chemistry

Post–Hartree–Fock

Post–Hartree–Fock is a chemistry 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 Post–Hartree–Fock rather than just read about it. In short: In computational chemistry, post–Hartree–Fock (post-HF) methods are the set of methods developed to improve on the Hartree–Fock (HF), or self-consistent field (SCF), method. They add electron correlation which is a more accurate way of including the repulsions between electrons than in the Hartree–Fock method where repulsions are only averaged.

Key takeaways

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

Reference excerpt

In computational chemistry, post–Hartree–Fock (post-HF) methods are the set of methods developed to improve on the Hartree–Fock (HF), or self-consistent field (SCF), method. They add electron correlation which is a more accurate way of including the repulsions between electrons than in the Hartree–Fock method where repulsions are only averaged.

Details In general, the SCF procedure makes several assumptions about the nature of the multi-body Schrödinger equation and its set of solutions:

For molecules, the Born–Oppenheimer approximation is inherently assumed. The true wavefunction should also be a function of the coordinates of each of the nuclei. Typically, relativistic effects are completely neglected. The momentum operator is assumed to be completely nonrelativistic. The basis set is composed of a finite number of orthogonal functions. The general wavefunction is a linear combination of functions from a complete (infinite) basis set. The energy eigenfunctions are assumed to be products of one-electron wavefunctions. The effects of electron correlation, beyond that of exchange energy resulting from the anti-symmetrization of the wavefunction, are completely neglected. For the great majority of systems under study, in particular for excited states and processes such as molecular dissociation reactions, the fourth item is by far the most important. As a result, the term post–Hartree–Fock method is typically used for methods of approximating the electron correlation of a system. Usually, post–Hartree–Fock methods give more accurate results than Hartree–Fock calculations, though at greater computational cost.

Post–Hartree–Fock methods Configuration interaction (CI) Coupled cluster (CC) Møller–Plesset perturbation theory (MP2, MP3, MP4, etc.) Quadratic configuration interaction (QCI) Algebraic Diagrammatic Construction (ADC) Quantum chemistry composite methods (G2, G3, CBS, T1. etc.)

Related methods Methods that use more than one determinant are not strictly post–Hartree–Fock methods, as they use a single determinant as reference, but they often use similar perturbation, or configuration interaction methods to improve the description of electron correlation. These methods include:

Multi-configurational self-consistent field (MCSCF) Multireference single and double configuration interaction (MRCISD) N-electron valence state perturbation theory (NEVPT).

References

Further reading Jensen, F. (1999). Introduction to Computational Chemistry. New York: John Wiley & Sons. ISBN 0471980854.

Worked examples

Example 1 — a first encounter with Post–Hartree–Fock

Start with the simplest possible case. Write down what Post–Hartree–Fock claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In chemistry, 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 Post–Hartree–Fock 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 Post–Hartree–Fock 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 Post–Hartree–Fock

In research: Post–Hartree–Fock appears in chemistry 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 Post–Hartree–Fock 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: Post–Hartree–Fock is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computational chemistry, Quantum chemistry, so understanding it makes those chapters shorter.
In everyday life: Look for Post–Hartree–Fock 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 Post–Hartree–Fock in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Post–Hartree–Fock 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 Post–Hartree–Fock out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Post–Hartree–Fock in simple terms?

Why does Post–Hartree–Fock matter?

Because it connects several chemistry 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 Post–Hartree–Fock?

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 Post–Hartree–Fock.