6.3 NVT sampling and thermostat choices
These are unexecuted teaching templates, with no ABACUS results. Baseline: ABACUS 3.9.0. Verify executable and external-tool versions.
6.3.1 Scientific question
How can a fixed-volume simulation sample a chosen temperature without confusing temperature control with physical correctness? NVT allows energy exchange with a heat bath while holding particle number and cell volume fixed. The instantaneous kinetic temperature fluctuates even in equilibrium. A perfectly flat temperature trace is not the goal. This lesson compares a Nose–Hoover chain protocol with the conservation diagnostic in the preceding NVE lesson. It uses the same silicon supercell and force-converged electronic model, and provides an unexecuted setup rather than an equilibrium claim.
6.3.2 Model and prerequisites
First pass the NVE time-step and force-noise checks. A thermostat does not repair an inaccurate force field or unstable integrator. Save the chosen reference cell and the mobile-atom count. State whether center-of-mass translation is removed and how constraints alter the degrees of freedom. Temperature inferred with 3N degrees of freedom can differ from one inferred with 3N−3; use the convention actually implemented and report it. Retain matched pseudopotentials and orbitals, a consistent electronic occupation policy and the validated k-point sampling. For a solid, the selected fixed volume determines the pressure reached at the target temperature; NVT does not independently enforce zero pressure.
6.3.3 Worked template and interpretation
Replace the listed keys in the complete parent INPUT. The chain thermostat is selected explicitly, while the three-element chain is a proposed numerical choice requiring validation. md_tfreq has inverse-femtosecond units, not a time constant in ps. The proposed 0.01 fs⁻¹ is therefore a frequency of 10 ps⁻¹; interpret coupling through the version's equations rather than casually identifying its reciprocal with every relaxation time. md_tfirst and md_tlast are both 300 K, so this setup requests a constant target rather than a heating ramp. Five hundred 1-fs steps provide only 0.5 ps and serve as commissioning. They cannot certify canonical sampling or rare-event statistics.
# Delta from the validated fixed-cell AIMD parent:
calculation md
suffix si_nvt
cal_force 1
symmetry 0
md_type nvt
md_thermostat nhc
md_dt 1.0
md_nstep 500
md_tfirst 300
md_tlast 300
md_tfreq 0.01
md_tchain 3
md_seed 17
md_dumpfreq 1
dump_vel 1
6.3.4 Physics and units
Kinetic temperature is derived from kinetic energy and the active degrees of freedom. Finite systems have real fluctuations, with relative fluctuations shrinking as system size grows. The canonical kinetic-energy variance gives a useful diagnostic when the constraints and sampling assumptions are appropriate. The electronic smearing temperature, if present, is a different modeling parameter from ionic temperature. Do not equate a metal's smearing width in Ry or eV with the thermostat target without an explicit physical argument. Potential energy is not conserved under NVT because the bath does work on the system.
6.3.5 Outputs and analysis
Read the time-resolved temperature, potential and kinetic energies from running_md.log and the structural trajectory from MD_dump, verifying column units and actual output cadence. Plot the target as a reference line and the instantaneous temperature as a fluctuating trace. Select an equilibration exclusion window using the behavior of energy, structure and temperature, not only one crossing of the target. Report the production-window mean, variance and block uncertainty. Inspect bond distances and lattice stress to detect a structural transformation or an inappropriate fixed volume. Preserve all equilibration data and document the excluded interval.
6.3.6 Convergence and acceptance
Compare weaker and stronger thermostat coupling while keeping the same force settings, time step, total physical duration and analysis policy. Check sensitivity of structural averages and fluctuations rather than choosing the trace that looks smoothest. Repeat with independent initial velocities or seeds. Divide production into blocks longer than the relevant autocorrelation time; a single short block cannot measure uncertainty. For dynamical correlations, recognize that thermostat coupling can modify the motion and consider validated NVE segments initialized from equilibrium states. Compare at least two supercell sizes if fluctuations or collective modes matter. A chosen coupling is acceptable only for the observable and time scale being studied.
6.3.7 Pitfalls and exercises
Simple velocity rescaling and Berendsen control can stabilize a mean temperature without guaranteeing the desired canonical fluctuations; the official documentation distinguishes thermostat families. Do not call a short ramp an equilibrium production run. Do not compare states at different volumes and attribute all differences to temperature. Exercises: (1) compute the appropriate degrees of freedom for an unconstrained periodic supercell with translation removed and explain how frozen atoms alter it. (2) Explain why a zero-width temperature distribution is suspicious in a finite canonical system. (3) Design independent-seed and coupling tests for a structural average, then explain why the same tests are insufficient to certify a transport coefficient.