MOLECULAR FORCES AND NEWTONIAN LAWS
CONTENTS 1 INTRODUCTION TO COMPUTER SIMULATIONS OF MOLECULES AND CONDENSED MATTER BORN–OPPENHEIMER APPROXIMATION AND THE BORN–OPPENHEIMER POTENTIAL ENERGY SURFACE CATEGORIZATION OF THE TASKS IN COMPUTER SIMULATIONS OF MOLECULES AND CONDENSED MATTERS ELECTRONIC STRUCTURE CALCULATIONS GEOMETRY OPTIMIZATION, STATIONARY POINTS ON PES, LOCAL MINIMUM, AND TRANSITION STATE METASTABLE STATE AND TRANSITION STATE SEARCHING MOLECULAR DYNAMICS FOR THE THERMAL E?ECTS EXTENSIONS OF MD: ENHANCED SAMPLING AND FREE ENERGY CALCULATIONS PATH INTEGRAL SIMULATIONS FOR THE QUANTUM NUCLEAR E?ECTS LAYOUT OF THE BOOK 2 QUANTUM CHEMISTRY METHODS AND DENSITY-FUNCTIONAL THEORY WAVE FUNCTION-BASED METHOD THE HARTREE AND HARTREE–FOCK APPROXIMATIONS BEYOND THE HARTREE–FOCK APPROXIMATION DENSITY-FUNCTIONAL THEORY THOMAS–FERMI THEORY DENSITY–FUNCTIONAL THEORY EXCHANGE–CORRELATION ENERGY INTERPRETATION OF THE KOHN–SHAM ENERGIES 3 PSEUDOPOTENTIALS, FULL POTENTIAL, AND BASIS SETS PSEUDOPOTENTIAL METHOD GENERATION OF THE PSEUDOPOTENTIAL IMPLICIT APPROXIMATIONS FROZEN CORE CORE–VALENCE LINEARIZATION PSEUDOIZATION FP-(L)APW+LO METHOD LAPW BASIS FUNCTIONS APW+LO BASIS FUNCTIONS CORE STATES POTENTIAL AND DENSITY 4 MANY-BODY GREEN’S FUNCTION THEORY AND THE GW APPROXIMATION GREEN’S FUNCTION METHOD THE GREEN’S FUNCTION THE DYSON EQUATION SELF-ENERGY: HEDIN EQUATIONS THE QUASI-PARTICLE CONCEPT GW APPROXIMATION G0W0 APPROXIMATION NUMERICAL IMPLEMENTATION OF AN ALL-ELECTRON G0W0 CODE: FHI-GAP SUMMARY OF THE G0W0 EQUATIONS THE MIXED BASIS MATRIX FORM OF THE G0W0 EQUATIONS BRILLOUIN-ZONE INTEGRATION OF THE POLARIZATION THE FREQUENCY INTEGRATION FLOWCHART MOLECULAR FORCES AND NEWTONIAN LAWS 5 MOLECULAR DYNAMICS INTRODUCTION TO MOLECULAR DYNAMICS THE VERLET ALGORITHM THE VELOCITY VERLET ALGORITHM THE LEAP FROG ALGORITHM OTHER ENSEMBLES ANDERSEN THERMOSTAT NOS´E–HOOVER THERMOSTAT NOS´E–HOOVER CHAIN LANGEVIN THERMOSTAT ANDERSEN AND PARRINELLO–RAHMAN BAROSTATS EXAMPLES FOR PRACTICAL SIMULATIONS IN REAL POLY-ATOMIC SYSTEMS 6 EXTENSION OF MOLECULAR DYNAMICS, ENHANCED SAMPLING AND THE FREE-ENERGY CALCULATIONS UMBRELLA SAMPLING AND ADAPTIVE UMBRELLA SAMPLING METHODS METADYNAMICS INTEGRATED TEMPERING SAMPLING THERMODYNAMIC INTEGRATION 7 QUANTUM NUCLEAR E?ECTS PATH INTEGRAL MOLECULAR SIMULATIONS PATH INTEGRAL REPRESENTATION OF THE PROPAGATOR PATH INTEGRAL REPRESENTATION OF THE DENSITY MATRIX STATISTICAL MECHANICS: PATH INTEGRAL MOLECULAR SIMULATIONS STAGING AND NORMAL-MODE TRANSFORMATIONS EVALUATION OF THE ZERO-POINT ENERGY EXTENSIONS BEYOND THE STATISTICAL STUDIES DI?ERENT SEMICLASSICAL DYNAMICAL METHODS CENTROID MOLECULAR DYNAMICS AND RING-POLYMER MOLECULAR DYNAMICS FREE ENERGY WITH ANHARMONIC QNES EXAMPLES IMPACT OF QNES ON STRUCTURES OF THE WATER-HYDROXYL OVERLAYERS ON TRANSITION METAL SURFACES IMPACT OF QUANTUM NUCLEAR E?ECTS ON THE STRENGTH OF HYDROGEN BONDS QUANTUM SIMULATION OF THE LOW-TEMPERATURE METALLIC LIQUID HYDROGEN SUMMARY