In molecular dynamics, you want to integrate the equations of motion with a time step of 2 fs to calculate atomic motion over 1 ns. How many time steps are needed?

Answer: C. 5×10⁵

Since 1 ns = 10⁻⁹ s and 2 fs = 2×10⁻¹⁵ s, the number of steps is 10⁻⁹/(2×10⁻¹⁵) = 5×10⁵. The time step must be small enough to divide the period of atomic vibration (around 100 fs) into several tens of steps, and for systems containing light hydrogen it is set to 1 fs or less. If the step is too large, errors in numerical integration such as the Verlet method destroy energy conservation and the calculation breaks down. 5×10² takes fs as 10⁻¹² s (ps), and 5×10⁸ takes ns as 10⁻⁶ s (µs). Because forces on all atoms are calculated at every step, nanoseconds to microseconds is the rough limit of the time that molecular dynamics can follow.