Radial coupling

The evaluation of the radial coupling matrix elements between molecular states of the same symmetry 3... 

The main features of the radial coupling matrix elements are presented in Fig. 2. In correspondence with the avoided crossings between the potential energy curves of singleelectron capture, sharp peaked functions appear at respectively 6.35, 7.50 and 8.30 a.u.. They are approximately 1.23, 2.53 and 12.21 a.u. high and respectively 0.75, 0.50 and less than 0.10 a.u. wide at half height. 

Fig. 2. a, b, c. Non-adiabatic radial coupling matrix elements for the states of single-electron capture. 

In relation with these avoided crossings, the radial coupling matrix elements present sharp peaks at respectively 5.4, 6.6, 7.55 and 9.5 a.u. (Fig. 5). We may notice that these radial couplings are almost insensitive to the choice of the origin of electronic coordinates. The most sensitive one is the g23 function at short internuclear distance range, but we may expect weak translational effects for such electron capture processes dominated by collisions at large distance of closest approach. 

Fig. 5.3, b. Non adiabatic radial coupling matrix elements between states, a) Origin N. b) Origin He. 

The partial cross-sections on the n = 3 levels are displayed in Table 4 and Fig. 6 and show a fairly good overall agreement with the experimental results of Cotte et al. [4,7] and Dijkkamp et al. [9j. From a numerical point of view, the error bar has been estimated experimentally to 30% by Cotte et al. [4,7] and to 5% by Dijkkamp et al. [9]. Theoretically, the error bar could be evaluated to about 20%., the main difficulty arising in the determination of the sharp radial couplings. 

In a recent work [36], Bak et al presented a new method to obtain first-order corrected radial couplings from MCSCF wavefnnctions and applied it to three E+ states of... 

The radial coupling matrix elements between all pairs of states of same symmetry have been calculated by means of the finite difference technique ... 

E.E.Nikitin, J.Troe, and V.G.Ushakov, Adiabatic and post-adiabatic channel description of atom-diatom long-range half-collision dynamics interchannel radial coupling for low-rank anisotropy. J. Chem. Phys. 102,4101 (1995)... 

Figure 2. (a) Radial coupling matrix elements between 3 + and 3A states of the S3+(3s23p)+H collision system (see labels in Figure la), (b) Radial coupling between 3n states of the S3+(3s23p) + H collision system (see labels in Figure lb). 

The potential energy curves and radial coupling matrix elements have been calculated for a distance Cq+-04 varying from 0.5 to 5 A. The charge transfer levels are presented in Figure 4 for the series q = (2-5). For the charges q = (2-4), the... 

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... 

In the adiabatic representation, Hei is diagonal and the transition among the adiabatic states of the same electronic symmetry is induced by the nonadiabatic radial coupling... 

Adiabatic states with different electronic symmetries couple not by the radial coupling of Eq. (4) but by nonadiabatic rotational (Coriolis) coupling, Hcor For X and II states of a diatomic molecule, the Coriolis coupling matrix element is given by (see Sec. Ill)... 

Note that the radial coupling Ttad loses its personality in the complex / -plane, especially at R R.. From Eqs. (2) and (3) we can easily show... 

This holds irrespective of the forms of V R), V2(R), and V(R). Furthermore, the radial coupling should satisfy the following condition even on the real axis in the case of curve crossing ... 

These selection rules alone are not sufficiently restrictive to classify states according to the magnitude of their widths. For that a consideration of the facility with which internal saddle excitation can couple to vibrational R motion is necessary. Decay occurs preferentially [6b] by radial coupling within saddle sequences corresponding to... 

Within the saddle sequence Eq. 9 implies that a state of the N-manifold decays preferentially to a state of the (iV — l)-manifold which then dissociates to e + H(N — 1) or e - - He (N — 1) if this is energetically possible. This is also consistent with the Hellman-Feynman theorem for radial coupling... 

Fig. 16. Calculated rotational and radial coupling matrix elements for various states in MgNa as a function of intemudear separation.

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