Density Functional Theory and Choosing a Functional
Working with the electron density rather than the full wavefunction makes accurate calculations affordable for molecules of real size. The price is that part of the energy comes from an approximate functional, and different functionals disagree.
What a learner can do afterwards
- Explains why the density is a smaller object to work with than a many-electron wavefunction
- Says what the exchange-correlation functional accounts for and why it has to be approximated
- Compares functional families on accuracy and cost and identifies what each is usually chosen for
- Identifies a case where a common functional is known to fail and states the usual repair
1 · Read
Hartree-Fock follows each electron in an average field, and the cost grows fast as molecules get bigger. A many-electron wavefunction sprawls across every electron at once. The density needs fewer variables: one value at each point in space. Working with the density keeps accurate calculations affordable for real-size molecules.
Part of the energy then comes from an exchange-correlation functional, which must be approximated. Exchange covers the effect of antisymmetry: electrons with the same spin keep apart. Correlation covers the rest of how electrons avoid each other beyond the average field. Nobody knows the exact combined form, so every choice trades accuracy against cost.
Functional families climb a ladder of cost and care. Simple local ones run fast but miss delicate effects. Hybrids mix in exact exchange and usually do better for molecules, at a higher price.
Stacking between flat rings is the classic failure for a dispersion-deficient functional: it calls the pair barely bound when experiment or a dispersion-inclusive method shows stronger binding. Add a dispersion correction to such a functional, and the missing attraction returns. Do not add another correction to a method that already includes dispersion.
The density keeps molecules affordable, and the functional you pick decides how accurate the result is.
2 · Watch
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.