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6.1 NVE energy conservation separates timestep and SCF error

These are unexecuted teaching inputs and starting models. Original diagrams are schematics, not calculated results. Validate version-specific syntax, licensed or authorized data, numerical convergence and the scientific model before using this workflow.

6.1.1 Model, units and provenance

Keep basis/potential files and executable versions traceable. Grid controls use Ry; common energy/force outputs use hartree and hartree/bohr. Read the unit in each output heading.

Shared inputs, conventions and evidence

Original schematic: NVE energy conservation separates timestep and SCF error. No numerical results are claimed.
Original schematic: NVE energy conservation separates timestep and SCF error. No numerical results are claimed.

6.1.2 Unexecuted inputs and explicit deltas

Use the accompanying instructions to identify the parent calculation and placement of every delta; a snippet is not automatically a standalone input. Preserve all blank-line and file-provenance requirements.

6.1.2.1 Input block 1

&MOTION
  &MD
    ENSEMBLE NVE
    STEPS 1000
    TIMESTEP [fs] 0.5
    TEMPERATURE [K] 300
  &END MD
  &PRINT
    &TRAJECTORY
      FORMAT XYZ
      &EACH
        MD 1
      &END EACH
    &END TRAJECTORY
    &VELOCITIES
      &EACH
        MD 1
      &END EACH
    &END VELOCITIES
  &END PRINT
&END MOTION

6.1.3 Worked investigation

Intuition. Born–Oppenheimer MD assumes sufficiently converged electronic forces at each nuclear step. A thermostat can hide numerical heating, so a short NVE diagnostic is valuable before production. Energy fluctuations caused by exchanging kinetic and potential energy are normal; systematic drift of their total can signal integration or force errors. Use a prepared water configuration and a common saved position/velocity state, not independently randomized velocities for every comparison.

Original input delta. Change RUN_TYPE to MD, remove GEO_OPT/CELL_OPT, and add the block below. TIMESTEP is in femtoseconds, TEMPERATURE in kelvin. The 1000-step duration is a smoke-test length, not a statistically adequate production trajectory. TEMPERATURE can initialize velocities when no velocity state is supplied; it is not an NVE thermostat.

See input block 1 above.

Workflow. 1. Start from a stable equilibrated or carefully prepared state and save the exact velocities. 2. Run a short NVE segment at 0.5 fs with a suitably tight SCF. 3. Repeat at 0.25 fs from the identical phase-space state for the same physical duration, doubling the step count. 4. At fixed timestep compare EPS_SCF, for example 1e−6, 1e−7 and 1e−8 as a diagnostic sweep. 5. Plot kinetic energy, potential energy and their sum versus physical time; report drift per atom per time with units and fitting interval. 6. Inspect exceptional steps with large SCF counts, close contacts or abrupt energy jumps.

Interpretation. Bounded oscillations of total energy can be compatible with a finite-step symplectic integrator; monotonic drift is a different signature. Reducing timestep should reduce integration error in an appropriate regime, whereas tightening SCF tests force consistency. Both can matter simultaneously. A linear drift estimate from a very short noisy segment has high uncertainty; inspect the trace and compare windows rather than trusting one regression slope.

Checks and limits. Constraints, altered masses, temperature rescaling, external fields and biased potentials change the conserved quantity or physical dynamics. Do not silently use deuterium masses to gain a larger timestep while reporting ordinary-water diffusion. Removing center-of-mass momentum continuously can alter dynamics and energy bookkeeping; document the choice. A restarted trajectory must preserve velocities as well as coordinates. Classical nuclei omit nuclear quantum effects; stable integration does not validate that approximation.

Exercise. Build a timestep×SCF matrix and distinguish numerical energy drift from ordinary temperature fluctuations. Select a setting using a declared tolerance and estimated cost per picosecond. Explain why an NVT temperature trace that stays near 300 K cannot substitute for this check.

Diagram. Three qualitative panels: anticorrelated kinetic/potential exchange, bounded total-energy oscillation, drifting total energy. EN labels: physical time, energy exchange, integration error, electronic-force error. Curves explicitly schematic.

6.1.5 Sources and further reading