“…If the electric field of light is treated as a perturbation, γ can be expressed in terms of the molecular properties as a sum-over-(electronic) states (SOS) expression:
where the ℏω p,q,r terms denote the photon energies; g , the electronic ground state; u , v , and w , the electronic excited states; E gu , the transition energy from state g to state u ; μ̂ j , the electric dipole moment operator along molecular axis j ; μ̅ j , the transition dipole moment between states u and v only if u and v are different, or if u and v are the same, then μ̅ j is the difference between the state dipole moments of state u and the ground state; i , the imaginary unit; Γ gu , a damping factor for excited state u , which is related to the excited-state lifetime; and I p,q,r , the average over the terms obtained by simultaneous permutation of the incident photon frequency and the dipole moment operator. In molecular systems where only one excited state is strongly coupled to the ground state and the primary components of the state dipole moments and transition dipole moments are aligned along one molecular axis x , the full SOS expression can be simplified to an essential-state model with three terms, − which in the static limit appears as …”