Introduction to the Fast Multipole Method

Introduction to Biomolecular Simulations Dawn of Quantum Biology What Makes Biomolecules Special Matching Computational and Experimental Conditions Mathematical Preliminaries Linear Algebra Spherical Coordinates Internal Coordinates Coordinate Transformation Differential and Integral Calculus Dirac Delta Function Linear Operators Function Minimization Mathematical Statistics Classical Mechanics The Newton Laws The Lagrange Equation Classical Electrostatics Electrostatic Potential Electric Field Curl and Divergence Gauss' Law Poisson and Laplace Equations The Legendre Polinomials Spherical Harmonics Multipole Expansion Fourier Series Many-Electron Systems The Schrodinger Equation The Born-Oppenheimer Approximation Variation Principle Perturbation Theory The Hartree-Fock Approximation Geometry Optimization Constrained Optimization using Lagrange Multipliers Coupled Perturbed Hartree-Fock Theory Vibrational Analysis The Semiempirical Theory The NDDO Approximation Energy Derivatives Linear Scaling Methods Initial Guess VFL Approximation and LocalSCF Method Multiple-Layer QM Models Implicit Solvent Model COSMO Classical Biomolecular Force Fields Mean Field Approximation Simulation of Bulk Liquids Determination of Electrostatic and Lennard-Jones Parameters Biomolecular Force Fields and Programs Long-Range Electrostatics Fast Multipole Method Ewald Sums Method Condensed Phase Translational Symmetry Periodic Structures Hartree-Fock Method for Periodic Systems Statistical Mechanics Statistical Ensembles Configuration Space Entropy Time-Correlation Function Radial Distribution Function Molecular Dynamics Hamiltonian Dynamics Langevin Dynamics Non-Hamiltonian Dynamics Constrained Dynamics Free Energy Calculations Free Energy Problem Potential of Mean Force Free Energy Pe11urbation Thermodynamic Integration The Weighted Histogram Analysis Method Sample Applications Structure Preconditioning Water Solvation Adding Ions Structure Relaxation by Using Force Fields Quantum Mechanical Molecular Dynamics Chemical Reactions Conformational Sampling Protein-Ligand Binding Free Energy High Performance Computing MPI Basics Submitting Multiple Jobs on Multiple Processors