Perturbative Expansion in Reciprocal Space: Bridging Microscopic and Mesoscopic Descriptions of Molecular Interactions
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929306979008512 |
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| author | Jin, Jaehyeok Reichman, David R. |
| author_facet | Jin, Jaehyeok Reichman, David R. |
| contents | Determining the Fourier representation of various molecular interactions is important for constructing density-based field theories from a microscopic point of view, enabling a multiscale bridge between microscopic and mesoscopic descriptions. However, due to the strongly repulsive nature of short-ranged interactions, interparticle interactions cannot be formally defined in Fourier space, which renders coarse-grained approaches in $\textit{k}$-space somewhat ambiguous. In this paper, we address this issue by designing a perturbative expansion of pair interactions in reciprocal space. Our perturbation theory, starting from reciprocal space, elucidates the microscopic origins underlying zeroth-order (long-range attractions) and divergent repulsive interactions from higher-order contributions. We propose a systematic framework for constructing a faithful Fourier space representation of molecular interactions, capturing key structural correlations in various systems, including simple model systems and molecular coarse-grained models of liquids. Building upon the Ornstein-Zernike equation, our approach can be combined with appropriate closure relations, and to further improve the closure approximations, we develop a bottom-up parametrization strategy for inferring the bridge function from microscopic statistics. By incorporating the bridge function into the Fourier representation, our findings suggest a systematic, bottom-up approach to performing coarse-graining in reciprocal space, leading to the systematic construction of a bottom-up classical field theory of complex aqueous systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05957 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Perturbative Expansion in Reciprocal Space: Bridging Microscopic and Mesoscopic Descriptions of Molecular Interactions Jin, Jaehyeok Reichman, David R. Chemical Physics Soft Condensed Matter Statistical Mechanics Computational Physics Determining the Fourier representation of various molecular interactions is important for constructing density-based field theories from a microscopic point of view, enabling a multiscale bridge between microscopic and mesoscopic descriptions. However, due to the strongly repulsive nature of short-ranged interactions, interparticle interactions cannot be formally defined in Fourier space, which renders coarse-grained approaches in $\textit{k}$-space somewhat ambiguous. In this paper, we address this issue by designing a perturbative expansion of pair interactions in reciprocal space. Our perturbation theory, starting from reciprocal space, elucidates the microscopic origins underlying zeroth-order (long-range attractions) and divergent repulsive interactions from higher-order contributions. We propose a systematic framework for constructing a faithful Fourier space representation of molecular interactions, capturing key structural correlations in various systems, including simple model systems and molecular coarse-grained models of liquids. Building upon the Ornstein-Zernike equation, our approach can be combined with appropriate closure relations, and to further improve the closure approximations, we develop a bottom-up parametrization strategy for inferring the bridge function from microscopic statistics. By incorporating the bridge function into the Fourier representation, our findings suggest a systematic, bottom-up approach to performing coarse-graining in reciprocal space, leading to the systematic construction of a bottom-up classical field theory of complex aqueous systems. |
| title | Perturbative Expansion in Reciprocal Space: Bridging Microscopic and Mesoscopic Descriptions of Molecular Interactions |
| topic | Chemical Physics Soft Condensed Matter Statistical Mechanics Computational Physics |
| url | https://arxiv.org/abs/2309.05957 |