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2.5 Method, basis and numerical convergence

The inputs on this page are educational templates that have not been executed for this course. Use an authorized installation, verify version-specific options and establish your own convergence.

2.5.1 Name the property and chemical regime

“Which functional is best?” lacks a target. Specify conformer energy, hydrogen-bond distance, electron affinity, excitation or barrier; their errors differ. Use relevant validation and benchmarks rather than keyword popularity. A basis limits the orbital expansion: polarization adds angular freedom, diffuse functions add spatial reach important for anions and some weak/diffuse states. A larger basis can also worsen linear dependence, SCF difficulty and cost. For heavy atoms, verify relativity, ECP assignment and core-electron counts; never paste an unidentified ECP.

HF, approximate DFT and correlated wavefunction methods treat correlation differently. Numerical convergence cannot remove model error. Dispersion, solvent, conformer sampling and electronic state can matter as much as basis enlargement.

2.5.2 A controlled DFT exercise

Use a separate input to change method while keeping a transparent comparison:

%Chk=water_dft.chk
%Mem=2GB
%NProcShared=2
#p B3LYP/6-31G(d) Opt=Tight Freq SCF=Tight Integral=UltraFine

Water DFT optimization and frequencies; explicit integration grid

0 1
O    0.000000    0.000000    0.000000
H    0.758000    0.000000    0.586000
H   -0.758000    0.000000    0.586000

B3LYP/6-31G(d) is an unexecuted demonstration, not state-of-the-art accuracy certification. Compare bond lengths, angle and harmonic frequencies with the RHF exercise. Lower absolute energy across different methods is not proof of better accuracy; compare meaningful observables or consistent relative quantities against evidence.

Integral=UltraFine makes the DFT integration grid explicit. Tighten grids/thresholds separately and assess the property, recording material sensitivity. The input states intent; output confirms actual settings. More precise numerical convergence within an inadequate model remains an inadequate prediction.

2.5.3 SCF diagnosis in order

  1. Verify geometry, charge/spin and basis assignments; algorithms cannot repair a nonsensical model.
  2. Read final iterations and error context, separating slow convergence, oscillation, numerical instability, resource kills and later-stage errors.
  3. For compatible HF/DFT cases, SCF=(XQC,Tight,MaxCycle=256) can add a quadratic-convergence fallback. It has method restrictions and is not a universal cure.
  4. Reused guesses require matching charge, spin, atom order and problem. A convenient checkpoint can steer a difficult case to the wrong solution.
  5. For open shells inspect spin expectation and state character. Stability analysis may help, but a stable determinant does not establish single-reference adequacy.
  6. Change one diagnostic setting at a time, retaining failed logs. Repeatedly increasing cycle limits conceals the underlying cause.

Do not relax final standards to obtain an attractive energy. A preliminary loose guess must be followed by the documented final calculation and checks. SCF keyword; CONFLEX SCF reference.

2.5.4 Reproducibility and deliverable

Save full inputs/logs, exact revision, initial/final geometries, charge/spin, method/basis/ECP, grid, dispersion/solvent, convergence, constraints and checkpoint lineage. Record job resources, exit and stationary-point evidence, units and parser version. Use electronic_energy_Eh, not an ambiguous energy column; missing results must remain missing rather than silently becoming zero.

Design a comparison table with one changed variable per row and an acceptance rule for the target quantity. Document failures and model limits. Further sources: official basis reference, CONFLEX basis documentation, LMU method and analysis teaching map.

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