physics

Quantum chemistry composite methods

Quantum chemistry composite methods 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 Quantum chemistry composite methods rather than just read about it. In short: Quantum chemistry composite methods (also referred to as thermochemical recipes) are computational chemistry methods that aim for high accuracy by combining the results of several calculations. They combine methods with a high level of theory and a small basis set with methods that employ lower levels of theory with larger basis sets.

Key takeaways

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

Reference excerpt

Quantum chemistry composite methods (also referred to as thermochemical recipes) are computational chemistry methods that aim for high accuracy by combining the results of several calculations. They combine methods with a high level of theory and a small basis set with methods that employ lower levels of theory with larger basis sets. They are commonly used to calculate thermodynamic quantities such as enthalpies of formation, atomization energies, ionization energies and electron affinities. They aim for chemical accuracy which is usually defined as within 1 kcal/mol of the experimental value. The first systematic model chemistry of this type with broad applicability was called Gaussian-1 (G1) introduced by John Pople. This was quickly replaced by the Gaussian-2 (G2) which has been used extensively. The Gaussian-3 (G3) was introduced later.

Gaussian-n theories

Gaussian-2 (G2) The G2 uses seven calculations:

the molecular geometry is obtained by a MP2 optimization using the 6-31G(d) basis set and all electrons included in the perturbation. This geometry is used for all subsequent calculations. The highest level of theory is a quadratic configuration interaction calculation with single and double excitations and a triples excitation contribution (QCISD(T)) with the 6-311G(d) basis set. Such a calculation in the Gaussian and Spartan programs also give the MP2 and MP4 energies which are also used. The effect of polarization functions is assessed using an MP4 calculation with the 6-311G(2df,p) basis set. The effect of diffuse functions is assessed using an MP4 calculation with the 6-311+G(d, p) basis set. The largest basis set is 6-311+G(3df,2p) used at the MP2 level of theory. A Hartree–Fock geometry optimization with the 6-31G(d) basis set used to give a geometry for: A frequency calculation with the 6-31G(d) basis set to obtain the zero-point vibrational energy (ZPVE) The various energy changes are assumed to be additive so the combined energy is given by:

EQCISD(T) from 2 + [EMP4 from 3 - EMP4 from 2] + [EMP4 from 4 - EMP4 from 2] + [EMP2 from 5 + EMP2 from 2 - EMP2 from 3 - EMP2 from 4] The second term corrects for the effect of adding the polarization functions. The third term corrects for the diffuse functions. The final term corrects for the larger basis set with the terms from steps 2, 3 and 4 preventing contributions from being counted twice. Two final corrections are made to this energy. The ZPVE is scaled by 0.8929. An empirical correction is then added to account for factors not considered above. This is called the higher level correction (HC) and is given by -0.00481 x (number of valence electrons) -0.00019 x (number of unpaired valence electrons). The two numbers are obtained calibrating the results against the experimental results for a set of molecules. The scaled ZPVE and the HLC are added to give the final energy. For some molecules containing one of the third row elements Ga–Xe, a further term is added to account for spin orbit coupling. Several variants of this procedure have been used. Removing steps 3 and 4 and relying only on the MP2 result from step 5 is significantly cheaper and only slightly less accurate. This is the G2MP2 method. Sometimes the geometry is obtained using a density functional theory method such as B3LYP and sometimes the QCISD(T) method in step 2 is replaced by the coupled cluster method CCSD(T). The G2(+) variant, where the "+" symbol refers to added diffuse functions, better describes anions than conventional G2 theory. The 6-31+G(d) basis set is used in place of the 6-31G(d) basis set for both the initial geometry optimization, as well as the second geometry optimization and frequency calculation. Additionally, the frozen-core approximation is made for the initial MP2 optimization, whereas G2 usually uses the full calculation.

Gaussian-3 (G3) The G3 is very similar to G2 but learns from the experience with G2 theory. The 6-311G basis set is replaced by the smaller 6-31G basis. The final MP2 calculations use a larger basis set, generally just called G3large, and correlating all the electrons not just the valence electrons as in G2 theory, additionally a spin-orbit correction term and an empirical correction for valence electrons are introduced. This gives some core correlation contributions to the final energy. The HLC takes the same form but with different empirical parameters.

Gaussian-4 (G4) G4 is a compound method in spirit of the other Gaussian theories and attempts to take the accuracy achieved with G3X one small step further. This involves the introduction of an extrapolation scheme for obtaining basis set limit Hartree-Fock energies, the use of geometries and thermochemical corrections calculated at B3LYP/6-31G(2df,p) level, a highest-level single point calculation at CCSD(T) instead of QCISD(T) level, and addition of extra polarization functions in the largest-basis set MP2 calculations. Thus, Gaussian 4 (G4) theory is an approach for the calculation of energies of molecular species containing first-row, second-row, and third row main group elements. G4 theory is an improved modification of the earlier approach G3 theory. The modifications to G3- theory are the change in an estimate of the Hartree–Fock energy limit, an expanded polarization set for the large basis set calculation, use of CCSD(T) energies, use of geometries from density functional theory and zero-point energies, and two added higher level correction parameters. According to the developers, this theory gives significant improvement over G3-theory. The G4 and the related G4MP2 methods have been extended to cover transition metals. A variant of G4MP2, termed G4(MP2)-6X, has been developed with an aim to improve the accuracy with essentially identical quantum chemistry components. It applies scaling to the energy components in addition to using the HLC. In the G4(MP2)-XK method that is related to G4(MP2)-6X, the Pople-type basis sets are replaced with customized Karlsruhe-type basis sets. In comparison with G4(MP2)-6X, which covers main-group elements up to krypton, G4(MP2)-XK is applicable to main-group elements up to radon.

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Worked examples

Example 1 — a first encounter with Quantum chemistry composite methods

Start with the simplest possible case. Write down what Quantum chemistry composite methods 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 Quantum chemistry composite methods 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 Quantum chemistry composite methods 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 Quantum chemistry composite methods

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

Read the reference excerpt below once, without taking notes.
Close the page and write down what Quantum chemistry composite methods 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.
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Frequently asked questions

What is Quantum chemistry composite methods in simple terms?

Why does Quantum chemistry composite methods 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 Quantum chemistry composite methods?

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 Quantum chemistry composite methods.