Self-consistent construction of grand potential functional with hierarchical integral equations and its application to solvation thermodynamics.

The construction of the density functional for grand potential is fundamental in understanding a broad range of interesting physical phenomena, such as phase equilibrium, interfacial thermodynamics, and solvation. However, the knowledge of a general functional accurately describing the many-body correlation of molecules is far from complete. Here, we propose a self-consistent construction of the grand potential functional based on the weighted density approximation (WDA) utilizing hierarchical integral equations. Different from our previous study [T. Yagi and H. Sato, J. Chem. Phys. 154, 124113, (2021)], we apply the WDA to the excess Helmholtz free energy functional rather than the bridge functional. To assess the performance of the present functional, we apply it to the solvation thermodynamics of Lennard-Jones fluids. Compared to the modified Benedict-Webb-Rubin equation of state, the present functional qualitatively predicts the liquid-vapor equilibrium. The solvation free energy obtained from the present functional provides a much better agreement with the Monte Carlo simulation result than the hypernetted chain functionals. It constitutes a general starting point for a systematic improvement in the accuracy of the grand potential functional.

Self-consistent construction of bridge functional based on the weighted density approximation.

A parameter-free bridge functional is presented using a weighted density approximation (WDA). The key point of this scheme is the utilization of Baxter's relation connecting the second-order direct correlation function (DCF) to the higher-order DCF with the density derivative. The free energy density required for the WDA is determined in a self-consistent manner using Baxter's relation and Percus's test particle method. This self-consistent scheme enables us to employ any type of potential model for simple liquids. The new functional is applied to calculate density distribution functions for the inhomogeneous fluids interacting via the hard-sphere, Lennard-Jones, and hard-core Yukawa potentials under an external field from a planar wall and a slit pore.

Experimental and theoretical study on p-aminophenylthyil radical geminate recombination in ionic liquids; analysis using the Smoluchowski-Collins-Kimball equation.

Recombination dynamics of geminate p-aminophenylthiyl (PAPT) radicals produced from the photodissociation of bis(p-aminophenyl) disulfide in ionic liquids (ILs) were investigated by transient absorption spectroscopy. ILs with various cationic species were used to examine the effect of viscosity and polarity on recombination dynamics. Experimentally obtained recombination yields and dynamics were found to be virtually independent of the cation species, despite the viscosity range of the solvent ILs being extensive, spanning from a few tens of mPa s to several hundred mPa s. We applied a theoretical analysis model based on the diffusion equation to the time profiles of the experimentally determined recombination yields of geminate PAPT radicals. The square well potential was incorporated into the diffusion equation to consider the concerted dynamics of solvent cage formation and recombination. A long-time asymptotic expression for the survival probability of the photodissociated products was derived and used to simulate the experimentally obtained time profile of the recombination yield. The time profiles in the range of 20-1000 ps and the final yield were successfully simulated by the asymptotic expression of the square well potential model. The optimized parameters used for the fit, including the mutual diffusion coefficient of the radical pairs, cage radius of the potential well, and well depth, were discussed in terms of the diffusion coefficient conventional theory and the potential mean force estimated from the molecular dynamics simulation for the photodissociation reaction in ILs.

Density functional theory for molecular liquids based on interaction site model and self-consistent integral equations for site-site pair correlation functions.

We propose a novel classical density functional theory (DFT) for inhomogeneous polyatomic liquids based on the grand canonical ensemble of a solute-solvent system. Different from the existing DFT for interaction site model developed by Chandler et al. [J. Chem. Phys. 85, 5971 (1986)], the fundamental quantities in the present theory are the radial density distributions around the atomic site of the solute molecule. With this development and the reference interaction site model equation, we provide self-consistent integral equations for calculating the site-site pair correlation function (PCF) and apply it to the structure of the Lennard-Jones dimer, HCl, and H2O molecular fluids. The site-site PCFs obtained from the new scheme agree well with those from Monte Carlo simulation results.

A simple model of planar membrane: An integral equation investigation.

A simple model of a lipid membrane, a binary mixture of saturated lipids and unsaturated lipids, was studied using an integral equation theory. The planar membrane is modeled as mixture of linear and bent molecules in two-dimensional space, and site-site radial distribution function, Kirkwood-Buff (KB) integral and related quantities were computed over the whole range of the molar fraction to understand their mixing behavior. We found that a close packing of linear molecules is enhanced as the fraction of bent molecules increases, but a long range correlation between the linear molecules is weakened. A high concentration of linear molecules promotes the demixing of linear molecules and bent molecules, and enhances the long range correlation between molecules. This implies that, the higher the concentration of linear molecules, the larger clusters tend to be formed. © 2018 Wiley Periodicals, Inc.