lead to the suggestion of several alternative mechanisms which are essentially electronic in nature. Among these alternatives one of the most prominent is the mechanism suggested by Mazin et al $^{8}$; inspired by the peculiar shape of the Fermi Surface (FS)19 they suggested an s ± superconducting order parameter, having different sign on the h and e -like sheets forming the FS. In this way superconductivity can be driven by a strong repulsive inter- band interaction (like spin fluctuations). The role of spin fluctuations in the Cooper pairing was proposed several years ago by Berk and Schrieffer $^{20}$; this mechanism requires a non- conventional ( i.e. not a simple s -wave) superconducting order parameter. The effective Hamiltonian of a system close to a magnetic instability ”pairs” states at k and k + q by an effective interaction matrix element, ultimately related to the q -vector and frequency dependent susceptibility χ ( q , ω ). Both the q -vector and frequency dependence of χ are important in determining the symmetry and possibly the anisotropy of the superconducting gap on the FS. Experiments, on the other hand, cannot make a definite statement on the symmetry of the order parameter 2,3 making it difficult to validate/invalidate this scenario. It is clear that the above mentioned electronic mechanisms rely crucially on the detailed knowledge of the susceptibility, χ ( q , ω ). Several calculations of the static χ have been re- ported on pnictides. The first ab-initio calculation of the χ ( q , 0) did not include matrix elements among Bloch states $^{8}$. Later calculations21–23 of χ$_{0}$ were mostly based on the tight- binding fits of the minimal bands manifold around E$_{F}$ , without inclusion of higher energy inter-band transitions. This approach suffers from the fact that, even though the main struc- ture of the static χ ( q , 0) can be determined by low energy transitions (without including many empty bands) no definite conclusions can be reached about the structure of χ ( q , ω ). Hence an ab-initio investigation of the full dynamical susceptibility, including a proper ac- count of the matrix elements involving Bloch states is highly desirable and is still lacking. To fill this gap, in this article we present an ab-initio determination of the static and dynamical independent-electron susceptibility of LaOFeAs, based on electronic structure calculations performed within DFT. The results will be a first step towards an understanding of the ma- terial properties and of the possible contribution of spin fluctuations to the superconducting pairing. 

The rest of the paper is organized as follows: Section II discusses the methodology and computational details. Section III contains the results. In particular, first the static suscep- tibility χ$_{0}$ ( q , 0) is discussed and then the results for the real and imaginary parts of χ$_{0}$ as a 

