Application Pseudo-Jahn-Teller interactions

Pseudo-JT interactions (PJT) refer to the second-order vibronic coupling between electronic states which are separated by a gap [11]. In this section we describe the 

Applying the Wigner-Eckart theorem to the matrix element yields  

The sum over the X components of the excited state, transforming as the A irrep, can be simplified by using the orthonormality property of the coupling coefficients fromEq. (6.16). 

Note that in case of a non-degenerate ground state the product E x S yields only one irrep, since the norm of the product character string equals the order of the group. 

The summation over ke A thus covers the entire product space of T x Combining the sum ruie of Eq. (6.83) with the total expression for the PJT, one finds  

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