The interactions and correlations of charged rodlike colloidal particles are investigated using an ab initio approach which includes many-body inter-rod forces induced by nonlinear counterion screening. It is found that these forces can satisfactorily be described by an eAective Yukawa segment model which in general differs from the traditional Derjaguin-Landau-Verwey-Overbeek theory. Whereas no simple analytical expression for the Yukawa parameters is available for the disordered phase, an exactly soluble cylindrical cell model reproduces the ab initio data quite well in the liquid-crystalline phase. PACS numbers: 82.70.Dd, 61.20.6y, 61.30. -v Charge-stabilized colloidal suspensions of rigid rodlike particles represent excellent realizations of liquid-crystalline systems on a mesoscopic length scale [1,2]. There are quite a number of concrete examples ranging from concentrated aqueous suspensions of tobacco-mosaic viruses (TMV) [3] or bacterial fd viruses [4] to cylindrical micellar aggregates [5] and ellipsoidal polystyrene latex particles [6]. In 1936 the first experimental proof of liquid-crystalline order was given by Bawden et al. [7] using a TMV suspension. Since then a flurry of experimental and theoretical investigations followed. Recent experiments, mainly for TMV, have essentially contributed to our understanding of the structural and dynamical correlations in the disordered phase [8] and have also revealed a complex phase diagram including nematic [9], smectic [10], columnar [11], and crystalline phases. Despite these numerous investigations, the full phase diagram for TMV is still not entirely understood over the full range of densities and added salt concentrations.Theoretically the knowledge of correlations and the phase diagram of a rodlike charged suspension is rather rudimentary, since the form of the inter-rod forces which is a necessary basic input for any statistical mechanics theory is not known exactly. Up to now theoretical work was directed along two lines. First the screened electrostatic interaction between rods was mapped onto that of hard spherocylinders [10,12] where the phase diagram is known [13]. This idea was first indicated by Onsager [14]. In view of the fact that the phase diagram depends sensitively on details of the interaction it becomes clear that this approach is too crude if quantitative predictions on correlations and on the complexity of the phase diagram are demanded. Second a more realistic description of the rod interaction was introduced and discussed by Klein and co-workers [15]. They studied a model of segments with point charges along the rods interacting via a pairwise Yukawa potential according to the classic Derjaguin-Landau-Verwey-Overbeek (DLVO) [16] theory of linear screening. This model is only justified in the limit of infinite dilution [17] but fails in the regime of strong interaction where liquid-solid phase transformations take place.In this Letter, ab initio simulations for charged rods in a salt-free suspension are reported based on the adiabatic "...