Adiabatic-to-diabatic transformation angle

Comparing this equation with Eq. (75), it is seen that the mixing angle p is, up to an additive constant, identical to the relevant adiabatic-to-diabatic transformation—angle y ... 

Figure 12, Results for the C2H molecule as calculated along a circle surrounding Che 2 A -3 A conical intersection, The conical intersection is located on the C2v line at a distance of 1,813 A from the CC axis, where ri (=CC distance) 1.2515 A. The center of the circle is located at the point of the conical intersection and defined in terms of a radius < . Shown are the non-adiabatic coupling matrix elements tcp((p ) and the adiabatic-to-diabatic transformation angles y((p i ) as calculated for (ii) and (b) where q = 0.2 A (c) and (d) where q = 0.3 A (e) and (/) where q = 0.4 A. Also shown are the positions of the two close-by (3,4) conical intersections (designated as X34).

Recalling y(s), the adiabatic-to-diabatic transformation angle [see Eqs. (74) and (75)] it is expected that the two angles are related. The connection is formed by the Hellmann-Feynman theorem, which yields the relation between the 5 component of the non-adiabatic coupling term, x, namely, rs, and the characteristic diabatic magnitudes [13]... 

In the two state case, the adiabatic to diabatic transformation is defined by the adiabatic-to-diabatic transformation angle (ADT angle) a R),... 

We want to obtain the coordinate-wise adiabatic-to-diabatic transformation matrix U R) [Eq. (5.9)] and the adiabatic-to-diabatic transformation angle a R). The NO2 conical intersection is located at C2v... 

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