Classical Electrostatics for Biomolecular Simulations

Abstract

CONTENTS 1. Introduction 779 1.1. Electrostatic Problem 780 2. Methods for Computing the Long-Range Electrostatic Interactions 781 2.1. Ewald Summations 782 2.2. Particle−Mesh Methods That Use Fourier Transforms 784 2.3. Particle−Mesh Methods in Real Space 784 2.4. Fast Multipole Methods 786 2.5. Local Methods 786 2.6. Truncation Methods 787 2.6.1. Reaction Field Methods 789 2.7. Charge-Group Methods 789 2.8. Treatments and Artifacts of Boundary Conditions 790 3. Accurate Representation of the Electronic Charge 791 3.1. Charge Assignment Schemes 791 3.2. Point Multipoles 792 3.3. Continuous Representations of Molecular Charge Density 793 3.4. Polarization 795 3.5. Charge Transfer 797 3.6. Polarizable Force fields 798 4. Electrostatics in Multiscale Modeling 800 4.1. Long-Range Electrostatics in QM/MM 800 4.2. Continuous Functions in QM/MM 801 4.3. Electrostatics in Coarse-Grained Models 802 5. Other Developments 804 6. Summary and Perspective 805 Author Information 806 Corresponding Author 806 Notes 806 Biographies 806 Acknowledgments 806 References 806

A critical appraisal of the zero-multipole method: Structural, thermodynamic, dielectric, and dynamical properties of a water system

“…Among the efforts for further increasing the computational a) Electronic address: wang_han@iapcm.ac.cn b) Electronic address: ifukuda@protein.osaka-u.ac.jp efficiency of this method, the smooth particle mesh Ewald (SPME) method 3 utilizes a mesh-based approach with smooth functions, leading to the success of the efficiency. 4,5 The PBC used in these methods means that every atom in the original MD cell interacts with the all other particles in the original cell and with all their individual copies placed in the periodically arranged image cells. The PBC is useful to mimic a bulk state and avoid the creation of an interface, whose treatment is nontrivial.…”

Assessing the accuracy of the isotropic periodic sum method through Madelung energy computation

“…1 A reference problem for condensed-phase systems where electrostatics plays a crucial role is the computation of the Madelung energy for ionic crystals. [2][3][4][5][6] This problem was first addressed by Madelung 2 and later solved exactly by Ewald.…”

“…Although working well for many systems, they have been argued in some cases to cause artifacts because of the imposed periodicity, 7,8 especially when nonuniform or non-neutral systems are concerned 9 (see Ref. 1 for updates and alternative views). In addition to this, for largesized systems the best scaling behavior of modern Ewald methods, such as the particle-mesh-Ewald (PME) method, 10 is Nlog (N) (N being the number of particles).…”

Efficient treatment of induced dipoles

“…1,2 The electrostatic terms, which typically are the most computationally demanding, can be accurately modeled by extending the fixed point-charge model to include higher order multipole moments [3][4][5] and polarization. 6 While the extra flexibility afforded by these terms allows for accurate descriptions of molecular interactions, the resulting increase in computational cost hinders the ability to properly sample configurational space.…”