Exercises: Turn Your Calculations into Evidence

Pre-reading: Silicon primitive cell self-consistent computing with Convergence test . It is recommended to complete this exercise before proceeding to property calculations. These five exercises provide tasks, blank tables, and inspection methods; the pages do not have precalculated energies, band gaps, or potential barriers. Learning time only refers to design and organization, actual queuing and calculation time are additional.

Objectives and deliverables

Choose a well-founded ENCUT and uniform k-grid for the fixed silicon primitive cell in the tutorial, and deliver a one-page conclusion, two convergence curves, original record table, and input list. The conclusion must answer "what quantity converges to what extent" and cannot just list recommended parameters. When you don't have a software license or computing resources, you can submit an input design and a blank report, clearly marked "Not yet running."

1. Keep the same POSCAR and potential file versions, recording the atomic number, functional, smearing, actual read ENCUT and grid. Each set of independent directories does not re-optimize the geometry during the test.
2. Fix the denser initial mesh and gradually increase ENCUT; fix the stabilized ENCUT and then refine the same family mesh. Finally, raise ENCUT once on the selected grid to check whether the two types of errors mask each other.
3. Check whether the electronic iterations converge and read the uniformly defined energy, maximum force and stress. Failure points are retained in the record and marked with reasons, and are not included in the normal convergence trend.
4. Uniformly normalized atomically, changes relative to the finest reference point are plotted. Look at multiple sets of trends at the end while reporting computational costs; don't make decisions based on two points that happen to be close together.

Acceptance example: The class goal of "less than 1 meV/atom compared to the finer two groups" from the introductory chapter can be used, but preface it with the caveat that it is only the energy threshold for this exercise. If the target is a small magnetic energy difference, force or stress, then corresponding standards must be established. Finally, the electronic solution error, basis set error, and k-point error are discussed respectively; functional approximation and model selection errors will not automatically disappear due to numerical convergence.

Self-check: expand the reasoning

Pre-reading: Static calculation and output , DOS and PBE band structure . This exercise is limited to non-magnetic silicon and PBE in the tutorial. First use the same set of convergence geometries to avoid mixing new factors such as HSE and SOC.

Objectives and deliverables

Deliver a file flow diagram, DOS diagram, band structure diagram and one page of cross-reference instructions. Each picture indicates the structure, method, energy zero point, sampling method and source file; beautiful graphics cannot replace numerical inspection. The band gap, band edge position and integration result can only be filled in by your own output. Leave the columns blank if not calculated.

1. Make regular grid SCF from converged structures, saving input, convergence evidence and CHGCAR. Record which step produced the file and which copy of it was used in subsequent steps.
2. Calculate DOS with a denser uniform grid self-consistent according to the Electronic Structure chapter, check ISTART, ICHARG and read files; energy grid encryption of DOS cannot replace k-point encryption.
3. Find the path band structure according to the PBE fixed charge process in an independent directory, and confirm that the path coordinates belong to the reciprocal basis of the current primitive cell. Outputs sampled only along high symmetry lines are not used for total energy or DOS integration.
4. Save the data without artificial translation and plot it explicitly using VBM or other interpretable common reference. Record the actual highest occupied state, lowest unoccupied state and corresponding sampling points, indicating that finite paths may miss band edges.
5. Change the sampling and smearing of DOS and observe whether the band edge and peak shape are stable; check the normalization, occupation and electron number of the integral state number, and do not mistake the sum of the projected components for the complete total state number.

Key points for acceptance: Others can reproduce your plot along the file stream and see the sampling errors and reference energy choices. When there are differences between DOS and path diagrams, meshing, smearing, energy alignment, and extreme value coverage should be explained first before discussing the physical reasons.

Pre-reading: Magnetic calculations or Defects . Choose only one of the two routes , complete the controllable small problems first, and do not require two studies to be carried out at the same time.

Objectives and deliverables

Submit a clear question, a comparison table, two to three necessary figures, and a statement of uncertainty. At least one comparison should be kept to rule out erroneous interpretations; if different initial guesses end up in the same state, or the finite size has not converged, this should also be reported truthfully.

1. Choice A: Magnetic state. Using the diatomic Fe model in the tutorial, first fix the same unit cell and numerical settings, and compare the initial guesses of parallel and antiparallel magnetic moments. The table records the initial MAGMOM, final local/total magnetic moment, electronic convergence state and uniformly defined energy respectively; do not regard the input label as the final magnetic state.
2. Option B: Neutral defect. Design a neutral vacancy in a silicon supercell and record the deleted atoms, bulk reference, and chemical potential definition. Complete the pure phase and defect calculations under the same theoretical setting first, and then design the inspection for increasing the supercell; this exercise does not extend to live correction.
3. Write which variables are fixed and which variables change in the comparison. For magnetic state comparison, you can fix the geometry first and then discuss the optimization of each state; for defect comparison, you need to check the influence of supercell, grid density, structural distortion and reference state.
4. Separate actual observation from inference: the lower energy of one state in a certain model does not mean that it proves the ground state of all possible magnetic orders of the material; the formation energy of a supercell does not mean that the periodic mirror effect has been eliminated.

Key points for acceptance: The magnetic route should prove that the comparison is the final state, and explain the projection definition of the local magnetic moment; the defect route should clearly state each item in the formation energy, the number of atoms, and the reference library. Both routes must allow numerical errors in the energy difference to be smaller than the scale of the effect in question, otherwise the conclusion should be retained.

Pre-reading: Surface and adsorption , NEB . This exercise delivers the solution first, so there is no need to run an entire expensive path at once to complete the job. The problem of choosing an adsorbate to migrate between two sites on the same surface avoids complex reactions that simultaneously change the composition.

Objectives and deliverables

Submit model schematic with unit cell orientation and layer labels, reference state list, two endpoint structures, NEB directory tree, and checklist. List the definitions of adsorption energy and migration barrier respectively; indicate whether the solution uses native NEB or installed VTST, and record the program and tool versions.

1. Select the crystal plane and coverage, determine the vacuum direction and fixing layer. Plan to check plate thickness, vacuum, in-plane dimensions and electronic sampling item by item; indicate whether there is a net dipole and whether corresponding corrections are needed.
2. List the composition, spin and calculation method of the adsorbed state, clean surface and isolated reference, and write the adsorption energy formula and symbol convention. Also confirm that composition and coverage are identical when comparing only two adsorption sites.
3. Optimize endpoints individually with consistent unit cells and constraints, checking final forces and expected structure. Atom numbers before and after migration must correspond; displacements are plotted to exclude unusually long paths caused by interpolation across period boundaries.
4. Create an initial intermediate image and check frame by frame for problems with atoms coming too close or penetrating the surface. List the acceptance criteria for endpoints, intermediate image forces, and path shapes; the highest energy discrete image itself does not prove that the saddle point has converged.
5. Explain how to add images or optimize paths to check potential barriers, and list transition state verification as a follow-up task. Normal NEB and climbing-image settings must be separated according to the advanced page, and plug-in optimizer parameters cannot be copied directly to the native program.

Key points for acceptance: The reviewer can tell what structure each energy term comes from, which atoms are fixed, and how the reaction coordinates are generated. When it is not yet running, only the plan and blank energy map coordinates are submitted. You cannot draw a guess curve and mark it as a calculated potential barrier.

Pre-reading: AIMD and Cost and Reproducibility Reporting . Select a target, such as the local coordination distribution of an equilibrium structure; if diffusion is chosen, it must be additionally discussed whether the transition events are sufficient and cannot rely solely on trajectory animation.

Objectives and deliverables

Submit a sampling timeline, parameter basis table, list of graphs to be generated, and stop/extension conditions. Specify the temperature, time step, thermostat, total number of steps, output intervals, and initial structure and velocity sources for fixed unit cell NVT. The short trajectories in the template can only be used to check the process and cannot guarantee statistical reliability in advance.

1. Do a short test first to check the electron step convergence, maximum abnormal force, temperature changes, and whether there are unreasonable collisions of atoms. Convert the number of steps by the time step into actual duration and check the total calculation cost.
2. Design short NVEs to examine the energy drift of the integral and electronic solutions, compared to smaller time steps or tighter electron convergence. The physical system in NVT will exchange energy with the thermostat, and the same "physical energy constant" criterion cannot be applied.
3. Thermal equilibrium cutoff points are selected based on the stationarity of temperature, energy and target structural quantities, and the thermalization phase is excluded from production statistics. Don’t prescribe that “the first half must be enough” and don’t just look at the average temperature.
4. Plan block statistics or independent initial velocity repetitions to check adjacent frame correlations. Increasing the number of saved frames does not equate to increasing independent samples; error estimates should reflect correlated time and limited sampling.
5. If looking for diffusion, explain how to deal with period crossovers, overall drift, and MSD fitting intervals; check whether there are enough independent transitions to distinguish between ballistic, local vibration, and diffusion intervals.

Key points for acceptance: The plan should answer "Which observations would cause me to extend the simulation, reduce the time step, or negate the conclusion?" Report the actual sampling duration, discarding intervals and statistical methods; if the target event does not occur, observations in a limited time window should be reported, and precise transport coefficients without statistical support cannot be given.

Read the file description and corresponding chapters first, and then complete the model, POTCAR and pre-calculation. Files with the suffix .template contain parameters to be changed and cannot be submitted as they are.