Hyperspherical coordinates electronic states

An alternative would be the hyperspherical coordinate system, introduced into the study of the ground-state helium by Gronwall [86], developed for nuclear reactions by Delves [87, 88], adopted in molecular reactive collisions by Smith [89], and initiated applications to two-electron excited QBSs by Macek [90]. The hyperradius p and one of the hyperangles, the radial hyperangle a, are defined by... 

The factor in brackets is the three-dimensional angular element associated with the Euler angles x, 0X, K> and the remaining factor is the volume element associated with the internal configuration variables p, o>x, yx on which the PES V depends. These p, Hx Jacobi symmetrized hyperspherical coordinates have been previously used in reactive scattering calculations for H3 in its ground adiabatic electronic state, ignoring the presence of the conical intersection with its first electronically excited state [44]. 

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