astronomy

Oxidation state localized orbitals

Oxidation state localized orbitals is a astronomy 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 Oxidation state localized orbitals rather than just read about it. In short: Oxidation state localized orbitals (OSLOs) is a new concept used to determine the oxidation states of each fragment for coordination complexes. Based on the result of density functional theory (DFT), all the occupied molecular orbitals are remixed to get the oxidation state localized orbitals.

Key takeaways

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

Reference excerpt

Oxidation state localized orbitals (OSLOs) is a new concept used to determine the oxidation states of each fragment for coordination complexes. Based on the result of density functional theory (DFT), all the occupied molecular orbitals are remixed to get the oxidation state localized orbitals. These orbitals are assigned to one of the fragments in this molecule based on the fragment orbital localization index (FOLI). After all the electrons are assigned, the oxidation states of each fragment could be obtained by calculating the difference between the number of electrons and protons in each fragment.

History Oxidation state is an important index to evaluate the charge distribution within molecules. The most common definition of oxidation state was established by IUPAC, which let the atom with higher electronegativity takes all the bonding electrons and calculated the difference between the number of electrons and protons around each atom to assign the oxidation states. However, the definition doesn't thoroughly consider the distribution of the bonding electrons and further restricts the applicability of oxidation states. To precisely assign the oxidation state for each component in the molecule, especially for organometallic complexes, several different research groups, including Pedro Salvador and Martin Head-Gordon, have developed different methods to determine the oxidation states. In 2009, Martin Head-Gordon group established a new method called localized orbitals bonding analysis (LOBA) to assign the electrons associated with each localized orbitals. However, this method failed to provide reasonable oxidation states since the orbitals cannot be localized for some complicated systems. To overcome this problem to get the correct assignment of oxidation states, in 2022, Martin Head-Gordon and Pedro Salvador decide to localize the electrons based on different fragments rather than atoms. Thus, they developed the method known as oxidation state localized orbitals (OSLOs), which can accurately assign electrons to different fragments to obtain the oxidation states of each fragment.

General methods

Generation of full set of orbitals Based on DFT, a full set of orbitals will compose the resulting OSLOs for each fragment. Then, these sets will be imported to the algorithm for further assignment of oxidation states and construction of OSLOs.

Localization measurement The extent of delocalization could be quantified by using Pipek's delocalization measurement. For orbitals which are highly localized, the Pipek's indexes will be very close to 1. On the other hand, for highly delocalized orbitals, the Pipek's indexes become larger.

D i = 1 ∑ ( N F i ) 2 {\displaystyle D_{i}={\frac {1}{\sum _{(}N_{F}^{i})^{2}}}}

However, this method cannot evaluate the localization extent on each fragment. Thus, a new measurement is necessary. The fragment orbital localization index (FOLI) is defined as the square root of the fragment population over the delocalization index:

D i F = ( D i N F i ) {\displaystyle D_{i}^{F}={\sqrt {({\tfrac {D_{i}}{N_{F}^{i}}})}}}

Based on this localization index, the localization extent on each fragment can be determined. with higher FOLI, it means the extent of localization on this fragment is relatively low, vice versa. Thus, after acquiring the FOLI, the electrons in each OSLO will be assigned to the fragment with the lowest FOLI.

Workflow First, based on the results of density functional theory calculations. The set with the minimal FOLI is selected for further analysis. Then, after calculating the FOLI for each set, the set with the minimal FOLI is selected. For the selected set, the OSLOs are removed and the oxidation states are assigned based on these OSLOs.In this method, the fragment with the higher electron population gets all the electrons in this orbital. For all the other sets, they become the input for the next-round analysis, and the process repeats until all OSLOs are constructed and all electrons are assigned.

Result

Significance The valence OSLOs of the molecule can also be constructed using the method. The oxidation state of the ligand and metal are also determined and show consistency with the expected Lewis structure and can provide great insight for evaluating the redox reactivity. Last FOLI and Δ-FOLI are two important values to evaluate the quality of the localization result. With the last FOLI closer to 1, it means that the OSLOs are highly localized on one fragment. On the other hand, Δ-FOLI is the difference between the last FOLI and the second-last FOLI. With a larger Δ-FOLI, it means the selected set of OSLOs is much better than other options, which indicates the unambiguity of this result.

Notable result

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Worked examples

Example 1 — a first encounter with Oxidation state localized orbitals

Start with the simplest possible case. Write down what Oxidation state localized orbitals claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 Oxidation state localized orbitals 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 Oxidation state localized orbitals 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 Oxidation state localized orbitals

In research: Oxidation state localized orbitals appears in astronomy 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 Oxidation state localized orbitals 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: Oxidation state localized orbitals is common in secondary-school and first-year university syllabi. It links to neighbouring topics Coordination chemistry, Coordination complexes, so understanding it makes those chapters shorter.
In everyday life: Look for Oxidation state localized orbitals 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 Oxidation state localized orbitals in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Oxidation state localized orbitals means in your own words.
Compare your version with the excerpt and mark what you missed.
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Frequently asked questions

What is Oxidation state localized orbitals in simple terms?

Why does Oxidation state localized orbitals matter?

Because it connects several astronomy 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 Oxidation state localized orbitals?

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 Oxidation state localized orbitals.