Diabatic and adiabatic potential curves

Then the vibrational matrix elements of He(R) are expressed in terms of Rn centroids, 

making the /(-centroid approximation, which is quite distinct from the /( -centroid expansion, namely, 

For near-degenerate vibrational levels of any two crossing potential curves, the i -centroid has the convenient property of being nearly equal to Rc, the F-value where the two curves cross (Schamps, 1977). Thus, 

The i -centroid approximation has repeatedly been tested numerically. For perturbations between levels of potentials that intersect exactly once, the R centroid approximation can be regarded as more accurate than experimentally measurable matrix elements. 

The validity of the l -centroid approximation is based on a stationary phase argument (see Section 5.1.1) (Tellinghuisen 1984). For two vibrational states, 

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Figure 3.5 Diabatic and adiabatic potential curves. The diabatic curves (solid lines) cross at Rc and are defined by neglecting the part of Hel that causes the adiabatic curves (dotted lines) to avoid crossing by 2if at Rc-...

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