Hartree-Fock and What a Basis Set Decides · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Solving for electrons, one field at a time

Science · Chemistry · ages 20-21
Name ______________________   Date ____________

  1. What does SCF convergence mean in a calculation using energy and density change tolerances?

    • Energy changes remain large from cycle to cycle
    • Energy and density changes meet the tolerances
    • No basis error or missing correlation remains

  2. How does Hartree-Fock treat interactions between electrons?

    • Average electron repulsion plus exchange
    • Exact coordinated motion of all electrons
    • Nuclear attraction with no repulsion term

  3. At fixed nuclei and for the same Hamiltonian, what is the exact ground-state electronic energy minus the minimum complete-basis HF energy called?

    • Kinetic energy
    • Nuclear repulsion energy
    • Correlation energy

  4. A calculation of a weakly interacting molecular pair poorly describes electron density far from the nuclei. Which basis change directly addresses this limitation?

    • Remove valence functions to shrink the basis
    • Add electrons to change the molecular charge
    • Add diffuse functions for more spatial reach

  5. What do polarisation functions add beyond the radial flexibility of a split-valence basis?

    • Higher angular momentum functions
    • Extra radial functions for valence
    • Extra electrons in basis functions

  6. Changing from a minimal basis to a split-valence basis adds basis functions but leaves valence radial flexibility unchanged.

    Circle one:   True   False

  7. Once SCF meets its tolerances, more cycles alone remove basis-set error and missing electron correlation.

    Circle one:   True   False

  8. Two converged HF calculations use the same anion geometry and spin. One basis is compact; the other adds diffuse functions and gives a lower energy. What follows?

    • The lower energy proves that HF describes all missing electron correlation.
    • The diffuse basis has more reach, but HF still misses electron correlation.
    • Meeting SCF tolerances makes both bases equally accurate for outer density.
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Solving for electrons, one field at a time W1-mt_EYSTCPuRNx-s1

  1. Energy and density changes meet the tolerances · Convergence means the stated energy and density change tests are satisfied. Basis error and missing electron correlation are separate issues.
  2. Average electron repulsion plus exchange · HF uses average electron repulsion and includes exchange through its antisymmetric wavefunction. It does not describe exact coordinated electron motion.
  3. Correlation energy · This difference defines correlation energy. Using the complete-basis HF reference separates missing electron correlation from finite-basis error.
  4. Add diffuse functions for more spatial reach · Diffuse functions decay slowly and help describe distant density. They address this basis limitation without changing the pair's charge or adding electron correlation.
  5. Higher angular momentum functions · Polarisation functions add angular flexibility. Extra radial functions allow size changes; neither addition changes the number of electrons.
  6. False · Split-valence sets provide several radial functions for valence orbitals. This lets their radial sizes vary more freely than in a minimal basis, so the statement is false.
  7. False · More cycles may tighten numerical convergence, but do not add basis functions or electron correlation. These limitations remain when the same HF calculation is repeated.
  8. The diffuse basis has more reach, but HF still misses electron correlation. · Diffuse functions extend the basis and can reduce its error for outer density. Both calculations still use HF, so the lower energy does not establish that missing correlation was recovered.
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