The theory of molecular two-photon spectroscopy in the gas phase

Abstract
We present here a detailed theoretical development of two-photon absorption (TPA) in the gas phase including rotational effects. A general formula for the transition probabilities between rovibronic states is derived in the rigid rotor approximation. Similarly to Raman theory the intensity of the rotational lines can be attributed to three independent contributions, which derive from the siotropic, antisymmetric and anisotropic part of the TPA-tensor. Each of these contributions carries a different geometrical factor so that they may be distinguished by polarization experiments. It follows directly from the theory that different rotational branches of one and the same band may differ in their polarization behaviour. Until recently, the latter effect, although central to symmetry assignments, has been overlooked. Application to the asymmetric rotor is discussed in detail and two-photon rotational band contour calculations of naphthalene-$h_{8}$ are presented.