Molecular dynamics Study Guide

📖 Core Concepts Molecular Dynamics (MD) – computer simulation that solves Newton’s equations of motion for atoms/molecules to generate time‑dependent trajectories. Force Field – set of analytical functions (bonded + non‑bonded) with parameters (charges, LJ radii, equilibrium lengths) that approximate the potential energy surface. Ensembles – statistical collections defining conserved variables: NVE (microcanonical) – N, V, E fixed; adiabatic. NVT (canonical) – N, V, T fixed; thermostat adds/removes energy. NPT (isothermal‑isobaric) – N, P, T fixed; thermostat + barostat. Thermostats & Barostats – algorithms that control temperature (e.g., Nosé–Hoover, Langevin) and pressure (e.g., Parrinello‑Rahman). Time Step – must resolve the fastest vibration (typically H‑bond stretch); classic MD uses 1 fs; SHAKE constraints allow ≈2 fs. Boundary Conditions – periodic boundaries mimic an infinite bulk by replicating the simulation box. Solvent Treatment – explicit (water molecules, ∼10× more particles) vs implicit (mean‑field dielectric). Long‑Range Electrostatics – Particle‑Mesh Ewald (PME) splits interactions into short‑range real‑space + reciprocal‑space; Fast Multipole Method (FMM) is an alternative. Integration Algorithms – symplectic (energy‑conserving) integrators such as Verlet, Velocity‑Verlet, Beeman; higher‑order Runge‑Kutta for stiff systems. --- 📌 Must Remember Newton’s equation: $mi \mathbf{a}i = -\nablai U(\mathbf{r})$ – forces are the negative gradient of the potential. Temperature from kinetic energy: $\frac{1}{2} n k{\mathrm{B}} T = \langle K \rangle$ where $n$ = degrees of freedom. Typical timestep: $1\;\text{fs}=10^{-15}\,\text{s}$ (unless constraints are used). Lennard‑Jones 6‑12 potential: $U{LJ}(r)=4\varepsilon\left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6}\right]$. Scaling: naïve all‑pair forces $O(N^{2})$ → PME / P3M $O(N\log N)$ → linear‑scaling methods (FMM). Ergodicity: for an ergodic system, a single long MD trajectory → ensemble averages. Explicit solvent cost: increases particle count 10×; necessary for viscosity, kinetic effects. Polarizable force fields add induced dipoles (Drude particles) → higher accuracy but higher cost. --- 🔄 Key Processes System Preparation Build molecular topology → assign force‑field parameters → add solvent (explicit or implicit). Energy Minimization Remove bad contacts (steepest‑descent or conjugate‑gradient). Equilibration NVT → bring temperature to target (apply thermostat). NPT → adjust density/pressure (add barostat). Production Run Choose ensemble matching property of interest. Record positions, velocities, energies at desired intervals. Analysis Compute observables (RMSD, diffusion coefficient, free energy). Validate against experimental data (NMR, X‑ray, thermodynamics). --- 🔍 Key Comparisons Explicit vs Implicit Solvent Explicit: captures friction, viscosity, specific hydrogen‑bonding; ≈10× more atoms. Implicit: faster; uses mean‑field dielectric; loses detailed solvent dynamics. NVE vs NVT vs NPT NVE: energy conserved, no thermostat/barostat – good for energy‑conservation checks. NVT: fixes temperature only – ideal for sampling at a single T. NPT: fixes both T and P – needed when density or pressure is a target property. Pair vs Many‑Body Potentials Pair: sum over atom pairs (e.g., Lennard‑Jones). Simpler, cheaper. Many‑Body: include three‑body terms (EAM, Tersoff) → better for metals, covalent networks. PME vs FMM PME: relies on FFT, best with periodic boundaries. FMM: works without periodicity, scales linearly, lower communication overhead. --- ⚠️ Common Misunderstandings “Force fields automatically include polarization.” Most classical FFs use fixed charges; polarizable FFs are a special class. “Longer simulation always yields better results.” Integration error and force‑field inaccuracies dominate after a point; proper equilibration matters more. “Cutoff distance can be arbitrarily small.” Too short a cutoff creates energy discontinuities and artifacts; use smoothing or shifted‑force methods. “NVT = constant energy.” Temperature control adds/removes energy; only NVE conserves total energy. --- 🧠 Mental Models / Intuition Energy Landscape – imagine a rugged mountain range; MD is a ball rolling under gravity, exploring valleys (low‑energy conformations). Ergodic Clock – the longer the clock runs, the more the ball samples all accessible valleys, making the time average ≈ ensemble average. Constraint as a “Speed Bump” – fixing fast H‑bond vibrations (SHAKE) removes the smallest bumps, letting you take larger strides (timestep). --- 🚩 Exceptions & Edge Cases Polarizable vs Fixed‑Charge FFs – use polarizable models when strong induction effects (e.g., ions in water) matter. High‑Pressure Simulations – need barostats that correctly handle anisotropic stress (e.g., Parrinello‑Rahman). Very Small Boxes – image‑image interactions become non‑physical; increase box size or use vacuum padding. Steered MD – external forces break equilibrium; interpret forces as non‑equilibrium work, not standard thermodynamic quantities. --- 📍 When to Use Which Ensemble Choice Property of interest = diffusion coefficient: use NVT after NPT equilibration to get correct density. Pressure‑dependent phase behavior: run NPT directly. Solvent Model Need accurate hydration shells or ligand binding: explicit water (TIP3P, SPC/E). Screening free energies for many mutants: implicit solvent (GB/SA). Long‑Range Electrostatics Periodic bulk system: PME (standard). Non‑periodic or massively parallel: FMM or cutoff + reaction‑field if acceptable. Force Field Type Metals or covalent networks: many‑body (EAM, Tersoff). Organic biomolecules: classical empirical FFs (AMBER, CHARMM). Time‑Step Enhancement Hydrogen‑heavy systems: apply SHAKE → can safely use 2 fs. --- 👀 Patterns to Recognize “Energy drift > 1 kJ/mol/ps” → timestep too large or integration algorithm unstable. Sharp spikes in temperature → thermostat coupling constant too weak or constraints failing. Radial distribution function (RDF) plateau at unrealistic values → cutoff too short or missing long‑range correction. Repeated “nanosecond” simulation of a protein that never unfolds → likely insufficient sampling; consider REMD or accelerated MD. --- 🗂️ Exam Traps Confusing NVT with constant energy – NVT uses a thermostat; only NVE conserves total energy. Assuming Lennard‑Jones parameters are universal – they are force‑field specific; mixing parameters without proper combining rules yields errors. Choosing PME for a non‑periodic system – leads to artificial interactions; either use vacuum padding or FMM. Neglecting the barostat in NPT – pressure will drift, giving wrong densities. “Longer timestep = faster simulation” – may cause integration instability, large energy drift, and meaningless results. ---