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Determining the Fourier representation of various molecular interactions isimportant for constructing density-based field theories from a microscopicpoint of view, enabling a multiscale bridge between microscopic and mesoscopicdescriptions. However, due to the strongly repulsive nature of short-rangedinteractions, interparticle interactions cannot be formally defined in Fourierspace, which renders coarse-grained approaches in $\textit{k}$-space somewhatambiguous. In this paper, we address this issue by designing a perturbativeexpansion of pair interactions in reciprocal space. Our perturbation theory,starting from reciprocal space, elucidates the microscopic origins underlyingzeroth-order (long-range attractions) and divergent repulsive interactions fromhigher-order contributions. We propose a systematic framework for constructinga faithful Fourier space representation of molecular interactions, capturingkey structural correlations in various systems, including simple model systemsand molecular coarse-grained models of liquids. Building upon theOrnstein-Zernike equation, our approach can be combined with appropriateclosure relations, and to further improve the closure approximations, wedevelop a bottom-up parametrization strategy for inferring the bridge functionfrom microscopic statistics. By incorporating the bridge function into theFourier representation, our findings suggest a systematic, bottom-up approachto performing coarse-graining in reciprocal space, leading to the systematicconstruction of a bottom-up classical field theory of complex aqueous systems.

Perturbative Expansion in Reciprocal Space: Bridging Microscopic and Mesoscopic Descriptions of Molecular Interactions