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1.3 Water single point and the meaning of energy

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.

1.3.1 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: Water single point and the meaning of energy. No numerical results are claimed.
Original schematic: Water single point and the meaning of energy. No numerical results are claimed.

1.3.2 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.

1.3.2.1 Input block 1

%chk=g03_water_sp.chk
%mem=2GB
%nprocshared=2
#p B3LYP/6-31G(d) SP SCF=Tight Int=UltraFine

Water fixed nuclear geometry baseline

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

1.3.3 Worked investigation

1.3.3.1 Intuition and prerequisites

A single-point calculation asks for electrons at fixed nuclear positions. It does not move an approximate drawing into an equilibrium structure. Here the deliberately simple water geometry has O–H distances close to 0.96 Å and a bent angle. The purpose is to recognize that electronic energy is conditional on geometry, method, basis, charge, and spin. You need cases 01–02 and a molecular viewer capable of reading XYZ or Gaussian coordinates.

See input block 1 above.

1.3.3.2 Workflow

  1. Calculate both O–H lengths from the coordinates and sketch the angle. Confirm ten electrons and a closed-shell singlet.
  2. Run the input and locate the final electronic energy, dipole vector, and basis-function count. Record units beside every quantity.
  3. Make a fresh input moving the positive-x hydrogen by +0.10 Å along x only. Keep every other choice fixed and use a new checkpoint.
  4. Subtract the two energies before converting units. Use 1 Eh≈2625.50 kJ mol−1 or 627.509 kcal mol−1, and label the result a fixed-geometry energy difference.
  5. Compare the dipole magnitude as well as energy. If the program reorients the molecule, do not compare raw vector components without transforming frames.

1.3.3.3 Interpret check and limits

The absolute electronic energy includes nuclear repulsion within the specified model, but no zero-point or finite-temperature correction. A difference between two arbitrary geometries is not automatically an activation barrier. Report SCF Done from the intended final job, not an early iteration or a different Link1 segment. The geometry must remain unchanged because SP was requested; inspect the geometry echoed in the log. A larger basis will often lower variational HF energies, but “more negative” across unrelated approximate methods is not a universal quality score. B3LYP/6-31G(d) here is an affordable teaching model, not a universal recommendation for interactions, anions, or quantitative spectroscopy.

Exercise Displace the same hydrogen by −0.10 Å, then compare the two finite differences. Can the three energies prove that the starting geometry is stationary? Explain what a gradient would add.

1.3.5 Sources and further reading