Density Functional Theory and Choosing a Functional · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Density instead of wavefunction

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

  1. Two electrons with the same spin keep apart, and electrons also avoid each other beyond the average field. What accounts for both effects?

    • Only the kinetic energy of the electrons
    • The exchange-correlation energy
    • Only the number of atoms

  2. Why work with the electron density instead of a many-electron wavefunction?

    • It uses fewer variables
    • It uses one variable for every electron
    • It makes the calculation exact

  3. What distinguishes functional families?

    • Their speed alone
    • Their basis-set size alone
    • Accuracy, cost and fit

  4. A local functional known to lack dispersion treatment calculates stacking as barely bound, while experiment shows stronger binding. Other interaction errors have been checked and are small. What is the likely cause?

    • A basis set too small for the rings
    • A functional missing dispersion attraction
    • An unoptimised geometry for the pair

  5. You need molecular energies accurate enough to compare delicate effects, and you can afford a costlier functional. Which functional family do you try first?

    • A simple local functional, which runs fast for large systems
    • A dispersion correction on its own, with no functional underneath
    • A hybrid, mixing exact exchange at higher cost

  6. The exact exchange-correlation functional is known and used everywhere.

    Circle one:   True   False

  7. A pricier functional always beats a cheaper one for every property.

    Circle one:   True   False

  8. A dispersion-deficient functional calculates stacking as barely bound. What do you propose?

    • Recompute with the same functional and no correction
    • Add a dispersion correction and recompute
    • Use a larger basis set with the same functional and no correction
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Answer key

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

Density instead of wavefunction W1-mt_mmuzLeA62V-s1

  1. The exchange-correlation energy · Exchange covers same-spin avoidance from antisymmetry, and correlation covers the remaining avoidance beyond the average field.
  2. It uses fewer variables · The density gives one value at each point in space. The wavefunction sprawls across every electron at once, so it needs far more variables.
  3. Accuracy, cost and fit · Families trade care against compute, fitting different jobs.
  4. A functional missing dispersion attraction · With other errors checked small, the known missing dispersion is the likely cause of the weak binding.
  5. A hybrid, mixing exact exchange at higher cost · Hybrids usually repay their price for molecules.
  6. False · It is unknown, which is why approximations exist.
  7. False · Families suit different jobs, so match the tool to the task.
  8. Add a dispersion correction and recompute · The correction restores the missing attraction between the rings.
Worksheet · LightMySky