Capability of X-ray diffraction to the determination of the macroscopic linear susceptibility in a crystalline environment: the case of 3-Methyl 4-Nitropyridine N-oxide (POM)

Abstract

In a recent work we have reported an investigation of the applicability of ground state electron density inferred from X-ray diffraction to the determination of the linear polarizability of an ‘in situ’ conjugated molecule labelled POM and corresponding to a nonlinear optical organic compound (F. Hamzaoui, A. Zanoun, G. Vergoten, J. Mol. Struct. 397 (1–3) (2004) 17–22). In this work and using the Unso¨ld approximation one can connect the susceptibility tensor of rank n to the multipolar charge distribution (in the fundamental state) of order 2n. Thus, the linear polarizability is associated to the quadrupole moment, whereas the first order hyperpolarizability is linked to the octupolar moment of the charge distribution. Using an approach similar to the one used for the determination of the linear polarizability, we present here the estimated values of the tensor b derived from the X-ray experiment. However more surprising is the good agreement between the calculation of the lowest order macroscopic optical nonlinearity as a tensor sum of molecular polarizabilities of the free molecule and the macroscopic non linear measurements, the generalization of this remark means that the crystalline effects are negligible in the estimation of nonlinear optical properties. However, it seems difficult to infer from the Unso¨ld approximation a faithful description of the molecular optical properties, whereas an estimation of the first order hyperpolarizability components of b seems out of reach.