of such surfaces and their major topographical details. The relevant 2x2 diabatic potential matrix W assumes the fomi... 

Now, we examine the effect of vibronic interactions on the two adiabatic potential energy surfaces of nonlinear molecules that belong to a degenerate electronic state, so-called static Jahn-Teller effect. 

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