Euler angles electronic states

Here, co represents the Euler angles (orbital Zeeman interaction, we see that it has off-diagonal matrix elements which link electronic states with A A = 0, 1, as well as purely diagonal elements. It is clearly desirable to remove the effect of these matrix elements by a suitable perturbative transformation to achieve an effective Zeeman Hamiltonian which acts only within the spin-rotational levels of a given electronic state rj, A, v), in the same way as the zero-field effective Hamiltonian in equation (7.183). 

The PI group operations are defined by their effect on the space-fixed coordinates of the atomic nuclei and electrons. Since our molecular wavefunctions are written in terms of the vibrational coordinates, the Euler angles and the angle p, we must first determine the effect of the PI group operations on these variables. In the case of inversion this can lead to certain problems both in the understanding of the concepts of molecular symmetry and in the proper use of group theoretical methods in the classification of the states of ammonia. 

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]. 

Ratio monoradical to diradical was 5 2. The values of hfc indicated a strong coupling between unpaired electrons. Zero field parameters were D / hc = 0.0120 cm E / hc = 0.0015 cm and Euler angle, p = 90°. The diradical was stable up to flie melting point of toluene. Diradical was a triplet state. Signal disappeared instantaneously on intenuption of UV irr. ... 

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