---
title: "Density Functional Theory and Choosing a Functional"
description: "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 fu"
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retrieved: 2026-09-12
---

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# 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.

Subject: Science · Area: Chemistry · Ages 20 to 21
Page: https://lightmysky.com/learn/science/density-functional-theory-and-choosing-a-functional-mt_mmuzLeA62V

## Ready when they can

- 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 names what each is usually chosen for
- Identifies a case where a common functional is known to fail and states the usual repair

## Lesson: Density instead of wavefunction

A many-electron wavefunction sprawls across every electron at once. The density is far smaller: one value at each point in space. Working with the density makes accurate calculations affordable for real-size molecules.

Part of the energy then comes from an exchange-correlation functional, which must be approximated. Nobody knows its exact form, so every choice trades accuracy against cost.

**Example.** 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.

**Tip.** Stacking between flat rings is the classic failure: common functionals call it barely bound. Add a dispersion correction, and the missing attraction returns.

**Recap.** The density keeps molecules affordable, and the functional you pick decides what is true.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Hartree-Fock and What a Basis Set Decides](https://lightmysky.com/learn/science/hartree-fock-and-what-a-basis-set-decides-mt_EYSTCPuRNx)

## Opens up

- [Excited States by Calculation and Simulated Electronic Spectra](https://lightmysky.com/learn/science/excited-states-by-calculation-and-simulated-electronic-spectra-mt_DsZ3wfCRkX)
- [Computed Geometries, Frequencies and Reaction Barriers](https://lightmysky.com/learn/science/computed-geometries-frequencies-and-reaction-barriers-mt_pdiFjK2wPe)