Linear and non-linear optical properties of periodic and antiperiodic dimers

The analytic expressions for the linear and non-linear optical response functions of a two-sites Holstein-Hubbard model with periodic and antiperiodic boundary conditions are obtained. They show that an antiperiodic dimer can be used to describe the main features of the linear optical spectrum of a half-filled dimerized mono-dimensional system. One also finds that the description of the non-linear optical properties are appropriate only for systems with the 2Ag above the 1Bu since only the ionic contribution to the Ag state can be described.