Coupling diabatic channel

Figure 1. Lower panel Minimum energy path of the four lower adiabatic states, correlating to Li( 5 )-tHF( E+) and Li( P)+HF( S+). Also, the ionic diabatic state has been qualitatively shown. Upper panel non-adiabatic couplings between the ground and first excited electronic states along the minimum energy path, as a function the internal Jacobi coordinates describing the Li+HF entrance channel.

Equations (3.5) and (3.33) are completely equivalent. In the diabatic representation, it is the potential matrix (3.6) that couples the different vibrational channels whereas in the adiabatic representation the matrices (3.35) and (3.36) impart the coupling between translation and vibration. Computationally more advantageous is the diabatic representation because the calculation of the matrices U and Q is in practice laborious. 

A.I.Maergoiz, E.E.Nikitin, and J.Troe, Diagrams of diabatic/adiabatic channels for two linear rotors coupled by long-range dipole-dipole interaction. Khim. Fiz. 12, 3 (1993)... 

Complex adiabatic energies (a) compared to resonance energies (b) for a model of a closed and an open channel described in reference (30). The zeroth order energy has been subtracted out. Unit cm , Interchannel coupling 200 cm . Crossing diabatic energy equal to the energy of the level with v = 18. 

The cross sections are calculated using a fully-quantal close-coupling formalism (1). In the p-diabatic representation, in which A(R) is null, electron capture is driven by off-diagonal elements of the diabatic potential matrix U(/ ), which is independent of the orientation of R. Introducing a partial-wave decomposition for the corresponding wave amplitudes leads to radial coupled equations for channels... 

Flux in channel n is therefore lost only via transition to another state/with a probability controlled solely by A. When many wavelengths of relative motion can be accommodated within the range of V, as at the higher energies favoured by the diabatic scheme, the fasti -variation of is mainly controlled by S, and the original diabatic set of coupled equations then reduce to the simpler set... 

The simplest model is the following the diabatic potentials are constant with V2 - Vx = A > 0 and the diabatic coupling is V e R where A = 2V0. Recently, Osherov and Voronin obtained the quantum mechanically exact analytical solution for this model in terms of the Meijer function (38). In the adiabatic representation this system presents a three-channel problem at E > V2 > Vu since there is no repulsive wall at R Rx in the lower adiabatic potential. They have obtained the analytical expression of a 3 X 3 transition matrix. Adding a repulsive potential wall at R Rx for the lower adiabatic channel and using the semiclassical idea of independent events of nonadiabatic transition at Rx and adiabatic wave propagation elsewhere, they derived the overall inelastic nonadiabatic transition probability Pl2 as follows ... 

Coriolis coupling (p. 906 and 912) critical points (p. 888) cross section (p. 901) curvature coupling (p. 906 and 914) cycloaddition reaction (p. 944) democratic coordinates (p. 898) diabatic and adiabatic states (p. 949) donating mode (p. 914) early and late reaction barriers (p. 895) electrophilic attack (p. 938) entrance and exit channels (p. 895) exo- and endothermic reactions (p. 909) femtosecond spectroscopy (p. 889) Franck-Condon factors (p. 962) intrinsic reaction coordinate (IRC) (p. 902) inverse Marcus region (p. 954) mass-weighted coordinates (p. 903)... 

In order to better understand the similarity between the coupled- and the uncoupled-surface results, we show the time evolution of the electronic populations in Fig. 4. The initial WP corresponds to H2(< = 0,j = 0) and is again prepared in the asymptotic reactant channel of the lower adiabatic sheet. [It is transformed to the diabatic representation using the S-matrix of Eq. (7) prior to propagation]. As can be seen from Fig. 4, we obtain a 0.71/0.29 population of the two component diabatic electronic states (shown by the dashed and solid lines) at t = 0. Therefore, the diabatic potentials do not approach the asymptotic adiabatic states of H - - H2 but represent a mixture of them. 

In Ref. 51, the relative population of the 0( Pj = 2,1,0) product fine-structure states were determined at different collision energies. The energy dependence in the change of the population of the 0( Pj = 2 l,o) fine-structure states from a diabatic one at Ec.m. = 1.6 eV to an adiabatic one at fec.m. = 2.5 eV was attributed to a reduction of nonadiabatic coupling in the exit channel due to the increase of translational energy released to the O + OH products with increasing collision energy [46g]. 

Photoionization out of several neutral states to several cation states may be simply included as separate terms of a split-operator scheme, assuming the ionized states do not strongly couple. Alternately, when the different ionization channels interact weakly, ionization out of each channel may be computed separately and the results combined. Examples of nonadiabatic dynamics seen through time-resolved photoelectron spectroscopy will be seen in Secs. 5.2 and 5.4. In the rest of this section, we will see examples of the diabatic representation for two classes of nonadiabatic interaction, the avoided crossing (Sec. 5.2.1.1) and the conical intersection (Sec. 5.2.1.2), and then discuss the necessary extensions to the standard vibrational wavefunction time-propagating schemes. 

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