Vibrational and environmental effects on NLO responses of molecular systems: what we can learn from a two-state model

Understanding the properties of molecular materials for NLO is an obvious prerequisite for their use in advanced applications. But a proper modeling of these systems is challenging: their large optical nonlinearity implies large and non-linear responses to several interactions besides applied electric fields, spoiling standard (linear) perturbative approaches to electron-vibration (e-ph) coupling and/or to environmental effects. The Holstein donor-acceptor dimer is a simple two state model, that, relevant to push-pull chromophores, contains he main ingredients to understand non-linearity in molecular materials. Exact solutions of the coupled e-ph problem are easily obtained for this toy-model and are used to test several common approximation schemes for the calculation of NLO responses. The non-linearity of the interaction between electronic and slow degrees of freedom shows up with the anharmonicity of the exact potential energy surfaces relevant to the ground and excited state, as well as with a large dependence of electronic properties on slow coordinates. Anharmonic corrections, negligible in vertical (coherent) linear and non-linear processes, are prominent in incoherent non-linear processes and are responsible for the large amplification of static NLO responses as due to the coupling of electronic an bosonic degrees of freedom. The dependence of the electronic dipole moments and polarizabilities on slow coordinates shows up with non-Condon effects in coherent processes, that are responsible for the large infrared and Raman intensity of the coupled vibrational modes, as well as for the opening of new vibrational channel contributions to NLO processes, with no counterpart in linear spectroscopy.