Integral Equations in Theory of Liquids: From Simple Fluids towards 3D Solvation Structure
- Gennady Chuev (Institute of Experimental and Theoretical Biophysics of Russian Academy of Sciences, Pushchino, Russia)
Abstract
1. Introduction to Solvation Phenomena. What is solvation? Why is so difficult to treat solvation? Multiscale origin of the solvation.
2. Key concepts of Integral Equations Theory (IET) for Liquids. Correlation function formalism and interaction potentials. Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy. The Born-Green-Yvon and Ornstein-Zernike (OZ) equations. Closures and bridge functional.
3. IE for simple fluids. Simple (HNC and PY) closures. Analytical methods and numerical schemes for solutions of OZ equation. Bridge reconstruction from simulations. Current status of the theory.
4. IE for molecular liquids. Molecular OZ equation. Problem of closures. Numerical schemes for solutions of molecular OZ equation. Expansion in spherical harmonics and 3D Fast Fourier Transform (FFT). Problems of polyatomic solutes. Interaction site formalism. 1D and 3D Reference Interaction Site Model (RISM). Numerical algorithms for solution of 1D and 3D RISM equations. Current status of the theory.
5. Beyond standard schemes. Nonuniform grids and grid-free methods. Wavelets for simple and molecular liquids. A problem of the bridge construction.
6. Conclusions and perspectives
