Related papers: Accurate Estimation of Solvation Free Energy Using…
Three different displacement based finite element formulations over arbitrary polygons are studied in this paper. The formulations considered are: the conventional polygonal finite element method (FEM) with Laplace interpolants, the…
This paper presents an approach for obtaining accurate interaction energies at the DFT level for systems where dispersion interactions are important. This approach combines Becke and Johnson's [J. Chem. Phys. 127, 154108 (2007)] method for…
We propose a predictive Density Functional Theory (DFT) for the calculation of solvation free energies. Our approach is based on a Helmholtz free-energy functional that is consistent with the perturbed-chain SAFT (PC-SAFT) equation of…
We used a thermodynamic integration scheme, which is specifically designed for disordered systems, to compute the interfacial free energy of the solid-liquid interface in the hard-sphere model. We separated the bulk contribution to the…
The high temperature expansion (HTE) of the specific heat of a spin system fails at low temperatures, even if it is combined with a Pad\'e approximation. On the other hand we often have information about the low temperature asymptotics…
The popular, stable, robust and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate…
The free energy of glasses cannot be estimated using thermodynamic integration, as glasses are intrinsically not in equilibrium. We present numerical simulations showing that, in contrast, plausible free-energy estimates of a Kob-Andersen…
We demonstrate that with two small modifications, the popular dielectric continuum model is capable of predicting, with high accuracy, ion solvation thermodynamics in numerous polar solvents, and ion solvation free energies in…
We present useful connections between the finite difference and the finite element methods for a model boundary value problem. We start from the observation that, in the finite element context, the interpolant of the solution in one…
We present a Monte Carlo simulation technique by which the free energy of disordered systems can be computed directly. It is based on thermodynamic integration. The central idea is to construct an analytically solvable reference system from…
Many biological processes involve numerous coupled degrees of freedom, yet free-energy estimation is often restricted to one-dimensional profiles to mitigate the high computational cost of multidimensional sampling. In this work, we extend…
A promising method for calculating free energy differences Delta F is to generate non-equilibrium data via ``fast-growth'' simulations or experiments -- and then use Jarzynski's equality. However, a difficulty with using Jarzynski's…
We use thermodynamic perturbation theory to calculate the free energies and resulting phase diagrams of binary systems of spherical colloidal particles and interacting polymer coils in good solvent within an effective one-component…
We study the conformational equilibria of two peptides using a novel statistical mechanics approach designed for calculating free energy differences between highly dis-similar conformational states. Our results elucidate the contrasting…
In computational engineering, ensuring the integrity and safety of structures in fields such as aerospace and civil engineering relies on accurate stress prediction. However, analytical methods are limited to simple test cases, and…
To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
Understanding how different classes of molecules move across biological membranes is a prerequisite to predicting a solute's permeation rate, which is a critical factor in the fields of drug design and pharmacology. We use biased Molecular…
This work addresses the question of whether it is possible to define simple pair-wise interaction terms to approximate free energies of proteins or polymers. Rather than ask how reliable a potential of mean force is, one can ask how…
In this paper, we present an approach to enhance interpolation and approximation error estimates. Based on a previously derived first-order Taylor-like formula, we demonstrate its applicability in improving the $P_1$-interpolation error…