chemistry

Natural bond orbital

Natural bond orbital 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 Natural bond orbital rather than just read about it. In short: In quantum chemistry, a natural bond orbital or NBO is a calculated bonding orbital with maximum electron density. The NBOs are one of a sequence of natural localized orbital sets that include "natural atomic orbitals" (NAO), "natural hybrid orbitals" (NHO), "natural bonding orbitals" (NBO) and "natural (semi-)localized molecular orbitals" (NLMO).

Key takeaways

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

Reference excerpt

In quantum chemistry, a natural bond orbital or NBO is a calculated bonding orbital with maximum electron density. The NBOs are one of a sequence of natural localized orbital sets that include "natural atomic orbitals" (NAO), "natural hybrid orbitals" (NHO), "natural bonding orbitals" (NBO) and "natural (semi-)localized molecular orbitals" (NLMO). These natural localized sets are intermediate between basis atomic orbitals (AO) and molecular orbitals (MO):

Atomic orbital → NAO → NHO → NBO → NLMO → Molecular orbital Natural (localized) orbitals are used in computational chemistry to calculate the distribution of electron density in atoms and in bonds between atoms. They have the "maximum-occupancy character" in localized 1-center and 2-center regions of the molecule. Natural bond orbitals (NBOs) include the highest possible percentage of the electron density, ideally close to 2.000, providing the most accurate possible “natural Lewis structure” of ψ. A high percentage of electron density (denoted %-ρL), often found to be >99% for common organic molecules, correspond with an accurate natural Lewis structure. The concept of natural orbitals was first introduced by Per-Olov Löwdin in 1955, to describe the unique set of orthonormal 1-electron functions that are intrinsic to the N-electron wavefunction.

Theory Each bonding NBO σAB (the donor) can be written in terms of two directed valence hybrids (NHOs) hA, hB on atoms A and B, with corresponding polarization coefficients cA, cB:

σAB = cA hΑ + cB hB The bonds vary smoothly from covalent (cA = cB) to ionic (cA >> cB) limit. Each valence bonding NBO σ must be paired with a corresponding valence antibonding NBO σ* (the acceptor) to complete the span of the valence space:

σAB* = cA hΑ − cB hB The bonding NBOs are of the "Lewis orbital"-type (occupation numbers near 2); antibonding NBOs are of the "non-Lewis orbital"-type (occupation numbers near 0). In an idealized Lewis structure, full Lewis orbitals (two electrons) are complemented by formally empty non-Lewis orbitals. Weak occupancies of the valence antibonds signal irreducible departures from an idealized localized Lewis structure, which means true "delocalization effects".

Lewis structures

With a computer program that can calculate NBOs, optimal Lewis structures can be found. An optimal Lewis structure can be defined as that one with the maximum amount of electronic charge in Lewis orbitals (Lewis charge). A low amount of electronic charge in Lewis orbitals indicates strong effects of electron delocalization. In resonance structures, major and minor contributing structures may exist. For amides, for example, NBO calculations show that the structure with a carbonyl double bond is the dominant Lewis structure. However, in NBO calculations, "covalent-ionic resonance" is not needed due to the inclusion of bond-polarity effects in the resonance structures. This is similar to other modern valence bond theory methods.

See also Molecular orbital theory Basis set (chemistry)

References

External links Homepage for the NBO computer program: http://nbo6.chem.wisc.edu/ IUPAC Gold Book definition: natural bond orbital (NBO) Free, open-source implementation for Atomic orbital → NAO transformation and Natural Population Analysis methods: JANPA package

Worked examples

Example 1 — a first encounter with Natural bond orbital

Start with the simplest possible case. Write down what Natural bond orbital 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 Natural bond orbital 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 Natural bond orbital 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 Natural bond orbital

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

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

Frequently asked questions

What is Natural bond orbital in simple terms?

Why does Natural bond orbital 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 Natural bond orbital?

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 Natural bond orbital.