Electron Correlation and Methods Past Hartree-Fock · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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What Hartree-Fock leaves out

Science · Chemistry · ages 23-24
Name ______________________   Date ____________

  1. What is the correlation energy?

    • The energy of the Hartree-Fock orbitals
    • The energy the nuclei repel each other with
    • Exact energy minus the Hartree-Fock energy

  2. What does Hartree-Fock miss?

    • The moment-by-moment dodging of electrons
    • The Pauli exclusion of same-spin electrons
    • The attraction between electrons and nuclei

  3. Coupled cluster costs far more than perturbation theory as molecules grow.

    Circle one:   True   False

  4. Why does a breaking bond need different treatment?

    • Two arrangements compete
    • Bonds never break inside calculations
    • Electrons move faster when stretched

  5. A small molecule at equilibrium and cost is no object: what do you choose?

    • Coupled cluster, with a small stated error
    • Hartree-Fock, since cost is no object
    • Perturbation, since it is always as accurate

  6. Which ranking of accuracy is right?

    • Both methods give the same accuracy
    • Coupled cluster beats perturbation
    • Perturbation beats coupled cluster

  7. A large molecule at equilibrium and a small computer: what do you choose?

    • Coupled cluster, whatever the wait
    • Hartree-Fock alone, which needs no error bars
    • Perturbation, accepting wider error bars

  8. A student runs a standard single-picture method on a breaking bond. What is wrong?

    • Nothing is wrong: one picture fits all bonds
    • It assumes one arrangement dominates
    • Breaking bonds need less care, not more
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Answer key

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

What Hartree-Fock leaves out W1-mt_3F5B8V7CGb-s1

  1. Exact energy minus the Hartree-Fock energy · The correlation energy is defined by the approximation it corrects: the exact energy minus the Hartree-Fock energy.
  2. The moment-by-moment dodging of electrons · Averaging erases the moment-by-moment dodging of electrons, and that missing motion is what Hartree-Fock leaves out.
  3. True · Fuller corrections cost more as molecules grow: MP2 grows as the fifth power of system size, and coupled cluster as the sixth or seventh.
  4. Two arrangements compete · No single arrangement dominates any more, so methods that assume one give poor energies.
  5. Coupled cluster, with a small stated error · With a small molecule and no limit on cost, coupled cluster gives the best accuracy, and you still state the small error that remains.
  6. Coupled cluster beats perturbation · Coupled cluster builds the fuller correction, so it is more accurate than the cheaper, rougher perturbation correction.
  7. Perturbation, accepting wider error bars · Choose a method the computer can run, here perturbation, and state the wider error it leaves.
  8. It assumes one arrangement dominates · The method assumes one arrangement dominates, but at a breaking bond two arrangements compete.
Worksheet · LightMySky