Nonempirical advanced density functional approaches ideally combine accuracy and tractability with transfer ability across different chemical environments and dimensionalities and overcome the shortcomings of traditional generalized gradient approximations (GGA). Starting from the exact solution of one- and two-electron systems, Bethe-Goldstone equation (BGE), we propose a nonempirical screened second-order BGE (sBGE2) correlation functional with a similar simplicity as the standard second-order perturbation theory (PT2). In conjunction with the exact exchange, the sBGE2 approximation provides an accurate description of both H2+ and H2 dissociations, constituting a big challenge in density functional theory (DFT) community. In analogy to the nonempirical extension of PBE to PBE0, the sBGE2 correlation is then taken as a building block to construct a nonempirical double-hybrid functional, termed ZRPS. The ZRPS approximation distinguishes itself by a satisfactory description of N2 and C2 dissociations which is not only a challenge for DFT but also for wave-function methods. More importantly, this difficult challenge is conquered by ZRPS together with a consistent improvement over its parent, PBE0, for various chemical situations, including atomization energies, reaction barriers and weak interaction.