Interaction between Spin-Singlet Excitations Forster

1 Interaction between Spin-Singlet Excitations (Forster) 

The integral in Equation 14.10 is equal to the sum of twice the Coulomb repulsion (ai jb) between the transition charge distributions ( )j([)i and ( )j(()b, minus the Coulomb repulsion (ab ji) between the transition charges l)a([)b and l j l i- This is referred to as the Eorster contribution. The second term is exponentially decreasing with distance and is referred to as the Dexter term. The original derivations were done by Th. Eorster and D. L. Dexter, respectively. 

Since the respective integrated charges are zero, the first non-zero term in (ai jb) is a dipole-dipole term. The interesting thing is that the two dipole moments are identical to the dipole moments for the transition charges ([) ( )a and ( )j 4), respectively. It is easy to derive that an interaction between two dipole moments decreases as R , where R is the distance between the atoms. The transition dipole-transition dipole interaction integral was first derived by Forster and is named after him. 

The Conlomb integral (ablji) in Equations 14.10 and 14.11 are between the charge densities of orbital prodncts where the two orbitals are on different centers. Hence, the two density distribntions decrease as e . This mnch faster decrease was originally derived by Dexter and the exponentially decreasing integral is named after him. 

The derivation of the Forster matrix element thus leads to the dipolar term 

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