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2.1 Basis sets as a controlled experiment

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.

2.1.1 Model, units and provenance

Geometry in Å; electronic energy in hartree; vibrational wavenumbers in cm⁻¹. Check each printed field and keep thermal and standard-state terms distinct.

Shared inputs, conventions and evidence

Original schematic: Basis sets as a controlled experiment. No numerical results are claimed.
Original schematic: Basis sets as a controlled experiment. No numerical results are claimed.

2.1.2 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.

2.1.2.1 Input block 1

%chk=g05_water_dz.chk
%mem=2GB
%nprocshared=2
#p HF/cc-pVDZ SP SCF=Tight

Water basis family fixed geometry

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

2.1.3 Worked investigation

2.1.3.1 Intuition and prerequisites

A basis set is the vocabulary available to the electronic wavefunction. Increasing the vocabulary can alter both energy and response properties. A useful convergence test keeps geometry and method fixed and varies one basis family in a planned sequence. Water is small enough that HF/cc-pVDZ, cc-pVTZ, and cc-pVQZ are suitable classroom comparisons when resources permit. These are not merely “small, medium, large” labels: they form a correlation-consistent hierarchy, and diffuse augmentation answers an additional physical need rather than only a size question. Prerequisites: case 03 geometry and the ability to extract energy and dipole.

See input block 1 above.

2.1.3.2 Workflow

  1. Run the DZ input. Prepare two copies replacing only cc-pVDZ with cc-pVTZ and cc-pVQZ, plus unique checkpoint/title names.
  2. Record basis-function count, energy in Eh, dipole in debye, elapsed time, and peak memory if the scheduler reports it.
  3. Calculate consecutive energy increments in kJ mol−1 and dipole changes. Keep full printed energies until subtraction is finished.
  4. Repeat DZ with aug-cc-pVDZ as a separate augmentation branch. Do not place it on the same cardinal-number axis as ordinary TZ without explanation.
  5. Decide which property and tolerance define adequacy for the next task. A total-energy threshold may be wasteful if the scientific target is an energy difference.

2.1.3.3 Interpret check and limits

Variational HF energy should not rise when the mathematical variational space strictly contains the old one, but arbitrary named basis sets are not guaranteed nested spaces. The practical expectation of systematic improvement must be checked rather than treated as an exact monotonicity theorem for every library combination. Basis convergence does not repair missing correlation. A converged dipole in one approximate method is still method-dependent. Diffuse functions can expose near-linear dependence; inspect warnings, the effective basis size, and sensitivity before interpreting an apparently dramatic improvement.

Exercise Propose separate tolerances for an educational dipole comparison and a 1 kJ mol−1 reaction-energy study. Explain why the latter also needs all reaction species and balanced electron counts.

2.1.5 Sources and further reading