Chemistry Labs

Theoretical and computational chemistry

Molecular dynamics (MD)

How numerical integration of Newton’s equations turns an interaction model into molecular trajectories and ensemble averages.

1 Lower secondary2 Upper secondary3 Undergraduate4 Advanced5 Research

IntuitionFollowing atoms through time

Molecular dynamics treats atoms as moving particles. A force field supplies their interactions; Newton’s laws advance their positions and velocities in small time steps, producing a trajectory rather than a static structure.

Observe a model trajectory and how temperature and interaction parameters alter atomic motion. A simulation trajectory is a finite sample, not by itself proof of equilibrium or convergence.

SchoolForces, energy, and temperature

Definition: Potential-energy model

A force field is a function U(r₁,…,rN) assigning potential energy to an atomic configuration. The force on atom i is the negative gradient, Fᵢ = −∇ᵢU.

mid2ri/dt2=Fi=−∇iUm_i d²r_i/dt² = F_i = −∇_i U

Example: Thermal speed scale

For one Cartesian velocity component in a classical system at temperature T, equipartition gives ½m⟨vₓ²⟩=½kBT. What does increasing T do to the root-mean-square velocity scale?

Solution

The component RMS speed is √(kBT/m); it grows as √T, not linearly with T.

UndergraduateIntegration and statistical mechanics

Velocity-Verlet is widely used because it is time-reversible and symplectic for conservative dynamics. A typical step updates position using current velocity and acceleration, evaluates new forces, then updates velocity using the average acceleration.

⟨A⟩NVT=∫Aexp(−βH)drdp/∫exp(−βH)drdp;β=1/(kBT)⟨A⟩_NVT = ∫A exp(−βH) dr dp / ∫exp(−βH) dr dp; β = 1/(k_B T)
EnsembleControlled quantitiesTypical use
NVEN, volume, energyIsolated-system dynamics
NVTN, volume, temperatureThermal equilibrium properties
NPTN, pressure, temperatureDensity at target pressure

Definition: Sampling and ergodicity

Ensemble averages are estimated from trajectory samples only when the sampled dynamics explores the relevant phase space adequately. Correlated frames do not count as independent observations; uncertainty requires block analysis or independent replicas.

AdvancedModel limits and advanced practice

Classical force fields usually omit explicit electronic rearrangement, so they cannot directly describe bond breaking, charge transfer, or electronic excitation. Reactive force fields and machine-learned potentials broaden the model, but require validation against suitable quantum data and careful extrapolation checks.

ResearchFrontier: longer and more faithful trajectories

References