## Transition dipole

In FORCE calculations, the transition dipole moment printed (T-DIPOLE) represents the electric dipole moment associated with the transition between the ground state and the vibrationally excited state.  The units are Debye.  To understand how it is calculated, consider a diatomic A-B, with RA-B  = 2.0 Ångstroms, and the partial charge on QA = -QB = 0.5 electrons. The ground-state dipole is 4.803*(RA-B )*(QA) or  4.803 Debye.  If the atoms A or B have p-orbitals, then adjustments would need to be made for hybridization effects, these would be a few percent of the dipole terms arising from the partial charges.

During the calculation of the Hessian matrix, each atom is displaced in the X, Y, and Z directions.  From these displacements, the derivative of the dipole with respect to motion in these directions, dD/dXA, dD/dYA,  and dD/dZA, can readily be calculated. Later on, the normal modes are generated.  The associated normalized eigenvectors, Ψ, represent the motion of the atoms in the normal modes. This allows the components of the transition dipole, d1n, to be calculated using:

d1n(X)=Σi dD/dXi,Ψ(X)i

and thus the transition dipole can be calculated:

d1n(X) = (d1n(X)2 + d1n(Y)2 +d1n(Z)2)1/2