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1. Dielectric continuum methods for quantum chemistry

   https://doi.org/10.1002/wcms.1519  

   Herbert, John M. ( March 2021 , WIREs Computational Molecular Science)

   This review describes the theory and implementation of implicit solvation models based on continuum electrostatics. Within quantum chemistry this formalism is sometimes synonymous with the polarizable continuum model, a particular boundary‐element approach to the problem defined by the Poisson or Poisson–Boltzmann equation, but that moniker belies the diversity of available methods. This work reviews the current state‐of‐the art, with emphasis on theory and methods rather than applications. The basics of continuum electrostatics are described, including the nonequilibrium polarization response upon excitation or ionization of the solute. Nonelectrostatic interactions, which must be included in the model in order to obtain accurate solvation energies, are also described. Numerical techniques for implementing the equations are discussed, including linear‐scaling algorithms that can be used in classical or mixed quantum/classical biomolecular electrostatics calculations. Anisotropic models that can describe interfacial solvation are briefly described.

   This article is categorized under:

   Electronic Structure Theory > Ab Initio Electronic Structure Methods

   Molecular and Statistical Mechanics > Free Energy Methods

    

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2. Comparison of the MSMS and NanoShaper molecular surface triangulation codes in the TABI Poisson–Boltzmann solver

   https://doi.org/10.1002/jcc.26692  

   Wilson, Leighton ; Krasny, Robert ( May 2021 , Journal of Computational Chemistry)

   The Poisson–Boltzmann (PB) implicit solvent model is a popular framework for studying the electrostatics of solvated biomolecules. In this model the dielectric interface between the biomolecule and solvent is often taken to be the molecular surface or solvent‐excluded surface (SES), and the quality of the SES triangulation is critical in boundary element simulations of the model. This work compares the performance of the MSMS and NanoShaper surface triangulation codes for a set of 38 biomolecules. While MSMS produces triangles of exceedingly small area and large aspect ratio, the two codes yield comparable values for the SES surface area and electrostatic solvation energy, where the latter calculations were performed using the treecode‐accelerated boundary integral (TABI) PB solver. However we found that NanoShaper is computationally more efficient and reliable than MSMS, especially when parameters are set to produce highly resolved triangulations.

    

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3. Efficient mesh refinement for the Poisson‐Boltzmann equation with boundary elements

   https://doi.org/10.1002/jcc.26506  

   Ramm, Vicente ; Chaudhry, Jehanzeb H. ; Cooper, Christopher D. ( March 2021 , Journal of Computational Chemistry)

   The Poisson‐Boltzmann equation is a widely used model to study electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate representations of the solute, which is usually a complicated geometry. Here, we utilize adjoint‐based analyses to form two goal‐oriented error estimates that allow us to determine the contribution of each discretization element (panel) to the numerical error in the solvation free energy. This information is useful to identify high‐error panels to then refine them adaptively to find optimal surface meshes. We present results for spheres and real molecular geometries, and see that elements with large error tend to be in regions where there is a high electrostatic potential. We also find that even though both estimates predict different total errors, they have similar performance as part of an adaptive mesh refinement scheme. Our test cases suggest that the adaptive mesh refinement scheme is very effective, as we are able to reduce the error one order of magnitude by increasing the mesh size less than 20% and come out to be more efficient than uniform refinement when computing error estimations. This result sets the basis toward efficient automatic mesh refinement schemes that produce optimal meshes for solvation energy calculations.

    

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4. Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics

   https://doi.org/10.1098/rspa.2023.0731  

   Huang, Zunding ; Li, Bo ( March 2024 , Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   The variational implicit-solvent model (VISM) is an efficient approach to biomolecular interactions, where electrostatic interactions are crucial. The total VISM free energy of a dielectric boundary (i.e. solute–solvent interface) consists of the interfacial energy, solute–solvent interaction energy and dielectric electrostatic energy. The last part is the maximum value of the classical and concave Poisson–Boltzmann (PB) energy functional of electrostatic potentials, with the maximizer being the equilibrium electrostatic potential governed by the PB equation. For the consistency of energy minimization and computational stability, here we propose alternatively to minimize the convex Legendre-transformed Poisson–Boltzmann (LTPB) electrostatic energy functional of all dielectric displacements constrained by Gauss’ Law in the solute region. Both integrable and discrete solute charge densities are treated, and the duality of the LTPB and PB functionals is established. A penalty method is designed for the constrained minimization of the LTPB functional. In application to biomolecular interactions, we minimize the total VISM free energy iteratively, while in each step of such iteration, minimize the LTPB energy. Convergence of such a min–min algorithm is shown. Our numerical results on the solvation of a single ion indicate that the LTPB performs better than the PB formulation, providing possibilities for efficient biomolecular simulations.

    

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5. Software Infrastructure for Next-Generation QM/MM−ΔMLP Force Fields

   https://doi.org/10.1021/acs.jpcb.4c01466  

   Giese, Timothy J ; Zeng, Jinzhe ; Lerew, Lauren ; McCarthy, Erika ; Tao, Yujun ; Ekesan, Şölen ; York, Darrin M ( June 2024 , The Journal of Physical Chemistry B)

   We present software infrastructure for the design and testing of new quantum mechanical/molecular mechanical and machine-learning potential (QM/MM−ΔMLP) force fields for a wide range of applications. The software integrates Amber’s molecular dynamics simulation capabilities with fast, approximate quantum models in the xtb package and machine-learning potential corrections in DeePMD-kit. The xtb package implements the recently developed density-functional tight-binding QM models with multipolar electrostatics and density-dependent dispersion (GFN2-xTB), and the interface with Amber enables their use in periodic boundary QM/MM simulations with linear-scaling QM/MM particle-mesh Ewald electrostatics. The accuracy of the semiempirical models is enhanced by including machine-learning correction potentials (ΔMLPs) enabled through an interface with the DeePMD-kit software. The goal of this paper is to present and validate the implementation of this software infrastructure in molecular dynamics and free energy simulations. The utility of the new infrastructure is demonstrated in proof-of-concept example applications. The software elements presented here are open source and freely available. Their interface provides a powerful enabling technology for the design of new QM/MM−ΔMLP models for studying a wide range of problems, including biomolecular reactivity and protein–ligand binding. 

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