Two-photon transition probability calculations: electronic transitions in the water molecule

The transition probabilities of the two-photon excitation from the ground electronic state to some low-lying excited electronic states in water are obtained in the approximation of vertical transitions and assuming a random orientation for the assembly of molecules. The calculations are performed by extending to the molecular system the methods previously employed for atoms, i.e. by exploiting the results of the RPA to compute the one-electron transition density matrices of both the initial-intermediate and the intermediate-final states. The effect of coupling of the excitation channels on the transition probabilities is estimated by comparing the RPA results with those obtained in the static-exchange separated-channels approximation. For each final state considered, the transition rate for linearly polarised photons together with a ratio of transition probabilities for different polarisation situations are reported. These quantities allow one to compute the transition rate at each frequency for every possible combination of polarisation and geometrical arrangement of the sources. A comparison is made between the results obtained using the length and the velocity forms of the perturbing operator.