Article
Chemistry, Multidisciplinary
Stefan D. Search, Christopher D. Cooper, Elwin van't Wout
Summary: The Poisson-Boltzmann equation is a useful tool to study electrostatics in molecular systems. This paper presents a generalized expression of the boundary integral representation of the implicit solvent model, which leads to new ways of computing the electrostatic potential. It also proposes a strategy to build efficient preconditioners for the resulting systems, improving the convergence of the linear solver. The authors perform benchmark tests on different formulations and preconditioners, focusing on time to solution, matrix conditioning, and eigenvalue spectrum. The results suggest that the optimal choice depends on the problem size, with simpler direct formulations being faster for small molecules and more involved second-kind equations being better for larger problems. The paper also introduces a fast Calderon preconditioner for first-kind formulations, which shows promise for future analysis.
JOURNAL OF COMPUTATIONAL CHEMISTRY
(2022)
Article
Mathematics, Applied
Bo Li, Zhengfang Zhang, Shenggao Zhou
Summary: In this paper, the classical Poisson-Boltzmann theory is generalized to include solute point charges and dielectric boundary in the solvation of charged molecules in aqueous solvent. By analyzing boundary variations, an explicit formula of dielectric boundary force is derived, describing the stable equilibrium state of the charged molecular system. The results align with molecular-level predictions, showing that the electrostatic force points from the high-dielectric solvent to the low-dielectric charged molecules.
JOURNAL OF NONLINEAR SCIENCE
(2021)
Article
Chemistry, Physical
Pragati Shaw, Ethan Wood, Tian Tang, Peter Berg
Summary: Levy et al. introduced the concept of electroneutrality breakdown in confined nanopores. They derived a Robin boundary condition to simplify the calculation without explicitly considering the dielectric medium. However, we point out that the approximations made in Levy et al.'s study can lead to significant errors, especially for nanochannels with a large aspect ratio.
JOURNAL OF COLLOID AND INTERFACE SCIENCE
(2023)
Article
Mathematics, Applied
Zhan Chen, Yuanzhen Shao
Summary: In the past decade, variational implicit solvation models (VISM) have been successful in predicting solvation energy. However, existing VISMs lack the uniqueness of an energy minimizing solute-solvent interface, hindering the study of important interface properties. To address this, a new constrained VISM is introduced and rigorously analyzed. The model examines the existence, uniqueness, and regularity of the energy minimizing interface, and derives a necessary condition for a sharp solute-solvent interface. Experimental validation and numerical implementation demonstrate accurate solvation energy calculations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Chemistry, Physical
Ali Behjatian, Madhavi Krishnan
Summary: This study presents a computational investigation on using electrostatic free energy measurements to detect the 3D conformational properties of nucleic acid molecules in solution. The results indicate that electrostatic free energy measurements can not only describe structural differences but also provide information on the local structure of the molecular interface.
JOURNAL OF CHEMICAL PHYSICS
(2022)
Article
Engineering, Multidisciplinary
Qingxia Zhang, Zhengfang Zhang, Mingyan He, Xinping Shao, Weifeng Chen
Summary: This paper investigates the size-modified electrostatic free energy in molecular solvation by considering the generalized Poisson-Boltzmann (PB) equation with uniform ionic and solvent molecular sizes. The first variation of the size-modified electrostatic free energy with respect to the location variation of the interface is derived using the concept of shape derivative. The explicit formula of the dielectric boundary force is obtained.
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS
(2023)
Article
Biochemistry & Molecular Biology
H. B. Mihiri Shashikala, Arghya Chakravorty, Shailesh Kumar Panday, Emil Alexov
Summary: Ions play significant roles in biological processes, both specifically and non-specifically binding to proteins. Experimental determination of non-specifically bound ions can be challenging, but the BION-2 method provides a more accurate prediction of their positions.
INTERNATIONAL JOURNAL OF MOLECULAR SCIENCES
(2021)
Review
Chemistry, Multidisciplinary
John M. Herbert
Summary: This review discusses the theory and implementation of implicit solvation models based on continuum electrostatics, emphasizing on theory and methods rather than applications. The article also describes numerical techniques for implementing the equations.
WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE
(2021)
Article
Chemistry, Physical
Jong-Sam Jon, Won-Kwang Ri, Kye-Ryong Sin, Yong-Chol Son, Kwang-Won Jo, Jong-Su Pak, Song-Jin Kim, Ye-Jin Ri, Yong-Chol An
Summary: Based on molecular kinetic consideration, a solvation effect-incorporated PB equation was derived, taking into account the dynamic properties of the ionic atmosphere and ion solvation shell. The equation introduced a solvated ionic screening thickness, incorporating both the ionic atmosphere thickness and the screening thickness of the solvation shell. The solution of the equation divided the total electric potential into two terms, representing the effects of ions on solvation shells and vice versa. Analytical expressions for ion-solvent molecular dipole moment interaction potential energy, activity coefficients, and mean lifetimes of solvation shells were established using the linearized SEI-PB equation. The SEI-PB equation was found to have peculiarity due to its inclusion of solvation effect and dielectric saturation, implicitly connecting the two.
JOURNAL OF MOLECULAR LIQUIDS
(2022)
Article
Mathematics, Applied
Dingqun Deng
Summary: This paper discusses the time-asymptotic stability of planar rarefaction wave solutions for the Vlasov-Poisson-Boltzmann (VPB) system in a three-dimensional rectangular duct without angular cutoff. The system is studied with periodic or specular-reflection boundary conditions, and physical boundaries are introduced to describe wave patterns of kinetic equations. The non-cutoff collision kernel is considered, and the stability and large time behavior of the rarefaction wave solution for the Boltzmann equation are also examined.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2023)
Article
Chemistry, Physical
Sanghamitra Sengupta, Jan Versluis, Huib J. Bakker
Summary: In this study, we investigated the influence of sodium chloride (NaCl) on the interface properties of water and dodecyl sulfate (DS-) surfactant using vibrational sum-frequency generation spectroscopy. We observed a highly nonlinear dependence of the O-H stretch vibrations of oriented water molecules on the NaCl concentration at the interface. This nonlinear dependence can be explained by the screening effects of the electric field of surface-bound DS- ions and the Coulomb repulsion between the headgroups of DS- ions in the surface plane. Within a limited concentration range of NaCl (10-100 mM), the latter effect significantly increased the signal of oriented water, indicating a two-dimensional hydrophobic collapse of the surfactant layer.
JOURNAL OF PHYSICAL CHEMISTRY LETTERS
(2023)
Article
Chemistry, Multidisciplinary
Vicente Ramm, Jehanzeb H. Chaudhry, Christopher D. Cooper
Summary: The study utilizes adjoint-based analyses to form error estimates, identifying high-error panels and adaptively refining them to achieve optimal surface meshes. Results show that elements with large errors are usually in regions with high electrostatic potential, and the adaptive mesh refinement scheme is more effective and efficient than uniform refinement in reducing errors in solvation energy calculations.
JOURNAL OF COMPUTATIONAL CHEMISTRY
(2021)
Article
Physics, Atomic, Molecular & Chemical
Jiahui Chen, Weihua Geng, Guo-Wei Wei
Summary: The study developed a machine learning-based implicit-solvent Monte Carlo method, combining the advantages of implicit solvent models to achieve significant advantages in speed and accuracy in molecular structure optimization and prediction.
CHINESE JOURNAL OF CHEMICAL PHYSICS
(2021)
Article
Mathematics, Applied
Chiu-Yen Kao, Seyyed Abbas Mohammadi
Summary: This paper studies both minimization and maximization problems of a Poisson's equation with Robin boundary conditions, analyzing the properties of extremizers and their performance on general domains, as well as investigating the asymptotic behaviors of optimal values. Explicit solutions are rare, but solutions on N-balls are obtained. Numerical efficient algorithms based on finite element methods, rearrangement techniques, and analytical results are proposed to determine extremizers in a few iterations on general domains.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Physics, Fluids & Plasmas
Kevin Koehn, Dennis Krueger, Efe Kemaneci, Liang Xu, Denis Eremin, Ralf Peter Brinkmann
Summary: The Poisson-Boltzmann (PB) equation is a nonlinear differential equation for the electric potential in conducting fluids, commonly justified through a variational principle. However, in the context of technological plasmas, a new variational principle based on entropy, particle number, and electromagnetic enthalpy has been proposed to provide a more realistic justification for the PB equation. This alternative principle allows for the justification of the PB equation for a wide range of technological plasmas under realistic assumptions.
PLASMA SOURCES SCIENCE & TECHNOLOGY
(2021)
