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.

Summary

Reference interaction site model (RISM) theories, including 3D-RISM, offer a powerful statistical mechanical approach to study molecular liquids. Recent advancements enhance their accuracy and applicability for complex solvation systems.

Related Concept Videos

Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision02:43

Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision

The ideal-gas equation, which is empirical, describes the behavior of gases by establishing relationships between their macroscopic properties. For example, Charles’ law states that volume and temperature are directly related. Gases, therefore, expand when heated at constant pressure. Although gas laws explain how the macroscopic properties change relative to one another, it does not explain the rationale behind it.
Kinetic Molecular Theory and Gas Laws Explain Properties of Gas Molecules02:34

Kinetic Molecular Theory and Gas Laws Explain Properties of Gas Molecules

The test of the kinetic molecular theory (KMT) and its postulates is its ability to explain and describe the behavior of a gas. The various gas laws (Boyle’s, Charles’s, Gay-Lussac’s, Avogadro’s, and Dalton’s laws) can be derived from the assumptions of the KMT, which have led chemists to believe that the assumptions of the theory accurately represent the properties of gas molecules.
Thermodynamic Properties of Ideal Solutions01:19

Thermodynamic Properties of Ideal Solutions

For an ideal liquid solution, the standard state of each component is defined as the pure liquid at the temperature and pressure of the solution. Similarly, for solid solutions, the standard state is the pure solid. The chemical potentials of the components in the ideal solution are compared to the chemical potentials of the pure substances in their standard states. These standard states provide a reference point for calculating the thermodynamic properties of ideal solutions.For ideal...
Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.
Distribution of Molecular Speeds01:27

Distribution of Molecular Speeds

The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
Kinetic Theory of an Ideal Gas01:12

Kinetic Theory of an Ideal Gas

A mole is defined as the amount of any substance that contains as many molecules as there are atoms in exactly 12 grams of carbon-12. An Italian scientist Amedeo Avogadro (1776–1856) formed the  hypothesis that equal volumes of gas at equal pressure and temperature contain equal numbers of molecules, independent of the type of gas. Later, the hypothesis was developed to form the SI unit for measuring the amount of any substance.
The number of molecules in one mole is called Avogadro's number...