physics

Hartree

Hartree is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hartree rather than just read about it. In short: The hartree (symbol: Eh), also known as the Hartree energy, is the unit of energy in the atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is Eh = 4.3597447222060(48)×10−18 J‍ = 27.211386245981(30) eV.

Key takeaways

Hartree belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hartree to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hartree from memory before moving on to harder problems.

Reference excerpt

The hartree (symbol: Eh), also known as the Hartree energy, is the unit of energy in the atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is Eh = 4.3597447222060(48)×10−18 J‍ = 27.211386245981(30) eV. The name "hartree" was suggested for this unit of energy. The hartree is approximately the negative electric potential energy of the electron in a hydrogen atom in its ground state and, by the virial theorem, approximately twice its ionization energy; the relationships are not exact because of the finite mass of the nucleus of the hydrogen atom and relativistic corrections. The hartree is usually used as a unit of energy in atomic physics and computational chemistry: for experimental measurements at the atomic scale, the electronvolt (eV) or the reciprocal centimetre (cm−1) are much more widely used.

Other relationships

E h = ℏ 2 m e a 0 2 = m e ( e 2 4 π ε 0 ℏ ) 2 = m e c 2 α 2 = ℏ c α a 0 {\displaystyle E_{\mathrm {h} }={\hbar ^{2} \over {m_{\mathrm {e} }a_{0}^{2}}}=m_{\mathrm {e} }\left({\frac {e^{2}}{4\pi \varepsilon _{0}\hbar }}\right)^{2}=m_{\mathrm {e} }c^{2}\alpha ^{2}={\hbar c\alpha \over {a_{0}}}}

= 2 Ry = 2 R∞hc = 27.211386245981(30) eV‍ = 4.3597447222060(48)×10−18 J‍ = 4.3597447222060(48)×10−11 erg ≘ 2625.4996394799(50) kJ/mol ≘ 627.5094740631(12) kcal/mol ≘ 219474.63136320(43) cm−1 ≘ 6579.683920502(13) THz where:

ħ is the reduced Planck constant, me is the electron mass, e is the elementary charge, a0 is the Bohr radius, ε0 is the electric constant, c is the speed of light in vacuum, and α is the fine-structure constant. Effective hartree units are used in semiconductor physics where e 2 {\displaystyle e^{2}} is replaced by e 2 / ε {\displaystyle e^{2}/\varepsilon } and ε {\displaystyle \varepsilon } is the static dielectric constant. Also, the electron mass is replaced by the effective band mass m ∗ {\displaystyle m^{*}} . The effective hartree in semiconductors becomes small enough to be measured in millielectronvolts (meV).

Worked examples

Example 1 — a first encounter with Hartree

Start with the simplest possible case. Write down what Hartree claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hartree before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hartree ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hartree

In research: Hartree appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hartree in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hartree is common in secondary-school and first-year university syllabi. It links to neighbouring topics Physical constants, Units of energy, so understanding it makes those chapters shorter.
In everyday life: Look for Hartree outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Hartree in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hartree means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hartree out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hartree in simple terms?

Why does Hartree matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hartree?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hartree.