Simple quantum chemical models of electronic excitation

5 Simple Quantum Chemical Models of Electronic Excitation 

Let us assume that organic molecules in their electronic ground state are reasonably well represented by a closed-shell electronic configuration built by filling electrons pairwise 

To calculate the transition moment M n m = e Wein Lri Weim (Equation 2.17), we represent the ground-state wavefunction by the closed-shell configuration 

Integration over the coordinates of those electrons that occupy the same orbital in o and Xi —/ gives unity, (/// (/// = 1, so the transition moment simplifies to Mei y = i/ iXr 7 , which involves only the orbitals xj/i and ij/j that participate in the transition. The operator Lri=X(xi, V/, z() and the electronic transition moment MeU j are vector quantities the coordinates xh yt and zt define the positions of the electrons e. To obtain the individual components of the electronic transition moment vector (Equation 4.20), we must integrate the products where u stands for x, y or z. The 

Equation 4.20 Electronic transition moment for a one electron transition f/j — ij/j 

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