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Statistical mechanical theories for polyatomic molecular liquid systems: RISM, 3D-RISM and other integral equation
Kodai Kanemaru1,2, Tsuyoshi Yamaguchi3, Norio Yoshida2
1Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan. kanemaru.kodai.5h@kyoto-u.ac.jp.
Abstract:
Integral equation theories for polyatomic molecular liquids provide a statistical mechanical framework for describing the structure and thermodynamics of the system. Among them, the reference interaction site model (RISM) theory and its three-dimensional extension, 3D-RISM, have become widely used to analyse solvation phenomena in complex chemical and biological systems. In these approaches, solvent distributions and thermodynamic quantities are obtained by solving the Ornstein-Zernike-like integral equations within the interaction-site representation of molecules. This review summarises the theoretical foundations of RISM-based integral equation theories and recent developments aimed at improving their accuracy and applicability. Particular attention is paid to methodological advances, hybrid approaches that combine with quantum-chemical calculations and theoretical extensions incorporating dynamics. These developments highlight the versatility of RISM-based methods for investigating solvation in complex molecular environments.
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